Testing for Heteroskedasticity in Bivariate Probit Models




Thorn, Thomas

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Two score tests for heteroskedasticity in the errors of a bivariate Probit model are developed, and numerous simulations are performed. These tests are based on an outer product of the gradient estimate of the information matrix, and are constructed using an artificial regression. The empirical sizes of both tests are found to be well-behaved, settling down to the nominal size under the asymptotic distribution as the sample size approaches 1000 observations. Similarly, the empirical powers of both tests increase quickly with sample size. The largest improvement in power occurs as the sample size increases from 250 to 500. An application with health care data from the German Socioeconomic Panel is performed, and strong evidence of heteroskedasticity is detected. This suggests that the maximum likelihood estimator for the standard bivariate Probit model will be inconsistent in this particular case.



heteroskedasticity, information matrix, artificial regression, German Socioeconomic Panel