3Errors in Uni-dimensional Data In standard time series or cross-sectional data sets, we must adjust for non-independent errors.Serial correlationErrors correlated across timeSpatial correlationErrors correlated across cross-sectionsHeteroskedasticityError variance changes over time or cross-sections
4Errors in Panel DataHeterogeneous serial correlationErrors correlated across time and differently for different cross-sections.Heterogeneous spatial correlationErrors correlated across cross-sections but differently for different time periods.Heterogeneous heteroskedasticityError variance changes over time, but does so differently for different cross-sections.Serial-spatial correlationPast errors from one cross-section are correlated with future errors from a different cross-section.
5Generalized Least Squares The error covariance matrix shows the covariances of error terms across different observations.
15Fixed versus Random Effects Under the random effects assumption, and are treated as stochastic.Under the fixed effects assumption, they are treated as fixed in repeated samples.
16Random vs. Fixed Effects Random Effects AssumptionPro: Estimators are more efficientCon: Estimators are inconsistent if any of the three errors are not IIN(0,σ2) across all dimensions.Fixed Effects AssumptionPro: Estimators are consistent regardless of and .Con: Estimators are less efficient. See Hausman test for endogeneity.
17Random vs. Fixed Cross-Sectional Effects Test statistic = 22
18Alternatives to Panel Techniques Separate RegressionsDrawbacksLess efficient estimators due to lost information about cross-sectional error covariance.Remove the ability to restrict parameter values across cross-sections.
19Alternatives to Panel Techniques Pooled RegressionDrawbacksLess efficient estimators due to lost information about cross-sectional error covariance.Restricts parameter values to be equal across cross-sections.
20Alternatives to Panel Techniques Pooled Regression with Cross-Sectional DummiesDrawbacksThis is the fixed effects panel technique.If the cross-sectional dummies are IIN, then parameter estimates are less efficient than under the random effects panel technique.
21Procedures to use with panel data Generalized least squares (GLS)Generalized method of moments (GMM)OLS with “automated” corrections for serial correlation, etc. is GLS.
22Extra stuffPanel data reveals information that is unattainable with non-panel data.
23Three-Dimensional Structure of the ASA-NBER Data Set
24Shock Occurrence vs. Shock Impact These shocks all impact inflation in quarter 9 but occur in different quarters.These shocks all occur in quarter 6 but impact inflation in different quarters.
25Cross-sectional shocks Shock Occurrence vs. Shock ImpactCumulative shocksCross-sectional shocksDiscrete shocks