Drivers of private grain storage. A computational-economics and empirical approach

This study develops a new method to empirically verify the competitive storage model and investigate the determinants of private carry-over grain stocks within a reduced-form approach. Storage is an important instrument for stabilizing food supply. Yet, analysis of carry-over grain stocks is usually done by two methodological approaches: Equilibrium modeling and comparison of price characteristics or econometric analysis. This paper develops a new way to analyze private grain storage combining both approaches. Based on the canonical competitive storage model we derive a reduced-form storage equation for grain stocks in an open economy based on domestic and global supply and income. This approximation allows characterizing grain stocking by a piece-wise linear function for a broad set of parameters and model assumptions. The results provide for the first time a direct confirmation of the competitive storage model based on observed stock data. Furthermore, the results may be used to analyze private-public storage interactions as well as to offer a more simple reduced-form storage modelling approach which is theoretically well-founded and based on rational expectations.The competitive storage model is used to analyze the dependency of carry-over stocks on the different input parameters. The model specification follows Gouel (2011) and Gouel and Jean (2012) but differs in explicitly including the rest of the world (RoW) as a second country, in including income shocks and excluding public stocks. Stockholders and producers are risk-neutral and profit maximizing, act competitively and have rational expectations. Competitive trade occurs until there are no more possibilities for spatial arbitrage; consumption is isoelastic. The model is calibrated for a broad set of parameters, namely the interest rate, the relative country size, the standard deviation of supply shocks, the demand and the supply elasticities. For all these variables, three different values have been used and the model is solved on a 9x9x9 grid of the state variables, namely the supply and the income shock in the country as well as the supply in RoW. This gives 3^5⋅9^3=177,147 observations in total. The simulations are conducted in Matlab and to solve the model, the CompEcon toolbox (Fackler and Miranda, 2011) and the RECS solver (Gouel, 2013b) are used. Then, a reduced form storage equation is derived, first for a simplified and then for the full model specification. After providing a qualitative explanation of this non-linear reduced form storage rule approximation, this rule is verified with the help of the simulation results. A two-step procedure is applied here. In the first step, it is shown that for each set of parameters individually, the reduced-form model is able to approximate simulated stock levels dependent on the state variables. In the second step it is tested whether the dependence on the different parameters (interest rate, elasticities …) can be captured by linear combinations of structural parameters. The model is found to be well-specified and the reduced form storage equation to be a good approximation of the stocks which results from solving the partial equilibrium model. While almost all parameters are both highly significant and relevant in terms of effect size, the interest rate is the only parameter which is consistently insignificant (considering that all parameters appear a few times in the reduced form storage equation). Finally, the reduced-form model is applied to empirical stock data for 63 countries using a non-linear least-square panel regression. USDA and FAO GIEWS data for stocks, production and demand from 1990 to 2013 for maize, rice, wheat, soy, and sorghum are used. GDP per capita is obtained from the World Bank and used to approximate income shocks. The Hodrick-Prescott filter is used for de-trending as well as for calculating supply shocks. Dividing stock and production data by the consumption trends gives stationary data. Two regression models are used for the empirical estimation. Both include country- and crop-specific mean stocks to account for unobserved heterogeneity resulting in a fixed-effect-like non-linear panel regression. One regression model controls for country-specific characteristics and heterogeneous response to state variables, the other assumes a homogenous response to state variables and uses therefore less parameters and interaction terms. Both models support the hypothesis that real-world stock data can be well explained by the competitive storage model and the considered reduced-form approximation. The aim of this study was to reconcile the complexity of the competitive storage model which lacks a closed-form solution with econometric modeling of agricultural fundamentals that is often used in applied and policy-related research. The resulting non-linear reduced-form model turned out to be both precise and flexible when applied to data generated by the competitive storage model. The basic qualitative behavior is as follows: Ending stocks are zero if domestic and global supplies are below a threshold which depends on GDP shocks and production in RoW. Above this threshold, stocks are piece-wise linear and increase with supply levels. The slope depends on the structural model parameters. The coefficients from the empirical estimation are largely in line with the expectations from the theoretical model. Structural characteristics of countries and crops, however, seem to have only a small impact on threshold levels and slopes. Three results are of direct policy relevance: First, operational stocks are on average roughly 11 percent of domestic consumption, implying that stock-to-use ratios have to be subtracted by 11 percentage points to yield the amount of stocks that are actually available for consumption smoothing. Second, domestic stocks respond strongly to the international supply situation which indicates a high degree of market integration. This underlines the need for multinational agreements and regulations about how to deal with supply shocks in individual countries as well as on the global level. Third, GDP shocks are important in the theoretical model but insignificant in the empirical validation. This might indicate that stockholders do not perform well in anticipating future demand. As a result, private storage levels might not be optimal providing a rational for interventions and information system might need to focus also on demand side factors rather than only on the supply side.