The Covariance Measure of Substitution: An Application to Financial Assets - O'Brien, James M. (The Review of Economics and Statistics, 1974)
IN his Economics and Information Theory, Theil (1967) developed a theorem which states that under certain conditions the covariance between the variation in the demand for two goods, holding constant prices and income, would measure the substitutability of the two goods (more precisely, will measure their Slutsky-Hicks substitution effect up to a negative scaler) (chapter 7). This theorem and the framework behind it have subsequently been used in further studies of commodity preferences and substitution (Barten (1968), Phlips (1971), and Phlips and Rouzier (1972)). If the covariance measure of substitution could be usefully applied to asset substitution, it could prove to be a valuable supplement to the more traditional measure of asset substitution, i.e., the estimation of relations between asset demand and asset yields. Theoretically, the measure can be applied to time-series or crosssection data. The measure might have a wider applicability to cross-section data than the traditional asset demand-yield measure since the latter can only be applied to assets with regional markets (e.g., deposits). Moreover, to some extent, it can be expected that errors or biases that might arise in the covariance measure would be independent of those incurred in using the traditional measure of asset substitutability. This paper will attempt to apply the covariance measure to estimating asset substitution among households. Part I considers the theoretical underpinnings of the covariance measure and its theoretical relation to the asset demandasset yield measure of substitutability. In part II an empirical formulation of the covariance measure is developed and applied to cross-section asset data for households and the results analyzed. The results are then compared to two earlier, and more limited, asset studies which used essentially a covariance type measure to assess substitutability. The results are also compared to those of household studies which have used the traditional method for estimating substitution among assets. Findings and suggestions for further study are summed up in the conclusion.