A simple multivariate test for asymmetry

Abstract

Since many macroeconomic models are linear, it is not desirable to use them with an asymmetric dependent variable. In this paper we formulate a univariate test for symmetry, based on the third central moment, and extend it to a multivariate test; the test does not require modelling and it is robust against serial correlation, autoregressive conditional heteroscedasticity and non-normality. In the empirical application of the test it is found that orthodox theory seem to be supported; consumption expenditure on durable goods is found to be symmetric while consumption expenditure on nondurable goods is asymmetric for the US and UK, with peaks being higher than troughs are deep. Also, the empirical importance of the choice between the univariate and the multivariate test for possibly correlated series is underscored; the results from the two approaches clearly differ. Given the widespread practice of using consumption expenditure on nondurable goods as the dependent variable in linear models for the US and the UK, our results might be noteworthy.