and structural change simultaneously within the specifications of the CGE model; and iii) an integrated statistical analysis to check for model precision and prediction and to test alternative ways of modeling historical structural change with the evolution of different parameters in the CGE model. In order to provide a practical approach and to ensure the consistency with economic theory in the behavioral equations, we follow the customary calibration process of CGE modeling. Finally, we develop a reference GAMS programming code that integrates the three steps of the procedure to facilitate use and further development of the technique by other analysts.<sup>6</sup> The code also matches CGE variables with the SAM cells, an approach that in turn greatly simplifies the structure of the code. In what follows, we describe in more detail the different steps of the methodology and how it is applied to estimate and calibrate a CGE model.

# The data step

As the basic source of information for a CGE model, a SAM provides the starting point for the calibration process. Although a time series of SAMs is still not available for most countries, intermittent estimates and updates are becoming more common, thanks to the efforts of national statistical agencies. At the global level, country SAMs are compiled and reconciled in globally consistent data sets as part of the research activities of GTAP and others. As more SAMs are estimated, each additional SAM provides new information to combine with previous SAMs to test and adjust prior assumptions about the parameters and components in the CGE model.

In this data step, we exploit the fact that SAM provides a transaction (flow) matrix approach to national accounting (see Stone 1962, and Pyatt and Round 1985). We also draw on Robinson et al. (2001) who, using limited up-to-date information (such as macro aggregates), employ the cross-entropy estimation method to update an existing SAM. Here, we apply the methodology for the purpose of pooling and adjusting a set of historical SAMs when auxiliary data to directly do so are incomplete, essentially making use of the SAM’s necessary consistency with macroeconomic aggregates in the national accounts.

More precisely, the first step is to adjust the nominal SAMs associated with different years by properly deflating them with price indices so that they are measured in the same base year prices and are hence comparable. The ideal way to do this is to separate the nominal magnitudes into their respective prices and quantities; and each cell in the SAM should be adjusted by the correct relative price index so that all individual cells are expressed in equivalent real terms. Where that is possible, it should clearly be employed. For many developing countries, however, the informational requirements will be daunting relative to the state of their statistical capacities (e.g. countries in Sub-Saharan Africa or newly formed countries after civil conflicts). Noise in the data, including the quality of price indices if available and the values of the specific SAM cells, will likely be very high.

In the absence of full information about prices and quantities, each SAM still brings new information about the economic structure of the country, albeit in nominal values. It adds new observational data and the

> 6 GAMS refers to the General Algebraic Modeling System; for more on GAMS, see www.gams.com. The GAMS code in this paper is available from the authors in the future when documentation is completed.

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