Economics Letters 12 (1983) 251-254 North-Holland 251 zyxwvutsrqpo A NOTE ON THE EFFECTS OF LINEAR APPROXIMATION ON HYPOTHESIS TESTING Anil K. BERA CORE, 1348 Lauoain -la - Neuve, Belgium Ray BYRON Australian National University, Canberra, ACT 2600, Australia Received 25 January 1983 In this note we demonstrate that the use of a linear approximation model may effect the usual F-test for linear hypothesis when the true model is non-linear. It has been observed frequently, especially in demand analysis, that the null hypotheses of linear parametric restrictions are rejected too often by the data. For example, Barten (1969) Byron (1970), Lluch (197 1) and Deaton (1974) observed that the symmetry and homogeneity restrictions are very often rejected, particularly in large demand systems. Laitinen (1978) and Meisner (1979) argued that this was due to the use of large sample tests when the sizes of the available samples were small or moderate [see also Bera et al. (1981)]. In this note, we demonstrate, within the context of a single equation model, that another possible reason for the ‘bias’ towards the rejection of linear hypotheses is the inappropriate use of linear approximation models when the true models are non-linear. As a by-product of our analysis, we also observe that the neglect of the remainder term in linear approximation can also effect the power of the test adversely. Let us consider the following non-linear regression equation ’ ’ Demand equations derived from general utility functions, in most cases, will be non-lin- ear. What are being used in empirical studies are some sort of linear approximations to non-linear equations. 0165-1765/83/$3.00 0 1983, Elsevier Science Publishers B.V. (North-Holland)