Econometric Analysis of Panel Data Panel Data Analysis –Fixed Effects Dummy Variable Estimator Between and Within Estimator First-Difference Estimator Panel-Robust Variance-Covariance Matrix –Heteroscedasticity and Autocorrelation –Cross Section Correlation –Hypothesis Testing To pool or Not to pool

Panel Data Analysis Fixed Effects Model –u i is fixed, independent of e it, and may be correlated with x it.

Fixed Effects Model Classical Assumptions –Strict Exogeneity –Homoschedasticity –No cross section and time series correlation

Fixed Effects Model Extensions –Weak Exogeneity

Fixed Effects Model Extensions –Heteroschedasticity

Fixed Effects Model Extensions –Time Series Correlation (with cross section independence for short panels)

Fixed Effects Model Extensions –Cross Section Correlation (with time series independence for long panels)

Dummy Variable Model Dummy Variable Representation –Note: X does not include constant term, otherwise one less number of dummy variables should be used.

Dummy Variable Model Dummy Variable Estimator (LSDV) Heteroscedasticity and Autocorrelation

Dummy Variable Model Panel-Robust Variance-Covariance Matrix

Within Model Within Model Representation

Within Model Model Assumptions

Within Model Within Estimator: FE-OLS

Within Model Within Estimator: GLS GLS = FE-OLS –Note:

Within Model Normality Assumption

Within Model Log-Likelihood Function ML Estimator

Within Model ML Estimator of  e 2 is downward biased even for large N: For balanced panel (T=T i : ),  e 2 should be estimated as:

Within Model Estimated Fixed Effects –For, is consistent but is inconsistent unless.

Within Model Panel-Robust Variance-Covariance Matrix –Consistent statistical inference for general heteroscedasticity, time series and cross section correlation.

First-Difference Model First-Difference Representation Model Assumptions

First-Difference Model First-Difference Estimator: FD-OLS Consistent statistical inference for general heteroscedasticity, time series and cross section correlation should be based on panel-robust variance- covariance matrix.

First-Difference Model First-Difference Estimator: GLS

Hypothesis Testing To Pool or Not to Pool? –F-Test based on dummy variable model: constant or zero coefficients for D w.r.t F(N-1,NT-N-K) –F-test based on fixed effects (unrestricted) model vs. pooled (restricted) model

Hypothesis Testing Heteroscedasticity Serial Correlation Spatial Correlation

Example: Investment Demand Grunfeld and Griliches [1960] –i = 10 firms: GM, CH, GE, WE, US, AF, DM, GY, UN, IBM; t = 20 years: –I it = Gross investment –F it = Market value –C it = Value of the stock of plant and equipment