# INTRODUCTION

CGE models are often criticized for weak empirical estimation of the parameters and for preserving static economic structures in long-term simulations. The problem is associated with the lack of reliable time-series data, most severe in developing countries, to support standard econometric estimation of parameters and shifts in structure. In particular, we have lacked a times series of social accounting matrices (SAMs) and their associated prices and quantities that provide the information base for these models. There are examples of econometric estimation of parts of the CGE model where some time series data are available—see Jorgenson and Yun (2013) and other work by Jorgenson and various coauthors (Jorgenson, D. W. 2011, Jorgenson, D. W. and M. P. Timmer 2011, Jorgenson, D. W., et al. 2012).

This paper uses an information-theoretic cross-entropy estimation approach in an environment of scarce data measured with error to estimate behavioral parameters, labor augmenting productivity, and other parameters in the model that shift over time to generate historically observed changes in economic structure. With noisy and limited observations common to developing countries, the unseen parameters of a CGE model cannot generally be observed and measured directly. In systems and information theory, this is described as a stochastic inverse problem: how to use available “information” to recover these unobserved and uncontrolled components. Robust solution methods consistent with the underlying ill-posed noisy information recovery problem have been developed under Bayesian inference and decision theory (see, for example, Golan et al. 1996, and Judge and Mittelhammer 2012).<sup>2</sup> In CGE model estimation, Arndt et al. (2002) used the cross-entropy method from information theory to estimate the trade substitution elasticities in a CGE model of Mozambique. Robinson et al. (2001) also utilized the cross-entropy method in data updating and estimation when available information was insufficient to construct a balanced new SAM.

In this paper, we extend and refine the cross-entropy estimation method to account for different levels of noise and amount of information in a sequential and particular way. We start with a collection of SAMs with identical accounts for the Republic of Korea (Korea) for various years. Even though the availability of such data to support is uncommon, it is still not enough to support standard econometric methods. Each new data set for later years provides new information to improve the estimation of parameters of a CGE model, updating priors that initially were based on scattered data and theoretical properties of various functions in the model. The statistical results recovered from this noisy and limited informational environment depend on how the CGE model is formulated; the more data, the more reliable the estimates of structural parameters. Furthermore, are the parameters stable? That is, even within a given set of specifications for a CGE model, the transformation of economic structure over time may be captured in alternative ways by the evolution of different parameters in the model and the entropy method described here provides a statistical approach for making model selection in this context. When only one SAM is available, a priori parameters such as trade elasticities are employed so that the structure of the economy, such as trade shares, are replicated and as depicted by the CGE model. With more SAMs, one can improve not only the posterior

> 2 Not always initially accepted, the Bayesian approach is now applied widely in decision and information theory, operations research, and more recently, in finance and macroeconomics, such as the recent methodology regarding dynamic stochastic general equilibrium (DSGE) modeling. A popular history of its development, the debates about its validity and uses, its triumphant applications in the great wars of the last century, and its recent uses is available in McGrayne, S. B. (2011).

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