More tests for heteroskedastic

More tests for heteroskedasticity

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A SHAZAM user may be interested in a test for heteroskedasticity that SHAZAM does not automatically compute. It may be possible to program the test with SHAZAM commands.

For example, the Park test is described in Gujarati [1995, p.369]. This test proposes that the error variance is a function of one explanatory variable, say X. Following OLS estimation the OLS estimated residuals are used in the auxiliary regression:

        log(ê_t²) = ₀ + ₁ log(X_t) + v_t

The test statistic is the t-ratio on the parameter estimate for ₁. If the t-ratio shows that the estimated parameter is significantly different from zero then there is evidence for heteroskedasticity. Since this is an approximate test it is appropriate to consider that the test statistic has an asymptotic normal distribution so that at a 5% significance level the critical value is 1.96.

The Park test is demonstrated with the next SHAZAM commands. The example considers that heteroskedasticity is a function of the variable X3.

SAMPLE 1 50READ (file) Y X1 X2 X3* Run the regression and save the estimated residuals in E.OLS Y X1 X2 X3 / RESID=E* Do some variable transformations.GENR EE=LOG(E*E)* Assume that the error variance is a function of the variable X3.GENR Z=LOG(X3**2)* Run an auxiliary regression and save the t-ratios in the variable TR.* (the ? is used to suppress output)?OLS EE Z / TRATIO=TR* The test statistic is the t-ratio for the estimated coefficient on Z.GEN1 PARK=TR(1)PRINT PARKSTOP

Note that the regressor in the auxiliary regression is generated with the command:

GENR Z=LOG(X3**2)

That is the variable is squared before taking logarithms. This ensures that there will be no problem with negative values of X3. As an exercise the user can verify that squaring the variable will not change the estimated t-ratio.

The auxiliary regression has a ? prefix to the OLS command. This tells SHAZAM to suppress all output from the OLS estimation. This can be useful to cut down on computer output that may not be of great interest. The OLS results of interest, the t-ratios, are saved in the variable TR with the TRATIO=TR option on the OLS command.