THE STABILITY OF SOME ANNUAL CONSUMPTION FUNCTIONS

IN a recent article Hendry (1983) presented estimates for the annual form of the error correction consumption function introduced in Davidson et al. (1978), hereafter referred to as DHSY. These estimates demonstrated the remarkable similarity in goodness of fit and parameter estimates for estimation based on the inter-war and post-war periods; and in the post-war period, for example, the standard error of the equation is just over 2% with all of the coefficients well determined. Also in a recent paper Pesaran and Evans (1984), hereafter PE, report a comparison based on the maximised log-likelihood value of some leading annual consumption functions for the United Kingdom, including a consumption function of their own which introduced a role for capital gains and losses in determining consumption expenditure. The purpose of this study is to take up some suggestions in Hendry (1983, p. 209) and Dufour (1982), that an examination of the residuals from recursive estimation is a useful adjunct to a simple scalar measures of comparison in assessing the properties of estimated equations. Both Hendry (1983) and PE (1984) report the calculation of some statistics which suggest that their specifications are stable; however, these statistics are reported for a few rather than a complete set of sub-periods. The use of the recursive residuals makes for an efficient calculation of stability statistics for all possible sub-periods, and hence avoids the need to limit the evidence on the stability of particular regressions. Of course, such a comprehensive approach could be a severe test of a regression (though the severity will depend on how the overall size of the several tests is controlled); nevertheless, such an approach seems useful if used in conjunction with further analysis attempting to explain or account for apparently significant outlying observations or indications of more prolonged changes. Besides the DHSY and PE consumption functions we also consider the model due to Hendry and von Ungern-Sternberg (1981), hereafter HUS, which takes account of a target asset-income ratio and adjusts income for inflation losses on net liquid assets. We also check that the DHSY equation reported in Hendry (1983) is a valid, in the statistical sense, simplification of an equation which has further lags of the explanatory variables and relaxes the assumptions of a unit income elasticity and price homogeneity. Other