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1、 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Chapter 14 Advanced Panel Data MethodsWooldridge: Introductory Econometrics: A Modern Approach, 5e 2013 Cengage Learning. All Rights Reserved. May n
2、ot be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Fixed effects estimationEstimate time-demeaned equation by OLSUses time variation within cross-sectional units (= within-estimator)Fixed effect, potentially corre-lated with explanatory variablesFor
3、m time-averages for each individualBecause (the fixed effect is removed) Advanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Example: Effect of training grants on firm scrap
4、rateFixed-effects estimation using the years 1987, 1988, 1989:Time-invariant reasons why one firm is more productive than another are controlled for. The important point is that these may be correlated with the other explanat. variables.Stars denote time-demeaning Training grants significantly impro
5、ve productivity (with a time lag) Advanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Discussion of fixed effects estimatorStrict exogeneity in the original model has to be a
6、ssumedThe R-squared of the demeaned equation is inappropriateThe effect of time-invariant variables cannot be estimatedBut the effect of interactions with time-invariant variables can be estimated (e.g. the interaction of education with time dummies)If a full set of time dummies are included, the ef
7、fect of variables whose change over time is constant cannot be estimated (e.g. experience)Degrees of freedom have to be adjusted because the N time averages are estimated in addition (resulting degrees of freedom = NT-N-k)Advanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May not
8、 be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Interpretation of fixed effects as dummy variable regressionThe fixed effects estimator is equivalent to introducing a dummy for each individual in the original regression and using pooled OLS:After f
9、ixed effects estimation, the fixed effects can be estimated as:For example, =1 if the observation stems from individual N, =0 otherwise Estimated individual effect for individual i Advanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or pos
10、ted to a publicly accessible website, in whole or in part. Fixed effects or first differencing?Remember that first differencing can also be used if T 2In the case T = 2, fixed effects and first differencing are identicalFor T 2, fixed effects is more efficient if classical assumptions holdFirst diff
11、erencing may be better in the case of severe serial correlation in the errors, for example if the errors follow a random walkIf T is very large (and N not so large), the panel has a pronounced time series character and problems such as strong dependence ariseIn these cases, it is probably better to
12、use first differencingOtherwise, it is a good idea to compute both and check robustnessAdvanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Random effects modelsRandom effects
13、 assumption: The individual effect is assumed to be random“ i.e. completely unrelated to explanatory variables The composite error ai + uit is uncorrelated with the explanatory variables but it is serially correlated for observations coming from the same i: For example, in a wage equation, for a giv
14、en individual the same unobserved ability appears in the error term of each period. Error terms are thus correlated across periods for this individual.Under the assumption that idiosyncratic errors are serially uncorrelated Advanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May n
15、ot be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Estimation in the random effects modelUnder the random effects assumptions explanatory variables are exogenous so that pooled OLS provides consistent estimatesIf OLS is used, standard errors have to
16、 be adjusted for the fact that errors are correlated over time for given i (= clustered standard errors)But, because of the serial correlation, OLS is not efficientOne can transform the model so that it satisfies the GM-assumptions: Quasi-demeaned data Error can be shown to satisfy GM-assumptions Ad
17、vanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Estimation in the random effects model (cont.)The quasi-demeaning parameter is unknown but it can be estimatedFGLS using the
18、 estimated is called random effects estimationIf the random effect is relatively unimportant compared to the idosyn-cratic error, FGLS will be close to pooled OLS (because )If the random effect is relatively important compared to the idiosyn-cratic term, FGLS will be similar to fixed effects (becaus
19、e )Random effects estimation works for time-invariant variableswithAdvanced PanelData Methods 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Example: Wage equation using panel dataRandom effects o
20、r fixed effects?In economics, unobserved individual effects are seldomly uncorrelated with explanatory variables so that fixed effects is more convincingRandom effects is used because many of the variables are time-invariant. But is the random effects assumption realistic? Advanced PanelData Methods
21、 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible website, in whole or in part. Correlated random effects approachThe individual-specific effect ai is split up into a part that is related to the time-averages of the expla-natory
22、 variables and a part ri that is unrelated to the explanatory variables.Advanced PanelData Methods (= Correlated Random Effect, CRE)The resulting model is an ordinary random effects model with uncorrelated random effect r i but with the time averages as additional regressors. It turns out that in th
23、is model, the resulting estimates for the explanatory variables are identical to those of the fixed effects estimator.Avantages: 1) One can test FE vs. (ordinary) RE, 2) One can incorporate time-invariant regressors 2013 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated
24、, or posted to a publicly accessible website, in whole or in part. Applying panel data methods to other data structuresPanel data methods can be used in other contexts where constant unobserved effects have to be removedExample: Wage equations for twins Equation for twin 1 in family iEquation for twin 2 in family iUnobserved genetic and family characteristics that do not vary across twins Estimate differenced equation by OLS Advanced PanelData Methods
《計量經濟學導論》ch
