格林面板数据讲义-7.ppt-道客多多

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1、Econometric Analysis of Panel Data,William GreeneDepartment of EconomicsStern School of Business,Econometric Analysis of Panel Data,7. Regression Extensions of Linear Individual Effects Models,Extensions,Heteroscedasticity (Baltagi, 5.1)Autocorrelation (Baltagi, 5.2)Covariance StructuresMeasurement

2、ErrorSpatial Autocorrelation,Generalized Regression,OLS Estimation,GLS Estimation,Heteroscedasticity,Naturally expected in microeconomic data, less so in macroeconomicModel PlatformsFixed EffectsRandom EffectsEstimationOLS with (or without) robust covariance matricesGLS and FGLSMaximum Likelihood,Ba

3、ltagi and Griffins Gasoline Data,World Gasoline Demand Data, 18 OECD Countries, 19 yearsVariables in the file areCOUNTRY = name of country YEAR = year, 1960-1978LGASPCAR = log of consumption per carLINCOMEP = log of per capita incomeLRPMG = log of real price of gasoline LCARPCAP = log of per capita

4、number of cars See Baltagi (2001, p. 24) for analysis of these data. The article on which the analysis is based is Baltagi, B. and Griffin, J., Gasoline Demand in the OECD: An Application of Pooling and Testing Procedures, European Economic Review, 22, 1983, pp. 117-137. The data were downloaded fro

5、m the website for Baltagis text.,Heteroscedastic Gasoline Data,LSDV Residuals,Evidence of Country Specific Heteroscedasticity,Heteroscedasticity in the FE Model,Ordinary Least SquaresWithin groups estimation as usual. Standard treatment this is just a (large) linear regression model.White estimator,

7、X|+-+-+-+-+-+-+ LINCOMEP .66224966 .07338604 9.024 .0000 -6.13942544 LRPMG -.32170246 .04409925 -7.295 .0000 -.52310321 LCARPCAP -.64048288 .02967885 -21.580 .0000 -9.04180473+-+-+-+-+-+-+ White Estimator+-+-+-+-+-+-+ LINCOMEP .66224966 .07277408 9.100 .0000 -6.13942544 LRPMG -.32170246 .05381258 -5

8、.978 .0000 -.52310321 LCARPCAP -.64048288 .03876145 -16.524 .0000 -9.04180473+-+-+-+-+-+-+ White Estimator using Grouping+-+-+-+-+-+-+ LINCOMEP .66224966 .06238100 10.616 .0000 -6.13942544 LRPMG -.32170246 .05197389 -6.190 .0000 -.52310321 LCARPCAP -.64048288 .03035538 -21.099 .0000 -9.04180473,Feas

9、ible GLS,Does Teaching Load Affect Faculty Size?Becker, W., Greene, W., Seigfried, J.,Random Effects Regressions,Modeling the Scedastic Function,Two Step Estimation,Heteroscedasticity in the RE Model,Ordinary Least Squares,Standard results for OLS in a GR modelConsistentUnbiasedInefficientVariance d

10、oes (we expect) converge to zero;,Estimating the Variance for OLS,White Estimator for OLS,Generalized Least Squares,Estimating the Variance Components: Baltagi,Invoking Mazodier and Trognon (1978) and Baltagi and Griffin (1988).,Estimating the Variance Components: Hsiao,Invoking Mazodier and Trognon

11、 (1978) and Baltagi and Griffin (1988).,So, whos right?,Maximum Likelihood,Conclusion Het. in Effects,Choose robust OLS or simple FGLS with moments based variances. Note the advantage of panel data individual specific variancesAs usual, the payoff is a function of Variance of the variancesThe extent

12、 to which variances are correlated with regressors.MLE and specific models for variances probably dont pay off much unless the model(s) for the variances is (are) of specific interest.,Autocorrelation,Source?Already present in RE model equicorrelated.Models:Autoregressive: i,t = i,t-1 + vit how to i

13、nterpret Unrestricted: (Already considered)Estimation requires an estimate of ,FGLS Fixed Effects,FGLS Random Effects,Microeconomic Data - Wages,+-+| Least Squares with Group Dummy Variables | LHS=LWAGE Mean = 6.676346 | Model size Parameters = 600 | Degrees of freedom = 3565 | Estd. Autocorrelation

17、,t) .775557 |+-+-+-+-+-+-+|Variable | Coefficient | Standard Error |t-ratio |P|T|t |+-+-+-+-+-+ LINCOMEP .40102837 .07557109 5.307 .0000 LRPMG -.24537285 .03187320 -7.698 .0000 LCARPCAP -.56357053 .03895343 -14.468 .0000+-+| Random Effects Model: v(i,t) = e(i,t) + u(i) | Estimates: Vare = .852489D-0

18、2 | Varu = .355708D-01 | Corrv(i,t),v(i,s) = .806673 |+-+-+-+-+-+-+ |Variable | Coefficient | Standard Error |b/St.Er.|P|Z|z | +-+-+-+-+-+ LINCOMEP .55269845 .05650603 9.781 .0000 LRPMG -.42499860 .03841943 -11.062 .0000 LCARPCAP -.60630501 .02446438 -24.783 .0000 Constant 1.98508335 .17572168 11.29

19、7 .0000,Covariance Structures,Model StructureSeemingly Unrelated RegressionsOLS Estimation and Panel Corrected Standard ErrorsGLS and FGLS Estimation problem of too many variance parameters estimatedApplication to World Gasoline Market,Covariance Structures,Generalized Regression,OLS Estimation,Pane

20、l Corrected Standard Errors,GLS,Computing FGLS,Finite Sample Problem of FGLS,Maximum Likelihood,Aggregation Test,Baltagi and Griffins Gasoline Data,World Gasoline Demand Data, 18 OECD Countries, 19 yearsVariables in the file areCOUNTRY = name of country YEAR = year, 1960-1978LGASPCAR = log of consum

21、ption per carLINCOMEP = log of per capita incomeLRPMG = log of real price of gasoline LCARPCAP = log of per capita number of cars See Baltagi (2001, p. 24) for analysis of these data. The article on which the analysis is based is Baltagi, B. and Griffin, J., Gasoline Demand in the OECD: An Applicati

22、on of Pooling and Testing Procedures, European Economic Review, 22, 1983, pp. 117-137. The data were downloaded from the website for Baltagis text.,OLS and PCSE,+-+| Groupwise Regression Models | Pooled OLS residual variance (SS/nT) .0436 | Test statistics for homoscedasticity: | Deg.Fr. = 17 C*(.95

27、5) = 182.86 C*(.99) = 196.61 | Test statistics against the correlation | Likelihood ratio statistic = 1010.7643 |+-+-+-+-+-+|Variable | Coefficient | Standard Error |b/St.Er.|P|Z|z |+-+-+-+-+-+ Constant 2.11399182 .00962111 219.724 .0000 LINCOMEP .80854298 .00219271 368.741 .0000 LRPMG -.79726940 .0

28、0123434 -645.909 .0000 LCARPCAP -.73962381 .00074366 -994.570 .0000,A Test Against Aggregation,Log Likelihood from restricted model = 655.093. Free parameters in and are 4 + 18(19)/2 = 175.Log Likelihood from model with separate country dummy variables = 876.126. Free parameters in and are 21 + 171

29、= 192Chi-squared17=2(876.126-655.093)=442.07Critical value=27.857. Homogeneity hypothesis is rejected a fortiori.,Measurement Error,General Conclusions About Measurement Error,In the presence of individual effects, inconsistency is in unknown directionsWith panel data, different transformations of t

30、he data (first differences, group mean deviations) estimate different functions of the parameters possible method of moments estimatorsModel may be estimable by minimum distance or GMMWith panel data, lagged values may provide suitable instruments for IV estimation.Various applications listed in Bal

31、tagi (pp. 187-190).,Application: A Twins Study,Wage Equation,Spatial Autocorrelation,Thanks to Luc Anselin, Ag. U. of Ill.,Per Capita Income in Monroe County, NY,Spatially Autocorrelated Data,Thanks Arthur J. Lembo Jr., Geography, Cornell.,Hypothesis of Spatial Autocorrelation,Thanks to Luc Anselin,

32、 Ag. U. of Ill.,Testing for Spatial Autocorrelation,Thanks again to Luc Anselin.,Modeling Spatial Autocorrelation,Spatially Autocorrelated Regression,Generalized Regression,Potentially very large N GPS data on agriculture plotsEstimation of . There is no natural residual based estimatorComplicated c

33、ovariance structure no simple transformations,Panel Data Application,Application from text,Alternative Formulations,Spatial Autocorrelation in a Panel,Qualitative Data,yit = a qualitative outcome adoption of a new method or technologySimilar model structureIntractable analytically(Ongoing research),

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格林 面板数据讲义-7.ppt

格林面板数据讲义-7.ppt