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

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econometrics 2

Econometrics 2

Pooled Cross Sections and Panel Data II

Pooled Cross Sections and Panel Data

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 data1
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

data structure
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
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

assumptions on the composite error term
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

correlated unobserved heterogeneity
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
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 estimation1
First-difference estimation
  • More general case: Several observed regressors, some may be time-invariant

Pooled Cross Sections and Panel Data

first difference estimation2
First-difference estimation

Pooled Cross Sections and Panel Data

policy analysis with panel data treatment effects
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
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 data1
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
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 example1
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 example2
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

next time
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