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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 18. Ordered Outcomes and Interval Censoring Agenda Some General Results on Heterogeneity and Panel Data General Results on QR and LDV Models Specific Models Ordered Probabilities Censored and Truncated Regressions Incidental Truncation – Sample Selection Hazard Models for Duration Generality of FE, RE, RPM, LCM i N i1 i,T i i i i 1 i Models generally defined by the likelihood for the observed data logL = f(y ,...y  , , , ), i= 1,...,N; t= 1,...,T Parameter heterogeneity: Random Parameters f(  z ) g( , ) Includes : Cross = α β θ = ∑ i i i i X z , β β Ω Section or Panel Special Cases: (1) Omitted heterogeneity (2) Fixed effects (3) Random effects (4) Random parameters (a) Discrete  latent class (b) Continuous  "random parameters" Limited Dependent Variable Models Latent Regression Model Transformations of the Dependent Variable Censoring – Masking Values of the LHS variable Truncation – Losing Values of the LHS variable Sample Selection – Data Mechanism Models for the Transformed Variable Implications for Conventional Estimators (OLS) Appropriate Estimation Methods (MLE) Model Framework for LDV Models it it it it it it it it it it y * x y T(y ) * Censoring is a treatment of the data y y * if y * is in (a) certain range(s) = some fixed value if y * is in some other range E.g.: y * = preference f ′ = β + ε = = it it it or a Candidate A (D) relative to preference for Candidate B (R) y = 1 if y * 0 (probit) E.g.: y * = expected net expenditure on capital equipment it = gross expenditure  depreciation y = Reported net investment if 0, or 0 We will examine other transformations. ≥ Ordered Probability and Interval Censored Data Models it it it it it it it 1 1 it 1 it 2 2 1 it J 2 it J 1 J 1 J 2 it it J 1 y * x y 0 if y * y 1 if 0 < y * , > 0 y 2 if < y * , > ... y J 1 if < y * , > y J if y * ′ = β + ε = ≤ = ≤ μ μ = μ ≤ μ μ μ = μ ≤ μ μ μ = μ An Ordered Preference Scale for Movies Latent RegressionPreferences Application: Health An Ordered Probability Model it it it it it it it it it it it 1 it it it 1 it i y * x y 0 if y * 0; Prob[y 0] Prob[x 0] = [x ] y 1 if 0 < y * ; Prob[y 1] Prob[x ]Prob[x ′ = β + ε ′ = ≤ = = β + ε...
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This note was uploaded on 01/05/2012 for the course B 55.9912 taught by Professor Willamgreene during the Fall '11 term at NYU.
 Fall '11
 WillamGreene

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