Tests of Equality Between Sets of Coefficients in Two Linear Regressions When Disturbance Variances Are Unequal: Some Small Sample Properties*

The Displacement Effect on Government Expenditure of Two Oil Crises: Japan, the United Kingdom and the United States*

“…Since the Chow test is inappropriate in the presence of heteroscedasticity, appropriate tests under heteroscedasticity have subsequently been developed by Watt (1979), Rothenberg (1984) and Honda and Ohtani (1986). The Wald test statistic proposed by Watt (1979) is given by J = (6, -~~) " S : ( X ; X I ) -'…”

“…AND 1975-1986SEARCH FOR THE STRUCTURAL CHANGE TIME-POINTS FORTHE PERIODS, 1960, 1960-1979 Nore THY denotes the time-point for which the modified Wald test statistic has the maximum value in the period considered, **denotes significance at the I per cent level and 'denotes significance at the 5 per cent level. The modified Wald tests are conducted by reference to a central chi-square distribution with k = 2 degrees of freedom.…”

A Bounds Test of Equality between Sets of Coefficients in Two Linear Regressions When Disturbance Variances are Unequal

“…A small sample test that can be employed in this case was suggested by Jayatissa (1977). Watt (1979) showed numerically, however, that in most situations the asymptotic Wald test is preferable to the Jayatissa test from the viewpoint of power, although the actual level of the Wald test is larger than the nominal level, which is given from the chi-squared table; the exact significance level is practically unobtainable, since the distribution of the test statistic depends complicatedly on the regressor variables and the disturbance variances. Rothenberg (1984) proposed an adjusting procedure of critical values of the Wald test so that the adjusted test may have the assigned significance level asymptotically up to the second order; his work is a generalization of the well-known result by Welch (1947) for the BehrensFisher problem.…”

Testing for Structural Stability and Predictive Failure: A Review

“…Since where Then under H b (bl = bz), See, for example, Watt (1979) and Honda (1982). I n fact, i t can be shown that in this case W is identical to the LR statistic for the test of model (4) against (1).…”