格林面板数据讲义-19

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1、Econometric Analysis of Panel Data,William Greene Department of Economics Stern School of Business,Econometric Analysis of Panel Data,19. Limited Dependent Variables And Models for Count Data,Censoring and Corner Solution Models,Censoring model: T(y*) = 0 if y* 0. (See text, pp. 518-519)Application:

2、 Fair, R., “A Theory of ExtramaritalAffairs,” JPE, 1978. Same structural form,The Tobit Model,Y* = x+, y = Max(0,y*), N0,2 Other censoring limits: y=Max(L,y*) = y-L=Max(0,y*-L). Change constant term and LHS variable Upper censoring: y=Min(U,y*) = U-y = Max(0,U-Y*). Change constant and LHS variable a

3、nd swap signs of estimated coefficients. Censoring limit is person specific: Same as above: Constant term becomes the variable with a coefficient fixed at 1. Censoring at both extremes: y=Max(L,Min(y*,U). A minor extension of the model. Easy to accommodate. (Already done in major software.) Interval

4、 censoring over the entire range. See yesterdays notes. (Tobin: “Estimation of Relationships for Limited Dependent Variables,” Econometrica, 1958. Tobins probit?),Conditional Mean Functions,Conditional Means,Predictions and Residuals,What variable do we want to predict? y*? Probably not not relevant

5、 y? Randomly drawn observation from the population y | y0? Maybe. Depends on the desired function What is the residual? y prediction? Probably not. What do you do with the zeros? Anything - x? Probably not. x is not the mean. Generalized residuals coming below.,OLS is Inconsistent - Attenuation,Esti

6、mating the Tobit Model,Hessian for Tobit Model,Simplified Hessian,Recovering Structural Parameters,Marginal Effects in Censored Regressions,A Decompositioin,Application: Fairs Data,F22.2 Fairs (1977) Extramarital Affairs Data, 601 Cross Section observations. Source: Fair (1977) and http:/fairmodel.e

7、con.yale.edu/rayfair/pdf/1978ADAT.ZIP. Several variables not used are denoted X1, ., X5.) y = Number of affairs in the past year, (0,1,2,3,4-10=7, more=12, mean = 1.46(Frequencies 451, 34, 17, 19, 42, 38) z1 = Sex, 0=female; mean=.476 z2 = Age, mean=32.5 z3 = Number of years married, mean=8.18 z4 =

8、Children, 0=no; mean=.715 z5 = Religiousness, 1=anti, ,5=very. Mean=3.12 z6 = Education, years, 9, 12, 16, 17, 18, 20; mean=16.2 z7 = Occupation, Hollingshead scale, 1,7; mean=4.19 z8 = Self rating of marriage. 1=very unhappy; 5=very happy,Fairs Study,Corner solution model Discovered the EM method i

9、n the Econometrica paper Used the tobit instead of the Poisson (or some other) count model Did not account for the censoring at the high end of the data,Estimated Tobit Model,Neglected Heterogeneity,Discarding the Limit Data,Regression with the Truncated Distribution,Estimated Tobit Model,Two Part S

10、pecifications,Panel Data Application,Pooling: Standard results, incuding “cluster” estimator(s) for asymptotic covariance matrices Random effects Butler and Moffitt same as for probit Mundlak/Wooldridge extension group means Extension to random parameters and latent class models Fixed effects: Some

11、surprises (Greene, Econometric Reviews, 2005),Fixed Effects MLE for Tobit,No bias in slopes. Large bias in estimator of ,FE Truncated Regression,Large bias in estimated slopes and standard deviation. Not much in marginal effects.,Models for Counts,German Health Care Usage Data, 7,293 Individuals, Va

12、rying Numbers of Periods Variables in the file are Data downloaded from Journal of Applied Econometrics Archive. This is an unbalanced panel with 7,293 individuals. They can be used for regression, count models, binary choice, ordered choice, and bivariate binary choice. This is a large data set. Th

13、ere are altogether 27,326 observations. The number of observations ranges from 1 to 7. (Frequencies are: 1=1525, 2=2158, 3=825, 4=926, 5=1051, 6=1000, 7=987). Note, the variable NUMOBS below tells how many observations there are for each person. This variable is repeated in each row of the data for

14、the person. (Downlo0aded from the JAE Archive)DOCTOR = 1(Number of doctor visits 0) HSAT = health satisfaction, coded 0 (low) - 10 (high) DOCVIS = number of doctor visits in last three months HOSPVIS = number of hospital visits in last calendar year PUBLIC = insured in public health insurance = 1; o

15、therwise = 0 ADDON = insured by add-on insurance = 1; otherswise = 0HHNINC = household nominal monthly net income in German marks / 10000.(4 observations with income=0 were dropped) HHKIDS = children under age 16 in the household = 1; otherwise = 0 EDUC = years of schooling AGE = age in yearsMARRIED

16、 = marital statusEDUC = years of education,Models for Count Data,Hospital Visits,Choice Based Sample: Censored at Y=10, then 90% of the zeros were deleted.,Hospital Visits,+-+ | Poisson Regression | | Number of observations 4916 | | Iterations completed 7 | | Log likelihood function -5967.059 | | Re

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