2 Minimum wage Download the dataset called minwage.dta. It contains data collected by David Card (Nobel Prize winner) and Alan Krueger on fast food restaurants in New Jersey (NJ) and eastern Pennsylvania (PA) during two interview waves in March and November/December of 1992. On April 1, 1992 New Jersey raised its min imum wage from 4.25 to 5.05 dollars. The minimum in Pennsylvania remained at the federal level of 4.25 dollars. Use this data to analyze the impact of the minimum wage increase in New Jersey on employment in the fast food industry. Throughout, variable names with a trailing 2 refer to the second (Nov./Dec.) wave of the data, and the same names without any number refer to the corresponding variable from the March wave. fte and fte2 are full time equivalent employment. It is the sum of the number of full-time employees and one-half the number of part-time employees, excluding managers. dfte refers to the change in full-time equivalent employment between the second and rst interview (fte2 fte). dw refers to the change in the starting wage between the second and rst interview, and sample is dummy variable that is equal to 1 if both wage and employment data are available in both the rst and second interview wave and 0 otherwise. For the following questions, only use observations that correspond to sample = 1. Failing to specify this restriction will lead Stata to make the calculations with the full set of available observations for each variable, so you may not be comparing the same set of restaurants between March and November, or you may compare wages and employment for di erent restaurants. a) Calculate the average starting wage (wagest) separately for restaurants in NJ and in PA, both for each interview wave. I) Calculate the di erence in the average wages between the second and rst interviews. II) Now calculate the di erence between NJ and PA of the time di erences just obtained. Page 2 III) What is the interpretation of such a di erence-in-di erences estimate of the wage e ect? Under what conditions does this provide a valid estimate of the minimum wage increase on wages in the fast food industry? IV) Interpret your nding. b) Repeat the same exercise as in (a) for full-time equivalent employment. How does the minimum wage increase impact relative employment in NJ restaurants? c) Di erence-in-di erence estimates can also be calculated from the following regression Yist = TREATis + POSTt + rDD(TREATis POSTt)+eist (1) where Yist is employment in the restaurant i in state s and period t, TREATiis is an indicator for the treatment area (NJ or low wage restaurants in NJ), POSTt is an indicator for the treatment period (Nov/Dec) and (TREATis POSTt, is the interaction of these two dummies. I) Write the equation separately for March and Nov/Dec and show that the DD model for two pe riods (t = 1; 2) can be estimated as Yis2 Yis1 = + rDD(TREATis POSTt)+eis2 +eis1 (2) II) What are the regression DD estimates on wages and employment using this regression? How do they compare to the results you found in (a) and (b)? III) The regression allows you to control for other factors. Repeat the regressions, entering a dummy variable for whether the restaurant is company-owned (co-owned, as compared to franchised) and three dummy variables for three of the four chains in the dataset (Burger King, KFC, Roy Rogers, and Wendys; you will have to construct the dummies from the variable (chain) or use ichain. IV) Do the results change when you enter restaurant-speci c covariates? Would you have expected the results to change? Explain why or why not. d) An alternative to comparing NJ and PA restaurants is comparing restaurants within NJ with high and low wages before the minimum wage increase. Restrict your sample to restaurants in NJ. I) Would you expect the DD assumptions to be satis ed more easily for the within-NJ comparison than for the NJ-PA comparison? II) Construct a variable for those restaurants paying starting wages of less than 5.00 dollars before the minimum wage increase. Use the regression to obtain a DD estimate of the employment and wage e ects of the minimum wage increase. What is the relative impact of the minimum wage on starting wages and employment within NJ? III) How does within NJ estimates compare to those obtained in part (c) for the NJ-PA comparison?