Econ 3120 1st Edition Lecture 26 Outline of Last Lecture I Difference in Differences Outline of Current Lecture II Counterfactual in Policies Current Lecture Effect 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 income workers 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 0 1highearni 2a f chnget 3highearni 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 0 1treati 2 postt 3treat 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 3 as 3 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 3 E yi post yi pre treat 1 E yi post yi pre treat 0 6 An alternative way to specify the differences in differences model is by running the model where the observations are at the individual level yi post yi pre 0 3treat uit 2 Note here that 3 E yi post yi pre treat 1 E yi post yi pre treat 0 which is equivelent to 3 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 0 3treat yi pre uit Thus we have 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 0 3treat yi pre uit