Análisis espacial del mercado de trabajo español a nivel macroeconómico: teoría y evidencia empírica.

PROGRAMA DE DOCTORADO EN ECONOMÍA TESIS DOCTORAL: Análisis Espacial del Mercado de Trabajo Español a nivel Macroeconómico: Teoría y evidencia empírica Presentada por Jaime Cuéllar Martín para optar al grado de Doctor por la Universidad de Valladolid Dirigida por los Profesores Dr. Ángel Luís Martín Román Profesor Titular de Fundamentos del Análisis Económico e Historia e Instituciones Económicas Dr. Alfonso Moral de Blas Profesor Contratado Doctor Fundamentos del Análisis Económico e Historia e Instituciones Económicas Universidad de Valladolid Segovia, noviembre de 2020 PROGRAMA DE DOCTORADO EN ECONOMÍA TESIS DOCTORAL: Análisis Espacial del Mercado de Trabajo Español a nivel Macroeconómico: Teoría y evidencia empírica Presentada por Jaime Cuéllar Martín para optar al grado de Doctor por la Universidad de Valladolid Dirigida por los Profesores Dr. Ángel Luís Martín Román Profesor Titular de Fundamentos del Análisis Económico e Historia e Instituciones Económicas Dr. Alfonso Moral de Blas Profesor Contratado Doctor Fundamentos del Análisis Económico e Historia e Instituciones Económicas Universidad de Valladolid Facultad de Ciencias Sociales Jurídicas y de la Comunicación Departamento de Fundamentos del Análisis Económico e Historia e Instituciones Económicas Universidad de Valladolid Segovia, noviembre de 2020 Agradecimientos La configuración de una tesis doctoral no resulta ser una tarea fácil. Uno de los aspectos más importantes es la ilusión con la que uno cuenta para poder afrontar todo el proceso. En mi caso, tuve claro desde el primer momento que quería dedicarme a esto de la investigación y la docencia desde que me encontré con la asignatura de Macroeconomía en el tercer curso de la carrera de Administración y Dirección de Empresas allá por el año 2012. La forma de poder comprender el comportamiento de las personas y las empresas dentro del entorno en el que vivimos siempre me ha parecido fascinante, sobre todo el tratar de razonar su comportamiento en el futuro, con todas las reservas del mundo, de acuerdo a una lógica económica. Es por esto, que los primeros agradecimientos de que esta tesis haya pasado de ser una “idea lejana” a una realidad son para mis dos directores, Ángel L. Martín-Román y Alfonso Moral de Blas, sin los cuales nada de esto podría haber sido posible, ni siquiera en el sueño más optimista. La paciencia con la que siempre han contado conmigo, las innumerables muestras de apoyo en los momentos más complicados y difíciles o la encomiable disposición que siempre han mostrado es algo muy difícil de valorar o incluso expresar. Sin embargo, pese a que todos estos aspectos han resultado ser determinantes, creo que hay dos elementos que han contribuido, si cabe, en mayor medida. El primero de ellos, es el conocimiento y experiencia que ambos me han transmitido a lo largo de todo este proceso de aprendizaje. En términos económicos, han invertido años de vida en mí, por lo que estoy inmensamente agradecido y totalmente convencido que será muy complicado que les pueda compensar por ello durante el resto de mi vida. En segundo, pero no por ello menos importante, es la cercanía y el buen trato que siempre han tenido, permitiendo que la relación de profesores-alumno evolucionase hasta una relación de amistad y compañerismo, sobre todo en los primeros momentos en los cuales empezaba a dar las primeras clases en la universidad, de nuevo, creo que esta deuda vital es totalmente impagable, por lo que solo cabe decir que de mayor quiero ser como vosotros. Dentro del ámbito académico, quería extender los agradecimientos a mis compañeros del Departamento de Fundamentos del Análisis Económico e Historia e Instituciones Económicas de la Universidad de Valladolid con los que he tenido la suerte de compartir despacho (la mítica aula 112) y disciplina. En este apartado, quiero destacar, de forma especial, la gran ayuda que me han prestado siempre tanto Jorge Lafuente del Cano como Diego Dueñas Fernández, al cual le deseo toda la suerte del mundo en la Universidad de Alcalá. Por otro lado, quería agradecer todas esas charlas con innumerables investigadores de esta disciplina en todos los congresos y reuniones científicas a las que he tenido la suerte de asistir, parte del conocimiento que ha quedado plasmado en esta tesis se debe también a ellos. Finalmente, me gustaría destacar la gratitud hacia mis compañeros de la Escuela de Doctorado, siempre dispuestos a resolver dudas y a colaborar de la forma más profesional y desinteresada posible. En este apartado quería destacar especialmente el apoyo de Javier Martín Román, además de ser un investigador excelente y un compañero ejemplar, su valor como amigo es imposible de cuantificar (¡además de ser seguidor del FC Barcelona, lo cual suma muchos enteros!). En lo personal, no quiero olvidarme del apoyo constante de todos mis familiares: mis tíos, mis primos y mis amigos, los cuales son aquella parte de la familia que a lo largo de tu vida vas eligiendo. Sin embargo, tal vez las dos personas más importantes hayan sido mis padres. He tenido la suerte de poder contar con su apoyo constante, especialmente en los días más difíciles, los cuales, pese a no tener ni idea de lo que les estaba hablando, siempre han sido capaces de aconsejarme de la mejor forma posible y, lo que es más importante, con la mejor intención posible. Debido a todo lo anterior, considero que esta tesis doctoral es tanto suya como mía. Finalmente, dentro de este apartado, también quiero extender estos agradecimientos a mis tres hermanas, cuyo apoyo ha sido también fundamental para poder ir superando las barreras que me iba encontrando conforme iba avanzado en esta peculiar aventura. ÍNDICE Composición de la tesis doctoral………………………………………………………………………………………...2 Introducción ......................................................................................................................................................................... .5 1. Justificación y objetivos de la investigación ............................................................................................. 7 2. Estructura de la tesis doctoral…………………………………………………………………………………. 10 3. Relevancia de la investigación doctoral……………………………………………………………………. 12 3.1. El análisis del mercado de trabajo: Los componentes del desempleo efectivo........... 12 3.2. La importancia del territorio en los mercados laborales……………………………………..13 3.3. El análisis de los efectos sociales en los mercados de trabajo regionales .................... 14 3.4. El papel de las políticas activas del mercado de trabajo a nivel territorial……………15 4. Metodología……………………………………………………………………………………………………………15 4.1. Descomposición del desempleo efectivo: Las fronteras estocásticas .............................. 15 4.2. Las técnicas de econometría espacial: Conceptos Clave ......................................................... 16 4.2.1. Estadísticos univariantes globales: La I de Moran global……………………………17 4.2.2. Estadísticos univariantes locales: La I de Moran local………………………………..18 4.2.3. Características de los modelos espaciales de datos de datos de panel………...18 4.3. Evaluación de políticas activas del mercado laboral: El análisis de diferencias en diferencias………………………………………………………………………………………………………...19 5. El análisis espacial de los mercados de trabajo: Una revisión bibliográfica………………...20 5.1. La descomposición del desempleo efectivo: Estrategias empíricas…………………..…..20 5.2. Análisis de la dependencia espacial en el desempleo: Una perspectiva regional.......21 5.3. Importancia macroeconómica de los efectos sociales.…….…………………………………...22 5.4. Evaluación de las políticas activas del mercado de trabajo en el contexto regional.23 6. Contribuciones de la investigación doctoral…………………………………………………………….. 24 CAPÍTULO 1. Natural and cyclical unemployment: A stochastic frontier decomposition and economic policy implications……………………………………………………………………………………..........26 CAPÍTULO 2 An Empirical Analysis of Natural and Cyclical Unemployment at the Provincial Level in Spain ……………………………………………………………………………………………………...………….77 CAPÍTULO 3. Labor supply and the business cycle: The “Bandwagon Worker Effect”…………129 CAPÍTULO 4. Una evaluación de impacto del segundo Plan Regional de Empleo de Castilla y León……………………………………………………………………………………………………………………………....167 Conclusiones .................................................................................................................................................................... .201 Bibliografía…………………………………………………………………………………………………………………….206 1 COMPOSICIÓN DE LA TESIS DOCTORAL De acuerdo con la normativa vigente para la presentación y defensa de la tesis doctoral en la Universidad de Valladolid (aprobado por el Consejo de Gobierno en sesión de 3 junio de 2016. BOCyL nº114 de 15 de junio), esta tesis doctoral se presenta en la modalidad “tesis por compendio de publicaciones”. En ella se incluyen un total de cuatro artículos, tres de ellos ya publicados en revistas científicas y el restante en proceso de evaluación en el momento del depósito. Los artículos 2º y 3º están publicados en revistas indexadas WOS SSCI JCR, mientras que el artículo 4º se encuentra publicado en una revista indexada SCOPUS, por lo que cumplen con los requisitos establecidos por la Comisión del Programa de Doctorado en Economía. A continuación, se incluyen los artículos que conforman la tesis doctoral, así como la revista en la que están publicados y su base indexación. Se recoge también la filiación de los coautores. 1. Martín‐Román, Á. L., Cuéllar‐Martín, J., & Moral, A. (2020). Natural and cyclical unemployment: A stochastic frontier decomposition and economic policy implications. Bulletin of Economic Research (en 3ª ronda de evaluación). Indexación: WOS SSCI JCR Impact Factor (2019): 0.333. Subject: Economics (Q4; 358/373). 2. Cuéllar-Martín, J., Martín-Román, Á. L., & Moral, A. (2019). An Empirical Analysis of Natural and Cyclical Unemployment at the Provincial Level in Spain. Applied Spatial Analysis and Policy, 12(3), 647-696. Doi.org/10.1007/s12061-018-9262-x. Indexación: WOS SSCI JCR Impact Factor (2019): 1.778. Subject: Environmental Studies (Q3; 91/123); Geography (Q3; 45/84); Regional & Urban Planning (Q4; 31/39). 3. Martín‐Román, Á. L., Cuéllar‐Martín, J., & Moral, A. (2020). Labor supply and the business cycle: The “Bandwagon Worker Effect”. Papers in Regional Science, Forthcoming. Doi.org/10.1111/pirs.12542. Indexación: WOS SSCI JCR Impact Factor (2019): 2.220. Subject: Economics (Q2; 96/373); Environmental Studies (Q3; 68/123); Geography (Q2; 37/84); Regional & Urban Planning (Q3; 23/39). 4. Martín-Román, Á. L., Moral, A., Martín-Román, J., & Cuéllar-Martín, J. (2018). Una evaluación de impacto del segundo Plan Regional de Empleo de Castilla y León. Revista de Estudios Regionales, (112), 177-208. Indexación: Elsevier. SCOPUS CiteScore (2019): 0.5. Subject: Sociology and Political Sciences (P33; 822/1.243); Development (P23; 183/239); Economics and Econometrics (P15; 537/637). 2 Filiaciones de los coautores: Ángel Luís Martín Román. Profesor Titular. Universidad de Valladolid. Alfonso Moral de Blas. Profesor Contratado Doctor. Universidad de Valladolid. Javier Martín Román. Profesor Ayudante. Universidad de Valladolid y Universidad Nacional de Educación a Distancia. 3 4 INTRODUCCIÓN 5 castellanoleonesas con lo ocurrido en el resto de provincias del país, obtenemos unos resultados muy distintos. En este caso, la tasa de ocupación de las provincias de esta región experimenta un incremento menor que lo observado en aquellas provincias españolas con las que se lleva a cabo la comparación. Lo anterior pone de manifiesto los escasos resultados obtenidos por parte del SPRECyL en las provincias de Castilla y León durante el periodo 20012003. Por lo que se refiere a los resultados obtenidos para la tasa de paro se puede afirmar que las medidas destinadas a luchar contra el desempleo sí tuvieron cierto éxito relativo. De esta manera, en general, la tasa de paro evolucionó de una forma similar a la experimentada por el resto de provincias españolas durante tal periodo objeto de estudio. Los cuatro capítulos anteriores completan la trayectoria investigadora realizada por el doctorando, los cuales, como hemos comentado con anterioridad, se integran en forma de capitulo uno, dos, tres y cuatro de la presente tesis doctoral. La anterior organización se explica de acuerdo a la necesidad de dotar a la tesis doctoral de un orden claro que ayude al lector a comprender los conceptos desarrollados con facilidad. Un elemento importante a destacar son los resultados de investigación obtenidos a partir de esta tesis doctoral. En concreto, el primer capítulo se encuentra en un periodo avanzado del proceso de publicación en la revista Bulletin of Economic Research. Esta revista esta indexada en el índice JCR (Journal Citations Report) en el cuarto cuartil de la categoría Economics según la clasificación del año 2019. Por su parte, el segundo capítulo se encuentra publicado en la revista Applied Spatial Analysis and Policy, la cual se encuentra indexada en el índice JCR (Journal Citatios Report) en el cuartil tercero, según la clasificación del año 2019, de la categoría Environmental Studies y Geography, y el cuarto cuartil en la categoría Regional and Urban Planning. El capítulo número tres, fue publicado en la revista Papers in Regional Science, revista indexada en el índice JCR en las categorías Environmental Studies (cuartil tercero), Geography (cuartil segundo), Economics (cuartil segundo) y Regional and Urban Planning (cuartil tercero) según la clasificación del año 2019. Finalmente, el cuarto y último capítulo ha sido publicado en la Revista de Estudios Regionales, indexada en el índice Scopus (Scimago Journal and Country Rank), en las categorías Development (percentil 23), Economics and Econometrics (percentil 15) y Sociology and Political Science (percentil 33) según la clasificación del año 2019. 3. Relevancia de la investigación doctoral 3.1 El análisis del mercado de trabajo: Los componentes del desempleo efectivo Durante las últimas décadas, una parte importante de los investigadores en economía laboral han centrado sus esfuerzos en entender las mecánicas que subyacen a la formación de las tasas de desempleo (Blanchard y Portugal, 2001; Bentolila et al. 2012). Uno de los aspectos más interesantes dentro de esta línea de investigación es la que estudia a los diferentes componentes del desempleo efectivo. Una sencilla descomposición del desempleo efectivo, expuesta en algunos libros de texto, es la que se define a través de la siguiente ecuación (Krugman, 2011): 𝐷𝑖𝑡 = 𝐷𝑖𝑡 𝐹+𝐷𝑖𝑡 𝑆𝑇 +𝐷𝑖𝑡 𝐶 (1) donde 𝐷𝑖𝑡 es la tasa de desempleo efectivo en la región i durante el instante t; 𝐷𝑖𝑡 𝐹 hace referencia al componente friccional; 𝐷𝑖𝑡 𝑆𝑇 alude al componente estructural, mientras que 𝐷𝑖𝑡 𝐶 indica la magnitud del componente cíclico del desempleo efectivo. Basándonos en lo anterior, una buena parte de la literatura macro labor ha considerado que, en el medio-largo plazo, incluso en ausencia de problemas relacionados con una demanda agregada insuficiente y bajo condiciones óptimas a nivel agregado, existe un cierto nivel de desempleo al que tienden las economías (Rogerson, 1997; Blanchard, 2018). A pesar de la 12 utilización de diversas nomenclaturas a lo largo de la historia, uno de las más empleadas podría ser la de tasa natural de desempleo (NRU), la cual, pese a no estar exenta de críticas, se ha instituido como uno de los conceptos macroeconómicos más utilizados en el ámbito de la economía laboral. En esta línea, la tasa natural de desempleo se podría definir como la suma del desempleo friccional y del desempleo estructural, modificando la ecuación (1) de la siguiente manera: 𝐷𝑖𝑡 =𝐷𝑖𝑡 𝑁𝑅𝑈 +𝐷𝑖𝑡 𝐶 (2) donde 𝐷𝑖𝑡 𝑁𝑅𝑈 haría referencia al componente natural de la tasa de desempleo efectivo. En este punto es necesario destacar que, el anterior razonamiento se basa en la idea de que los componentes del desempleo efectivo no pueden alcanzar cotas negativas. Dicho de otra manera, tanto el desempleo efectivo como sus componentes son positivos, lo que conceptualiza a la tasa de desempleo natural como un límite inferior al que tiende el desempleo efectivo en el medio-largo plazo. Una vez hemos descrito lo anterior, el principal problema reside en la cuantificación de los componentes del desempleo efectivo, ya que tanto el componente natural como el componente cíclico son elementos inobservables en las estadísticas laborales. Para superar este hándicap, nuestra investigación se inspira, principalmente, en los trabajos de Hofler y Murphy (1989), Warren (1991) y Aysun et al. (2014), aplicando la técnica econométrica de las fronteras estocásticas en su versión de costes para hallar una estimación de ambos componentes. 3.2 La importancia del territorio en los mercados laborales El estudio del papel que el territorio ejerce sobre las dinámicas económicas regionales experimentó un notable impulso conforme la rama de la econometría espacial y las técnicas asociadas a esta se perfeccionaban. Buena parte del impulso investigador inicial se encontró motivado por el descubrimiento de fenómenos comunes entre las unidades de estudio (ciudades, barrios, provincias, países etc.), lo que conllevó al cuestionamiento y al tratamiento de estas como entidades ajenas a todo efecto externo. Los investigadores observaron que, en la mayoría de los países analizados, los territorios se conformaban mediante áreas económicas integradas, lo que generaba fenómenos económicos comunes en todos ellos. En otras palabras, los shocks económicos que afectaban a una zona en particular no limitaban su radio de acción a la misma, sino que se dispersaban por las áreas vecinas provocando efectos similares en ellas (Blanchard y Katz, 1992; Elhorst, 2003; Niebuhr, 2003; Halleck-Vega y Elhorst, 2017). La conclusión que se extrae del párrafo anterior es clara, la evidencia empírica enfatiza el papel de los efectos espaciales para comprender los procesos económicos que se dan en el mundo actual. Como hemos comentado anteriormente, la inclusión del territorio generó una amplia batería de estadísticos y técnicas econométricas que contribuían a analizar los efectos económicos subyacentes, entre las que podemos destacar a los estadísticos descriptivos espaciales clásicos (I de Moran global, C de Geary, G de Getis, estadísticos LISA etc.), hasta las técnicas espaciales de panel más complejas (modelo de retardo espacial, modelo de error espacial, modelo espacial de Durbin etc.). Lo anterior contribuyó al desarrollo de numerosos campos del análisis económico, como pueden ser los procesos de convergencia económica (Rey y Montouri, 1999; Le Gallo y Chasco, 2008; Maza y Villaverde, 2009), la interdependencia de las tasas de desempleo en los mercados de trabajo regionales (Jimeno y Bentolila, 1998; Overman y Puga, 2002; López-Bazo et al. 2005; Filiztekin, 2009; Kondo, 2015; Halleck-Vega and Elhorst, 2016) o el análisis de la participación laboral en el mercado de trabajo (Möller y Aldashev, 2006; Elhorst y Zeilstra, 2007; Fogli y Veldkamp, 2011; Halleck-Vega y Elhorst, 2014). 13 Es precisamente en estos dos últimos campos en los que nuestra tesis doctoral trata de aportar conocimiento científico. En primer lugar, es necesario mencionar que, muchos de los artículos anteriormente reseñados, centraban su análisis en las tasas de desempleo efectivas, ofreciendo evidencia empírica de la existencia de clústers entre las tasas de desempleo regionales, detectada mediante la constatación de la existencia de autocorrelación espacial positiva entre los territorios. Conclusiones de este estilo son las que se encuentran en trabajos como los Overman y Puga (2002) en el caso del Reino Unido, López-Bazo et al. (2005) para España o Kondo (2015) para los municipios japoneses durante el periodo 1980-2005. Sin embargo, pocas investigaciones han centrado su análisis en estudiar cuáles son los componentes del desempleo efectivo que generan dicha dependencia espacial, lo que podría contribuir al desarrollo de un mayor conocimiento sobre el mismo. En esta tesis doctoral analizamos si existe dependencia espacial en los dos componentes del desempleo comentados en la sección anterior: componente natural del desempleo y componente cíclico. Este enfoque nos permitirá comprender cuál de los dos componentes es el encargado de explicar la persistencia espacial y temporal que exhiben las tasas de desempleo a nivel regional. Por consiguiente, nuestro análisis nos permitirá conocer a los factores que actúan como motores dentro del proceso de integración territorial, pudiendo ser los elementos de oferta, incluidos en el componente natural o bien los factores de demanda agregada a través del componente cíclico. 3.3 El análisis de los efectos sociales en los mercados de trabajo regionales Esta tesis doctoral relaciona a la economía laboral y a la investigación espacial con el estudio de los efectos sociales o peer effects (Dietz, 2002). Muchos trabajos han puesto de manifiesto la importancia que ejercen las redes sociales de contactos a la hora de moldear las decisiones que toman los individuos dentro del mercado laboral, lo que favorece la integración de los mercados laborales regionales (Collewet et al. 2017). Este es el motivo por el cual creemos que los efectos sociales juegan un rol determinante dentro de la economía regional, ya que generan comportamientos homogéneos que contribuyen a crear áreas económicas integradas en las cuales los individuos se retroalimentan entre sí a través de las acciones de su grupo de referencia (Manski, 2000). Sin embargo, no existen muchos ejemplos en la literatura económica que centren sus esfuerzos en estudiar la acción de los efectos sociales en un ámbito tan importante como es la participación laboral de los individuos en función del estado del ciclo económico. Es cierto que existe una gran cantidad de trabajos que estudian la relación entre las tasas de actividad a nivel de país o región, focalizándose la mayoría de ellos en el nivel de estas variables (Halleck-Vega y Elhorst, 2017). Dentro de este tipo de análisis, los trabajos de Vendrik (1998) o Grodner y Kniesner (2008) sugieren la existencia de un cierto efecto arrastre en los mercados laborales, lo que conlleva a que las preferencias de los agentes se encuentren interrelacionadas, reforzando el argumento que considera que las regiones no son entidades completamente aisladas entre sí. Es en este ámbito en el cual nuestro trabajo pretende avanzar en el conocimiento científico mediante el desarrollo de un novedoso marco teórico que contribuye al conocimiento de la economía regional a través del papel de los efectos sociales. Nuestra principal aportación reside en la acuñación de un concepto teórico (Bandwagon Worker Effect) que aúna parte de los avances de las investigaciones previamente citadas. Otro elemento a tener en cuenta es que, desde nuestro conocimiento, no existe ningún tipo de análisis regional que estudie dichos efectos en el caso de España, por lo que consideramos que nuestro trabajo puede aportar luz al fenómeno de la integración territorial de los mercados de trabajo que varias investigaciones alumbraban. 14 3.4 El papel de las políticas activas del mercado de trabajo a nivel territorial La evaluación de las políticas públicas centradas en reforzar y mejorar el funcionamiento del mercado trabajo se han erigido como un elemento determinante a la hora de considerar si la acción por parte del sector público ha generado los resultados deseados. Podríamos considerar que este tipo de análisis ayudan a los responsables de política económica a la toma de sus decisiones futuras con una mayor cantidad de información disponible (Card et al, 2010; Kluve, 2010). En otras palabras, la evaluación del impacto de las políticas activas del mercado laboral trata de cuantificar cuales han sido los efectos concretos de una política económica determinada, eliminando los posibles efectos generados por otro tipo de variables sociales, políticas o económicas relevantes (García-Serrano, 2007; Toharia et al. 2008). Pese a la existencia de una abundante evidencia empírica a nivel europeo e internacional, España destaca por ser un caso en el cual la evaluación de las políticas activas del mercado laboral no cuenta con un análisis tan extenso como en el caso de otros países. Este es precisamente otro de los objetivos de este estudio: evaluar el papel de las políticas activas del mercado laboral dentro del contexto regional español. A través de un enfoque metodológico basado en las técnicas experimentales incluidas en el trabajo de Meyer (1995), tratamos de aislar el efecto concreto sobre la ocupación y el desempleo de una política activa del mercado laboral aplicada en la región de Castilla y León durante el periodo 2001-2003 (Segundo Plan Regional de Empleo de Castilla y León (SPRECyL)). De acuerdo a lo anterior, consideramos que nuestro análisis puede tener una doble relevancia en la investigación en economía. En primer lugar, aportamos evidencia empírica solida al análisis de los mercados de trabajo regionales en España desde una perspectiva macroeconómica, contribuyendo al análisis de la eficacia de las actuaciones del sector público sobre los mercados de trabajo y ayudando a la toma de decisiones futuras con un mayor conocimiento e información. En segundo lugar, creemos que la elección de Castilla y León como “campo de pruebas” puede ayudar a conocer en mayor medida cual es el grado de eficacia de este tipo de actuaciones públicas a nivel territorial y económico. De acuerdo con la información aportada por el Instituto Nacional de Estadística (INE), Castilla y León es la región más extensa en España (94.224 km2), contando con un total de nueve unidades NUTS-3: Ávila, Burgos, León, Palencia, Salamanca, Segovia, Soria, Valladolid y Zamora. A nivel europeo, la región representa en torno al 2% del territorio total (4,369,364 km2), siendo la tercera región, dentro de las unidades NUTS-2, más extensa en Europa, excediendo incluso la extensión de algunos países como Portugal (88,847 km2), Irlanda (70,601 km2), Dinamarca (43,162 km2) o Bélgica (30,668 km2). Los datos anteriores ponen de relevancia la importancia de nuestro análisis a la hora de evaluar la efectividad de las políticas activas del mercado laboral en España. 4. Metodología 4.1. Descomposición del desempleo efectivo: Las fronteras estocásticas La institucionalización de la técnica de las fronteras estocásticas se encuentra en los trabajos pioneros de Aigner et al. (1977) y Meeusen y van den Broeck (1977). Uno de los elementos más importantes es que, en estos estudios, se formalizan parte de los avances científicos de trabajos anteriores a la hora de generar una estructura de error compuesto, lo que es clave para la utilización de las fronteras estocásticas. Dicha técnica econométrica, nos permite estimar el límite inferior de la tasa de desempleo efectiva (componente natural), junto con la posible ineficiencia asociada al mismo (componente cíclico). Un elemento clave en este punto es la consideración adoptada en los trabajos de Hofler y Murphy (1989) y Aysun et al. (2014), en 15 donde se establece que todos los componentes del desempleo efectivo tienen como límite inferior el valor 0. Dicho con otras palabras, ningún componente del desempleo efectivo puede alcanzar cotas negativas De tal manera que, si entendemos el proceso de formación de la tasa de desempleo efectiva como un fenómeno en el cual intervienen factores de oferta agregada y factores de demanda agregada, es posible hallar una descomposición del mismo a través del componente natural del desempleo y del componente cíclico. De acuerdo con esta hipótesis, la tasa natural de desempleo se constituye como un límite inferior al que la economía tenderá en el medio/largo plazo. De lo anterior se deriva que, la existencia de una tasa de desempleo efectiva superior a la tasa natural de desempleo se debe a un comportamiento ineficiente dentro del mercado de trabajo, ya que este “exceso” de desempleo, asociado al componente cíclico, podría corregirse mediante la aplicación de políticas económicas de demanda agregada. Por consiguiente, la ecuación (3) nos permite formalizar al componente natural de la siguiente manera: 𝐷𝑖𝑡 𝑁𝑅𝑈 = 𝑋𝑖𝑡𝛽𝑖 + 𝑣𝑖𝑡 (3) donde 𝑋𝑖𝑡 es un vector de variables explicativas que engloba a factores de oferta agregada; 𝛽𝑖 un vector de coeficientes que deben de ser estimados y 𝑣𝑖𝑡 el componente aleatorio del error compuesto. Como hemos mencionado anteriormente, este componente es únicamente uno de los dos que definen al desempleo efectivo, el cual se explica a través de la ecuación (4): 𝐷𝑖𝑡 = 𝐷𝑖𝑡 𝑁𝑅𝑈 + 𝑢𝑖𝑡 (4) siendo 𝑢𝑖𝑡 =𝐷𝑖𝑡 𝐶 , asociando así al desempleo cíclico con el termino ineficiente mencionado anteriormente. Finalmente, agrupando las expresiones (3) y (4) obtenemos el modelo a estimar que nos permitirá descomponer al desempleo efectivo en su componente natural y en su componente cíclico mediante la aplicación de una frontera estocástica en su modalidad de costes: 𝐷𝑖𝑡 = 𝑋𝑖𝑡𝛽𝑖+ 𝜉𝑖𝑡 (5) donde: 𝜉𝑖𝑡 = 𝑣𝑖𝑡 +𝑢𝑖𝑡 Por lo que, aplicando dicho enfoque a nuestro análisis del mercado laboral, no solo podremos estimar el mínimo nivel de desempleo efectivo existente a nivel macroeconómico (componente natural), sino que también sería posible cuantificar el exceso de desempleo existente debido a la existencia de comportamientos macroeconómicos ineficientes en un entorno determinado (componente cíclico) para los distintos mercados de trabajo de las regiones españolas. 4.2. Las técnicas de econometría espacial: Conceptos clave Una de las definiciones más completas de la econometría espacial es la que se ofrece en Elhorst (2014), donde se especifica a la econometría espacial como aquel “apéndice dentro de la econometría encargado de estudiar los efectos derivados de las interacciones espaciales entre las unidades geográficas objeto de estudio”. 3 Una vez comentado lo anterior, debemos 3 Pese a lo que pueda sugerir el término “unidades geográficas”, el lector no debe limitarse a considerar dentro del mismo, únicamente, a grandes unidades administrativas, (Ej: comunidades autónomas o provincias en España). Sino que dentro de esta categoría se incluye a una gran variedad de agentes económicos sobre los que el papel de territorio puede tener una importancia capital (municipios, jurisdicciones, barrios, mercados de trabajo regionales etc.). 16 centrarnos en lo que se ha denominado como dependencia espacial, la cual refleja una situación en la que los valores de una variable “i” perteneciente a una unidad geográfica determinada, dependen de los valores observados en las áreas vecinas de la misma (LeSage y Pace, 2010). En este sentido, el termino vecino (neigborhood en inglés) toma una importancia capital, ya que se denomina así a los agentes económicos (ciudades, municipios, provincias etc.) que comparten una cierta vinculación económica, territorial, política, social etc. Por lo que, los fenómenos que se desarrollan en cada uno de ellos, generan efectos significativos en los agentes económicos afines o emparentados entre sí. Para poder incorporar estas directrices a la vecindad de las unidades objeto de estudio, la econometría espacial emplea un término conocido como matriz de dependencia espacial (𝑊). Este elemento alude a una matriz de dimensiones 𝑁 𝑥 𝑁 que se encarga de recoger las relaciones sociales, económicas, territoriales etc. que subyacen entre los elementos a analizar, transformando unidades independientes en elementos integrados entre sí (LeSage y Pace, 2010). Una vez hemos solucionado la cuestión anterior, debemos de fijar un criterio de vecindad entre las unidades espaciales para poder construir los pesos que integran a la matriz espacial 𝑊. En los artículos que integran esta tesis doctoral en los que se aplican este tipo de técnicas, hemos centrado la atención en dos de los criterios de vecindad más utilizados dentro de la econometría espacial: a) K – vecinos más cercanos y b) distancia geográfica. Ambos criterios serán expuestos en profundidad en los capítulos dos y tres de este documento. 4.2.1 Estadísticos univariantes globales: La I de Moran global Por otra parte, dentro de las técnicas de econometría espacial empleadas para detectar la presencia de dependencia espacial en las unidades de estudio, una de las herramientas más utilizadas son los estadísticos univariantes, los cuales se clasifican en dos grandes grupos. En primer lugar, encontramos a los estadísticos globales, los cuales tratan de obtener un valor promedio de la dependencia espacial existente utilizando todo el conjunto de datos disponibles de las unidades objeto de estudio. Existen tres estadísticos descriptivos utilizados para cuantificar la existencia de dependencia espacial global: I de Moran (Moran, 1948); c de Geary (Geary, 1954) y G de Getis y Ord (Getis y Ord, 1992). De entre todos ellos, nosotros nos centraremos en exponer el primero de ellos, debido a que es el estadístico de econometría espacial empleado en los dos artículos que integran el capítulo dos y tres de este documento. El motivo por el cual hemos decidido centrarnos y emplear dicho estadístico es debido a que el contrate basado en la I de Moran global es el estadístico más empleado en los análisis de dependencia espacial durante los últimos años. La expresión que define a la I de Moran global es la que se muestra a continuación (Moran, 1948): 𝐼= 𝑛 𝑆0∗ ∑𝑆𝑊𝑖,𝑗 𝑛 𝑖,𝑗 (𝑥𝑖−𝑥)(𝑥𝑗−𝑥) ∑ (𝑥𝑖−𝑥)2 𝑛 𝑖=1 (6) donde 𝑛 es el tamaño de la muestra objeto de estudio, 𝑆𝑊𝑖𝑗 hace referencia a los componentes de la matriz espacial empleada, 𝑥𝑖 representa el valor de la variable 𝑥 en la unidad 𝑖, 𝑥𝑗 representa el valor de la variable 𝑥 en la unidad 𝑗, 𝑆0 es igual a ∑ ∑ 𝑆𝑊𝑖𝑗𝑗𝑖 y finalmente 𝑥 se corresponde con la media de la muestra de los datos representados de la variable 𝑥. A modo de generar una exposición simplificada y no excesivamente técnica del anterior concepto, diremos que los valores que la I de Moran global fluctúan dentro del intervalo [1,-1]. Si el valor obtenido es cercano a 1, la interpretación es que existirá dependencia espacial positiva entre los valores observados dentro de las unidades objeto de estudio. En otras palabras, la existencia de dependencia espacial positiva nos informará de que existen áreas con altos (bajos) valores de la variable objeto de estudio rodeadas por otras áreas cuyos valores 17 también resultan ser altos (bajos) para dicha variable. Por el contrario, existirá dependencia espacial negativa si los valores arrojados por la I de Moran se aproximan a -1, indicando que las áreas donde los valores objeto de estudio sean bajos (altos) se encontrarán próximas a otros territorios en los cuales los valores obtenidos son altos (bajos). 4.2.2 Estadísticos univariantes locales: La I de Moran local A diferencia de los estadísticos globales, los estadísticos locales o LISA (Local Indicators of Spatial Association, por su nomenclatura en inglés), estudian la existencia de dependencia espacial de un subconjunto de datos (Anselin, 1995). Estos estadísticos, según lo expuesto en Anselin (1995), descomponen a las anteriores medidas globales, generando unos nuevos indicadores que cumplen dos premisas fundamentales: a) El valor LISA de cada observación indica el alcance de la significancia espacial alrededor de la observación y b) La suma de todos los LISA es proporcional al indicador global de asociación espacial. En esta línea, nos centraremos en la exposición de este concepto a través de la ecuación (7): 𝐼𝑖= 𝑛(𝑥𝑖−𝑥) ∑ (𝑥𝑖−𝑥)2 𝑛 𝑗=1 ∑𝑤𝑖𝑗(𝑥𝑗−𝑥) 𝑛 𝑗=1 (7) donde 𝑤𝑖𝑗 simboliza un elemento de la matriz de pesos espaciales 𝑊 elegida. La interpretación de este estadístico es un tanto diferente a la de los estadísticos globales, en parte por su mayor especificidad a la hora de informar acerca de la existencia de dependencia espacial. En este caso, obtendremos una clasificación formada por cuatro grupos distintos: a) Alto-Alto: Valores altos de 𝑥𝑖 y de 𝑤𝑥𝑖; b) Bajo-Bajo: Valores bajos de 𝑥𝑖 y de 𝑤𝑥𝑖; c) Alto-Bajo: Valores altos de 𝑥𝑖 y bajos de 𝑤𝑥𝑖 y d) Bajo-Alto: Valores bajos de 𝑥𝑖 y altos de 𝑤𝑥𝑖. Finalmente, debido a la complejidad del análisis anterior, dicha información ha sido incorporada a los capítulos de la tesis doctoral mediante un mapa provincial del territorio español en los cuales se ofrece información acerca de la localización y el grupo de clasificación de los clústeres locales de dependencia espacial detectados. 4.2.3 Características de los modelos espaciales de datos de panel A lo largo de la tesis doctoral, empleamos técnicas econométricas de panel para comprobar la robustez de nuestros resultados y ofrecer un análisis complementario a los resultados obtenidos por parte de la I de Moran global y local. Concretamente, en nuestro análisis empleamos tres de los paneles espaciales más utilizados dentro de la econometría espacial durante el último siglo, como son el modelo espacial de retardo espacial (SAR por sus siglas en inglés), el modelo de error espacial (SEM) y finalmente el modelo espacial de Durbin (SDM). El primero de ellos, modelo de retardo espacial (SAR), se especifica a través de la expresión (8): 𝑦𝑖𝑡 = 𝜌𝑊𝑦𝑡+𝑋𝑡β𝑖+𝜀𝑡 (8) siendo 𝜀𝑡~𝑁[0,𝜎𝜀 2𝐼𝑛] El elemento principal de dicho modelo es el término 𝜌𝑊𝑦𝑡, informándonos acerca de si existe evidencia empírica de dependencia espacial positiva (en el caso de que su valor sea positivo) o negativa (en el caso de que obtengamos un valor negativo). El segundo modelo empleado es el modelo de espacial del error (SEM), el cual se desarrolla mediante la siguiente ecuación (9): 𝑦𝑖𝑡 =𝑋𝑡β𝑖+𝜀𝑡 (9) 18 siendo 𝜀𝑡=𝜌𝑊𝜀𝑡+𝛾𝑡, mientras que 𝛾𝑡~𝑁[0,𝜎𝛾 2𝐼𝑛]. La principal diferencia de este modelo respecto al SAR es que se incorpora al coeficiente o parámetro espacial autoregresivo (𝜌) en el error estándar del modelo, debido a que la existencia de dependencia espacial puede estar presente en el modelo entre las variables que no se incluyen en el mismo. De acuerdo con lo anterior, la no inclusión de ciertas variables en el modelo generaría problemas respecto a su construcción en forma de variables explicativas omitidas, las cuales resultan ser importantes a la hora de detectar dependencia espacial entre las unidades objeto de estudio. El último modelo espacial para datos de panel empleado es el modelo espacial de Durbin (SDM): 𝑦𝑖𝑡 = 𝜌𝑊𝑦𝑡+𝑋𝑡β𝑖+μ+𝑊𝑋𝑡𝜑+𝜀𝑡 (10) donde 𝑊𝑋𝑡𝜑 captura el efecto de la variable explicativa 𝑋𝑡 de las regiones vecinas sobre la variable dependiente (𝑦𝑡) de la región en cuestión. La novedad principal de este tipo de modelo reside en la inclusión del coeficiente espacial autoregresivo (𝜑). Este término, se encarga de capturar el efecto espacial que las variables exógenas ejercen sobre la variable dependiente del modelo. De esta manera, podemos testar si la dependencia espacial de nuestro modelo se debe a la acción de interacciones endógenas (𝜌𝑊𝑦𝑡) o bien es consecuencia de efectos exógenos (𝑊𝑋𝑡𝜑). Debido a lo anterior, el SDM resulta ser el modelo más completo en de los tres utilizados. 4.3. Evaluación de políticas activas del mercado laboral: El análisis de diferencias en diferencias Para conocer el efecto concreto de una política activa aplicada al mercado laboral, los economistas deben de aislar el efecto del resto de fenómenos que operan a la vez que dicha política activa (Heckman et al. 1999; Malo et al. 1999; Vooren et al. 2019). En caso contrario, podríamos caer en el error de atribuir un efecto concreto a la acción de una política determinada (por ejemplo, un plan de empleo sobre una región especifica) cuando en realidad lo que estamos observando es la suma de varios efectos económicos, sociales y políticos que operan al mismo tiempo que la política que queremos evaluar (estado del ciclo económico, coyuntura internacional etc.). Uno de los enfoques más famosos y empleados por parte de los investigadores a la hora de evaluar las políticas activas del mercado laboral es mediante el análisis cuasi-experimental desarrollado en el trabajo de Meyer (1995). Según este análisis, la evaluación de una política determinada (tratamiento según su denominación técnica) debe de llevarse a cabo mediante la división exógena, la cual no es decidida por el investigador, de las unidades de estudio en dos grupos determinados: a) Grupo de tratamiento, el cual se encuentra formado por las unidades objeto de estudio que han recibido el tratamiento (aplicación de una política activa del mercado laboral), y b) Grupo de control, del que forman parte aquellas unidades que no han recibido el tratamiento que se pretende analizar. Este enfoque nos permitirá aislar el efecto de fenómenos que afectan de forma simultánea a los integrantes de ambos grupos y detectar cual ha sido el efecto especifico del tratamiento que pretendemos analizar. Una vez se ha definido el enfoque a emplear, es necesario describir que técnica econométrica se va a implementar para poder llevarlo a cabo, la cual se corresponde con el análisis de diferencias en diferencias (Card y Krueger, 1994; Martín-Román, 2007). Brevemente, esta técnica se ocupa de comparar los resultados de una variable en una población tratada con los que presenta esta misma variable en otra población no expuesta al tratamiento. De esta manera es posible discernir si las diferencias observadas en las variables objetivo vienen explicadas por 19 la exposición del grupo tratado a la intervención exógena. Un ejemplo de la formalización del análisis de diferencias en diferencias es el que se presenta en la siguiente ecuación: 𝑌𝑖𝑡 =𝛽0(𝑖)+𝑋𝑖𝑡𝛽1+ 𝑋𝑖𝑡𝑍𝑖𝑡𝛽2+𝜀𝑖𝑡 (11) donde 𝑌𝑖𝑡 indica la variable laboral estudiada, 𝛽0 presenta el término constante, 𝑋𝑖𝑡 es una variable dicotómica que toma el valor 1 para los años en los cuales se aplica el tratamiento y el valor 0 para el resto del periodo objeto de estudio y 𝜀𝑖𝑡 hace referencia al termino de error. Sin embargo, la variable esencial para analizar el impacto del tratamiento resulta de multiplicar dos variables categóricas 𝑋𝑖𝑡 y 𝑍𝑖𝑡, siendo esta última una variable que toma el valor 1 para aquellas unidades que forman parte del grupo de tratamiento y 0 para los elementos que integran el grupo de control. 5. El análisis espacial de los mercados de trabajo: Una revisión bibliográfica 5.1. La descomposición del desempleo efectivo: Estrategias empíricas La descomposición del desempleo efectivo se ha erigido como uno de los temas centrales dentro de la rama de la economía laboral a lo largo de los últimos años. Existen varios enfoques, no siempre excluyentes, que generan distintas perspectivas en torno a cuáles son los elementos principales que componen y explican al desempleo efectivo (Bean, 1994). Uno de los enfoques más originales empleado en los últimos años ha sido el de las fronteras estocásticas, el cual se constituye como la técnica principal de descomposición del desempleo utilizada en la presente tesis doctoral. La investigación de Warren (1991) se considera como uno de los trabajos pioneros dentro de este tema de estudio. Este trabajo toma como punto de partida los modelos de emparejamiento del mercado de trabajo. En base a esto, se aplica el enfoque de los modelos de crecimiento del empleo cuando la economía se encuentra en el estado estacionario para deducir la expresión de la tasa de desempleo. En una segunda etapa, mediante la aplicación de un modelo OLS, el autor obtiene la tasa media de desempleo para el sector manufacturero de Estados Unidos, aplicando, posteriormente, una frontera estocástica de producción para hallar el desempleo friccional. Finalmente, mediante la resta de ambas tasas estimadas, obtiene una medida de la ineficiencia de ese mercado de trabajo. Un enfoque complementario es el de Bodman (1999), el cual toma como punto de partida el modelo teórico expuesto en Warren (1991). Las principales diferencias surgen de la perspectiva regional y de la modelización del término de ineficiencia del error que se realiza siguiendo la propuesta de Battese y Coelli (1995). Sin embargo, existen dos trabajos que desarrollan un enfoque muy similar al nuestro y que se han constituido como una de las principales referencias tanto en el plano teórico como a la hora de la aplicación de las estrategias empíricas. El primero de estos trabajos es el de Hofler y Murphy (1989). Estos autores plantean un modelo para hallar el componente friccional del desempleo mediante el cual es posible descomponer a la tasa de desempleo efectiva en un componente friccional y en un componente encargado de capturar el exceso de oferta laboral existente en el mercado laboral. A través de este marco teórico, en una primera etapa, el artículo descompone las tasas de desempleo de los cincuenta estados de EEUU, durante el periodo 1960-1979, a través de la utilización de una frontera estocástica en su modalidad de costes. Esta estrategia empírica es crucial para la investigación, ya que asocia el límite inferior estimado mediante la frontera al componente friccional, concluyendo que todo el desempleo restante es debido a la existencia de exceso de oferta laboral en el mercado de trabajo estadounidense. Finalmente, en una segunda etapa, los autores completan su análisis a través de la utilización de diferentes variables demográficas, sectoriales e institucionales para determinar cuál es el elemento clave 20 a la hora de explicar al componente friccional del desempleo efectivo. El segundo trabajo clave es el de Aysun et al. (2014), en donde se combinan elementos de las tres investigaciones anteriores, basándose en la premisa que establece que los componentes del desempleo efectivo nunca pueden tomar valores negativos o inferiores a cero. Por un lado, utiliza un modelo y una metodología muy similar a la observada en Warren (1991) para extraer el componente friccional del desempleo. Por otro lado, aplica una frontera costes para hallar el componente estructural de la tasa de desempleo como se hacía en Hofler y Murphy (1989), mediante una especificación de la curva de Philips con expectativas. De esta manera, los autores obtienen una medida del desempleo estructural de EEUU durante el periodo 1960-2010, que es siempre inferior al componente efectivo. Los anteriores trabajos se configuran como el elemento crucial sobre el que construimos nuestro análisis de la descomposición del desempleo efectivo en los artículos que integran el primer y el segundo capítulo de la tesis doctoral. Sin embargo, en el primer capítulo, también empleamos otras técnicas econométricas muy utilizadas en la literatura a la hora de descomponer el desempleo efectivo: Los filtros univariantes. En este caso podemos destacar un total de tres filtros univariantes, el filtro de Hodrick-Prescott (Hodrick-Prescott, 1997), el filtro de Baxter-King (Baxter-King, 1999) y la descomposición por tendencia cuadrática. Dichas técnicas econométricas han sido frecuentemente empleadas, en un contexto laboral, a la hora de estimar relaciones empíricas tan famosas como puede ser la ley de Okun, concretamente para obtener los componentes cíclicos de las variables estudiadas (Perman y Tavera, 2005; Adanu, 2005). 5.2. Análisis de la dependencia espacial en el desempleo: Una perspectiva regional El estudio de la importancia del territorio sobre la economía ha cobrado una gran importancia dentro del mundo científico según los investigadores iban descubriendo el crucial papel que este ejercía a la hora de entender las dinámicas económicas. Uno de los trabajos más importantes dentro de esta literatura es del de Blanchard y Katz (1992). En este trabajo centrado en los estados de EEUU, los autores ofrecen evidencia empírica acerca de los efectos que los shocks macroeconómicos ejercen sobre los diferentes territorios en un espacio temporal de cuarenta años. También, ambos autores destacan la notable importancia que la localización territorial ejerce a la hora de determinar los efectos de dichos shocks, considerándose este elemento como uno de los más importantes a la hora de explicar el devenir futuro de las regiones estadounidenses. Es en este caso donde se presta una atención especial al fenómeno de la migración de los agentes económicos como elemento crucial a la hora de explicar la disipación y absorción de los shocks. A raíz del gran impacto de dicho trabajo y del rápido desarrollo de la economía regional, algunos autores europeos llevaron a cabo análisis similares para Europa, como por ejemplo el trabajo de Decressin y Fatás (1995). En este trabajo se comparan las dinámicas económicas de los países pertenecientes a la Unión Europea con las detectadas en EEUU, observándose notables cambios en los mecanismos de ajuste laboral (participación laboral en Europa frente a migración en EEUU). Otro elemento a destacar es el reducido papel que se le otorga al nivel de desempleo existente a la hora de actuar como estabilizador económico de ambas zonas. La casuística anterior sugiere que, los agentes económicos actúan en función del nivel de las propias tasas de desempleo natural regionales en vez de la tasa agregada cuando toman sus decisiones económicas. Es precisamente a la hora de analizar las dinámicas del desempleo regional en donde el número de trabajos existentes es notorio. Uno de los estudios clásicos más citados es el de Overman y Puga (2002). En este trabajo, centrado en Europa durante el periodo 1986-1990, se obtienen resultados que ya apuntaban a algunas de las dinámicas comentadas y tratadas en nuestra propia investigación: La polarización creciente entre regiones de alto desempleo y regiones de bajo desempleo. Estos autores apuntan a que uno de los fenómenos importantes que contribuyen a explicar la polarización existente es la existencia de contigüidad 21 Natural and cyclical unemployment: a stochastic frontier decomposition and economic policy implications Ángel L. Martín-Román* Jaime Cuéllar-Martín Alfonso Moral Department of Economic Analysis, University of Valladolid ABSTRACT This work splits effective unemployment into two components: The natural unemployment, and the cyclical unemployment. For that purpose, an estimation of stochastic cost frontier is performed. The study is focused on the 17 autonomous communities in Spain over the period 1982-2012. Results evidence a greater importance of the natural component as the principal determinant of effective unemployment. When comparing these results with those obtained applying univariate filters, the distribution in the components of the effective unemployment changes, increasing the importance of cyclical unemployment. This result indicates that the policymakers have a greater margin of action to implement aggregate demand policies. Key words: Unemployment rate, labor market, stochastic frontiers, decomposition of unemployment. JEL Codes: E24, J08, J64, R23 * Corresponding author (email address: angell[email protected]) ACKNOWLEDGEMENTS: The first and second authors were partially supported by the Spanish Ministry of Economy, Industry and Competitiveness under project ECO2017-82227-P. The third author has been partially supported by Ministry of Economy, Industry and Competitiveness under project CSO2015-69439-R. 28 I. INTRODUCTION. The Spanish labor market over the last few decades has been characterized by having generated exceptionally high unemployment rates when compared to those seen elsewhere in Europe (Bentolila and Jimeno, 2003; Jaumotte, 2011). The explanations, as to the reasons, behind such high and persistent levels of unemployment have been set out in many academic papers 1 . A further issue which has been the subject of much inquiry in the literature (Jimeno and Bentolila, 1998; Bande et al., 2008; Romero-Ávila and Usabiaga, 2008; Bande and Karanassou, 2013; Porras and Martín-Román, 2018) is the enormous disparity between unemployment rates in the various regions in Spain and their persistence over time. The objective of this paper is to put forward a methodological proposal to decompose the actual unemployment rate into two components: the natural unemployment rate and the cyclical unemployment rate. This is an issue extensively addressed in the literature studying the macroeconomics of the labor market, but in a very different way as done in this piece of research. Here, we assume that cyclical unemployment cannot take negative values since it is difficult to imagine a world with more unemployed persons than the sum of structural and frictional unemployment, even when the economy is booming. That would be the case when the Natural Rate of Unemployment (NRU, hereinafter) is considered to be the same as the notion of NAIRU. We do not follow this path in this paper. Instead, we make use of a composed error model econometric methodology to guarantee that the non-negative cyclical unemployment assumption is fulfilled. To sum up, the main aim of this paper is to estimate the NRU with the stochastic frontier (SF, hereinafter) technique and then to compare it with some of the most popular procedures to do it, such as the Hodrick-Prescott (HP, hereinafter) and Baxter-King (BK, hereinafter) filters or the Quadratic-Trend (QT, hereinafter) regression. This paper contributes to the unemployment rate decomposition literature. In this vein, we might assert that we align ourselves within the compartmentalization view in the macroeconomics of the labor market. According to Karanassou et al. (2007, 2010) this is only one of the competing theories to explain aggregate labor markets functioning, together with the “Chain Reaction Theory (CRT) or prolonged adjustment view” and the “Hysteresis hypothesis”. By assuming the unemployment compartmentalization standpoint, we would be adopting some of economic principles usually linked to a “frictionless equilibrium” in the labor market (Karanassou et al., 2007). However, the concept of NRU is far from being a clear-cut notion even within the compartmentalization literature (Rogerson, 1997). As will be discussed in greater detail ahead, our approach fits well into some of definitions of the NRU enumerated by Rogerson (1997). At the same time, HP filtering is considered by Rogerson (1997) as another conceivable definition of what the NRU actually is. In this way, we think that this article not only provides a fresh estimate of the NRU to an already extensive literature but clarifies the own NRU concept. Hence, the comparison between our SF estimation of the NRU and those of the HP, BK and QT could be thought as an appraisal of different conceptions of the NRU within the compartmentalization hypothesis 1 The exceptional works of Blanchard and Wolfers (2000) and Blanchard (2006) highlight the role played by labor institutions when causing high unemployment rates in the face of adverse macroeconomic shocks. Another study which provides information on the topic under discussion is the work of Nickell et al. (2005). 29 As regards the innovation and the value added of the paper, first we should point out that the literature on SF estimation of the NRU is quite scarce compared to other sorts of NRU estimates. After the seminal work by Hofler and Murphy (1989), there are only a few additional references. To the best of our knowledge, only the works of Warren (1991), Bodman (1999) or, more recently, Aysun et al. (2014) and Cuéllar-Martín et al. (2018) could be deemed to be closely related to this article. Furthermore, and as a second innovative element, here we develop a theoretical framework to justify our empirical approach of modelling the NRU as a lower envelope by using the SF estimation (i.e. a cost frontier in the usual terminology). In the third place, we offer, for the first time as far as we know, a systematic statistical comparison of the SF estimates of the NRU with the much more standard estimates by means of time-series filtering techniques. That contrast between different econometric procedures could serve as an assessment tool for making informed decisions. It is worth mentioning that such an assessment should be carried out not in terms of goodness of prediction, since in the end the NRU concept is unobservable, but in terms of economic policy implications, as we shall explain below. To carry out the empirical strategy, the present work takes advantage of the spatial and temporal variability of regional unemployment rates in Spain. We make use of a database which provides information on the 17 autonomous communities in Spain for the period between 1982 and 2012 2 . Regarding the main results obtained, our methodological proposal reduces the weight of the natural component of unemployment in favor of the cyclical, as compared to the NRU estimates using time-series filtering techniques. These results might have significant potential implications for economic policy as they could provide greater scope of action for policy-makers seeking to fight unemployment. More precisely, our results seem to suggest that the scope for Keynesian economic policy measures (i.e. aggregate demand stimulus policies) is greater than previously thought, as a consequence of the larger scale of the cyclical unemployment. The remainder of the work is organized as follows. Section 2 outlines the theories on unemployment compartmentalization and reviews the literature on unemployment decomposition. Section 3 shows a formal model connecting our conceptual framework to our empirical strategy. Section 4 sets out the methodological aspects, both in terms of the SF analysis used in the decomposition as well as the univariate filters employed in the subsequent comparison. Section 5 details the database used and provides a brief explanation of the variables applied in the study. Section 6 offers the main results obtained when decomposing unemployment through the SF. Section 7 compares SF estimates with the decompositions obtained from the univariate filters. Section 8 sets out certain economic policy implications. Finally, section 9 sums up the main conclusions to emerge from the work. 2 Spanish autonomous communities correspond to the second level (NUTS-2) of the Nomenclature of Territorial Units for statistics. For further information concerning the concept of NUTS, see: http://ec.europa.eu/eurostat/web/nuts/overview. 30 II. UNEMPLOYMENT COMPOSITION: THEORIES AND FACTS. II.1. Theories on unemployment compartmentalization. As Karanassou et al. (2007, 2010) states, there are three fundamental views of the labor market regarding the movements in unemployment: (1) the frictionless equilibrium view; (2) the hysteresis view; and (3) the chain reaction theory, or prolonged adjustment view. Besides other implications for the aggregate labor market modelling or the macroeconomic policy, that distinction entails a conception on how the actual unemployment rate might be broken down into different components, which is the main aim of this piece of research. In the first place, the “frictionless equilibrium view” establishes a clear-cut distinction between two types of unemployment: natural and cyclical unemployment. Within this hypothesis, the former is assumed to be a long-run equilibrium concept, giving rise to the notion of NRU, whereas the latter is associated to short-run fluctuations. This, in turn, leads to the idea of compartmentalization, which suggests that the unemployment rate can be decomposed into its two constituent components by means of econometric procedures. This interpretation of the macroeconomics of the labor markets has been defended on the grounds of the analysis of the role of shocks and institutions (see, among others, Layard et al., 1991; Blanchard and Wolfers, 2000), of the structuralist theory of unemployment (see, for instance, Phelps, 1994; Phelps and Zoega, 2001), or from a purely institutionalist standpoint (e.g., Nickell et al., 2005). See Blanchard (2006) for an assessment of this literature. Secondly and fairly opposed to the previous hypothesis, the “hysteresis view” affirms that all the short-run fluctuations automatically turn into long-run changes in the unemployment rate (Blanchard and Summers, 1986 and 1987; Røed, 1997; León-Ledesma, 2002; Raurich et al., 2006). In this way, transitory business cycle shocks bring about permanent variations in the unemployment rate. Hence, according to this theory, it is not possible to distinguish long-run equilibrium from cyclical fluctuations. In practical terms, this theory implies that the unemployment rate in a specific period of time strongly depends on its past values. From an econometric viewpoint, the above would correspond to an unemployment rate being characterized by not following a "random walk". That is, by the presence of a unit root in such a series, with a value of the autoregressive parameter equal to unity. Thirdly, the “prolonged adjustment view”, or “chain reaction theory” of unemployment establishes that the labor market adjusts only slowly to external shocks. There are several reasons for that sluggish adjustment, among them we could highlight: (1) employment adjustment costs (e.g. firing and hiring costs, see for instance Cabo and Martín-Román, 2019 for a recent formal model on that); (2) wage staggering (Ascari, 2003; Karanassou and Sala, 2012); (3) price stickiness (Andersen, 1998); or (4) labor force participation adjustment (see Martín-Román et al., 2018 for a fresh analysis with a regional economics perspective). This hypothesis might be thought as an intermediate case between the “frictionless equilibrium view” and the “hysteresis view”. Moreover, this theory addresses the idea of “frictional growth”, a phenomenon that encloses the interplay of lagged endogenous variables (frictions) and growing exogenous variables (growth drivers). Thus, when the exogenous variables have nonzero long-run growth rates (e.g., capital accumulation, population growth) unemployment does not gravitate 31 towards its NRU. The CRT was originally developed by Karanassou and Snower (1996, 1997, 1998). In this same vein, see also Karanassou et al. (2003, 2004, 2006, 2007, 2010). For the aforementioned reasons, there is currently some debate as to whether or not compartmentalization is an appropriate stylized representation of the aggregate labor market. In this sense, Karanassou et al. (2007) state that compartmentalizing the unemployment rate into its natural and cyclical components does not fit with the European (or even the US) experience since the 80’s, providing theoretical arguments for their point: in a frictionless world, even allowing for imperfect competition in goods and labor markets, the short-run and long-run are separate from each other. Thus, temporary labor demand shocks generate short-run variations in unemployment, while in the long run, the NRU responds to changes in the capital stock, the labor force or the technological level. If, on the contrary, one assumes that labor market decisions are characterized by prolonged adjustments (see for instance Kunz, 2009), then the compartmentalization of the natural and cyclical unemployment rates vanishes, and is only valid under rather restrictive assumptions. Furthermore, Karanassou et al. (2010) or Bande and Karanassou (2013) maintain that under the phenomenon of “frictional growth”, i.e., the interplay of growing variables with labor market lagged adjustment processes, the effective natural rate does not converge towards the NRU, and therefore the latter cannot be regarded as a reference point for policy recommendations. At this point, we should make clear, however, that the approach proposed in this paper assumes the compartmentalization of unemployment into its natural and cyclical components. Put differently, it might be said that we align ourselves with the “frictionless equilibrium view” to a great extent. Although the “hysteresis” and the CRT views have challenged the “frictionless equilibrium view” in recent years, we still feel that the latter is still a widespread view. In this vein, a recent paper by Blanchard (2018) questions the concept of NRU itself. 3 He analyses critically the notion of NRU from both macroeconomic and microeconomic grounds. Nevertheless, and despite this criticism, Blanchard finally states that: “Policymakers should keep the natural rate hypothesis as their null hypothesis, but also keep an open mind and put some weight on the alternatives”. Therefore, in our view, this statement reinforces the methodological approach followed here. Furthermore, we find several motives to keep on using this interpretation on the aggregate labor market functioning. For example, all that literature analyzing the so-called gap version of the Okun’s Law precisely correlates the cyclical component of the unemployment rate with the business cycle, measured usually by means of the cyclical component of the GDP time series too. This approach tacitly assumes the compartmentalization view and has produced, and still is producing, a great amount of academic work. See, for instance, Lee (2000), Freeman (2000), Cuaresma (2003), Adanu (2005), Perman and Tavera (2005), Apergis and Rezitis (2003), Villaverde and Maza (2007, 2009), Marinkov and Geldenhuys (2007), Moosa (2008), Herwartz and Niebuhr (2011), Ball et al. (2013) or Bande and Martín-Román (2018). Therefore, it could be affirmed that the compartmentalization view is implicitly adopted in this extensive research field. Secondly, and despite of the challenging approaches of the hysteresis and 3 It is worth mentioning though that Blanchard uses the concepts of NRU and NAIRU interchangeably, which is not the case in this paper (see next subsection). 32 prolonged adjustment theories, the compartmentalization view is still inherent in many of the works modelling the macroeconomics of the labor markets by preeminent scholars nowadays. Some current examples of this strand of research are Daly et al. (2012) or Diamond (2013). Hence, although this second motive might be considered as an “argument from authority”, we still feel it is a valid reason 4 . The third argument in favor of following the compartmentalization view has to do with the regional economics perspective of this paper. Thus, it has been quite common to make use of the compartmentalization hypothesis when analyzing the aggregate regional labor market. Some outstanding examples of this literature are Marston (1985), Partridge and Rickman (1997), López-Bazo et al. (2005), Cracolici et al. (2007). Again, an extensive strand of research is adopting implicitly the approach followed here (as in the case of the first argument). A final reason is related to economic policy objectives. In the aforementioned paper, Blanchard (2018) also states that: “the general advice must be that central banks should keep the natural rate hypothesis (…) as their baseline.” In any case, and despite asserting that our paper follows the mainstream view of unemployment compartmentalization, there will be several features that distinguish our approach from those other more standard empirical methodologies (e.g. filter decompositions) described in a later subsection. The most remarkable difference is that we elaborate a formal framework in which cyclical unemployment cannot be associated with negative values and, even more importantly, we employ an econometric technique to guarantee that such an assumption is fulfilled. More specifically, we apply a composed error model to break down the unemployment rate. The SF methodology has been already used previously with this purpose. Thus, the seminal work by Hofler and Murphy (1989) established the basic foundations to perform aggregate unemployment breakdown by means of this technique. Then, the works by Warren (1991), Bodman (1999) and more recently Aysun et al. (2014) have followed this path. In a later subsection, we will review this literature more in depth. II.2. A reflection on the concept of NRU. As is obvious from the previous discussion the NRU plays a key role in this research. However, that concept is far from being a crystal-clear idea, rather it is a polyhedral notion that has been used differently by distinct authors during the 80s and the 90s. Following Rogerson (1997), among these alternative definitions of the term we could find: (1) the average rate of unemployment (Blanchard and Fischer, 1989); (2) the equilibrium rate of unemployment (Blanchard and Fischer, 1989; Johnson and Layard, 1986); (3) the unemployment in the long run (Johnson and Layard, 1986); (4) the normal unemployment rate that results when workers and firms correctly perceive the levels and rates of change of price and wages (Hall and Lilien, 1986); (5) the steady state rate of unemployment (Mankiw, 1994); (6) the lowest sustainable rate of unemployment (Auerbach and Kotlikoff, 1995); (7) the trend component of unemployment generated by the HP filter 5 (Rogerson, 1997); (8) the efficient rate of unemployment (Clark et al., 1979) and (9) the unemployment at full employment (Hahn, 1980). 4 We also acknowledge here that long ago, many prominent scholars criticized the usefulness of this theoretical tool, the monographic issue of the Journal of Economic Perspectives, vol. 11 (1) Winter 1997 is a good example. 5 Actually, Rogerson (1997) attributes this definition to Christiano. Allegedly this definition was given in a private conversation between the two of them. 33 Although it could seem tempting to paraphrase Solow (1986): “(…) it is not clear what we are talking about when we talk about the natural rate”, we really believe that the underlying issue is that, frequently, different economists are talking about different clear-cut concepts. In this paper we aligned ourselves with some of the aforementioned views on the NRU. We deem that our concept of the NRU fits well with definitions (6) “lowest sustainable rate of unemployment” and (8) “efficient rate of unemployment” and, to some extent, with definition (9) “unemployment at full employment”, if we assume that full employment is that level associated to the best scenario regarding the state of the business cycle. Moreover, it is worth stressing that in this paper our main objective is to compare and contrast the estimates of the NRU attained with the SF technique with those of the definition (7) “trend component of unemployment generated by the HP filter”. As a matter of fact, the list provided by Rogerson (1997) is rather useful to position our paper in the literature. From our standpoint, this piece of research might be thought as a methodological proposal to estimate the concept of NRU understood as an “efficient rate of unemployment”, and then to compare such an estimate with that of the definition (7) or with those obtained by using other types of time-series filters. At this point, one important clarification should be made concerning the terms NRU and Non-Accelerating Inflation Rate of Unemployment, or NAIRU. Although the two concepts are frequently used indistinctly, there are several differences which call into question that the NRU and the NAIRU are truly equivalent concepts. Following the work of Espinosa-Vega and Russell (1997), the two notions stem from quite differing schools of economic thought. Moreover, Tobin (1997) maintains that “the NAIRU and the NRU are not synonyms”. The NAIRU is a relation at the macroeconomic level which, in a nutshell, relates observed unemployment to inflation. Should the effective unemployment rate exceeds the NAIRU, then the inflation rate ought to fall and vice versa. In contrast, following Grant (2002), the NRU is an equilibrium unemployment rate which is mainly determined by the institutional and demographic characteristics of the economy. For the purposes of the present work, what is important is to realize that the concept of NAIRU is linked to a cyclical unemployment rate that could take negative values at certain periods (those in which the inflation rate rises). After all, a relatively simple estimation of the NAIRU is the intersection of an expectationsaugmented Phillips curve with the “X” axis, with the effective unemployment rate being either higher or lower than said value. Hence, the notion of NAIRU proves extremely useful in order to understand inflationary pressures in macroeconomic models. Nonetheless, if we considered the NAIRU as the sum of frictional and structural unemployment (as some textbooks do), that would be equivalent to stating that such sum should be greater than effective unemployment during periods of increasing inflation. Therefore, it is easy to understand why the NAIRU is an influential macroeconomic notion. But taking a more labor-economicsoriented perspective, it is a bit complicated to conceive a labor market in which there are less unemployed persons than the sum of those unemployed workers as a consequence of structural reasons plus those unemployed individuals as a consequence of imperfect information (frictional unemployment). Put differently, if we think of a more or less conventional labor market, it is difficult to imagine a situation in which there are “negative” unemployed workers by cyclical motives, which would be the case when the NAIRU is higher than the actual unemployment rate. This is so because unemployment is always a positive number in labor market 34 modelling. To sum up, we recognize the value of the NAIRU as an abstraction to interpret the inflation rate movements in macroeconomic models, but we do not follow that path here. Instead, we focus on the NRU idea and suppose that all the components making up that unemployment rate have to be positive numbers. To guarantee this last assumption we make use of the SF technique. This is our methodological approach, which will be assessed by comparing our estimates with the more standard procedures to break down unemployment explained in the next subsection. II.3. Empirical strategies to decompose the unemployment rate. Decomposing the unemployment rate into its different types is a recurring theme in economic literature, for which a range of different methods have been used 6 . One common option when obtaining the components of effective unemployment is to use univariate statistical filters to split the unemployment rate into various elements. Two of the most widely used filters are undoubtedly the HP Filter (Hodrick and Prescott, 1997) and the BK Filter (Baxter and King, 1999). These filters are usually accompanied by decomposition through the QT decomposition, most probably due to the simplicity of its application. The HP Filter has often been used when estimating Okun’s Law in an effort to extract the natural component and the cyclical component from effective unemployment (Apergis and Rezitis, 2003; Perman and Tavera, 2005; Adanu, 2005; Villaverde and Maza, 2007, 2009; Ball et al., 2013). The QT decomposition has also been widely used in economic literature related to Okun’s Law, most likely because it offers very similar results to the HP Filter (Adanu, 2005; Villaverde and Maza, 2007, 2009). Finally, there are also various studies in which the BK Filter has been used in the same context as the two previous ones (Freeman, 2000; Apergis and Rezitis, 2003; Villaverde and Maza, 2009). The economic literature has also drawn on another set of “more complex” econometric techniques in an attempt to obtain the various components of effective unemployment. Prominent amongst these are the models based on the Phillips curve to estimate the natural component of effective unemployment (Blomqvist, 1988; Hahn, 1996; Apergis, 2005), techniques based on the Kalman Filter (Moosa, 1997; Mocan, 1999; Salemi, 1999), or estimations based on structural autoregressive vectors (SVAR) (King and Morley, 2007). However, few studies have been found which use the SF approach to decompose the effective rate of unemployment. One of the pioneering works in this sense is Warren (1991) which uses frontier estimation to obtain the frictional component of the unemployment rate. Warren (1991) takes matching models in the labor market as a starting point. With this background, he applies an approach based on a model of employment growth when the economy is in steady state to derive the expression of the unemployment rate in the steady state 7 . At a second stage, and by applying an OLS model, Warren (1991) obtains the mean unemployment rate for the US manufacturing industry between April 1969 and December 1979. A SF of production is subsequently applied to determine frictional 6 The work of Bean (1994) provides a comprehensive review of the topic in hand. 7 It is precisely the use of information concerning vacancies which means that in the present work we are unable to apply Warren’s approach (1991). It is a well-known fact that information concerning vacancies in Spain is extremely poor. 35 unemployment in the manufacturing industry. Finally, by subtracting both estimated rates a measure of inefficiency for said labor market is derived. Another study carried out along the same line is that of Bodman (1999) who takes the theoretical model set out in Warren (1991) as a starting point. The main differences emerge from the regional perspective (the analysis is carried out for all the states in Australia) and from how the inefficiency term of the error is modeled, which is estimated following the proposal of Battese and Coelli (1995). Having obtained frictional unemployment and the inefficiency of the error term, Bodman (1999) finds a positive effect on the inefficiency of Labor Party administration in most of the states analyzed. One study more closely aligned to the approach adopted in the present research is that of Hofler and Murphy (1989). These authors draw on a database of unemployment rates containing both transversal and temporal information for the US, considering that there is a lower-envelope function which the authors link to the notion of frictional unemployment rate. They model frictional unemployment using deterministic components such as the SF in its cost version (a lower frontier), and the distance from that lower frontier to effective unemployment which they term “excess supply unemployment” in the labor market 8 . At a second stage, they find that it is the variables related to social transfers, the size of the youth labor force, female participation rates, educational attainment and net migration rate, which account for both the level of frictional unemployment in each state as well as the changes to occur between 1960 and 1979. Finally, in the research carried out by Aysun et al. (2014) elements from the three previous studies are combined, using the modeling of one upper and one lower SF to decompose the unemployment rate into its various components. One the one hand, they use a model and a method which are similar to that used in Warren (1991) to extract the frictional component of unemployment. They also apply a cost SF to ascertain the structural component of the unemployment rate as was done in Hofler and Murphy (1989), using a specification of the expectationsaugmented Phillips curve. The authors thus obtain a measure of structural unemployment which is always lower than the effective component. III. THEORETICAL FRAMEWORK. III.1. The model. In this section we elaborate a theoretical model in order to link our conceptual setting with our methodological approach. As this model it totally instrumental to grasp the basic underlying idea in this paper, it will be constructed as the simplest model possible. To fix ideas, we define the three types of unemployment we are going to model in the same way as basic economics textbooks do (see, for instance, Krugman et al., 2011): Frictional unemployment (𝑈𝐹) is unemployment due to the time workers spend in job search; Structural unemployment (𝑈𝑆𝑇) is unemployment that results when there are more people seeking jobs in a labor 8 The model put forward in Hofler and Murphy (1989) to illustrate frictional unemployment corresponds to the following equation: 𝑈𝑡𝑗 = 𝛽0+ 𝛽1𝑡+ 𝛽2𝑡2+ 𝑤𝑡𝑗 ⏟ 𝐹𝑡𝑗 + 𝜗𝑡𝑗. where 𝑈𝑡𝑗 refers to the unemployment rate during period t and state j, 𝐹𝑡𝑗 encompasses the components of frictional unemployment and 𝜗𝑡𝑗 reflects excess supply. The lower SF (cost frontier) approach is used to separate 𝑤𝑡𝑗 from 𝜗𝑡𝑗 and to find the lower frontier which corresponds to the frictional component of unemployment. 36 market than there are jobs available at the current wage; Cyclical unemployment (𝑈𝐶) is a deviation in the actual rate of unemployment from the natural rate due to downturns in the business cycle. For the sake of simplicity, we begin with a constant labor force (i.e. it does not depend on any variable, particularly does not depend on the real wage rate): 𝐿𝑆= 𝐿=100 (1) The previous assumption normalizes the size of the labor force and allows us to pass from unemployed persons to unemployment rate straightforwardly. Then we use a quite standard upward sloping aggregate effective labor supply in the employment (𝑁) and real wage (𝑊) space: 𝑁𝑆= 𝜌1𝑊−𝜌0 (2) These two graphical devices are displayed in Figure 1. The difference between 𝐿𝑆and 𝑁𝑆 highlights the fact that not all active workers are immediately available for work. As the market real wage increases, it exceeds the “dynamic” reservation wage (or that of the job-search theory) of a higher number of workers, with the latter more willing to accept the jobs they find. As a result, the distance between 𝐿𝑆and 𝑁𝑆 is lower for higher salaries. Said horizontal difference between the two curves is what we will call later frictional unemployment (𝑈𝐹). Figure 1. Frictional, structural and cyclical unemployment. Source: Authors’ own. 𝑾 𝑵,𝑳 𝝅 𝟎 (𝒚𝒎𝒂𝒙) 𝑳 𝝅 𝟎 (𝒚𝒎𝒂𝒙) 𝝅𝟏 𝝆𝟎 𝝆𝟏 𝝅 𝟎 (𝒚 𝟎 ) 𝝅 𝟎 (𝒚 𝟎 ) 𝝅𝟏 𝑳𝑺 A B C D E F 𝑾𝑷𝑪 𝑾𝑪𝑩 𝝆 𝟏 𝝅 𝟎 (𝒚𝒎𝒂𝒙)−𝝅 𝟏 𝝆 𝟎 𝝅𝟏+𝝆𝟏 37 unemployment is modelled as a non-negative disturbance 𝑈𝑖𝑡 𝐶= 𝑢𝑖𝑡 ≥0. Finally, assuming linearity, 𝑓(𝑋𝑖𝑡)=𝛽𝑋𝑖𝑡, the “econometric” version of (11) would be: 𝑈𝑖𝑡 =𝛽1𝑋𝑖𝑡 +𝑣𝑖𝑡 +𝑢𝑖𝑡 (14) where 𝑣𝑖𝑡 is a random conventional disturbance. Equation (14) implicitly assumes that cyclical unemployment has a minimum value equal to 0. Otherwise, situations could emerge in which the NRU was higher than actual effective unemployment, as already pointed out 19 . In other words, the 𝑈𝑖𝑡 𝑁𝑅 component acts as a limit or lower boundary for effective unemployment (𝑈𝑖𝑡 ≥𝑈𝑖𝑡 𝑁𝑅). IV. METHODOLOGY. This section is also divided into two parts. In the first, a brief explanation is given of the SF technique used to decompose unemployment. In the second, a description is provided of the univariate filters employed to accomplish the work’s second objective. IV.1. SF analysis. The decomposition presented in the conceptual framework is based on the assumption that all the components are positive. As a result, the NRU constitutes a minimum value below which effective unemployment cannot fall, and any deviation from this minimum is considered inefficiency that can be corrected by applying aggregate demand policies. As already pointed out in subsection III.3, this is a composed-error model which can be estimated using SF. The first econometric models to introduce this technique are to be found in the seminal papers of Aigner et al. (1977) and Meeusen and van Den Broeck (1977) 20 . In its costs version, this estimation technique allows a minimum value which is situated below the observed dependent variable to be identified. As already pointed out, the ultimate goal is to separate the effective rate of unemployment (𝑈𝑖𝑡) into two components: the natural unemployment (𝑈𝑖𝑡 𝑁𝑅) and the cyclical unemployment (𝑈𝑖𝑡 𝐶) 21 . However, in order to identify the two components, the starting point is to specify the natural unemployment as shown in equation (15): 𝑈𝑖𝑡 𝑁𝑅 = 𝛽1𝑋𝑖𝑡 + 𝑣𝑖𝑡 (15) where 𝑋𝑖𝑡 is a vector of explanatory variables, 𝛽1 is the vector of coefficients to be estimated and 𝑣𝑖𝑡 is a statistical noise deemed symmetrically and independently distributed as a 𝑁(0,𝜎𝑣 2). This natural component constitutes a lower envelope or 19 In the microeconomic literature, see for example Revoredo-Giha et al. (2009), Sav (2012) or Duncan et al. (2012), the “frontier cost” is the minimum possible and can never exceed the observed cost. Hofler and Murphy (1989) and Aysun et al. (2014) extrapolate this idea to the labor market to decompose the unemployment rate. We modify this interpretation slightly and apply it to the Spanish labor market. 20 Kumbhakar and Lovell (2003) and Greene (2008) provide a highly detailed exposition of this type of econometric technique. See Burns and Weyman-Jones (1996) for an application of that technique in the case of the study of the efficiency in the electric distribution. 21 As highlighted previously, the lack of sufficiently extensive and time-comparable information concerning existing vacancies in the labor market makes it extremely difficult to extract the frictional component (𝑈𝑖𝑡 𝐹) using the econometric techniques observed in some of the works referred to in the literature review. As a result, said component will be estimated together with the structural component of unemployment. 44 cost frontier below which the effective unemployment rate will never fall. However, the natural unemployment formulated econometrically in equation (15) is not observed directly. The available information corresponds to the effective unemployment rate which is greater than or equal to the natural (𝑈𝑖𝑡≥𝑈𝑖𝑡 𝑁𝑅). The effective rate of unemployment may thus be represented as the sum of 𝑈𝑖𝑡 𝑁𝑅 and a non-negative random disturbance identified with cyclical unemployment (𝑈𝑖𝑡 𝐶), through the following mathematical expression: 𝑈𝑖𝑡 = 𝑈𝑖𝑡 𝑁𝑅 + 𝑢𝑖𝑡 (16) where: 𝑢𝑖𝑡 = 𝑈𝑖𝑡 𝐶 and 𝑢𝑖𝑡 is an error term which is expected to be positive and independently distributed. It should again be stressed that this term will always take a positive value or one equal to 0 in the best of cases (Aysun et al., 2014). Finally, by grouping equations (15) and (16), we obtain expression (17) which coincides with equation (14), previously presented: 𝑈𝑖𝑡 = 𝛽1𝑋𝑖𝑡 + 𝜀𝑖𝑡 (17) where: 𝜀𝑖𝑡 = 𝑣𝑖𝑡 +𝑢𝑖𝑡. Taking account of the final specification of equation (17), and the presence of a composed error econometric model, 𝑢𝑖𝑡 and 𝑣𝑖𝑡 are assumed to be independent of each other and identically distributed across observations. Then, we maximize the log-likelihood function of a stochastic frontier model by using the Newton–Raphson method, and the estimated variance covariance matrix is calculated as the inverse of the negative Hessian. This type of estimation allows us to obtain the two error components separately and to calculate the variance of each. It is thus possible to apply a statistical test to determine the existence of the frontier and whether it is a production or a cost frontier. As it will be shown, in our case, a lower SF (cost frontier) is estimated which, according to our approach, coincides with the natural unemployment (𝑈𝑖𝑡 𝑁𝑅) and implies a lower limit for 𝑈𝑖𝑡. Nevertheless, in order to estimate 𝑢𝑖𝑡, which is here identified with 𝑈𝑖𝑡 𝐶, it is necessary to make assumptions about the distribution of the two error components of 𝜀𝑖𝑡 (Jondrow et al., 1982). In the case of the 𝑣𝑖𝑡 component, there would appear to be no problem since there seems to be a strong consensus in the empirical literature that said component is distributed in the form 𝑁(0,𝜎𝑣 2), as we state before. The main problem emerges when it is needed to consider the distribution of the 𝑢𝑖𝑡 term. Here, several distributions are proposed in the econometric literature: Normal Truncated (Stevenson, 1980), Semi-Normal (Aigner et al., 1977), Exponential (Meeusen and van Den Broeck, 1977) and Gamma (Greene, 1990). For the present study, and as occurs in the works of Hofler and Murphy (1989) and Aysun et al. (2014), Semi-Normal distribution is chosen for this error component. IV.2. Univariate filters. In order to put our proposed decomposition into perspective it is useful to compare it to other alternative methods used in the literature. To achieve this, three univariate filters are used which also allow effective unemployment to be 45 decomposed, the HP Filter, the QT decomposition, and finally, the BK Filter 22 . These filters have been widely used when analyzing time series and enable any time series (𝐾𝑡) to be broken down into its two components: the trend (𝑇𝑡) and the cycle (𝐶𝑡). At this point, it should be stressed that several of the studies cited previously in this text and which use these filters link the trend component to the concept of the NRU and the NAIRU, and make no “clear” distinction between the two (Perman and Tavera, 2005; Adanu, 2005; Villaverde and Maza, 2007, 2009; Ball et al., 2013). In a similar line, the work of Blanchard and Katz (1997) defines the NRU as follows: “(…) The natural rate of unemployment is typically interpreted as the rate of unemployment consistent with constant (non-accelerating) inflation”, referring to the context of the Phillips curve and establishing no differences between NRU and NAIRU. Based on this, we are able to compare our estimations of the NRU with those obtained using the HP Filter, with the QT decomposition or with the BK Filter. This comparison is also carried out for the cyclical component. Applying these filters to our effective unemployment series at a regional scale yields the following equations: 𝑈𝑖𝑡 =𝑈𝑖𝑡 𝐻𝑃𝑇 +𝑈𝑖𝑡 𝐻𝑃𝐶 (18.1) 𝑈𝑖𝑡 =𝑈𝑖𝑡 𝑄𝑇𝑇+𝑈𝑖𝑡 𝑄𝑇𝐶 (18.2) 𝑈𝑖𝑡 =𝑈𝑖𝑡 𝐵𝐾𝑇 +𝑈𝑖𝑡 𝐵𝐾𝐶 (18.3) where 𝑈𝑖𝑡 is the effective unemployment in region i at time t; 𝑈𝑖𝑡 𝐻𝑃𝑇, 𝑈𝑖𝑡 𝑄𝑇𝑇 and 𝑈𝑖𝑡 𝐵𝐾𝑇 refer to the trend component of the effective unemployment obtained through the HP Filter, the QT decomposition, and the BK Filter, respectively, for each region i at time t. Finally, 𝑈𝑖𝑡 𝐻𝑃𝐶, 𝑈𝑖𝑡 𝑄𝑇𝐶 and 𝑈𝑖𝑡 𝐵𝐾𝐶 refer to the cyclical components obtained through each filter for region i in year t. V. DATABASE The data used in the present study were obtained from the Spanish Labor Force Survey (Encuesta de Población Activa, EPA) published by the National Statistics Institute (Instituto Nacional de Estadística, INE), the Statistic of Collective Bargaining Agreements (Estadística de Convenios Colectivos de Trabajo, ECCT), the Statistic of Labor Court Issues (Estadística de Asuntos Judiciales Sociales, EAJS), the Official State Gazette (Boletín Oficial del Estado, BOE), the BDMORES Regional Database and the Valencian Institute of Economic Research (Instituto Valenciano de Investigaciones Económicas, IVIE). All the variables used have an annual frequency for the period between 1982 and 2012 and are 22 See Hodrick and Prescott (1997) for a more detailed explanation of the HP Filter. For a more extended definition of the BK Filter, see Baxter and King (1999) and Pizarro (2001). The QT decomposition is a purely deterministic procedure, the aim being to model the element to be decomposed through a quadratic trend process: 𝑍𝑖𝑡 = 𝛿0+ 𝛿1𝑇+ 𝛿2𝑇2+ 𝜔𝑖,𝑡 In this case, 𝑍𝑖𝑡 is the variable to be decomposed, 𝛿0 is the constant term of the equation, 𝑇 and 𝑇2 are the components of the quadratic trend, and finally 𝜔𝑖,𝑡 is the error term. However, in the literature using QT decomposition, this latter term would, in turn, reflect the cyclical component of the variable we aim to decompose. 46 disaggregated for the 17 Spanish autonomous communities 23 . A summary of the variables used in this study, how they have been defined and their source may be found in table A1 in the Appendix. The first part of the empirical analysis involves decomposing the regional unemployment rate. As a result, this is the dependent variable and the central one in our empirical work. In order to carry out the decomposition, different explanatory variables which might affect the evolution of the unemployment rate are used (Hofler and Murphy, 1989; Aysun et al., 2014). The two first explanatory variables contained in table A1 in the Appendix have a demographic component. The first of these is the female activity rate and reflects the impact of women’s labor participation in the effective rate of unemployment 24 . According to Elhorst (2003), the influence of this variable on the unemployment rate gives rise to diverse results. The second of the explanatory variables is the percentage represented by the population of 16 to 24 year-olds with regard to the total in each autonomous community. This variable is included as there is empirical evidence of a positive correlation between the weight of the youth population and the unemployment rate (Johnson and Kneebone, 1991; Murphy and Payne, 2003). This might be due to the fact that the young, as a result of their limited work experience, are less skilled when it comes to finding jobs than their older counterparts. Their having less specific human capital might also prove to be a determining factor when accounting for high youth unemployment rates. Based on this, younger people tend to suffer longer periods out of work 25 . The second group of regressors is made up of a series of variables reflecting the industry composition of regional employment. The extant literature would seem to point to one of the causes of the differing unemployment rates at a regional scale being the industry composition of labor in each region 26 . Differences in wages, job skills or competitiveness are key factors influencing the impact which the industry composition has on unemployment levels 27 . In a context where the Spanish regions evidence substantial differences in terms of industry composition, this is expected to be a determining factor underlying regional differences in unemployment rates. Another regressor is the share of net capital stock out of the total number of employed in real terms. This variable is included to compute the regional level of capitalization in each territory (Bande and Karanassou, 2013; Bande and Karanassou, 2014) 28 . Finally, we include three variables in order to capture the effect of labor market institutions on the evolution of the effective unemployment 29 . The first of 23 The autonomous cities of Ceuta and Melilla have been excluded from the research due to the scant representativeness of some of the variables used. 24 Lázaro et al. (2000), Azmat et al. (2006) and Bertola et al. (2007) point to some of the driving factors behind the recurring female unemployment rates. 25 In Maguire et al. (2013), some references explaining the reasons underlying the high rates of unemployment amongst youngsters in Spain (16-24 year olds) over the period 2007-2013 may be found. 26 See Elhorst (2003). 27 See Summers et al. (1986). 28 For a more detailed definition about the construction of the net capital stock, see http://web2016.ivie.es/wpcontent/uploads/2017/02/Metodolog%C3%ADa_basedatos_stockcapital_ED.pdf. 29 Furthermore, we also computed the so-called unemployment benefit coverage rate, defined as the ratio of unemployment benefit recipients to unemployed persons, aiming at controlling for the effects of an institution like unemployment insurance. However, we are not confident about the meaningfulness of the results due to the obvious endogeneity problems in that econometric regression (since unemployed workers can be found on the lefthand side and on the right hand side of the equation). As instrumental variables procedures in SF estimation are not straightforward to implement, we finally made the decision of no reporting these results. It is worth 47 these variables is the Kaitz Index (Kaitz, 1970), which attempts to account for the influence of minimum wage legislation. It is defined as the ratio of the minimum to the average wage. The advantage of this index is that it shows cross-regional variation despite the fact that in Spain there is a single national minimum (PérezDominguez et al., 2002; Galán and Puente, 2015). In the second place, the Employment Protection Legislation (EPL) in Spain, as in the case of the minimum wage, exhibits no cross-regional variation since there exists a single national regulation. Thus, in order to account for the effects of this institution we draw on a growing literature studying the impact of judicial rulings over labor market variables and its relationship with firing costs (Gabuthy and Lambert, 2008; Goerke and Pannenberg, 2010; Martín-Román et al., 2013; Jimeno et al., 2015). The underlying idea is that labor courts located in a specific region ruling systematically more likely in favor of employees increase firing costs for employers operating in that area. A formal proof of this statement can be found in Martín-Román et al. (2013). To take into account this effect, we include in the econometric specification the percentage of dismissal cases ruled (totally or partially) in favor of employees as a measure of the EPL 30 . The third institutional variable intends to measure the influence of the collective bargaining structure over effective unemployment. The seminal work of Calmfors and Driffill (1988) and the survey of Flanagan (1999) pose different effects over the unemployment rate depending on the type and the level of centralization of collective bargaining. Other studies look into whether these different structures have distinct impacts on the wages of the workers covered (Dahl et al. 2013). For the Spanish case, Bande et al. (2007, 2008) focus their attention on the wage setting mechanism at a regional level and its influence on the evolution of the Spanish regional unemployment. In the current paper, we use the share of workers covered by a firm-level agreement as a variable accounting for the role of collective bargaining in the wage setting process. Table A2 in the Appendix shows some descriptive statistics of the variables referred to earlier which reflect the interregional differences between them. VI. RESULTS. The first part of this section involves the decomposition of the effective rate of unemployment into the natural unemployment (𝑈𝑖𝑡 𝑁𝑅) and the cyclical unemployment (𝑈𝑖𝑡 𝐶) through the use of the SF. The second part tests the robustness of the results by modelling the inefficiency component and by using an alternative estimator that exploits the first difference transformation. VI.1. Decomposition of effective unemployment. Having introduced the SF technique as a decomposition mechanism for effective unemployment, the results corresponding to the SF estimations are now presented. This is where the present work differs slightly from the proposal put forward by mentioning though that overall outcomes were robust regardless the inclusion or not of that covariate. These results are available upon request to the authors. 30 To have an idea of the sizeable cross-regional variation found in labor court rulings concerning labor disputes over layoffs in Spain, see Martín-Román et al (2015). 48 Hofler and Murphy (1989), since we opt for a more comprehensive parameterization of the frontier 31 . In this regard, five different econometric specifications have been used in the estimates carried out, which are the specific versions of the general equation (17). Equation (19) is the benchmark specification (specification 1), we include, as control covariates, the demographic features (𝑋𝑖𝑡) (percentage of youth population and female participation rate), industry composition (𝑍𝑖𝑡) (percentage of people employed in agriculture, manufacturing, services and energy) together with a dichotomous variable (𝐷2001) which takes the value 1 after 2001 and 0 in the previous years 32 . We also employed seven additional specifications to test the robustness of the results. Equation (20) adds a lineal trend (𝑇) to the previous control covariates (specification 2). Expression (21) decomposes the service industry in two components: Retailing (𝑆𝑅𝐼𝑖𝑡) and non-retailing industry (𝑆𝑁𝑅𝐼𝑖𝑡), so 𝑍′𝑖𝑡 is a vector that represent the previous industry decomposition with this separation in the services industry (specification 3) 33 . Equation (22) incorporates the share of net capital stock out of the total number of employed in real terms (𝑅𝐾𝑆𝑖𝑡) (specification 4). Finally, expression (23) includes as institutional variables (𝐼𝑖𝑡) the Kaitz Index, the percentage of dismissal cases ruled (totally or partially) in favor employees and the share of workers covered by a firm-level agreement (specifications 5, 6, 7 and 8). It should also be pointed out that fixed regional effects have been used in all the specifications to reflect unobservable heterogeneity at a territorial scale (𝜇𝑖) In this case both, 𝛽0 and 𝜇𝑖 are fixed constants and additional restrictions to estimate them are required. One way to do that is to introduce the restriction ∑𝜇𝑖 𝑛 𝐼=1 =0. Then, the fixed effect 𝜇𝑖 represents deviations from the mean intercept 𝛽0 34 . Finally 𝑣𝑖𝑡 is assumed to be independently 𝑁(0,𝜎𝑣 2) distributed over the observations, and 𝑢𝑖𝑡 are independently 𝑁+(0,𝜎𝑣 2) distributed with truncation point at 0: : 𝑈𝑖𝑡 = 𝛽0+ 𝛽1𝑋𝑖𝑡 +𝛽2𝑍𝑖𝑡 +𝛽3𝐷2001+𝑣𝑖𝑡 +𝜇𝑖+𝑢𝑖𝑡 (19) 𝑈𝑖𝑡 = 𝛽0+ 𝛽1𝑋𝑖𝑡 +𝛽2𝑍𝑖𝑡 +𝛽3𝐷2001+𝛽4𝑇+𝑣𝑖𝑡 +𝜇𝑖+𝑢𝑖𝑡 (20) 𝑈𝑖𝑡 = 𝛽0+ 𝛽1𝑋𝑖𝑡 +𝛽2𝑍′𝑖𝑡 +𝛽3𝐷2001+𝑣𝑖𝑡 +𝜇𝑖+𝑢𝑖𝑡 (21) 𝑈𝑖𝑡 = 𝛽0+ 𝛽1𝑋𝑖𝑡 +𝛽2𝑍𝑖𝑡 +𝛽3𝐷2001+ 𝛽4𝑅𝐾𝑆𝑖𝑡 +𝑣𝑖𝑡 +𝜇𝑖+𝑢𝑖𝑡 (22) 𝑈𝑖𝑡 = 𝛽0+ 𝛽1𝑋𝑖𝑡 +𝛽2𝑍𝑖𝑡 +𝛽3𝐷2001+ 𝛽4𝐼𝑖𝑡 +𝑣𝑖𝑡 +𝜇𝑖+𝑢𝑖𝑡 (23) 31 This greater parameterization of the frontier relates to an interest in capturing some important determinant factors of the NRU. It has to be taken into account that the Hofler and Murphy (1989) approach considers only the frictional unemployment to be part of the frontier, whereas in our proposal the frontier is made up of both the frictional and the structural unemployment. 32 This dummy variable is introduced due to the fact that in 2001 methodological changes were made which affect how unemployment is measured. The methodological changes made may be seen at http://www.ine.es/epa02/meto2002.htm. 33 For a more detailed explanation about the services in the retailing and non-retailing industry, see http://web2011.ivie.es/downloads/caphum/series-2013/metodologia-series-capital-humano-1964-2013.pdf. 34 Hsiao (2014). 49 Table A3 in the Appendix shows the results obtained for the eight SF estimations. Broadly speaking, it can be seen a great similarity between the coefficients obtained. It can also be seen that in all cases, it can be accepted that there is a cost frontier at a 1% level of statistical significance with the exception of specifications 6 and 8 (which are statistically significant at a 10% level). A close look at the variables used when modeling the frontier yields the following conclusions. The female activity rate has a positive and significant effect on NRU at a regional scale, an effect reinforced when a trend is included in the model. This result seems to indicate that the gradual incorporation of women into the labor market since the early 1980s has led to an increase in regional NRUs, due mainly to the fact that female unemployment rates are higher than those of men. With regard to the second demographic variable, a positive and significant effect of the percentage of young people on regional NRUs can also be seen. This effect is common to all specifications and has a greater coefficient than that of the female activity rate is found 35 . These results are consistent with the hypotheses formulated earlier concerning the youth population and reflect the importance of youth unemployment when determining aggregate unemployment levels 36 . The second group of control covariates included in the model concern the industry composition. As with the previous case, all display a positive and highly significant effect in all specifications, reflecting the fact that, ceteris paribus, all the industries evidence a higher NRU than the one used as a reference. Given that the variable excluded is the percentage of workers in the construction industry, it may be concluded that the remaining industries display higher levels of unemployment and that it is the percentage of workers in the energy industry and in the service industry which are the most relevant variables when explaining unemployment levels. The previous result also holds when we decomposed the service industry especially for the non-retailing industry (specification 3).It can also be seen how manufacturing and construction are the industries which have had the least impact on the dependent variable. One tentative explanation to account for these results might be found in the great weight which low-skilled jobs have in the service industry. In agreement with the literature, times of crisis cause long periods of unemployment amongst low-skilled workers, which increases their own rate of structural unemployment 37 . If we add to this the fact that in the service industry there is high job turnover and that in many instances firms offer little or no training 38 , we are left with a low-skilled workforce with low employability. As for the dichotomous variable reflecting the methodological change in how unemployment is measured after 2001, it has a negative and highly significant effect on all specifications. This result indicates that the new methodology adopted by the INE contributes towards lowering the effective rate of unemployment. On the other hand, the linear trend included in specification 2 does not prove to be significant and the share of net capital stock in the specification 4 displays a positive value over the effective unemployment. The last group of control variables 35 López‐Bazo et al. (2005) also report a positive effect of the percentage of the youth population (16-25) on unemployment, and establish that said variable contributes significantly to explaining regional disparities in unemployment. 36 Dolado et al. (1999, 2000) and Dolado et al. (2002) show some of the causes and consequences of the “inefficient” functioning of the labor market for young people in Spain. 37 Using a panel that includes 21 OECD countries, Oesch (2010) offers empirical evidence concerning which variables most impact on low-skilled worker unemployment rates. 38 A good example for the case of Spain might be certain jobs in the tourist industry. 50 is those related to the labor market institutions. The Kaitz Index is included in specifications 5 and 8, and exhibits a negative but not statistically significant coefficient. One possible explanation for this result is the relative low levels for the minimum wage in Spain during the time period considered in our database, which exerts a limited pressure over the wage distribution. In the case of the EPL indicator (percentage of dismissal cases ruled totally or partially in favor of workers) we obtain positive and highly significant effect in the specifications 6 and 8. This means that higher percentages of dismissal cases ruled in favor of workers tend to increase the level of unemployment in the economy 39 . Finally, the share of workers covered by a firm-level agreement also shows a negative and not statistically significant coefficient in the specifications 7 and 8.According to the results in table A3 and following the AIC and the BIC criteria, the best estimate is achieved with specification 4. Following that specification, predictions are made regarding the values of the frontier and inefficiency. It is thus possible to obtain the decomposition of the effective unemployment rate in the components previously referred to: 𝑈𝑖𝑡 𝑁𝑅 and 𝑈𝑖𝑡 𝐶. The estimations of 𝑈𝑖𝑡 𝑁𝑅 have been obtained by standard linear predictions through the coefficients and the variables employed to model the frontier. In the case of 𝑈𝑖𝑡 𝐶, the technique produces estimates via 𝐸(𝑢𝑖𝑡|𝜀𝑖𝑡) that is defined as follow (Jondrow et al., 1982): 𝐸(𝑢𝑖𝑡|𝜀𝑖𝑡)=𝜎∗[𝑓(𝜀𝜆/𝜎) 1−𝐹(𝜀𝜆/𝜎)−(𝜀𝜆 𝜎)] (24) Where f and F represent the standard normal density and cumulative distribution function respectively, 𝜀𝑖𝑡 =𝑣𝑖𝑡 +𝑢𝑖𝑡, 𝜆=𝜎𝑢𝜎𝑣 ⁄, 𝜎∗=𝜎𝑢2𝜎𝑣2𝜎2 ⁄ and 𝜎2=𝜎𝑢2+𝜎𝑣2 Figure 3 shows the evolution of the NRU (𝑈𝑖𝑡 𝑁𝑅) for all the autonomous communities 40 . The mean value of this component throughout the whole period is 12.72 percentage points. Above the mean, we find certain extreme mean values such as Andalusia (23.00%), Extremadura (19.70%) and the Canary Islands (16.62%). The regions which evidence a lower mean 𝑈𝑖𝑡 𝑁𝑅 value are the Balearic Islands (7.19%), Navarre (7.76%) and La Rioja (8.45%) 41 . A different set of insights comes from the relative values, i.e. the importance of 𝑈𝑖𝑡 𝑁𝑅 when explaining overall levels of effective unemployment. It is once again the regions displaying the highest levels of NRU which account for the greatest percentage of effective unemployment. Specifically, this component explains about the 90% of the effective unemployment in Andalusia, 84% in Extremadura and around the 82% in the Canary Islands. In the case of the regions in which the 𝑈𝑖𝑡 𝑁𝑅 has less weight on effective unemployment, these are the Balearic Islands (58.36%), Navarre (70.24%) and La Rioja (74.31%), although Aragon with a rate of 74.95% joins the list. Finally, it is worth reflecting briefly on the similarity in the profile displayed by the evolution of this component of unemployment in all the autonomous communities. Said similarity is less clear at the start of the period but becomes more intense after the mid-90s, displaying a noticeable “U” shape. 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𝐴𝑃𝑖𝑡 : Total active population Labor Force Survey (EPA), published by the National Institute of Statistics (INE) Female activity rate (𝐹𝐴𝑅𝑖𝑡) 𝐹𝐴𝑅𝑖𝑡 = 𝐴𝐹𝑃𝑖𝑡 𝐹𝑃𝑂𝑃 16−65𝑖𝑡∗100 𝐴𝐹𝑃𝑖𝑡 : Total active female population 𝐹𝑃𝑂𝑃 16−65𝑖𝑡: Female population of working age. Labor Force Survey (EPA), published by the National Institute of Statistics (INE) Percentage of youth population (𝑃𝑌𝑃𝑖𝑡) 𝑃𝑌𝑃𝑖𝑡 = 𝑌𝑂𝑈𝑁𝐺𝑖𝑡 𝑃𝑂𝑃𝑖𝑡 ∗100 𝑌𝑂𝑈𝑁𝐺𝑖𝑡 : Total population of 16 to 24 year-olds. 𝑃𝑂𝑃𝑖𝑡 : Total population Labor Force Survey (EPA), published by the National Institute of Statistics (INE) Number of employed in the agricultural industry (𝐴𝑔𝑟𝑖𝑖𝑡) 𝐴𝑔𝑟𝑖𝑖𝑡 = 𝐴𝐺𝑅𝐼𝑖𝑡 𝑇𝐸𝑚𝑝𝑖𝑡∗100 𝐴𝐺𝑅𝐼𝑖𝑡: Total number of those employed in the agricultural industry 𝑇𝐸𝑚𝑝𝑖𝑡: Total number of employed Valencian Institute of Economic Research (IVIE) Number of employed in the manufacturing industry (𝑀𝑎𝑛𝑖𝑡) 𝑀𝑎𝑛𝑖𝑡 = 𝑀𝐴𝑁𝑖𝑡 𝑇𝐸𝑚𝑝𝑖𝑡∗100 𝑀𝐴𝑁𝑖𝑡: Total number of those employed in the manufacturing industry. 𝑇𝐸𝑚𝑝𝑖𝑡: Total number of employed. Valencian Institute of Economic Research (IVIE) Number of employed in the service industry (𝑆𝑒𝑟𝑣𝑖𝑡) 𝑆𝑒𝑟𝑣𝑖𝑡 = 𝑆𝐸𝑅𝑉𝑖𝑡 𝑇𝐸𝑚𝑝𝑖𝑡∗100 𝑆𝐸𝑅𝑉𝑖𝑡: Total number of those employed in the service industry 𝑇𝐸𝑚𝑝𝑖𝑡: Total number of employed. Valencian Institute of Economic Research (IVIE) Percentage of employed in the services in the retailing industry (𝑆𝑅𝐼𝑖𝑡) 𝑆𝑅𝐼𝑖𝑡 = 𝑆𝑒𝑟𝑣 𝑅𝑒𝑡 𝐼𝑛𝑑𝑖𝑡 𝑇𝐸𝑚𝑝𝑖𝑡 ∗100 𝑆𝑒𝑟𝑣 𝑅𝑒𝑡 𝐼𝑛𝑑𝑖𝑡: Total number of those employed in the services (retailing industry). 𝑇𝐸𝑚𝑝𝑖𝑡: Total number of employed. Valencian Institute of Economic Research (IVIE) Percentage of employed in the services in the nonretailing industry (𝑆𝑁𝑅𝐼𝑖𝑡) 𝑆𝑁𝑅𝐼𝑖𝑡 = 𝑆𝑒𝑟𝑣 𝑁𝑜𝑛 𝑅𝑒𝑡 𝐼𝑛𝑑𝑖𝑡 𝑇𝐸𝑚𝑝𝑖𝑡 ∗100 𝑆𝑒𝑟𝑣 𝑁𝑜𝑛 𝑅𝑒𝑡 𝐼𝑛𝑑𝑖𝑡: Total number of those employed in the services (non-retailing industry) 𝑇𝐸𝑚𝑝𝑖𝑡: Total number of employed. Valencian Institute of Economic Research (IVIE) Number of employed in the energy industry (𝐸𝑛𝑒𝑟𝑖𝑡) 𝐸𝑛𝑒𝑟𝑖𝑡 = 𝐸𝑁𝐸𝑅𝑖𝑡 𝑇𝐸𝑚𝑝𝑖𝑡 ∗100 𝐸𝑁𝐸𝑅𝑖𝑡: Total number of those employed in the energy industry. 𝑇𝐸𝑚𝑝𝑖𝑡: Total number of employed. Valencian Institute of Economic Research (IVIE) Share of net capital stock (in real terms) out of the total number of employed (𝑅𝐾𝑆𝑖𝑡) 𝑅𝐾𝑆𝑖𝑡 = 𝑁𝐾𝑆𝑖𝑡 𝑇𝐸𝑚𝑝𝑖𝑡 𝑁𝐾𝑆𝑖𝑡: Net capital stock (in real terms) (base year: 2010). 𝑇𝐸𝑚𝑝𝑖𝑡: Total number of employed. Valencian Institute of Economic Research (IVIE) 67 Table A1. (continuation) Gross Domestic Product growth rate (∆𝐺𝐷𝑃𝑖𝑡) ∆𝐺𝐷𝑃𝑖𝑡 = 𝐺𝐷𝑃𝑖𝑡 −𝐺𝐷𝑃𝑖𝑡−1 𝐺𝐷𝑃𝑖𝑡 𝐺𝐷𝑃𝑖𝑡: Real Gross Domestic Product. BD.MORES Regional Database (2008 bases) Kaitz Index (𝐾𝐼𝑖𝑡) 𝐾𝐼𝑖𝑡 = 𝑀𝑊𝑡 𝐴𝑊𝑖𝑡 ∗100 𝑀𝑊𝑡: Minimum nominal wage that a worker receives for a working journey. 𝐴𝑊𝑖𝑡: Average nominal wage of the workers. Official State Gazette (BOE) BD-MORES Regional Database (2008 bases) Percentage of judicial rulings favorable and partially favorable to the workers in dismissal matters (𝐽𝑆𝑖𝑡) 𝐽𝑆𝑖𝑡 = 𝑆𝐹𝑃𝐹𝑖𝑡 𝑇𝐽𝐽𝑖𝑡 ∗100 𝑆𝐹𝑃𝐹𝑖𝑡: Sum of judicial sentences that are favorable and partially favorable to the workers in dismissal matters. 𝑇𝐽𝐽𝑖𝑡: Total number of judicial sentences in dismissal matters. Statistic of labor court issues (EAJS) Share of workers with labor agreement at firm level (𝑆𝑊𝐹𝐴𝑖𝑡) 𝑆𝑊𝐹𝐴𝑖𝑡 = 𝑇𝑊𝐹𝐴𝑖𝑡 𝑇𝐿𝐴𝑖𝑡 ∗100 𝑇𝑊𝐹𝐴𝑖𝑡: Total number of workers with labor agreement at firm level 𝑇𝐿𝐴𝑖𝑡: Total number of workers with labor agreement. Statistic of collective bargaining agreements (ECCT) 68 Table A2. Mean value and deviation of the variables used in the estimation. 𝑈𝑖𝑡 𝐹𝐴𝑅𝑖𝑡 𝑃𝑌𝑃𝑖𝑡 𝐴𝑔𝑟𝑖𝑖𝑡 𝑀𝑎𝑛𝑖𝑡 𝑆𝑒𝑟𝑣𝑖𝑡 𝑆𝑅𝐼𝑖𝑡 𝑆𝑁𝑅𝐼𝑖𝑡 𝐸𝑛𝑒𝑟𝑖𝑡 𝑅𝐾𝑆𝑖𝑡 ∆𝐺𝐷𝑃𝑖𝑡 𝐾𝐼𝑖𝑡 𝐽𝑆𝑖𝑡 𝑆𝑊𝐹𝐴𝑖𝑡 Andalusia 25.54 35.75 18.76 13.06 12.07 62.93 46.55 16.37 0.82 136.28 2.57 28.93 41.32 7.58 (6.52) (9.23) (3.59) (4.57) (2.52) (6.90) (5.25) (1.98) (0.09) (19.15) (2.54) (3.28) (7.67) (1.37) Aragon 11.76 37.76 14.36 10.72 23.14 56.18 41.57 14.61 1.15 153.81 2.29 24.51 41.85 17.08 (4.44) (8.81) (2.63) (4.91) (2.58) (6.45) (4.88) (1.75) (0.42) (23.29) (2.36) (1.75) (13.79) (3.00) Asturias 15.85 35.51 14.05 11.99 16.69 57.10 43.56 13.54 4.58 143.40 1.37 24.39 42.51 26.89 (4.47) (5.43) (3.25) (6.56) (2.47) (10.03) (7.34) (3.02) (2.29) (27.70) (2.62) (1.44) (4.84) (8.94) Balearic Islands 12.32 45.23 15.92 4.13 11.95 70.24 59.26 10.97 1.10 167.38 2.40 25.71 37.43 4.66 (4.58) (9.33) (2.64) (3.29) (4.29) (6.91) (5.82) (1.39) (0.39) (21.39) (3.01) (1.94) (8.87) (2.06) Canary Islands 20.30 42.03 18.97 7.62 7.03 72.95 56.90 16.05 1.04 149.62 2.48 27.85 38.34 9.59 (6.44) (8.39) (4.57) (4.34) (1.80) (6.26) (4.87) (2.00) (0.27) (19.93) ((2.83) (2.11) (4.44) (3.18) Cantabria 15.00 36.89 15.43 11.38 20.42 56.94 43.07 13.87 0.86 152.66 1.77 26.17 45.52 22.00 (4.95) (7.54) (3.36) (7.01) (3.19) (8.83) (7.01) (2.13) (0.20) (20.35) (3.07) (2.85) (4.89) (5.38) Castilla-La Mancha 15.20 33.28 16.56 14.78 18.74 52.18 36.84 15.33 0.96 144.54 2.55 27.87 46.22 6.92 (4.78) (9.22) (2.68) (7.62) (2.12) (8.26) (5.23) (3.13) (0.17) (29.88) (3.41) (2.87) (8.80) (1.56) Castile and Leon 15.14 35.60 14.95 15.03 16.89 55.70 39.99 15.71 1.88 153.83 1.91 25.80 46.98 13.58 (4.09) (6.91) (3.26) (7.81) (0.92) (7.90) (5.50) (2.54) (0.73) (30.50) (1.81) (1.64) (10.91) (3.38) Catalonia 15.07 44.42 15.58 3.58 28.12 58.23 48.37 9.85 0.87 162.38 2.39 22.79 34.20 11.87 (5.37) (8.29) (3.16) (1.50) (6.07) (6.97) (5.98) (1.25) (0.22) (14.72) (2.45) (1.48) (9.11) (16.17) Valencian Community 16.83 41.14 16.54 7.16 24.22 58.25 47.01 11.24 0.54 155.59 2.29 27.80 51.96 5.01 (5.38) (7.55) (3.27) (3.75) (4.66) (6.89) (5.86) (1.42) (0.10) (14.93) (2.59) (2.54) (12.82) (0.51) Extremadura 23.42 33.47 17.21 18.81 9.75 57.64 38.13 19.51 0.87 146.06 2.70 30.58 42.54 4.59 (5.92) (7.83) (2.91) (7.68) (0.64) (7.26) (3.54) (3.98) (0.23) (22.41) (3.73) (3.42) (7.54) (2.07) Galicia 13.73 42.58 14.94 23.27 16.02 50.01 37.84 12.16 0.74 114.67 1.89 27.56 45.05 14.03 (3.67) (3.09) (3.10) (12.94) (1.64) (11.10) (7.87) (3.27) (0.13) (32.74) (2.23) (1.63) (7.34) (2.70) Community of Madrid 13.96 42.68 16.69 1.01 16.37 73.14 56.19 16.94 1.01 165.64 2.84 22.86 38.52 12.33 (4.92) (10.66) (3.64) (0.31) (5.08) (5.08) (6.44) (1.93) (0.19) (13.36) (2.66) (1.76) (9.89) (2.92) Region of Murcia 17.21 39.33 18.64 14.58 18.05 56.05 42.47 13.58 0.81 143.29 3.00 30.69 34.55 3.88 (5.65) (8.22) (3.41) (3.75) (3.84) (6.02) (4.73) (1.72) (0.30) (18.65) (2.93) (3.34) (14.93) (1.59) Navarre 11.05 40.10 15.47 7.84 29.72 52.96 39.63 13.32 0.60 166.29 2.30 23.87 40.49 15.43 (4.29) (9.15) (3.30) (3.48) (3.39) (5.63) (4.85) (1.24) (0.16) (26.20) (2.75) (1.59) (7.80) (3.84) Basque Country 15.91 40.72 15.47 2.96 29.52 59.03 46.35 12.68 0.69 150.91 1.96 22.47 41.61 19.50 (5.87) (7.53) (4.24) (1.65) (5.76) (6.86) (5.58) (1.57) (0.14) (18.72) (2.35) (2.26) (8.53) (4.36) La Rioja 11.37 37.01 14.87 10.96 30.02 49.65 36.58 13.06 0.34 152.13 2.26 24.88 41.23 13.52 (4.21) (9.29) (2.57) (4.53) (3.42) (6.20) (5.59) (1.44) (0.20) (22.14) (2.62) (1.42) (8.87) (3.22) Total 15.86 39.03 16.14 10.52 19.34 58.78 44.72 14.05 1.11 150.50 2.29 26.16 41.78 12.26 (6.35) (8.84) (3.58) (8.12) (7.81) (10.10) (8.91) (3.23) (1.11) (25.64) (2.73) (3.38) (10.20) (8.26) Notes: Information provided by the INE and the IVIE. In brackets the standard deviations of the variables. Source: Authors’ own. 69 Figure A2. Cyclical unemployment by estimation method and autonomous community (1982-2012). Notes: “Cyc U (SF)”, refers to the SF estimations. “Cyc U (HP)”, refers to estimations obtained from the HP filter. “Cyc U (QT)”, refers to estimations obtained from the QT decomposition. “Cyc U (BK)” refers to estimations obtained from the BK Filter. Source: Authors’ own 76 CAPÍTULO 2 An empirical analysis of natural and cyclical unemployment at the province level in Spain 77 78 An Empirical Analysis of Natural and Cyclical Unemployment at the Provincial Level in Spain Jaime Cuéllar-Martín 1 & Ángel L. Martín-Román 1 &Alfonso Moral 1 Received: 27 July 2017 /Accepted: 18 May 2018 / Published online: 5 June 2018 #Springer Science+Business Media B.V., part of Springer Nature 2018 Abstract Differences in regional unemployment rates, as well as their formation mechanism and persistence, have given rise to many papers in recent decades. The present work contributes to this strand of literature from two different perspectives. In the first part of our work, we follow the methodological proposal put forward by Hofler and Murphy (1989)andAysunetal.(2014). We use a stochastic cost frontier to break down actual Spanish provincial unemployment (NUTS-3) into two different estimation components: the first associated with aggregate supply side factors, and the other more related to aggregate demand side factors. The second part of our research analyses the existence of spatial dependence patterns among Spanish provinces in actual unemployment and in the two above-mentioned components. The decomposition carried out in the first part of our research tells us what margin policymakers have when dealing with unemployment reductions by means of aggregate supply and aggregate demand policies. Finally, spatial analysis of unemployment rates in Spanish provinces may also have significant implications from the standpoint of economic policy since we find common formation patterns or clusters of unemployment. Keywords Unemployment .Local labour markets .Spatial dependence JEL Classification E24 .J64 .R11 Introduction In recent years the number of scientific works analysing local and regional disparities in unemployment rates has grown substantially, underpinning the importance of the topic. Appl. Spatial Analysis (2019) 12:647–696 https://doi.org/10.1007/s12061-018-9262-x *Ángel L. Martín-Román [email protected] 1 Department of Economic Analysis, University of Valladolid, Valladolid, Spain 79 In this kind of analysis, the case of Spain proves particularly appealing given the regional disparities in the unemployment rate and the extent to which these have persisted over the years (Jimeno and Bentolila 1998; Bande et al. 2008; RomeroÁvila and Usabiaga 2008;SalaandTrivín2014). The objective of this paper is twofold. Firstly, we decompose the actual unemployment rate into two different components: the natural rate of unemployment and the cyclical rate of unemployment. Secondly, we test whether there is spatial dependence between provincial figures in the two types of unemployment. In doing so, the present work goes a step further within the above-mentioned strand of literature. The added value of this research is that it offers a more enlightened vision of the disparities among actual local unemployment rates in Spain, at the same time identifying which mechanisms lie behind such a rate. The econometric technique used to break down the unemployment rate is the so-called the stochastic frontier method, which is also an innovation in this kind of analysis for the case of Spain. 1 Actual unemployment decomposition heralds a significant advance in this type of analysis since it is a relatively novel and, at the same time, useful contribution towards understanding the dynamics underlying the formation of disparities among actual unemployment rates in the local Spanish context. As well as identifying the factors that underlie the components causing actual unemployment, this decomposition sheds light on which variables impact most on unemployment rates at a local level, and which exert the greatest influence on its progression over time. This may prove extremely useful vis-à-vis gaining an insight into how much manoeuvring space policymakers have when devising and implementing economic policy measures at a territorial level. The second part of the empirical work (spatial analysis) also has added value. To the best of our knowledge, previous literature on local labour markets has explored spatial dependence between levels of what we call actual unemployment, but not between natural or cyclical unemployment rates in the different spatial units. This feature adds novelty to the paper. Moreover, spatial analysis might also offer a guide to policymakers when taking decisions. In order to undertake this analysis, we first examine the existence of spatial dependence at an overall level based on the values of Moran’s I statistic (Moran 1950). These statistics allow us to compare the existence or lack of correlation at a global scale but do not allow us to evaluate the local structure of spatial correlation. For this reason, we go one step further and build local statistics LISA (BLocal Indicators of Spatial Association^). 2 It is thus possible to decompose the global statistic and to locate any possible clusters associated to the actual provincial unemployment rate. As a measure of robustness, various alternative definitions of neighbourhood are also applied. In this paper, we check two main hypotheses. The first concerns the higher unemployment levels observed in the Spanish economy, even during boom periods. We test whether the structural and frictional components (i.e. natural unemployment) constitute the main part of actual or total employment. Put differently, we test whether natural 1 This methodology is applied to a database which provides information on the 50 Spanish provinces for the period between 1984 and 2012. The 50 Spanish provinces correspond to the third level (NUTS-3) of the Nomenclature of Territorial Units for statistics. For further information concerning the concept of NUTS, see: http://ec.europa.eu/eurostat/web/nuts/overview. 2 See the work of Anselin (1995) for an explanation of that type of analysis and the work of Posada et al. (2017) for an application of this analysis for the Spanish case. 648 J. Cuéllar-Martín et al. 80 unemployment is more important than cyclical unemployment in Spain, both during average as well as recession years. The second hypothesis is based on the idea of a nonrandom distribution of unemployment rates among the different NUTS3 spatial units in Spain. In this second case, we aim to test whether there is spatial correlation among the unemployment rates of a specific Spanish province and the unemployment rates of its neighbouring provinces, and whether such a correlation is mainly driven by the natural component of actual unemployment. The remainder of the work is organised as follows. Section BLiterature review^ offers a review of the literature related to the topic in hand. Section BConceptual framework^examines the conceptual framework on which the decomposition of actual provincial unemployment rates is based. Section BDatabase^sets out the method used in the econometric analysis. Section BResults^provides a brief description of the databases employed and defines the variables used. Section BConclusions^presents and explains the results, both with regard to the decomposition of actual provincial unemployment rates as well as in the progression and spatial analysis of their components. Finally, last section sums up the most relevant conclusions to emerge from the research and posits some economic policy measures. Literature Review Since the present work presents two clearly differentiated blocks, the bibliographical review is also conducted in two distinct sub-sections. A first sub-section thus addresses studies which, from the perspective of unemployment decomposition, adopt the stochastic frontier approach, whilst the second sub-section includes some of the research which has explored the issue of regional unemployment from a range of perspectives. Decomposition of Unemployment Decomposing unemployment into its different components is a common theme in economic literature, and a variety of techniques has been employed for this purpose. 3 One of the most widely used options involves applying univariate statistical filters. 4 Few works, however, adopt the econometric approach of stochastic frontiers. One of the pioneering works in this technique was Warren (1991). Said work uses the stochastic frontiers technique to decompose the unemployment rate, also drawing on information concerning vacancies. 5 Using the number of vacancies and the number of persons unemployed, an efficient matching function is estimated through an upper stochastic frontier. Based on this, the author determines the frictional component of unemployment for the USA for the period stretching from April 1969 to December 1979. Another work which follows the same line is that of Bodman (1999) who takes 3 The work of Fabiani and Mestre (2000) sets out some of these techniques applied to the case of the European Union. 4 The Hodrick-Prescott filter (Hodrick and Prescott 1997) and the Baxter-King filter (Baxter and King 1999) are some of the most widely used in the literature. 5 It is precisely this use of information concerning vacancies which makes it impossible for the present paper to adopt the technique used by Warren (1991). It is well known that information concerning vacancies in Spain is extremely poor. An Empirical Analysis of Natural and Cyclical Unemployment at the... 649 81 the model set out by Warren (1991) as a starting point, and models the inefficiency term of the error following the proposal of Battese and Coelli (1995). One work which follows a closer line to the approach adopted in the present research is that of Hofler and Murphy (1989) where the authors posit a model for ascertaining the frictional component of unemployment in which the unemployment rate is split into one frictional component and another that captures an excess of aggregate supply in the labour market. Hofler and Murphy (1989) estimate a stochastic cost frontier using the unemployment rate of the fifty US states for the period 1960–1979. They find great variability in the frictional component of unemployment and an increase for most states during the period analysed. Finally, Aysun et al. (2014) propose a method for estimating the structural component of the unemployment rate for the USA from 1960 to 2010. This article merges elements from the three previous studies. A very similar approach to the one employed in Warren (1991) is initially used to extract frictional unemployment. Secondly, and by applying a stochastic cost frontier, they estimate the structural component of the unemployment rate by using a specification of the expectation augmented Phillips curve. By adopting this procedure, Aysun et al. (2014) calculate a measure of structural unemployment which is always below the actual component. Analysis of Unemployment from a Regional Perspective In recent years, economists have shown increasing interest in how labour markets function at a regional level, which has given rise to a large number of studies. Overman and Puga (2002) report results for some European regions for the period 1986–1996. Their study points to an ever-growing polarisation between Bhigh^unemployment and Blow^unemployment regions, depending on the spatial influence exerted by their neighbours. Patacchini and Zenou (2007) explore the existence of imbalances in unemployment for the UK and find a strong positive spatial dependence between relative local unemployment rates. Their study points to an increase in spatial dependence over time, which is explained to a large degree by flows of individuals between local areas. Cracolici et al. (2007) adopt a very similar approach to Overman and Puga (2002). The main innovation provided in their work is its contribution to the empirical evidence concerning spatial and temporal persistence for the 103 Italian provinces between 1998 and 2003. The explanation given by the authors for this process of Bclustering^is due to factors which fit in with the hypothesis of imbalance (Marston 1985) for 1998. However, for 2003 the factors leading to this Bclustering^are far more closely linked to elements related to the equilibrium hypothesis (Marston 1985). Finally, they stress the influence of labour demand factors as the key dynamic underlying the polarisation of unemployment between provinces in the north (Blow^unemployment) and the south (Bhigh^unemployment). Filiztekin (2009) reports a strong spatial dependence of regional unemployment rates in Turkey. The author finds that the factors which most contribute to shaping the distribution of unemployment are the growth in employment in 1980 and human capital in the year 2000. Basile et al. (2009) also underpin the role played by the imbalance between labour supply and demand as well as the Bbrain drain^which occurs through migration. These two elements prove to be the most determinant when accounting for the provincial differences in unemployment in Italy in the period 1995–2007. 650 J. Cuéllar-Martín et al. 82 Kondo (2015) conducts a slightly different analysis to those employed in the abovementioned works. His research provides empirical evidence related to the persistent unemployment rates in certain Japanese municipalities over the period 1980–2005. Using spatial econometrics, the author finds clusters in municipal unemployment rates with positive spatial dependence. The study also shows the existence of major differences in terms of sex and age with regard to the spatial dependence of unemployment rates. It also reflects how municipalities with Bhigh^unemployment tend to remain in this situation throughout the time period studied. Halleck-Vega and Elhorst (2016) employ a Bsimultaneous model^and try to account for serial dynamics, spatial dependence and common factors using data on overall unemployment for 12 regions in the Netherlands over the period 1973–2013. They find empirical evidence concerning the existence of strong and weak spatial dependence in their data. As regards the analysis of differences in the issue of unemployment between the various Spanish regions, the works of López-Bazo et al. (2002,2005) use exploratory techniques at the spatial level merged with classical spatial regression analysis. Both studies highlight the strong polarisation of Spanish provinces into two groups (Bhigh^ and Blow^relative unemployment). Adopting a different perspective, Huertas et al. (2006) apply the model introduced in the work of Blanchard and Katz (1992) to determine the degree of persistence of unemployment in Andalusia and Extremadura over the period spanning from the third quarter of 1976 to the fourth of 2004. The authors conclude that a positive shock in labour demand at the provincial level triggers a permanent impact on labour force participation in Andalusia and the unemployment rate in Extremadura, and they highlight the scant worker mobility in the two regions. The study by Bande et al. (2008) focuses on the 17 autonomous communities (NUTS-2) in Spain over the period 1980–2000. The findings point to a greater disparity of relative unemployment rates in Spanish autonomous communities during upturns, and to a reduction thereof during periods of economic recession. The explanation given is based on a strong Bmimicking effect^in the wage bargaining mechanism in Spanish regions. Said effect is heightened due to the change in this mechanism’slevelof centralisation and coordination, giving rise to a worsening in terms of unemployment in regions with lower productivity. More recent works such as those of Azorín (2013) provide conclusions evidencing a strong polarisation reflected in the group of Spanish provinces displaying Bhigh^ unemployment rates in the southern half of the country and a group of provinces with noticeably Blow^unemployment rates in the northern half of the country. López-Bazo and Motellón (2013) adopt an approach based on the use of microdata for Spanish autonomous communities in 1999, 2004 and 2009. Their study finds that regional disparities between unemployment rates persist over time. The authors also highlight the determinant role played by variables related to the educational features of the population in regions with Bhigh^and Blow^unemployment. Conceptual Framework This section is also made up of two blocks. The first block sets out and explains the different components involved in the actual unemployment rate. The second block An Empirical Analysis of Natural and Cyclical Unemployment at the... 651 83 presents some of the social and economic phenomena found in the literature, and which contribute to the formation of clusters in unemployment. Components of the Actual Unemployment Rate It has been common in economic literature to break down aggregate unemployment into different components, as shown in Eq. (1) 6 : Uit ¼UF it þUST it þUC it ð1Þ where U it is the actual unemployment rate in province i at time t; UF it is the frictional unemployment rate; UST it is the structural unemployment rate and, finally, UC it represents the cyclical unemployment rate. In line with the Bjob search theory^, the existence of asymmetric or imperfect information amongst job-seekers and employers means that labour market matching takes some time and that there will always be some people unemployed. This is what leads to frictional unemployment. 7 Structural unemployment is commonly assumed to be linked to aggregate supply factors (as opposed to UC it , which is considered to be linked to aggregate demand factors). 8 Imbalances between labour supply and demand cause situations in whichthere arebothpeople unemployed and unoccupied vacancies in firms, thus leading to unemployment. 9 Based on the above, macroeconomic literature has established that the sum of frictional unemployment and structural unemployment gives rise to the socalled Bnatural rate of unemployment^or BNRU^. 10 This Bnatural rate of unemployment^acts as equilibrium unemployment in the long or medium term for the unemployment observed and is expressed formally through Eq. (2): UNR it ¼UF it þUST it ð2Þ where UNR it is the natural rate of unemployment in province iat time t. The natural rate of unemployment is related to aggregate supply determinants at a macroeconomic level, and explains that there will always be Bsome^level of unemployment. 11 Nevertheless, during times of Blow^economic growth, or during recessions 6 Even in textbooks like Krugman et al. (2011), this classification can be found. 7 This theory was developed by Mortensen (1970) and McCall (1970). See Lippman and McCall (1976a,b), Mortensen (1986) and Mortensen and Pissarides (1999), for a review of the issue in question. One recent example of this type of literature is the work of Tatsiramos and van Ours (2014). 8 The same happens with the frictional component (UF it ). 9 These imbalances arise as a result of a certain amount of institutional rigidity, linked to the downward rigidity of wages (minimum wage, collective bargaining, etc.) or employment protection, amongst others. Other factors which also impact strongly on the imbalances between supply and demand are: inflow and outflow in the labour market, labour force skills, low labour productivity, the industry composition of employment or the demographic structure of the population, to name but a few (Jackman and Roper 1987; Blanchard and Jimeno 1995;Blanchard2017). 10 Rogerson (1997) provides a number of explanations, definitions and nomenclature of the concept. 11 Even when macroeconomic conditions reach optimal levels and there are no problems of insufficient aggregate demand. 652 J. Cuéllar-Martín et al. 84 sparked by adverse demand shocks, aggregate demand would also be Binsufficient^. 12 As a result, a further element, which we already identified as cyclical unemployment, must be added to the previous factors. This idea may be expressed by means of Eq (3): Uit ¼UNR it þUC it ð3Þ Cyclical unemployment (UC it ) is the final component in Eq. (1) and in Eq. (3). Insufficient aggregate demand leads to a drop in sales in business. This in turn, sparks a reduction in labour demand due to the fact that it is derived demand (in Appendix 2, Fig. 9depicts a very simple labour market graphically illustrating what was pointed out previously). At this point, an important clarification should be made concerning the aims of the present work between the notion of the natural rate of unemployment (NRU) and the non-accelerating inflation rate of unemployment (NAIRU). The two concepts are often used indistinctly, and yet various studies question whether the NRU and NAIRU are interchangeable concepts. Tobin (1997) establishes that the NAIRU and NRU are not one and the same. On the one hand, the NAIRU reflects a relation at a macroeconomic level, whereas the NRU is a rate of unemployment equilibrium influenced by institutional demographic features of the economy, and refers to aspects that are far more microeconomic in nature (Grant 2002). The NAIRU is associated with negative cyclical unemployment at certain periods (when the inflation rate rises). This leads to the sum of frictional unemployment and structural unemployment being greater than actual unemployment. In our view, this situation is somewhat Bstriking^for labour economics models which tend to have more of a microeconomic basis. These models consider that actual unemployment comprises three components of Eq (1), although none of them should be negative (in other words, UF it ≥0;UST it ≥0;UC it ≥0). In the current work, we are more interested in the concept of NRU than NAIRU, since inflation plays no relevant role here. Based on the above, we seek to measure how much unemployment remains when there is no problem of insufficient aggregate demand. It is thus possible to quantify how much unemployment is attributable to aggregate supply factors and how much to aggregate demand factors for each province and year. Said minimum level of unemployment can be obtained as a stochastic cost frontier based on estimating a composite error econometric model. As a result, we partially follow the proposal put forward by Hofler and Murphy (1989) and more recently by Aysun et al. (2014), set out earlier. Factors Generating Spatial Dependence in Unemployment In our work, we also try to test for the presence of spatial dependence in actual unemployment rates and in its two components. For this reason, this section explores some of the phenomena whose characteristics display certain social and economic features that help us to explain why similar rates of unemployment can be found in certain neighbouring areas. 12 Due, for example, to a fall in consumer or business confidence. A contractive monetary policy or a cut in public spending might explain the existence of insufficient aggregate demand. An Empirical Analysis of Natural and Cyclical Unemployment at the... 653 85 Two more independent variables that could be considered as factors affecting frictional and/or structural unemployment in a province have been used. The first is the amount of net capital stock (in real terms) divided by the total number of employed persons in each province. This variable seeks to measure the level of capitalizationof the economy in each area (Bande and Karanassou 2013; Bande and Karanassou 2014). 35 The second variable is the percentage of temporary employment over total employment. Several works have addressed the effect of temporary work on the labour market in different countries, with mixed evidence about the effects on different elements of this market (Booth et al. 2002;Doladoetal.2002; Kahn 2010; Bentolila et al. 2012). In order to provide more detailed information concerning the variables used, Appendix 1(Table 4) offers some descriptive statistics. Results This section is divided into three blocks. The first shows the results of decomposing the unemployment rate. The second examines the existence of the spatial dependence of the actual unemployment rate and its components. Finally, the third block discusses the implications of the results to emerge. Decomposing the Actual Unemployment Rate In this section, we present the results of our baseline specification, which is explained in Eq. (7) and which we refer to as specification 1. Several additional specifications are also examined in order to test said benchmark specification. For instance, specification 2 modifies the vector of the industry composition of labour and decomposes the service industry into retailing (SRI it ) and nonretailing industries (SNRI it ). 36 Specification 3 incorporates another covariate which is the amount of net capital stock (in real terms) divided by the total number of employed persons in each province. The fourth specification adds another regressor, this one being the percentage of temporary employment over total employment (Temp it ). 37 Specification 5 only incorporates time fixed effects to the baseline specification. Moreover, we carried out our analysis for two different subperiods (specification 6 and specification 7), using the benchmark model as the reference. The first subperiod starts in 1987 and ends in 1999, the second subperiod covers from 2000 to 2012. Our two subperiods incorporate a full business cycle for the Spanish economy. 35 For a more detailed definition about the construction of net capital stock, see http://web2016.ivie.es/wpcontent/uploads/2017/02/Metodolog%C3%ADa_basedatos_stockcapital_ED.pdf 36 For a more detailed explanation about services in the retailing industry (SRI it ) and services in the nonretailing industry (SNRI it ), see http://web2011.ivie.es/downloads/caphum/series-2013/metodologia-seriescapital-humano-1964-2013.pdf 37 As regards the impact of temporary employment, we searched for data with provincial disaggregation but failed to find a database covering our whole period. Therefore, we built the percentage of temporary employment over total employment for each NUTS2 spatial unit (autonomous community) in Spain, and applied these figures to each province (NUTS3 spatial unit) depending on the autonomous community to which it belongs. Given the lack of adequate data, we have also been forced to carry out the empirical work for the period from 1991 to 2012). 660 J. Cuéllar-Martín et al. 92 Table 1presents the results obtained for each specification. Firstly, it should be pointed out that all specifications display a stochastic cost frontier at a 1% level of significance, 38 except specifications 4 and 6, whose statistical significance is 10%. If we commence by analysing industry variables, it can be seen how all the independent variables show positive and significant values, except the agriculture industry in specification 5, indicating that, generally, all industries give rise to higher natural rates of unemployment compared to the reference industry, the construction industry. It can also be seen that the greatest effect on structural unemployment, for all specifications, corresponds to the service industry and the energy industry, both of which display similar values. This result might be due to the weight which certain low-skilled jobs have in the service industry. Low-skilled workers are subject to higher turnover rates and are given little training by firms. 39 This leads to a low-skilled labour force with low employability and also triggers structural unemployment in this industry. 40 The demographic variables (FPR it and PYPP it ) also display a positive sign for all specifications. In line with the above, it should be mentioned that for specifications 2 and 7 the percentage of the youth population is not statistically significant. The coefficient of the FPR it implies that female integration into the labour market has helped to raise actual unemployment rates at an aggregate level, partly due to the fact that their unemployment rates are almost higher than men’s. For its part, the coefficient related to the weight of the youth population in general bears out the hypothesis posited earlier that the young are less skilled at job-seeking than their more mature counterparts. It also reflects the difficulty said group has in finding work as a result of their possessing Bless^ specific capital. Finally, it highlights the importance of youth unemployment when explaining the natural rate of unemployment. 41 The results of the variables of human capital are consistent with the hypothesis put forward earlier and evidence a reducing effect on natural unemployment. As the human capital of employed persons increases, the less likely they are to become unemployed Fig. 1 Distribution of actual provincial unemployment rates. Source: Authors’own 38 The test of maximum likelihood rejects the notion that variance of the disturbance measuring inefficiency is zero. 39 A good example for the case of Spain might be certain jobs in the tourism industry. 40 Using a panel including 21 OECD countries, Oesch (2010) provides empirical evidence concerning which variables most impact on unemployment among low-skilled workers. 41 The works of Dolado et al. (1999 and 2000) and Dolado et al. (2002) offer some explanations of the Bdeficient^functioning of the labour market for the case of young people in Spain. An Empirical Analysis of Natural and Cyclical Unemployment at the... 661 93 (Nickell and Bell 1996). It can also be seen that individuals with tertiary education are less likely to be unemployed than other who only have secondary education. 42 The RKS variable displays a positive sign (specifications 3 and 4). The percentage of temporary employment over total employment (Temp it ) presents a negative sign, such that when the proportion of employees with a temporary contract rises, natural unemployment falls (specification 4). It can also be stated that methodological changes implemented by the INE in 2001 had a negative impact. This indicates that the new method adopted by the INE contributed to reducing provincial unemployment. Finally, specification 5, with time fixed effects, offers very similar results to those previously commented on. Having verified the robustness of the benchmark model, the estimates obtained have been used to compute the figures concerning the frontier (natural unemployment) and the inefficiency term (cyclical unemployment). Based on these estimates, the relationship between the actual unemployment rate and its components, the natural rate of unemployment and cyclical unemployment at a provincial level, are presented in the scatter plots of Figs. 2and 3. 43 In Fig. 2, it can be clearly seen that the relationship between these elements is positive and significant. High values of actual unemployment are associated with high values of the natural unemployment rate with a correlation equal to 0.893 and an R 2 equal to 0.798. When focusing our attention on the relationship between the actual unemployment rate and the cyclical component (Fig. 3), we notice there is a clear positive association, albeit weaker than in the previous case. The statistical correlation (0.440) and R 2 (0.193) value are also weaker. Complementing the previous analysis, Fig. 5in Appendix 1depicts the progression of the natural rate of unemployment for all Spanish provinces during the period 1984–2012. 44 The mean of that component for the whole period reaches a value of 13.29 although there is considerable interterritorial variability, as the value of its variance indicates (44.60). The provinces displaying the highest mean value are Cadiz (27.35), Cordoba (23.45) and Seville (23.30), and those which behave best are Lleida (4.13), Soria (5.73) and Huesca (6.24). 45 Figure 5in Appendix 1also shows that the profile of the natural component is quite similar for all provinces. At the start of the period, it seems to remain fairly stable and at the end evidences a BU^shaped figure spanning the late 1990s and early part of the twenty-first century. As a result, there is a reduction in the natural rate of unemployment at the turn of the twenty-first century which, more or less, comes to an end with the onset of the economic crisis for the vast majority of provinces. Figure 6in Appendix 1shows the estimations of cyclical unemployment (UC it ) at a provincial scale. 46 In aggregate terms, this component shows a mean value equal to 2.96, which represents approximately one fifth of the natural 42 The previous result is maintained when we use the percentage of employed persons with secondary education and the percentage of employed persons with tertiary education in each province, rather than the share of the active population with secondary education (SE it ) and the share of the active population with tertiary education (TE it ). 43 Some negative values have been obtained when estimating the natural rate of unemployment for certain provinces. Despite this, said values account for only a very small part compared to the total number of estimations, and in all cases are below 2% of the total number of estimations obtained. 44 Estimations were performed based on the basic specification. Tests were carried out using the rest of the specifications and the results are very similar. These results are available from the authors upon request. 45 Detailed results are available upon request from the authors. 46 Estimations of cyclical unemployment have also been conducted using the basic specification. Tests were carried out using the rest of the specifications with the results being very similar. These results are available from the authors upon request. 662 J. Cuéllar-Martín et al. 94 Table 1 Econometric specifications Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Specification 6 Specification 7 C−84.510 (−15.84) −72.280*** (−13.21) −73.640*** (−14.87) −56.380*** (−9.36) −2.478 (−0.53) −67.448*** (−7.86) −111.580*** (−14.52) Agri 0.726*** (14.28) 0.680*** (13.52) 0.612*** (13.07) 0.585*** (9.87) −0.151*** (−3.06) 0.224*** (2.75) 1.343*** (18.27) Man 0.772*** (12.76) 0.658*** (10.75) 0.456*** (7.89) 0.268*** (3.96) 0.063 (1.21) 0.247*** (2.59) 0.884*** (10.39) Serv 1.397*** (29.53) 1.004*** (20.64) 0.759*** (12.90) 0.279*** (5.69) 0.792*** (8.93) 1.591*** (28.60) SRI 1.192*** (22.18) SNRI 1.685*** (28.18) Ener 1.273*** (9.48) 1.197*** (9.07) 1.175*** (9.86) 1.044*** (5.66) 0.234** (2.26) 1.055*** (5.09) 2.117*** (6.92) FPR 0.162*** (6.03) 0.172*** (6.55) 0.167*** (7.00) 0.211*** (6.70) 0.164*** (6.63) 0.133*** (2.62) 0.270*** (5.83) PYPP 0.294** (2.41) 0.052 (0.43) 0.488*** (4.32) 0.803*** (6.13) 0.637*** (6.10) 1.742*** (7.38) 0.037 (0.18) SE −0.081*** (−4.36) −0.085*** (−4.64) −0.093*** (−5.53) −0.049*** (−2.59) −0.068*** (−3.94) 0.031 (1.08) −0.152*** (−5.22) TE −0.731*** (−13.38) −0.840*** (−15.04) −0.787*** (−15.44) −0.509*** (−8.03) −0.521*** (−11.28) −0.349*** (−4.47) −0.553*** (−6.97) RKS 0.108*** (17.66) 0.094*** (14.03) Temp −0.262*** (−9.52) An Empirical Analysis of Natural and Cyclical Unemployment at the... 663 95 Table 1 (continued) Specification 1 Specification 2 Specification 3 Specification 4 Specification 5 Specification 6 Specification 7 PFE/TFE YES/NO YES/NO YES/NO YES/NO YES/YES YES/NO YES/NO Cost Frontier 0.000*** 11.97 0.000*** 13.46 0.000*** 19.01 0.056* 2.53 0.000*** 12.05 0.055* 2.54 0.000*** 12.51 N°. of obs 1450 1450 1450 1100 1450 650 650 The dependent variable is the actual unemployment rate in each province. All specifications, except specification 6, include the dichotomous variable D2001. The results associated to this variable are not shown. BCost Frontier^refers to the test of maximum likelihood for determining whether a cost frontier exists or not. *, ** and *** indicate significance at 10%, 5 and 1%, respectively. In brackets, the value corresponding to the Bz^statistic. Results associated to the provincial fixed effects and the time fixed effects are not shown Source: Authors’own 664 J. Cuéllar-Martín et al. 96 component. As occurred earlier, cyclical unemployment also displays significant interprovincial diversity, with the variance of this component being equal to 2.35 in this case. Girona (3.55), Castellon (3.43) and Guadalajara (3.40) are the provinces with the highest mean values, and Navarra (2.63), Burgos (2.64) and Pontevedra (2.68) those with the lowest. Below the mean, we also find Madrid, Alava and Biscay. 47 Finally, certain similarities can also be found in the progression of all of them, with a final upturn coinciding with period linked to the Great Recession. At this point, it seems logical to dedicate a few lines to examining what happened in the above-mentioned Great Recession years, which had important implications for the Spanish labour market. The substantial increase in actual unemployment in the Spanish provinces could be explained to a greater extent by the progression of the natural rate of unemployment than by the progression of the cyclical rate of unemployment. Put differently, and in line with our theoretical framework, the results obtained in this paper seem to suggest that the sizeable increase in the actual unemployment rates is better explained by aggregate supply factors than by aggregate demand factors. 48 To conclude this section, we would like to reflect on potential endogeneity problems in our model. According to econometric theory, there are three possible sources of endogeneity: measurement errors, omitted variables bias, and the simultaneity problem. This could generate some correlation among the regressors of the model and the two components of the error term in the econometric model. Controlling for spatial fixed effects (as we do in this paper) alleviates the omitted variable bias problem and possible measurement errors. With regard to simultaneity, since we have two different error terms, each should be discussed separately. In the case of possible correlation among the regressors and the inefficiency term, we feel that it should not really be a problem based on theoretical grounds. R-Squared=0.798 -10 010 20 30 40 Natural Unemployment Rate (Provincial) 010 20 30 40 Actual Unemployment Rate (Provincial) Fig. 2 Scatter plot of actual and natural unemployment rates (1984–2012). Source: Authors’own 47 Detailed results are available upon request from the authors. 48 See Jimeno and Santos (2014) for a more comprehensive explanation about the effects of this period in the case of Spain. An Empirical Analysis of Natural and Cyclical Unemployment at the... 665 97 This is because the two components that make up actual unemployment differ in Bnature^: natural unemployment is determined by aggregate supply side variables, whereas cyclical unemployment is determined by aggregate demand side factors. Consequently, all the variables included in the frontier are intended to capture supply side determinants and should theoretically be orthogonal with cyclical unemployment. In this sense, we closely follow the same approach as Summers et al. (1986), Hofler and Murphy (1989), and Aysun et al. (2014), who include covariates such as industry composition, demographic variables or certain measures of human capital to explain both frictional and structural unemployment. The other source of potential endogeneity might be the possible correlation between the regressors and the random error (v it ). In our view, the variables most likely to be affected by the double directionality problem would be the female activity rate and human capital measures. In order to check whether this is actually an issue, we tested whether eliminating the previously mentioned variables from our baseline regression would substantially modify the estimates of natural and cyclical unemployment. Results did not alter significantly. Therefore, given the robustness of the results in the different alternative specifications, it seems logical to assume that endogeneity is not a major concern in our model. Spatial Analysis of the Actual Unemployment Rate and its Components Having performed the decomposition, the next step involves analysing the spatial dependence of each component. In order to achieve this goal, it is necessary to start by defining the matrices. This work uses four different spatial matrices. The first considers the five nearest neighbours to each province (Knn = 5). 49 The second is an inverse distance matrix which penalises the spatial units that are furthest away from one another with an alpha (α) parameter equal to 1 (Inv). 50 The third is also an inverse distance matrix, but is based on an 49 This type of spatial matrix is also used in Basile et al. (2009). 50 This type of spatial matrix is also used in Akçagün (2017). R-Squared=0.193 -10 010 20 30 40 Cyclical Unemployment Rate (Provincial) 010 20 30 40 Actual Unemployment Rate (Provincial) Fig. 3 Scatter plot of actual and cyclical unemployment rates (1984–2012). Source: Authors’own 666 J. Cuéllar-Martín et al. 98 alpha parameter which adopts the value 2; in this case the penalisation is greater compared to the second matrix (Inv2). Finally, the fourth is an administrative matrix which considers only provinces belonging to the same autonomous community to be neighbours (Admin). Table 2shows the values corresponding to Global Moran’s I. Data evidence a strong positive spatial dependence both in the actual provincial unemployment rates as well as in their natural component, for all the spatial matrices. The actual unemployment rate shows positive and significant values at a 1% level over the whole period. Even though the values are highly stable they appear to increase over time, albeit only slightly. This phenomenon is observable for all the spatial matrices used in this research. What was stated earlier indicates that actual unemployment rates resemble those of their neighbours as time passes. These results are borne out by the diagrams corresponding to section A of Fig. 7of Appendix 1(for the five nearest neighbours’matrix). Results evidence a strong positive dependence which is reflected in the greater concentration of points in the first and third quadrant, particularly in the final year of the sample. 51 The results corresponding to the spatial analysis of the natural rate of unemployment are very similar to those presented for the actual unemployment rate. All the values of Global Moran’s I are positive and significant at a 1% level. In this case, mean values are on average lower (except inthe case ofthe administrative matrix) and display less variability, evidencing greater stability of Moran’s I over the whole period. The Moran’s I scatterplot diagrams for the five nearest neighbours’matrix shown in section B of Fig. 7of Appendix 1once again bear out all the results mentioned. 52 In all the years presented, a strong positive spatial dependence can be seen, with significant concentrations of points in the first and third quadrants. In the case of cyclical unemployment, the situation is not as clear. Global Moran’sI points to a positive spatial dependence although, except for the administrative matrix, this only occurs as of 1996 in a generalised way for the rest of the spatial matrices. It can also be seen how the value of Global Moran’s I is lower than for the two previous cases. This lower spatial dependence is also evident when observing the diagrams shown in section C of Fig. 7of Appendix 1,for the five nearest neighbours’matrix. 53 The points no longer display such a clear pattern and are distributed over the four quadrants. Having verified the existence of the positive spatial dependence of the unemployment rate and its components, the next step is to determine where the areas of Bhigh^and Blow^unemployment are situated and whether these persist over time. The three panels of Fig. 4show the results obtained using the local statistics of Moran’s I for the unemployment rate and its components, and 51 The diagrams obtained for the remaining spatial matrices also point to the existence of spatial dependence for the actual unemployment rate in a way similar to that observed in the five nearest neighbours’matrix. Detailed results are available upon request from the authors. 52 As noted in the previous case, the remaining spatial matrices also point to the existence of spatial dependence regarding the natural rate of unemployment. 53 Again, the diagrams obtained with different spatial matrices seem to indicate the existence of spatial dependence for the cyclical rate of unemployment (except for the administrative matrix). An Empirical Analysis of Natural and Cyclical Unemployment at the... 667 99 for the four years in the sample. 54 In panel A), corresponding to the actual unemployment rate, two clearly defined geographical areas emerge. First, there is a cluster of Bhigh^unemployment located in the south of Spain, which remains very stable over the four years studied, and which includes most of the provinces in Andalusia as well as Badajoz (in addition to Ciudad Real in 2012). Second, there is an area of Blow^unemployment in the north of Spain and which shifts over time towards the Basque Country, Navarre and Aragón, particularly after the second half of the 1990s. These results are also confirmed based on the local scatterplot diagrams presented in section A) of Fig. 8of Appendix 1. The same results obtained in panel A for the actual unemployment rate also hold true in panel B for the natural rate of unemployment. The cluster of very stable Bhigh^unemployment found in the provinces of the southern half of the country is seen to remain. There is also another cluster of Blow^unemployment that emerges in the north-east of the peninsula. That cluster changes over time and finally, in 2012, also appears in the north-east of the peninsula. Once again, this result is consistent with what is shown in section B in Fig. 8which appears in Appendix 1. In the case of cyclical unemployment, the situation is far more erratic. There are clusters of Bhigh^and Blow^unemployment, but without any kind of territorial consistency in the years shown. This lack of any pattern is also apparent in section C of Fig. 8of Appendix 1, with greater randomness in the distribution of the points. Finally, one goal of this paper is to identify and measure spatial dependence both in the natural and the cyclical components of actual unemployment. To do this, we closely follow previous literature on unemployment decomposition by means of stochastic frontier procedures (e.g. Aysun et al. 2014), in a first step, so as to obtain the figures of both components. However, when analysing spatial dependence of aggregate regional unemployment, standard practice has sought to correct such a spatial dependence by including the spatial lag of the dependent variable and the spatial lags of the independent variables in the econometric specification (e.g. Elhorst 2014). Although our initial aim was not to follow this path, we carried out an additional specification in which we include the previously mentioned spatial lags. The results of this empirical exercise can be found in Appendix 3. As a general comment, it can be said that the estimates of natural and cyclical unemployment rates are very similar to those obtained in our baseline econometric specification. Implications of the Results The previous results highlight the existence of two well-defined clusters of unemployment: one of Bhigh^actual unemployment in the southern half of 54 The results shown have been obtained using the Knn = 5 matrix. Nevertheless, tests have been carried out using the remaining spatial matrices and the conclusions are similar. The results of these tests are available upon request from the authors. Tests were also conducted after removing the islands. The values of the statistics did not alter substantially. 668 J. Cuéllar-Martín et al. 100 Table 2 Global Moran’sI Knn = 5 Inv Inv2 U i,t UNR i;tUC i;tU i,t UNR i;tUC i;tU i,t Year I z (I) I z (I) I z (I) I z (I) I z (I) I z (I) I 1984 0.532*** 6.918 0.706*** 9.102 0.021 0.533 0.170*** 9.303 0.228*** 12.103 −0.012 0.439 0.360*** 1985 0.559*** 7.376 0.639*** 8.262 −0.004 0.209 0.172*** 9.337 0.196*** 10.547 −0.011 0.449 0.366*** 1986 0.637*** 8.232 0.604*** 7.853 −0.018 0.035 0.178*** 9.669 0.182*** 9.894 −0.017 0.198 0.385*** 1987 0.673*** 8.699 0.668*** 8.623 0.027 0.606 0.201*** 10.801 0.204*** 10.952 −0.008 0.607 0.434*** 1988 0.654*** 8.458 0.620*** 8.016 0.121* 1.879 0.189*** 10.202 0.193*** 10.377 0.014* 1.792 0.413*** 1989 0.657*** 8.487 0.678*** 8.725 0.171** 2.483 0.200*** 10.715 0.218*** 11.573 0.029** 2.465 0.426*** 1990 0.653*** 8.434 0.697*** 8.953 0.130** 1.998 0.200*** 10.725 0.227*** 12.018 0.031*** 2.659 0.425*** 1991 0.672*** 8.694 0.666*** 8.602 0.125* 1.859 0.214*** 11.434 0.219*** 11.682 0.026** 2.298 0.449*** 1992 0.705*** 9.082 0.641*** 8.269 −0.019 0.023 0.228*** 12.104 0.213*** 11.361 −0.011 0.482 0.471*** 1993 0.664*** 8.576 0.714*** 9.217 0.063 1.047 0.219*** 11.681 0.238*** 12.614 −0.003 0.857 0.450*** 1994 0.664*** 8.636 0.721*** 9.370 0.102 1.536 0.219*** 11.718 0.238*** 12.678 0.019* 1.925 0.453*** 1995 0.667*** 8.674 0.710*** 9.220 0.077 1.221 0.225*** 12.025 0.231*** 12.324 0.016* 1.758 0.458*** 1996 0.684*** 8.852 0.772*** 9.991 0.152** 2.172 0.231*** 12.269 0.245*** 13.030 0.026** 2.251 0.467*** 1997 0.707*** 9.131 0.737*** 9.547 0.284*** 3.821 0.242*** 12.804 0.242*** 12.850 0.069*** 4.367 0.492*** 1998 0.739*** 9.596 0.729*** 9.429 0.184*** 2.571 0.239*** 12.718 0.250*** 13.212 0.034*** 2.685 0.488*** 1999 0.736*** 9.523 0.714*** 9.203 0.233*** 3.180 0.238*** 12.667 0.250*** 13.157 0.049*** 3.409 0.495*** 2000 0.749*** 9.681 0.738*** 9.491 0.327*** 4.358 0.248*** 13.124 0.251*** 13.221 0.082*** 5.008 0.512*** 2001 0.663*** 8.730 0.674*** 8.752 0.070 1.238 0.217*** 11.813 0.217*** 11.642 0.000 1.092 0.444*** 2002 0.654*** 8.593 0.616*** 8.009 −0.096 −0.955 0.215*** 11.662 0.213*** 11.433 −0.018 0.121 0.436*** 2003 0.651*** 8.444 0.654*** 8.484 −0.047 −0.335 0.216*** 11.546 0.220*** 11.730 −0.022 −0.059 0.437*** An Empirical Analysis of Natural and Cyclical Unemployment at the... 669 101 of the cyclical component should not be overlooked. As regards the second objective, the presence of overall positive spatial dependence has been evident both in actual unemployment rates at a provincial scale as well as in the natural component. In the case of the cyclical component, a certain spatial dependence has also been apparent, although it is neither as persistent nor as significant. All of this points to neither actual unemployment nor its components being distributed randomly in the spatial context. The results also point to the creation of two large clusters for actual unemployment and its natural component; one of Blow^unemployment in the north-east of the Iberian Peninsula and another of Bhigh^unemployment in the south. Nevertheless, the behaviour of the cyclical component would appear to be more erratic, and there does not seem to be any consistency in the clusters it generates. This process involving the formation of unemployment clusters seems to be due to a number of reasons. On the one hand, the action of the BPeer Effect^(through the BSocial Network Peer Effect^ and the BSocial Cost Peer Effect^), the BCommuting Effect^and the BMigration Effect^might be explaining the spatial dependence through frictional unemployment. On the other hand, the BSpillover Effect^(through the BStandard Spillover Effect^) might also trigger spatial patterns through structural unemployment. Finally, the erratic behaviour of the clusters observed in the cyclical component might be accounted for by what we refer to as the BFiscal Policy Spillover Effect^. The present work seeks to provide a tentative explanation for the spatial patterns found in unemployment (and its components) as well as their temporal persistence. We have been able to pinpoint factors which play a role among individuals in the labour market, already highlighted in previous studies, and which provide social and economic support to the notion of cluster formation. Determining the relative importance of each component of actual unemployment is key to understanding how much manoeuvring room the authorities have when applying aggregate demand or aggregate supply policies and to gauging the possible impact each might have. All of this highlights the need to undertake urgent labour reform (Blanchard et al. 2014). For its part, pinpointing the clusters of the components of actual unemployment and shedding light on which factors drive their creation might help those in charge of economic policy to gain an insight into the dominant dynamics underlying actual unemployment. A better understanding of the mechanisms which underlie the formation of the actual unemployment rate and the factors which generate spatial patterns is key to achieving the objective of convergence in low levels of unemployment. This will help to eliminate the disparities which exist at a provincial scale between areas of Bhigh^ and Blow^unemployment and which are basically due to their natural rates of unemployment. Acknowledgements The authors are grateful to Roberto Bande, Hector Sala, and Enrique López-Bazo as well as to participants at the XLII Reunión de Estudios Regionales,theXII Jornadas de Economía Laboral, and the 57th ERSA Congress for their comments to an earlier draft. The first and second authors were partially supported by the Spanish Ministry of Economy, Industry and Competitiveness under project ECO201782227-P. The third author has been partially supported by Ministry of Economy, Industry and Competitiveness under project CSO2015-69439-R. 676 J. Cuéllar-Martín et al. 108 Table 3 Description of variables and data sources Variable Definition Source Actual unemployment rate in province i in year t (U it ) Uit ¼UNEMit APit *100 UNEM it : Total number of those unemployed in province iin period t. AP it : Total active population in province iin period t. Labour Force Survey (EPA), published by the National Institute of Statistics (INE) Percentage of employed in the agricultural industry in province iin year t (Agri it ) Agriit ¼AGRIit TEmpit *100 AGRI it : Total number of those employed in the agricultural industry in province iin period t. TEmp it : Total number of employed in province i in period t. Valencian Institute of Economic Research (IVIE) Percentage of employed in the manufacturing industry in province iin year t (Man it ) Manit ¼MANit TEmpit *100 MAN it : Total number of those employed in the manufacturing industry in province iin period t. TEmp it : Total number of employed in province iin period t. Valencian Institute of Economic Research (IVIE) Percentage of employed in the service industry in province iin year t (Serv it ) Servit ¼SERVit TEmpit *100 SERV it : Total number of those employed in the service industry in province iin period t. TEmp it : Total number of those employed in province iin period t. Valencian Institute of Economic Research (IVIE) Percentage of employed in services in the retailing industry in province iin year t (SRI it ) SRIit ¼Serv Ret Indit TEmpit *100 Serv Ret Ind it : Total number of those employed in services in the retailing industry in province iin period t. TEmp it : Total number of those employed in province iin period t. Valencian Institute of Economic Research (IVIE) Percentage of employed in services in the non-retailing industry in province iin year t (SNRI it ) SNRIit ¼Serv Non Ret Indit TEmpit *100 Serv Non Ret Ind it :Total number of those employed in services in the non-retailing industry in province iin period t. TEmp it : Total number of those employed in province i in period t. Valencian Institute of Economic Research (IVIE) APPENDIX 1: Tables and Figures An Empirical Analysis of Natural and Cyclical Unemployment at the... 677 109 Table 3 (continued) Variable Definition Source Percentage of employed in the energy industry in province iin year t (Ener it ) Enerit ¼ENERit TEmpit *100 ENER it : Total number of those employed in the energy industry in province iin period t. TEmp it : Total number of those employed in province i in period t. Valencian Institute of Economic Research (IVIE) Percentage of employed in the construction industry in province iin year t (Const it ) Constit ¼CONSTit TEmpit *100 CONST it : Total number of those employed in the construction industry in province iin period t. TEmp it : Total number of those employed in province i in period t. Valencian Institute of Economic Research (IVIE) Female participation rate in province iin year t (FPR it ) FPRit ¼AFPit FPOP 16−65it *100 AFP it : Total active female population in province iin period t. FPOP 16 −65 it : Female population of working age in province i in period t. Labour Force Survey (EPA), published by the National Institute of Statistics (INE) Percentage of youth population in province iin year t (PYPP it ) PYPPit ¼YOUNGit POPit *100 YOUNG it : Total population of 15 to 24 year-olds in province iin period t. POP it : Total population in province iin period t. Labour Force Survey (EPA), published by the National Institute of Statistics (INE) Percentage of active population with secondary education in province iin year t (SE it ) SEit ¼SECit POP 16−65it *100 SEC it : Total number of active workers with secondary education in province iin period t. POP 16 −65 it : Population of working age in province iin period t. Valencian Institute of Economic Research (IVIE) Percentage of active population with tertiary education in province iin year t (TE it ) TEit ¼TERTit POP 16−65it *100 TERT it : Total number of active workers with tertiary education in province iin period t. POP 16 −65 it : Population of working age in province iin period t. Valencian Institute of Economic Research (IVIE) Share of net capital stock (in real terms) out of the total number of employed in province iin year t (RKS it ) RKSit ¼NKSit TEmpit NKS it : Net capital stock (in real terms) in province iin period t (base year: 2010). TEmp it : Total number of those employed in province iin period t. Valencian Institute of Economic Research (IVIE) 678 J. Cuéllar-Martín et al. 110 Table 3 (continued) Variable Definition Source Percentage of temporary employment over the total number of employed in autonomous community iin year t (Temp it ) Tempit ¼Fixed Term Empit TEmpjt *100 Fixed Term Emp it : Total number of those employed who have a fixed term contract in autonomous community iin period t. TEmp jt : Total number of those employed in autonomous community jin period t. Survey of Labour Situation (ECL), published by the Ministry of Labour and Social Security. Source: Authors’own An Empirical Analysis of Natural and Cyclical Unemployment at the... 679 111 Table 4 Mean value and deviation of the variables used in the estimation U Agri Man Serv SRI SNRI Ener FPR PYPP SE TE RKS Temp Alava 13.40 4.41 34.93 53.49 38.38 15.11 0.37 43.71 13.94 54.60 18.47 164.69 28.02 4.72 2.55 4.56 6.49 5.28 1.89 0.19 8.19 3.30 10.85 5.88 6.14 4.98 Albacete 18.11 13.19 19.31 56.16 38.84 17.31 0.66 37.91 15.04 49.60 13.71 122.58 38.88 6.84 6.74 3.06 7.82 4.43 3.79 0.31 8.49 2.21 13.27 5.45 28.94 6.35 Alicante 18.00 6.10 23.89 59.33 48.63 10.69 0.46 43.14 14.58 52.57 12.43 166.50 34.13 5.54 2.75 5.46 6.82 5.33 1.97 0.18 5.00 2.69 13.90 4.84 14.98 5.97 Almeria 18.86 25.03 6.09 56.64 43.95 12.69 0.63 41.16 15.96 42.79 12.58 128.66 41.17 6.78 7.11 1.40 6.48 5.97 1.84 0.25 10.74 2.23 13.02 2.87 18.64 5.97 Asturias 15.99 11.36 16.37 58.11 44.19 13.92 4.36 35.93 12.63 51.03 16.76 146.43 31.66 4.59 6.31 2.22 9.55 7.16 2.72 2.21 5.37 2.72 12.62 5.73 25.97 4.24 Avila 14.67 18.85 11.68 54.46 37.53 16.92 0.46 31.60 12.62 49.19 13.70 165.80 31.23 5.18 8.44 2.18 6.47 5.10 2.07 0.27 7.33 2.00 15.66 3.72 33.51 4.25 Badajoz 26.34 17.33 10.18 59.82 39.69 20.13 0.64 34.08 14.97 49.55 13.26 129.11 40.47 6.88 5.75 1.05 5.71 2.66 3.44 0.28 8.25 1.79 16.71 4.41 25.29 4.68 Balearic Islands 12.31 3.54 11.55 71.10 59.97 11.12 1.08 46.17 14.15 55.78 12.13 169.95 35.21 4.70 2.49 4.14 6.26 5.32 1.29 0.40 8.88 2.34 14.49 3.47 19.60 5.40 Barcelona 15.98 1.19 30.16 59.81 50.19 9.62 0.77 45.34 13.90 53.43 17.30 156.18 27.87 6.08 0.31 7.01 6.78 6.28 0.89 0.21 8.02 2.93 8.06 5.15 17.40 4.43 Biscay 17.44 2.31 24.42 63.69 50.32 13.37 0.94 40.53 13.47 52.76 22.93 150.74 28.02 6.15 1.30 5.20 5.95 5.14 1.39 0.26 7.01 3.41 7.49 6.26 17.20 4.98 Burgos 12.88 11.04 25.91 53.21 39.79 13.41 0.67 37.92 13.10 52.16 16.19 156.59 31.23 3.80 5.65 2.07 5.53 4.74 1.60 0.24 8.24 2.50 10.95 5.19 21.56 4.25 Caceres 19.95 18.65 8.96 56.93 37.26 19.67 1.24 34.49 14.09 46.00 13.99 178.19 40.47 680 J. Cuéllar-Martín et al. 112 Table 4 (continued) U Agri Man Serv SRI SNRI Ener FPR PYPP SE TE RKS Temp 5.12 9.10 1.03 7.76 3.63 4.40 0.48 6.41 2.02 18.13 5.10 16.79 4.68 Cadiz 30.52 9.05 12.66 65.76 45.81 19.94 1.36 35.38 16.48 45.99 12.71 137.00 41.17 7.52 4.05 3.41 7.04 5.51 2.62 0.35 8.83 2.79 13.18 4.14 14.95 5.97 Cantabria 15.17 10.48 20.02 58.04 43.83 14.21 0.84 37.61 13.55 55.24 16.16 155.00 32.09 5.08 6.28 2.88 8.03 6.59 1.74 0.20 7.25 2.71 12.46 4.71 18.86 5.15 Castellon 12.06 10.68 26.37 52.24 41.79 10.45 0.67 41.85 13.96 55.21 12.33 167.87 34.13 6.00 5.94 3.57 6.77 5.79 1.33 0.21 7.59 2.22 18.47 3.72 20.16 5.97 Ciudad Real 16.49 13.21 15.16 54.56 38.25 16.31 1.68 31.68 14.61 48.19 12.71 151.92 38.88 5.28 5.43 1.72 6.16 3.42 3.04 0.55 7.88 1.71 12.94 3.86 36.37 6.35 Cordoba 26.33 15.69 15.02 58.29 42.12 16.17 1.14 35.34 15.18 46.14 13.28 132.18 41.17 6.05 4.59 2.08 5.90 3.80 2.52 0.53 8.83 2.07 14.07 4.13 23.62 5.97 Corunna 14.28 17.40 15.27 55.73 41.89 13.84 1.18 40.74 13.45 46.63 15.44 123.80 35.53 3.36 10.16 1.73 8.82 6.10 2.95 0.26 5.50 2.81 16.15 6.72 27.90 6.18 Cuenca 12.70 25.90 12.51 48.45 33.68 14.76 0.58 28.94 13.17 46.16 11.79 150.50 38.88 4.20 10.46 1.73 8.11 4.87 3.67 0.33 7.43 1.82 13.16 3.31 38.69 6.35 Girona 10.79 6.19 23.63 57.55 47.57 9.98 0.49 49.72 13.56 56.02 13.06 179.41 27.87 4.66 2.73 4.25 6.10 4.94 1.54 0.16 6.39 2.21 13.53 4.13 13.85 4.43 Granada 24.93 13.43 9.60 64.77 46.00 18.77 0.57 35.30 15.61 44.78 17.20 138.25 41.17 6.70 4.79 1.45 6.02 4.75 1.86 0.20 8.48 2.47 12.21 4.88 19.34 5.97 Guadalajara 13.21 8.78 18.56 58.46 40.64 17.81 1.60 36.02 13.15 45.24 17.51 207.22 38.88 4.35 4.52 4.03 9.02 8.03 2.40 0.45 11.42 1.96 13.52 4.39 22.59 6.35 Guipuzcoa 13.84 2.68 32.69 56.95 45.68 11.26 0.41 42.21 13.51 53.09 19.80 150.58 28.02 6.44 1.49 5.36 6.53 5.48 1.39 0.16 7.17 3.53 9.59 7.25 26.32 4.98 Huelva 25.81 17.31 13.10 56.21 40.11 16.09 1.60 35.65 15.57 48.93 11.60 166.77 41.17 An Empirical Analysis of Natural and Cyclical Unemployment at the... 681 113 Table 4 (continued) U Agri Man Serv SRI SNRI Ener FPR PYPP SE TE RKS Temp 6.74 2.81 4.34 6.30 4.72 2.67 0.44 9.29 2.29 16.01 3.88 18.10 5.97 Huesca 9.06 17.49 17.00 53.21 38.16 15.05 1.11 36.68 12.14 51.16 16.20 209.08 30.10 3.26 6.23 1.95 7.17 5.71 2.47 0.55 9.01 1.82 13.19 4.36 27.93 4.17 Jaen 24.09 18.67 16.34 53.96 37.29 16.66 0.52 32.27 15.36 46.94 12.34 120.02 41.17 6.24 6.19 3.45 7.77 4.87 3.14 0.19 7.90 1.90 13.67 4.11 23.05 5.97 Leon 14.61 15.99 11.78 56.18 41.91 14.26 5.76 36.67 12.81 51.03 15.93 164.53 31.23 3.95 9.90 1.56 10.36 7.17 3.35 2.78 4.26 2.37 12.62 4.34 35.86 4.25 Lleida 7.28 15.80 15.86 55.36 41.93 13.42 0.75 40.77 12.97 48.17 14.73 161.12 27.87 3.49 6.10 1.93 6.18 3.92 2.74 0.42 8.46 1.99 13.23 3.79 20.75 4.43 Lugo 10.24 37.87 10.49 42.90 31.37 11.53 0.48 45.04 11.60 45.72 10.93 110.28 35.53 3.19 14.45 1.84 11.62 7.92 3.85 0.20 3.19 1.75 17.90 4.72 40.71 6.18 Madrid 13.85 0.96 15.94 73.58 56.73 16.84 1.00 43.61 14.70 50.13 25.23 166.41 27.37 5.05 0.24 4.97 4.96 6.30 1.96 0.19 10.39 3.09 5.49 6.94 13.47 3.24 Malaga 25.25 6.44 8.99 71.19 56.92 14.27 0.44 39.40 15.34 48.23 13.22 158.19 41.17 8.04 2.91 2.64 5.80 5.05 2.02 0.17 7.16 2.73 12.81 3.91 15.68 5.97 Murcia 17.30 13.96 17.60 56.95 43.19 13.75 0.78 40.23 15.86 49.47 13.89 145.05 37.46 5.83 2.99 3.54 5.08 3.94 1.64 0.29 7.70 2.63 11.76 4.39 17.93 5.93 Navarre 10.83 7.38 29.42 53.58 40.03 13.55 0.61 40.98 13.59 52.31 20.18 168.98 30.36 4.30 3.09 3.29 5.26 4.75 0.92 0.15 8.80 2.69 9.69 5.68 24.89 3.13 Ourense 12.08 25.53 14.79 48.32 34.52 13.79 0.56 42.36 11.73 42.62 12.89 121.97 35.53 4.51 17.78 3.35 13.93 9.44 4.70 0.26 3.09 1.99 17.45 5.76 45.21 6.18 Palencia 14.91 13.83 18.87 55.48 38.73 16.74 2.32 34.06 13.00 45.06 16.04 164.59 31.23 5.05 4.30 1.72 5.75 3.88 2.63 0.89 7.64 2.15 11.14 4.19 33.49 4.25 Palmas (Las) 20.93 6.11 7.32 74.93 58.92 16.01 0.97 43.46 16.47 51.21 13.02 140.40 39.82 682 J. Cuéllar-Martín et al. 114 Table 4 (continued) U Agri Man Serv SRI SNRI Ener FPR PYPP SE TE RKS Temp 7.33 3.24 2.66 6.18 5.31 1.71 0.25 8.18 3.53 13.81 2.70 15.15 5.32 Pontevedra 16.37 18.13 20.19 51.20 40.10 11.10 0.33 44.05 14.59 51.25 12.53 114.62 35.53 4.13 10.46 1.48 9.57 7.35 2.32 0.11 3.40 3.00 16.58 4.96 25.93 6.18 Rioja (La) 11.39 10.45 29.64 50.33 37.06 13.27 0.34 37.62 13.29 48.39 17.02 154.72 27.99 4.36 4.21 3.20 5.81 5.46 1.22 0.21 9.30 2.20 13.21 4.73 20.42 4.13 Salamanca 18.26 13.60 11.32 62.75 42.72 20.02 0.95 35.75 13.39 42.41 20.88 157.28 31.23 5.15 6.87 1.94 7.38 4.25 3.78 0.32 7.72 2.57 11.58 7.64 27.57 4.25 Saragossa 12.69 6.93 25.15 59.36 44.91 14.45 0.56 40.01 13.22 50.25 19.12 137.41 30.10 5.15 3.31 3.32 5.44 4.17 1.51 0.18 8.19 2.46 9.59 6.09 20.24 4.17 S C Tenerife 19.83 7.83 6.45 72.43 55.63 16.79 1.04 42.37 15.60 47.98 14.86 164.04 39.82 6.11 4.03 1.05 5.37 4.39 1.73 0.38 7.82 3.17 11.28 3.93 25.39 5.32 Segovia 11.36 16.94 15.39 56.19 39.25 16.94 0.44 38.48 13.25 47.21 17.50 155.70 31.23 3.22 7.24 2.07 7.05 5.64 2.88 0.25 6.66 2.31 11.67 4.67 31.99 4.25 Seville 26.04 9.30 13.21 67.18 49.68 17.50 0.74 37.91 15.97 49.93 16.27 130.57 41.17 6.89 3.99 2.57 6.23 4.90 1.75 0.21 8.98 2.83 13.26 5.41 17.77 5.97 Soria 8.64 17.59 21.21 50.94 32.26 18.68 0.73 36.23 11.91 49.02 17.47 161.08 31.23 2.90 6.88 2.24 4.54 3.14 2.02 0.42 9.04 1.89 16.15 4.08 19.60 4.25 Tarragona 12.75 9.62 18.32 56.72 45.50 11.21 1.86 43.46 13.83 52.89 12.69 203.17 27.87 4.45 4.55 1.70 5.97 4.40 2.02 0.71 8.39 2.35 11.28 3.59 13.00 4.43 Teruel 9.29 18.26 18.26 47.48 30.61 16.87 4.62 32.77 11.87 47.88 14.43 198.24 30.10 3.65 6.65 2.03 6.66 4.33 2.90 2.48 9.42 1.29 14.89 3.42 33.38 4.17 Toledo 13.85 11.68 23.82 49.41 35.47 13.93 0.45 35.01 14.14 49.02 10.93 143.32 38.88 5.10 6.81 3.82 9.07 6.35 2.87 0.21 10.06 1.79 15.27 4.23 27.75 6.35 Valencia 17.14 6.14 23.18 60.30 48.23 12.07 0.55 41.29 14.41 53.23 16.49 148.74 34.13 An Empirical Analysis of Natural and Cyclical Unemployment at the... 683 115 Table 4 (continued) U Agri Man Serv SRI SNRI Ener FPR PYPP SE TE RKS Temp 5.76 3.31 4.62 6.49 6.08 1.12 0.12 8.58 2.73 12.12 5.02 16.13 5.97 Valladolid 18.18 6.75 22.17 60.19 44.26 15.92 0.57 39.47 14.26 51.01 19.46 145.61 31.23 5.86 3.29 4.39 7.17 5.46 2.29 0.24 8.66 3.35 11.13 6.48 26.94 4.25 Zamora 16.28 25.17 10.12 51.96 35.74 16.21 0.66 28.99 12.07 37.12 13.83 162.02 31.23 4.51 9.56 2.10 6.80 4.54 2.84 0.32 5.54 1.91 9.01 3.97 40.00 4.25 Total 16.25 12.84 17.62 57.64 42.74 14.89 1.07 38.63 13.95 49.21 15.30 154.06 34.36 7.48 9.69 7.65 9.84 8.66 3.69 1.26 8.99 2.74 13.60 5.69 33.21 7.03 The first value refers to the mean value and the second value to the standard deviation Source: Authors’own. Information provided by the INE, IVIE and the ECL 684 J. Cuéllar-Martín et al. 116 0 20 40 0 20 40 0 20 40 0 20 40 0 20 40 0 20 40 0 20 40 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 Albacete Alicante Almeria Asturias Badajoz Balearic Islands Barcelona Burgos Cantabria Castellon Ciudad Real Corunna Cuenca Caceres Cadiz Cordoba Girona Granada Guadalajara Guipuzcoa Huelva Huesca Jaen Leon Lleida Lugo Madrid Murcia Malaga Navarre Ourense Palencia Palmas (Las) Pontevedra Rioja (La) Salamanca S C Tenerife Segovia Seville Soria Tarragona Teruel Toledo Valencia Valladolid Biscay Zamora Saragossa Alava Avila Fig. 5 Natural unemployment (UNR it ) by province (1984–2012). Source: Authors’own 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 0 5 10 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 1980 1990 2000 2010 Albacete Alicante Almeria Asturias Badajoz Balearic Islands Barcelona Burgos Cantabria Castellon Ciudad Real Corunna Cuenca Caceres Cadiz Cordoba Girona Granada Guadalajara Guipuzcoa Huelva Huesca Jaen Leon Lleida Lugo Madrid Murcia Malaga Navarre Ourense Palencia Palmas (Las) Pontevedra Rioja (La) Salamanca S C Tenerife Segovia Seville Soria Tarragona Teruel Toledo Valencia Valladolid Biscay Zamora Saragossa Alava Avila Fig. 6 Cyclical unemployment (UC it ) by province (1984–2012). Source: Authors’own An Empirical Analysis of Natural and Cyclical Unemployment at the... 685 117 concluded that spatial dependence also seems to be caused by factors different from those variables considered in this paper. References Aigner, D., Lovell, C. K., & Schmidt, P. (1977). 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Cuéllar-Martín et al. 128 CAPÍTULO 3 Labor supply and the business cycle: The “Bandwagon Worker Effect” 129 130 FULL ARTICLE Labor supply and the business cycle: The “bandwagon worker effect”  Angel L. Martín-Román | Jaime Cuéllar-Martín | Alfonso Moral Department of Economic Analysis, University of Valladolid, Spain Correspondence  Angel L. Martín Román, Department of Economic Analysis, University of Valladolid, Spain. Email: [email protected] Funding information Spanish Ministry of Economy, Industry, and Competitiveness, Grant/Award Numbers: CSO2015-69439-R, ECO2017-82227-P Abstract The relationship between labour force participation and the business cycle is a common topic in economic literature. However, few studies have examined if the cyclical sensitivity of labour force participation is influenced by social effects. In this paper, we construct a theoretical model defining a relatively new hypothesis, the bandwagon worker effect (BWE). We use spatial econometrics techniques to test the existence of the BWE in the local labour markets in Spain. Our results reveal a positive spatial dependence in the cyclical sensitivity of labour force participation that decreases as we fix a laxer neighbourhood criterion, which verifies the existence of the BWE. KEYWORDS bandwagon effect, business cycle, labour force participation, regional labour markets, spatial dependence JEL CLASSIFICATION C23; D03; E32; J21; R23 1|INTRODUCTION The aim of this paper is to analyse how the relationship between the business cycle and labour force participation (LFP) may be influenced by social effects. 1 The so-called bandwagon effect (BE) is now a useful element to better 1 By social effects in this paper we mean the social influence over an individual's behaviourbehaviour of the perceived average behaviourbehaviour of his/her peers. Manski (1993, 2000) and Dietz's (2002) name them social interactions or neighborhood effects and account for the different types of social effects (i.e. endogenous effects or peer effects, correlated effects and exogenous effects). Martín-Román, Moral de Blas, and Martínez-Matute (2015) delve into that issue from a spatial analysis perspective. Received: 14 December 2018 Revised: 8 May 2020 Accepted: 8 May 2020 DOI: 10.1111/pirs.12542 © 2020 The Author(s). Papers in Regional Science © 2020 RSAI Pap Reg Sci. 2020;1–36. wileyonlinelibrary.com/journal/pirs 1 131 understand the demand for goods and services (Leibenstein, 1950). Because the labour supply is, ultimately, demand for leisure, we deem that the BE might also operate in the labour market. Notably, some studies have already explored this possibility (Blomquist, 1993; Grodner & Kniesner, 2006, 2008; Vendrik, 1998). Additionally, papers have investigated the influence of social influence over individuals' decisions to participate in the labour market (e.g., Clark & Summers, 1982; Kapteyn & Woittiez, 1987; Romme, 1990; Vendrik, 1998; Neumark & Postlewaite, 1998). Or more closely related to this research, because they have explicitly adopted a spatial approach, we refer to Fogli and Veldkamp (2011) and Halleck-Vega and Elhorst (2017). 2 However, no one has studied the effect of that social influence on the cyclical sensitivity of the aggregate labour supply. Our research links this social effect to the cyclical properties of LFP and coins a relatively new hypothesis, the bandwagon worker effect (BWE). The relationship between the business cycle and LFP has produced much academic work. This body of research has produced two key concepts: added worker effect (AWE) and discouraged worker effect (DWE). Here, we develop a theoretical framework in which the BWE interacts with the AWE and DWE to better understand cyclical movements in the labour supply. In a second step, we test empirically whether the BWE is a significant factor when considered together with the AWE and the DWE. According to our review of the literature, we are the first to present and discuss this hypothesis. 3 This is the value added of the paper. The critical assumption of this research is that an individual's labour supply decisions are conditioned to a certain extent by his/her neighbours' decisions regarding their labour market activity. To formalize that idea, in our conceptual framework, individuals emulate to some degree their neighbours' behaviour with regard to their labour supply decisions. The aforementioned social effect may also be interpreted by an aggregation process, as a positive spatial correlation among the spatial units considered. Thus, the previous discussion implies that the participation rate (PR) of a spatial unit surrounded by high-level PR spatial units would higher than otherwise and vice versa. This positive spatial correlation between the levels of labour PRs can be translated into a positive spatial correlation between the cyclical sensitivity of those PRs. Hence, we assume that a geographical neighbourhood is a tool to capture the degree and the intensity of the social effects, as will be explained in greater detail later. 4 We assume global spatial correlation for four reasons. First, from a conceptual point of view, we posit that the social phenomenon analysed should cause feedback effects because of its nature. Second, the literature on this topic indicates the same direction (Fogli & Veldkamp, 2011). Third, our theoretical setting also assumes a global spatial dependence. Finally, econometric reasons, discussed later, support this view. We use Spanish data because the amplitude of the Spanish business cycle is larger than that of most of the developed countries. Furthermore, it is possible to find a sufficiently long time series and with an appropriate spatial disaggregation to conduct feasible a study such as this. 5 In addition, Spain is made up of 50 provinces (NUTS 3 regions), 6 which allows us to apply spatial econometric techniques with a high degree of reliability and accuracy. The results obtained show a positive, significant global spatial dependence in the cyclical sensitivity of the LFP in the Spanish provinces. According to our theoretical approach, this finding proves that the BWE is a key phenomenon to help understand the overall functioning of the aggregate labour market. Moreover, we find that as the neighbourhood definition becomes laxer, the strength of the social effect diminishes. This outcome is consistent with the theoretical framework developed here. 2 There are a number of papers analyzing some spatial aspects of the aggregate labor markets, published recently (e.g., Cracolici, Cuffaro, & Nijkamp, 2007; Halleck-Vega & Elhorst, 2014, 2016; Overman & Puga, 2002), that are somehow related to this research too. 3 Fogli and Veldkamp (2011) do build a theoretical model to account for social effects on female LFP from a geographical perspective and test that hypothesis by using spatial econometrics techniques, as we do in this research. Nevertheless, neither the theoretical setting nor the empirical strategy is the same as ours. Moreover, the aim of their investigation differs from ours. 4 See, for instance, Martín-Román, Moral de Blas & Martínez-Matute (2015). 5 In this vein, Ball, Leigh, and Loungani (2017), Bande and Martín-Román (2018), and Porras-Arena and Martín-Román (2019) have provided empirical evidence of the large size of the Spanish business cycle, particularly with regard to the labour market outcomes. 6 The 50 Spanish provinces correspond to the third level (NUTS 3) of the Nomenclature of Territorial Units for statistics, see: http://ec.europa.eu/eurostat/ web/nuts/overview. 2MARTÍN-ROMÁN ET AL. 132 The remainder of the work is organized as follows. Section 2 offers a review of the literature related to the topic. Section 3 develops the theoretical model. Section 4 presents the methodology used to study the relationship between the labour PRs and the business cycle and to test the BWE. Section 5 describes and explains the results obtained in the cyclical sensitivity analysis and in the spatial dependence analysis. Section 6 includes extensions to the empirical analysis and sensitivity checks. Section 7 offers economic policy implications. Finally, Section 8 sums up the most relevant conclusions. 2|LITERATURE REVIEW Based on the discussion in Section 1, several strands of literature are relevant to our inquiry. First, the research on the LFP pattern over the business cycle constitutes the conceptual basis on which we build our approach. Spatial analysis is also at the core of this research because our theoretical framework predicts a spatial relationship that affects the LFP reaction to the business cycle and because such a relationship is then tested by means of spatial econometrics' techniques. Thus, the literature that has analysed spatial labour markets' functioning is also of interest. The last strand of literature has examined the influence of social effects on labour market outcomes, and we pay particular attention to research that has used spatial analysis to determine the influence of such social effects. The relationship between the LFP and the business cycle has been an active research topic for decades. The interest is probably because of its crucial implications on the correct measurement of actual unemployment and, as a consequence, on the correct intensity of the monetary and fiscal policies to be implemented. The two key concepts in the relationship between the business cycle and the LFP are the AWE (Humphrey, 1940; Woytinsky, 1940) and the DWE (Long, 1953; Mincer, 1962) hypotheses. According to the conventional view of the AWE (Woytinsky, 1940), some breadwinners lose their jobs during an economic downturn. As a consequence, their spouses would experience a reduction in non-labour income, reducing their reservation wage, and at an aggregate level, increasing the labour force. The opposite would be true in an economic boom. Hence, this effect establishes an overestimation of the unemployment rate during downturns and recessions and vice versa during strong economic growth periods. The original idea of the DWE (Long, 1953, 1958) holds that when the likelihood of finding a job decreases, some workers cease their active job searches (i.e., they become inactive), and that the opposite occurs when the likelihood of finding a job increases. The rationale behind this is that as the expectations of finding a job decrease, the transaction costs linked to the search process could exceed the benefits expected. In summary, through this effect, the LFP exhibits a pro-cyclical pattern of an underestimation of the unemployment rate in booming periods and an overestimation during downturns and recessions. As these two hypotheses predict opposite patterns for LFP changes throughout the business cycle, determining which prevails over the other is an empirical question. The observed evidence on these two effects is mixed: Some studies have demonstrated a prevalence of AWE over DWE, and others have demonstrated that DWE is stronger than AWE, depending on various factors of the labour market analysed (e.g., geographical location, gender). For instance, Wachter (1972, 1974) and Tano (1993) have demonstrated that both effects offset each other. Specifically, in Maloney (1987) and Emerson (2011), the AWE has dominated in the United States. Del Boca, Locatelli, and Pasqua (2000) and Ghignoni and Verashchagina (2016) have identified the same effect for Italy. Parker and Skoufias (2004) detect empirical evidence of a prevailing AWE in Mexico, and Gałecka-Burdziak and Pater (2016) do the same for Poland. In the Spanish case, this effect is dominant in Prieto-Rodríguez and Rodríguez-Gutiérrez (2000, 2003), and partially in Congregado, Golpe, and Van Stel (2011). Regarding the research to find a prevailing DWE, the pioneering work by Long (1958) and Clark and Summers (1981), Leppel and Clain (1995), or Benati (2001) have demonstrated that this effect predominates in the United States. In Darby, Hart, and Vecchi (2001), the DWE is predominant for the case of women between 45 and 54 years old in Japan, France, and the United States. Similarly, empirical evidence of a noticeable DWE, in net terms, MARTÍN-ROMÁN ET AL.3 133 provinces (NUTS 3) in the period 1977–2015 (Table A2 in Appendix C provides detailed information on the variables). Table 2 exposes the results of estimating equation 5 when the cyclical components of the variables are obtained by the application of the HP filter with λ= 400. Additionally, and because of the length of the period, we analyse what occurs in two shorter periods: 1977–1996 and 1997–2015. In this manner, we test more precisely the effect of the business cycle over the LFPRs in Spain and the robustness of the results. There are three main reasons to split the full period into these two sub-periods. First, each of these two sub-periods represents, approximately, a complete business cycle. Second, in the last years of the 1990s, Spain experienced a large wave of immigration (Carrasco, Jimeno, & Ortega, 2008) that generated notable changes in the economic dynamics of the Spanish labour market (Farré, González, & Ortega, 2011). Third, the length of these two sub-periods is approximately equal (20 and 19 years, respectively). columns (2) and (3) inTable 2 present the estimations of these sub-periods. The results show 22 statistically significant coefficients for the period 1977–2015, and the DWE prevails over the AWE in nineteen of them. In the first sub-period (1977–1996), 27 provinces present statistically significant results, and the DWE is the most relevant effect. The AWE is present only in four territories. For the second subperiod (1997–2015), seven provinces show statistically significant results, and the DWE is the predominant effect in four of them. To test the robustness of the results, we re-estimate the sensitivity of the LFP with the cyclical components obtained by using the QT procedure and the HP filter with λ= 100 (Table A3 in Appendix C). For the whole period, the results are similar to those obtained before, with many statistically significant results, especially when we employ the QT procedure. The principal effect is the DWE, which is present in 30 out of the 34 provinces that have statistically significant results. For the two sub-periods, the DWE also predominates in most of the provinces where the results are statistically significant. We only found the AWE in Lugo and Corunna (A) between 1977 and 1996 and in Palencia, Caceres and Huelva between 1997 and 2015. In the case of the HP filter with λ= 100, we obtain the same results. The DWE also predominates for the whole period and for the first sub-period. Figure A2 in Appendix C includes two scatterplots that confirm the robustness of the estimations. The results obtained by the HP filter with λ= 400 and λ= 100 are positively correlated with an R 2 equal to 0.85 and a correlation coefficient (ρ) of 0.92. Additionally, the same pattern is maintained when we observe the relationship between the estimations of the HP filter with λ= 400 and the QT procedure; in this case, the R-squared is 0.79, and ρis 0.89. 5.2 |Spatial analysis of the cyclical sensitivities We have estimated the cyclical sensitivities. Now, we study whether there is a social influence in our results. The theoretical model suggested that the PR cyclical pattern of a specific area is positively related to the cyclical pattern shown in the PRs of neighbouring areas. This effect, named BWE, may be easily tested by means of spatial econometric techniques in line with those expressed in Equation 4. To begin the analysis, we must establish a neighbourhood criterion such as the k-nearest neighbours (Knn) or the inverse distance (ID). 20 To achieve the goal of this paper, we determine that ID and nearest neighbour are the appropriate spatial weight matrices because part of the contribution of this research is to test if the social effect is weaker when spatial proximity is less evident. The advantage of these two types of spatial matrices is that we can graduate spatial proximity in a continuous manner. In addition, the distance matrix enhances the importance of proximity with less weight to farther locations (Bertinelli & Nicolini, 2005). It is true that, by using contiguity spatial matrices, we can define the first-order neighbourhood, second neighbourhood, and so forth; however, we conclude that this is insufficiently continuous. Moreover, we have islands in our database, causing the well-known drawbacks of the contiguity spatial matrices. Notably, we did not 20 See O'Sullivan and Unwin (2010) for more detailed information about the Knn and ID matrixes. 10 MARTÍN-ROMÁN ET AL. 140 TABLE 2 Cyclical sensitivity of the LFP (HP λ= 400) 1977–2015 1977–1996 1997–2015 Alava −0.140* −0.320*** −0.006 Albacete 0.030 −0.031 0.040 Alicante −0.087 −0.223** −0.007 Almeria −0.112** −0.557*** −0.039 Asturias −0.006 0.001 0.009 Avila 0.046 0.185** 0.076 Badajoz 0.003 −0.207*** 0.106 Balearic Islands −0.043 −0.245** 0.038 Barcelona −0.055 −0.052 −0.062 Burgos −0.134* −0.152 −0.109 Caceres 0.102** −0.040 0.159*** Cadiz 0.047 0.012 0.050 Cantabria −0.170** −0.179 −0.187** Castellon de la Plana −0.139** −0.275** −0.090 Ciudad Real −0.068 −0.105 −0.033 Cordoba 0.000 −0.173** 0.076 Corunna (A) 0.080 0.633*** −0.105 Cuenca −0.041 −0.155 0.010 Girona −0.259*** −0.512*** −0.142 Granada −0.010 −0.218*** 0.057 Guadalajara −0.190*** −0.265*** −0.085 Guipuzcoa −0.169** −0.105 −0.293** Huelva 0.075* −0.112* 0.189*** Huesca −0.080 0.002 −0.140 Jaen 0.029 −0.176** 0.130** Leon 0.007 −0.342* 0.055 Lleida −0.138 0.335** −0.170 Lugo 0.164* 0.508** 0.109 Madrid −0.142** −0.063 −0.196** Malaga 0.034 0.020 0.043 Murcia −0.095* −0.418*** −0.032 Navarre −0.178** −0.141 −0.194 Orense −0.076 −0.707*** 0.033 Palencia 0.034 −0.113 0.121 Palmas (Las) −0.094* −0.208** −0.013 Pontevedra −0.090 0.007 −0.115 Rioja (La) −0.158** −0.185** −0.134 Salamanca 0.072 0.053 0.111 S C Tenerife 0.031 0.010 0.010 Segovia −0.077 0.053 −0.140 Seville −0.077* −0.051 −0.074 (Continues) MARTÍN-ROMÁN ET AL.11 141 use socioeconomic weight matrices because our phenomenon has a clear spatial rationale. In this paper, we use ten different Knn matrices (K=1…10) where the specification of the spatial weights is: SWi,j =1, if centroid ofjisoneof theknearest centroids to that ofi 0, otherwise :  We also apply ten ID matrices for different values of α(α= 3,2.75,…0.75) and the following spatial weights: SWij =d−α ij ,ifi6¼ j 0, otherwise , where αis any positive parameter, and d i,j is the distance between regions iand j. Table 3 presents the results of Global Moran's Ifor the cyclical sensitivity of the LFP obtained with the HP method with λ= 400. 21 For the period 1977–2015, the results show a positive spatial dependence with both sets of matrices. The analysis of the sub-periods indicates that between 1977 and 1996, a positive spatial dependence is observed either when we consider less than three neighbours or when the distance is more penalized. From 1997 to 2015, a positive spatial dependence is again observed for all the matrices, but it is weaker than in the case of the whole period. Additionally, a test to detect local spatial dependence is implemented. The local Moran's Istatistic and two neighbouring matrices are used: five nearest neighbours and ID with α= 1. The results show a higher concentration of DWE in the northeast of Spain, whereas the AWE is more common in the east and south (figure A3 in Appendix C). To test the robustness of our results, we perform the spatial analysis using the values obtained by the QT procedure and the HP filter with λ=100 (Table A4 in Appendix C). In the case of the QT procedure, the results show positive spatial dependence both for the whole period and for the two sub-periods. This effect is stronger than before and occurs for the two sets of spatial matrices. If we use the HP filter with λ= 100, the results are similar to those obtained with λ= 400. The spatial dependence is present both for the entire period and for the two groups of matrices. The analysis by sub-periods only shows spatial dependence between 1997 and 2015 and for some spatial 21 We also perform the same analysis by putting a value equal to 0 in those provinces where we have obtained results of the cyclical sensitivities that are not statistically significant (no prevalence of either the AWE or the DWE over the other in these territories). The results are very similar to what we present inTable 3. Detailed results are available from the authors upon request TABLE 2 (Continued) 1977–2015 1977–1996 1997–2015 Soria −0.135 −0.526*** 0.066 Tarragona −0.245*** −0.378*** −0.116 Teruel −0.126 −0.268* −0.151 Toledo −0.080 −0.131 0.005 Valencia −0.095** −0.115* −0.116 Valladolid −0.231*** −0.400*** −0.117 Vizcaya −0.119* −0.081 −0.177 Zamora −0.170** −0.163 −0.213** Saragossa −0.063 −0.139* −0.038 Note: *, **, and ***shows statistical significance at 10%, 5%, and 1% levels, respectively. 12 MARTÍN-ROMÁN ET AL. 142 matrices. Figures 2 and 3 present the scatter plots of Global Moran's I for the HP filter (λ= 400) when three Knn matrices (K = 1, 3 and 5) and three ID matrices (α= 1, 2 and 3) are used. The spatial correlation that is present in figures 2 and 3 is consistent with the interaction presented in figure 1 and allows us to confirm the presence of the BWE. This corroborates the existence of a social effect, which causes the cyclical sensitivity of the LFP in one territory to be influenced by what occurs in its neighbouring regions. 22 FIGURE 2 Global scatterplot diagrams of Moran's I (HP λ= 400) (1977–2015) 22 Detailed results for the other spatial matrices and the other two methods (QT procedure and HP (λ= 100)) are available from the authors upon request. TABLE 3 Global spatial dependence analysis (HP λ= 400) 1977–2015 1977–1996 1997–2015 Knn = 1 0.517*** 0.385** 0.398** Knn = 2 0.376*** 0.196* 0.306*** Knn = 3 0.336*** 0.112 0.297*** Knn = 4 0.344*** 0.059 0.287*** Knn = 5 0.303*** 0.002 0.255*** Knn = 6 0.277*** −0.015 0.259*** Knn = 7 0.249*** 0.003 0.218*** Knn = 8 0.242*** 0.003 0.228*** Knn = 9 0.220*** −0.028 0.214*** Knn = 10 0.203*** −0.048 0.193*** ID (α= 3) 0.299*** 0.166** 0.238*** ID (α= 2.75) 0.283*** 0.144** 0.229*** ID (α= 2.50) 0.265*** 0.121** 0.219*** ID (α= 2.25) 0.244*** 0.098** 0.206*** ID (α= 2) 0.220*** 0.075* 0.190*** ID (α= 1.75) 0.193*** 0.053* 0.170*** ID (α= 1.50) 0.163*** 0.033 0.147*** ID (α= 1.25) 0.130*** 0.016 0.121*** ID (α= 1) 0.098*** 0.003 0.093*** ID (α= 0.75) 0.065*** −0.007 0.064*** Notes: The values in the table refer to the Global Moran's I. The null hypothesis refers to the absence of spatial dependence. *, **, and *** show statistical significance at 10%, 5%, and 1% levels, respectively. MARTÍN-ROMÁN ET AL.13 143 The next step in the spatial analysis is to study the evolution of the spatial dependence before changes in neighbourhood parameters. As explained, each neighbourhood criterion includes ten different levels. Depending on the spatial correlation at each level, we can understand how the social effect works. The results inTable 3 show that as we increase the number of neighbours (or we reduce the αparameter), the spatial correlation coefficient decreases. To explain this point in more detail, Figures 4 and 5 depict the evolution of the spatial correlation as the matrix parameters of the two sets change. The decreasing slope in both figures indicates that the BWE is caused by what occurs in the nearest territories. As we increase the number of provinces that we consider neighbours, the social effect tends to disappear. 23 6|EXTENSIONS The results presented in Section 5 have demonstrated the existence of a BWE; thus, we must broaden the analysis to discard other possible explanations. To this end, two spatial models are presented that allow us to confirmation of the influence of the closest environment and global spillovers, from a geographical point of view, over the cyclical FIGURE 4 Evolution of the global spatial dependence of the Knn matrixes (1977–2015) (HP λ= 400) 23 Detailed results for the other two methods (QT procedure and HP with λ= 100) are available from the authors upon request. FIGURE 3 Global scatterplot diagrams of Moran's I (HP λ= 400) (1977–2015) 14 MARTÍN-ROMÁN ET AL. 144 sensitivity of the PR. Appendix B also includes a sensitivity analysis with specifications that control for population composition, methodological changes, labour reforms, or data structure. Regarding cross-sectional dependence, a logical assumption is that the correlation should be related to the variables not included in the model and would be detected by estimating an SEM such as that presented in Equation 7: CPRit =α+βi1 CURit +β2D2001 +μi+εit,ð7Þ εit =λWεit +ηi,t with ηi,t ~ N0:σ2 ηIn hi : From the results obtained in this new estimation, the spatial correlation of the cyclical sensitivity is tested again with the two previous weight matrices (ID and five nearest neighbours). The results presented in Figure 6 show that the spatial correlation decreases slowly. However, a statistically significant BWE is maintained even when spatial dependence in the errors is also detected (Table A5 in Appendix C includes the cyclical sensitivity coefficients and the lambda parameter related to the SEM). The second spatial approach is the spatial lag model or spatial autoregressive model (SAR). This model is a global spillover specification that includes an additional term obtained as the product of the spatial weight matrix and the cyclical component of the PR, in Equation 8: CPRit =α+ρWCPRit +βi1 CURit +β2D2001 +μi+εit:ð8Þ In this case, because of the presence of the spatial lag of the dependent variable, a change in a single observation (region) associated with any given explanatory variable affects the region (direct impact) and potentially affects all other regions indirectly (indirect impact). The total effect is the sum of both the direct and the indirect or global effect and is obtained as β i1 (1 −ρW) −1 . When the global spatial correlation test over that total effect is performed, the Moran I is not significantly different from 0 (Figure 7). This result makes sense because the SAR model captures the global spillovers and the spatial lag coefficient of the dependent variable is positive and significant (Table A5 in Appendix C includes the total effects of changes in CUR variables and the rho parameter). 24 24 As an additional measure of robustness, we have estimated a spatial Durbin model that includes the spatial lag in the cyclical component of the unemployment rate; once again, the rho parameter was positive and significant (results are available upon request of the authors). FIGURE 5 Evolution of the global spatial dependence of the Inverse Distance matrixes (1977–2015) (HP λ= 400) MARTÍN-ROMÁN ET AL.15 145 The similarity in magnitude and significance of ρand λseems to indicate that the spatial correlation was included in the disturbance of the SEM (LeSage, 2014). If we add to this that the spatial dependence on the cyclical sensitivity is still present when estimating the SEM and disappears with the SAR model, we consider that the latter is the true data-generating process. These results, and especially the value of the ρparameter in the SAR model, confirm the presence of global spatial dependence (LeSage & Pace, 2009; García-López, Nicolini, & Roig, 2020; López-Torres, Nicolini, & Prior, 2017) and therefore also the BWE hypothesis. 7|DISCUSSION AND POLICY IMPLICATIONS We have offered empirical evidence of the existence of the BWE; thus, in the following paragraphs, we propose economic policy implications. We organize the economic policy implications and recommendations into three categories: proposals related to the heterogeneity in the cyclical response of the LFP in different spatial units; economic policy consequences related to the spatial dependence in the LFP cyclical patterns (i.e., the significance of the BWE); and policy suggestions resulting from the particular administrative hierarchy among NUTS 2 and NUTS 3 units in Spain. FIGURE 6 Global scatterplot diagrams of Moran's I: SEM (1977–2015) (HP λ= 400) FIGURE 7 Global scatterplot diagrams of Moran's I: SAR (1977–2015) (HP λ= 400) 16 MARTÍN-ROMÁN ET AL. 146 First, our results show that local labour markets react differently to cyclical fluctuations. More precisely, we find that in some Spanish NUTS 3 units, the DWE dominates the AWE; in other units, the AWE is stronger than the DWE; and there are spatial units where both effects offset each other. In general, the economic measures should be conducted while considering the territorial context; thus, policy-makers should not design economic policies that have the same intensity of effect in all regions. In other words, different territories require policies tailored to the labour market dynamics of each territory. More specifically, this spatial heterogeneity has implications for the implementation of both aggregate demand policies and policies on the supply side. As aforementioned, during a downturn, if the DWE dominates the AWE, the unemployment rate is understated, whereas if the AWE prevails over the DWE, the unemployment rate is overstated. Evidently, the opposite is true during an economic upturn. Hence, an obvious economic policy implication of our results is that in those geographical areas in which we have estimated a prevailing DWE, economic authorities ought to implement a more expansionary fiscal policy (e.g., government spending increases or tax cuts) than indicated by the official unemployment rate during a recession. Following the same line of reasoning, but from an aggregate supply perspective, additional active labour market policies (e.g., training schemes, public employment services) should be applied in those spatial units with a predominant DWE during downturns, and vice versa. In addition, our estimates of the Spanish spatial units with a prevailing DWE or AWE serve as a guideline for policy-makers to better distribute a limited fiscal budget in different business cycle phases. Policy-makers should devote less (more) budgetary resources to spatial units with a predominant AWE during recessions (expansions) than suggested by the measured unemployment rate and more (less) to those with a prevailing DWE. This economic policy rule would enhance efficiency as long as the fiscal budget remained unchanged at the aggregate level. Second, our evidence shows a significant spatial dependence in the cyclical sensitivity of LFP, that is, what we name the BWE. Thus, cyclical patterns that the labour force follows in a given territory are guided and conditioned by the behaviour of its neighbouring territories. For this reason, it is necessary to consider this social effect when analysing the policy implications of the labour market policies. For instance, the implementation of macroeconomic policies by the regional governments could cause spillover effects beyond those initially expected. The obvious economic policy implication regarding this topic is that regions cannot be studied in isolation from each other but interact with their neighbours. However, this statement is too general. A more specific economic policy implication regarding the influence of the BWE is that the policies implemented should pay more attention to the existence of spatial areas rather than single spatial units to better understand the relationship between the labour market participation and the state of the business cycle. If the BWE is a relevant socioeconomic phenomenon, we might expect the DWE and the AWE to spread across neighbouring spatial units during economic upturns and downturns. In this manner, the overstatement or understatement of true unemployment across spatial units would be contagious, and consequently, the correct economic policy; even more importantly, the correct intensity of such a policy should be determined by adopting a supra-provincial perspective. The last group of economic policy implications is related to the particular administrative division of the Spanish territory NUTS 3 units in Spain (provinces), which are grouped into NUTS 2 units (autonomous communities) in some cases but not in others. Thus, in a limited number of cases (Madrid, Balearic Islands, Asturias, Cantabria, Rioja (La), Murcia, and Navarre), a coincidence is observed between the NUTS 2 and NUTS 3 levels, but this does not occur in the remaining 43 Spanish provinces. Furthermore, our findings imply that the actions of the regional governments at the NUTS 2 level could affect either other NUTS 2 territories or NUTS 3 units that do not belong to that region. More importantly, Spanish NUTS 2 units manage a significant portion of the government's budget, whereas NUTS 3 units run much less of it. 25 This entails the autonomous communities playing a key role from an economic and political point of view, and the Spanish provinces have a limited capacity to act. As our results point to a strong 25 Spanish NUTS 2 (autonomous communities) represented approximately 30% of public expenditure in Spain during 2015 and 2016. NUTS 3 units (provinces) was approximately 11% of public spending in Spain during those same years (OECD, 2017). MARTÍN-ROMÁN ET AL.17 147 interdependence at the NUTS 3 level, co-ordination of economic policies among neighbouring NUTS 2 regional governments is required because there are critical spillover effects beyond the NUTS 2 level administrative division. The aforementioned issue could be addressed from two points of view. First, political leaders governing neighbouring autonomous communities might spontaneously seek higher co-ordination in their policies against unemployment. In this vein, supra-regional committees managing labour market policies could be created to co-ordinate political efforts to minimize the true unemployment problem, by devising strategies that account for the spillover effects. Second, if regional (NUTS-2) governments do not reach an agreement by themselves, the Spanish central government might act to promote such an agreement. Here, again, there are two options: (i) the Spanish central government might create by itself an inter-regional committee where the representatives in charge of labour issues in each autonomous community could hold discussions with other regional representatives to make agreements that seek the co-ordination; and (ii) the Spanish central government might directly act to solve this question. More precisely, it could create a political institution that depends on the Ministry of Labour (e.g., a Secretary of State or a General Directorate), devoted exclusively to co-ordinating different regional labour market policies. 26 8|CONCLUSIONS The main purpose of this paper is to test whether the relationship between the business cycle and LFP in any given area is affected by the behaviour of its neighbours. To achieve this objective, we first elaborate a microeconomic decision model to conceptualize the AWE and the DWE. In a second stage, using an aggregation process, we incorporate the BWE as a social effect. Finally, we use spatial econometrics techniques to test for the existence of the BWE in Spanish local labour markets. The first part of this work studies the cyclical sensitiveness of the LFP by employing a panel dataset composed of the 50 Spanish provinces during the period 1977–2015. Additionally, because of the length of the period of study, we extend our analysis to two sub-periods (1977–1996 and 1997–2015). Regardless of the method used to obtain the cyclical components of the variables (HP with λ=400, HP with λ=100, or QT), we conclude that the DWE dominates in most of the territories and in periods where the coefficients are significant. Our theoretical model demonstrates that the cyclical sensitivity of the LFP in one area is influenced by the behaviour of its neighbours. To study that finding, after conducting a macroeconomic aggregation process, we coined the BWE and tested it with standard spatial econometric techniques we derived directly from our theoretical discussion. Using different neighbourhood criteria, the results reveal the presence of a positive global spatial dependence in the cyclical sensitivity of the LFP in the Spanish local labour markets. This is consistent with what we illustrate in our theoretical framework and verifies the existence of the BWE. Finally, the empirical analysis shows that the intensity of the BWE is not linear, that is, as we fix a laxer neighbourhood criterion, the strength of the BWE decreases. Based on our work, we propose economic policy implications that affect the outcome of the regional labour markets. First, policy-makers should consider that the regions may react differently to the economic shocks of the business cycle. Thus, the policies should be applied while considering the economic dynamics of each zone because the application of economic policy with the same intensity for all the regions could lead to heterogeneous results. Another notable factor is that the territories interact with their neighbours; thus, they are not fully independent of each other. In this manner, policy-makers should focus on spatial areas instead of spatial units because of the existence of social effects among the territories that might condition the outcome of the economic policies. Our work corroborates that social effects play a key role in implementing labour market policies. This implies that these phenomena could generate types of effects that are not initially planned and that affect the economic dynamics of 26 Coordination among different actors is proposed, but in practice this could be quite challenging. A main consideration is thus how feasible this wouldbe (e.g., coordination failure, transaction costs, and so on and so forth). These issues might be included within the scope of the political economy and constitute an appealing avenue for future research. 18 MARTÍN-ROMÁN ET AL. 148 neighbouring areas, even when the neighbours belong to a different territorial administration. That interdependence at the NUTS 3 level requires co-ordination of the economic policies among neighbouring NUTS 2 regional governments. ACKNOWLEDGEMENTS The first and second authors were partially supported by the Spanish Ministry of Economy, Industry, and Competitiveness under project ECO2017-82227-P. The third author was partially supported by the Ministry of Economy, Industry, and Competitiveness under project RTI2018-099666-B-100. ORCID  Angel L. Martín-Román https://orcid.org/0000-0002-4777-4324 Alfonso Moral https://orcid.org/0000-0001-5462-8133 REFERENCES Backus, D. K., & Kehoe, P. J. (1992). 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