Pooled Cross Sections and Panel Data II Econometrics 2 Pooled Cross Sections and Panel Data II Pooled Cross Sections and Panel Data

Pooled Cross Sections and Panel Data Last time: Pooling independent cross sections across time (13.1-2). Combine cross sections obtained at different points in time. ”Partial” pooling: Allow the coefficients of some variables to change between time periods. Include time dummies and interaction effects. Wage equation example (data in CPS78_85, see homepage): Significant change in the ”return to education” from 1978 to 1985. No significant change in the ”gender gap” between 1978 and 1985. Policy analysis: Locating a garbage incinerator: Significantly negative causal effect on the prices of nearby houses. Diff-in-diff approach: Differences in space of differences over time Pooled Cross Sections and Panel Data

Pooled Cross Sections and Panel Data Today: Two-period panel data: Follow the same individuals over two periods (13.3-4) Unobserved effects model: Time-invariant and idiosyncratic effects Omitted variables bias (heterogeneity bias) First-difference estimation Policy analysis with two-period panel data Pooled Cross Sections and Panel Data

Pooled Cross Sections and Panel Data Data structure Panel data: Same n individuals in period 1 and period 2. Period 1: Period 2: Total of 2n observations on n individuals Period 2 could be some years (months, weeks, …) after period 1 Also called longitudinal data. Simple case: One regressor. Simply want to estimate the effect of x on y. Pooled Cross Sections and Panel Data

Unobserved effects model Time dummy: Same values for all individuals Composite error term: Unobserved fixed effect (unobserved heterogeneity): Time-invariant Specific to each individual Idiosyncratic error: Varies over individuals and time: ”Regular” error term Pooled Cross Sections and Panel Data

Assumptions on the composite error term Assume that (conditional on the regressors): Note: We will make no assumption on (for now). Pooled Cross Sections and Panel Data

Correlated unobserved heterogeneity Unobserved time-invariant effect could well be correlated with the observed variable: Pooling the observations and estimating the model by OLS: Will result in inconsistent estimates. Problem cannot be solved if the available data is just a single cross section of information on and Fixed effect panel data solution: Estimate a model in which: The parameter of interest, , is identified The fixed effect, , does not appear. One such method is first-differencing. Pooled Cross Sections and Panel Data

First-difference estimation Model: The unobserved fixed effect is ”differenced” away. We have a cross section of first differences that allows us to estimate consistently (given the assumptions on ). Pooled Cross Sections and Panel Data

First-difference estimation More general case: Several observed regressors, some may be time-invariant Pooled Cross Sections and Panel Data

First-difference estimation Pooled Cross Sections and Panel Data

Policy analysis with panel data (treatment effects) Panel data even more useful for policy analysis than a time series of cross sections. Program evaluation: Want to measure the causal effect of an individual participating in some programme ”Active labour market policy” programme Subsidies to firms to make them innovate, become more productive, export, …. Potential problem: Individuals select into the program Or they are assigned to the program based on individual characteristics that are related to the outcome variable. Outcome measures: Post-programme wage, R&D expenses, productivity, export intensity, … Pooled Cross Sections and Panel Data

Policy analysis with panel data Model: Note: Similar to model used for independent cross sections Panel data allows error component structure: Control for time-invariant characteristics of participants ( ) and non-participants ( ) including variables that are likely to affect the participation decision. Pooled Cross Sections and Panel Data

Policy analysis with panel data First-differenced model: If participation only in period 2 (”before-after”) the OLS estimate becomes simply Diff-in-diff estimate. Panel structure: No assumption needed on Still need to assume that and are uncorrelated for consistency. Review the incinerator example. Pooled Cross Sections and Panel Data

Policy analysis with panel data: Example Example: The effect of a grant to firms for job training. Aim of program: Enhance the productivity of workers in the firm. Effect measure: ”Scrap rate” (proportion of produced items that have defects): Many defects = low average level of productivity in the firm Few defects = high productivity. Model: How can we obtain a consistent estimate of any causal effect, ? Pooled Cross Sections and Panel Data

Policy analysis with panel data: Example Problem: Participation may be related to unobserved firm effects (worker and manager ability, the amount of capital available,…). Unobserved effects likely to be directly related to productivity. OLS on pooled set of observations: Diff-in-diff approach: Pooled Cross Sections and Panel Data

Policy analysis with panel data: Example Questions: Are there indications of heterogeneity bias here? What is the likely direction of any bias? How do firms select into the job training program? Pooled Cross Sections and Panel Data

Pooled Cross Sections and Panel Data Next time Thursday this week! Panel data with several observations over time for the same individual units. W sec. 13.5, 14.1. Exercises start this week! Pooled Cross Sections and Panel Data