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1、Chapter 13,Pooling Cross Sections across Time:Simple Panel Data Methods,Wooldridge:Introductory Econometrics:A Modern Approach,5e,Policy analysis with pooled cross sectionsTwo or more independently sampled cross sections can be used to evaluate the impact of a certain event or policy changeExample:E
2、ffect of new garbage incinerator on housing pricesExamine the effect of the location of a house on its price before and after the garbage incinerator was built:,After incinerator was built,Before incinerator was built,Pooled Cross Sections and Simple Panel Data Methods,Example:Garbage incinerator an
3、d housing prices(cont.)It would be wrong to conclude from the regression after the incinerator is there that being near the incinerator depresses prices so stronglyOne has to compare with the situation before the incinerator was built:In the given case,this is equivalent toThis is the so called diff
4、erence-in-differences estimator(DiD),Incinerator depresses prices but location was one with lower prices anyway,Pooled Cross Sections and Simple Panel Data Methods,Difference-in-differences in a regression frameworkIn this way standard errors for the DiD-effect can be obtainedIf houses sold before a
5、nd after the incinerator was built were sys-tematically different,further explanatory variables should be includedThis will also reduce the error variance and thus standard errorsBefore/After comparisons in natural experiments“DiD can be used to evaluate policy changes or other exogenous events,Diff
6、erential effect of being in the location and after the incinerator was built,Pooled Cross Sections and Simple Panel Data Methods,Policy evaluation using difference-in-differences,Compare the difference in outcomes of the units that are affected by the policy change(=treatment group)and those who are
7、 not affected(=control group)before and after the policy was enacted.For example,the level of unemployment benefits is cut but only for group A(=treatment group).Group A normally has longer unemployment durations than group B(=control group).If the diffe-rence in unemployment durations between group
8、 A and group B becomes smaller after the reform,reducing unemployment benefits reduces unemployment duration for those affected.Caution:Difference-in-differences only works if the difference in outcomes between the two groups is not changed by other factors than the policy change(e.g.there must be n
9、o differential trends).,Compare outcomes of the two groups before and after the policy change,Pooled Cross Sections and Simple Panel Data Methods,Two-period panel data analysisExample:Effect of unemployment on city crime rateAssume that no other explanatory variables are available.Will it be possibl
10、e to estimate the causal effect of unemployment on crime?Yes,if cities are observed for at least two periods and other factors affecting crime stay approximately constant over those periods:,Unobserved time-constant factors(=fixed effect),Other unobserved factors(=idiosyncratic error),Time dummy for
11、 the second period,Pooled Cross Sections and Simple Panel Data Methods,Example:Effect of unemployment on city crime rate(cont.)Estimate differenced equation by OLS:,Subtract:,Secular increase in crime,+1 percentage point unemploy-ment rate leads to 2.22 more crimes per 1,000 people,Fixed effect drop
12、s out!,Pooled Cross Sections and Simple Panel Data Methods,Discussion of first-differenced panel estimatorFurther explanatory variables may be included in original equationNote that there may be arbitrary correlation between the unobserved time-invariant characteristics and the included explanatory
13、variablesOLS in the original equation would therefore be inconsistentThe first-differenced panel estimator is thus a way to consistently estimate causal effects in the presence of time-invariant endogeneityFor consistency,strict exogeneity has to hold in the original equationFirst-differenced estimates will be imprecise if explanatory variables vary only little over time(no estimate possible if time-invariant),Pooled Cross Sections and Simple Panel Data Methods,
