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## PowerPoint Slideshow about 'Econometrics' - dusty

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The Classical Model

- yi = Zid +ai + hiyim = zim’d +ai + himyim = fim’b + bi’g +ai + him(i=1,…n; m=1,…M)
- E(hi) = 0, E(zimhim) = 0, E(aihim) = 0
- Note: E(zimai) = 0 is not assumed.
- E(hihi’) = sh2IM

Fixed-Effects Estimator

- First Difference EstimatesIf m is a time index, then the model can be transformed as:yim = fim’b + him(i=1,…,n; m=2,…,M)

Fixed-Effects Estimator

- Between Estimates

Fixed-Effects Estimator

- Within EstimatesE(hi*) = 0,E(fim*him*’) = 0,E(hi*hi*’) = sh2[IM-(1/M)1MxM] = sh2Q

Random-Effects Estimator

- Random-Effects Modelyim = zim’d + (ai + him)eim =ai + him
- E(ei) = 0,E(zimeim) = 0E(eiei’) = sa21MxM + sh2IM = S

Parameters Estimation

- To obtain the between estimates, OLS is used.
- To obtain the within estimates, pooled OLS is used (with correction of the degrees of freedom).
- Random-effects model requires the estimate of q from the between and within estimates of variances. Then pooled OLS is used on the transformed model.
- Using xtreg in Stata.

Hypotheses Testing

- Testing for fixed-effects
- F-test for ai = 0 jointly

- Testing for random-effects
- Breusch-Pagan LM 2-test for sa2 = 0

R2

- Three concepts of R2
- Between
- Within (from pooled OLS)
- Totalyim = fim’b + bi’g +ai + him(i=1,…n; m=1,…M)

Parameters Estimation

- Random-effects model can also be estimated with maximum likelihood method.
- GLS estimation (with non-classical variance-covariance matrix, see xtgls in Stata)
- Mixed fixed-effects and random-effects (xtmixed in Stata)
- Autocorrelation in panels (xtregar in Stata)
- Dynamic panel data models (xtabond in Stata)

Endogenous Regressors

- yi = Zid +ai + hi
- yi = Z1id1 +Z2id2 +ai + hi
- Z1iis predetermined, Z2i is endogenous.
- Xi = [X1i,X2i] is exogenous.X1iis included, X2i is excluded instruments.Set X1i = Z1i, #X2i #Z2i

Endogenous Regressors

- yi = Zid +ai + hi with instrumental variables Xi.E(Ximhim)=0, E(Zimhim)0, E(aihim)=0E(hi)=0, E(hihi’)=sh2IM
- IV method (xtivreg in Stata) can be applied to:
- First-Difference Estimates
- Between Estimates
- Fixed-Effects or Within Estimates
- Random-Effects Estimates

Conditional Heteroscedasticity

- Robust (or White) estimates of standard errors can be obtained to improve consistency of the estimates.
- GMM methods can be applied to panel data models with conditional heteroscedasticity and random regressors (xtivreg2 in Stata).
- Testing for overidentifying restrictions such as Hansen or Sargan test for panel data models is possible (xtoverid in Stata).

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