Econ 281 DiD Estimator

Econ 281 DiD Estimator - The Difference-in-Differences...

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1 The Difference-in-Differences Estimator Introduction to Econometrics Econ 281
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2 Regression and Causal Effects Let’s remind ourselves of the Roy/Rubin causal model We can then define the following 0 Earning of individual i when not treated i Y = 1 Earning of individual i when treated i Y = 1 if treated 0 if not treated i D =
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3 Regression and Causal Effects We are interested in Problem: Unless we can observe parallel universes we can never observe an individual in both states!! What we DO observe is 10 ii YY ( ) 01 0 i i i Y Y D =+
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4 Regression and Causal Effects Start out with Rewrite this as Where ( ) 01 0 ii i i i YY Y Y D = +−⋅ i YD u β = +⋅ + () ( ) ( ) 00 1 1 0 0 0 i i i i EY Y Y u Y ββ == =
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5 Regression and Causal Effects Let’s look at the Conditional expectations Take the difference () 01 |1 ii EY D Eu D ββ = =+ + = ( ) 0 |0 D D β = = ( ) ( ) 1 | 0 = | 1 | 0 D D D D =− = += −= Treatment Effect + Selection Bias
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6 Regression and Causal Effects This means The treatment effect can be estimated with a regression if there is no selection bias, for example with experimental data that selection is present when the error term and the treatment in the regression are correlated
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7 Difference-in-Differences (DiD) This is probably the simplest estimator that we can use with panel data Quasi-Experimental data come from (presumably exogenous) shocks to one entity but not another Minimum Wage increase in only one state Large influx of immigrants to a labor market Increase of disability benefits for a particular group The effect of the exogenous variation in the treatment can be measured
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8 Difference-in-Differences (DiD) We need two groups Treatment Group Control Group
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Econ 281 DiD Estimator - The Difference-in-Differences...

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