1. WLS Estimator Under the assumption that a firm needs to provide its employers with retirement benefits, either in the form of pension and/or 401K plan. We believe that how much a firm cares about its employees determines its 401K plan participation. Historically, firms that cared about their employees offered a traditional (defined benefit) pension plan instead of 401K since 401K places signicant responsibility on the employees for their investment decisions. However, in the recent decades, that these "good" firms have largely shifted towards 401K plans at least in part to reduce the burden of pension on the firm's cash flows. Thus, we can use the age of 401K as a proxy for a rm's effort in taking care of employers. The data set (PSBPR401K.txt) contains the 401K participation rate (Prate) for individual firms, firm matching rate ( Mrate J, the number of years that a firm has been offering 401K plan (Age), and the total number of employees ( Totemp ). Of course, a firm's matching rate will also affect the participation rate. In the following equation, we investigate what determines the participation rate, i.e., Prate =o+f31Age +132 Mrate+ u (a) According to what i have described above, what sign do you expected for Bl and (32 ? Is each OLS coefcient 3.- estimate significance under the homoscedasticity assumption? (b) Perform the White's heteroscedasticity test. (c) Find the heteroscedasticity consistent variancecovaria nce matrix, and re-test the significance of each estimate in (a). (d) Suppose ]11( \"2):\" 0+q1 Mrate+n . Estimate {3 again by Weighted Least Squares and test the significance of each estimate. (e) Comparing standard errors of the estimates from (a), (c), and {d}, what can you conclude in general? 2. IV Estimator The 401K participation equation in question 1 might be subject to the endogeneity issues. The increasing number of firms offering 401K plan and the rising participation rate could have been driven by the