How Reliable is Partial Equilibrium Analysis?

Abstract

IN the empirical literature on market interferences a variety of numerical techniques have been used to analyse competitive equilibria which are not directly observable. Harberger (1963, 1966), and Johnson and Mieskowski (1970), for instance, in their analyses of factor market distortions in the United States economy use a mixture of differential calculus and linearization assumptions to estimate efficiency losses and distributional impacts of particular market interferences. Acceptance seems to be implied in these procedures of the reliability of approximate methods for calculating unobservable equilibria. This issue of reliability forms the subject matter of the present paper.' A recent joint paper (1972) examined the robustness of Harberger's results (1966) when a competitive for the United States economy in the absence of distortionary taxation was calculated using a procedure for the computation of competitive equilibria due to Scarf (1967, 1969, 1973). The results for particular parameterizations suggested that the gain in simplicity of approximate methods may in some circumstances counterbalance the precision of more refined computational devices. These results, however, were obtained for a problem of small dimensionality and limited complexity, and the comparison between Harberger's results and true general solutions was made only on the basis of one summary statistic. In addition, the approximate solution device used by Harberger (1966) does not correspond to conventional notions of either or general analysis. It is thus of some importance that the comparison between general solutions and various forms of analysis be carried further before any conclusions on computational experience are used as a guide in other contexts. These issues are taken up here in the context of a-particular model which allows different forms of analysis to be used and compared to general solutions. The results presented are put forward as evidence on computational experience. This paper considers a general model of the United Kingdom economy used in recent work on an assessment of tax changes in the United Kingdom economy (1973). Using this model the gain2 to the United Kingdom from the abolition of the distortionary features of capital income taxation is calculated by various methods and compared to the general solution. Section II presents a characterization of competitive equilibria for an economy with taxation used in a recent paper by Shoven and Whalley (1973) which underlies the United Kingdom tax model. As no explicit statement of partial equilibrium analysis is to be found in the literature, two alternative characterizations of such procedures which are later applied to the model, are devel-