1. Pooled Cross Sections and Panel Data II
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. 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

5. 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

6. 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

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. 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