Final answer:
To allow the variance of the error term, u, in the sleeping behavior model to differ between men and women, introduce an interaction term. Estimate the parameters of the model for heteroskedasticity and compare the estimated variances of u for men and women to determine if the variance is higher for men or for women. Use a hypothesis test to assess the statistical significance of the difference in variances.
Step-by-step explanation:
To allow the variance of the error term, u, in the sleeping behavior model to differ between men and women, we can introduce an interaction term between the male dummy variable (male) and u. The modified model is: sleep = β0 + β1*totwrk + β2*educ + β3*age + β4*age^2 + β5*yngkid + β6*male + β7*(male*u) + u. This model allows for different variances of u for men and women, while the variance does not depend on other factors.
To estimate the parameters of the model for heteroskedasticity, we need to first estimate the sleep equation by OLS and obtain the OLS residuals. Then, we can use these residuals to estimate the parameters of the modified model. By comparing the estimated variances of u for men and women, we can determine if the variance is higher for men or for women.
To test if the variance of u is statistically different for men and women, we can use a hypothesis test. The null hypothesis would be that the variances are equal, and the alternative hypothesis would be that the variances are different. We can perform a F-test or a likelihood ratio test to assess the statistical significance of the difference.