برآورد پارامتر برای یک مدل تعادل عمومی قابل محاسبه: روش حداکثر آنتروپی

We introduce a maximum entropy approach to parameter estimation for computable general equilibrium (CGE) models. The approach applies information theory to estimating a system of non-linear simultaneous equations. It has a number of advantages. First, it imposes all general equilibrium constraints. Second, it permits incorporation of prior information on parameter values. Third, it can be applied in the absence of copious data. Finally, it supplies measures of the capacity of the model to reproduce the historical record and the statistical significance of parameter estimates. The method is applied to estimating a CGE model of Mozambique.

Computable general equilibrium (CGE) models have become workhorses for policy analysis. Despite their popularity, CGE models are frequently criticized for resting on weak empirical foundations, particularly for estimates of behavioral parameters (Shoven and Whalley, 1992 and McKitrick, 1998). The problem is not confined to CGE models, but has been recognized for complex simulation models in general (Schmalensee et al., 1998). For developed countries, some major microeconometric exercises have been undertaken to estimate behavioral parameters, notably trade parameters. These include efforts by the IMPACT project, the US International Trade Commission, and the US Central Intelligence Agency (Goodman, 1973, Alaouze, 1976, Alaouze, 1977, Alaouze et al., 1977, Shiells et al., 1989, Shiells, 1991, Shiells and Reinert, 1991 and Shiells et al., 1993). Despite these and other efforts, the microeconometrics literature is widely viewed as providing only spotty coverage of the parameters of interest (Hansen and Heckman, 1996 and McKitrick, 1998). In addition, it is far from clear that results from microeconometric studies can be appropriately applied to the more aggregate sectoral and household representations usually present in CGE models (Hansen and Heckman, 1996 and Dawkins et al., 1999). For developing countries, the lack of an empirical basis for behavioral parameters is even more severe. As a result, debate over appropriate values for behavioral parameters remains highly contentious. This is particularly true for trade parameters in CGE models employing Armington type trade assumptions. The dearth of estimates of behavioral parameters has generally led analysts to specify functional relationships that require relatively few behavioral parameters. Hence, the ubiquity of the constant elasticity of substitution (CES) functional form in applied general equilibrium analysis. This parsimony with respect to the number of behavioral parameters comes at a cost in terms of flexibility in representing technology or preferences (Jorgenson, 1984, Uzawa, 1962 and McFadden, 1963). Direct econometric approaches to estimating CGE models have been used (Jorgenson, 1984, Jorgenson and Slesnick, 1997 and McKitrick, 1998). However, lack of data, computational and conceptual difficulties in estimation, and uncertainty concerning the validity of resulting estimates have comprised formidable barriers to application of the econometric approach. Existing applications reflect these difficulties. First, econometric estimates, such as those obtained by Jorgenson (1984), are almost always obtained using annual data. The elasticities obtained are thus short run. However, many CGE analyses consider a significantly longer adjustment time frame, often 3–5 years. Short run elasticities are likely to understate the response capacity of agents over this longer time frame. Second, given the large number of parameters to be estimated, long time series data for numerous variables are required to provide sufficient degrees of freedom for estimation. In many cases, the economy is likely to have undergone structural changes over the period, which may or may not be appropriately reflected in the estimation procedure. Finally, even those econometric estimates designed specifically to feed parameter estimates to CGE models (e.g. Jorgenson, 1984, Jorgenson and Slesnick, 1997 and McKitrick, 1998) undertake estimation without imposition of the full set of general equilibrium constraints. While the estimated parameters might provide a highly plausible description of historical production and consumption data sets, the estimated values will not be fully compatible with the general equilibrium system they are designed to represent. For example, predicted values from separate econometric production and consumption systems have the potential to grossly violate product balance conditions for some years of historical data. As an alternative to the econometric approach, some CGE researchers employ a simple ‘validation’ procedure by which they run a model forward over a historical period and compare results for some variables. The results can provide a basis for revising estimates of some important parameters, recalibrating the model in a kind of informal Bayesian estimation procedure. Examples of this approach include Gehlhar, 1994, Kehoe et al., 1995 and Dixon et al., 1997. Unlike econometric approaches, this approach makes very limited use of the historical record and provides no statistical basis for judging the robustness of estimated parameters. In this article, we introduce a maximum entropy (ME) approach to estimation of behavioral parameters for a CGE model. The ME approach is similar to the econometric approach of Jorgenson (1984) in that: (i) the full historical record can be employed; and (ii) statistical tests for estimated parameter values are available. It is similar to the multi-period validation/calibration approach in that: (i) the full model tracks the historical record; and (ii) the ME approach can be applied in the absence of copious data. The ME approach allows one to use all available data, take into account all relevant constraints, employ prior information about parameter values, and apply variable weights to alternative historical targets. Available information does not need to be complete or even internally consistent. The philosophy of the ME approach is to use all available information, but do not assume any information you do not have (such as strong assumptions about the distribution of error terms). In the following, Section 2 introduces maximum entropy estimation. Section 3 describes the ME approach as applied to a CGE model. 4 and 5 present an application to Mozambique. Section 6 concludes and provides suggestions for future research.

The maximum entropy approach offers strong promise as a formal method of parameter estimation. The estimated trade parameters for Mozambique point strongly to the need for development efforts to aid in the transformation of domestic products into export products. It also indicates high transformation elasticities between imported and domestically produced food. The application illustrates the power of the ME approach to derive useful economic implications from limited data. This property is extremely valuable, particularly in developing country contexts. Nevertheless, in terms of future research, it would be of interest to apply the method to a country with a longer and more reliable series of data.