4. Economists at the Economic Institute for Labor Studies are examining the effects of minimum wage laws on employment. (a) They have assembled a panel data set containing observations of firms in the years 2009 and 2011. For each firm they have information on the number of workers during each year and the firm's location. Firms are located either in county A or county B. In 2009 the minimum wage was set at $7 per hour in both counties. However, in 2010 the governor of county B decided to increase the minimum wage to $10 per hour. Using the information below, what was the average treatment effect of the policy? [15 marks] (b) 1 County Year Employment 2 A 2009 416 3 A 2011 432 4 B 2009 422 5 B 2011 405 Explain in detail how the fixed effects model is estimated and how it eliminates heterogeneity. [30 marks] (c) Explain why it is important that time-series variables are 'stationary'. Outline a method that can be used to transform a non-stationary series into a stationary one. [20 marks] (d) Leo McGary is investigating the relationship between minimum wages and the level of employment in Schnfeld. He has assembled an annual time series data set containing the level of employment and the minimum wage rate between 1950 and 1987. He intends to estimate the equation Iprepop, = Bo+Blavgmin + & (3) where Iprepop, is the number of people employed during year t; and lavgmin, is the minimum wage rate in each year. He has carried out a variety of tests reported below. (i) (ii) Provide a detailed explanation on how you would establish whether it is appropriate to estimate equation (3) in levels using OLS. Under what conditions would you use an OLS estimator on equation (3)? [30 marks] Based on the output below (over the next two pages), is it appropriate for Leo to estimate equation (3) using OLS in levels? [5 marks] dfaller 1prepop, trend regress Dickey-Fuller test for unit root 2(6) Number of obs 37 Interpolated Dickey-Fuller Teat Statistic 1 Critical Value 5 Critical Value 10% Critical Value -1.792 -4.270 -3.552 -3.211 Mackinnon approximate p-value for 2(t) 0.7086 . Coef. Std. Ers. t PISI [95% Conf. Interval) trend cons -1013718 .1012066 0006918 .0008774 -.1643636 .0822562 -1.79 0.002 -0.79 0.436 -2.00 0.054 -.3070483 0243047 .0024748 -3315324 0010912 .0028052 dfuller lavgain, trend regress Dickey-Fuller test for unit root 2(t) umber of obs 37 Interpolated Dickey-Fuller Test Statistic 1 Critical Value Critical Value 10% Critical Value -1.410 -4.270 -3.552 -3.211 Mackinnon approximate p-value for 2(t) 0.8580 Coef. Std. Err, t [95% Conf. Interval] Lavin trend cons -.1422542 .0089454 -.0892692 .1009027 .0001232 .1518255 -1.41 0.168 1.10 0.279 -0.59 0.560 -.3473133 .0628048 -.0075629 -3978157 .0254536 .2192773 reg 1prepop lavgmin Source $5 df MS 36)-> Model Residual 230868472 1 .230868472 .088989878 36 .002471941 Total .319858351 37 .00864482 Number of obs - Prob > F R-squared Adj R-squared Root MSE -.04972 38 93.40 0.0000 0.7218 0.7141 Conf. Std. Err. t [95% Conf. Intervall cone -.089704 .0092822 -.9386112 .0080852 -9.66 -116.09 0.000 0.000 -.1085291 -.9550087 -.070679 -.9222136 predict error, resid dfuller error, nocons regress Dickey-Fuller test for unit root 2(t) Teat Statistic -2.000 Sumber of obs 37 Interpolated Dickey-Fuller Critical Value Critical Value 10 Critical Value -2.641 -1.950 -1.605 D.error Coef. Std. Err. % Pritl [95% Conf. Interval) error L1. -2058495 .1029261 -2.00 0.053 -.4145932 .0028942