PANEL DATAPANEL DATA

1. Dummy Variable Regression1. Dummy Variable Regression

2. LSDV Estimator2. LSDV Estimator

3. Panel Data Fixed Effects Estimator3. Panel Data Fixed Effects Estimator

4. Panel Data Random Effects Estimator4. Panel Data Random Effects Estimator

Using Group DummiesUsing Group Dummies

Suppose our model is: Suppose our model is: YYii = = + + XXii + + iiThere are two categories: DThere are two categories: Dii = { 1 if i belongs to group 1 = { 1 if i belongs to group 1

0 otherwise0 otherwise

We run the regression: We run the regression: YYii = = 11 + + 22DDii + + 11XXii + + 22DDiiXXii + + ii

In interpreting the results, we should read two regressions:In interpreting the results, we should read two regressions:

YYii = ( = (11++22) + () + (11++22)X)Xii + + i i for group 1 for group 1

YYii = = 11 + + 11XXii + + i i for group 0for group 0

If If 22 ≠ 0 , then ≠ 0 , then YYii for for groupgroup 1 has a different mean 1 has a different mean

If If 2 2 ≠ 0 , then ≠ 0 , then YYii for for groupgroup 1 has a different sensitivity to 1 has a different sensitivity to XX

LSDV ModelLSDV Model

If category (individual) effects are significant, then eIf category (individual) effects are significant, then ei,ti,t is not is not

white noise (correlated with ewhite noise (correlated with ei,t-1i,t-1 and/or X and/or Xi,ti,t) which means OLS ) which means OLS

without dummies is biased and inconsistent. without dummies is biased and inconsistent.

For this reason, we may fail to find a significant relationship For this reason, we may fail to find a significant relationship between between YY and and X1X1..

If you control for group effects, however, you will get unbiased If you control for group effects, however, you will get unbiased results.results.

Fixed Effects Panel EstimatorFixed Effects Panel Estimator

An equivalent approach to the dummy variables An equivalent approach to the dummy variables pooled OLS estimator is the Fixed Effects (FE) pooled OLS estimator is the Fixed Effects (FE) estimator (it produces identical results). estimator (it produces identical results).

FE estimator is useful when we have a very large FE estimator is useful when we have a very large number of cross-sectional units (so that creating number of cross-sectional units (so that creating so many dummy variables would overcrowd the so many dummy variables would overcrowd the regression equation).regression equation).

LSDV and Panel Data FE Models will provide identical results:

Understanding the Procedure of the FE EstimatorUnderstanding the Procedure of the FE Estimator

1) For each group calculate group average over time.1) For each group calculate group average over time.

2) Obtain the time-demeaned data: 2) Obtain the time-demeaned data:

3) Run the regression on time-demeaned data:3) Run the regression on time-demeaned data:

Now, the error term is white noise. Hence, the FE Now, the error term is white noise. Hence, the FE estimator is unbiased. estimator is unbiased.

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STATA Fixed Effects Model OutputSTATA Fixed Effects Model Output

Random Effects (RE) estimator would be useful if Random Effects (RE) estimator would be useful if some explanatory variables remain constant over some explanatory variables remain constant over time.time.

It assumes that group effects are uncorrelated with It assumes that group effects are uncorrelated with regressors, hence it must be checked whether this regressors, hence it must be checked whether this assumption is satisfied.assumption is satisfied.

Fixed Effects (FE) Fixed Effects (FE) estimator measures the relationship estimator measures the relationship based on time variation within a cross-sectional unit.based on time variation within a cross-sectional unit.

Between Effects (BE) Between Effects (BE) estimator measures the relationship estimator measures the relationship based on cross-sectional variation at each time period.based on cross-sectional variation at each time period.

Random Effects (RE) estimator is a weighted average of the two.

Understanding the Procedure of the RE EstimatorUnderstanding the Procedure of the RE Estimator

1) For each group calculate group average over time. (as 1) For each group calculate group average over time. (as before) before)

2) Obtain the quasi-demeaned data: 2) Obtain the quasi-demeaned data:

where where

3) Run the regression on quasi-demeaned data:3) Run the regression on quasi-demeaned data:

Again, the error term is white noise. Hence, the RE Again, the error term is white noise. Hence, the RE estimator is unbiased. estimator is unbiased.

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Usually, one needs to apply all of the FE, BE, RE estimators, Usually, one needs to apply all of the FE, BE, RE estimators, respectively, to gain insight on which models is the most respectively, to gain insight on which models is the most appropriate.appropriate.

Recall: RE is consistent only if Cov (XRecall: RE is consistent only if Cov (Xii, u, uii) = 0. Under H) = 0. Under H00 (below), RE is more efficient than FE. (below), RE is more efficient than FE.

Hausman TestHausman Test: :

HH00: difference in FE and RE is not systematic: difference in FE and RE is not systematic

HHAA: RE cannot be used: RE cannot be used

STATA commands:STATA commands: xtreg r f e, fe xtreg r f e, fe estimates store fixedestimates store fixed xtreg r f e, rextreg r f e, re estimates store randomestimates store random hausman fixed randomhausman fixed random(Hausman test is not available in menu)