What effect does having public health insurance have on the number of doctor visits a person has during a year? Using 1988 data,rwm88_small, from Germany we will explore this question. The data file \(r w m 88\) contains more observations. The data were used by Regina T. Riphahn, Achim Wambach, and Andreas Million, "Incentive Effects in the Demand for Health Care: A Bivariate Panel Count Data Estimation," Journal of Applied Econometrics, Vol. 18, No. 4, 2003, pp. 387-405.

a. Construct a histogram of DOCVIS. How many doctor visits do most patients in the survey have during the year? What are the mean and median number of doctor visits? What is the 90th percentile?

b. Test the null hypothesis that the population mean number of doctor visits for those with public insurance is the same as those who do not have public insurance. Use the \(5 \%\) level of significance and a one-tail test.

c. Estimate the regression model with dependent variable DOCVIS and explanatory variables FEMALE, HHKIDS, MARRIED, SELF, EDUC2, HHNINC2. Comment on the signs and significance of these predictor variables.

d. Estimate the regression model with dependent variable DOCVIS and explanatory variables FEMALE, HHKIDS, MARRIED, SELF, EDUC2, HHNINC2 separately for those with public insurance and those who do not have public insurance. Use equation (7.37) to obtain the estimate of the average treatment effect of public insurance.

e. Estimate the regression model with dependent variable DOCVIS and the explanatory variables FEMALE, HHKIDS, MARRIED, SELF, EDUC2, HHNINC2 in "deviation from the mean" form. That is, for each variable \(x\) create the variable \(\tilde{x}=x-\bar{x}\), where \(\bar{x}\) is the sample mean. Compare these results to those in (c).

f. Estimate the regression model with dependent variable DOCVIS and the explanatory variables FEMALE, HHKIDS, MARRIED, SELF, EDUC2, HHNINC2, along with PUBLIC and PUBLIC times each of the variables in deviation about the mean form. What is the estimated average treatment effect? Is it statistically significant at the 5\% level?