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Econometrics 2

Econometrics 2

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Econometrics 2

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

  2. 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

  3. 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

  4. 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

  5. Unobserved effects model • 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

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

  7. 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

  8. 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

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

  10. First-difference estimation Pooled Cross Sections and Panel Data

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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