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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 10. Dynamic Models, Heterogeneity and Nonstationary Panel Data Cross Country Growth Convergence 1 i,t i,t i,t i,t i,t i,t i,t1 i,t1 i,t 1 i i,t 1 i,t i i,t 1 Y K (A L ) A index of technology K capital stock = I + (1 )K I s Y Investment Savings L labor (1 n )L αα = = = δ = = = = = + Solow  Swan Growth Model Equilibrium Model for Steady i,t i i i i,t 1 i,t i i i i i i logY t log Y (1 )g , g=technological growth rate "convergence" parameter; 1 = rate of convergence to steady state Cross country comparisons of convergence rat = μ + θ + λ + ε θ = λ λ = λ State I ncome es are the focus of study. Heterogeneous Dynamic Model i,t i i i,t 1 i it i,t i i i logY logY x Long run effect of interest is 1 Average (over countries) effect: or 1 (1) "Fixed Effects:" Separate regressions, then average results. (2) Country means (o = μ + λ + θ + ε θ β = λ θ β λ ver time)  can be manipulated to produce consistent estimators of desired parameters (3) Time series of means across countries (does not work at all) (4) Pooled  no way to obtain consistent est i i i imates. (5) Mixed Fixed (Weinhold  Hsiao): Build separate into the equation with "fixed effects," treat u as random. λ θ = θ + “Fixed Effects” Approach i,t i i i,t 1 i it i,t i i i i i i N N i i 1 i 1 i i N i 1 i N i 1 logY logY x , = 1 1 ˆ ˆ (1) Separate regressions; , , ˆ ˆ 1 1 ˆ ˆ (2) Average estimates = or ˆ N N 1 ˆ (1/ N) ˆ Function of averages: = 1 (1/ N) = = = = = μ + λ + θ + ε θ θ β = β λ λ μ λ θ θ β = Σ = Σ β λ Σ θ β Σ i i N i i= 1 ˆ In each case, each term i has variance O(1/T) Each average has variance O(1/N)...
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 Fall '11
 WillamGreene
 Econometrics, βi, λI, Unit root test, log y i,t

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