Agricultural Commodity Price Volatility and Its ...

Report EUR 26183 EN

2 0 1 3

Ayça Dönmez and Emiliano Magrini

A GARCH-MIDAS Approach

Agricultural Commodity Price Volatility and Its Macroeconomic Determinants

European Commission

Joint Research Centre

Institute for Prospective Technological Studies

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JRC84138

EUR 26183 EN

ISBN 978-92-79-33245-6 (pdf)

ISSN 1831-9424 (online)

doi:10.2791/23669

Luxembourg: Publications Office of the European Union, 2013

© European Union, 2013

Reproduction is authorised provided the source is acknowledged.

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Table of Contents 1. Introduction.......................................................................................................................................................................................................2 2. Methodology: The GARCH-MIDAS Approach ..................................................................................................................................4 3. Model selection and estimation with realised volatility .........................................................................................................5

3.1 Returns Data and Realized Volatility.........................................................................................................................................5

3.2 The Empirical Estimation with Realised Volatility .............................................................................................................6

4. Estimation with the Macroeconomic Determinants ..................................................................................................................8 4.1 Selected drivers of the low-frequency price volatility .................................................................................................8

4.2 The Empirical Estimation with Macroeconomic Determinants.............................................................................10

5. Conclusion .....................................................................................................................................................................................................15 References ...........................................................................................................................................................................................................17 Appendix................................................................................................................................................................................................................21 List of Tables

Table 1: The GARCH-MIDAS model with realized volatility for the period 1986-2012.............................................7 Table 2: The GARCH-MIDAS model for wheat with macroeconomic variables (1986-2012).............................11 Table 3: The GARCH-MIDAS model for corn with macroeconomic variables (1986-2012).................................11 Table 4: The GARCH-MIDAS model for soybean with macroeconomic variables (1986-2012)........................12 Table 5: Estimation results for θ under different subsamples .............................................................................................14 Table A. 1: Descriptive Statistics (1986-2012) ..............................................................................................................................21 Table A. 2: Unit Root Tests..........................................................................................................................................................................21 Table A. 3: The GARCH-MIDAS model for wheat with macroeconomic variables (1986-2005) .......................22 Table A. 4: The GARCH-MIDAS model for wheat with macroeconomic variables (2006-2012) .......................22 Table A. 5: The GARCH-MIDAS model for corn with macroeconomic variables (1986-2005) ...........................23 Table A. 6: The GARCH-MIDAS model for corn with macroeconomic variables (2006-2012) ...........................23 Table A. 7: The GARCH-MIDAS model for soybean with macroeconomic variables (1986-2005) ..................24 Table A. 8: The GARCH-MIDAS model for soybean with macroeconomic variables (2006-2012) ..................24

List of Figures

Figure A. 1: Optimal lag structure for wheat ...................................................................................................................................25 Figure A. 2: Optimal lag structure for corn .......................................................................................................................................25 Figure A. 3: Optimal lag structure for soybean ..............................................................................................................................25 Figure A. 4: Conditional Volatility and its low-frequency component for wheat ........................................................26 Figure A. 5: Conditional Volatility and its low-frequency component for corn ............................................................26 Figure A. 6: Conditional Volatility and its low-frequency component for soybean ...................................................27

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1. Introduction

The large agricultural commodity price swings observed in the last years - especially during the period 2006-2009 - raised an extensive debate on the main determinants behind these unexpected fluctuations. The vast literature on price volatility has constantly reflected that an excessive price movement is harmful for both producers and consumers, particularly for those who are not able to cope with that new source of economic uncertainty. As consequence, individuating the main determinants of price volatility becomes a key issue for policy-makers to intervene and reduce the potential negative effects in terms of welfare.

Although some aspects of the price volatility in the agricultural markets are yet not completely explored (e.g. the role played by the financial markets and the speculative activity of the index traders), there are some key concepts largely accepted by the scientific community. Since agricultural commodity price volatility preserves some specific features linked to the market characteristics and policy implications, the comparison with any other market becomes a difficult task to accomplish (Piot-Lepetit and M'Barek, 2011). In particular, the fluctuations of the agricultural commodity prices are strictly linked to the market fundamentals such as supply, demand, storage with their relative shocks (e.g. weather, technological progress, population growth and etc) and they are driven by other macroeconomic structural factors which horizontally influence different crops at the same time (such as energy and fertilizer prices, exchange rates, interest rate and etc). Besides, price volatility can be addressed by the government through specific agricultural and trade policies as well as it could be exacerbated by profit-seeking stakeholders like financial investors. Following Brümmer et al. (2013), we can classify the existing literature on the analyses of the volatility drivers in three main blocks1: (i) descriptive models which do not estimate directly the causal relationship between price volatility and its drivers (e.g. Clapp, 2009; Gilbert and Morgan, 2010; Wright, 2011; Anderson and Nelgen, 2012; Chandrasekhar, 2012; Nissanke, 2012); (ii) studies based on mathematical modelling such as partial equilibrium models (e.g. Miao et al., 2011; Babcock, 2012); and (iii) empirical models which use reduced-form (Balcombe, 2009; Ott, 2013), cointegration analysis (Pietola et al., 2010), or different specifications of the GARCH(1,1) model (e.g. Zheng et al., 2008; Roach, 2010; Hayo et al.,2012; Karali and Power, 2013). Especially for the studies investigating a causal relationship between price volatility and its drivers, the possibility to provide a comprehensive analysis is limited because of the data frequency mismatch between daily (or potentially intra-daily) spot/futures prices and monthly/quarterly/annual observations of supply-demand factors (e.g. stocks, consumption, production, trade flows, etc.). It clearly generates a trade-off between the possibility of exploiting efficiently all the information provided by the high-frequency data on prices and the necessity of investigating the linkages between the low-frequency macro-economic determinants. On one side, some authors address this problem by using daily prices for the calculation of volatility with the cost of having the possibility to focus only on the relationship with monetary or financial factors (Hayo et al., 2012). On the other side, some authors aggregate the higher frequency data to lower frequency by simply averaging, summing or assuming a representative high frequency data point in time as a proxy for low frequency observation (e.g. the last week of a month to aggregate weekly data to monthly data). Aggregation generally impedes extracting available information embedded in high frequency data and hence leads to information loss. This typically deteriorates the estimation precision and generates poorer analysis overall. Among various examples of aggregation in price volatility studies, Zheng et al. (2008) use monthly prices while Balcombe (2009), Pietola et al. (2010) and Ott (2013) calculate annual measure of volatility based on a limited number of observations in order to match the lower frequency of macroeconomic data. One attempt to overcome this problem with mixtures of different frequencies was provided by the studies of Roach (2010) and Karali and 1 The main focus of this work is on the drivers of the agricultural commodity price volatility, therefore we do not cover the discussion on the measurement of the price volatility itself in our study. For a review on this topic see Brümmer et al. (2013)

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Power (2013) which exploit the Spline-GARCH model proposed by Engle and Rangel (2008) to isolate different components of agricultural commodity price volatility. In the Spline-GARCH model, the daily equity volatility is a product of a slowly varying deterministic component and a mean reverting unit GARCH. Unlike conventional GARCH or stochastic volatility models, the Spline-GARCH permits unconditional volatility to change over time. Specifically, Roach (2010) and Karali and Power (2013) analyse the link between price volatility and macroeconomic determinants using a two-step procedure. In the first step, they extract the slowly varying component of volatility using the Spline-GARCH model together with high frequency price data and artificially build a measure of fluctuation by taking the sample average of the low-frequency component. In the second step, they estimate a reduced-form model to link the estimated price volatility to the macroeconomic determinants. Despite the fact that this method was supported to achieve a better fit than the simple GARCH approach, it still suffers from several shortcomings. First of all, the unconditional variance is modelled in a deterministic and non-parametric manner, preventing the possibility to incorporate directly macroeconomic data (Ghysels and Wang, 2011). Second, the two-step procedure may not be the most efficient solution because averaging daily/monthly data at monthly/annual level generally leads to a significant amount of information loss. Finally, Roach (2010) and Karali and Power (2013) do not take into consideration the impact of the lags of the macro-economic drivers on price volatility, imposing exclusively a contemporary relationship which is hardly the case in the agricultural commodity markets.

The objective of this paper is to investigate the main drivers of the agricultural price volatility by using a unified framework that is able to take into consideration both high and low frequency components of volatility while combining the information provided by daily prices and monthly/quarterly/annual macroeconomic variables. At this purpose, we will exploit a new class of model called GARCH-MIDAS, recently proposed by Engle et al (2013). Departing from Engle and Rangle (2008), the GARCH-MIDAS model smooths the unconditional volatility through the mixed data sampling (MIDAS) filtering of Ghysels, et al (2005) and allows for incorporating low-frequency macroeconomic data (monthly/quarterly/annual). The main contributions of our analysis with respect to the previous works can be summarized in four principal points: 1) we drastically reduce the trade-off between the accuracy of the volatility measurement provided by the high-frequency data on prices and the necessity to match it with low-frequency macro-economic variables; 2) we analyse the volatility drivers of wheat, corn and soybean prices from 1986 to 2012 by using a unified framework which is capable of disentangling the high and low frequency volatility components while avoiding any loss of efficiency due to multi-step procedures; 3) we analyse the causal relationship between price volatility and its determinants in a dynamic perspective going beyond the usual contemporary analysis; 4) finally, we are able to rank the macroeconomic determinants of the price volatility in order of importance, individuating which are the most sensible key drivers to be addressed by the policy makers.

The major findings of this paper can be summarised as follows. We observe that modelling the agricultural commodity price volatility as the product of high and low frequency components is more efficient than filtering it through a standard GARCH(1,1) model. In terms of macroeconomic determinants, we find that the incorporation of economic fundamentals into the estimation drastically improves the capability of explaining the dynamics of unconditional price volatility in most of the cases. After combing wheat, corn and soybean daily prices with monthly market-specific and common macroeconomic drivers over the period 1986-2012, we observe that supply-demand indicators and conventional speculation proxies becomes critical in explaining the low-frequency component of volatility. Specifically, we find that the most important factors which contribute to exacerbate price volatility are inventory reductions, booms in the global economic activity, weather anomalies and – different from the previous studies – an increase in the Working T-index, which measures the excess of non-commercial activity beyond what is needed to balance commercial needs on the derivative markets. At the same time, monetary factors and energy markets play significant but less important role over the full sample. Finally, after testing and confirming the presence of a structural break in the price volatility in coincidence with the recent large price swings, we focus on the period following the recent price spikes

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(2006-2012). The results show that the monetary factors – especially interest rate – become essential to describe agricultural price fluctuations, suggesting also that the heterogeneity in the effects of the drivers on the different crops is decreasing.

The paper is organised in the following order: section 2 introduces the methodology of the GARCH-MIDAS approach; dataset and estimation results are divided into two sections where section 3 focuses on the realized volatility and section 4 displays the details on macro variables; and section 5 presents the conclusion.

2. Methodology: The GARCH-MIDAS Approach

The GARCH-MIDAS model presented by Engel et al. (2013) is based on the assumption that unexpected returns can be written as follows:

( ) titittititi grEr ,,,,1, ετ ⋅=− − (1)

where tir , is the log return on day i during month/quarter/year t ( tNi ,...,1=∀ ; tN is the number of

days in period t); ( )tiE ,1− is the conditional expectation given information at day ( )1−i of any

arbitrary period t; and ( )1,0~~,1, Ntiti −Φε with ti ,1−Φ denoting the information set including the

history of returns up to day ( )1−i of period t . Volatility is decomposed into two separate components as in the tradition of the component GARCH models introduced by Engle and Lee (1999)2. Namely, tig ,

characterizes daily fluctuations associated with transitory (or short-lived) effects of volatility while the secular or low-frequency component τt represents the unconditional volatility and it is aimed to capture slowly-varying deterministic conditions in the economy. Assuming that ( )titi rE ,,1− is equal toμ , we can

rewrite equation (1) as:

ttititti Nigr ,...,1,,,, =∀+= ετμ (2)

In the GARCH-MIDAS model, the tig , component is assumed to be a (daily) GARCH (1,1) process,

namely:

( ) ( )ti

t

titi g

rg ,1

2,1

, 1 −− +

−+−−= β

τμ

αβα (3)

where α > 0, β > 0 and α + β < 1. Following a long tradition started with the works of Merton (1980) and Schwert (1989) we model the low-frequency τt component using realised volatility. However, unlike those previous studies, we utilize MIDAS regression to model τt component in (2), i.e.:

( )∑=

−+=K

kktkt RVm

121 ,ωωϕθτ (4)

where tRV is the fixed time span3 realised volatility at time t:

∑=

=tN

itit rRV

1

2, (5)

2 Note that Engle and Lee (1999) use an additive volatility component model (i.e. two additive GARCH(1,1) models) while the Spline-GARCH and the GARCH-MIDAS models are based on multiplicative decomposition of the conditional variance. 3 There are two different options for the MIDAS filtering: (1) fixed-time span and (2) rolling window. Rolling window let both τ and g change at daily frequency. Since we would like to capture macro variables which are available in lower frequencies than daily frequency, our study is based on fixed-time span.

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and φk() is the function defining the weighting scheme of MIDAS filters. Engle et. al (2013) proposed two different functions for the weighting scheme: the Beta and the Exponentially weighted lag structure. Following Joyeux and Girardin (2013) and Engle et. al, (2013) who showed that they yield similar results, we decide to use the Beta lag structure due to its flexibility to accommodate various lag structures:

( ) ( ) ( )( ) ( )∑

=

−−

−−

−

−= K

j

k

KjKj

KkKk

1

11

11

2121

21

1

1,ωω

ωω

ωωϕ (6)

In (6), different combinations of ω1 and ω2 values can accommodate monotonically increasing, monotonically decreasing and also uni-modal hump-shaped weighting schemes 4 . It is worth to emphasize that the GARCH-MIDAS model presented in (2)-(6) has a fixed parameter space, i.e.

{ }21 ,,,,,, ωωθβαμ m=Θ , which makes it more parsimonious compared to other component volatility models. This feature is exploited to compare different models with various time span t (e.g. month, quarter, annual) and different number of lags K. In particular, we choose the time period t by comparing the values of log-likelihood functions and, subsequently, define the optimum number of lags, K, through the minimization of the Bayesian Information Criteria (BIC).

Engel et al. (2013) propose an additional specification for the fixed span τt component which is basically the log version of (4) and corresponds to the class of models allowing us to insert macroeconomic variables:

( )∑=

−+=K

kktkt Xm

121 ,log ωωϕθτ (7)

where Xt-k represents the k lag of the covariate we want to link to the low-frequency component τt. Equation (7) represents the key element for building direct linkages between price volatility and macroeconomic variables. First of all, it enables us to use data sampled at different frequencies with the help of MIDAS filtering. In fact, financial data with high frequency i (daily, hourly, intra-daily) can directly be combined with macro variables available at lower frequencies t (monthly, quarterly, annual), which help us to optimize the usage of information at hand. Second, the number of parameters to estimate is fixed regardless of the number of lags which can be modified to capture the impact of persistency. That makes the model parameterization parsimonious. Finally, the non-negative weights attached to the lagged variables lead to positive estimates of volatility while enabling different schemes of weighting5.

3. Model selection and estimation with realised volatility

In this section, we describe data on returns and provide the estimation of the model with realised volatility6.

3.1 Returns Data and Realized Volatility We focus our analysis on three agricultural commodities: wheat, corn and soybean. From an

economic point of view, the focus on those products can be explained by the fact that cereal prices are key elements for understanding the characteristics of the agricultural markets and the food sector. From 4 See Ghysels et al. (2007) for a broad discussion on the different patterns which can be obtained through Beta lags. 5 More details on the theory of MIDAS regression can be found in Ghysels et al (2007). 6 Note that all calculations presented in this and following sections were performed by using Global Optimization toolbox and multiple starting point approach in MATLAB version R2013a.

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a practical point of view, they present the availability of reliable time series on daily futures prices and other low-frequency financial data that we want to include in our analysis. For calculating the returns, we use daily settlement prices of the first nearby futures contracts traded at the Chicago Board of Trade (CBOT) from the 1st January 1986 to 31st December 20127. The reasons to use futures prices instead of spot prices are largely acknowledged by the literature: (i) they are standardized and promote accuracy; ii) they perform as risk-transfer tool for hedgers and speculators; (iii) they provide information to the market over the price formation and, practically speaking, (iv) they are sampled at high frequency (Hernandez and Torero, 2010). However, building a unique series for the futures prices requires some data manipulation because it is needed to combine different contracts with a limited life span (Gutierrez, 2013). In order to avoid the well-known Samuelson effect supporting that the price volatility increases as the contract approaches its delivery date (Samuelson, 1965), we follow the conventional method where we take the nearest contract up to the first day of its maturity month and then we roll over to the next contract (e.g. Miffre and Rallis, 2007; Gilbert, 2010; Hernandez and Torero, 2010; Gutierrez, 2013) . The delivery months for wheat and corn are March, May, July, September and December while for soybean they are January, March, May, July, August, September and November.

The realized volatility (RV) used in equation (4) of the GARCH-MIDAS model is calculated as in equation (5). In order to take into consideration the effect of seasonality induced by the harvest cycles during a calendar year8, we seasonally adjust the monthly and quarterly RV series before fitting MIDAS regression, as suggested by Ghysels et al. (2006). In particular, we remove the periodic pattern using a multiplicative-type of adjustment: we firstly regress the RV series over monthly/quarterly dummies and then we divide the observed realised volatility by the predicted value of the regression.

3.2 The Empirical Estimation with Realised Volatility For estimating the parameters of the GARCH-MIDAS model we use the conventional quasi maximum

likelihood estimation (QMLE) method. In particular, we minimize the following log-likelihood function:

( ) ( )∑∑= = ⎥

⎥⎦

⎤

⎢⎢⎣

⎡ −+−∝

T

t

N

i tit

ittit

t

gr

gLLF1 1

2

log21

τμ

τ (8)

In order to allow for possible misspecification of the likelihood function and achieve robust results,

we derive the Quasi-Maximum Likelihood Estimators (QMLE)9. We use 11 =ω and 12 >ω to have a monotonically decreasing pattern over the lags, which is typical of volatility filters.

Building an optimal model representation with macroeconomic variables requires the selection of the time span t and the MIDAS lag years k which are used in the MIDAS polynomial specification of the low-frequency component τ. Our estimations suggest that monthly specification always outperforms the quarterly and annual representations of the low-frequency component. Following to the time span selection, we use the BIC criteria to define the optimum lag number10. Figures A.1-A.3 represent the estimated lag weights of the GARCH-MIDAS model with monthly RV for one to three MIDAS lag years. 7 Even if the data on futures contracts are available before 1986, we focus on that period because of data availability constraints on some macroeconomic variables we want to include in the analysis; particularly for what concerns data on derivative market positions (See section 4) 8 The presence of seasonality in the agricultural commodity price volatility has been largely acknowledged by the literature. For example, see Anderson (1985); Kenyon et al. (1987); Yang and Brorsen (1993); Karali and Thurman (2010); Piot-Lepetit and M'barek (2011); Karali and Power (2013). 9 More details on estimation and the regularity conditions of the GARCH-MIDAS model can be found in Ghysels and Wang (2011). 10 The LLF and BIC results are available upon request for both time span and optimal lag structure selections.

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For wheat and soybean, Figure A.1 and Figure A.3 respectively show that the optimal weights decay to zero around 20 months of lags, regardless if we select two or three years of MIDAS lags. Note that the model with one year MIDAS lag is not proper for exploiting all the information provided by the past values of RV since the weights do not converge to zero. For corn, Figure A.2 shows a different pattern where the optimal weights decay to zero with both one and two years of MIDAS lags while the model with three years of MIDAS lags does not converge to zero. Nevertheless, the BIC criteria for the three crops suggest that two years of MIDAS lags achieves the best fit, implying that the best representation is given by the model with t=month and k=24. Table 1: The GARCH-MIDAS model with realized volatility for the period 1986-2012

Crop μ α β m θ ω LLF/BIC GARCH(1,1)

Wheat -0.0004 0.0667 0.8779 0.0000 0.0002 4.9853 17055.58 17038.1888 -2.19 7.37 38.53 2.29 9.85 1.82 -5.42 34.77

Corn -0.0002 0.0858 0.8857 0.0000 0.0002 2.1433 17935.83 17916.9234 -1.39 8.44 57.69 1.08 5.68 2.91 -5.69 37.82

Soybean 0.0000 0.0722 0.9027 0.0001 0.0001 4.0278 18228.01 18224.6246 0.07 8.70 66.21 2.36 2.98 8.67 -5.79 6.76

The restrictions on GARCH(1,1) model with respect to the GARCH-MIDAS model are two (θ=ω=0). The 5% critical value for the chi-square with two degrees of freedom is equal to 5.99.

Table 1 reports the parameter estimates of the GARCH-MIDAS model with realised volatility represented in equations (1)-(6). For each crop, the first six columns present the parameter estimates with the robust t-statistics computed by Bollerslev and Wooldridge (1992) standard errors below. The seventh column reports the value of the log likelihood function (LLF) and below the Bayesian Information Criteria (BIC). In addition to the models with the realised volatility, we also estimate a restricted specification of equation (4) with θ=0 which reduces the GARCH-MIDAS model to a GARCH (1,1) model with constant unconditional variance (Conrad et al., 2012). Since the GARCH(1,1) model is nested in the GARCH-MIDAS specification, the comparison of the two models is straightforward. The last column of Table 1 presents the value of the LLF of the GARCH(1,1) with the chi-square test statistic of the log likelihood ratio test with respect to the GARCH-MIDAS model below. Figures A.4-A.6 in the Appendix show the annualised volatility components of the GARCH-MIDAS models for the three crops over the period 1986-2012. It is observed that the MIDAS filter applied to the realised volatility allows for extracting a τ component which is smoother than the total price volatility as it was expected. Nevertheless, it must be noted that the τ component still follows the path of the total volatility and increases substantially in the last decade, especially for wheat and corn. According to Table 1, all of the parameters are statistically significant and respect the expected sign, except μ in the case of corn and soybean and m in the case of corn where the coefficients are not statistically different from zero. Moreover, the estimation results for θ are always significant and positive indicating that the information contained in the last two years of RV contributes to explain the low-frequency component of the price volatility. Not surprisingly, the higher the level of past RV, the higher the level of τ. Finally, the last column of Table 1 reveals that the GARCH-MIDAS models outperform the standard GARCH(1,1) model in all three cases. This result supports that a time-varying unconditional variance model

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accommodates better the agricultural price volatility behaviour. It is also worth to note that while the sum of α and β is always close to one in the GARCH model (i.e. 0.994 for wheat; 0.993 for corn; and 0.989 for soybean), in the GARCH-MIDAS model the sum is significantly lower, indicating a lower persistence in the low-frequency volatility component. This result is in line with other works based on component models such as Engel and Rangel (2008) and Engle et al. (2013). 4. Estimation with the Macroeconomic Determinants

In this section, we analyse the link between the agricultural commodity price volatility and a broad

range of drivers which are related to market fundamentals, common macroeconomic factors and financial activity.

4.1 Selected drivers of the low-frequency price volatility Market fundamentals used for modelling price volatility in the agricultural sector are usually linked

to the information available on supply, demand and inventories. In particular, both theoretical and empirical literatures agree that information on inventories is a fundamental factor to explain price volatility for storable commodity such as cereals. The theoretical background – provided by the well-known competitive storage model originally introduced by Gustafson (1958) – suggests a negative relationship between stocks and price volatility due to the fact that demand and supply shocks are better absorbed by the market during high inventory periods (Williams and Wright, 1991). From an empirical point of view, the impact of inventories on the volatility of the agricultural commodity prices is usually captured by using the stock-to-use ratio (e.g. Roache, 2010 Karali and Power, 2013; Ott, 2013). At this purpose, we use the ratio between the end-of-year stocks and the total consumption at global level which is projected each month by the United States Department of Agriculture (USDA) and published in the World Agricultural Supply and Demand Estimates (WASDE) reports11.

Moreover, we introduce the information on global weather pattern to take into consideration unexpected shocks to foreseen harvests. In particular, we use the Southern Oscillation Index (SOI) anomalies which measure the deviations between air-pressure differentials in the Pacific Ocean and their historical averages (Brunner, 2002)12. Prolonged periods of positive SOI values indicate that sea water is cooler than the expected values of La Niña episodes and are associated with increasing droughts at the mid-latitudes, where grain production is concentrated (Algieri, 2013). Therefore, we expect positive relationship between the SOI and price volatility because the episodes of droughts are responsible for supply-side shocks and thinner markets.

Another factor influencing price volatility through the supply-demand channel is related to the structure of the world market which determines the availability of the agricultural commodities. Using the WASDE projections, we look at the relative size of the international market for each commodity. In particular, we calculate the market thinness as the share of imports and exports within the global consumption (OECD, 2008; Algieri, 2013). The size of the global market has been highly debated by the literature as a consequence of the evident increase of export restrictions and hoarding behaviour during 11 As reported by Stigler and Prakash (2011), the monthly WASDE projections are preferable to ex-post annual measures because the latter are usually imperfect approximations derived as a residual between supply and demand identity and since they capture ex-post information, they do not influence agents' behaviour. On the other side, forecasts on future stocks are relevant in trading decisions and play a relevant role in price determination, including volatility outcome. 12 The SOI data are taken from the National Oceanic and Atmospheric Administration (NOAA)'s National Climatic Data Center (NCDC).

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the recent food crisis. The attempt of the national-level policies to insulate their domestic market from international price volatility usually has the opposite effect of reducing stability and predictability of prices (Anderson and Nelgen, 2012). As consequence, the expected relationship between the market thinness index and the low-frequency component of volatility is negative. The hoarding behaviour at both public and private level of some major importing countries would be reflected in an increase of the global size of the market, especially after the recent food crisis (Timmer, 2010). In this case, the expected relationship with the price volatility is in the opposite direction, i.e. the higher the index the higher the price volatility. Therefore, the coefficient of the market thinness index provides the net effect of two contrasting forces.

The last driver linked to the market fundamentals is related to the demand component and specifically to the biofuel production which is mainly triggered by the US and EU biofuel policies over the last decade. Especially in the US, as the inclusion of corn and soybean into biofuel production has been extensive, the availability for food and feed purposes have reduced and have made the market thinner and more sensible to other exogenous shocks (Wright, 2011). As a result, we expect to observe a positive relationship between biofuels demand and the volatility of those three commodities' prices. In order to capture the impact of biofuels on volatility, we use the monthly US biofuels production provided by the US Energy Information Administration (EIA) which is assumed to be equal to the consumption plus the biomass inputs to the production of fuel ethanol and biodiesel13.

In addition to the structural elements determined by market fundamentals, the agricultural commodity price volatility is affected by several other macroeconomic factors which horizontally influence different crops at the same time. First of all, price volatility is expected to increase during economic booms and to decrease during recessions (e.g. Roache, 2010; Karali and Power, 2013; Ott, 2013). For capturing the impact of the economic cycles, we consider the monthly index of global real economic activity provided by Kilian (2009) which is based on the dry cargo single voyage ocean freight rates and captures shifts in the demand for industrial commodities at global level. Secondly, price volatility is influenced by the energy market and especially by crude oil price behaviour because it determines the fuel and other input prices (i.e. fertilizers) and affects the demand for biofuels. To capture the impact of the oil price volatility in our model, we calculate the monthly realised volatility of the West Texas Intermediate (WTI) daily nearby futures and we expect to find a positive relationship with the low-frequency component of the agricultural commodity price volatility. We also consider monetary factors such as the US-Dollar exchange rate volatility and the US interest rate. The explanation for the former factor is quite straightforward mainly because the international transactions of the agricultural commodities are denominated in USD and then non-USD producers aim to adjust the purchasing power of their export revenues. As consequence, an increase in the volatility of the USD should trigger an increase in the commodity price fluctuations caused by the realignment of the purchasing power parities. We measure the USD volatility by calculating the monthly realised volatility of the daily Nominal Major Currencies Dollar Index released by the Board of Governors of the Federal Reserve System 14. Finally, we expect to observe a negative relationship between the interest rate and price volatility. As argued in Frankel (2007), a decline in the interest rate has the effect of reducing the opportunity cost to hold inventories, increasing the commodity demand, making the market thinner and reducing the market's ability to cope with any other shock. Moreover, low interest rates are likely to emerge from loosened monetary policies and excessive liquidity on the market is often blamed to exacerbate price fluctuations, especially in short run. We control for the impact of the interest rate using the US Treasury 3-month bill released by the Board of Governors of the Federal Reserve System. 13 We use data on US biofuels because they are the only available dataset at monthly frequency. 14 A measure of monthly real exchange rate volatility would be more appropriate in this case but information on relative prices is not available at daily frequency. It means that such prices should be interpolated from monthly consumer price indices. Nevertheless, Baum et al, (2004) showed that the month to month movements of the real exchange rate are dominated by the movement in nominal rates, therefore using nominal or real rates in monthly analyses does not affect the final results.

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The last group of drivers we consider regards the recent debate on the role of derivative markets and speculative activity in the price formation of the agricultural commodities. After the recent price boom and bust observed during the period 2006-2009, economists, market analysts and policymakers had started to investigate deeper if financial markets are driving the agricultural commodity prices away from the underlying equilibrium determined by the fundamentals, i.e. the so-called Masters Hypothesis (Masters, 2008). While the main part of the literature focused on the linkages between financial markets and price levels15, few attempts have been made to investigate whether the speculative activity is stimulating price volatility or not (Roache, 2010; Ott, 2012, 2013). We take the conventional approach to measure the financialisation and speculation through two proxies: the Scalping Index and the Working-T Index. The former is the ratio of volume to open interest in future contracts traded at the CBOT and reflects market liquidity. In particular, it detects the attempt of earning profits within very short period of time (Robles et al. 2009; Du et al, 2011). The latter is based on the distinction between traders involved in the physical business of commodities for hedging reasons (commercial) and the ones simply driven by profit-seeking behaviour (non-commercial). The index presented by Working(1960) is defined as follows:

T= 1 + NCS/ (CL + CS) if CS > CL T = 1 + NCL /(CL + CS) if CL > CS

where NCS (NCL) indicates non-commercial short (long) positions and CS (CL) indicates commercial short (long) positions. The Working-T index measures the excess of non-commercial positions beyond what is technically needed to balance commercial needs, and this excess is measured relative to open interest positions. The monthly average index is built using the weekly data provided by the U.S Commodity Futures Trading Commission (CFTC) in its Historical Commitments of Traders (COT) reports on futures contracts traded at the CBOT.

4.2 The Empirical Estimation with Macroeconomic Determinants In this section, we will focus on the analysis of the impact of the macroeconomic variables on the

low-frequency volatility component using the log version of the model in equation (7). In order to use stationary time series in our estimations, we apply Augmented Dickey Fuller (ADF) unit root tests on the macroeconomic variables (see Table A.2). In most of the cases the null hypothesis that the variable contains a unit root process is rejected at 5% level. The exceptions are the stock-to-use ratio, the market thinness index, the biofuel production and the interest rate. In these cases we run our model using first differences instead of the level.

Following Engel et al. (2013), Asgharian et al. (2013) and Conrad et al. (2012), we estimate the GARCH-MIDAS models with one macroeconomic time series each time. As in the previous section, Tables 2-4 present the estimated parameters for wheat, corn and soybean, respectively, as well as the log-likelihood and the BIC values. In this case, LLF and BIC are particularly useful for ranking the different macroeconomic variables in order to understand which ones show the best fit. We also add the last column which reports the likelihood-ratio tests between the GARCH-MIDAS and GARCH(1,1) models together with its relative p-value. Before focusing on the sign and significance of θ - which gives us the impact of the macroeconomic variables on the low-frequency component τ - we briefly comment on the other parameters. We see from Table 2-4 that μ is either very close to zero or not significantly different from zero for all of the three crops. Moreover, α and β are always strongly significant as well as their sum is quite close to one, indicating a high level of persistence in the price volatility, once we control for macroeconomic determinants. Specifically, the average of the sum of α and β are all close to one: it is 0.9932 for wheat; 0.9917 for corn and 0.9883 for soybean. 15 The resulting literature has not been capable of clarifying the real effects of the increasing presence of non-commercial investors on the commodity price level and its volatility yet.

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Table 2: The GARCH-MIDAS model for wheat with macroeconomic variables (1986-2012)

μ α β m θ ω LLF/BIC χ2/pvalue

% Δ Stock 0.000 0.048 0.947 -8.101 -11.221 26.650 17043.058 9.739-2.020 5.804 101.344 -44.161 -17.425 182.359 -5.414 0.008

SOI 0.000 0.052 0.943 -8.069 0.050 5.853 17038.560 0.742-2.045 6.270 102.181 -41.803 0.702 4.800 -5.413 0.690

% Δ Market Thinness 0.000 0.051 0.943 -8.071 -3.336 282.780 17038.850 1.323-2.050 6.300 103.583 -44.473 -1.069 0.355 -5.413 0.516

% Δ Biofuels Production 0.000 0.052 0.941 -8.158 8.878 1.271 17039.588 2.799-2.040 6.273 98.112 -44.779 5.958 3.185 -5.413 0.247

Kilian Index 0.000 0.053 0.940 -8.047 1.833 2.110 17042.350 8.322-2.076 6.435 97.992 -40.433 2.537 0.537 -5.414 0.016

Oil Price Volatility 0.000 0.053 0.940 -8.871 21.315 1.044 17040.124 3.870-2.065 6.417 98.715 -53.961 6.252 0.711 -5.413 0.144

Exhange Rate Volatility 0.000 0.051 0.943 -7.249 -103.826 2.732 17040.759 5.140-2.009 6.479 107.998 -33.584 -39.787 1.222 -5.414 0.077

Δ Interest Rate 0.000 0.052 0.943 -8.058 0.535 9.314 17039.133 1.888-2.033 6.521 105.766 -44.694 3.784 7.534 -5.413 0.389

Scalping Index 0.000 0.055 0.936 -9.924 5.693 2.082 17042.073 7.768-2.068 3.811 42.308 -2.853 0.518 1.043 -5.414 0.021

Working T Index 0.000 0.053 0.937 -16.379 7.091 1.408 17047.711 19.044-2.070 5.067 59.359 -3.645 1.848 0.653 -5.416 0.000

GARCH (1,1) 0.000 0.052 0.943 0.000 - - 17038.189 --2.029 6.352 103.533 5.458 - - -5.415 -

WHEAT (1986-2012)

Table 3: The GARCH-MIDAS model for corn with macroeconomic variables (1986-2012)


% Δ Stock 0.000 0.075 0.918 -8.143 -7.148 12.062 17917.830 1.812-1.253 8.887 97.641 -41.480 -32.181 21.472 -5.686 0.404

SOI 0.000 0.076 0.915 -8.224 0.221 5.279 17923.161 12.475-1.243 8.421 86.826 -39.248 2.489 8.240 -5.688 0.002


% Δ Biofuels Production 0.000 0.075 0.917 -8.218 6.282 1.306 17917.557 1.267-1.254 8.520 93.059 -39.704 5.859 3.657 -5.686 0.531

Kilian Index 0.000 0.074 0.917 -8.178 1.600 3.319 17921.873 9.899-1.287 8.350 91.027 -38.536 3.032 0.869 -5.687 0.007


Exhange Rate Volatility 0.000 0.074 0.919 -8.223 7.148 284.777 17917.480 1.114-1.238 8.795 97.382 -43.556 2.810 0.875 -5.686 0.573

Δ Interest Rate 0.000 0.074 0.919 -8.179 -0.851 1.000 17917.485 1.122-1.240 8.758 96.921 -39.229 -1.481 1.969 -5.686 0.571

Scalping Index 0.000 0.076 0.915 -9.736 4.845 1.072 17923.059 12.272-1.312 8.699 90.193 -17.966 2.944 1.878 -5.688 0.002

Working T Index 0.000 0.079 0.910 -22.798 13.338 1.000 17933.266 32.686-1.254 8.945 59.429 -6.036 4.140 0.211 -5.691 0.000

GARCH (1,1) 0.000 0.074 0.918 0.000 - - 17916.923 --1.254 8.728 96.394 4.885 - - -5.689 -

CORN (1986-2012)

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Table 4: The GARCH-MIDAS model for soybean with macroeconomic variables (1986-2012)


% Δ Stock 0.000 0.067 0.922 -8.388 4.565 264.868 18227.199 5.150-0.080 9.277 111.144 -47.749 6.989 0.981 -5.793 0.076

SOI 0.000 0.067 0.919 -8.469 0.143 5.362 18228.919 8.589-0.082 9.160 101.079 -58.469 2.087 0.914 -5.793 0.014


% Δ Biofuels Production 0.000 0.066 0.924 -8.387 -1.729 12.629 18227.643 6.036-0.052 9.050 108.738 -51.604 -1.630 16.789 -5.793 0.049

Kilian Index 0.000 0.068 0.918 -8.457 1.649 2.801 18232.321 15.392-0.057 9.131 98.762 -63.693 3.903 5.713 -5.794 0.000


Exhange Rate Volatility 0.000 0.067 0.922 -8.495 12.110 270.785 18226.281 3.313-0.058 9.262 108.000 -52.963 56.168 3.291 -5.793 0.191

Δ Interest Rate 0.000 0.068 0.921 -8.401 -0.322 30.561 18225.816 2.382-0.072 9.329 109.116 -52.211 -1.347 687.653 -5.792 0.304

Scalping Index 0.000 0.068 0.922 -8.508 0.221 299.995 18225.676 2.102-0.038 9.104 106.752 -43.275 1.169 6.715 -5.792 0.350

Working T Index 0.000 0.068 0.921 -12.368 3.594 1.000 18225.437 1.625-0.049 9.260 106.821 -108.893 28.811 0.975 -5.792 0.444

GARCH (1,1) 0.000 0.068 0.922 0.000 - - 18224.625 --0.041 9.221 107.665 6.215 - - -5.795 -

SOYBEAN (1986-2012)

If we focus on θ which is the most interesting parameter in the present exercise, it can be observed in Table 2-4 that, in general, the GARCH-MIDAS model behaves as expected in almost all the cases with few exceptions. For wheat, all the parameters show the expected sign (except for the exchange rate volatility) and are strongly significant for almost all the variables. Specifically, the MIDAS estimates confirm that an increase in stock-to-use ratio, the size of the global market and the interest rate contribute to a reduction in price volatility while weather anomalies, biofuels production, the level of global economic activity, oil price volatility and speculation proxies have positive impacts. However, the t-stats show that weather anomalies, international market thinness and scalping index are not statistically significant indicating that these variables are not helping to explain the low-frequency component of wheat price volatility. Moreover, if we look at the log-likelihood values in the second to last column of Table 2, we see that the GARCH-MIDAS models which achieve the best fit are, respectively, those with the Working T Index, the stock-to-use ratio and the Kilian index. This is confirmed by comparisons to the restricted GARCH (1,1) model, too. We also calculate the magnitude of the impact of a change in the X at time (t-1) on the low-frequency component at time t16. For example, an increase in the Working T index from 1 to 1.1 in the current month - which implies a 10% increase of the speculation in excess technically needed to meet commercial hedging needs - would increase next month's volatility by 5.26%. At the same time, a 1% increase in the variation of the stock-to-use ratio would decrease volatility by 0.99% while the cumulative effect after 6 month of 1% increase would reduce the low-frequency component of volatility by almost 3%. In the case of wheat, the empirical estimates seem to support the idea that the different demand components generated by both the derivative markets and consumption purposes are the main drivers of the wheat price volatility during the period 1986-2012. In particular, it is worth to note that the demand for speculative purpose carried out by non-commercial actors on the derivative markets significantly influences the low-frequency 16 Following Engel et al. (2013) and Conrad et al. (2012), the calculation is done by computing the formula exp(θφ1(ω)) -1. For example, in the case of wheat, the estimated parameters for the model with the SOI index are θ=0.05 and ω2=5.853. Considering that ω1=1, the weighting function gives φ1(ω)=0.225 while the impact of unit change at time (t-1) in the SOI index would increase the price volatility by exp(0.05*0.225) - 1 ≈ 0.0114, or 1.14%.

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component according to those results. This supports the so-called Master Hypothesis. On the contrary, monetary and trade policies, as well as energy markets seem to be relatively less important.

For what concerns corn, all the parameters reported in Table 3 respect the expected sign – except for the change in the interest rate – and all are statistically significant at 1%. Looking at the log-likelihood values, we see that the best fit are achieved by the models with the Working T Index, the SOI and the Scalping Index , respectively, and it is also confirmed by their comparison with the restricted GARCH (1,1) model. In particular, a 10% increase in the excessive speculation in the current month would increase next month volatility by 7.85% while a unit increase in the variation of the SOI would increase it by 4.64%. Overall, the activity of non-commercial actors seems to be the main factor in explaining the low-frequency volatility path in the corn market and - in terms of magnitude – the impact of the speculative pressure is higher with respect to the wheat case. Moreover, supply shocks caused by weather anomalies are the other key factors; differently form the wheat case where the demand for consumption purposes is more important.

Lastly, Table 4 reports the results for soybean. In this case two estimated parameters do not follow the expected sign (i.e. stock-to-use ratio and biofuels production) while three are not statistically significant (i.e. biofuels production, interest rate and scalping index). In particular, quite surprisingly the sign for the variation of the stock-to-use ratio is significantly positive. However, it must be taken into consideration that the variable used in this exercise is based on a monthly projection of the end-of-year stocks and its influence on the price volatility leaded by the reaction of the traders in the market. In other words, the changes between the expected and estimated signs of parameters can be caused by possible imprecision in the provided information, especially in the early parts of our sample, or conditioned by the irrational market behaviour observed recently and triggered by the massive increase of non-commercial agents in the agricultural commodity markets (Stigler and Prakash, 2011). The second to last column of the Table 4 shows that for soybean, the best fit is achieved by the models with the Kilian index, the SOI and the oil price volatility, respectively. An increase of 0.1 in the Kilian index increases the low-frequency component of soybean price volatility by 2.08% while a unit change in the SOI increase it by 3.02%, which is slightly lower than the impact on corn. Therefore, the main drivers of the price volatility of soybean are quite different from the other two crops we analyse. In particular, the derivative markets are not playing the same role as in the previous two crops and the, macroeconomic fundamentals based on demand and supply elements are the most important drivers, together with the energy market influencing the production costs and investment decisions.

One possible limitation of the estimation provided with the full sample is that the low-frequency component of price volatility can present structural breaks. As noted by Engel et al. (2013), one could argue that the GARCH-MIDAS models can accommodate structural breaks via the movements in τ. However, we would prefer to test whether our full sample presents breaks or not and re-estimate the models considering possible changes in the price volatility dynamics. The easiest way to test for structural breaks is to compare the log-likelihood function for the full sample with those of the sub-samples suggested by the empirical evidence. In this case, testing the presence of a break in coincidence with the large price swings observed after the food price crisis in 2006 can be suggested as a straightforward option. Following Engel et al. (2013), we test this hypothesis calculating:

⎥⎦

⎤⎢⎣

⎡−− ∑

−= samplessubiifull LLFLLF2 ~ )(2 dfχ

where df indicates the number of parameters times the number of restrictions, which corresponds to one minus the number of subsamples. In our case, we test the structural breaks using the standard version of the GARCH-MIDAS model with realised volatility which has six parameters and two subsamples (1986-2005 and 2006-2012), that is six degrees of freedom.

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Table 5: Estimation results for θ under different subsamples

1986-2005 2006-2012 1986-2005 2006-2012 1986-2005 2006-2012

% Δ Stock-to-use -8.9404 -11.8618 -3.5917 40.5514 5.6922 -76.4814-1.752 -26.103 -3.090 49.887 7.840 -92.402

SOI -0.1147 0.2161 0.1511 0.1635 0.1421 0.0584-1.358 2.798 2.171 1.450 2.177 1.087

% Δ Market Thinness -5.6300 76.7653 -11.5555 -16.8248 -37.4932 7.3728-20.932 71.855 -10.811 -11.829 -73.721 0.236

% Δ Biofuels Production 9.3667 20.8714 -0.6148 19.8499 -1.9374 20.482952.816 15.052 -0.752 3.705 -1.670 34.531

Kilian Index 0.9041 1.1952 0.6926 0.9726 1.7013 1.22810.479 1.898 0.921 0.077 2.108 0.956

Oil Price Volatility 23.7555 8.7843 21.2413 7.7182 14.5021 14.87240.499 4.973 8.263 4.071 19.433 25.528

Exhange Rate Volatility -120.6437 33.5615 -120.1176 55.2355 21.6755 -14.4027-502.671 6.470 -171.280 18.786 19.904 -125.707

Δ Interest Rate -1.2415 -2.4777 -0.5979 -2.0309 -0.3415 -3.3906-2.140 -4.602 -0.385 -2.335 -0.774 -3.127

Scalping Index 9.9327 1.0335 1.3042 1.4483 0.5422 -0.55243.609 2.043 1.744 0.894 1.951 -0.554

Working T Index 5.8320 2.6982 8.7532 1.2620 2.0723 -5.551312.653 1.706 5.320 0.632 3.199 -4.818

Wheat Corn Soybean

The tests indicate the presence of structural breaks for all the three crops17. In order to accommodate the presence of structural breaks in the model and closely investigate if the effect of macroeconomic drivers on the low-frequency component changes over time, we re-estimate the models for each subsample. Table A.3-A.8 in Appendix provides the full tables with all the parameters while - for the sake of simplicity - Table 5 focuses only on θ parameters. Considering that the first period (1986-2005) covers almost three forth of our original sample, it is not surprising that it does not show substantial differences with the previous exercise in terms of sign and significance of the macroeconomic variables as well as of their relative importance. The only interesting exception is for biofuels production. In fact, it is worth to note that the parameters in the GARCH-MIDAS models with biofuels for corn and soybean are negative and not significant in the first period while they become positive and strongly significant in the second period (2006-2012). The result confirms the hypothesis that US and EU biofuel policies over the last decade contributed to exacerbate the recent excessive fluctuations of the agricultural commodity prices. On the contrary, the second period (2006-2012) reflects more differences compared to the full sample analysis. For example, the size of the global market for wheat and soybean shows a positively sign whereas it was negative in the full sample case. This result suggests that after the recent price spikes, the hoarding behaviour effect prevails over the impact of trade restrictions, which supports the idea that price volatility has been influenced by governments and private actors who are looking for precautionary purchases caused by panic and extreme shortages in national markets (e.g. Timmer, 2010). For corn, the stock-to-use ratio sign inverts from negative to positive, indicating that this market can be affected by imperfect information flows or irrational agents. For soybean, the signs of the speculation proxies change from positive to negative suggesting that the speculative pressure has 17 In particular, for wheat the chi-square test statistic is equal to 12.21 (p-value=0.057); for corn it is equal to 28.90 (p-value=0.000); and for soybean it is equal to 12.99 (p-value=0.043).

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actually contributed to reduce the low-frequency component of volatility for this crop in the last six years.

Focusing on the best fit achieved by the GARCH-MIDAS models for the period 2006-2012, we face an interesting difference with respect to the full sample: the speculation proxies are not among the main driving factors of price volatility. In fact, the best fit is achieved by the GARCH-MIDAS models with the US interest rate variation in all three cases. The empirical estimates are in line with those who sustain that the low interest rate observed in the last years had the effect of reducing the opportunity cost to hold inventories, increasing the commodity demand, making the market thinner and less capable to cope with any other shock (e.g., Frankel, 2007, 2010).

The results also support the recent empirical literature which finds little or no evidence of the influence of the speculation activity on both level and volatility of the agricultural commodity prices in the last decade (e.g. Brunetti and Buyuksahin, 2009; Stoll and Whaley, 2010; Sanders et al., 2010; Irwin and Sanders, 2011 and 2012; Ott, 2013). At this purpose, two aspects should be taken into consideration for explaining the result. From a methodological point of view, we build our proxies using only futures open interest positions in order to have more complete series at the cost of excluding the data on options market and long-only index traders which cover shorter periods. Therefore, the variables used in the present exercise may not catch properly the effect of the derivative markets on the agricultural price volatility over the period 2006-2012 because they are not able to synthetize the complexity of the financial products developed in the recent years (e.g. commodity indices, long-only index-funds, exchanged-traded funds, exchange-traded notes, over-the-counter swaps, etc.). From an economic point of view, despite the large increase in both non-commercial positions and long-only index participation in the agricultural markets, over the period 2006-2012 the level of speculative pressure remained in the range or below of its historical levels. This contradiction is easily explained by the fact that the much publicized increase in the long speculative positions has been followed by a similar or even larger increase in the short-hedging activity making the speculation proxies decrease during the recent high volatility period. Therefore, as suggested by Sanders et al. (2010), even adjusting the analysis by using the index traders' positions would not change the final results.

5. Conclusion This paper examines the drivers of the agricultural commodity price volatility, aiming to contribute to

the analysis of one of the most heavily debated topics in the literature after the recent food price spikes., We analyse the macroeconomic determinants of the agricultural price volatility by the GARCH-MIDAS of Engel et al. (2013) which is a new class component volatility model providing a unified framework to work with data in different time frequencies. In particular, we assume that the volatility can be represented as the multiplication of a high and a low frequency component. The high-frequency component reflects transitory or short-lived effects as daily fluctuations of volatility and a mean reverting GARCH(1,1) is used to formulate it. The low frequency component characterizes the unconditional volatility to capture slowly-varying or highly persistent conditions in the economy and the MIDAS regression introduced by Ghysels et al. (2005) is used for modelling it. Differently from the previous studies in the literature, we manage to link the information coming from the high-frequency data on daily prices directly to the macroeconomic determinants sampled at lower-frequency (i.e. monthly) in one single model without information loss resulting from aggregation.

Our analysis focuses on the price volatility in the cereal market (i.e. wheat, corn and soybean) over the period 1986-2012. A broad list of potential drivers is proposed in order to capture the effect of market fundamentals, common macroeconomic factors and derivative market activity. The initial exercise with realised volatility is performed in order to define the optimum low-frequency time span and the number of lags required for the MIDAS filter. The results show that the best fit is achieved by a

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monthly specification with two-years of lags. Moreover, we show that the GARCH-MIDAS models always outperform the standard GARCH(1,1), indicating that a time-varying unconditional variance model accommodates better the agricultural price volatility behaviour.

Once we estimate the models using the macroeconomic determinants, we observe that supply-demand indicators and conventional speculation proxies play important role in explaining the low-frequency component of volatility. However, there are some differences in estimation results for different crops. In particular, the results suggest that inventory reductions are more important in exacerbating the price volatility in the wheat market while for corn and soybean weather shocks are more relevant. The global real economic activity influences both the wheat and the soybean markets, while for corn; it has a significant but less important impact. Finally, the excess of non-commercial activity on the derivative markets, measured by the commonly used speculation proxies (Working-T Index and Scalping Index) seems to contribute to increase the low-frequency component of volatility for wheat and corn, while they do not seem to have an impact on the soybean market. Besides, it should also be mentioned that monetary factors (interest rate and exchange rate) and energy markets (oil price volatility) play a significant but less important role over the full sample in all markets.

In order to address one possible limitation of the model concerning the presence of structural breaks in the unconditional volatility, we test and confirm the presence of a break in coincidence with the recent large price swings. After re-estimating the models under the consideration of a structural break, we observe substantial differences between the full sample and the period 2006-2012. For example, biofuels production acquires discrete importance for both corn and soybean, supporting the hypothesis that US and EU biofuel policies over the last decade contributed to exacerbate the recent excessive fluctuations of the agricultural commodity prices. In terms of trade policies, the hoarding behaviour at both public and private level of some major importing countries seems to have a more considerable impact than trade restriction policies. Finally, the heterogeneity in the effects of the drivers on different crops seems to decrease over the period 2006-2012. In fact, monetary factors - especially interest rate - become a leading factor in explaining the recent price volatility in all three markets while the activity on the derivative market does not play a crucial role anymore. This can be due to the inadequacy of traditional speculation measures in capturing the impact of the non-commercial actors operating through highly-sophisticated financial products or simply to the real lack of connection between price volatility and financialisation of the agricultural commodities.

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Appendix Table A. 1: Descriptive Statistics (1986-2012)

Mean STD Skew Kurt Min Max

Stock-to-use Ratio Wheat 0.233 0.033 0.408 2.424 0.174 0.313Corn 0.168 0.054 1.981 7.306 0.101 0.388Soybean 0.191 0.047 0.263 1.967 0.102 0.302

SOI 0.153 1.648 0.021 3.095 -5.200 4.800Market Thinness Wheat 0.386 0.028 -0.267 2.043 0.327 0.439

Corn 0.248 0.031 0.506 2.700 0.192 0.327Soybean 0.580 0.078 0.524 2.201 0.465 0.762

Biofuels Production 46.143 52.077 1.426 3.517 6.710 186.070Kilian Index -0.017 0.241 0.436 2.796 -0.570 0.584Oil Price Volatility 0.037 0.021 1.893 8.067 0.009 0.147Exhange Rate Volatility 0.008 0.004 1.652 7.595 0.001 0.032Interest Rate 3.787 2.364 -0.154 2.019 0.010 8.820Scalping Index Wheat 0.322 0.150 1.044 4.022 0.026 0.876

Corn 0.314 0.254 10.545 156.769 0.037 4.118Soybean 0.488 0.157 0.632 4.329 0.063 1.085

Working T Index Wheat 1.168 0.069 0.111 2.488 1.024 1.391Corn 1.091 0.055 0.685 2.903 1.009 1.263Soybean 1.101 0.046 0.662 2.687 1.019 1.230

Table A. 2: Unit Root Tests

Stock-to-use Ratio Wheat -2.899 -12.351Corn -2.532 -17.087Soybean -2.270 -13.045

SOI -4.669Market Thinness Wheat -2.596 -17.342

Corn -2.278 -11.775Soybean -0.170 -10.836

Biofuels Production Trend -0.837 -14.818Kilian Index -2.887Oil Price Volatility -5.536Exhange Rate Volatility -7.185Interest Rate Trend -2.844 -6.151Scalping Index Wheat -5.831

Corn -20.066Soybean -4.349

Working T Index Wheat -5.646Corn -6.111Soybean -6.884

Level First Difference

5% critical value -2.88 (no trend) and -3.44 (with trend). Statistically significantvalues are shown in bold

22

Table A. 3: The GARCH-MIDAS model for wheat with macroeconomic variables (1986-2005)

μ α β m θ ω LLF/BIC

% Δ Stock-to-use -0.0004 0.0550 0.9325 -8.3965 -8.9404 28.4738 12937.545-2.093 5.036 67.147 -50.432 -1.752 6.783 -5.689

SOI -0.0004 0.0564 0.9302 -8.4089 -0.1147 1.0978 12935.928-2.113 5.489 70.568 -55.238 -1.358 0.769 -5.689

% Δ Market Thinness -0.0004 0.0566 0.9307 -8.3856 -5.6300 41.3926 12935.823-2.117 5.503 70.122 -53.922 -20.932 94.945 -5.689

% Δ Biofuels Production -0.0004 0.0581 0.9268 -8.4675 9.3667 1.4155 12936.433-2.100 5.530 66.495 -59.834 52.816 3.059 -5.689

Kilian Index -0.0004 0.0571 0.9291 -8.3487 0.9041 10.5206 12936.014-2.127 5.621 68.522 -41.889 0.479 23.446 -5.689

Oil Price Volatility -0.0004 0.0582 0.9245 -9.2693 23.7555 1.0000 12938.473-2.047 4.163 61.623 -4.769 0.499 0.192 -5.690

Exhange Rate Volatility -0.0004 0.0577 0.9280 -7.4974 -120.6437 1.9166 12937.546-2.082 5.493 68.378 -46.870 -502.671 2.557 -5.689

Δ Interest Rate -0.0004 0.0572 0.9280 -8.4239 -1.2415 1.0000 12936.194-2.107 5.466 67.072 -59.381 -2.140 2.757 -5.689

Scalping Index -0.0004 0.0597 0.9133 -11.5115 9.9327 1.5640 12939.470-2.192 5.559 51.981 -13.319 3.609 3.487 -5.690

Working T Index -0.0004 0.0593 0.9144 -15.2090 5.8320 1.0644 12945.243-2.119 5.302 47.642 -28.460 12.653 1.684 -5.693

WHEAT (1986-2005)

Table A. 4: The GARCH-MIDAS model for wheat with macroeconomic variables (2006-2012)


% Δ Stock-to-use -0.0002 0.0446 0.9390 -7.5379 -11.8618 55.9452 4115.147-0.290 2.137 27.089 -47.861 -26.103 32.984 -4.685

SOI -0.0002 0.0548 0.9011 -7.7327 0.2161 4.3100 4118.294-0.447 2.885 19.700 -70.529 2.798 2.927 -4.689

% Δ Market Thinness -0.0002 0.0512 0.9240 -7.5686 76.7653 4.9345 4115.395-0.301 2.818 27.823 -62.737 71.855 1.677 -4.686

% Δ Biofuels Production -0.0002 0.0529 0.9129 -7.8552 20.8714 1.0000 4116.203-0.440 2.733 20.882 -72.900 15.052 0.360 -4.687

Kilian Index -0.0002 0.0514 0.9149 -7.7603 1.1952 1.4942 4116.263-0.434 2.783 24.263 -44.078 1.898 2.152 -4.687


Exhange Rate Volatility -0.0002 0.0549 0.9145 -7.8112 33.5615 5.4391 4114.549-0.361 2.863 24.738 -67.770 6.470 1.792 -4.685

Δ Interest Rate -0.0001 0.0514 0.8884 -7.6179 -2.4777 2.6518 4120.536-0.280 3.554 27.103 -98.561 -4.602 3.779 -4.692

Scalping Index -0.0002 0.0529 0.9202 -7.8913 1.0335 16.1216 4116.477-0.302 2.447 22.007 -41.457 2.043 7.147 -4.687

Working T Index -0.0002 0.0514 0.9241 -10.7450 2.6982 1.0000 4114.003-0.330 2.600 25.630 -5.713 1.706 0.674 -4.684

WHEAT (2006-2012)

23

Table A. 5: The GARCH-MIDAS model for corn with macroeconomic variables (1986-2005)


% Δ Stock-to-use -0.0003 0.0906 0.8905 -8.5850 -3.5917 30.8588 13634.489-1.943 7.975 61.604 -48.301 -3.090 858.667 -5.998

SOI -0.0003 0.0916 0.8868 -8.6034 0.1511 8.7696 13638.234-1.927 7.921 59.509 -53.815 2.171 32.429 -6.000


% Δ Biofuels Production -0.0003 0.0894 0.8913 -8.5916 -0.6148 11.9466 13634.128-1.966 7.713 59.810 -52.357 -0.752 13.263 -5.998

Kilian Index -0.0003 0.0893 0.8911 -8.5666 0.6926 7.1104 13634.932-2.002 7.873 59.435 -50.766 0.921 6.319 -5.998


Exhange Rate Volatility -0.0003 0.0918 0.8885 -7.6947 -120.1176 1.0004 13636.095-1.972 8.009 61.139 -42.342 -171.280 1.740 -5.999

Δ Interest Rate -0.0003 0.0902 0.8908 -8.6013 -0.5979 1.0000 13634.269-1.936 7.907 60.710 -49.600 -0.385 0.288 -5.998

Scalping Index -0.0003 0.0897 0.8897 -9.0031 1.3042 5.2868 13637.638-1.978 7.891 59.819 -30.495 1.744 10.930 -5.999

Working T Index -0.0003 0.0915 0.8860 -18.1154 8.7532 1.0000 13642.439-1.916 8.171 60.707 -10.193 5.320 0.604 -6.001

CORN (1986-2005)

Table A. 6: The GARCH-MIDAS model for corn with macroeconomic variables (2006-2012)


% Δ Stock-to-use 0.0005 0.0459 0.9301 -7.7367 40.5514 1.6278 4311.3081.038 2.341 25.819 -64.415 49.887 1.243 -4.888

SOI 0.0005 0.0488 0.9196 -7.8765 0.1635 2.5868 4312.8511.025 2.004 18.057 -52.855 1.450 2.120 -4.889

% Δ Market Thinness 0.0006 0.0596 0.8917 -7.7238 -16.8248 6.3309 4312.7981.142 1.734 10.765 -81.952 -11.829 2.748 -4.889

% Δ Biofuels Production 0.0005 0.0517 0.9096 -8.0420 19.8499 1.0000 4313.5890.942 1.680 12.824 -63.340 3.705 2.330 -4.890

Kilian Index 0.0005 0.0521 0.9094 -7.9271 0.9726 1.0000 4312.5300.684 0.345 2.200 -2.365 0.077 0.040 -4.889

Oil Price Volatility 0.0005 0.0473 0.9194 -8.0253 7.7182 299.2381 4315.6641.089 2.077 18.020 -68.811 4.071 4.280 -4.893

Exhange Rate Volatility 0.0006 0.0601 0.8967 -8.2014 55.2355 3.5929 4313.2311.090 2.192 15.339 -79.443 18.786 3.200 -4.890

Δ Interest Rate 0.0005 0.0595 0.8898 -7.7717 -2.0309 1.0000 4315.1841.030 1.728 10.427 -81.875 -2.335 1.060 -4.892

Scalping Index 0.0005 0.0536 0.9093 -8.2298 1.4483 7.9666 4313.2121.070 1.727 13.382 -14.571 0.894 1.079 -4.890

Working T Index 0.0005 0.0502 0.9220 -9.1357 1.2620 1.0000 4310.9441.027 2.308 22.737 -4.078 0.632 0.233 -4.887

CORN (2006-2012)

24

Table A. 7: The GARCH-MIDAS model for soybean with macroeconomic variables (1986-2005) μ α β m θ ω LLF/BIC

% Δ Stock-to-use -0.0002 0.0710 0.9166 -8.5166 5.6922 299.7421 13449.503-1.048 7.998 85.777 -49.012 7.840 0.478 -5.918

SOI -0.0002 0.0726 0.9111 -8.5583 0.1421 6.2641 13449.845-1.052 7.575 75.462 -55.143 2.177 6.460 -5.918


% Δ Biofuels Production -0.0002 0.0698 0.9173 -8.5224 -1.9374 11.3572 13449.309-1.032 7.489 80.762 -48.425 -1.670 24.027 -5.918

Kilian Index -0.0002 0.0726 0.9102 -8.4844 1.7013 4.9469 13450.474-1.046 7.789 75.491 -55.631 2.108 7.220 -5.918


Exhange Rate Volatility -0.0002 0.0713 0.9160 -8.6913 21.6755 291.4991 13449.859-1.059 7.956 84.225 -50.114 19.904 7.075 -5.918

Δ Interest Rate -0.0002 0.0730 0.9139 -8.5271 -0.3415 14.4253 13446.969-1.051 7.772 81.807 -48.023 -0.774 39.273 -5.917

Scalping Index -0.0002 0.0716 0.9149 -8.7961 0.5422 299.8444 13448.708-1.031 7.605 79.833 -40.435 1.951 6.598 -5.917

Working T Index -0.0002 0.0719 0.9147 -10.8100 2.0723 27.5743 13447.982-1.033 7.789 81.630 -15.515 3.199 86.454 -5.917

SOYBEAN (1986-2005)

Table A. 8: The GARCH-MIDAS model for soybean with macroeconomic variables (2006-2012)


% Δ Stock-to-use 0.0006 0.0531 0.9331 -8.2087 -76.4814 1.0397 4786.3841.756 4.374 60.705 -42.943 -92.402 2.533 -5.454

SOI 0.0006 0.0542 0.9328 -8.2684 0.0584 43.1595 4786.1301.798 4.627 65.297 -42.003 1.087 27.211 -5.454

% Δ Market Thinness 0.0006 0.0527 0.9351 -8.2285 7.3728 236.9969 4786.3181.637 2.944 45.983 -31.458 0.236 0.080 -5.454

% Δ Biofuels Production 0.0006 0.0554 0.9299 -8.5301 20.4829 1.2147 4786.7121.791 4.431 58.918 -46.666 34.531 4.054 -5.454

Kilian Index 0.0007 0.0548 0.9304 -8.4641 1.2281 1.2919 4786.2461.806 4.453 60.020 -25.502 0.956 1.547 -5.454

Oil Price Volatility 0.0007 0.0583 0.9234 -8.7815 14.8724 3.5189 4786.1921.826 4.446 35.723 -48.464 25.528 0.316 -5.454

Exhange Rate Volatility 0.0006 0.0563 0.9320 -8.0825 -14.4027 40.0416 4785.8831.781 4.759 66.787 -38.504 -125.707 80.581 -5.453

Δ Interest Rate 0.0006 0.0543 0.9170 -8.3513 -3.3906 2.2053 4789.4111.765 4.228 42.234 -58.742 -3.127 3.047 -5.457

Scalping Index 0.0007 0.0555 0.9313 -7.9395 -0.5524 1.2161 4785.5071.802 4.545 63.253 -15.945 -0.554 5.033 -5.453

Working T Index 0.0007 0.0504 0.9356 -2.0515 -5.5513 11.6189 4788.8871.916 4.119 58.358 -1.561 -4.818 3.325 -5.457

SOYBEAN (2006-2012)

25

Figure A. 1: Optimal lag structure for wheat

Figure A. 2: Optimal lag structure for corn

Figure A. 3: Optimal lag structure for soybean

26

Figure A. 4: Conditional Volatility and its low-frequency component for wheat

Figure A. 5: Conditional Volatility and its low-frequency component for corn

27

Figure A. 6: Conditional Volatility and its low-frequency component for soybean

European Commission

EUR 26183 – Joint Research Centre – Institute for Prospective Technological Studies

Title: Agricultural Commodity Price Volatility and Its Macroeconomic Determinants: A GARCH-MIDAS Approach

Authors: Ayça Dönmez and Emiliano Magrini

Luxembourg: Publications Office of the European Union

2013- 27 pp. – 21.0 x 29.7 cm

EUR – Scientific and Technical Research series – ISSN 1831-9424 (online)

ISBN 978-92-79-33245-6 (pdf)

doi:10.2791/23669

Abstract

This paper investigates the main drivers of the agricultural commodity price volatility using the GARCH-MIDAS model of Engel et al. (2013), a new

class of component models that allows for isolating the low-frequency component of volatility and taking into consideration macroeconomic

factors via mixed data sampling. We show that modelling the agricultural price volatility as the product of high and low frequency components is

more efficient than filtering it through a standard GARCH(1,1) model. After combing wheat, corn and soybean daily prices with monthly market

specific and common macroeconomic drivers over the period 1986-2012, it appears that supply-demand indicators and conventional speculation

proxies are crucial in explaining the low-frequency component of volatility while monetary factors and energy markets play significant but less

important role. Nevertheless, when we consider only the period following the recent price spikes (2006-2012), the monetary factors – especially

interest rate – become essential to describe agricultural price fluctuations, suggesting also that the heterogeneity in the effects of the drivers on

different crops is decreasing.

As the Commission’s in-house science service, the Joint Research Centre’s mission is to provide EU policies with independent, evidence-based scientific and technical support throughout the whole policy cycle. Working in close cooperation with policy Directorates-General, the JRC addresses key societal challenges while stimulating innovation through developing new standards, methods and tools, and sharing and transferring its know-how to the Member States and international community. Key policy areas include: environment and climate change; energy and transport; agriculture and food security; health and consumer protection; information society and digital agenda; safety and security including nuclear; all supported through a cross-cutting and multi-disciplinary approach.

LF-NA-26183-EN-N

Agricultural Commodity Price Volatility and Its ...

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