Modelling the global wheat market using a GVAR model

Transcription

1 Wageningen University Agricultural Economics and Rural Policy Modelling the global wheat market using a GVAR model MSc Thesis by Elselien Breman

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3 Wageningen University Agricultural Economics and Rural Policy Modelling the global wheat market using a GVAR model MSc Thesis by Elselien Breman

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5 Acknowledgment This MSc thesis has been written in order to complete the Master Management, Economics and Consumer studies, specialisation Agricultural Economics and Rural Policy, at Wageningen University. I have been working on this thesis from February until August 2014 at the chair group Agricultural Economics and Rural Policy. During this time I enjoyed working on such a challenging subject. This thesis was examined by dr. ir. J.H.M. Peerlings and supervised by dr. ir. C. Gardebroek. I would like to offer my special thanks to my supervisor Koos Gardebroek for his valuable advice, his constructive feedback, for his time and effort he put in my work and the pleasant way in which we worked together. I hope you will enjoy reading my thesis. Elselien Breman Wageningen, augustus

6 Table of Contents Abstract Introduction Background Research objective and research questions Structure of the thesis The GVAR modelling approach Applications of the GVAR model Model characteristics Weights Order of integration and lag order Co-integrating relationships Testing weak exogeneity Testing for structural breaks Solving the GVAR model Analysis The GVAR model for the global wheat market Included countries and variables Country-specific models Data and construction of weights Data Missing observations Construction of weights Specification and estimation of the country-specific models Order of integration and lag order Co-integrating relationships Estimation of the country-specific equations The domestic wheat price and its foreign counterpart Testing weak exogeneity Solving the GVAR Model solution Simulation possibilities Reliability of weights Conclusion and discussion

7 8.1 Conclusion Discussion Recommendations for further research References Appendices Appendix A Appendix B Appendix C Appendix D Appendix E

8 Abstract Due to its multilateral nature, the global wheat market requires to be analysed from a global perspective such that foreign shocks and international spill-overs can be taken into account. Therefore, this report proposes to analyse the global wheat market with a relatively new modelling strategy in agricultural market studies: the GVAR model. The GVAR modelling approach is useful in global modelling since it provides, in comparison to unrestricted VAR models, a solution to the high dimensions of complex systems by using weighted average foreign variables which are assumed to be weakly exogenous. The objective of this report is to analyse the advantages and disadvantages of using a GVAR modelling approach for the global wheat market. To this extent, existing literature is analysed and the key characteristics of the model are explored. Next, a relatively small model of the global wheat market is developed including five major exporting countries and monthly data on their wheat export prices, their nominal exchange rate and the oil price. The country-specific weights are constructed using export shares, which are then used to develop country-specific foreign wheat price variables. After estimating the country-specific equations, the global model is solved. To test the reliability of the weights, the model is also estimated as an unrestricted VECM with the same model structure. Although the GVAR modelling approach was found to be suitable to model the global wheat market, two disadvantages were found that call for further research. First, the weakly exogeneity assumption of the US variables was rejected and no appropriate solution was found. Further research could elaborate different solution strategies and their theoretical implications. Second, the analysis shows that the reliability of the weights is questionable. Further research could improve testing methods of the reliability of weights and a comparative study of different methods to construct the weights can be carried out. 4

9 1. Introduction The first chapter of this report includes background information on the GVAR model and its suitability for modelling the global wheat market. Further, it includes the research objective and the research questions. The final paragraph concerns the structure of the thesis. 1.1 Background Globalization is increasing, causing further integration of commodity and financial markets across the world. As a consequence, co-movement of business cycles increases and international dependencies become stronger (Kose et al., 2003). The stronger co-movement of business cycles is reflected in the more pronounced co-movement of macroeconomic variables across countries, such as output and inflation (Dees et al., 2007a). As discussed by di Mauro and Smith (2013), co-movement can be channelled through commonly observed and unobserved shocks and factors, but due to the strong dependencies also through specific national shocks and even spill-over effects are able to reach wider across the world. This has important implications for analysing global markets, since domestic and common shocks or policy changes affect economies worldwide and modelling approaches should take all these interdependencies and channels of transmissions into account. As many agricultural commodities are traded worldwide, they are also subject to international economic interdependences. There has been increasing attention for agricultural commodity analyses after the world food crisis in which food price volatility and price levels rapidly increased, reaching significant high levels in 2008 and 2011 and causing severe problems, especially among the poor. Attention of academics and policy makers was drawn to the causes of this food crisis. Extreme weather events, low stocks, high oil prices, increasing demand for biofuels, speculation and trade shocks have been widely discussed as possible causes (Headey, 2011). One of the most traded agricultural commodities in the world is wheat, from which 20 percent of the total production is traded internationally (FAOSTAT, 2014). While many countries worldwide import wheat for human consumption and for the use of compound feed in the livestock sector, there are only a few big exporters on the market (USA, EU, Australia and Canada). As other agricultural commodities, prices of wheat increased significantly during the food crisis. Strong interdependencies also influence the global wheat market. Macroeconomic variables influence e.g. the demand for wheat, so when these variables co-move between countries, shocks in one country s macroeconomic variables can have an effect on domestic wheat markets in other countries. But besides the co-movement of macroeconomic variables, there are more interdependencies among countries on the global wheat market due to high amount of trade that is taking place. Therefore, shocks in one country affect other countries directly since trade flows adjust. For example, the strong wheat import dependency of many developing countries makes that policy changes or environmental shocks in producing countries have a direct effect on the availability and price development in the importing countries. But also common factors play an important role, such as the oil price, influencing both the global wheat market on the demand side (for the use of biofuel) and supply side (as agricultural input). So, due to its multilateral nature and the more pronounced international interdependencies, the international wheat market calls to be analysed from a global perspective such that the integration of economies and the spill-over effects across nations can be considered. 5

10 In analysing global commodity markets two different types of models are commonly used; Computable General Equilibrium (CGE) models and time-series econometric models. CGE models are simulation models based on economic theory where parameters are calibrated and most often yearly data is used. Time-series econometric models, on the other hand, are based on time-series observations, parameters are estimated and higher frequency data (monthly, weekly, daily) can be used. One of the critiques of econometric models is their often weak theoretical basis, while CGE s are complex and results are difficult to interpret (Piermartini et al., 2005). The model that is presented in this thesis is a Global Vector Auto-Regression (GVAR) model. Although a GVAR model is a macro-econometric model and relies on time-series observations, it is estimated subject to longrun relationships that are obtained from economic theory. Due to this structure, the long-run relationships are consistent with economic theory while the short run relationships are still consistent with the time-series observations (di Mauro and Smith, 2013). Besides the fact that the model is taking economic theory into account, another advantage of the GVAR modelling approach is that it allows for international linkages among a large number of countries. First developed by Pesaran et al. (2004a), the GVAR model is used by a variety of authors for the purpose of answering different research questions, mostly in the field of financial market analyses. Yet, for the first time in literature, the model is only recently used to model international trade and global imbalances by Bussière et al. (2009). In this working paper Bussière et al. (2009) show how the GVAR methodology offers opportunities for modelling and analysing trade worldwide; it demonstrates that with this methodology cross-country spill overs can be modelled since individual country trade models are linked together and that the framework is able to model export and import flows simultaneously, which in existing literature are most often estimated separately. The GVAR model shows to be well suitable for policy analyses and simulation exercises in which the impact of specific shocks can be determined, but it is also useful for forecasting exercises (Bussière et al., 2009; Pesaran et al., 2009). The most important feature of the GVAR modelling approach is that it accounts for the interaction and interdependencies between as many countries or regions as desirable. The model is constructed in two steps; in the first step country-specific VAR models are estimated and in the second step all the estimated coefficients are stacked together and solved in one system, the GVAR. The countryspecific models include domestic variables and common foreign variables, which link the countryspecific models to each other and makes co-integration possible not only between domestic variables of a country but also between the domestic and foreign variables. In these specific-country models long-run co-integrating relationships can be tested and imposed. The foreign variables are a weighted average of the countries included in the sample and are assumed (and tested) to be weakly exogenous. Assuming the foreign variables to be weakly exogenous, as di Mauro and Smith (2013) discuss, is a key characteristic of the model. In this way the number of equations to be estimated is significantly reduced and therefore it bypasses the curse of dimensionality which is a common problem in global macroeconomic modelling using unrestricted VAR models (Chudik and Smith, 2013). From the solution of the GVAR impulse response functions can be developed, which investigate the effects of a shock in one of the variables on the other variables in the model (Pesaran and Smith, 2006b). These functions are useful in analysing the interdependencies of the countries involved and the transmission of shocks among them. Due to the multilateral nature and the interaction of various variables on the global wheat market, analysing and modelling this market with the use of a GVAR methodology seems promising. Gutierrez and Piras (2013) shared the same thought and analysed wheat export prices using a GVAR modelling 6

11 approach, but further extension in this research field has not yet been made. Since this modelling approach is rather new in the global modelling of agricultural commodities, there are still a lot of challenges and opportunities. Hence, the aim of this thesis is to discover the possibilities of applying the GVAR methodology in modelling the international wheat market. 1.2 Research objective and research questions The objective of this thesis is to investigate the advantages and disadvantages of the GVAR modelling approach in analysing the international wheat market. The first part of this report will provide a theoretical overview of the GVAR modelling approach in which the following research questions will be answered by a study of existing literature; To which purpose and in which manner is the GVAR modelling approach used in the existing literature? What are the specific characteristics of a GVAR model and which steps are taken in the GVAR modelling approach? In the second part of the report a small GVAR model of the international wheat market will be developed. This exercise is carried out to investigate which challenges one encounters in modelling the global wheat market using this methodology. After preforming this analysis, the following research question will be answered; What are the arguments for and against using a GVAR modelling approach in analysing the global wheat market? 1.3 Structure of the thesis Chapter 2 presents a theoretical overview of the GVAR modelling approach. It shows applications of the approach in economic literature, the specific characteristics of the model and it describes the different steps that need to be taken in the GVAR modelling approach. In chapter 3 the GVAR model for the global wheat market is presented. This chapter shows how the model is structured and which variables are taken into account. Chapter 4 shows the data that is used in the model and clarifies the construction of the weights. Chapter 5 elaborates the empirical model and shows the argumentation for the chosen model structure. Estimation of the country-specific equations is performed and the weakly exogeneity assumption is tested. Chapter 6 elaborates the solution of the global model and the simulation possibilities. In chapter 7 the reliability of the constructed weights is considered by estimating the same structure in a unrestricted vector error-correction model. Chapter 8 presents the answers to the stated research questions and provides a critical reflection on the analysis. Furthermore, recommendations for further research are given. 7

12 2. The GVAR modelling approach Starting from the early 2000 s the GVAR modelling approach has been used in different global modelling exercises to answer various research questions. In the first paragraph of this chapter the existing literature on GVAR modelling is briefly discussed. In the second paragraph the model characteristics will be explained along the lines of the different steps that are taken in the GVAR modelling approach. These steps include constructing the weights, determining the order of integration and the number of lags, defining the co-integrating relationships, testing the assumption of weak exogeneity and testing for structural breaks. In the third paragraph the solution strategy of the GVAR as a system is given and finally the analysis possibilities are discussed Applications of the GVAR model The GVAR model was introduced by Pesaran et al. (2004a) in which they emphasized the growing interconnections and interdependencies between national and international factors in financial markets and the implications for financial policy and risk management analyses. To this end they developed a global macro econometric model that allows for interconnections and interdependencies among a wide range of countries suitable in generating forecasts: the GVAR model. The approach was developed further in a number of subsequent studies. Pesaran and Smith (2006b) show that the country-specific models used in the GVAR modelling approach can be derived as the solution to a Dynamic Stochastic General Equilibrium (DSGE) model, but having the benefits that possible presence of long-run relationships based on theory can be tested. Subsequently, Dees et al. (2007b) used the model to test for the presence of certain long-run relationships in the world economy, focusing on interest rates, real output, inflation and exchange rates. Dees et al. (2007a) build on the work of Pesaran et al. (2004a) where they provide a common factor interpretation of the country-specific foreign variables and derive the GVAR model as an approximation of a global factor model. Pesaran et al. (2009) used the approach to generate forecasts from different GVAR models and then compared these with forecasts of univariate autoregressive and random walk models and showed that the averaged forecasts of the GVAR models performed better. Until then, the GVAR model was used to answer various research questions but these were mainly all focused on financial market analyses and the interdependencies between countries in these markets. The first time that the GVAR model was used to analyse international trade flows was by Bussière et al. (2009). They used a GVAR model to provide more insights in the dynamics behind global trade flows and focussed on the issue of global trade imbalances. They argue that due to the multilateral nature of global trade flows, the GVAR model seems to be an appropriate choice in analysing the dynamics of these flows for two reasons. First, this model allows for the interactions between the large number of countries that play a role in this analysis. Second, import and export flows can be modelled simultaneously in a GVAR model. Since imports and exports seem to move together this is an important feature. They show that the impulse response functions originating from the GVAR model provide good opportunities for analysing different shocks and their channels of transmission. 2.2 Model characteristics This paragraph outlines the model characteristics and the different steps that are taken in the GVAR modelling approach, using the work of Pesaran et al. (2004a) as a theoretical basis. 8

13 The GVAR modelling approach distinguishes itself with a two-step procedure. In the first step country-specific VAR models 1 are estimated and in the second step all the estimated coefficients of these country-specific VAR models are stacked together and solved in one system, the GVAR. The country-specific VAR models contain country-specific domestic variables and foreign variables. These foreign variables most often contain (i) global common observed factors, e.g. the oil price, and (ii) the counterparts of the domestic variables. These counterparts are weighted averages of the domestic variables of the countries included in the model and therefore allow for the interaction between the variables of the different countries. The counterparts of the domestic variables also serve as a proxy for common unobserved factors, such as technological change (di Mauro and Smith, 2013). Assume that there are N+1 countries or regions representing the global economy. Let be a x 1 vector of country-specific variables and let be a x 1 vector of foreign variables, both specific to country where Country 0 is the reference country, most often represented by the United States. Then, as shown by Pesaran et al. (2004a), these two vectors can be combined in the following country-specific VARX(1,1) 2 model (1) where is a x 1 vector of constants and is a x 1 vector capturing the parameters of the deterministic trends of the variables. is a x matrix of lagged coefficients, and are x matrices of coefficients belonging to the foreign variables and is a x 1 vector of individual country-specific shocks for which is assumed that they are serially uncorrelated. From equation (1) follows that only the country-specific domestic variables are explained in this VAR model, whereas the country-specific foreign variables are not explained in this system. In fact, the country-specific foreign variables are assumed to be weakly exogenous, giving advantages in modelling high dimensional systems like these. If the country-specific foreign variables would all be assumed endogenous, the model would be of such a high dimension that estimation would be infeasible (di Mauro and Smith, 2013). The opposite extreme would be to assume the foreign variables to be fully exogenous, which would mean there is no feedback of the country-specific domestic variables on their foreign counterparts. This is not desirable, since the domestic and foreign variables are jointly determined. As di Mauro and Smith (2013) argue, by assuming the foreign country-specific variables to be weakly exogenous it assumes that the individual countries are presented as small economies with respect to the rest of the world. This implies that short run fluctuations in a country can influence the foreign country-specific variable, but fluctuations from the domestic long-run equilibria do not influence the foreign country-specific variable. Therefore, in conclusion, the domestic variables do depend on the foreign country-specific variables and their lagged variables, but in turn the deviation from the long-run equilibria in one country does not influence the foreign country-specific variables (di Mauro and Smith, 2013). This assumption can be eased for the US, for which the assumption of a small economy would not be appropriate, by including some of the foreign variables as endogenous. One feature that comes with this assumption is that while the individual country-specific shocks are not serially correlated they are assumed to be 1 For general information on VAR models see Verbeek (2012) p A VARX model is a VAR model including (weakly) exogenous variables. 9

14 cross-sectionally, across the countries, weakly correlated (Dees et al., 2007a). This implies that shocks across countries can be correlated, but this does not result in correlation of the country specific variables with the residual,. If this would be the case, would be endogenous instead of weakly exogenous Weights After selecting the relevant model variables, foreign country-specific variables can be constructed by weighting the various domestic variables, such that (2) where, with, are the weights given to country used in the construction of the foreign variable of country, where is equal to 0 and the sum of is always equal to 1. Following equation (2), the foreign country-specific variables are weighted averages of the domestic variables of all countries included in the model. There are three different ways to construct these weights. The first, most simple one, is by assuming equal weights for all countries, which would imply that for all and hence one would use the same foreign variable for all country-specific VAR models 3. When all countries taken into account are of the same importance to each other, this assumption could be used. But since in the global economy, as well as on the global wheat market, market shares are not equally distributed among market players and certain countries trade more with each other than with others, the relative importance of the countries to each other can be assumed to be diverse and then this assumption would not be favourable. The second option does take this into account, by using country-specific weights such that the weights capture the relative importance of country in the economy or specific market of country. These weights are fixed and usually an average of a certain representative time period. The data that is used to construct the weights depends on the context of the modelling exercise and the associated variables. For example, Pesaran et al. (2004a) use trade shares to indicate the weights for output while they use capital flows to indicate the weights for interest rates. The third option is comparable with the former, but distinguishes itself by taking timevarying weights instead of using fixed weights, which can be constructed by taking moving averages of a certain number of years. This option could be favourable when dealing with e.g. emerging economies, for which trade shares rapidly increase. In the existing literature on GVAR modelling option two is most often used, assuming that estimation of the foreign variables are close to each other either using fixed country-specific weights or variable trade weights. Dees et al. (2007a) examine this by estimating the GVAR model both with fixed country-specific trade weights as well as with rolling three-year moving averages of the annual trade weights and show that both procedures result in very similar outcomes. 3 This assumption also implies that does not have to be equal to zero and therefore will also be part of its own weighted average foreign variable. 10

15 2.2.2 Order of integration and lag order After constructing the foreign variables, the next step is to determine the order of integration of both the domestic as well as the foreign variables to ensure the time-series data is stationary. Testing for unit roots can be done with the Augmented Dickey-Fuller test and the KPSS test (Verbeek, 2012: 294). When variables are of the same order of integration, a co-integrating relationship among these variables can exists. Next, the number of lags that should be included in the model has to be determined. In equation (1) a model is presented, but the country-specific models can be estimated with different numbers of lags, where are the number of lags used for the domestic variables and the number of lags used for the foreign variables. Important is that the number of lags can differ between the country-specific models and between the domestic variables and the foreign variables within a country-specific model. The numbers of lags can be selected using the Akaike Information Criteria (AIC) or the Bayesian Information Criterion (BIC), in which a model with a lower criteria score is preferred. In all of the existing literature mentioned above, the maximum number of lags is set to 2, for both the domestic and foreign variables. A maximum lag order is put in place because the more lags are included in the model, the more parameters are to be estimated and the lower the degrees of freedom Co-integrating relationships When the order of integration and the number of lags is determined, the numbers of co-integrating vectors for each country-specific VAR model can be identified. To identify the number of cointegrating vectors, the error correction representation of formula (1) is given by (3) which can be re-written, using the fact that, as where (4), (5) (6) Now let, than contains the error-correction terms for country which are the linear combinations of variables in the vector that are stationary (I(0)). The rank of, indicated by, is equivalent to the number of cointegrating vectors in the country-specific model. The number of co-integrating vectors is the number of stable long-run equilibrium relations among the domestic and the country-specific foreign variables in the country-specific models. The maximum number of error-correction terms that can exist is. Identifying the amount of cointegrating vectors implies testing the rank of, which can be done using the Johansen trace test or the maximum eigenvalue test (Verbeek, 2012: 359). 11

16 2.2.4 Testing weak exogeneity Before the estimated country-specific VAR models can be stacked together and solved as one system, it is important to test whether the assumption that the foreign country-specific variables are weakly exogenous holds. By assuming that the variables are weakly exogenous, one assumes all countries are small economies with respect to the rest of the world. In practice it is possible that this assumption does not hold for every country and every variable. This could be the case on the global wheat market, where only a few big exporters dominate and therefore could have an important influence on the global market. Pesaran et al. (2004a) provide three conditions that the model should fulfil such that all the star variables can be assumed to be weakly exogenous: (1) the global model should be stable, (2) all the weights used in the construction of the foreign-specific variables should be relatively small and (3) the individual country-specific shocks are cross-sectionally weakly correlated. However, these conditions are not tested directly. Rather the implications of this assumption are tested, which is the non-significance of co-integrating relationship of a country on its foreign star variable. The long-run equilibria are reflected in the identified co-integrating relationships. When is assumed to be weakly exogenous, then a deviation from the long-run equilibria in country does not have any effect on. This assumption can be tested by running a regression of the foreign variables in first differences,, including the error correction terms describing the co-integrating relationships as an independent variable. With a standard F-test, the joint null hypothesis that the parameters of the error correction terms are not significantly different from zero can be tested (Pesaran et al., 2004a). When the null hypothesis is accepted, the short term development in is not influenced by the deviations from the long-run equilibria in country and weak exogeneity can be assumed Testing for structural breaks While it is not a crucial step in the GVAR modelling approach, one could test whether the estimated parameters are stable. In the applications of the GVAR modelling approach, a wide range of countries and regions are included with a relative long time-series for each of the variables. Working with such long time-series data and including many countries and regions, the possibility of structural breaks in the time-series and the instability of the parameters over time increases. These structural breaks, or shifts in the time-series, can occur from e.g. regime shifts or technological changes and can affect the evolution of key economic variables such as output growth and exchange rates (Pesaran et al., 2006a.). But more specifically on the wheat market, extreme weather events, trade agreements or trade barriers can influence the trade flows among countries in such an extent that a structural break occurs. A way to take these structural breaks into account is by using time dummies for specific events that are known for causing a structural break, as Bussière et al. (2009) did for the German reunification. After dummies for known structural breaks are included, the parameter stability can be tested. There are several tests that can be used, e.g. di Mauro and Smith (2013:22) compare the results of various test statistics to conclude whether or not the estimated parameters are stable. 12

17 2.3 Solving the GVAR model The country-specific models can be estimated based on the reduced rank regression or with ordinary least squares (OLS). Pesaran et al. (2004a) argue that estimating with the reduced rank approach is preferred since it allows the variables to have unit roots and the possibility of co-integration but that the country-specific models can also be estimated consistently with OLS. After the country-specific models are estimated they can be stacked together so that the global system can be solved as a whole. For this purpose equation (1) is rewritten, considering that, as where and are defined following equation (5) and (6), respectively. To be able to solve the country-specific models in one system, all the country-specific endogenous variables are collected in a global vector. This vector is of size x1 where is the sum of all the country-specific endogenous variables in the system. Now the country-specific weights play an important role, that act as a link between the countryspecific models and the global model, combined in the matrix such that (7). (8) The matrix is a ( x ) x matrix constructed from the country-specific weights. The matrix links the country-specific variables and to the total of all country-specific endogenous variables in the model,. The country-specific foreign variables that are included in the countryspecific models are a weighted average of the variables of the other countries. Including this matrix ensures that the country-specific foreign variables are written in terms of the endogenous lagged variables. As a result, the country-specific models are only a function of the lagged values of the domestic variables which makes the analysis of the system as a whole possible. Using equation (8), the country-specific models in equation (7) can be rewritten as. (9) These country-specific equations can be stacked together such that the following GVAR model arises where (10), (11). (12) 13

18 Following Pesaran et al. (2004a), is a x matrix and generally of full rank. Being a square matrix of full rank means that we can use the inverse of,, to find the solution for ;. (13) In this global model, interactions among the countries can be channelled through; (i) The dependence of the country specific domestic variables,, on the foreign countryspecific variables and their lagged variables. (ii) The dependence of the country specific domestic variables,, on common global weakly exogenous variables, such as the oil price, which are included in the foreign country-specific variables,. (iii) The weakly dependence of shocks in country with shocks in country. 2.4 Analysis Solving the GVAR gives opportunities to analyse the importance and effects of different shocks and the channels in which transmission takes place. First of all, the simultaneous effects of the foreign variables on their domestic counterparts can be analysed to give an insight in the international linkages between the domestic and the foreign variables within a country (di Mauro and Smith, 2013). Furthermore, from the solution of the global GVAR model impulse response functions can be computed (Pesaran et al., 2004a). With these response functions the transmission of specific country shocks can be analysed across countries. For example, a depreciation in one country shows the effects on all the domestic variables of the other countries taken into account. But in some instances we can speak of a global shock rather than a shock originating from one country, an example of such a shock is development in technology. To this purpose, Dees et al. (2007a) also show how the generalized impulse response function can be used to analyse the dynamics of the transmission of such a global shock. 14

19 3. The GVAR model for the global wheat market This chapter presents the GVAR model for the global wheat market. In this first paragraph the countries and the variables that are included in the model will be discussed. The second paragraph elaborates the structure of the country-specific models Included countries and variables The purpose of this study is to analyse interdependencies in price movements on the global wheat market in recent years using a global VAR model. The recent period of time distinguishes itself by outstanding wheat price peaks. As discussed in the first chapter, many studies analysed the causes of these price peaks. Extreme weather events, the depreciation of the US dollar, low stocks, the high oil price and demand for biofuel are examples of causes that were widely discussed. These possible explanations of the food crisis are factors mostly influencing the supply side of the wheat market, rather than the demand side. Demand of wheat is to a great extent explained by income and population growth, which are rather stable. For this reason this study will only include the major export countries that play a role on the wheat market, assuming that recent price peaks were caused by events influencing the supply side of the global wheat market rather than the demand side. The exporters that are included in this model are Argentina, Australia, Canada, the EU and the US. These countries are spread across the globe and account together for almost 80% of all wheat exports between 2007 and 2011 (FAOSTAT, 2014). To analyse the price movements on the global wheat market, the model will include the following variables: wheat export prices, exchange rates and the price of oil. The exchange rate is one of the macroeconomic variables that play an important role on the international agricultural market, which influences how international prices are translated to domestic prices. There are many studies that link the depreciation of the US dollar to the high commodity prices during the food crisis. Although this relationship is widely discussed only a few tried to quantify it. Mitchel (2008) indicates that the increase in (dollar-denominated) food prices due to the depreciation of the US dollar would be around 20%. The second variable that is included in the model is the oil price. The international oil price and prices of agricultural commodities are linked to each other on the input side through different channels. First of all, the energy that is used in agricultural production is mainly oil-based (such as the farm vehicles and machinery that are mostly powered by fossil fuels). Furthermore, the prices of fertilizer and other chemicals used in the production process are either produced from energy or use a lot of energy in their production process (Mitchell, 2008). Heady and Fan (2008) show that the oil price increase has a big impact on the production costs through these two channels. They estimate that due to the increased oil price the costs of US production of corn, wheat and soybeans increased by 30-40% over relative to a situation in which the oil-related prices only increased by inflation. At last, a higher oil price also increases the cost for transportation. Additionally, higher oil prices induce higher demand for biofuels (de Gorter, 2008). Although wheat is not a major feedstock for biofuel production, higher biofuel demand can lead to lower supply of wheat since farmers will substitute wheat for a crop that is demanded for biofuel production. By including the exchange rate and the price of oil into the model, we are able to analyse the effects of a shock in one of these variables and its way of transmission among the different countries. The last variable and the most important one is the wheat price, which will serve the main goal of the model: to analyse the interdependencies in the price movements across the countries. It is chosen not to 15

20 include specific supply and demand variables due to the limitation of data, since monthly data is chosen, and because it will not contribute to the main goal of the analysis. Nevertheless, the model is still suitable to analyse the effect of supply shocks even though supply side variables are not directly taken into account. For instance, production shortfalls due to extreme weather events can still be analysed by imposing a corresponding price increase in the specific country. 3.2 Country-specific models The primary variables of interest in this model are the domestic prices and the country-specific foreign counterparts. The country-specific foreign wheat prices,, ensure that shocks in the domestic price of country are channeled through to the domestic prices of all other countries and the other way around. The degree to which these shocks are channelled through depends on the weights used to construct the domestic variables out of the country-specific foreign prices. The foreign wheat prices are constructed as follows. (14) where equals zero and the sum of is always equal to 1 for any country. So, is not included in its own weighted average foreign variable. This method is desirable since the model only includes 5 countries and therefore the share of in could be significantly large, endangering the weakly exogenous assumption of. In the existing literature on GVAR modelling such as Dees et al. (2007), the oil price is often treated as endogenous in the country-specific model for the US, assuming that due to the large size of the US economy US macroeconomic variables will influence the oil price. Our model deviates from existing GVAR models, since it does not include a wide range of macroeconomic factors but focuses solely on wheat price developments. Therefore we assume the oil price to be exogenous for wheat prices and include the oil price as exogenous variable in all country-specific models. The same assumption is made for the exchange rate. In existing literature this variable is often chosen to be endogenous, such that the exchange rate is explained by the (macroeconomic) variables in the model. We assume that wheat prices will not influence the exchange rate in a country and therefore we assume the exchange rate to be exogenous in our model. These assumptions reduce the global VAR model to a model where each country only has one endogenous variable, the price of wheat. Hereby, each country-specific model will be reduced to the following autoregressive distributed lag (ADL) model (15) where is the price of wheat, the country-specific foreign price of wheat, which is a weighted average of the other countries wheat prices, the exchange rate and the oil price. The lag orders are given by and, where is the number of lags used for the domestic variable and the number of lags used for the (weakly) exogenous variables. By imposing the same lag order for the (weakly) exogenous variables the model is given a certain structure. However, the values for and can still differ from each other and between the different countries. 16

21 4. Data and construction of weights This chapter will first define the dataset that is used in the analyses. Next, a solution is given for missing observations in the time series. At the end of the chapter the data and the method that are used for the construction of the weights is elaborated. 4.1 Data For all the variables, monthly data is used covering the period from July 2001 until April The dataset for the wheat prices is shown in figure 4.1. Figure 4.1. Monthly wheat prices for major exporters (USD/tonne) Argentina Australia Canada EU US Source: International Grains Council (2012). Missing observations constructed by author. Table 4.1 shows the definition of the variables and the source that is used to collect the data. The wheat export prices are defined as the monthly average export price quotations in US dollar per ton. The data comes from the World Grain Statistics 2012 report published by the International Grains Council (2012). The nominal exchange rate included in the model embodies the national currency units per special drawing right (SDR) end of period and is obtained from the International Financial Statistics (2014) published by the International Monetary Fund. There are three main standards that serve as a reference price for crude oil; the Brent, Dubai and West Texas Intermediate. Since the model aims to cover the global wheat market an average of these three is taken to reflect the international crude oil market. Therefore, the variable for the oil price is an equally weighted average of the spot price of the Brent, Dubai and West Texas Intermediate expressed in US dollars per barrel. The data source for this time series is the World Bank Commodity Price data (the Pink Sheet) (2014). 17

22 Table 4.1. Definition and data source of the included variables Variable Definition Source Wheat export price in US International Grains Council dollars per ton (2012) Nominal crude oil price in US dollars per barrel obtained as an equally weighted average of the spot price of Brent, Dubai and West Texas Intermediate National currency per SDR, end of period World Bank Commodity Price Data (Pink Sheet) (2014) International Financial Statistics (2014) Missing observations While the datasets of the oil price and the exchange rates where fully available for all countries and months, the datasets for the price of wheat from the International Grains Council (2012) contained missing observations. Table A.1 in appendix A gives an overview of all the missing observations, their time span and the way in which the missing observations were estimated. In most of the cases it concerned only one or two missing observations at a time, which could be solved by interpolation. But in other cases there happened to be a period of time in which observations were contiguously missing. A linear interpolation in this case would not provide a realistic estimation, simply because the time span of the missing observations was too long. For Australia this was the case and this paragraph will display how the missing observations were estimated. The original dataset for Australia is shown in figure 4.2 indicated with the blue line. This dataset contains 14 missing observations, starting from October 2007 until November A proxy should be found such that the relationship between the proxy and the price of wheat in Australia can be established. Subsequently, the missing observations can be estimated based on this relationship and the available data of the proxy. Due to data limitations, there were only a few options that could be used as a proxy. The first option is to estimate these missing observations using the wheat prices in the other countries included in the model, since we expect co-movement between them. But this would jeopardize our model results. The model is especially built to analyse the interdependencies in the price movement across the different countries. When the missing observations are estimated based on the wheat prices in the other counties, co-movement between these prices in this period of time will be strong because it is explicitly imposed. Therefore, the outcome will be a result of the way the missing observations are estimated rather than a result of the interdependencies between the countries. Another argument against this method is that important country-specific supply side factors will not be taken into account, such as extreme weather events. Therefore, it is desirable to obtain a proxy that will reflect these changes in supply. This could be realised using the Australian price of a comparable agricultural commodity as a proxy. For this reason, together with the availability of the data, the Australian price of barley is chosen as a proxy, for which yearly production is lower than the production of wheat but as for wheat a large share of its production is exported on the world market. The dataset originates from the GIEWS Food Price Data and Analysis Tool (FAO, 2014) which is a part of the FAO Initiative on Soaring Food Prices (ISFP) and is indicated with the green line in figure

23 Figure 4.2 Australian monthly wheat and barley prices (USD/tonne) Wheat Barley Source wheat prices: International Grains Council, Source barley prices: FAO, For the first period of time, from April 2003 until September 2007, both time series of wheat and barley were found to be integrated of order 2 after testing for unit roots using the Dickey-Fuller and the KPSS test. Equation (16) shows the relationship of the price of wheat and the price of barley in levels. Subsequently, Dickey-Fuller tests were performed on the residuals,, to test for unit roots in order to see if there is a co-integrating relationship between the two time series. The residuals were found to be integrated of order 1, showing that not the time series in levels but their first differences are co-integrated. Given the presence of co-integration the following error correction model is estimated (16) (17) where the part between parentheses is the error correction term, representing the stationary residuals of the relationship between wheat and barley in first differences. For the second period of time, from December 2008 until March 2012, both time series of wheat and barley were found to be integrated of order 1 and no co-integration between the time series in this period was found. Therefore the following regression in first differences was estimated. (18) To take into account all the information available in estimating the missing observations, a combination of forecasting and backcasting is used. Equation (17) is used to forecast the missing 19

24 observations while equation (18) is used to backcast the missing observations. Since forecasts further away from October 2007 and backcasts further back than October 2008 increase in uncertainty, a weighted average of these two values is used to construct imputed values with minimal uncertainty: (19) where is the number of the missing observations, ranging from 1 (=October 2007) to 14 (=November 2008) and the value for missing observation originating from forecasting (backcasting) with equation (17) ((18)). Thus, the estimated value for the first missing observations depends mainly on the forecasted values whereas the estimated values for the last missing observations depends mainly on the backcasted values. This approach results in the wheat price indicated in figure 4.3 and is then used in the succeeding analyses. Figure 4.3 Modified Australian monthly wheat prices (USD/tonne) Construction of weights The country-specific weights serve as a tool to construct the country-specific foreign variables from the domestic variables and represent the degree to which one country depends on the other countries in the sample. In this model the weights are based on trade shares, assuming that the countries are linked to each other through arbitrage. Because the model only includes exporters, the weights are not based on trade flows between one and another. The reason for this is that trade between the exporters is not determining the relative importance of the countries to each other, since trade between these exporters will be small or negligible. Rather, the relative importance will be determined by the share that the country is holding in total exports. For example, a supply shock in a country that is a big exporter will influence country more than a supply shock in a country that exports minor quantities. Therefore the weights are constructed as the average share over of a country s exports volume in total exports of all the other countries included in the model, such that (20) 20