The Pooled Regression a Presence of omitted effects yit=Xi B+C +et, observation for person i at time t y =x B+ci+E, T, observations in group =Xβ+c+ Ei note c=(cCp…C y =XB+C +E, 2is, T, observations in the sample a Potential bias/inconsistency of ols-depends on fixed or random
The Pooled Regression Presence of omitted effects Potential bias/inconsistency of OLS – depends on ‘fixed’ or ‘random’ it it i it i i i i i i i i i i i i N i=1 i y = +c +ε , observation for person i at time t = +c + , T observations in group i = + + , note (c ,c ,...,c ) = + + , T observations in the sample = x β y Xβ i ε Xβ c ε c y Xβ c ε
Cornwell and Rupert Data Cornwell and Rupert Returns to Schooling data, 595 Individuals, 7 Years Variables in the file are EXP york experience WKS weeks worked OCC occupation, 1 if blue collar, IND 1 if manufacturing industry SoUtH 1 if resides in south SMSA 1 if resides in a city(smsa MS 1 if married FEM 1 if female UNION 1 if wage set by union contract ED ears of education BLK 1 if individual is black LWAGE log of wage s dependent variable in regressions These data were analyzed in Cornwell, C. and rupert p,"Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators, Journal of Applied Econometrics, 3, 1988, pp 149-155. See Baltagi, page 122 for further analysis. The data were downloaded from the website for Baltagi s text
Cornwell and Rupert Data Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 Years Variables in the file are EXP = work experience WKS = weeks worked OCC = occupation, 1 if blue collar, IND = 1 if manufacturing industry SOUTH = 1 if resides in south SMSA = 1 if resides in a city (SMSA) MS = 1 if married FEM = 1 if female UNION = 1 if wage set by unioin contract ED = years of education BLK = 1 if individual is black LWAGE = log of wage = dependent variable in regressions These data were analyzed in Cornwell, C. and Rupert, P., "Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators," Journal of Applied Econometrics, 3, 1988, pp. 149-155. See Baltagi, page 122 for further analysis. The data were downloaded from the website for Baltagi's text
Application: Cornell and Rupert VAriable I Coefficient i Standard Error ib/StEr IP[IZ1>Z I Mean of xI 一+一-- Constant 5.66098218 04685914120.808 000 OCc 11220205 01464317 7.662 0000 51116447 SMSA 15504405 01233744 12.567 65378151 MS 09569050 02133490 4.485 81440576 F硎A 39478212 02603413 15.164 11260504 05688005 00267743 21.244 0000 12.8453782 EXP 01043785 00054206 19.256 0000 19.8537815 Covariance matrix for the model is adjusted for data clustering Sample of 4165 observations contained 595 clusters defined by 7 observations (fixed number)in each cluster Sample of 4165 observations contained 1 strata defined by 4165 observations (fixed number in each stratum Constant 5.66098218 10026368 56.461 0000 OCc 11220205 02653437 4.229 0000 51116447 SMSA 15504405 02540156 6.104 000D 65378151 09569050 04656766 2.055 0399 81440576 FEM 39478212 05319458 0000 11260504 05688005 00568214 10.010 0000 12.8453782 EXP 01043785 00131647 7.929.0000 19.8537815
Application: Cornell and Rupert
Using First Differences yit =x' B+C +et, observation for person i at time t Eliminating the heterogeneity yt=ytYt1=(Ax)+△c+△Et =(△x)B+ut Note: Time invariant variables become zero Time trend becomes the constant term Time dummy variables become(1, 0, 0...)
Using First Differences Eliminating the heterogeneity it it i,t-1 it i it it it y = y -y = ( ) + c + ε = ( ) + u Note: Time invariant variables become zero Time trend becomes the constant term Time dummy variables become x β x β (1,0,0...) it it i it y = +c + xβ ε , observation for person i at time t
OLS with First Differences With strict exogeneity of xi, C), ols regression of lyit on Axi is unbiased and consistent but inefficient 8 2 1 00 2 Var 813-62 000 O(Toeplitz forr 8 T-1 2 GLS is unpleasantly complicated. In order to compute a first step estimator of o, 2 we would use fixed effects. We should just stop there. Or, use OLS in first differences and use Newey-West with one lag
OLS with First Differences With strict exogeneity of (Xi ,ci ), OLS regression of Δyit on Δxit is unbiased and consistent but inefficient. i i 2 2 i,2 i,1 2 2 2 i,3 i,2 2 2 2 2 i,T i,T 1 2 0 0 2 Var (Toeplitz form) 0 0 2 − − − − − − = − − − − GLS is unpleasantly complicated. In order to compute a first step estimator of σε 2 we would use fixed effects. We should just stop there. Or, use OLS in first differences and use Newey-West with one lag