that instrumental variable (IV) techniques must be used for estimation. In order to justify
the use of IV techniques we must show that endogenous variable satisfies the
endogeneity test. To test the exogeneity of the price ratio variable, we use the Davidson
and MacKinnon (1993) test.22 The null hyothesis of the test states that using the ordinary
least squares estimator would ( OLS) that is, the OLS fixed effect model would result in
consistent estimates and the presence of endogeneity among the regressors would not bias
the OLS results. Rejection of the the null hypothesis indicates the need to use
instrumental variable techniques. We fail to reject the null hypothesis for both models,
indicating that endogeinety of the price ratio variable is not a potential problem and the
results from OLS fixed effects estimation would be consistent.
Finally due to the panel nature of our data set we test for any evidence of serial
correlation . We use the Wooldridge test for serial correlation in panel data models
correlation.23 The null hypothesis of this test states that there is no serial correlation.
Significance of the F-statistics indicates that there is presence of serial correlation. In
both the models we fail to reject the null hypothesis indicating that serial correlation is
not a problem.
22
This test is similar to to the Durbin-Wu-Hausman test. Davidson and Mackinnon (1993) show that that
this superior to the Hausman test in that we are always able to compute a test statistic. On the other hand,
computation of a test statistic under the Hausman test is possible when the difference between estimated
covariances matrices results in a positive definite matrix.Thus it is difficult to compute a reasonable test
statistic using standard matrix inversion techniques. See Davidson and Mackinnon (1993) for details.
23
Under this test the null hypothesis states that the residuals from the regression performed on first
differenced variables should have an autocorrelation value of about -0.5. That is when we regress lagged
residuals on current residuals, the coefficient on the lagged residuals should be -0.5. Ducker (2003) show
that this test performs well when the sample size is reasonable. See Wooldridge (2002) and Drukker (2003)
for more details.
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