Economics Letters 12 (1983) 283-287 North-Holland 283 THE INDEPENDENCE OF TESTS FOR STRUCTURAL CHANGE IN REGRESSION MODELS G.D.A. PHILLIPS and B.P. MCCABE * University of Leeds, Leeds LS2 PTJ, UK Received October 8 1982 It is shown that the common tests for stability of regression coefficients and of the disturbance variance in linear regression models are independent. This enables the size of the joint test procedure to be controlled exactly. 1. Introduction Tests for changes in the coefficients of linear regression models are frequently used by econometricians. When sufficient observations are available both before and after the suspected change to enable estimates of the regression coefficients to be obtained, the appropriate test is the analysis of covariance (AOC) test. In the case where there are insufficient observations to compute a second regression, the Chow test may be used. These tests are discussed, for example, by Chow (1960) and Fisher ( 1970). In many cases when a structural change occurs it seems unrealistic to suppose that only the regression coefficients are affected. In particular, the disturbance variance may also change; yet the AOC test is conducted on the assumption that this has not happened. It is, therefore, desirable to test for both types of effect although it appears that this is seldom done in practice. One difficulty in doing this is that the logically prior test for stability of the disturbance variance introduces pre-test bias when * Helpful discussions with Tony Lancaster and comments from Andrew Harvey and Jane Black are thankfully acknowledged. 0165-1765/83/$3.00 0 1983, Elsevier Science Publishers B.V. (North-Holland)