PanelDataNotes-11 (1)

PanelDataNotes-11 (1) - Econometric Analysis of Panel Data...

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Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business
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Econometric Analysis of Panel Data 11. Parameter Heterogeneity – “Heterogeneous Panels”
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Agenda Random Parameter Models Fixed effects Random effects Heterogeneity in Dynamic Panels Random Coefficient Vectors-Classical vs.  Bayesian General RPM Swamy/Hsiao/Hildreth/Houck Hierarchical  and “Two Step” Models ‘True’ Random Parameter Variation Discrete – Latent Class Continuous Classical Bayesian
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A Capital Asset Pricing Model 2 it 0t 1t i 2t i 3t i it it 0t 1t Mt 0t 2t R s R  one period percentage return  expected return on a riskless security (stochastic)  expected premium on the 'market' portfolio, R R  "nonline = γ + γ β + γ β + γ + η = γ = γ = - γ = % % % % % % % % % % % % 3t 2 it i i i ar" risk effect  "nonbeta risk" term Data are [R , , ,s ], generated by auxiliary regressions Coefficients are 'random' through time. Fama - MacBeth, "Risk, Return, and Equilibrium: Empirical Tes γ = β β % % ts," Journal of Political Economy, 1974.
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Heterogeneous Production Model i,t i i i,t i i,t i,t Health HEXP EDUC i country,  t=year Health =  health care outcome, e.g., life expectancy HEXP = health care expenditure EDUC = education Parameter heterogeneity:     Discrete?  Aids domin = α + β + γ + ε = ated vs. QOL dominated     Continuous? Cross cultural heterogeneity World Health Organization, "The 2000 World Health Report"
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Parameter Heterogeneity it i it it i it i i i i i i X i i i i y c y u ,         E[u | ] 0 --> Random effects       E[u | ] 0 --> Fixed effects       E E[u | ] 0.       Var[u | ] not yet defined - = + + ε = α + + ε α = α + = = it it Unobserved Effects   Random Constants x β x β X X X X  so far, constant.
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Parameter Heterogeneity it it i i i X i i i i y E[ | ] zero or nonzero - to be defined E [E[ | ]] =  Var[ | ] to be defined, constant or variable = + ε = + it i i Generalize to Random Parameters x β u β β u X u X 0 u X "The Pooling Problem : " What is the consequence of estimating under the erroneous assumption of constant parameters.  (Theil, 1960, "The Aggregation Problem")  (Maddala, 1970s - 1990s, "The Pooling Problem")
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Fixed Effects (Hildreth, Houck, Hsiao, Swamy) it it i i i i i i i i i i i X i i X i i i y , each observation , T  observations Assume (temporarily) T  > K. E[ | ] =g( ) (conditional mean) P[ | ] =( -E[ ])  (projection) E [E[ | ]] = E [P[ | ]] = Var[ | = + ε = + = + it i i i i i x β y X β ε u β β u X X u X X X θ u X u X 0 u X i ]  constant but nonzero = Γ
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OLS and GLS Are Inconsistent i i i i i i i i i i i i i i i , T  observations , T  observations E[ | ] E[ | ] E[ | ] = + = + = + + = + = + i i i i i i i i y X β ε u β β y X X u β ε y X w β w X X u X X 0 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.

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PanelDataNotes-11 (1) - Econometric Analysis of Panel Data...

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