Ch 13 Pooled Cross Sections Across Time Simple

Ch. 13. Pooled Cross Sections Across Time: Simple Panel Data. • Pooled Cross Sections • Difference-in-Difference for treatment effects • How Di. D can eliminate bias in cross-sectional OLS. • Potential sources of bias after Di. D • Panel Data • • First Difference for two period panel data. Fixed effects for multi-period panel data. How first differencing or fixed effects can eliminate bias in OLS Potential issues with FD and FE models

Pooling Cross Sections across Time: Simple Panel Data Methods • Policy analysis with pooled cross sections • Two or more independently sampled cross sections can be used to evaluate the impact of a certain event or policy change • Effect of new garbage incinerator’s location on housing prices • Examine 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

Pooling Cross Sections across Time: Simple Panel Data Methods • Garbage incinerator and housing prices • Note: near incinerator had negative effect on housing prices before incinerator was built? Why? • Would be inappropriate to interpret negative effect of incinerator after it‘s built as a causal effect. Some of effect is due to fact that incinerator was built near lower price homes. • More appropriate to look at difference-in-difference (Di. D) after incinerator was built: p near – p far = -30, 688. 27 before incinerator was built: = p near – p far = -18, 824. 37 = -11, 863. 9 difference in differences (Di. D)

Pooling Cross Sections across Time: Simple Panel Data Methods • Differential effect of being in the location and after the incinerator was built

Pooling Cross Sections across Time: Simple Panel Data Methods • Policy evaluation using difference-in-differences Compare outcomes of the two groups before and after the policy change

Pooling Cross Sections across Time: Simple Panel Data Methods • Two-period panel data (Fixed Effect) analysis • Example: Effect of unemployment on city crime rate • Assume that no other explanatory variables are available. Will it be possible 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: Time dummy for the second period Unobserved city specific time -invariant actors (= fixed effect) Examples of time-constant variables that might affect city crime? Other unobserved factors (= idiosyncratic error)

Pooling Cross Sections across Time: Simple Panel Data Methods • Effect of unemployment on city crime rate • Estimate differenced equation by OLS: Secular increase in crime across all cities. Fixed effect drops out + 1 percentage point unemployment rate leads to 2. 22 more crimes per 1, 000 people

Pooling Cross Sections across Time: Simple Panel Data Methods • Discussion of first-differenced panel estimator • Further explanatory variables may be included in original equation • There may be arbitrary correlation between the unobserved time-invariant characteristics and the included explanatory variables • For example, suppose cities with less educated workers (virtually a time-invariant characteristic) have higher crime and also higher unemployment – how would this bias OLS estimate of effect of unemployment? • First differences cause effect of any time-invariant variables to be differenced out of the regression. Eliminates bias from exclusion of important timeinvariant variables that would emerge in OLS. • First-differenced estimates will be imprecise if explanatory variables vary little over time (no estimate possible if time-invariant)

Panel Data Methods with More than 2 Periods. • Fixed effects estimation Fixed effect, potentially correlated with explanatory variables Form time-averages for each individual Because (the fixed effect is removed) • Estimate deviations from i-specific means using OLS • Estimates rely on time variation within cross-sectional units • (= within estimator) • xtset & xtreg in Stata.

Advanced Panel Data Methods • Example: Effect of training grants on firm scrap rate (number of defective items per 100 produced) Time-invariant reasons why one firm is more productive than another are controlled for. The important point is that these may be correlated with the other explanatory variables. Fixed-effects estimation using the years 1987, 1988, and 1989: Stars denote time -demeaning Training grants significantly improve productivity (with a time lag)

Advanced Panel Data Methods • Discussion of fixed effects estimator • Strict exogeneity in the original model has to be assumed • The R 2 of the demeaned equation is inappropriate measure of R 2 • The effect of time-invariant variables cannot be estimated • The effect of interactions with time-invariant variables can be estimated (e. g. the interaction of education with time dummies) • If a full set of time dummies are included, the effect of variables whose change over time is constant cannot be estimated (e. g. age) • Degrees of freedom have to be adjusted because the individual specific averages are estimated in addition to other coefficients (resulting degrees of freedom = NT-N-k)

Advanced Panel Data Methods (Ch. 14) • Applying panel data methods to other data structures • Panel data methods can be used in other contexts where constant unobserved effects have to be removed • Example: Wage equations for twins Unobserved genetic and family characteristics that do not vary across twins Equation for twin 1 in family i Equation for twin 2 in family i Estimate differenced equation by OLS