The Japanese consumption function

Abstract

A theory of seasonal cointegration and integration is discussed in Hylleberg, Engle, Granger, and Yoo (1990) and tests for seasonal unit roots are also developed. To estimate and test for seasonal cointegration at each frequency, a two-step procedure similar to the one suggested by Engle and Granger (1987) is investigated in this paper. Using Japanese dataon consumption and income, evidence in favour of seasonal cointegration at frequency 1 4 is found. An economic interpretation of this cointegrating relation is presented using the notion of a slightly impatient borrowing-constrained utility-maximizing consumer. While the test statistics for noncointegration occurring at the frequency 1 2 of a cycle have the same distribution as the test statistic obtained for the zero frequency case by Engle and Granger (1987) and Engle and Yoo (1987), the distribution of the test statistics for noncointegration at the frequency 1 4 (and 3 4 ) is derived based on the asymptotic distribution theory for testing a pair of complex roots on the unit circle [Ahtola and Tiao (1987), Chan and Wei (1988)]. The critical values and evidence on the power of the test are obtained through Monte Carlo simulations.