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1、Panel Data Methods yit b0 b1xit1 bkxitk uit 1Economics 20 Prof Anderson A True Panel vs A Pooled Cross Section w Often loosely use the term panel data to refer to any data set that has both a cross sectional dimension and a time series dimension w More precisely it s only data following the same cro
2、ss section units over time w Otherwise it s a pooled cross section 2Economics 20 Prof Anderson Pooled Cross Sections w We may want to pool cross sections just to get bigger sample sizes w We may want to pool cross sections to investigate the effect of time w We may want to pool cross sections to inv
3、estigate whether relationships have changed over time 3Economics 20 Prof Anderson Difference in Differences w Say random assignment to treatment and control groups like in a medical experiment w One can then simply compare the change in outcomes across the treatment and control groups to estimate th
4、e treatment effect w For time 1 2 groups A B y2 B y2 A y1 B y1 A or equivalently y2 B y1 B y2 A y1 A is the difference in differences 4Economics 20 Prof Anderson Difference in Differences cont w A regression framework using time and treatment dummy variables can calculate this difference in differen
5、ce as well w Consider the model yit b0 b1treatmentit b2afterit b3treatmentit afterit uit w The estimated b3 will be the difference in differences in the group means 5Economics 20 Prof Anderson Difference in Differences cont w When don t truly have random assignment the regression form becomes very u
6、seful w Additional x s can be added to the regression to control for differences across the treatment and control groups w Sometimes referred to as a natural experiment especially when a policy change is being analyzed 6Economics 20 Prof Anderson Two Period Panel Data w It s possible to use a panel
7、just like pooled cross sections but can do more than that w Panel data can be used to address some kinds of omitted variable bias w If can think of the omitted variables as being fixed over time then can model as having a composite error 7Economics 20 Prof Anderson Unobserved Fixed Effects w Suppose
8、 the population model is yit b0 d0d2t b1xit1 bkxitk ai uit w Here we have added a time constant component to the error uit ai uit w If ai is correlated with the x s OLS will be biased since we ai is part of the error term w With panel data we can difference out the unobserved fixed effect 8Economics
9、 20 Prof Anderson First differences w We can subtract one period from the other to obtain Dyi d0 b1Dxi1 bkDxik Dui w This model has no correlation between the x s and the error term so no bias w Need to be careful about organization of the data to be sure compute correct change 9Economics 20 Prof An
10、derson Differencing w Multiple Periods w Can extend this method to more periods w Simply difference adjacent periods w So if 3 periods then subtract period 1 from period 2 period 2 from period 3 and have 2 observations per individual w Simply estimate by OLS assuming the Duit are uncorrelated over time 10Economics 20 Prof Anderson
