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Unformatted text preview: Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business Econometric Analysis of Panel Data 16. Nonlinear Effects Models and Models for Binary Choice Panel Data and Binary Choice Models U it = α + β ’x it + ε it + Person i specific effect Fixed effects using “dummy” variables U it = α i + β ’x it + ε it Random effects using omitted heterogeneity U it = α + β ’x it + ( ε it + v i ) Same outcome mechanism: Y it = [U it > 0] Effects are not removed by differencing the data. Need a direct estimation approach. Application – Doctor Visits German Health Care Usage Data, 7,293 Individuals, Varying 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. There 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 the person. (Downlo0aded from the JAE Archive) DOCTOR = 1(Number of doctor visits > 0) HHNINC = 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 years MARRIED = marital status EDUC = years of education Application: Innovations Pooled Estimation it it it i t Ignoring panel data nature; P(y 1 ) F( ). Estimation is based on the marginal distribution. logL= (1 y ) log(1 F( )) y logF( ) Partial likelihood methods. (Include a 'robust' covaria ′ = = ′ ′ + ∑ ∑ it it it it x x β x x β β nce matrix.) What assumptions are needed to make this work? Strict exogeneity? Dynamic completeness? (No lagged effects) Somewhat strong assumptions. Latent common effects are usually not ignored. The “Panel Probit Model” it it it it it it 12 1T i1 12 2,T i2 iT 1T 2,T The German innovation data: T= 5 (N= 1270) y * = x + , y 1[x + > 0] 1 ... 1 ... ~ N , ... ... ... ... ... 1 ′ ′ ε = ε ρ ρ ε ÷ ÷ ÷ ρ ρ ε ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ÷ ε ρ ρ β β M M FIML i5 i5 i1 i1 N i1 i5 i 1 (2y 1) (2y 1) N 1 5 i 1 5 / 2 1/ 2 1 i1 i2 12 i1 i5 15 i1 i2 12 i2 i2 22 logL log Prob[y ,..., y ] log ... g(  *)dv ...dv g(  *) (2 )  *  exp[ (1/ 2) ( *)...
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 Fall '11
 WillamGreene
 Likelihood function, Random effects model, Logit, log likelihood, log likelihood function, probit model

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