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Tuesday, 21 June 2016

Pooled or Population-Average Estimators with Stata (Panel)




Pooled estimator simply regress \({{y}_{it}}\) on an intercept and \({{x}_{it}}\) using both between (cross-section) and within (time-series) variation in the data.

Pooled or population-average estimator are consistent if the RE model is appropriate and are inconsistent if the FE model is appropriate.

From discussion in within and between variation,  the individual-spesific-effects model for the scalar dependent variable \({{y}_{it}}\) specifies that;

\({{y}_{it}}={{\alpha }_{i}}+{{\text{{x}'}}_{it}}\beta +{{\varepsilon }_{it}}\)                                                            (1)

where \({{\text{{x}'}}_{it}}\) are regressor, \({{\alpha }_{i}}\) are random individual-spesific-effects, and \({{\varepsilon }_{it}}\) is and idiosyncratic error

Pooled OLS estimator can be motivated from the individual-effects model by rewriting Eq (1) as the pooled model.

\(lwage=\alpha +{{\beta }_{1}}ex{{p}_{it}}+{{\beta }_{2}}exp{{2}_{it}}+{{\beta }_{3}}wk{{s}_{it}}+{{\beta }_{4}}e{{d}_{it}}+\left( {{\alpha }_{i}}-\alpha +{{u}_{it}} \right)\)                                (2)


Consistency of OLS requires that the error term \(\left( {{\alpha }_{i}}-\alpha +{{u}_{it}} \right)\) be uncorrelated with independent variables.

So pooled OLS is consistent in the in the RE model but inconsistent in the FE model because then \({{\alpha }_{i}}\)  is correlated with independent variables.

The pooled estimator, or PA estimator is obtained by using the xtreg command with the pa option.

The option is corr( ) for place different restriction on the error correlation, and vce(robust) to obtain cluster-robust standard errors.

We use the data Paneldata01.

xtset id t


Assumed that there are AR(2) error process in model Eq(2), to estimate PA,

xtreg lwage exp exp2 wks ed, pa corr(2) vce(robust)







 











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