A New Monthly Indicator of Global Real Economic Activity

Ravazzolo, Francesco; Vespignani, Joaquin L. Working Paper A New Monthly Indicator of Global Real Economic Activity Working Paper, No. 06/2015 Provided in Cooperation with: Norges Bank, Oslo Suggested Citation: Ravazzolo, Francesco; Vespignani, Joaquin L. (2015) : A New Monthly Indicator of Global Real Economic Activity, Working Paper, No. 06/2015, ISBN 978-82-7553-861-9, Norges Bank, Oslo, https://hdl.handle.net/11250/2495868 This Version is available at: https://hdl.handle.net/10419/210073 Standard-Nutzungsbedingungen: Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden. Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen. Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in EconStor may be saved and copied for your personal and scholarly purposes. You are not to copy documents for public or commercial purposes, to exhibit the documents publicly, to make them publicly available on the internet, or to distribute or otherwise use the documents in public. If the documents have been made available under an Open Content Licence (especially Creative Commons Licences), you may exercise further usage rights as specified in the indicated licence. https://creativecommons.org/licenses/by-nc-nd/4.0/deed.no A new monthly indicator of global real economic activity NORGES BANK RESEARCH 06 | 2015 AUTHORS: FRANCESCO RAVAZZOLO JOAQUIN L. VESPIGNANI WORKING PAPER NORGES BANK WORKING PAPER XX | 2014 RAPPORTNAVN 2 Working papers fra Norges Bank, fra 1992/1 til 2009/2 kan bestilles over e-post: [email protected] Fra 1999 og senere er publikasjonene tilgjengelige på www.norges-bank.no Working papers inneholder forskningsarbeider og utredninger som vanligvis ikke har fått sin endelige form. Hensikten er blant annet at forfatteren kan motta kommentarer fra kolleger og andre interesserte. Synspunkter og konklusjoner i arbeidene står for forfatternes regning. Working papers from Norges Bank, from 1992/1 to 2009/2 can be ordered by e-mail: [email protected] Working papers from 1999 onwards are available on www.norges-bank.no Norges Bank’s working papers present research projects and reports (not usually in their final form) and are intended inter alia to enable the author to benefit from the comments of colleagues and other interested parties. Views and conclusions expressed in working papers are the responsibility of the authors alone. ISSN 1502-8143 (online) ISBN 978-82-7553-861-9 (online) Page 1 of 38 A New Monthly Indicator of Global Real Economic Activity April 13, 2015 Francesco Ravazzoloa and Joaquin L. Vespignanib+ aNorges Bank and BI Norwegian Business School, Norway bUniversity of Tasmania, Tasmanian School of Business and Economics, and Centre for Applied Macroeconomic Analysis, Australia Abstract In modelling macroeconomic time series, often a monthly indicator of global real economic activity is used. We propose a new indicator, named World steel production, and compare it to other existing indicators, precisely the Kilian’s index of global real economic activity and the index of OECD World industrial production. We develop an econometric approach based on desirable econometric properties in relation to the quarterly measure of World or global gross domestic product to evaluate and to choose across different alternatives. The method is designed to evaluate short-term, long-term and predictability properties of the indicators. World steel production is proven to be the best monthly indicator of global economic activity in terms of our econometric properties. Kilian’s index of global real economic activity also accurately predicts World GDP growth rates. When extending the analysis to an out-ofsample exercise, both Kilian’s index of global real economic activity and the World steel production produce accurate forecasts for World GDP, confirming evidence provided by the econometric properties. Specifically, a forecast combination of the three indices produces statistically significant gains up to 40% at nowcast and more than 10% at longer horizons relative to an autoregressive benchmark. Keywords: Global real economic activity, World steel production, Forecasting JEL Codes: E1, E3, C1, C5, C8 * This Working Paper should not be reported as representing the views of Norges Bank. The views expressed are those of the authors and do not necessarily reflect those of Norges Bank. We thank Farooq Akram, Hilde Bjørnland, Lutz Kilian, Jim Stock and Leif Anders Thorsrud, as well as seminar and conference participants at Norges Bank and University of Melbourne. +Corresponding author: Joaquin L. Vespignani; University of Tasmania, School of Economics and Finance, Australia; Tel. No: +61 3 62262825; E-mail address: Joaquin.Vespi[email protected]u Page 2 of 38 Introduction In time series macroeconomic analysis often an indicator of global real economic activity is used to represent the World economy. World or global gross domestic product (GDP), measured at quarterly frequency in United States (US) dollars using purchasing power parity, is broadly accepted and frequently used as a measure of global economic activity. However, there is a lack of degrees of freedom associated with quarterly data. To address this issue, economic modellers commonly turn to a monthly indicator of global economic activity. Consequently, several monthly indicators of activity have been used in the literature to measure real economic activity (at both country and global level). 1 This paper develops a novel econometric approach to evaluating and choosing across existing and new proposed monthly indicators of global economic activity. We believe that an indicator shall have desirable econometric properties in relation to the quarterly measure of World or global gross domestic product that shall be tested before to use. We propose eight features that focus on shortand long-term properties of the indicators and their relationship with a quarterly measure of global output based on cointegration, correlation, fitting and mixed-frequency in-sample predictability considerations. In particular, there are two measures of global real economic activity popular among empirical researchers. The first such measure, taken from the Organisation for Economic Cooperation and Development (OECD) Monthly Economic Indicators (MEI), is aggregated industrial production for OECD countries. The second measure is the global real economic activity (rea) index proposed by Kilian (2009). Industrial production has been widely used as a measure of real economic activity at both country and global level. At country level, among others, Mullineaux (1980), Grilli and Roubini (1996), Bernanke et al. (1997), Kim (2001), 1 We concentrate our analysis on observable indicators and do not consider unobservable global factors, such as global factors extracted by large datasets. Our properties can be applied to these series too and can also be extended to account for desirable properties when, for example, extracting the factors. Page 3 of 38 and Kim and Roubini (2001) have used industrial production as a proxy for real economic activity for large developed economies. Similarly, Mackowiak (2007) measured real economic activity at country level for emerging economies using industrial production. 2 Not without controversy, the index of industrial production for aggregated OECD economies has been widely used as a proxy for global real economic activity. For example, Gerlach (1988) uses both the industrial production index for OECD countries and US industrial production as a proxy for global real economic activity in the study of World business cycles under different exchange rate regimes. Furthermore, Ciccarelli and Mojon (2010) use the industrial production index for OECD economies in studying global inflation. Kilian (2009) developed an index of global real economic activity using data of dry cargo single voyage ocean freight rates. Since 2009, this indicator has become a popular choice to represent global real economic activity, in particular for oil price studies. Among others, Apergis and Miller (2009) model the effect of oil shocks on different country stock prices using this index. Alquist and Kilian (2010) forecast the price of crude oil futures. They use this index in assessing the predictive power of their proposed model. Basher et al. (2011) use this index to study the relationship between oil prices, exchange rates and emerging stock markets. Vespignani and Ratti (2013) build a SVAR model to describe the influence of global liquidity on oil prices using Kilian’s real index as a proxy for global economic activity. Baumeister and Kilian (2013) use this index, in conjunction with other variables, to forecast real oil prices. 2 For large developed economies: Mullineaux (1980) in studying the relationship between unemployment, output and inflation for the US, Grilli and Roubini (1996) in studying liquidity models for G7 economies, Bernanke et al. (1997) in studying the effect of oil price shocks for the U.S economy, Kim (2001) in addressing international transmissions of monetary shocks for non-US G6 economies and Kim and Roubini (2001) in developing a model for exchange anomalies for non-US G7 economies. For emerging economies Mackowiak (2007) studies the transmission mechanism of US shocks to emerging economies, including the following countries Chile, Hong Kong, Korea, Malaysia, Mexico, Philippines, Singapore and Thailand. Page 4 of 38 We extend the indicator set with a new proposed indicator: World steel production. Steel is an important input component of global economic activity and we test whether it can be considered as a reliable indicator. Results indicate that World steel production is the preferred monthly indicator for our econometric properties. Kilian’s real index also does reasonably well for the properties on global output growth. Then, we extend our evidence from the in-sample econometric approach to an out-of-sample exercise. We confirm the insample results and find that the World steel production and Kilian’s real index produces accurate forecasts for World GDP. Therefore, our econometric approach provides accurate information for both in-sample and out-of-sample analyses. Moreover, using a forecast combination of the three indices produces statistically significant gains up to 40% at nowcast and more than 10% at longer horizons relative to an autoregressive benchmark. The remainder of the paper is organised as follows: Section 2 provides a review of current indicators of global real economic activity used in the literature. Section 3 proposes a new indicator of global real economic activity. Section 4 proposes a new econometric approach to evaluating monthly indicators of global economic activity. Section 5 presents the results of the econometric approach proposed in the previous section. Section 6 sets up an exercise to forecast World GDP. Section 7 concludes. 2. Current indicators of global real economic activity In this section we describe two popular choices of monthly indicators of global real economic activity: OECD industrial production and Kilian’s real index. In Figure 1, World GDP, OECD industrial production (both in log-first difference form) and the Kilian’s real index are compared using quarterly frequency. 3 It can be observed that OECD industrial production does not capture the unprecedented increase in global aggregate demand 3 Note that Kilian’s real index provided by the author in first difference. Page 5 of 38 registered in the late 1990s, which originated from emerging economies. World GDP, Kilian’s real index and World Steel Production (not shown in Figure 1) capture these effects. However, all these indexes seem to capture very well the Great Moderation (1985-2002), and the global financial crisis (GFC). 4 2.1 OECD industrial production This index is available from the OECD monthly economic indicators (MEI) database from January 1975 to the present. The popularity of using this index to represent global real economic activity can be partially attributed to the fact that prior to 2009 there were few alternative time series of reasonable length that were representative of monthly global real economic activity. This index is constructed with data from 34 OECD countries. 5 According to the OECD MEI definition: “Area totals for industrial production are annually chain-linked Laspeyres indices. The weights for each yearly link are based on the previous year's gross domestic product in construction adjusted by GDP purchasing power parity. ” The use of this index as a proxy for global real economic activity relies on two assumptions. The first assumption is that the industrial sector is a good representation of the full economy. The second assumption is that the OECD economies are representative of the World economy. Prior to 1990, both assumptions were reasonable, as manufacturing sectors were a large part of most economies and economic growth was concentrated in developed 4 The term the Great Moderation was first coined by Ben Bernanke in 2004 based on the Stock and Watson (2002) study. Kilian (2008), Kilian (2009), Kilian and Hicks (2013) and Humphreys (2010) attribute the rise in oil prices and commodity prices from 2003 to 2008 to the rapid economic growth and demand from emerging economies respectively. 5 These countries are: Australia, Austria, Belgium, Canada, Chile, the Czech Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Israel, Italy, Japan, Korea, Luxembourg, the Netherlands, New Zealand, Norway, Mexico, Poland, Portugal, the Slovak Republic, Slovenia, Spain, Sweden, Switzerland, Turkey, the United Kingdom and the United States. Page 6 of 38 economies. However, most recent empirical evidence indicates a diversion between industrial production and GDP. For example, Steindel (2004) argues that the relationship between industrial production and the goods output component of GDP has diverged significantly since the 2001 recession in the US. Steindel (2004) attributes this departure to the growth of imports and the increase of services inputs of all goods. Similarly, Herrera et al. (2011) attribute the possible divergence of GDP and industrial production to two factors. First, GDP is a measure of the valued added in the economy, while industrial production measures gross output; and, second, industrial production excludes services whose contribution to GDP has increased over time in the US. In Kilian’s (2009) influential study on oil prices, he disputes the use of this indicator as a proxy for global real economic activity. Kilian’s main critique is that OECD industrial production excludes emerging economies in Asia such as China and India, whose demand for industrial raw materials is thought to be fuelling the surge in industrial commodity and oil prices since 2002. 6 Similarly, with reference to global output, Engel and Rogers (2006) note that in terms of purchasing power parity, the combined GDP of emerging economies such as Brazil, China, India, Indonesia, Korea, Mexico, Philippines, and Thailand was 2.43 times the GDP of the US. Crucini et al. (2012) also observe that the share of global output of G7 economies has declined in recent decades while the share of emerging economies such as China and India has increased. Kose et al. (2012) indicate that emerging market economies (specifically China and India) have become major contributors to World output over the period 2003-2007. Kilian (2009) also questions the lack of clarity in which the weights of the OECD industrial index are defined, given different exchange rates across countries. 6 Support for this view can also be found in Hamilton (2013) and Kilian and Hicks (2013). Page 13 of 38 series are non-stationary and integrated of the same order and there exists a parameter α such that: 𝑢𝑡=log⁡(𝐺𝑅𝐸𝐴𝑡 𝑞)−𝛼log⁡(𝐺𝐺𝐷𝑃𝑡) (1) is a stationary process. Where: 𝑢𝑡⁡is the error term, 𝐺𝑅𝐸𝐴𝑡 𝑞 is the global monthly indicator of real aggregate demand. The superscript q is used to denote that the monthly series was converted to a quarterly series using the simple average. 𝐺𝐺𝐷𝑃𝑡 is World GDP and 𝛼 is a parameter to be estimated. Aggregate distance properties Property 2: When 𝐺𝐺𝐷𝑃𝑡 and 𝐺𝑅𝐸𝐴𝑡 𝑞 are indexed from the same start period, the square aggregated distance between these two series should be minimised. Formally; 𝑀𝑖𝑛⁡∑√(log⁡(𝐺𝐺𝐷𝑃)𝑡−log⁡(𝐺𝑅𝐸𝐴𝑡 𝑞))2 𝑛 𝑖=1 ⁡(2) Property 3: When 𝐺𝐺𝐷𝑃𝑡 and 𝐺𝑅𝐸𝐴𝑡 𝑞 are first differenced and indexed from the same start period, the square aggregate distance between these two series should be minimised. Formally; 𝑀𝑖𝑛⁡∑√(∆log⁡(𝐺𝐺𝐷𝑃𝑡)−∆log⁡(𝐺𝑅𝐸𝐴𝑡 𝑞))2 𝑛 𝑖=1 ⁡(3) Where: ∆ is the first difference operator and log is short for logarithm. Property 4: When 𝐺𝐺𝐷𝑃𝑡 and 𝐺𝑅𝐸𝐴𝑡 𝑞 are detrended and indexed from the same start period, the square aggregate distance between these two series should be minimised. Formally; Page 14 of 38 𝑀𝑖𝑛⁡∑√[(𝐺𝐺𝐷𝑃𝑡−𝛽𝑡)−(𝐺𝑅𝐸𝐴𝑡 𝑞−𝛿𝑡)]2 𝑛 𝑖=1 ⁡(4) Where 𝑡=(1,2,…,𝑛) is a time trend and 𝛽 and 𝛿 are parameters to be estimated using ordinary least square regression. Correlation properties Property 5: Maximise correlation between ∆𝐺𝐺𝐷𝑃𝑡 and ∆𝐺𝑅𝐸𝐴𝑡 𝑞. Formally; 𝑀𝑎𝑥 [ 𝑛∑∆𝐺𝐺𝐷𝑃𝑡∗∆𝐺𝑅𝐸𝐴𝑡 𝑞−(∑∆𝐺𝐺𝐷𝑃𝑡)∗(∑∆𝐺𝑅𝐸𝐴𝑡 𝑞) √𝑛∑(∆𝐺𝐺𝐷𝑃𝑡)2−∑(∆𝐺𝐺𝐷𝑃𝑡)2⁡√𝑛∑(∆𝐺𝑅𝐸𝐴𝑡 𝑞)2−∑(∆𝐺𝑅𝐸𝐴𝑡 𝑞)2 ] ⁡⁡⁡⁡⁡(5) Property 6: Maximise correlation between d𝐺𝐺𝐷𝑃𝑡 and 𝑑𝐺𝑅𝐸𝐴𝑡 𝑞. Formally: 𝑀𝑎𝑥 [ 𝑛∑𝑑𝐺𝐺𝐷𝑃𝑡∗𝑑𝐺𝑅𝐸𝐴𝑡 𝑞−(∑𝑑𝐺𝐺𝐷𝑃𝑡)∗(∑𝑑𝐺𝑅𝐸𝐴𝑡 𝑞) √𝑛∑(𝑑𝐺𝐺𝐷𝑃𝑡)2−∑(𝑑𝐺𝐺𝐷𝑃𝑡)2⁡√𝑛∑(𝑑𝐺𝑅𝐸𝐴𝑡 𝑞)2−∑(𝑑𝐺𝑅𝐸𝐴𝑡 𝑞)2 ] ⁡⁡⁡⁡⁡(6) Where 𝑑𝐺𝐺𝐷𝑃𝑡=𝐺𝐺𝐷𝑃𝑡−𝛽𝑇 and ⁡𝑑𝐺𝑅𝐸𝐴𝑡 𝑞=⁡𝐺𝑅𝐸𝐴𝑡 𝑞−𝛿𝑇 , where 𝑇 is a lineal trend. Predictability Properties Property 7: This property states that: a desirable feature of the global real economic activity monthly indicator is to be able to predict quarterly World GDP when both series are transformed to a stationary process by using first difference transformation. The 𝑅2 and Page 15 of 38 adjusted 𝑅2 are used as an indicator of predictability power. We notice that different frequencies of the variables require mixed-frequency analysis. 17 Formally, 𝑀𝑎𝑥⁡𝑅2⁡[∆𝐺𝐺𝐷𝑃𝑡=𝛽0+𝛽1𝐵(𝐿1 𝑚 ⁄;𝜃)∆𝐺𝐴𝐷𝑡−ℎ (𝑚) +𝜀𝑡⁡]⁡⁡⁡(7) Where ⁡(𝐿1 𝑚 ⁄;𝜃)=∑𝑏(𝑘;𝜃)𝐿(𝑘−1)/𝑚 𝐾 𝑘=1 , and 𝐿𝑠/𝑚𝐺𝐴𝐷𝑡−1−𝑠/𝑚 (𝑚) , and t is indexes at quarterly frequency and 𝑚=3 and is the higher sampling frequency. ∆ is the first difference operator . Property 8: This property states that: a desirable feature of the global aggregate demand monthly indicator is to be able to forecast quarterly World GDP when both series are transformed to a stationary process by detrending both series. The 𝑅2 and adjusted 𝑅2 are used as indicator of nowcating power. Formally, 𝑀𝑎𝑥⁡𝑅2⁡[𝑑𝐺𝐺𝐷𝑃𝑡=𝛽0+𝛽1𝐵(𝐿1 𝑚 ⁄;𝜃)𝑑𝐺𝐴𝐷𝑡−ℎ (𝑚) +𝜀𝑡⁡]⁡⁡⁡(8) Where ⁡(𝐿1 𝑚 ⁄;𝜃)=∑𝑏(𝑘;𝜃)𝐿(𝑘−1)/𝑚 𝐾 𝑘=1 , and 𝐿𝑠/𝑚𝐺𝐴𝐷𝑡−1−𝑠/𝑚 (𝑚) , and t is indexes at quarterly frequency and 𝑚=3 and is the higher sampling frequency. 𝑑 is detrended operator. 5. Results of the econometric approach The results of our econometric approach for OECD industrial production, Kilian’s real index and World steel production are summarised in Table 6. In this table, we rank the indicators according to the 7 numerical properties (we exclude property 1) developed in 17 For the sake of brevity we use the terminology predictability for in-sample predictability or fitting; and the terminology “forecastability” for out-of-sample forecasting. Page 16 of 38 section 4. The best performance for each property is indicated by the number 1, while the worst by the number 3. Property 1 is the only non-numerical feature in this table. Results show that OECD industrial production and World steel production are individually cointegrated with World GDP while Kilian’s real index is not (as is expected). 18 Properties 3, 5 and 7 are distinguished with a darker background to denote exercises built with data in first difference or short term. Considering all properties, World steel production presents the most promising results out of the three indicators. This indicator yields the best results with regard to properties 2, 3, 4, 6, 7 and 8 and the second best results in property 5. Kilian’s real index yields the best results when first difference data is used, being the best indicator according to properties 5 and the second best in property 3, 7 and confirming Kilian’s assertion that this index is a global business cycles index. OECD industrial production general performs badly in terms of these properties, being ranked third in properties 3, 5 and 8 and second in properties 2, 4, 6 and 7. Rows 9, 10 and 11 in Table 6 present the average results for properties in first difference, detrended and for all numerical properties (2 to 8), respectively. World steel production outperforms all other 2 indicators in terms of first difference and detrended properties. Although, Kilian’s real also performs very well in tracking global GDP growth rates. Finally, average results for all numerical properties also produce favourable results for World steel production revealing the lower average score of 1.14, while Kilian’s real index and OECD industrial production achieve an average score of 2.28 and 2.42 (respectively). Results in detail are discussed below. 18 Kilian’s index is already constructed in first difference. For property 1, we have constructed a chain index from the starting period (1990:Q1=100) for the Kilian’s index of global real economic activity. Page 17 of 38 5.1 Long-run properties In Table 2 the stationary properties of the data are reported. For this purpose both the Augmented Dickey-Fuller (ADF) test and the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) are estimated for all variables. For robustness purposes, both methods, which have inverse null hypotheses, have been used. 19 The null hypothesis for the ADF test is the variable has a unit root and the null hypothesis for the KPSS test is that the variable is stationary. Both tests results suggest that World GDP, OECD industrial production and World steel production are non-stationary variables. Kilian’s real index presents mixed results. However, as describe by Kilian (2009), this index is a measure of the business cycle and constructed by aggregating different growth rates (for different dry cargos and routes), consequently it is reasonable to assume that it is stationary. 20 5.1.1 Property 1 In Table 3, results for the VAR Johansen’s cointegration test are presented. 21 In this table we evaluate the cointegration relationship between World GDP and OECD industrial production, and World GDP and World steel production. Results for the Trace and Maximum eigenvalue tests are reported in Table 2 and 3 respectively. In specifying these tests with no intercept and no trend, both tests suggest only one cointegrating relationship between the three relationships tested. Specifically, in Table 2, it is observed that the null hypothesis of the number of cointegrating vectors is less than or equal to r is rejected when 𝑟=0⁡at the 5% level, for the 19 Testing the inverse null hypothesis can be seen as a robustness analysis to determine the stationary properties of the data, ideally both tests should agree. Jin and Frechette (2004) show that a disagreement in results of these tests is a sign that the data could be fractionally integrated. 20 Our constructed chain index from the starting period for the Kilian’s index of global real economic activity is appears to be non-stationary, but both eigenvalue and trace tests suggest no cointegration vector between Kilian’s chained index and the log of world GDP. 21 For more detail of this test, please see Enders (2004; pp. 362), and Engle and Granger (1987). Page 18 of 38 cointegrating vector between OECD industrial production and World GDP, and for World steel production and World GDP. The null hypothesis that the number of cointegration vectors is 𝑟≤0⁡cannot be rejected even at the 10% level for the two cases, pointing to only one cointegrating vector. In Table 3, results for the Maximum eigenvalue confirm these results. The null hypothesis that the number of cointegrating vectors is r can only be rejected when r = 0 at the 5% level for the relationship between OECD industrial production and World GDP and for World steel production and World GDP; while the hypotheses of either r = 1 cannot be rejected even at the 10% level for both cases. Consequently, this first exercise supports the use of either OECD industrial production or World steel production as indicators of World economic activity. 5.2 Aggregate distance properties In properties 2, 3 and 4 we evaluate the aggregate distance between World GDP and the monthly indicators to be evaluated in levels, first difference and detrended series respectively. In these 3 exercises, all indicators are re-scaled by constructing an index where the first observation is 1990:Q1=100. For comparative purposes, Kilian’s real index is not transformed to logs and previously re-scaled by dividing this index by 100 given that this index is constructed in first difference. 22 The ranking of these properties 2, 3 and 4 are reported in table 6, rows 2, 3 and 4 respectively, where the indicator with lowest distance is reported as number 1, the second lowest distance number 2, and the third lowest distance number 3. 22 We also test this property by using the chained index version of Kilian’s real index. Results for the chained index worsen significantly with respect to the unchained version of Kilian’s index. Page 19 of 38 5.2.1 Property 2 In Table 6, row 2, results are presented for property 2, where the aggregate distance of the log-level of World GDP with respect to monthly indicators of World growth valued added (at quarterly frequency) is evaluated. It can be seen that World steel production ranked first with the lowest log-level distance value of 2.61, followed by OECD industrial production with a log-level distance value of 4.06, and Kilian’s real index fourth with a log-level distance value of 8.2. 5.2.2 Property 3 In the third row of Table 6, results are presented for property 3, where the aggregate distance of the first difference of World GDP with respect to monthly indicators of World growth valued added (at quarterly frequency) is evaluated. Note that World steel production indicator ranked first with the lowest distance of 0.59, followed by Kilian’s real index with second lowest distance value of 0.72 and OECD industrial production with third lowest distance value of 1.03. 5.2.3 Property 4 In the fourth row of Table 6, results are presented for property 4, where the aggregate distance of the detrended version of World GDP with respect to monthly indexes of World growth valued added (at quarterly frequency) is evaluated. It can be observed that World steel production indicator ranked first with the lowest distance with respect to World GDP of 2.68, followed by OECD industrial production with second lowest distance value of 3.12, and Kilian’s real index with fourth lowest distance value of 3.21. 5.3 Correlation properties Page 20 of 38 In this set of properties, the correlation between World GDP and monthly global indicator of growth value added is investigated. 5.3.1 Property 5 Results for property 5 are presented in the fifth row of Table 6. Kilian’s real index shows the highest correlation with World GDP with a correlation coefficient of 0.29, indicating that this index is by far the best index in terms of representing short-term global economic fluctuations. All other indicators present a small and negative correlation in first difference. World steel production has a correlation coefficient of -0.09 and OECD industrial production has a correlation coefficient of -0.10. 5.3.2 Property 6 Row 6 in Table 6 shows results of the correlation between detrended World GDP and the corresponding series for World monthly indicator of economic activity. These correlations are much higher than those observed in property 5. The detrended index of World GDP is highly correlated with World steel production (correlation coefficient of 0.96). OECD industrial production’s correlation with World GDP is 0.90 while Kilian’s real index correlation is with World GDP is only 0.45. 5.4 Predictability properties In 7 and 8, the predictability properties of monthly Global indicator of economic activity on World GDP are investigated. In 7 and 8, the first difference transformation and detrended World GDP (respectively) are predicted using monthly global indicators. 5.4.1 Property 7 Page 21 of 38 In Table 4, results of property 7 are presented. In the second, third, fourth and fifth columns results of World steel production, OECD industrial production and Kilian’s real index respectively are presented. In evaluating this feature, the higher R2 and adjusted R2 are observed in the fifth column, showing that World steel production monthly indicator observations within a quarter (M1, M2 and M3) and its lags predict up to 58% of World GDP, following by both; OECD industrial production and Kilian’s real index with 47%. 5.4.2 Property 8 Results for property 8 are presented in Table 5. In the second column, World steel production presents by far the highest R2 and adjusted R2 predicting up to 75% of variation in World GDP, following by Kilian’s real index (47%) and OECD industrial production (36%). 6. Forecasting World GDP 6.1 Exercise set-up The analysis above has focused on developing econometric properties to investigate features of monthly indicators of Global real economic activity to explain contemporaneously World GDP. We extend this by evaluating the out-of-sample predictability power of these indices. Inoue and Kilian (2004) examine the question of in-sample versus out-of-sample testing of predictability, motivated by the finding that positive in-sample evidence of predictability is often not associated with out-of-sample predictability. Ashley, Granger and Schmalensee (1980) claim that in-sample inference without out-of-sample verification is likely to be spurious, with an out-of-sample approach inherently involving less overfitting. Inoue and Kilian (2004) assert that this argument is not compelling since there is ample opportunity for the researcher to data mine in a simulated out-of-sample study, and because data snooping adjustments can be made to both tests. Therefore, we view the results we Page 22 of 38 obtain as a natural complement to the set of in-sample evidence reported in the previous section. We split the full quarterly sample 1991Q1-2013Q1 into two periods: an initial insample period 1991Q1-1999Q4 and the out-of-sample (OOS) period 2000Q1-2013Q1. For each of the 53 OOS values, we produce from 1to 8-step ahead forecasts using several different models based on the indicators of Global real economy. Precisely, we apply the following models: 𝑑𝐺𝐺𝐷𝑃𝑡=𝛼+𝛽⁡⁡𝑑𝐺𝐺𝐷𝑃𝑡−1 +𝛾⁡𝑋𝑖,𝑡−1 +⁡𝜀𝑡 (9) where 𝑋𝑖,𝑡−1 is one of the four indicators of Global real economy activity, that is Kilian’s real index, OECD industrial production and World steel production; and 𝜀𝑡 is the error term with zero mean and 𝜎2 variance. Each model produces an h-step ahead forecast of detrended World GDP, 𝑑𝐺𝐺𝐷𝑃𝑡+ℎ, our preferred measure of value added GDP, as: 𝑑𝐺𝐺𝐷𝑃 𝑖,𝑡+ℎ =𝑎+𝑏⁡⁡𝑑𝐺𝐺𝐷𝑃𝑡+𝑐⁡𝑋𝑖,𝑡 (10) where a, b and c are the OLS estimates of unknown parameters α and β in equation (9). 23 The indicators are monthly variables and we convert them to quarterly observation 𝑋𝑖,𝑡 using the most updated available information. 24 The release date of data varies between series. The timeliest indicator is the World steel production that is published with a month delay. On the contrary, OECD industrial production is published with longer delays; and the Kilian’s real index depends on the author publishing the new information. We assume OECD industrial production and Kilian’s real index is available with 3-month delays, even if there is evidence of longer publication delay. World GDP is also published with delay, but the length of delay 23 We fix the autoregressive lag to 1 because this model outperforms models with more lags. Irrespectively, results are qualitative similar for models with more autoregressive lags. 24 Since the four indicators are indices, the last observation should contain all the history information. Page 29 of 38 Mackowiak, B., 2007. External shocks, U.S. monetary policy and macroeconomic fluctuations in emerging markets. Journal of Monetary Economics, 54, 2512-2530. Meuldijk, J., 1940. Der englische Schiffbau w¨ahrend der Periode 1870-1912 und das Problem des Ersatzbaues. Weltwirtschaftliches Archiv, 52 , 524–549. In Klovland (2004) Miron, J.A. and Romer, C.D., 1990. A new monthly index of industrial production, 1884– 1940. The Journal of Economic History, 50(02), 321-337. Mullineaux, D., 1980. Unemployment, industrial production, and inflation uncertainty in the United States. The Review of Economics and Statistics, 62 (2), 163-169. Nelson, C.R. and Plosser, C.I., 1982. Trends and random walks in macroeconmic time series : Some evidence and implications. Journal of Monetary Economics, 10(2), 139-162. Panagariya, A., 2004. Miracles and debacles: In defence of trade openness. The World Economy, 27(8) 1149-1171. Ravazzolo, F. and Rothman, P., 2012. Oil and U.S. GDP: A Real-Time Out-of-Sample Examination. Journal of Money, Credit and Banking, 45(2-3), 449-463. Radetzki, M., 2006. The anatomy of three commodity booms. Resources Policy 31, 56–64. Romer, M. P., 1986. Increasing returns to long run growth. Journal of Political Economy 94(5), 1002-37. Romer, M. P., 1992. Two strategies for economic development: Using ideas and producing ideas. World Bank Annual Conference on Economic Development, Washington D. C.. The World Bank. Ratti, R.A. and Vespignani, J.L., 2013. Why are crude oil prices high when global activity is weak? Economics Letters, 121(1), 133-136. Smets, F. and Wouters, R., 2007. Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach. American Economic Review, 97(3): 586-606. Steindel, C., 2004. The relationship between manufacturing production and goods output. Current Issues in Economics and Finance, Federal Reserve Bank of New York, vol. 10. Stock, J. and Watson, M., 2002. Has the business cycle changed and why? NBER Macroeconomics Annual. Stopford, M., 1997. Maritime Economics. 2nd ed. London: Routledge. Stout, B.A, 2012. Handbook of Energy for Wold Agriculture. Tinbergen, J., 1959. Tonnage and Freight. In Jan Tinbergen Selected Papers, 93–111. NorthHolland, Amsterdam in Klovland (2004). Page 30 of 38 Timmermann, A., 2006. Forecast combinations. Vol. 1 of Handbook of Economic Forecasting. Elsevier, 135 – 196. World Economic Outlook, The international Monetary fund (IMF) 2014. Recovery Strengthens, Remains Uneven. Zarnowitz, V., 1987. The regularity of business cycles. NBER Working Papers 2381, National Bureau of Economic Research, Inc. Page 31 of 38 Table 1: Test for unit roots 1999:1-2012:12: Data in level Null Hypothesis for ADF test: the variable has a unit root Alternative Hypothesis for ADF test: the variable has not a unit root Null Hypothesis for KPSS test: variable is stationary Alternative Hypothesis for KPSS test: variable is not stationary Log-Level ADF KPSS First difference ADF KPSS log⁡(𝑂𝐸𝐶𝐷𝐼𝑃𝑡) -1.29 1.15*** ∆log⁡(𝑂𝐸𝐶𝐷𝐼𝑃𝑡) 1.15** 0.07 log(GSTEEL𝑡) 0.56 -6.67*** ∆log(GSTEEL𝑡) 1.20*** 0.25 log(SHIP𝑡) -2.93** -10.08*** ∆log(SHIP𝑡) -0.35* 0.04 log⁡(𝐺𝐺𝐷𝑃𝑡) 0.12 3.13*** ∆log⁡(𝐺𝐺𝐷𝑃𝑡) 1.26*** 0.17 Note: The first difference of the series is indicated by ∆.The lag selection criteria for the ADF is based on Schwarz information Criteria (SIC) and for the KPSS is the Newey-West Bandwidth. One star * indicates rejection of the null hypothesis at 10% level; two stars ** at 5% level; and three stars *** at 1% level. Table 2. Unrestricted cointegration rank test (Trace) Null hypothesis: The number of cointegrating vectors is less than or equal to r Alternative hypothesis: There are more than r cointegrating vectors Hypothesized Null Alt. log⁡(𝑂𝐸𝐶𝐷𝐼𝑃𝑡) and log⁡(𝐺𝐺𝐷𝑃𝑡) log⁡(𝐺𝑆𝑇𝐸𝐸𝐿𝑡) and log⁡(𝐺𝐺𝐷𝑃𝑡) r=0, r≥1 0.02** 0.01** r≤1, r≥2 0.70 0.13 Note: Values reported are p-values MacKinnon-Haug-Michelis (1999). One star * indicates rejection of the null hypothesis at 10% level; two stars ** at 5% level; and three stars *** at 1% level. Lags are selected using Bayesian information criterion. Table 3. Unrestricted cointegration rank test (Maximum eigenvalue) Null hypothesis: The number of cointegrating vectors is r Alternative hypothesis: There are more than r cointegrating vectors Hypothesized: Null Alt. log⁡(𝑂𝐸𝐶𝐷𝐼𝑃𝑡) and log⁡(𝐺𝐺𝐷𝑃𝑡) log⁡(𝐺𝑆𝑇𝐸𝐸𝐿𝑡) and log⁡(𝐺𝐺𝐷𝑃𝑡) r=0, r=1 0.01* 0.03** r=1, r=2 0.70 0.13 Note: Values reported are p-values MacKinnon-Haug-Michelis (1999). One star * indicates rejection of the null hypothesis at 10% level; two stars ** at 5% level; and three stars *** at 1% level. Lags are selected using Bayesian information criterion. Page 32 of 38 Table 4: Predictability for World GDP (first difference) Independent variable, first difference Global GDP World Steel production OECD Industrial production Kilian’s rea index Constant 0.028*** (0.001) 0.029*** (0.001) 0.032*** (0.001) M1 first difference 0.011 (0.067) -0.207 (0.268) 0.005 (0.00) M2 first difference 0.081 (0.061) 0.109 (0.274) 0.02** (0.001) M3 first difference -0.005 (0.026) -0.010 (0.082) 0.005 (0.005) M1 first difference (-1) 0.013 (0.079) 0.066 (0.323) -0.0001 (0.0001) M2 first difference (-1) 0,123* (0,067) 0.080 (0.312) 0.0001 (0.0001) M3 first difference (-1) -0.032 (0.028) 0.106 (0.103) 0.0001 (0.0001) M1 first difference (-2) 0.001 (0.007) 0.302 (0.334) 0.0000 (0.0002) M2 first difference (-2) 0.145* (0.075) 0.255 (0.169) 0.0000 (0.0002) M3 first difference (-2) 0.078 (0.051) 0.176 (0.273) 0.0001 (0.0002) M1 first difference (-3) 0.014 (0.059) 0.027 (0.292) 0.0000 (0.0002) M2 first difference (-3) 0.011 (0.007) 0.089 (0.234) 0.0001 (0.0002) M3 first difference (-3) -0.048 (0.068) 0.066 (0.323) -0.0001 (0.0002) M1 first difference (-4) 0.036 (0.044) -0.276 (0.225) -0.0004 (0.0001) M2 first difference (-4) 0.080 (0.046) -0.0163 (0.261) 0.0002 (0.0002) M3 first difference (-4) -0.073 (0.068) -0.179 (0.212) 0.0000 (0.0002) R2 0.58 0.47 0.47 Adj.R2 0.50 0.36 0.36 Note: Four lags are used as indicated by the Akike Information Criterion. One star * indicates the coefficient is statistically different than zero at 10% level; two stars ** at 5% level; and three stars *** at 1% level. Page 33 of 38 Table 5: Predictability for World GDP (detrended) Independent variable, first difference Global GDP World Steel production OECD Industrial production Kilian’s rea index Constant 0.0002 (0.0034) -0.0052 (0.005) -0.0129** (0.0048) M1 first difference 0.1738 (0.2327) -2.5007* (1.4019) -0.0002 (0.0009) M2 first difference 0.1542 (0.2191) 0.5349 (1.3669) 0.0007 (0.0008) M3 first difference -0.1854** (0.0966) -1.5306** (0.4206) -0.0004 (0.0003) M1 first difference (-1) 0.1408 (0.2346) -1.5265 (1.3376) -0.0004 (0.0009) M2 first difference (-1) 0.1127 (0.2271) -0.3645 (1.3316) 0.0011 (0.0008) M3 first difference (-1) 0.1153 (0.1539) 0.7582 (0.7847) 0.0000 (0.0004) M1 first difference (-2) 0.0223 (0.2234) -1.1945 (1.2707) 0.0000 (0.0008) M2 first difference (-2) 0.2575 (0.2303) 0.6770 (1.3578) 0.0009 (0.0008) M3 first difference (-2) -0.0919 (0.2324) 0.7470 (1.0909) -0.0002 (0.0008) M1 first difference (-3) -0.10187 (0.2023) 0.4511 (1.2175) -0.0011 (0.0007) M2 first difference (-3) 0.1710 (0.2040) -0.0675 (1.2175) 0.0012 (0.0007) M3 first difference (-3) -0.1582 (0.2532) 2.0232 (1.2892) -0.0007 (0.001) M1 first difference (-4) 0.0130 (0.1671) 0.3629 (1.3484) -0.0002 (0.0006) M2 first difference (-4) 0.2516 (0.2022) -0.5767 (1.1292) 0.0014* (0.0007) M3 first difference (-4) -0.3363 (0.2202) 1.8867 (1.3227) 0.0002 (0.0009) R2 0.75 0.36 0.44 Adj.R2 0.70 0.26 0.32 Note: Four lags are used as indicated by the Akike Information Criterion. One star * indicates the coefficient is statistically different than zero at 10% level; two stars ** at 5% level; and three stars *** at 1% level. Page 34 of 38 Table 6: Econometric property results Kilian’s rea index OECD IP Steel Production Property 1 - Yes Yes Property 2 3 2 1 Property 3 2 3 1 Property 4 3 2 1 Property 5 1 3 2 Property 6 3 2 1 Property 7 2 2 1 Property 8 2 3 1 First difference properties (average) 1.66 2.66 1.33 Detrended properties (average) 2.66 2.33 1 All properties (average) 2.28 2.42 1.14 Note: For properties 1 and 2, where data in log-level is used, we have constructed a chain index from the starting period (1990:Q1=100) for the Kilian’s index of global real economic activity. Although this chain index appears to be non-stationary, results for property 1 shows that both eigenvalue and trace tests suggest not cointegration vector between Kilian’s real chained index and the log of world GDP. For property 2, Kilian’s real index chained index worsens results significantly with respect to the unchained index. Table 7: Forecasting World detrended GDP: MSPE Hor 1 2 3 4 5 6 7 8 AR 0.017 0.065 0.134 0.211 0.284 0.347 0.402 0.455 Kilian’s rea index 0.695* 0.708 0.693 0.715 0.747 0.763 0.781 0.816* OECD IP 0.828 0.922 1.030 1.131 1.218 1.287 1.332 1.355 Steel Production 0.734** 0.732* 0.687* 0.664* 0.710 0.828 0.948 1.014 FC 0.596*** 0.609*** 0.605** 0.624*** 0.680** 0.762* 0.837 0.884 Note: The table reports the Mean Square Prediction Error of the various alternative models to predict World detrended GDP over the sample 2000Q1-2013Q1. The column “AR” reports the MSPE value for the AR(1) benchmark model; the other columns present the ratio of the alternative model’s MSPE to the benchmark’s MSPE. Bold numbers indicate the alternative model provides lower MSPE. The alternative models refer to AR(1) model extended with one of the monthly indicators of Global real economic activity studied in the paper and and a combination (FC) of them. We measure statistical significance relative to the prevailing mean model using the Clark and West (2006) tests for equality of the average loss. One star * indicates significance at 10% level; two stars ** at 5% level; and three stars *** at 1% level. Page 35 of 38 Figure 1: OECD industrial production index and World GDP in log first difference (right scale), Kilian’s real index (left scale): 1990:Q1 to 2013:Q1 Note: The series have been seasonally adjusted by the authors using census X12 method. Figure 2: World Steel Production (right scale) vs. World GDP (left scale): Quarterly data 1990:Q1 to 2013:Q1 a) Data in Levels Page 36 of 38 b) Logs of detrended data c) Logs of first diffrence Page 37 of 38 Figure 3: Giacomini and Rossi (2010) Fluctuation Test for Equal Out-of-Sample Predictability at h=1 Note: Giacomini and Rossi (2010) Fluctuation test based on sequences of Clark and West (2007) test statistics (for testing model (1) against model (2)), with µ=0.5 and m=P, where m = the size of the rolling window of CW statistics and P = the number of OOS observations, for the OOS period 2000Q1-2013Q1, such that the length of each window of CW statistics is 28 quarters, i.e., 7 years. The x-axis refers to the last value of each sample. Fluctuation test critical value at the 10% significance level in dotted lines; if the Fluctuation test statistic exceeds the critical value, the null that the benchmark model is the true model is rejected for the particular window. Benchmark model is an AR(1), alternative models in legend are defined in Section 6. Page 38 of 38 Figure 4: Giacomini and Rossi (2010) Fluctuation Test for Equal Out-of-Sample Predictability at h=8. Note: See Figure 3.