Analysis of preferences for freight transport using advanced choice models

Tesis Doctoral Analysis of preferences for freight transport using advanced choice models Ana Isabel Arencibia Pérez Las Palmas de Gran Canaria Septiembre 2015 1 2 3 Anexo I 4 5 Anexo II Departamento/Instituto/Facultad: Facultad de Economía, Empresa y Turismo. Programa de doctorado: Programa Oficial de Doctorado en Perspectivas Científicas sobre el Turismo y la Dirección de Empresas Turísticas. Título de la Tesis Analysis of preferences for freight transport using advanced choice models. Tesis Doctoral presentada por D/Dª Ana Isabel Arencibia Pérez. Dirigida por el Dr/a. D/Dª. Concepción Román García. Codirigida por el Dr/a. D/Dª. María Feo Valero. El/la Director/a, El/la Codirector/a El/la Doctorando/a, (firma) (firma) (firma) Las Palmas de Gran Canaria, a 21 de septiembre de 2015. 6 7 Agradecimientos Me gustaría comenzar agradeciendo el apoyo financiero recibido por el Ministerio de Fomento a través del proyecto "Modelización de previsiones de tráfico de mercancías y posibilidades de transporte intermodal con Europa (PREVITRANS)", perteneciente al expediente P4/08, en la convocatoria de ayudas del Programa Nacional de Cooperación público-privada, Subprograma de proyectos relativos a transporte e infraestructuras, en el marco del Plan Nacional de I+D+i, 2008-2011. Realizar una tesis doctoral es toda una aventura. Y en esta aventura, en la que voluntariamente me embarqué, he tenido que lidiar con diferentes carreteras, vías y mares. Por suerte, no he estado sola. Desde el comienzo de esta aventura he podido contar con el apoyo y la tutela de Concepción Román y María Feo. Tenerlas como directoras ha sido todo un lujo, no sólo por lo que me han aportado desde el punto de vista académico sino sobre todo por su calidad personal. No como director pero sí como profesional, apoyo y consejero, quiero dar las gracias a Juan Carlos Martín, con el que también he podido contar desde el principio. Gracias a Leandro García por su acogida y profesionalidad durante mi estancia de investigación en la Fundación Valencia Port. Gracias al Departamento de Análisis Económico Aplicado (DAEA), al Instituto Universitario de Turismo y Desarrollo Económico Sostenible (Tides), y al personal que componen ambos órganos por acogerme y por aportarme tanto. Gracias a Juan Luis Jiménez porque aunque en un momento fuimos “más becarios que personas” él siempre ha sido “uno de los nuestros”. Gracias por estar siempre disponible, y por aguantar a un Francisco con muy mal genio y a una secretaria con mucha guasa. Mil gracias a mis Mariposas. Gracias a ustedes esto ha sido mucho más fácil. Que empezásemos siendo compañeras y a día de hoy seamos amigas es lo mejor que me llevo de esta aventura desde el lado personal. Y desde el lado más familiar también tengo mucho que agradecer, pues siempre he contado con el apoyo incondicional de mi familia y amigos. Gracias a todos porque a pesar de no entender muy bien que era eso de la tesis, nunca dejaron de preguntarme y de aportarme todo el apoyo del mundo. Los baches que haya podido tener durante la elaboración de mi tesis doctoral se han hecho mucho más llevaderos gracias a ustedes. Sobre todo cuando me tocó sufrir la muerte de mi marido. Adrián, desde donde quiera que estés, gracias, porque parte de la consecución de esta meta también es tuya. A mis padres nunca podré agradecerles lo suficiente todo lo que siempre han hecho por mí. A ellos les debo todo y por eso les doy las gracias. Y termino con el GRACIAS más grande hacia mi hija. Adriana, gracias, porque cuando todo se tornó completamente oscuro, tú fuiste la luz de un nuevo camino. 8 15 Capítulo 1. Introducción y resumen general 1.1 Motivación y objetivos El transporte de mercancías es una pieza clave en el desarrollo económico de un país. Este tiene un efecto directo tanto sobre la disponibilidad de bienes como sobre los precios a los que estos se venden en el mercado. Es un sector formado por un gran número de empresas, de diverso tamaño y con alto nivel de especialización en determinados segmentos de mercado. La complejidad y heterogeneidad que encierra el transporte de mercancías hace que sea mucho más difícil de analizar que el transporte de pasajeros. Esta es una de las principales razones por las que el sector ha sido menos estudiado. De hecho, muchos de los estudios que se han llevado a cabo en este ámbito se han centrado en el análisis de las cantidades realmente demandadas más que en el estudio de los factores que determinan dicha demanda. La enorme dificultad que entraña la obtención de datos apropiados sin duda constituye uno de los principales motivos de la menor evidencia empírica disponible sobre esta cuestión. Sin embargo, dentro de la estructura productiva 16 de un país, la importancia del transporte de mercancías resulta más que evidente, tanto en el proceso logístico como en el desarrollo económico en general. Esta importancia aumenta cada vez más con la intensificación de la internacionalización de la economía. Normalmente, los bienes no son consumidos en el mismo lugar donde son producidos, lo que implica un proceso en el cual se han de tomar numerosas decisiones interrelacionadas para garantizar que los bienes alcancen su destino. La elección del modo de transporte apropiado se encuentra entre las más importantes de estas decisiones y merece por tanto un análisis detallado, “sobre todo/más aún” si tenemos en cuenta la influencia que la elección de uno u otro modo acabará teniendo sobre el impacto total del sistema de transporte en el bienestar social y medioambiental de los ciudadanos. Por lo tanto, resulta esencial disponer de un buen conocimiento de los factores que afectan la elección del modo para la evaluación de políticas del transporte de mercancías. En efecto, dada la evolución histórica de la distribución modal en España a lo largo de las últimas décadas, caracterizada por un claro predominio del transporte por carretera, la compatibilidad de un mayor crecimiento económico con un desarrollo sostenible del sistema de transporte va a demandar un considerable esfuerzo inversor por parte de las autoridades responsables. Sin embargo, la imperante necesidad de compatibilizar gasto en inversión y estabilidad presupuestaria obliga a los responsables de la política nacional de infraestructuras y transporte a llevar a cabo una evaluación de proyectos 17 cada vez más rigurosa que permita maximizar la eficiencia de los recursos asignados. La capacidad para tomar decisiones eficientes dependerá no obstante del grado de conocimiento que sobre la demanda de transporte se tenga, así como de la precisión con la que se consigan cuantificar los beneficios y costes socioeconómicos asociados a las distintas actuaciones posibles (análisis coste-beneficio, ACB). De esta forma, cada vez son más numerosos los organismos que incorporan el análisis coste-beneficio (ACB) en la evaluación de proyectos de transporte. A diferencia del análisis financiero, en el que únicamente se tiene en cuenta la corriente de ingresos y costes en los que incurre el operador a lo largo del proyecto, en el ACB el beneficio social neto se obtiene mediante la comparación de los beneficios y costes socioeconómicos de todos los agentes afectados por el proyecto. Dichos beneficios y costes incluyen tanto elementos cuyo efecto es fácilmente cuantificable en términos monetarios –puesto que existe un valor de mercadocomo elementos tales como el valor del tiempo para los cuales no existe una medición directa en unidades monetarias y cuya valoración económica plantea por tanto mayores dificultades. Los ahorros en el tiempo constituyen uno de los mayores beneficios derivados de las inversiones en infraestructuras de transporte, tanto en el ámbito de pasajeros como en el de mercancías. A pesar de su importancia, los investigadores aún no han podido 18 alcanzar un consenso, ni sobre la magnitud, ni sobre la naturaleza de los valores del tiempo que deben emplearse en la evaluación de proyectos. La falta de consenso es incluso mayor en lo relativo al transporte de mercancías. En efecto, si bien en relación al transporte de pasajeros puede considerarse que existe cierta evidencia empírica, las dificultades asociadas a la obtención de información en el ámbito de mercancías limitan enormemente las aplicaciones prácticas disponibles y con ello el debate metodológico en torno a la valoración del tiempo de tránsito en dicha área. Dado que el sector del transporte constituye un sector clave de actividad, la Comisión Europea trata de elaborar e impulsar políticas de transporte fiables, eficientes y sostenibles que se traduzcan en un sector próspero y competitivo, pero sin olvidar su objetivo prioritario de compatibilizar el incremento de demanda con un desarrollo sostenible del sistema de transporte. En efecto, mientras que los objetivos de la política común de transporte (PCT) inicial se sustentaban en la voluntad de mejorar las condiciones de vida de los ciudadanos europeos -la realización del mercado interior de transporte permite incrementar la competitividad de los servicios de transporte tanto en términos cuantitativos como cualitativos y con ello la competitividad de las mercancías europeas-, el eje principal de la actual PCT es la definición de una estrategia que permita conjugar el crecimiento económico derivado de la conformación del mercado 19 común con el desarrollo sostenible del sistema de transporte no sólo desde un punto de vista económico, sino también desde un punto de vista social y medioambiental. Ante la apertura de los mercados de transporte y el establecimiento de condiciones de competencia ecuánimes entre los distintos modos de transporte, así como dentro de cada uno de ellos, el transporte de personas y mercancías ha aumentado considerablemente en las últimas tres décadas. No obstante, esto conlleva a su vez un incremento de los costes sociales y medioambientales. De ahí que la política europea de transporte actual aúne esfuerzos para el establecimiento de un principio de “movilidad sostenible”. En líneas generales, la política europea de transporte centra sus esfuerzos en hacer frente a una competencia cada vez mayor fuera de la Unión Europea, y alcanzar un nivel de calidad equitativo en las diferentes infraestructuras del transporte dentro de la UE. Asimismo, se pretende evitar la dependencia del petróleo empleando menos energía y usando otra energía que sea más limpia, reducir la emisión de gases de efecto invernadero, así como disminuir la congestión existente en el tráfico aéreo y por carretera. Las actuaciones de política se han orientado, por tanto, hacia el re-equilibrio del patrón modal, favoreciendo el uso de medios de transporte más sostenibles. La meta es asegurar una gestión eficiente y económica de una movilidad cada vez mayor de personas y mercancías, tratando de minimizar las externalidades negativas que genera este aumento en el número de desplazamientos realizados como, por ejemplo, la 20 contaminación ambiental, el ruido o la congestión, sobre todo en el tráfico por carretera. Se necesita, por tanto, de una visión global que integre medios de transporte con un menor impacto medioambiental, una intermodalidad o el uso combinado de dos o más modos de transporte dentro de una misma cadena, y una atribución equitativa de los costes que generan los diferentes modos de transporte, para alcanzar condiciones de libre competencia entre los mismos. De este modo, en sus Libros Blancos de Transporte de 2001 y 2011, la Comisión establece una serie de pautas a seguir para alcanzar dicho objetivo que se pueden dividir en cuatro bloques de actuación diferenciados. El primero de ellos, aborda aquellas medidas destinadas a alcanzar el reequilibrio del patrón modal y con ello la desconexión entre crecimiento económico y crecimiento de la demanda de transporte sin que para ello sea necesario restringir la movilidad de las personas y de los bienes. El segundo bloque, comprende las medidas que fomentan el desarrollo de los modos alternativos al transporte íntegro por carretera: el transporte marítimo, ferroviario y la combinación de modos para equilibrar el número de transportes que contaminan. Para poder alcanzar el trasvase modal deseado resulta indispensable que los modos de transporte alternativos sean percibidos por el usuario como modos eficientes, capaces de ofertar un servicio de calidad. Con ese objetivo se han puesto en marcha medidas que incidan sobre los modos alternativos mediante la mejora de sus infraestructuras y la puesta en práctica de iniciativas que permitan resolver sus principales ineficiencias, permitiendo de esta 21 forma que constituyan una auténtica competencia para la carretera y desarrollen todo su potencial. Del mismo modo, abarca aquellas medidas destinadas a eliminar los cuellos de botella transfronterizos en los desplazamientos internacionales. El tercer bloque, abarca las medidas relacionadas con la seguridad vial y la transparencia de costes en todos los medios de transporte. Y, por último, el cuarto bloque hace mención a la necesidad de combatir las consecuencias de la globalización del transporte. Todos estos objetivos afectan directamente tanto al transporte de pasajeros como al transporte de mercancías, por lo que resulta fundamental identificar de forma correcta a los tomadores de decisiones en estos ámbitos. Sin embargo, en la comparación entre el sector de pasajeros y el de mercancías, esta identificación resulta mucho más complicada en el segundo caso, dada su heterogeneidad y el elevado número de aspectos y agentes interrelacionados. Resulta fundamental, por tanto, conocer de la manera más precisa posible cómo son las preferencias de los decisores en la gestión del transporte de mercancías. Para ello, la aplicación de las metodologías apropiadas que permitan decidir qué políticas resultan socialmente más rentables, es una tarea especialmente necesaria. Los juicios de los agentes que deciden acerca de la gestión del transporte dependen básicamente de sus creencias o expectativas acerca de las diferentes características o atributos asociados con el servicio y de la importancia de los mismos (Engel et al., 22 1995). Las creencias de estos individuos conllevan asociaciones entre el servicio ofrecido y sus principales características. Estas asociaciones se derivan de su experiencia directa con el servicio prestado, y de sus experiencias pasadas con otros servicios de análoga naturaleza. El peso de los atributos está generalmente relacionado con la importancia relativa que los agentes otorgan a cada atributo. Esto implica que los atributos para medir las preferencias en relación a un servicio, dependan en gran medida del contexto, por lo que, deberían seleccionarse de manera que reflejen tanto la problemática sujeta a evaluación, como el entorno en el que se provee el servicio investigado. En este sentido, se han formulado muchos modelos para evaluar las preferencias de los individuos como una suma ponderada de las creencias acerca de los atributos del servicio, teniendo en cuenta la importancia relativa de dichos atributos. Estos métodos se asemejan a los modelos de decisión multi-atributo que están basados en la teoría del valor o de la utilidad (Keeney y Raiffa, 1993). Estos modelos se han utilizado, en muchas ocasiones, para ordenar conjuntos de alternativas de decisión, caracterizados por múltiples atributos, y son particularmente adecuados para resolver problemas de decisión donde es realmente importante y necesario obtener preferencias cardinales o un ranking de las alternativas disponibles. 23 Dadas las motivaciones expuestas previamente, el objetivo principal de esta tesis doctoral es profundizar en el estudio de las preferencias de los responsables de la toma de decisiones en relación a la elección modal en el transporte de mercancías mediante el desarrollo de modelos avanzados de elección discreta que incorporen los últimos desarrollos alcanzados tanto en lo relativo al diseño de los cuestionarios y obtención de los datos como en lo relativo a la especificación del modelo. El conocimiento en profundidad de dichas preferencias aportará información muy valiosa a la hora de aplicar políticas adecuadas dentro del sector. De este modo, la investigación desarrollada se centra en tres objetivos específicos. En primer lugar, analizar la demanda del transporte de mercancías en un contexto de elección modal a través del uso de modelos de elección, basados en los supuestos tradicionales de las teorías de elección. Para lograr dicho objetivo, se dedica un esfuerzo sustancial a la creación de una base de datos de preferencias declaradas (PD) obtenida a partir del diseño de experimentos eficientes de elección discreta. A partir de ahí, se estudia la heterogeneidad de las preferencias, se obtienen las medidas de disposición a pagar y se analiza la respuesta de la demanda ante distintos escenarios de política. En segundo lugar, evaluar la existencia de asimetrías en las preferencias, cuantificando las discrepancias entre las medidas de la disposición a pagar y la disposición a aceptar por variaciones en el nivel de servicio de los atributos más relevantes que definen la 24 elección modal en el transporte de mercancías. Para ello, se aplican modelos que relajan algunas de las hipótesis de los modelos tradicionales y se incorporan elementos recogidos en la Prospect Theory (Kahneman y Tversky, 1979). Finalmente, en tercer lugar, analizar la heterogeneidad no observada en las preferencias identificando diferentes segmentos o clases latentes. En este caso, la elección modal se estudia considerando modelos de clase latente que incorporan a la especificación de utilidad el efecto de penalizaciones cuando se superan ciertos valores umbrales o cutoffs, previamente declarados por el decisor. De esta forma, el modelo planteado también se aleja de los supuestos tradicionales que asumen el comportamiento compensatorio de los decisores como es caso de los modelos con utilidad lineal en los atributos. 1.2 Metodología El conocimiento de las preferencias de los agentes implicados en los servicios de transporte públicos y privados constituye hoy en día uno de los mayores desafíos del análisis económico debido a la importancia de sus resultados, tanto para las empresas que suministran dichos servicios como para las administraciones públicas encargadas de supervisarlas. 31 k ik k ik i x x k V x x        (1.4) siendo 𝜃𝑥𝑘 + el efecto marginal sobre 𝑉𝑖 de un incremento en 𝑥𝑖𝑘 sobre el valor de referencia 𝑥𝑘 para el atributo k; 𝜃𝑥𝑘 − el efecto marginal en 𝑉𝑖 de un decremento en 𝑥𝑖𝑘 con respecto a 𝑥𝑘; 𝑥𝑖𝑘 += max(𝑥𝑖𝑘 − 𝑥𝑘, 0)𝑦 𝑥𝑖𝑘 −= max(𝑥𝑘− 𝑥𝑖𝑘, 0). En el modelo asimétrico los signos de los parámetros deben ser interpretados de manera apropiada. Así, cuando xi es un atributo no deseable, los signos esperados de los parámetros correspondientes son 𝜃𝑥 +< 0 y 𝜃𝑥 −> 0, dado que 0 0 xi i ixi if x x V xif x x             . Por el contrario, para los atributos deseables yi, los signos esperados para los parámetros correspondientes son 00 yy y    , dado que 0 0 yi i iyi if y y V yif y y             . Tal y como señalaron Masiero y Maggi (2010), la estimación de los diferentes parámetros de ganancias y pérdidas con respecto a los valores de referencia permite analizar las asimetrías en la función de utilidad y, por ende, el cumplimiento o no de la hipótesis de aversión a la pérdida, la cual establece que el impacto en términos 32 monetarios producido por una reducción en el nivel de servicio es superior al producido por una mejora. En el marco de la utilidad simétrica, las variaciones positivas y negativas respecto a un valor de referencia tienen el mismo impacto en la utilidad. En consecuencia, la DAP por mejorar el nivel de servicio y la DAA una compensación por un empeoramiento de dicho nivel, representan magnitudes idénticas. Cuando se considera la especificación asimétrica, estamos en condiciones de obtener una valoración diferente de las ganancias y las pérdidas y, en consecuencia, la DAP y la DAA difieren entre sí. En este sentido, para los atributos no deseables, estas medidas se definen como: x c DAP       y x c DAA      (1.5) Por contra, para los atributos deseables obtenemos que: y c DAP       y y c DAA      (1.6) 33 Donde se ha añadido convenientemente un signo negativo con el fin de obtener magnitudes positivas. Otro aspecto crítico en el análisis de las preferencias de los consumidores es la incorporación de valores umbrales o cut-offs en la percepción de los atributos al proceso de toma de decisiones. Durante décadas, el marco de maximización de la utilidad, donde se asume que los tomadores de decisiones son plenamente racionales y están completamente informados, se ha aplicado con éxito en muchos campos diferentes para modelizar las elecciones de los consumidores. En este sentido, el modelo de utilidad aleatoria con especificación lineal en los parámetros para la utilidad sistemática, supone implícitamente conductas compensatorias por parte de los tomadores de decisiones, es decir, los individuos consideran compensaciones entre los atributos cuando evalúan la utilidad de las diferentes alternativas. Sin embargo, otros científicos sociales han señalado que las personas pueden tener una capacidad limitada a la hora de procesar la información (por ejemplo, Simon, 1955; Tversky y Kahneman, 1974) cuando están tratando de elegir la mejor opción teniendo en cuenta sus restricciones o limitaciones; reconociendo que este marco representa sólo una de las muchas reglas de decisión utilizadas por los individuos (Payne et al., 1993). En este sentido, los individuos pueden exhibir un comportamiento no compensatorio, tales como en el proceso de eliminación por aspectos (EPA) propuesto por Tversky (1972), donde ciertas alternativas pueden ser retiradas del conjunto de elección, si sus atributos no cumplen con unos valores umbral 34 o límites. Esto ha dado lugar a modelos más sofisticados donde las decisiones se modelizan en dos etapas (Manski, 1977). En primer lugar, las alternativas en el conjunto de elección vienen determinadas por un proceso no compensatorio, como el EPA, y en segundo lugar, las restantes son evaluadas utilizando una regla de decisión compensatoria. Aunque esta formulación en dos etapas parece más apropiada, su aplicación no está libre de complejidad, ya que el número de conjuntos de elección aumenta exponencialmente con el número de alternativas consideradas. Como ha señalado Swait (2001), muchas de las aplicaciones que incorporan cut-offs al análisis de toma de decisiones se basan en la heurística, donde estos valores umbral se ven como restricciones "duras" impuestas a los atributos. Esto significa que dichos umbrales no pueden ser violados para que una elección se considere válida. Tal es el caso de la regla de decisión EPA o el método propuesto por Cantillo y Ortúzar (2005). Por el contrario, otros autores confirman empíricamente que los individuos realmente violan sus umbrales previamente establecidos (véase, por ejemplo Huber y Klein, 1991; y Swait, 2001). La información que proporcionan los cut-off es fácil de obtener en la fase de entrevista preguntando a los individuos sobre el nivel mínimo de servicio requerido para cada uno de los atributos. Sin embargo, en muchos casos, durante la obtención de dicha información -por ejemplo, a través de un experimento de elección discretala violación de estos umbrales se produce al observar que los individuos eligen alternativas donde no se cumplen estos límites autoimpuestos. En este sentido, Swait 35 (2001) propone una ampliación del marco de maximización de la utilidad compensatoria tradicional donde: i) los cut-off o umbrales se incorporan de forma exógena; y ii) es posible para el consumidor el tratamiento de estas restricciones como "suaves" al permitir su violación a un determinado coste. Por lo tanto, la utilidad se especifica como una función lineal a trozos donde se agrega un componente de penalización a la función de utilidad convencional lineal en los parámetros. Esta penalización captura el efecto negativo de los atributos cuando se sobrepasan estos umbrales y viene representada por la expresión   _max 0, CO X j X CoX   cuando X es un atributo no deseable, como es el coste de transporte. Se puede obtener una expresión similar para los atributos deseables, como puede ser la frecuencia del servicio. El modelo econométrico resultante será fácil de estimar con el uso de un software estándar, ya que su derivación dependerá de las hipótesis formuladas acerca de la estructura del término de error. También es importante señalar que, dado que los umbrales o puntos de corte en el modelo de Swait son específicos para cada individuo, los puntos de corte de la función de utilidad a trozos varían entre individuos, lo que pone de relieve el potencial del modelo para capturar la heterogeneidad en relación a la percepción de todos los atributos. 36 Otro aspecto relevante en el análisis del comportamiento de los consumidores es el estudio de la heterogeneidad de las preferencias. Desde un punto de vista amplio, el análisis de la heterogeneidad de las preferencias ha sido durante mucho tiempo objeto de atención por parte de los investigadores en muchos campos diferentes. Cuando se trata con datos de elección discreta, este problema se puede abordar desde diferentes perspectivas. En presencia de modelos simples, como el modelo MNL, donde los parámetros son fijos entre los individuos, la heterogeneidad sistemática sólo puede abordarse considerando interacciones de los atributos modales con variables socioeconómicas o covariables. Los modelos de la familia ML tienen capacidad para analizar una gran variedad de heterogeneidad de las preferencias, permitiendo la especificación de distribuciones aleatorias continuas para los parámetros del modelo, pero tienen el inconveniente de que los supuestos sobre las distribuciones de los parámetros deben ser realizados por el investigador. Por contra, el Modelo de Clases Latentes (LCM) propuesto por Greene y Hensher (2003) para el análisis de datos de elección discreta, representa una versión semiparamétrica del MNL que se asemeja al modelo ML, en la medida que la heterogeneidad en la población está representada por parámetros que siguen una distribución idéntica entre individuos. Dado que no se requiere un supuesto previo sobre la distribución de los parámetros, esto representa una ventaja con respecto al modelo ML. 37 El LCM se basa en la idea de que los individuos pertenecen a diferentes segmentos o clases con preferencias idénticas dentro de las clases y estima la probabilidad de pertenencia a una clase junto con los parámetros de las preferencias de la clase. La definición del número apropiado de clases es, sin embargo, una cuestión crítica cuando se utiliza este modelo, ya que debe ser determinado de forma exógena por el analista. Aunque Greene y Hensher (2003) reconocen que los diferentes modelos tienen tanto ventajas como desventajas, después de la publicación de su trabajo seminal, el uso de LCM para analizar heterogeneidad no observable se ha convertido en una metodología consolidada, ya que proporciona interpretaciones intuitivas para los profesionales y los responsables políticos, siendo al mismo tiempo fácil de estimar. 1.3 Datos La base de datos utilizada en esta tesis doctoral se ha obtenido a partir de una muestra representativa de las empresas productoras/distribuidoras de productos manufacturados que en el año 2010 gestionaron envíos unitizados en el corredor que une la Comunidad de Madrid con los Países Bajos, Bélgica, norte de Francia y oeste de Alemania. En el periodo de referencia, este corredor representaba el 4,3% del tráfico existente entre España y los países objeto de estudio. Cabe mencionar, además, que este corredor era 38 uno de los pocos corredores en España donde realmente existía una competencia real entre los modos de transporte analizados: carretera, ferrocarril y marítimo. Dentro de cada una de esas empresas, se concertó una entrevista personal con la persona encargada de gestionar el transporte de los envíos en el corredor objeto de estudio. La duración media de las entrevistas realizadas fue de 20 minutos en los que, utilizando como soporte un ordenador portátil, se guiaba al entrevistado/a a lo largo del cuestionario diseñado en la versión 6.6 del software Sawtooth. Además, el uso de un software especializado nos permitió ajustar in situ el ejercicio de preferencias declaradas (PD) a los niveles del servicio efectivamente utilizados en el envío de referencia, lo que nos permite incrementar el realismo del ejercicio y con ello la calidad de las respuestas obtenidas. La presencia de un encuestador con un amplio conocimiento tanto de los objetivos concretos del proyecto como del tipo de información relevante para la estimación del modelo y su posterior interpretación nos permitió asegurarnos que el entrevistado comprendía plenamente el experimento planteado y que se tomaba el tiempo necesario para evaluar las diferentes opciones que se le planteaban. La cualificación y conocimiento del proyecto por parte de los encuestadores sin duda contribuyó a incrementar la calidad de la información obtenida. 39 La muestra así obtenida se compone de 93 empresas localizadas en la Comunidad de Madrid. Dichas empresas fueron seleccionadas al azar del Directorio de Empresas Exportadoras e Importadoras, elaborado por el Consejo Superior Español de la Cámaras de Comercio (http://aduanas.camaras.org), representando el 4,4% del total de empresas recogidas identificadas en dicho directorio como exportadoras/importadoras a los países objeto de estudio. Cada una de las empresas entrevistadas -durante los meses de octubre y noviembre de 2011proporcionó información sobre su envío representativo en el corredor objeto de estudio, lo que permitió obtener 1674 observaciones de preferencias declaradas (18 por envío). El cuestionario utilizado durante las entrevistas personales se dividía en cuatro grandes bloques: - El primer bloque tenía por objetivo la obtención de información general sobre las características de la empresa y sobre su dimensión logística. - A continuación se le solicitaba información sobre las características de su envío más representativo en el corredor objeto de estudio y sobre las características del servicio de transporte en ese momento empleado (coste, tiempo, retrasos, frecuencia, antelación con la que debe contratar el servicio), así como sobre el nivel de servicio mínimo exigido para cada uno de los atributos (cut-off). . 40 - El tercer bloque permitía obtener información sobre la importancia teóricamente concedida por el entrevistado a los distintos atributos del servicio de transporte en el proceso de elección del proveedor y el nivel de calidad percibida del servicio ofertado actualmente utilizado en el envío de referencia. - Finalmente, en base a la información proporcionada sobre las características del servicio de transporte se realizaron los dos juegos de preferencias declaradas obtenidos a partir del diseño de experimentos de elección discreta. El objetivo principal de un diseño experimental es determinar el efecto independiente de los diferentes atributos considerados sobre determinados resultados observables que, en el caso particular de los experimentos de elección discreta, están representados por las elecciones realizadas por los individuos que participan en el experimento (Rose y Bliemer, 2009). Un experimento de elección discreta consiste en una muestra de individuos que se enfrentan a una serie de situaciones de elección en las que se les pide que seleccionen la alternativa más preferida entre un conjunto finito de opciones. Las alternativas se definen en términos de los diferentes valores, o niveles, que los atributos pueden tomar. Técnicamente, el diseño experimental consiste en la disposición de los niveles de los atributos de una determinada manera en la matriz del diseño X, cuyas columnas y filas están normalmente asociadas a los atributos de las alternativas y las situaciones de elección respectivamente (Bliemer y Rose, 2006; Rose y Bliemer, 2008). 47 de 972 observaciones. Aunque nuestro tamaño final de la muestra no fue tan grande como se hubiera deseado, la estrategia de realizar el trabajo de campo en dos fases para crear un diseño eficiente específico para cada empresa contribuye a compensar el reducido tamaño de la muestra. 1.4 Estructura de la tesis y contenido El contenido de esta tesis doctoral está organizado en cuatro capítulos independientes. Los tres capítulos que siguen a esta introducción están escritos en inglés y siguen la estructura de un artículo científico tal y como exigen la mayoría de las publicaciones en el ámbito de la tesis. Es importante señalar que todas las investigaciones aquí presentadas se basan en la explotación de la misma base de datos utilizando diversos enfoques de modelización. Así, el enfoque de modelización planteado parte inicialmente de especificaciones generales basadas en los supuestos tradicionales de las teorías de la elección hasta llegar a modelos que permiten asumir la existencia de comportamiento no compensatorio y preferencias asimétricas. El segundo capítulo, Modelling mode choice for freight transporte using advanced choice experiment, presenta el contenido de un artículo que ha sido publicado 1 en mayo 1 http://dx.doi.org/10.1016/j.tra.2015.03.027 48 de 2015 en la revista Transportation Research Part A: Policy and Practice. Este artículo ha sido el fruto de una investigación centrada en analizar la demanda del transporte de mercancías en un contexto de elección modal, haciendo uso de técnicas de elección avanzadas. Con este fin, se realizó una encuesta de preferencias declaradas con el objeto de estimar las preferencias de los encargados de gestionar el transporte de mercancías para los principales atributos que definen el servicio ofrecido por los diferentes modos de transporte. Desde un punto de vista metodológico, la investigación se centra en dos cuestiones fundamentales en la construcción de experimentos de elección eficientes. En primer lugar, en la obtención de información previa de buena calidad acerca de los parámetros; y en segundo lugar, en la mejora de la calidad de los datos experimentales mediante la adaptación de un diseño eficiente específico para cada encuestado en la muestra. Con estos datos, se estiman diferentes modelos Logit Mixto que incorporan efectos de correlación del panel y que analizan heterogeneidad sistemática y aleatoria. Para el mejor modelo de todos, se obtiene la DAP por mejorar el nivel de servicio y la elasticidad de las probabilidades de elección para los diferentes atributos. Nuestro modelo proporciona resultados interesantes que se pueden utilizar para analizar el posible desvío de tráfico de la carretera (la opción actual) a modos alternativos, ferrocarril o marítimo, así como para ayudar en la obtención de la distribución modal del tráfico comercial entre España y la Unión Europea, que actualmente pasa a través de los Pirineos. 49 El tercer capítulo lleva por título, Analyzing discrepancies between willingness to pay and willingness to accept for freight transport attributes, y constituye el contenido de un segundo artículo que se encuentra pendiente de revisión en la revista Trasportation Research Part E: Logistics and Transportation Review. En este capítulo se analiza la existencia de discrepancias entre las medidas de la DAP y la DAA para los atributos más relevantes que definen la elección modal en el transporte de mercancías. La especificación de una función de utilidad asimétrica, con respecto a los valores de referencia establecidos por el nivel actual del servicio que perciben los responsables de la gestión del transporte de mercancías, permite comprobar la existencia de asimetrías importantes en la percepción de los costes de transporte. Por lo tanto, la reparametrización y la estimación de los modelos en el espacio de la DAP y la DAA facilitan la cuantificación de las discrepancias entre la DAP y la DAA, para los atributos considerados en el análisis, siendo estos el tiempo de tránsito, la frecuencia del servicio y retrasos en el tiempo de entrega. Una estimación precisa de estas cifras resulta fundamental para llevar a cabo un análisis coste-beneficio correcto, con el fin de asignar los recursos limitados de las infraestructuras de transporte, así como para definir servicios de transporte alternativos a la carretera que sean capaces de atraer grandes volúmenes de carga. Finalmente, el cuarto capítulo se presenta bajo el título, A latent class model with attributes cut-offs to analyze model choice for freight transport. En este último trabajo, 50 se explota la base de datos para abordar el estudio de la heterogeneidad de las preferencias estimando modelos de clase latente. Estos modelos representan una versión semiparamétrica del MNL que se asemeja al modelo ML, en el sentido de que la heterogeneidad en la población está representada por parámetros que siguen una distribución discreta idéntica entre los individuos. De este modo, es posible identificar las preferencias de los individuos que pertenecen a diferentes segmentos o clases así como la probabilidad de pertenencia a cada una de ellas, obteniéndose una interpretación muy intuitiva para los profesionales y responsables de la toma de decisiones políticas. Además, en este artículo se incorpora la especificación de valores umbrales o cut-offs en la percepción de los atributos. De esta forma, a la parte lineal de la función de utilidad se le añaden términos que cuantifican la penalización establecida cuando el valor de un determinado atributo no alcanza los niveles establecidos por dichos umbrales. El análisis del efecto de los cut-offs en combinación con el estudio de la heterogeneidad no observable supone un aspecto novedoso de este trabajo, lo cual refuerza el valor añadido de esta investigación dentro de la literatura empírica. 51 1.5 Conclusiones generales La investigación llevada a cabo en esta tesis doctoral permite obtener un conocimiento minucioso y detallado de las preferencias de los decisores en relación a la elección de modo de transporte de mercancías en el corredor objeto de estudio. De esta forma, la aplicación de diversos modelos de elección discreta ha permitido analizar cuáles son los factores determinantes en la elección modal, permitiendo arrojar algo de luz en el debate acerca del re-equilibrio del patrón modal en los flujos de mercancías entre España y Europa. Gran parte de la discusión en la primera parte de la investigación se ha centrado en la calidad de los datos, lo cual es especialmente relevante cuando se trabaja con datos experimentales. La aplicación de las técnicas más avanzadas en la construcción de diseños de preferencias declaradas así como el cuidado especial que se tuvo durante la fase de construcción del experimento permitió concentrar los esfuerzos en un aspecto crítico cuando se trabaja con datos experimentales: la reducción del sesgo hipotético. En este sentido, se obtuvo información a priori de buena calidad para los parámetros a partir de un modelo preliminar estimado con datos ortogonales. Posteriormente, se creó un diseño eficiente específico para cada encuestado con el fin de mejorar la eficiencia en la construcción del experimento, algo que no es una práctica habitual debido a los altos costes de implementación. Por otra parte, las dificultades relacionadas con la 52 recopilación de datos en el sector del transporte de mercancías refuerzan aún más este argumento. En este sentido, dedicar esfuerzos para mejorar la forma en que los datos se recogen es de suma importancia. La riqueza de la información proporcionada por el conjunto de datos representa, por tanto, un aspecto relevante de esta investigación. En una primera aproximación, los resultados obtenidos confirman la conveniencia de las políticas llevadas a cabo tanto a nivel europeo como nacional, a favor de cobrar por el uso de las infraestructuras y la internalización de los costes externos relacionados con el transporte. De hecho, de acuerdo con los modelos estimados, las acciones con mayor impacto en la desviación del tráfico hacia modos alternativos son aquellas que afectan el coste del transporte. La incorporación de elementos de la Prospect Theory al estudio de las preferencias permitió identificar la existencia de asimetrías en la precepción de algunos de los atributos, especialmente en el caso de los costes de transporte. En este sentido, la reparametrización y estimación de los modelos en el espacio de las disposiciones a pagar permitió contrastar estadísticamente la existencia de importantes discrepancias entre la DAP por mejoras en el nivel de servicio y la DAA una compensación cuando éste empeora. Estos resultados, a su vez, permitieron contrastar la hipótesis de aversión a la pérdida, que establece que el impacto en términos monetarios producido por una reducción en el nivel de servicio es superior al producido por una mejora mejoras. 53 Como resultado, la información obtenida sobre estas discrepancias es esencial a la hora de definir alternativas al transporte por carretera que sean capaces de atraer a la demanda. De este modo, si se obtiene que la DAA es mucho mayor que la DAP, se deben considerar reducciones sustanciales en el coste de transporte a fin de compensar la reducción en el nivel de servicio por el uso del transporte ferroviario. Por otra parte, si la DAP es baja, los aumentos en el precio por usar un mejor servicio de transporte marítimo de corta distancia no deben ser muy elevados. Finalmente, el análisis de la heterogeneidad de las preferencias utilizando modelos de clase latente nos permitió identificar la existencia de cinco clases con preferencias diferenciadas, de las cuáles dos de ellas se correspondían con grupos residuales. Estos grupos estaban integrados por un reducido número de entrevistados que, a la vista de los resultados arrojados, podrían corresponder a individuos que no entendieron o no tomaron en serio el experimento. Este resultado refuerza el argumento planteado por muchos investigadores que sugieren dedicar recursos suficientes a la fase de recopilación de datos, ya que esto contribuye positivamente en la calidad de los resultados en etapas posteriores del trabajo. Los tres segmentos restantes proporcionan información interesante sobre la percepción de los atributos que definen la elección modal, así como de las penalizaciones impuestas cuando éstos no satisfacen los umbrales correspondientes a un nivel de servicio 54 aceptable. Las principales diferencias entre estos grupos se deben fundamentalmente a los diferentes patrones que rigen el comportamiento compensatorio. En este sentido, cabe destacar la existencia de grupos que no consideran algunos atributos cuando se enfrentan a las decisiones de elección modal. En particular, vale la pena destacar la baja significatividad detectada para la penalización de la frecuencia en dos de las clases, y para la penalización del retraso en grupo restante. En general se puede concluir que la incorporación de valores umbrales a la especificación de la utilidad proporciona un conocimiento más preciso sobre las preferencias, especialmente cuando la calidad del servicio se reduce por debajo de niveles aceptables. Por otra parte, la comparación de estos resultados con los obtenidos con la especificación MNL convencional, permite detectar la existencia de sesgos importantes en los valores de las DAP; observándose que los modelos que no abordan de forma adecuada el estudio de la heterogeneidad de las preferencias producen sobreestimaciones importantes para una parte sustancial de la población. Dado el papel relevante de los valores de las DAP en la evaluación de las políticas de transporte, la aplicación de métodos que mejoren la detección de diferentes segmentos de mercado se considera esencial para un mejor uso de los recursos públicos. 55 1.6 Líneas de investigación futuras Son muchos los aspectos no tratados en esta tesis y que pueden ser abordados en investigaciones futuras. Su enfoque metodológico está relacionado con la visión más contemporánea de las teorías de la elección que contemplan la introducción de factores psicológicos en el proceso de toma de decisiones y en los modelos empíricos de decisión. Según reconoce McFadden (1999), el reto al que deben enfrentarse los economistas es hacer que el Chicago man (que actúa de acuerdo al modelo económico estándar en cuanto a percepción, preferencias y racionalidad) evolucione en la dirección del Kahneman-Tversky man (que incorpora emociones, afectos y otros factores psicológicos en la toma de decisiones). Este nuevo enfoque reconoce que el proceso de toma de decisiones depende de la naturaleza del problema, del contexto, de la situación social y de los individuos. BenAkiva et al. (1999) abordan este problema e identifican una serie de factores psicológicos tanto observables como no observables (o latentes) que afectan al proceso de la toma de decisiones. La idea es incluir, en este nuevo marco teórico, las relaciones que cuantifican las actitudes, las percepciones y otros elementos psicológicos; explicar cómo se forman y cómo influyen en la elección. Desde un punto metodológico, una de las formas de abordar el problema es mediante la estimación de modelos híbridos que integran los modelos de variable latente (para 56 cuantificar los factores no observables) con modelos de elección discreta. En el caso particular de esta investigación, la incorporación de variables relacionadas con la percepción del nivel de servicio actual así como de la importancia relativa que cada decisor concede a los principales atributos, pueden ayudar a comprender mejor el proceso de toma de decisiones. Desde un punto de vista meramente aplicado, señalar que la población objeto de estudio en el marco de la presente tesis se limitó a los cargadores. Sin embargo, tal y como se señaló anteriormente, en el ámbito de las mercancías las decisiones no suelen recaer sobre un único decisor, sino que en ellas pueden/suelen intervenir todos los agentes implicados en la cadena de transporte: cargador, receptor, transitario/operador logístico y transportista. La incorporación a la población objeto de estudio de estos dos últimos grupos de decisores –transitarios y transportistaspermitiría ahondar sobre el papel que juega cada uno de ellos en las distintas decisiones vinculadas al transporte y obtener evidencia empírica sobre las diferencias en las preferencias de unos y otros, lo cual es sumamente útil en términos de política. En relación con los atributos, una vez ratificado el papel que juegan los principales atributos de transporte (coste, tiempo, frecuencia, fiabilidad), futuras investigaciones deberían ahondar sobre el papel que juegan atributos de transporte hasta el momento 63 McFadden, D. (1974). The measurement of urban travel demand. Journal of Publics Economics, 3, 303-328. McFadden, D. (1999). Rationality for Economists? Journal of Risk and Uncertainty, 19, 73-105. Ortúzar, J. de D. & Willumsen, L.G. (2011). Modelling Transport. 4th edition, John Wiley & Sons, Chichester. Payne, J., Bettman, J., & Johnson, E. (1993). The Adaptive Decision Maker. Cambridge University Press, New York. Polak, J. & Arunotayanun K. (2009). Accommodating supply chain structure in models of freight mode choice. Proceedings of the 12th International Conference of Travel Behavior Research, Jaipur, India. Rich, J., Holmblad, P. M., & Hansen, C. O. (2009). A weighted logit freight modechoice model. Transportation Research Part E: Logistics and Transportation Review, 45(6), 1006–1019. Simon, H. A. (1955). A behavioral model of rational choice. The Quarterly Journal of Economics, 69(1), 99–118. Swait, J. (2001). A non-compensatory choice model incorporating attribute cutoffs. Transportation Research Part B, 35, 903-928. 64 Rose, J. M., & Bliemer, M. C. J. (2009). Constructing Efficient Stated Choice Experimental Designs. Transport Reviews, 29(5), 587–617. Rose, J. M., Bliemer, M. C. J., Hensher, D. a., & Collins, A. T. (2008). Designing efficient stated choice experiments in the presence of reference alternatives. Transportation Research Part B: Methodological, 42(4), 395–406. Train, K. (2009). Discrete Choice Methods with Simulation, 2nd edition, Cambridge University Press, Cambridge. Tversky, A. (1972). Elimination by aspects: a theory of choice. Psychological Review, 79, 281–299. Tversky, A. & Kahneman, D. (1974). Judgment under uncertainty: heuristics and biases. Science, 185(4157), 1124–1131. 65 Capítulo 2. Modelling mode choice for freight transport using advanced choice experiments Abstract: In this paper we use advanced choice modelling techniques to analyze demand for freight transport in a context of modal choice. To this end, a stated preference (SP) survey was conducted in order to estimate freight shipper preferences for the main attributes that define the service offered by the different transport modes. From a methodological point of view, we focus on two critical issues in the construction of efficient choice experiments. Firstly, in obtaining good quality prior information about the parameters; and secondly, in the improved quality of the experimental data by tailoring a specific efficient design for every respondent in the sample. With these data, different mixed logit models incorporating panel correlation effects and accounting for systematic and random taste heterogeneity are estimated. For the best model specification we obtain the willingness to pay for improving the level of service and the elasticity of the choice probabilities for the different attributes. Our model provide interesting results that can be used to analyze the potential diversion of traffic from road (the current option) to alternative modes, rail or maritime, as well as to help in the obtaining of the modal distribution of commercial traffic between Spain and the European Union, currently passing through the Pyrenees. KEYWORDS: Freight Transport, Discrete Choice Experiments, Stated Preference, Willingness to Pay, Discrete Choice Models. 2.1 Introduction Even though the current economic crisis is taking some pressure off the saturation of roads, thus relieving traffic in the two main Pyrenean corridors that connect Spain with Europe, it is still of vital importance in the Spanish transport agenda. The very sensitive 66 natural environment through which the traffic flows and the high economic cost of expanding road capacities in mountainous areas make it even more necessary to shift a significant amount of cargo from road to rail and maritime intermodal alternatives. Thus, rebalancing the modal pattern and improving the efficiency of the transport system is paramount in determining the appropriate basis for the Spanish economic growth. Road pricing schemes and subsidies to intermodal alternatives, such as the Ecobonus, without a doubt increase the competitiveness of rail and maritime logistics chains. However, the fact that the modal shift objectives set out in the 2001 Transport White Paper (European Commission, 2001) have still not been accomplished indicates the importance given to qualitative aspects of the transport service and the need to further increase the efficiency and quality of intermodal alternatives. Given the historical trend of the modal distribution for freight transport over the past decades in Spain (characterised by the prevalence of road transport), the compatibility of higher economic growth with sustainable development of the transport system will demand considerable investment by the authorities. However, the urgent need to reconcile investment spending and budgetary stability requires national policy makers to carry out a rigorous assessment of transport projects in order to attain efficient resource allocation. The ability to make investment decisions however will depend on the degree of knowledge of the transport demand as well as on the accuracy with which benefits and costs associated to different actions are quantified. Thus, an increasing number of agencies incorporate cost-benefit analysis (CBA) in the evaluation of transport projects. Unlike financial analysis, which only takes into account current income and costs incurred by the operator throughout the project, in CBA net social benefits are obtained by comparing benefits and socioeconomic costs of all stakeholders involved in the project. These benefits and costs include both, elements easily quantifiable in monetary terms and elements, such as the value of time, for which there is no direct measurement therefore, making their economic assessment more difficult. Savings in travel time represents one of the most important benefits derived from infrastructure investments in the case of freight and passenger transport. Despite being the main benefit for the majority of transport projects, researchers have not been able to reach a consensus neither in the magnitude nor in the nature of the value-of-time figures 67 used in project evaluation. The absence of consensus is even higher with regard to freight transport. Indeed, the difficulties associated with obtaining information in this area limit the scope of empirical applications and thereby the methodological debate around the valuation of freight transit time. As pointed out by Ben-Akiva et al. (2008), the modelling for freight transport demand has evolved significantly over the past decades, from the use of aggregate models based on global data of shippers and shipments, to the use of more sophisticated disaggregated models based on individual data. In this regard, Tavasszy and de Jong (2014), BenAkiva et al. (2013), Nuzzolo et al. (2013a) and Chow et al. (2010) provide interesting reviews of the state-of-the-art literature regarding freight transport modelling. In contrast with passenger transport, the use of behavioural models to analyse freight transport demand has been much more limited because of the difficulties associated with data collection. Feo-Valero et al. (2011) identify the most critical issues in freight transport demand modelling; highlighting the identification of the decision-maker, the heterogeneity of the transport flows and the definition of the explanatory variables. Despite these difficulties, the use of freight disaggregate models is increasingly widespread. In this sense, we can cite the work of Bergantino et al. (2013), Masiero and Hensher (2012), Arunotayanun and Polak (2011), Feo et al. (2011), Rich et al. (2009), Polak and Arunotayanun (2009), Bergantino and Bolis (2008), Beuthe and Bouffioux (2008), Brook and Trifts (2008), de Jong and Ben-Akiva (2007), Daniellis and Marcucci (2005), Marcucci and Scaccia (2004), Shinghal and Fowkes (2002), Kurri et al. (2000), Nuzzolo and Russo (1997), and Modenese-Vieira (1992) among the more recent contributions, many of them using stated preference (SP) techniques. According to the sequential four-step model, transport demand consists in the analysis of four different stages: trip production, trip distribution, modal split and traffic assignment (Ortúzar and Willumsen, 2011). As recognised by de Jong et al. (2012), this structure has been adopted in freight transport modelling with some success, though additional steps are sometimes required in order to transform trade flows, normally expressed in monetary units, into transport vehicle flows. This paper aims to contribute to the field of freight transport demand analysis by estimating a discrete choice model that can be used to analyse the potential diversion of traffic from road to alternative modes, rail or maritime, as well as to help in the obtaining of the modal distribution of 68 commercial traffic between Spain and the European Union, currently passing through the Pyrenees. In particular, the analysis is focused on modelling the third stage of the conventional four-step disaggregate model: the mode choice. This stage is one of most relevant as modal distribution results are among the main factors explaining freight transport externalities (de Jong, 2014a). To this end, a SP survey, based firstly on an orthogonal design and secondly, on an efficient discrete choice experiment, was conducted in order to analyse the freight shipper preferences for the attributes that define the service offered by the different transport modes. From a methodological point of view, we focus on two critical issues in the construction of efficient designs. The first is on obtaining good quality information about the parameters; and, the second, on the improved quality of the experimental data by tailoring a specific efficient design for every respondent in the sample. Extended information on the difficulties linked to the use of tailored efficient designs in the area of freight transport and how the proposed two-step fieldwork copes with them can be found in Feo et al. (2014), where the analysis is focused on the context of modal choice between road and rail in a domestic corridor in Spain. Whereas the advantages of using efficient designs have been widely acknowledged by many authors, not many applications have been focussed on trying to address these two problems together. In fact, this research, together with the work of Feo et al. (2014), is to our knowledge, the only contribution using individual-specific efficient designs in the field of freight transport. Furthermore, the present study is the only one that analyses modal competition at an international level. 2.2 Data collection and experimental design The population studied in this application are the producers / distributors of manufactured goods, that in 2010 handled unitised shipments in the corridor linking Madrid with the Netherlands / Belgium / Northern France / West Germany (see Figure 2.1). This corridor accounted for 4.3% of traffic channelled between Spain and continental Europe in the reference period. It is also important to point out that there is effective competition among the transport modes under analysis in this corridor: road, rail and maritime. 69 Whilst in previous research the analysis was circumscribed to freight forwarders (Feo et al., 2011), in this application the population being studied is confined to the company responsible for sending the shipment (shipper or receiver), in order to increase the population size and the response rate. To ensure that the company selected corresponded to the real decision-maker, certain filter questions were included in the questionnaire before starting the interview. Figure 2.1 Corridor analysed. A personal interview was arranged with the person responsible for managing the transport shipments in the corridor under study. The average length of the interviews was about 20 minutes in which, using a laptop, the interviewee was guided along the questionnaire designed in Sawtooth Software release 6.6. The use of computer support and specialised software not only helped us to minimise errors in data collection, but also allowed us to customise the interview to the context of each respondent. The surveys were conducted during October and November 2011 by a group of properly trained interviewers whose qualifications and knowledge on the project contributed to increasing the quality of the information obtained. The total sample consisted of 93 companies located in the Autonomous Region of Madrid. Each firm provided information about the representative shipment in the corridor allowing us to obtain a total of 1674 statistical SP observations (18 per shipment). Companies were randomly selected from the directory of Spanish Exporting 70 and Importing Companies developed by the Spanish High Council of Chambers of Commerce (http://aduanas.camaras.org). Our sample represented 4.4% of total Madrilenian companies identified in the directory as exporting or importing to the countries under study in 2010. As the analysed transport corridor is restricted to Northern France and West Germany and to non-refrigerated-unitised shipments, it is reasonable to expect a higher percentage. In a second wave of surveys conducted during the first semester of 2012, we used information obtained previously to improve the choice experiment, tailoring an efficient design for each respondent who participated in the first phase of the study. The questionnaire was divided into four main sections: i) the first section was designed to obtain general information about the characteristics of the company and its logistic dimension; ii) the second was devoted to collecting information on the main characteristics of the reference shipment (cost, transit time, delays, etc.) as well as on the minimum level of service required for each of the attributes; iii) the third section provided information on the importance of the main attributes that define the transport service, as well as the level of quality perceived; iv) finally, the fourth section was devoted to collecting the decision-maker preferences in an SP game. Table 2.1 shows the composition of the sample by type of company (producer or distributor) and size (micro, small, medium and large), and the modal distribution of shipments identified during the fieldwork. Transport alternatives used at the time of the fieldwork were pure road transport and intermodal alternatives using rail, maritime or air as the main mode of transport and road for the origin and destination haulage. As can be seen most of the companies are small and medium size firms. Our sample is therefore consistent with the Spanish production structure. Information regarding the proportion of companies having a specific logistic department is also displayed. The results obtained show, as might be expected, a positive correlation between the size of the company and its involvement in logistics management. Bigger companies with specific logistics departments should be in a better position to optimise transport chains and should be therefore more willing to use alternative modes. On the contrary, small companies that do not have such supporting structures for logistics are more likely to be inclined to continue using their current transport option. The results obtained partially 71 confirm this hypothesis as, while road is the dominant mode in all cases, the share of intermodal modes increases slightly as company size increases. Concerning the distinction between producers and distributors, our initial hypothesis was that the latter would pay more attention to logistics issues than the former –as their core activity was precisely distributing goodsand they would therefore display more diverse modal splits. However in our sample the road transport quota is roughly the same for both types of companies. Figure 2.2 shows the level of importance of the following factors in the choice of transport provider for the reference shipment: transport cost, transit time, frequency, punctuality, absence of losses and damages, flexibility 2 , track and trace, environmental impact and schedules 3 . This graph provides quick and visual information on the distribution of the assessments made by the companies included in the sample considering a five-point Likert scale, where 1 means "very low" and 5 means "very high" importance. Figures in brackets under the attribute name represent the average score obtained by the attribute from a maximum of 5 points. According to these results, the most important criterion is the reliability in delivery times, that is, punctuality; the transport cost and the transit time, with an average score of above 4 points. In contrast, the less valued attribute is the environmental impact of the transport chain with an average score close to 3 points. 2 Flexibility was defined as the capacity of the transport provider to adapt to unexpected changes in the requirements of the demand, for example a last-minute change in the size of the shipment, or on the final destination. 3 Transport providers’ schedules meeting the needs of the company. 72 Table 2.1 Modal distribution of the shipments to Europe in the sample. Type of firm (Size) Nº of companies (%/Total) Nº of companies with a logistics department Road (%) IntermodalMaritime (road-searoad) (%) IntermodalRail (road-railroad) (%) IntermodalAir (road-airroad) (%) Micro firm (< 10 workers) 17 (18%) 3 (18%) 95 1 0 4 Small (between 10 and 49 workers) 38 (41%) 18 (47%) 92 2 0 6 Medium (between 50 and 250 workers) 31 (33%) 22 (71%) 87 2 1 10 Large (> 250 workers) 7 (8%) 7 (100%) 86 8 3 3 Total 93 93 89 3 1 7 Producer 69 (74%) 41 (59%) 89 4 1 6 Distributor 34 (26%) 15 (44%) 90 1 0 9 Total 93 93 89 3 1 7 Figure 2.2 Importance of factors in the choice of transport provider for the reference shipment. 0% 10% 20% 30% 40% 50% 60% 70% 80% 90% 100% COST (4.57/5) TRANSITTIME (4.34/5) FREQUENCY (3.66/5) PUNCTUALITY (4.75/5) DAMAGES (4.59/5) FLEXIBILITY (4.03/5) TRACK&TRACE (3.82/5) ENVIRONMENTAL IMPACT (3.01/5) SCHEDULES (3.9/5) VERYLOW(1/5) LOW(2/5) MEDIUM(3/5) HIGH(4/5) VERYHIGH(5/5) 79 2.2.1.3 Efficient design One of the most popular methods to construct efficient designs is based on the minimisation of the D-error, which is defined in terms of the asymptotic variancecovariance (VC) matrix, which depends, in turn, on the second derivatives of the loglikelihood function. Recently, many authors have highlighted the advantages of using efficient designs when dealing with SC data. Among the most important, we can cite the ability of efficient designs to obtain more reliable estimates with a smaller sample size (Bliemer and Rose, 2005). Moreover, the difficulty entailed in the computation of the D-error varies with the complexity of the choice model to be estimated. Therefore, even in the case of the simplest multinomial Logit model, the value of the D-error varies with the design matrix and the value of the unknown parameters. To cope with these two critical issues in the construction of our experimental dataset in the present paper: i) we use good quality prior information about unknown parameters by using estimates derived from the previous orthogonal design; and ii) we try to achieve the highest possible efficiency by generating a specific efficient design for every respondent, using previous information about the current option to define attribute levels and parameter priors obtained in the above section. In this regard and in order to gain realism in the outcomes of the experiment, we customise the levels of the attributes to the respondent’s current experience. Thus, alternatives presented in the choice sets are different for each respondent and are defined by pivoting attribute level values around the reference alternative. As the efficiency of the design depends on the attribute values, in an ideal situation a specific design should be created for every single respondent. In this paper we follow the recommendation of Rose et al. (2008) by collecting data in two different phases and optimising the design for each individual based on their reference levels. Although the generation of a specific design to each individual could confound individual heterogeneity with design heterogeneity, to the best of our knowledge this problem does not have a satisfactory solution in cases where customising the design to gain realism in the choice task is paramount 8 . 8 Personal communication (John Rose, May 2013). 80 Attributes and levels corresponding to the two games are presented in Tables 2.5 and 2.6. On this occasion, as we already had accurate information on the levels of service displayed by the reference alternative, the levels of frequency and delays were readjusted to the current level of service in order to further increase the realism of the experiment. N-gene software (ChoiceMetrics, 2009) was used to build the efficient design for every individual in the sample considering a multinomial Logit specification. A web questionnaire including only the new choice games was administered to all firms that participated in the first phase of the study. Previous contact by telephone with the appropriate person helped us to improve the response rate. At the end of this second wave of interviews we obtained a total of 972 observations corresponding to 54 companies, which represent 58% of the initial sample. Our final sample might therefore not be as large as otherwise desired, but this makes our two-step fieldwork and the use of efficient designs all the more relevant, as they allow us to obtain more reliable estimates with smaller sample sizes. The descriptive statistics for the attributes of the current alternative are presented in Table 2.7. As the variables present a different degree of dispersion, in order to have a better idea of the shape of the distribution, the corresponding quartiles (Qi) are also reported. In this regard, it is worth highlighting the high figure obtained (2.4) for the coefficient of variation (CV) in the cost, which indicates the high dispersion in the observations corresponding to this variable. This is mainly explained by the different nature of the shipments analysed in this study. 81 Table 2.5 Attributes and levels for game 1. Efficient design. Attributes – levels Current alternative Intermodal alternative game 1 Door-to-door transport cost (Euros per shipment) 1 Current level - 25% 2 -15% 3 -10% Door-to-door transit time (Days) 1 Current level +1 day 2 +2 days 3 +3 days Delay (Days) Current level ≤ 1 day 1 -0.5 day +0.5 day 2 Current level +1 day 3 +0.5 day +1.5 days Delay (Days) Current level > 1 day 1 -0.5 day +0.5 days 2 Current level +1 days 3 +0.5 day +2 days Service frequency (Nº of weekly departures) 1 Current level 1 weekly departures 2 2 weekly departures 3 3 weekly departures Table 2.6 Attributes and levels for game 2. Efficient design. Attributes Current alternative Intermodal alternative game 2 Door-to-door transport cost (Euros per shipment) 1 Current level + 20% 2 +10% 3 +5% Door-to-door transit time (Days) 1 Current level Current level 2 -0.5 day 3 -1 day Delay (Days) Current level ≤ 0.5 day 1 Current level -0.5 day 2 +0.5 day Current level Delay (Days) Current level = 1 day 1 Current level -1 day 2 +0.5 day -0.5 day 3 +1 day Current level Delay (Days) Current level > 1 day 1 -0.5 day -2 days 2 Current level -1.5 days 3 +0.5 day -1 day Service frequency (Nº of weekly departures) Current level ≤ 2 dep/week 1 Current level 2 weekly departures 2 3 weekly departures 3 5 weekly departures (Mon to Fri) Service frequency (Nº of weekly departures) Current level = 3 dep/week 1 Current level 3 weekly departures 2 5 weekly departures (Mon to Fri) 3 5 weekly departures (Mon to Sun) Service frequency (Nº of weekly departures) Current level > 3 dep/week 1 Current level 5 weekly departures (Mon to Fri) 2 5 weekly departures (Mon to Sat) 3 5 weekly departures (Mon to Sun) 82 Table 2.7 Descriptive statistics. Attributes of the current alternative. Attributes Mean Std. Dev. CV Xmin Xmax Q1 Q2 Q3 Cost (Euros per shipment) 722.31 1009.70 1.4 20 6000 100 300 1150 Transit time (Days) 3.64 1.78 0.49 1 10 2 3 4 Service frequency (Nº of weekly departures) 3.24 1.53 0.47 1 5 2 3 5 Delay (Days) 1.83 1.09 0.6 0.5 4.5 1 1.5 2.5 2.3 Modelling mode choice for freight transport Discrete choice models have been widely used to study individuals’ behaviour in the mode choice context. Their theoretical underpinnings are found in the theory of rational choice and in the utility maximisation behavioural rule. Thus, the utility of alternative j to the decision maker n is represented by the random variable jn jn jn UV   ; where jn V is the deterministic or observable utility and  jq is a random term representing the portion of utility unknown to the analyst. Therefore, under the assumption of utility maximisation, it is only possible to model the choice probability of the different alternatives. Different assumptions about the distribution of the unobserved portion of utility jn  result in different representations of the choice model. Thus, the widely used Multinomial Logit (MNL) and Nested Logit (NL) models are obtained when jn  are independent and identically distributed (iid) extreme value and a type of generalised extreme value, respectively (see Train, 2009 and Ortúzar and Willumsen, 2011 to obtain more details about the derivation of the choice probabilities for the different choice models). The Mixed Logit (ML) model solves the main limitations of the MNL and NL models. It allows for random taste variation, unrestricted substitution patterns and even correlation in unobserved factors over time, which is particularly useful when dealing with SP or panel data. It is a very flexible model that can approximate any random utility model with total precision. Under the random coefficient version, the utility of alternative j for an individual q is represented by jn n jn jn Ux    , where, jn x is a vector of observed attributes of alternative j for decision-maker n, jn  is a set of random 83 variables iid extreme value, and n  is a vector of random coefficients. In the error component formulation of the ML model, the utility is represented by jn jn n jn jn U x z        , where jn x and jn z are vectors of observed attributes of the alternative j for individual n,  is a vector of fixed coefficients, n  is a vector of random terms with zero mean and covariance W; and jn  are defined as above. With the purpose of analysing the relative importance of the factors affecting modal choice in the context of freight transport, different discrete choice models were estimated using the data set obtained from the efficient design. The estimation results are presented in Table 2.8. The first model MNL3 corresponds to a multinomial Logit model with a linear utility specification similar to that represented in equation (2.2). All parameter estimates in MNL3 present the expected sign and are significant at the 95% confidence level. But the multinomial Logit model is very restrictive as error terms are assumed to be independent across observations and all coefficients are forced to be the same for all individuals. Therefore, with this model, all observations are treated as independent and tastes are considered homogeneous in the population. 84 Table 2.8 Estimation results. Efficient design data. Attributes Estimate (t-test) MNL3 ML1 ML2 ML3 ASC (Current option) 0.349 0.409 0.404 0.393 (3.95) (2.78) (2.50) (2.34) Cost (C) Euros per shipment θc -0.00568 -0.00670 Mean -0.00951 (-7.94) Mean -0.0151 (-6.02) (-8.86) (-9.15) Std err 0.00503 (3.78) Std err 0.00544 (3.73) Transit time (T) Days θt -0.294 -0.328 -0.378 -0.261 (-4.12) (-4.28) (-4.38) (-2.74) Delay (D) Days θd 0.356 -0.384 -0.474 -0.488 (-5.79) (-5.80) (-5.90) (-5.92) Frequency (F) Nº of weekly departures θf 0.0897 0.122 Mean 0.162 (2.42) (2.42 Mean 0.162 (2.39) (2.4) (2.35) Std err 0.503 (3.78) Std err 0.465 (3.28) Interaction C*C1 - - - - 0.00615 - - - - (2.82) Interaction T*T1 - - - - -0.374 - - - - (-2.81) Theta - 0.581 (5.95) 0.721 (5.68) 0.773 (5.92) 0.147 0.176 0.183 0.197 Adjusted 0.140 0.167 0.171 0.183 l*(0) -673.739 -673.739 -673.739 -673.739 l*(θ) -574.523 -555.386 -550.422 -540.704 Observations 972 972 972 972 As individuals in our data set provide responses in different choice situations a flexible model of the family of mixed Logit is more appropriate. Thus, in the remaining models we considered a mixed Logit specification including an error component able to account for potential panel correlation ( ). In order to obtain homoscedasticity, the common error components of the two alternatives are assumed to distribute standard Normal for all observations corresponding to the same respondent and were multiplied by a parameter theta to be estimated, as in Hess et al. (2008). In model ML1 all parameters are specified as fixed values and resulted significant with a 2  2  road, intermodal i in i    i  85 consistent sign. The parameter theta, in all models resulted significant, indicating the presence of correlation among responses from the same individual. To analyse random taste heterogeneity different random parameter Logit models were estimated. In order to select the candidate set of random coefficients, the Lagrange Multiplier test, as recommended in Hensher and Greene (2003), was applied for different sets of random parameter candidates. Unfortunately none of the tests carried out allowed us to reject the null hypothesis of non-random coefficients. Therefore, we proceeded with the direct specification of random parameters and considering all possible combinations; started by assuming all parameters were random and then examined their estimated standard deviations (as suggested in Hensher and Greene, 2003). The best model specification (ML2) was that assuming that cost and frequency parameters follow the Normal distribution. As in the former case, all parameters were significant at the 95% confidence level. Although the mean of the random parameters presented a consistent sign, it is important to point out that, in the case of frequency, the probability of obtaining an inconsistent marginal utility is relatively high (0.37). This result is a consequence of the high dispersion obtained for this random parameter. With regards the latter, one possible explanation could be that, as is the case in the application developed by Feo et al. (2014), while a part of the sample is indeed valuing frequency, the other has a zero value or near-zero value, so in the end the significance of the frequency coefficient for the whole of the population is diminished by the presence of indifferent respondents. Indeed, the results in Figure 2.2 corroborate this hypothesis, as frequency is the attribute -among those finally included in the SPdisplaying the highest heterogeneity: almost 45% of the sample gave a score of 3 points or less to frequency, while for transport cost, transit time and delays this proportion is 10% or less. Our next step in future research will be to test this hypothesis considering alternative specifications including attribute cut-offs and latent class models. To analyse the presence of systematic taste variation, several interactions between socioeconomic variables and service attributes were specified. After testing all possible combinations the best model specification was ML3, where we were only able to find significant interactions between cost and C1 (which is equal to one if the respondent firm is a producer) and between transit time and T1 (which is equal to one if the supplier is a producer). This means that the disutility of transport cost is lower when the 86 responsible of the shipment (i.e. the respondent) is a producer than when it is a distributor. This result could be the reflection of the fact that, while the core activity of the former is the production of the good, the core activity of the latter is its distribution, transport being therefore a key determinant of its relative competitiveness. In contrast, the negative perception of transit time is higher when the supplier of the freight is a producer. In that case the result suggests that distributors display larger inventories than producers, which allows them to reduce total delivery times (time from when the order was placed until the shipment is delivered) and therefore to incur in larger transit times (transport time). As in model ML2, the cost and frequency parameters are normally distributed, and the marginal utility of the frequency is not consistent with a probability of similar magnitude. As ML3 presents the best fit to our data set, this model will be used in model applications in the next section. Regarding the alternative specific constant, it was specified in the current option and was significant and positive, suggesting the existence of an inertia effect or reluctance to change the mode of transport. Finally, it is worth pointing out that, in our models, all attributes are treated as continuous variables and are specified in the linear form. With this specification we are limited to considering only linear effects with respect to attribute variations. In this regard, Marcucci and Gatta (2014) highlight the importance of testing for the existence of non-linear effects of the different levels of the explanatory variables. These authors treat attributes as discrete variables considering effects coding when defining the corresponding dummies (Hensher et al. 2005), and they find significant differences when comparing WTP measures obtained with linear specifications. As our discrete choice experiment is customised to respondent experience, attribute levels differ across individuals. Therefore, in order to undertake a similar analysis using our data set, a convenient segmentation of each attribute would be required. 87 2.4 Model application 2.4.1 Willingness to pay measures Willingness to pay (WTP) measures represent a key element in the evaluation of transport projects as well as in the design of pricing strategies for transport operators. They provide a quantitative measure of the monetary cost that a user would pay for improving the level of service in the attributes of transport alternatives. WTP measures are obtained from the estimation of discrete choice models as the ratio between the marginal utility of a given attribute and the marginal utility of the transport cost. When random parameters are included in the utility specification, WTP figures are random variables and simulation methods are required to simulate the distribution of the corresponding WTP, which is normally unknown. This is the case when the denominator of the WTP expression distributes Normal, as in our case. In order to obtain plausible values the corresponding distribution of the random parameter is truncated for those values with consistent marginal utility (i.e. with the appropriate sign). Table 2.9 presents WTP figures obtained for model ML3. In a first approach, the WTP figures were approximated by the mean of their corresponding simulated distribution. As the mean could be highly affected by the presence of undesirable outliers (note that the denominator of the WTP could have near 0 values, the median of the distributions was also computed and it is considered a more appropriate measure of the WTP. These two representative figures of the WTP were compared with that obtained by computing the WTP at the estimated mean of the random parameters, observing substantial discrepancies, especially in the case of service frequency. In order to provide the 95% confidence interval for WTP, the 2.5 and 97.5 percentiles are calculated. In all cases the median is lower than the mean, giving distributions that are skewed to the right (see Figure 2.3). In general, WTP figures are higher when the respondent firm is a producer (i.e. when C1=1). When the supplier is a producer (i.e. when T1=1) the highest WTP is obtained for saving transit time (ranging from 41,74 to 67,27 €/day in the case of the median of the distribution). In contrast, when T1=0, the highest WTP is for reducing delay time. This figure ranges in the case of the median from 32,23 to 51,93 €/day. 88 Table 2.9 Willingness to pay figures. Model ML3. Attribute Computed at the mean of the estimated parameters Simulated distribution of the WTP Mean Median Percentile 2.5 Percentile 97.5 C1=0 Transit time (T1=0) 17.28 20.79 17.24 10.12 53.71 Transit time (T1=1) 42.05 50.33 41.74 24.50 130.06 Service frequency 10.73 35.20 26.07 1.28 120.86 Delay Time 32.32 38.86 32.23 18.92 100.42 C1=1 Transit time (T1=0) 29.16 38.85 27.78 13.33 143.30 Transit time (T1=1) 70.95 94.08 67.27 32.28 347.00 Service frequency 18.10 65.06 42.30 2.09 279.97 Delay Time 54.53 72.64 51.94 24.93 267.94 In order to test for the validity of our models, WTP figures are compared with those obtained in recent literature. In this sense, a summary of results obtained in previous studies can be consulted in de Jong (2014b) and Rotaris et al. (2012). Regarding the value of transit time our results are in line with those obtained by de Jong (2008) and Fries et al. (2010). Nuzzolo et al. (2013b), using aggregate models obtained VOT figures ranging from 11.71 to 65.89 €/h, depending on the mode; and Zamparini and Reggiani (2007) report average values equal to 30.16 $1999 /h for European countries, when comparing several research projects using stated preferences data. Fowkes et al. (2004) reported a value of delay equivalent to 64 pounds per hour, which is fairly consistent with our figures. Less evidence has been found regarding the monetary value of the service frequency, which in many contexts did not result significant. 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Analyzing discrepancies between willingness to pay and willingness to accept for freight transport attributes Abstract: In this paper we analyze the existence of discrepancies between the measures of willingness to pay (WTP) and willingness to accept (WTA) for the most relevant attributes that define modal choice in freight transport. The analysis is based on data obtained from a discrete choice experiment where decision makers were faced to the choice between road (the current mode) and an intermodal alternative in the corridor linking the regions of Madrid with the Netherland / Belgium / Northern France / West Germany. The specification of an asymmetric utility function with respect to the reference values provided by the current level of service perceived by freight forwarders allowed us to test for the existence of substantial asymmetries in perception of the transport cost. Hence, the re-parameterization and estimation of our models in the WTP/WTA space helped us to quantify the discrepancies between the WTP and WTA for the attributes included in the choice experiment, namely transit time, service frequency and delays in delivery time. An accurate estimation of these figures is deemed essential both, to carry out the correct cost-benefit analysis in order to allocate the limited resources for transport infrastructures and to define alternative transport services to road capable to attract substantial volumes of freight. KEYWORDS: Freight Transport, Discrete Choice Experiments, Stated Preference, Prospect Theory, Reference alternative, Asymmetric preferences, Willingness to pay, Willingness to accept. 102 3.1 Introduction There are more and more authors that question the validity of the neoclassical theories of consumer behaviour to analyze individuals' preferences. In this regard, the incorporation of elements of the prospect theory to model situations that involve decision making has contributed to a better understanding of the aspects that govern individuals' decisions. As pointed out by Barberis (2013), after more than thirty years, prospect theory is still viewed as the best way to evaluate how consumers make decisions under risk and riskless settings. The prospect theory was developed by Kahneman and Tversky (1979) and establishes that when people have to make a decision under risk, gains and losses are valued in a different way. In choice situations under risk, they demonstrate the existence of loss aversion, implying that decision makers are more concerned about losses than profits. In other words, individuals prefer to avoid a loss rather than obtain a profit of the same magnitude. Kahneman and Tversky (1979) suggest that the expected utility theory is not a good descriptive model when individuals have to make decisions under risk. They support this statement by showing different choice situations in which preferences do not accomplish the postulates of the expected utility theory. In a more recent work, Tversky and Kahneman (1991) presented the reference dependent utility specification to explain consumer choices in riskless situations, demonstrating that decision making depends on a reference level or status quo, which affects preference formation. The idea behind this theory is also that losses have larger effect on preferences than gains. In this way, they broaden their former approach to model choices under uncertainty or risk (Kahneman and Tversky, 1979). Therefore, the utility function considered is asymmetric and is based on three fundamental aspects: i) reference dependence, ii) loss aversion and iii) diminishing sensitivity. Thus, Tversky and Kahneman (1991) consider that the significant discrepancy observed between the minimum amount a person is willing to accept for the loss of a good and the maximum amount he is willing to pay for getting it, is due to loss aversion, among other aspects. Both willingness to pay (WTP) and willingness to accept (WTA) measures represent an important input in the social appraisal of different projects and policies. 103 The analysis of transport mode choice has been traditionally based on the estimation of models that consider the specification of symmetrical preferences. In the particular case of freight transport we can find significant contributions in the works of de Jong (2013), Brooks et al. (2012), Samimi et al. (2011), Arunotayanun and Polak (2011), Puckett et al. (2011), Cascetta et al. (2009), Train and Wilson (2008), García Menéndez et al. (2004), Bolis and Maggi (2003), Shinghal and Fowkes (2002), Abdelwahab (1998), and Jeffs and Hills (1990); among others. As a common characteristic, all models presented in these works give an identical treatment to the effect of increases and reductions in the level of service. These effects are represented by the marginal utility of each attribute and in the case of linear utility functions they correspond to the parameter accompanying this attribute. One of the most important implications of this approach is that the WTP to improve the quality of service is identical to the WTA compensation when quality is reduced. The progress made during the past decades in the development of software that allows creating sophisticated choice experiments and estimating more flexible choice models has facilitated the incorporation of elements of the prospect theory to the model specification and thus achieving a better understanding of consumers behaviour. In the freight transport context, the work by Kurri et al. (2007), when obtaining estimates of the value of time in Finland, is the first reference found in the literature which incorporates an asymmetric specification for the utility function. In a more recent work Masiero and Hensher (2010, 2011), Masiero and Maggi (2010) and Masiero and Rose (2013) use reference dependent utility specifications to test for different aspects of the prospect theory such as, loss aversion and diminishing sensitivity, comparing results with that obtained when the traditional symmetric model is used. A similar approach is used by Hess et al. (2008), De Borger and Fosgerau (2008) and Rose and Masiero (2010) in the field of passenger transport. In all these papers, specific choice experiments are created in order to allow for the specification of gains and losses as positive and negative variations with respect to the attribute values in the reference alternative; obtaining, in most cases, a better fit when the asymmetric specification is considered. In this regard, an important issue is how to define the attribute levels in the experiment as this influences responses of the interviewees. Also, a shift in the reference point may affect individuals’ preference formation, producing behavioural reactions to gains and losses. Thus, Masiero and Hensher (2010) found increases in loss 104 aversion for cost and time attributes when negative changes in the reference alternative are produced. An important implication resulting from the asymmetric specification is the ease to derive estimates of the WTP and WTA figures that can be obtained from the ratio between the corresponding marginal utilities. This in turn, allows quantifying the gap existing between these two figures. As many authors have concluded (see e.g. Hess et al., 2008; de Borger and Fosgerau, 2008; Grutters et al., 2008; Masiero and Hensher, 2010; Masiero and Hensher, 2011; Masiero and Maggi, 2010; Masiero and Rose, 2013), the obvious differences observed between the WTP and WTA measures, show that the monetary value attached to losses (WTA) is higher than that attached to gains (WTP), confirming the loss aversion hypothesis of the prospect theory. In this sense, the assumption of symmetric preferences would lead to overestimate the WTP and to underestimate the WTA, with the corresponding implications for social appraisal. Given that the WTA is normally greater than the WTP, Horowitz and McConnell (2002) concluded that the ratio between these two figures is highest for public and nonmarket goods and lowest when forms of money are introduced in the choice experiment. In this regard, Hanemann (1991) in the context of public-good valuation, analyzes from a theoretical point of view how much WTP and WTA can differ, suggesting that when quantity changes are produced, differences between WTP and WTA depend not only on income effect but also on substitution effect. Thus when substitution effect is small discrepancies are higher. This author also highlights that the large discrepancies between WTP and WTA are not a problem of the methodology employed in the survey “but of a general perception on the part of the individuals surveyed that the privatemarket goods available in their choice set are, collectively, a rather imperfect substitute for the public good under consideration”. Also Horowitz and McConnell (2003) indicate that the discrepancy observed between WTP and WTA measures can have two possible interpretations. On one hand, they consider that this difference can be seen as a deficiency of survey methods such us contingent valuation (in contrast with Hanneman, 1991), adding that “a weak version of this interpretation is that willingness to pay questions measure preference but willingness to accept question do not”. On another hand, they establish that the 111 3.3.1 WTP and WTA measures One of the most attractive advantages of using discrete choice models to analyze transport demand is their ability to obtain the WTP figures for improvements in the level of service in a very simple way. WTP measures quantify in monetary terms the effect of policies involving changes in the attributes; being the value of travel time savings one of most widely used in the evaluation of transport projects. Once model estimates are obtained, the WTP measures can be derived as the ratio between the marginal utility for the corresponding attribute and the marginal utility of the cost, which according to discrete choice theory is equal to minus the marginal utility of income; that is to say / / ik i Vx VC   . Under the symmetric utility framework, positive and negative variations with respect a reference value have the same impact on the utility and, consequently, the WTP for improving the level of service and WTA a compensation for reducing it are constrained to be identical. When the asymmetric specification is considered, we are able to obtain a different valuation for gains and losses, and consequently the WTP and the WTA measures differ. In this regard, for undesirable attributes, these measures are defined as: x c WTP       and x c WTA      (3.4) In contrast, for desirable attributes we obtain: y c WTP       and y c WTA      (3.5) Where a convenient negative sign has been added in the above expressions in order to obtain positive figures 9 . 9 Note that the subjective value for desirable attributes (such as service frequency), obtained as the ratio between the marginal utility of the attribute and the marginal utility of the travel cost yields a negative figure, which must be considered in absolute value when it is interpreted as the willingness to pay for improving or the willingness to accept a compensation for reducing the quality of service. 112 3.4 Model results Estimation results corresponding to the specifications discussed above are presented in this section. Different asymmetric models are considered comparing results with the symmetric specification. Also, some models are estimated in both, the preference and the WTP/WTA space. In all cases, maximum likelihood estimates for the unknown set of parameters were obtained with the software Biogeme 2.0 (Bierlaire, 2003). 3.4.1 Asymmetric models estimated in the preference space Estimation results corresponding to models estimated in the preference space are presented in Table 3.3. The first model MNL1 corresponds to a MNL model considering the symmetric utility specification given by expression (3.3). This model proved to be our best model in a previous research (see Arencibia et al., 2015), and its results will be compared with those obtained in different asymmetric specifications. MNL2 and MNL3 correspond the asymmetric utility (3.3) for MNL models, with and without the specification of an alternative specific constant (ASC) in the current option, respectively. It is important to highlight the low significance obtained for the parameter corresponding to reductions in service frequency , that in the case of MNL2 was even estimated with the opposite sign to that we expected. According to prospect theory, the loss aversion occurs when the absolute value of the coefficient attached to a loss is greater than that attached to a gain. Looking at the magnitude of the parameters' estimates, the loss aversion hypothesis is only held for the cost in MNL2, and for all attributes, except the frequency, in the model MNL3. This suggests that the effect of loss aversion could be confounded with the effect of the ASC in MNL2. Analogously, in models MNL4 and MNL5, we specify the reductions in service frequency interacting with the dummy Fm, being equal to one when the number of departures per week is lower than 5, and zero otherwise; this turned the variable to be significant and with the correct sign. In this regard, it is important to point out that different threshold values were tested obtaining a significant negative impact in frequency reduction when the current level of service frequency for the road is not F   113 perceived as very high (i.e. less than one departure per day during the weekdays) 10 .Therefore, for the rest of the models presented in this paper, we considered this specification for this variable. In these two models all parameters have been estimated with the expected sign and most of them are significant at the 95% confidence level. The only exceptions are increases in delay (significant at 93%) for MNL4 and increases in frequency (significant at 90%) and reductions in transit time (significant at 84%) for MNL5. According to the size of the parameters, in MNL4 the loss aversion is held for cost and frequency and in MNL5 is held for all attributes except for delay. Although this deserves a more in deep analysis testing for the statistical significance of the asymmetries, as we will see bellow, these results points out to the difficulties of rail to compete with road transport, as this mode always entails higher transit times and lower service frequency. ML1 and ML2 correspond to ML models, with fixed parameters accounting for the potential panel correlation existing in SP data. In these cases, the high significance obtained for the standard deviation of the error component confirmed the existence of correlation among responses belonging to the same respondent. The rest of the parameters were estimated with the expected sign and most of them were significant at the 95% significance level. The magnitude of the parameters in ML2 supports the assumption of loss aversion for all the attributes. However, as these figures represent point estimates subject to some error, the statistical significance of the loss aversion hypothesis should be tested. In the last rows of Table 3.3, the t-ratio values for test under the null hypothesis 0    are reported 11 . These results indicate that, in our data set, loss aversion is highly significant for the cost in most of models and for the rest of the attributes only in some cases. In particular, for delays and transit time the loss aversion hypothesis is not supported by any of our models. This should be interpreted as if the decision makers are perceiving the same impact for improvements and worsenings of the same magnitude for these attributes. 10 In our sample the average service frequency for road is 3.2 departures per week and the percentile P61 is 5, meaning that for near 40% of the sample the current level of service frequency is 5 or higher. Thus, we can infer that figures below 5 are considered as a not very good service. 11 ( ) var( ) var( ) 2cov( , )t                  114 Table 3.3 Estimation results for asymmetric models in the preference space. Attributes Estimates (t-test) MNL1 MNL2 MNL3 MNL4 MNL5 ML1 ML2 ASC ASC  -0.349 -0.635 - -0.420 - -0.642 - (-3.95) (-2.64) - (-1.8) - (-2.16) - Cost C  -0.006 - - - - - (-8.86) - - - - - Cost+ C   - -0.009 -0.011 -0.010 -0.011 -0.010 -0.011 - (-6.15) (-7.15) (-6.32) (-7.12) (-5.08) (-6.42) CostC   - - 0.004 0.004 0.004 0.004 0.005 0.004 - (5.77) (5.49) (5.63) (5.42) (5.22) (4.98) Frequency F  0.090 - - - - - (2.04) - - - - - Frequency+ F   - 0.232 0.110 0.179 0.102 0.244 0.140 - (2.96) (1.75) (2.36) (1.63) (2.79) (1.92) FrequencyF   - 0.044 -0.025 - - - - (0.62) (-0.37) - - - Frequency *Fm *F Fm   - - - -0.477 -0.572 -0.350 -0.482 - - - (-2.34) (-2.89) (-1.52) (-2.16) Delay D  -0.356 - - - - - (-5.79) - - - - - Delay+ D   - -0.246 -0.369 -0.245 -0.334 -0.267 -0.378 - (-1.79) (-2.91) (-1.79) (-2.64) (-1.80) (-2.75) DelayD   - 0.536 0.328 0.483 0.344 0.537 0.355 - (3.57) (2.58) (3.22) (2.68) (3.22) (2.48) Transit Time T  -0.294 - - - - - (-4.12) - - - - - Transit Time+ T   - -0.206 -0.382 -0.218 -0.344 -0.221 -0.375 - (-2.1) (-5.32) (2.23) (-4.98) (-2.09) (-4.75) Transit TimeT   - 0.631 0.258 0.511 0.263 0.646 0.344 - (2.67) (1.36) (2.18) (1.39) (2.58) (1.65) Sigma σ - - - - 0.737 0.727 - - - - (5.54) (5.48) 2  0.147 0.161 0.156 0.166 0.163 0.188 0.185 Adjusted 2  0.140 0.148 0.144 0.152 0.151 0.174 0.171 l*(0) -673.739 -673.739 -673.739 -673.739 673.739 -673.739 -673.739 l*(C) -655.833 -655.833 -655.833 -655.833 -655.833 -655.833 -655.833 l*(θ) -574.523 -546.963 -568.505 -562.042 -563.670 -546.841 -549.229 Observations 972 972 972 972 972 972 972 Number of Draws (Type) - - - - - 200 200 - - - - - MLHS MLHS Run Time - - - - - 10:50:49 14:50:29 t-test for H0: 0 CC    - -3.07 -4.19 -3.29 -4.27 -1.75 -3.24 t-test for H0: 0 FF    - 2.28 0.88 -1.29 -2.23 -0.40 -1.40 t-test for H0: 0 DD    - 1.12 -0.18 0.92 0.03 0.95 -0.09 t-test for H0: 0 TT    - 1.46 -0.60 1.01 -0.40 1.35 -0.13 115 As pointed out by Masiero and Maggi (2010), the existence of loss aversion is sufficient to guarantee the existence of discrepancies between the WTP and the WTA in the sense that it implies that the condition WTP<WTA is held. However, the existence of strong asymmetries in the cost coefficients, as happens in our case, could suggest the existence of discrepancies between the WTP and the WTA even if the rest of the attributes are perceived as symmetrical, as these parameters go in the denominator of the WTP/WTA expressions. When this happens, the re-parameterization of the model to estimate parameters in the WTP/WTA space (Train and Weeks, 2005) could be a convenient solution to test for the statistical discrepancies between these two figures. Table 3.4 presents the WTP and WTA figures for models estimated in the preference space. Although results vary among the different models, in all cases significant discrepancies between these two figures can be observed which contrast with figures obtained for the symmetric model MNL1. In all the models, the higher discrepancy is obtained for the frequency, ranging the ratio WTA/WTP from 2.6 to 16.2. For the rest of the attributes, this ratio ranges from 1 to 4, except for ML1 where the lack of loss aversion for delay and transit time yields a WTP higher than the WTA. Table 3.4 WTP and WTA measures for asymmetric models in the preference space. Attribute Frequency (€/depature) Delay (€/day) Transit Time (€/day) MNL1 WTP=WTA 15.79 62.68 51.76 MNL4 WTP 18.28 49.34 52.20 WTA 118.36 60.79 54.09 MNL5 WTP 9.56* 31.9 24.6* WTA 155 90.3 93.1 ML1 WTP 25.55 56.23* 67.64 WTA 65.79* 50.19 41.54 ML2 WTP 12.39 31.42 30.44 WTA 108.31 84.94 84.27 *Obatined with numerator parameters not significant at the 90% confidence level Finally, regarding the overall goodness of fit, both the Rho-square and the loglikelihood at convergence reported in Table 3.3, indicate that the asymmetric specifications outperforms the symmetric one in all models. According to these two 116 figures, ML models proved to be statistically superior. When comparing ML1 and ML2 using the log-likelihood ratio test (LR=4.776) the null hypothesis is accepted at the 97% confidence level, suggesting that these two models are quite similar; thus the model ML2 would be preferred as it provides more consistent results. With the aim of analyzing the statistical significance of the potential discrepancies between the WTP and WTA, in the next section, we re-parameterize models MNL5 and ML2 in order to obtain direct estimates of the WTP and WTA measures. 3.4.2 Asymmetric models estimated in the WTP/WTA space To estimate our models in the WTP/WTA space, we follow the recommendation of Train and Weeks (2005) and re-parameterize equation (3.3) of the observable utility, obtaining in a non-linear-in-the-parameter function. Thus, the utility of alternative i is expressed in terms of the WTP and WTA measures through the following expression:         ( ) ( ) ( ) i i k ik k ik r ir r ir xx yy kk rr i i ik ik ir ir c c c c i i ik i i c i c i x x y y kr i c i c i c c c c kr i c i c i x c V c c x x y y V c c x x y y V c c WTA x                                                                                    k ik ik ir ir ir ir x c y c y c kr WTP x WTP y WTA y               (3.6) Thus, WTP and WTA together with i c   and i c   are parameters to be estimated. The results of the estimated models in the WTP/WTA space are shown in Table 3.5. The model MNL6 is the counterpart to MNL5 in Table 3.3, whereas ML3 and ML4 are equivalent to ML2, the only difference is that in ML4 a random parameter following the Normal distribution is specified for i c . During the modelling process, many different specifications were tested, being those presented in Table 3.5 the ones that provided the best and more consistent results. All parameter estimates resulted significant at the 95% or 90% (WTP for frequency in MNL6 and WTA for frequency in ML4) confidence level, with the only exception of WTP for transit time in MNL6. According to the magnitude of the parameters, in all models, point estimates for the WTA are notably 117 higher than those obtained for the corresponding WTP for all the attributes included in the analysis. Table 3.5 Estimation results for asymmetric models in the WTP/WTA space. Attributes Estimates (t-test) MNL6 ML3 ML4 Cost+ C   Mean -0.011 -0.011 -0.021 (-7.12) (-6.42) (-5.11) Stand. Dev. - - -0.013 - - (-2.96) CostC   0.004 0.004 0.004 (5.42) (4.98) (4.70) WTA Frequency F WTA 155 109 113 (2.54) (1.99) (1.89) WTA Delay D WTA 90.3 85 100 (2.53) (2.58) (2.68) WTA Transit Time T WTA 93.1 84.4 94.2 (4.73) (4.29) (4.28) WTP Frequency F WTP 9.56 12.3 8.33 (1.68) (1.96) (2.26) WTP Delay D WTP 31.9 31.4 19.6 (2.65) (2.44) (2.55) WTP Transit Time T WTA 24.6 30.4 24.8 (1.42) (1.69) (2.34) Sigma Σ - 0.727 0.763 - (5.48) (5.89) ρ2 0.163 0.185 0.193 Adjusted ρ2 0.151 0.171 0.178 l*(0) -673.739 -673.739 -673.74 l*(C) -655.833 -655.833 -655.83 l*(θ) -563.670 -549.229 -543.780 Observations 972 972 972 Number of Draws (Type) - 200 200 - MLHS MLHS Run Time - 11:53:27 10:36:30 t-test for H0: 0 CC    -4.27 -3.24 -4.00 t-test for H0: 0 FF WTA WTP 2.36 1.74 1.74 t-test for H0: 0 DD WTA WTP 1.36 1.29 1.93 t-test for H0: 0 TT WTA WTP 2.56 1.87 2.72 118 In order to test for the statistical significance of these discrepancies, an asymptotic t-test under the null hypothesis 0 kk xx WTA WTP was performed. Test results, presented at the bottom of Table 3.5, suggest the existence of discrepancies between the WTP and the WTA measures for most freight transport attributes analyzed. In particular, for model ML4, the one with the better fit, all discrepancies are statistically significant at confidence levels higher than 90%. The ratio between the WTA and WTP for all the models is presented in Table 3.6. As can be seen, the variation of this ratio is rather high in all models, ranging, in the case of ML4, from 3.80 for transit time to 13.57 for service frequency. A possible explanation for these high discrepancies could be found in the high level of satisfaction perceived for the current transport service in this corridor. In fact, for the attributes considered in this analysis, the obtained satisfaction average scores are higher than 4 in a five-point Likert scale, where 1 represents "very low" and 5 "very good" (see Arencibia et al., 2015). This means, that decision makers are not willing to pay very much for improvements, as they are very satisfied with the current level of service, but they would claim high compensations in case of reductions, that may eventually put them below their admissible threshold values. Results obtained in this analysis are therefore consistent with postulates of prospect theory regarding loss aversion hypothesis, where losses are much more valued than gains. Thus, in freight transport, the reduction in cost that a company would accept in the presence of a worsening of one of the attributes that define the transport service is greater than the money they would be willing to pay for improving this attribute in the same magnitude. Table 3.6 Ratio between WTA and WTP. Attribute Ratio WTA/WTP MNL6 ML3 ML4 Frequency 16.21 8.86 13.57 Delay 2.83 2.71 5.10 Transit Time 3.78 2.78 3.80 119 3.5 Conclusions In this paper we use reference-dependent utility specifications to quantify discrepancies between the WTP and WTA for important service attributes that affect mode choice for freight transport, namely, transit time, service frequency and delays. Our case study is focused on routes that analyze modal competition at the international level, which represents one of the contributions of this research. In particular, our analysis points to a priority objective of the European transport policy: the diversion of freight traffic from road to more sustainable modes of transport, mainly rail and short-sea shipping. As a result, the information obtained about the discrepancies between the WTP and the WTA measures is essential to properly define alternative services to current road transport, which be able to attract demand. If we obtain that the WTA is much higher than the WTP, substantial reductions in transport cost should be considered in order to compensate the reduction in the level of service for using rail transport. On another hand, if the WTP is low, increases in price for using a better short sea shipping service should not be very high. Our data set is based on specific efficient SCE created for each respondent by pivoting attribute levels around the reference alternative. This allowed us to gain realism in the hypothetical settings created by the choice experiment. The specification of asymmetric utility functions, in the preference space, with respect the current level of service perceived by freight forwarders allowed us to test for the existence of substantial asymmetries and loss aversion in perception of the transport cost, in the corridor under analysis. Even though for these models, the loss aversion hypothesis could not be tested for the rest of the parameters individually, at a reasonable confidence level, models exhibiting asymmetries provided better fit to our data set than those with symmetrical preferences. As the cost parameters are fundamental for the transformation of utility units into monetary terms, the former models were re-parameterized yielding value functions in the WTP/WTA space. With this alternative model formulation, WTP and WTA play the role of estimated parameters, resulting discrepancies among them being statistically significant. 120 Our results offer a new evidence of the existence of asymmetrical response to deviations with respect to reference values, highlighting the importance of incorporating the elements of prospect theory to the analysis of consumers decisions. In this sense, it is possible to obtain a better understanding of the decision making process as well as to obtain more accurate measures of both, costs and benefits in transport projects and traffic forecasts. To accomplish this, the application of the appropriate stated choice techniques would be greatly helpful. Finally, results such as those presented here would be of great interest for freight forwarders and policy makers in order to obtain a more accurate evaluation of transport projects and policies in the European context. 3.6 References Abdelwahab, W. M. (1998). Elasticities of mode choice probabilities and market elasticities of demand: Evidence from a simultaneous mode choice/shipmentsize freight transport model. Transportation Research Part E: Logistics and Transportation Review, 34E(4), 257-266. Arencibia, A. I., Feo-Valero, M., García-Menéndez, L., & Román, C. (2015). Modelling mode choice for freight transport using advanced choice experiments. Transportation Research Part A: Policy and Practice, 75, 252–267. Arunotayanun, K., & Polak, J. W. (2011). Taste heterogeneity and market segmentation in freight shippers’ mode choice behaviour. Transportation Research Part E: Logistics and Transportation Review, 47(2), 138–148. Barberis, N. C. (2013). Thirty Years of Prospect Theory in Economics: A Review and Assessment. Journal of Economic Perspectives, 27(1), 173–196. Bierlaire, M. (2003). BIOGEME. A free package for the estimation of discrete choice models. Proceedings of the 3rd Swiss Transport Research Conference. Ascona, Switzerland. Bliemer, M.C.J., Rose, J.M. 2005. Efficiency and Sample Size Requirements for Stated Choice Studies. Report ITLS-WP-05-08, Institute of Transport and Logistics Studies, University of Sydney. 127 MNL that resembles the ML model, in the sense that heterogeneity in the population is represented by parameters following a discrete distribution identical across individuals. As no previous assumption about parameters distribution is required this represents an advantage with respect to the ML model. The LCM is based on the idea that individuals belong to different segments or classes with identical preferences within classes and estimates the class membership probability together with the class preference parameters. The definition of the appropriate number of classes is, however, a critical issue when using this model as it must be exogenously determined by the analyst. Although Greene and Hensher (2003) recognize that the different models have both, advantages and disadvantages, after the publication of their seminal paper, the use of LCMs to analyze non-observable heterogeneity has become a well-established methodology, as it provides intuitive interpretations for practitioners and policymakers, being at the same time easy to estimate. In this regard, we can cite the works of Wen and Lai (2010) and Shen (2009) among some significant contributions; the first, in an airline choice context and, the second, in a transport mode choice one. In terms of elasticity, both investigations determine that the use of MNL model, where a class division is not set, causes the sensitivity of service attributes tend to be over-estimated or under-estimated. In particular, in the field of freight transport we can cite the works by Massiani et al. (2007), Greene and Hensher (2013) and Feng et al. (2013), which analyze the existence of heterogeneous segments through the estimation of a LCM in a framework of discrete choice experiments. The estimation results of this model are compared with the results of the estimation of a MNL and a ML model. In all these cases, two is the optimal number of classes, and all the authors come to the same conclusion: the LCM provides a better fit than the MNL and the ML, and is better in terms of significance and predictive capability. In general, what is observed is an increased use of LC models in the stated choice framework (e.g. Grisolía and Willis, 2012; and Amador et al, 2014.). Even, Baerenklau (2010) employs this type of model in an aggregate count data context. This ranks the latent class model as an effective tool to further analyze the preferences of the individuals, and to determine ranges of willingness to pay. This makes possible to use the LCM advantages to set marketing, policy and managerial implications. So, increasingly, there are more authors that use 128 this type of models in different sectors (see e.g. Bhatnagar and Ghose, 2004, Scarpa and Thiene, 2005, and Pulido-Sanchez Fernandez Rivero, 2010). However, Provencher and Moore (2006) argue that, given that both the LCM and the ML model offers advantages, the choice of one model or another depends on the judgment made by the researcher about the correlation of preference parameters. Another critical issue in the analysis of consumers preferences is the incorporation of attribute cut-offs or threshold values to the decision making process. During decades, the utility maximization framework, where decision makers are assumed fully rational and fully informed, has been successfully applied in many different fields to model consumers’ choices. In this regard, the random utility model with linear-in-theparameter specification for the systematic utility, implicitly assumes compensatory behavior by decision makers, i.e. the individuals consider trade-offs among the attributes when evaluating the utility of the different alternatives. However, some other social scientists have pointed out that individuals may have limited capability in processing information (e.g. Simon, 1955; Tversky and Kahneman,1974) when they are trying to choose the best option given their constraints; recognizing that this framework represents only one of the many decision rules used by individuals (Payne et al., 1993). In this sense, individuals may exhibit non-compensatory behavior, such as in the process of elimination by aspects (EBA) proposed in Tversky (1972), where certain alternatives can be removed from the choice set, if their attributes do not meet some threshold values. This has led to more sophisticated models where decisions are modelled in two-stages (Manski, 1977). First, alternatives in the choice set are determined by a non-compensatory process, such as the EBA, and secondly, the remaining ones are evaluated using a compensatory decision rule. Although this twostage formulation seems more appropriate, its implementation is not absent of complexity, as the number of choice sets increases exponentially with the number of alternatives considered. Based on Manski (1977) and Williams and Ortuzar (1982) ideas, Cantillo and Ortúzar (2005) formulate a hybrid semi-compensatory two-stage model incorporating endogenous thresholds for the acceptance of the attributes in the choice process. Using synthetic and real data, these authors conclude that models incorporating noncompensatory behavior outperform traditional specifications such as the MNL model. 129 As pointed out by Swait (2001) many of the applications incorporating cut-offs to the decision making analysis are based on heuristics where these threshold values are viewed as “hard” constraints imposed on the attributes. This means that cut-offs cannot be violated for a choice to be considered valid. Such is the case of the EBA decision rule or the method proposed in Cantillo and Ortuzar (2005). In contrast, some other authors confirm empirically that individuals actually violate their previously stated cutoffs (see e.g. Huber and Klein, 1991; and Swait, 2001). Cut-off information is easy to obtain during the interview phase by asking individuals about the minimum level of service required for each of the attributes. However, in many cases, during the elicitation of preferences –e.g. through a stated choice experimentthe violation of these cut-offs is produced by observing that individuals choose alternatives where these selfimposed constraints are not met. In this regard, Swait (2001, p. 907) explains this phenomenon pointing out that when viewed in isolation, the cut-off of each attribute “reflects a decision maker behavioral intent”, but when all attributes are jointly analyzed, “decision makers may be willing to either change or violate cut-offs”. Thus the penalty imposed by an attribute cut-off violation can be compensated by an increase in the level of service for other attributes. In this sense, Swait (2001) propose an extension to the traditional compensatory utility maximization framework where: i) cutoffs are incorporated exogenously; and ii) it is possible for the consumer to treat these constraints as “soft” by permitting their violation at certain cost. Thus, the utility is specified as a piecewise linear function where a penalty component is added to the conventional linear-in-the-parameter non-penalized utility function. This penalty captures the negative effect of the attributes when cut-offs are violated. The resulting econometric model will be easy to estimate using standard software, as its derivation will depend on the assumptions made about the structure of the error term. It is also important to point out that, as cut-offs in Swait’s model are individual-specific, the breakpoints of the piecewise utility function vary across individuals, which highlights the potential of the model to capture heterogeneity regarding the perception of all the attributes. In this paper we use stated preference data to analyze modal choice for freight transport when information about attributes cut-offs, as proposed in Swait (2001), is introduced in the utility specification. Also, non-observable heterogeneity is analyzed by the specification of a LCM that allowed us to estimate not only the effect of the main 130 attributes defining modal choice within each class, but also how the violation of these cut-offs is perceived. Our results will allow us to detect the presence of important biases produced in the willingness to pay (WTP) figures when a MNL specification is considered. The main purpose of this research is to shed some light in the understanding of shippers’ preferences when they face mode choice decisions. A better understanding of preference heterogeneity by identifying different market segments is a key element in the evaluation of freight transport policies; in particular, those applied in the European Union promoting a more balanced modal share towards the use of more sustainable transport modes such as rail and maritime transport. In this regard, a better knowledge about the impact of the different attributes as well as the penalties imposed when attributes cut-offs are violated within the different segments provides new insights for practitioners and policy makers. Although the specification of attributes cut-offs is not new in the literature of freight transport demand modelling (see. e.g. the interesting contributions of Marcucci and Scaccia, 2004; Danielis and Marcucci, 2007; and Feo-Valero el al., 2014), to our knowledge, the quantification of these effects in conjunction with the analysis of nonobservable heterogeneity, through the estimation of LCM models, has not been previously applied, which reinforces the added value of the present research for the empirical literature. 4.2 Data and research context Our analysis is based on data obtained from a discrete choice experiment where decision makers were faced to the choice between the current option (road) and an intermodal alternative. In order to create realistic choice sets, the choice experiment consisted in two separate games with nine choice scenarios each. In the first one, the individual has to choose between the current option and a cheaper hypothetical intermodal alternative offering a worse or similar level service in the rest of the attributes. In contrast, the second game faced decision makers to the choice between the current alternative and an intermodal option that was more expensive but offered better level service in the other attributes. Although alternatives in both games were presented 131 as unlabeled, it is important to point out that the first game implicitly assumed the choice between road and rail (that represents the intermodal option road-rail-road); and the second one, the choice between road and a motorway of the sea service (roadmaritime-road). The population under analysis is represented by companies producing/distributing manufactured goods that during 2010 managed shipments of unitized freight in the corridor linking Madrid with the Netherlands, Belgium, Northern France and West Germany. In the reference period, this corridor accounted for 4.3% of the existing traffic between Spain and continental Europe. It is also worth mentioning that this is one of the few corridors in Spain where there exists real competition between the transport modes analyzed: road, rail and maritime. Our questionnaire was organized into four sections, including questions about: i) the characteristics of the company and its logistics perspective; ii) the characteristics of the reference shipment (cost, transit time, delays, etc.); iii) the importance of the main attributes that define the transport service, the perceived level of quality as well as the attributes cut-offs; and iv) the preferences of the decision maker by completing the two choice games. To ensure that the respondent corresponded with the real decision maker, some filter questions were included at the beginning of the questionnaire that helped us to arrange the personal interview with the person in charge of the transport shipment. In order to gain efficiency in the creation of our choice scenarios, the fieldwork was organized in two separate phases. First, the information collected about the reference shipment was used to create an orthogonal design where attributes’ levels were pivoted around these reference values. Once preferences in the different choice scenarios were collected, estimation results obtained in this preliminary phase were used as the required parameters priors for the construction of the D-efficient choice experiment (see e.g. Bliemer and Rose, 2005) that was conducted during the second phase of fieldwork. Again, the information about the reference shipment was used to tailor an individualspecific efficient design using the specialized software N-gene (Choicemetrics, 2009). As pointed out by Rose et al. (2008), this allowed us to improve the quality of our choice experiment and reduce the hypothetical bias. A more extensive description of this phase can be consulted in Arencibia et al. (2015). 132 A total sample of 93 companies located in the Autonomous Region of Madrid completed the questionnaire during the first phase, representing 4.4% of the Madrilenian companies identified in the directory as exporting or importing to the countries under study in 2010. Companies were randomly selected from the directory of Spanish Exporting and Importing Companies developed by the Spanish High Council of Chambers of Commerce (http://aduanas.camaras.org) and a properly trained group of interviewers helped us to collect information by means of personal interviews. During the second phase of the fieldwork, a web questionnaire including only the new efficient choice games was administered to all firms that participated in the first phase of the study. At the end of this second wave of interviews 54 of the 93 companies completed the questionnaire, yielding a total of 972 observations. Although our final sample size was not as large as desired, our two-step fieldwork strategy to create individual specific efficient designs helps to compensate our reduced sample size. Transport cost, transit time, days of delay in delivery times and service frequency were the attributes included in the two choice experiments. The levels of variation considered for these variables are presented in Tables A1 and A2 in the Appendix. It is important to point out that the levels of frequency and delays were re-defined according to the current level of service in order to further increase the realism of the experiment. As it has been already pointed out, the analysis incorporating ‘soft’ cut-offs allows the alternative to be chosen even if one or more cut-offs are violated. The analysis presented in Table 4.1 counts the number of choice scenarios where the different cutoffs are violated in each alternative. Thus, for example, the cost cut-off is violated in the intermodal alternative in 354 of the 972 choice scenarios. Despite that, this alternative is chosen in 139 cases, representing a significant percentage of the total sample (14%), which means that the cost excess is compensated by a better service in other attributes. A similar effect is observed for delay and, to a lesser extent for transit time and service frequency (see figures in bold in the table). In the case of road, only delay cut-offs are violated (41% of the choice scenarios) and this alternative is chosen in 20% of the cases. It is also interesting to note that an alternative can be chosen even if more than one cutoffs are violated. As shown in the analysis presented in Table 4.2, the intermodal alternative is chosen in 106 cases (11%) even though more than one attribute exceeds the threshold value. 133 Table 4.1 Analysis of cut-offs violations. Cut-off Chosen alternative Total Road Intermodal Nº of choice scenarios % Nº of choice scenarios % Nº of choice scenarios % Cut-offs violations (intermodal alternative) Cost 215 22% 139 14% 354 36% Transit time 212 22% 79 8% 291 30% Service frequency 125 13% 55 6% 180 19% Delay 312 32% 174 18% 486 50% Cut-offs violations (road) Cost 0 0% 0 0% 0 0% Transit time 0 0% 0 0% 0 0% Service frequency 0 0% 0 0% 0 0% Delay 191 20% 209 22% 400 41% Table 4.2 Number of cut-offs violated in the intermodal alternative. Number of cut-off violated Chosen alternative Total Road Intermodal Nº of choice scenarios % Nº of choice scenarios % Nº of choice scenarios % 0 52 5% 80 8% 132 14% 1 273 28% 207 21% 480 49% 2 171 18% 78 8% 249 26% 3 83 9% 28 3% 111 11% 4.3 Model specification Following the formulation of Greene and Hensher (2003), the basic assumptions of the LCM state that individuals’ behavior –modal choice in our caseis determined by the attributes of the alternatives and by certain latent heterogeneity that is not observed by the analyst. Thus, the model assumes that the population consists of a number Q of latent classes that is exogenously determined and unobserved heterogeneity is captured by these classes through the estimation of a parameter vector for each class. 134 Assuming that the underlying behavioral choice model is a MNL, the derivation of the choice probability for the LCM is based on two equations: i) the choice probability of the different alternatives; and ii) the membership probability to the different classes; where the error components in both models are independent and follow the Gumbel distribution. In this regard, the conditional probability that individual i in class q chooses alternative j in choice situation t among Jit available alternatives is: | 1 exp( ) ( ) ( | ) exp( ) it q itj it q it J q itj j x P j P y j q x        (4.1) Where yit represents the choice made by i in choice situation t, xitj is the attribute vector of alternative j for individual i in choice situation t; and q  is the vector of taste unknown parameters in class q; being q itj x  the utility of alternative j for individual i in class q. For convenience, we simplify notation in expression (4.1) and will allow |it q P represents the probability of the specific choice made by individual i in class q in choice situation t. Thus, given the sequence of choices made by individual i 12 [ , ,...., ] i i i i iT y y y y in class q, his contribution to the likelihood function is: || 1 i T i q it q t PP   (4.2) The prior membership probability of individual i to class q is: 1 exp( ) 1,...., exp( ) qi iq Q qi q z H q Q z      (4.3) where zi is a vector of observable characteristics, such as socioeconomic covariates, that could explain class membership, and q  is a vector of unknown parameters. Given the nature of these explanatory variables we choose conveniently class Q as reference, thus 135 Q  were normalized to 0 to allow model identification. If it were not possible to find a vector of significant explanatory variables, class membership would only be explained by the constant term. In this case, the prior class membership probability will be constant across individuals. Thus, the unconditional probability Pi that the individual i makes the sequence of choices yi is obtained by taking the expectation over all the Q classes. | 1 Q i i q iq q P P H   (4.4) Model parameters can be estimated using the standard procedure of maximum likelihood. Once parameter estimates are obtained, estimates of the probability of class membership ˆiq H and the conditional probability of the sequence of choices | ˆiq P can be calculated. Thus, the Byes rule can be used to obtain the individual specific posterior estimate of the latent class membership, conditional on his sequence of choices as: | | | 1 ˆˆ ˆˆˆ qi iq qi Q qi iq q PH HPH   (4.5) From expression (4.5) we can derive posterior estimates of the individual specific parameter vector through the expression: |´ 1 ˆˆ ˆ Q i qi q qH    (4.6) This provides very rich information as not only the behavior of the different classes or segments can be analyzed, but also at the individual level. In our mode choice model, we follow the approach proposed in Swait (2001) to incorporate “soft” cut-offs to the utility specification. Thus, the utility of the road and the intermodal alternative is as follows: 136   penalized utility non-penalized utility road road road road road road _ road road int int int int int non-penalized utility max 0, C T F D CO D C T F D U ASC C T F D D CoD U C T F D                               _ int _ int int _ int _ int penalized utility max 0, max 0, max 0, max 0, CO C CO T CO F CO D C CoC T CoT CoF F D CoD             (4.7) where ASCroad is the alternative specific constant of the road; Cj, Tj, Fj,and Dj represent cost, transit time, service frequency and delay for the alternative j, respectively; CoC, CoT, CoF and CoD represent the cut-offs of cost, transit time, service frequency and delay, respectively; .and βs are parameters to be estimated. With this formulation the penalized utility captures the additional disutility associated to the magnitude of cut-offs violations. Thus, a negative sign is expected for parameters in in this component of the utility. The non-penalized utility represents the conventional linear-in-the parameter specification used in mode choice models. It is worth noting that the penalized utility for road consists only in the part corresponding to delays, as for the rest of the attributes cut-offs were not violated, as discussed in the previous sections. In order to properly interpret the model marginal effects, it is important to point out that the part-worth utilities are represented by non-smooth functions that present a kink precisely at the cut-off point. Thus, a concave decreasing shape is expected for the partworth utility of undesirable attributes, such as cost, transit time and delays; whereas a concave increasing shape is expected for attributes producing a positive effect on the utility, as in the case of service frequency. Hence, if Xj represents an undesirable attribute for the alternative j, its marginal effect is given by the following expression: _ if if Xj j X CO X j j X CoX U X CoX X         (4.8) Where both X  and _CO X  are expected to be negative. In contrast, if Yj represents a desirable attribute for the alternative j, its marginal effect is: 143 Using expression (4.6) it is possible to obtain posterior estimates of individual specific parameters and to obtain the corresponding individual specific WTP figures for the different firms in our sample. Graphics in Figure 4.2 represent the kernel density estimates of WTP sample distributions. The solid lines correspond to kernel density estimates when the attribute cut-off is not violated. Dashed lines represent distributions when cut-offs are violated. In many cases the distribution presents a sort of multimodal shape. These local maximum could be interpreted as segments inferred from the latent classes identified in the parameter space. Thus, for example, in the upper left graphic, in the distribution of the value of time when time cut-off is violated, two different groups are clearly identified that correspond to individual with value of time less than 50€/day and those whose WTP for saving transit time lies between 100 and 150 €/day. Looking at the area below the density curve, the first group represents a more significant portion of the market. In contrast, when the cut-off penalty is not applied, the value of time is more evenly distributed across individuals. The median of the WTP distributions are presented in Table 4.6. Again we observe that these figures differ substantially from those obtained with the MNL model, especially when cut-offs penalties are imposed where the MNL model overestimates all these effects. 144 Table 4.5 Willingness to pay figures for the different classes. Willingness to pay MNL LCM Class 1 Class 2 Class 3 Class 4 Class 5 C<CoC C>CoC C<CoC C>CoC C<CoC C>CoC C<CoC C>CoC C<CoC C>CoC C<CoC C>CoC Transit time (€/day) T<CoT 32.90 12.11 - - - - 27.90 11.25 96.07 38.22 - - T>CoT 126.40 46.52 20.40 1.14 - - - - 131.00 52.12 - - Service frequency (€/service) F>CoF 17.09 6.29 - - - - 10.36 4.18 21.11 8.40 - - F<CoF 182.45 67.14 - - - - - - 312.82 124.44 - - Delay (€/day) D<CoD 55.25 20.33 - - - - 20.61 8.31 59.88 23.82 - - D>CoD 117.03 43.07 65.48 3.67 - - 41.18 16.60 - - - - 145 Figure 4.2 WTP distributions. Kernel density estimates. C<CoC C>CoC Table 4.6 Median of the WTP distribution. Attributes Median of the WTP distribution C<CoC C>CoC Transit time (€/day) T<CoT 28.19 11.25 T>CoT 31.81 12.50 Service frequency (€/service) F>CoF 10.46 4.17 F<CoF 42.42 5.23 Delay (€/day) D<CoD 20.78 8.28 D>CoD 41.05 8.90 -150 -100 -50 0 50 100 150 200 0 0.005 0.01 0.015 0.02 0.025 WTP(€/day) Kernel density VALUE OF TIME T<CoT T>CoT -150 -100 -50 0 50 100 0 0.005 0.01 0.015 0.02 0.025 0.03 WTP(€/day) Kernel density VALUE OF TIME T<CoT T>CoT -10 -5 0 5 10 15 20 25 30 35 40 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 WTP(€/departure) Kernel density VALUE OF FREQUENCY F>CoF F<CoF 050 100 150 200 250 300 0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1 WTP(€/departure) Kernel density VALUE OF FREQUENCY F>CoF F<CoF -150 -100 -50 0 50 100 150 200 250 300 0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016 0.018 0.02 WTP(€/day) Kernel density VALUE OF DELAY D<CoD D>CoD -100 -80 -60 -40 -20 0 20 40 60 80 100 0 0.005 0.01 0.015 0.02 0.025 0.03 0.035 0.04 0.045 0.05 WTP(€/day) Kernel density VALUE OF DELAY D<CoD D>CoD 146 4.5 Conclusions In this paper we analyzed taste heterogeneity in shippers preferences in a mode choice context through the estimation of a LCM based on the specification of a penalized utility that allowed us to quantify the penalty effect produced when the attributes of the alternatives did not meet acceptable level of service constraints that were previously imposed by respondents during the interview phase. The analysis uses a stated preference data set that collected information about shipments in the corridor that links Madrid, by road, with important cities in Central Europe. The context of the experiment faced respondents (current road users) to an intermodal alternative that contemplated the use of more sustainable modes of transport, such as rail and short sea shipping. During the modeling process different models were tested in relation to the number of classes or segments, with best results obtained when five classes considered; finding that two of such classes corresponded to residual groups of individuals who seemed not to have understood or taken the experiment seriously. This result reinforces the argument raised by many authors to devote sufficient resources to the data collection phase, as this contributes positively in the quality of the results. The three remaining segments provided us with interesting information regarding the perception of modal choice attributes and their corresponding cut-offs penalties. The main differences are due to different patterns found in relation to their compensating behavior. In this regard, it is worth to highlight the existence of groups that do not consider some attributes when faced to modal choice decisions. In particular, it is worth to highlight the low significance detected for the cut-off penalty of service frequency in two of the classes, and that of the delay in the other group. Notwithstanding, the estimation of the attributes penalties provides a more accurate knowledge about preferences, especially when service quality is reduced below acceptable levels. When testing our results against those obtained for the conventional MNL specification, we detected the presence of important biases in the WTP figures; observing that models not accounting properly for the analysis of taste heterogeneity can yield important overestimates for a substantial portion of the population. Given the relevant role of the WTP figures in the evaluation of transport policies, the application of methods that 147 enhance the detection of different market segments is deemed essential for a better use of public resources. 4.6 References Amador, F. J., González-Marrero, R. M., Rizzi, L.I., & Román, C. (2014). El Valor Para Los Conductores de Reducir El Riesgo de Accidentes de Pasajeros Y Peatones: Una Aproximación de Clases Latentes. XVIII Congreso Panamericano de Ingeniería de Tránsito, Transporte y Logística. Santander. España. Arencibia, A.I., Feo-Valero, M., García-Menéndez, L., & Román, C. (2015). 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