PanelDataNotes-7

PanelDataNotes-7 - Econometric Analysis of Panel Data...

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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 7. Regression Extensions of Linear Individual Effects Models Extensions Heteroscedasticity (Baltagi, 5.1) Autocorrelation (Baltagi, 5.2) Covariance Structures Measurement Error Spatial Autocorrelation Generalized Regression it it i it i i i it it i it y [ ] Var[ | , ] (Dimension TxT), positive definite y u [ ] ′ = + α + ε = + ÷ = ′ = + + ε = i i i i i i i i i Accommodating Autocorrelation (and Heteroscedasticity) Fixed Effects : x β β y X D ε α X D = ε Σ Ω Σ Random Effects : x β y X i i 2 i u i i u + Var[u | ] (Dimension TxT.) + ′ = σ i i i i β ε i+ X ii + = ε Σ Ω OLS Estimation i i i 1 N N i 1 i 1 [ ] = [ ] u + = Coefficient Estimator, M = F or R ˆ Robust C- = = = + + ÷ = + + ′ ′ = Σ Σ F F i i i i F i R R i i i R i M M M M M i i i i β Fixed Effects : y X D Z w ε θ α Random Effects : y X i Z w β ε θ Least Squares Z Z Z y θ 1 1 N N N i 1 i 1 i 1 ovariance Matrix based on the White Estimator ˆ ˆ ˆ Est.Asy.Var[ ]-- = = = ′ ′ ′ ′ = Σ Σ Σ M M M M M M M M M i i i i i i i i Z Z Z w w Z Z Z θ GLS Estimation 2 2 2 2 2 u i 2 1 N N i 1 i 1 No natural format (yet) [I ]= ˆ ˆ ˆ ˆ ˆ , I 1 ε ε ε- = = ′ ′ = σ σ σ + ρ σ ρ ′ ′ = Σ Σ =- i M-1 M M-1 M-1 R i i i i i i i Fixed Effects : Random Effects : ii + I = ii Ω Φ (Feasible) Generalized Least Squares Z Z Z y θ Φ Φ Φ 2 i 1 2 N i 1 T ˆ ˆ ˆ Est.Asy.Var[ ] ˆ- ε = ′ + ρ ′ = σ Σ M-1 M R i i i ii Z Z θ Φ Heteroscedasticity Naturally expected in microeconomic data, less so in macroeconomic Model Platforms Fixed Effects Random Effects Estimation OLS with (or without) robust covariance matrices GLS and FGLS Maximum Likelihood 2 2 it i it it it i ,it y , E[ | ] ε ′ = α + + ε ε = σ x X β 2 2 it it i it it i ,it 2 2 i i u,i y u , E[ | ] E[u | ] ε ′ = + + ε ε = σ = σ x X β X Baltagi and Griffin’s Gasoline Data World Gasoline Demand Data, 18 OECD Countries, 19 years Variables in the file are COUNTRY = name of country YEAR = year, 1960-1978 LGASPCAR = log of consumption per car LINCOMEP = log of per capita income LRPMG = log of real price of gasoline LCARPCAP = log of per capita number of cars See Baltagi (2001, p. 24) for analysis of these data. The article on which the analysis is based is Baltagi, B. and Griffin, J., "Gasoline Demand in the OECD: An analysis is based is Baltagi, B....
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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-7 - Econometric Analysis of Panel Data...

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