To do so, we first applied the Lagrange multiplier test
by Davidson and MacKinnon (1984, pp. 4–5) to test for heteroskedasticity and a method suggested by Woodridge (2002, p. 483) to test for autocorrelation of the two univariate probit models (i.e., uncompensated care and efficiency models). We did this for the two univariate probit models because there is not an equivalent test for examining these potential problems in bivariate probit
models. The results ( f statistics) of the Lagrange multiplier
test indicated that heteroskedasticity existed in the uncompensated care model. The autocorrelation test showed that autocorrelation was present in both the uncompensated care and the efficiency models. Given this, we employed the modified Newly–West method to correct the standard errors for both univariate probit models (Hardin,
1996). For the bivariate probit models, we used robust standard error estimation. Both sets of estimated models are