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Econ 3120 1st Edition Lecture 26Outline of Last Lecture I. Difference in DifferencesOutline of Current Lecture II. Counterfactual in PoliciesCurrent LectureEffect of Worker Compensation Laws on Weeks out of Work A seminal study of worker’s compensation laws by Meyer, Viscusi, and Durbin (1995) examined the effects of the increase in a cap in weekly earnings covered by workers’ compensation on time spent out of work. The change affected high-incomeworkers, but not low-income workers. Thus, we can assign workers to treatment and control groups based on income, and examine outcomes before and after the policy change. The estimating equation is log(duratit) = β0 +β1highearni +β2a f chnget +β3highearni ∗ a f chnget +uit 5 In this case, the critical assumption is that the average change in duration for the low-income group equals the average change for the high-income group if the policy hadn’t been implemented. This equation was estimated as: log(ddurat) = 1.126 (0.031) +0.256 (0.047) highearn+0.0077 (0.0447) a f chnge +0.191 (0.069) a f chnge ∗ highearn What are the conclusions from this analysis? 3.2 Difference in Differences Using Panel Data Suppose we are evaluating a program in India that provides a random set of primary schools in India with additional teachers to teach remedial skills to lower-performing students. We collect data before and after the program, so we thus have a panel dataset on children’s test scores. That is, we have two observations for all children. As before, we can run a difference in differences model: yit = β0 +β1treati +β2 postt +β3treat ∗ post +uit (1) where our outcome yit represents child i’s test score at time t, treat indicates inclusion in the treatment group, post indicates that the observation is from after the program, and uit is an individualspecific error component. Note that one problem with equation (1) is that we almost certainly have violated the serial correlation MLR assumption if we run this regression using OLS. Because each individual has 2 observations, the errors of the same individual will likely be correlated. There are some pretty straightforward ways to deal with this, but we won’t have time to cover them in this class. For our purposes, we can use the OLS estimates as unbiased and consistent, but we have to take the standard error estimates less seriously. As before, we can write β3 as: β3 = E(yit|treat = 1, post =1)−E(yit|treat = 1, post = 0) −[E(yit|treat = 0, post = 1)−E(yit|treat = 0, post = 0)] If we have a “balanced” panel, that is, if each individual has exactly two observations, this is equivalent to β3 = E(yi,post −yi,pre|treat = 1)−E(yi,post −yi,pre|treat = 0) 6 An alternative way to specify the differences-in-differences modelis by running the model where the observations are at the individual level: yi,post −yi,pre = β0 +β3treat +uit (2) Note here that β3 = E(yi,post −yi,pre|treat = 1)−E(yi,post −yi,pre|treat = 0) which is equivelent to β3 in the panel model (1) above. Using equation (2), we can see that this is just a special case of a lagged These notes represent a detailed interpretation of the professor’s lecture. GradeBuddy is best used as a supplement to your own notes, not as a substitute.dependent variable model: move yi,pre to the right hand side: yi,post = β0 +β3treat +yi,pre +uit Thus, wehave a lagged dependent variable model where the coefficient on the lagged variable is restricted to be 1. We can thus make a more flexible model by allowing this coefficient to vary: yi,post = β0 +β3treat +δyi,pre

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