Before After and Difference in Difference Estimators Overview

Before After and Difference in Difference Estimators Overview of nonexperimental approaches: Before After and Difference in Difference Estimators Henrik Winterhager Econometrics III

Before After and Difference in Difference Estimators 2 Henrik Winterhager 1. Non-experimental approaches with panel data 2. Before After Estimators 3. Difference in Difference Estimators Hagen, Tobias und Bernd Fitzenberger (2004), Mikroökonometrische Methoden zur Ex-post-Evaluation, in: Hagen, Tobias und Alexander Spermann, Hartz-Gesetze – Methodische Ansätze zu einer Evaluierung, ZEW-Wirtschaftsanalysen, 74, S. 45 -72 Econometrics III

Before After and Difference in Difference Estimators Evaluation with non-experimental approaches Cross Section Data Instrumental Variables Approach (IV) „Propensity Score Matching“ „Regression Discontinuit y Design“ Henrik Winterhager Panel Data „Propensity Before After Estimators Difference in Difference Estimators (Di. D) Score Matching“ + Di. D Multivariate Separation Rate Models („Timing of Events“) Econometrics III

Before After and Difference in Difference Estimators use Panel Data: Data for certain observation units (individuals / households / enterprises) for several points in time àCross Section and Time Series elements (See later slides) Henrik Winterhager Econometrics III

Before After and Difference in Difference Model: Estimators αi: individual effect, taken to be constant over time t and specific to the individual cross section unit i θt: macroeconomic effect constant over the individual cross section εit: „white-noise“-disturbance 5 Henrik Winterhager Econometrics III

Before After and Difference in Difference Estimators Assumption: Participants of treatment group and control group differ in unobserved time-constant characteristics: For instance: Motivation, Management Skills, Intelligence Question: What treatment effect is caused on an outcome variable y of the treated? Henrik Winterhager Econometrics III

Before After and Difference in Difference Estimators Before After Estimators Concept: Comparison of an individual‘s outcome before and after a treatment ATT is estimated by: t: Point in time after treatment t‘: Point in time before treatment 7 Henrik Winterhager Econometrics III

Before After and Difference in Difference Calculation of the difference in average outcome variable before and after the treatment Estimators Elimination of time constant individual effects Difference is equivalent to the treatment‘s causal effect Assumption: E[y 0 t|C=1] = E[y 0 t‘|C=1] 8 Henrik Winterhager Econometrics III

Before After and Difference in Difference Problem: Assumption is violated in case of: Estimators • macroeconomic shocks (θt≠ 0) • Lifecycle effects (e. g. : Outcome variable „income“ changes with age) 9 Henrik Winterhager • Anticipation effects (e. g. : Job search intensity diminishes before participation in a job creation scheme) Econometrics III

Before After and Difference in Difference Solution: Difference in Difference Estimators ATT is estimated by: 10 Henrik Winterhager Idea: Outcome variable change in treatment group over time in excess of outcome variable change in non tr. group over time Econometrics III

Before After and Difference in Difference Estimators By calculating the differences twice, time constant individual effect as well as time varying effects identical over individuals are eliminated. Assumption: E[y 0 t-y 0 t‘|C=1] = E[y 0 t-y 0 t‘|C=0], i. e. Lifecycle effects on participants and non participants are identical Henrik Winterhager Econometrics III