PanelDataNotes-4-MDE

PanelDataNotes-4-MDE - 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 4-A. Minimum Distance Estimation
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Chamberlain’s Model Chamberlain (1984) “Panel Data,” Handbook of  Econometrics Innovation: treat the panel as a system of equations:  SUR Models, See Wooldridge, Ch. 7 through p. 172. Assumptions: Balanced panel Minimal restrictions on variances and covariances of  disturbances (zero means, finite fourth moments) Model the correlation between effects and regressors
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Chamberlain (2) it i it i i i i y , each observation   , T observations for individual i Assuming no time invariant variables in  . (To be picked up when we examine Hausman and Taylor.) Re: Mundlak's treatment = α + + ε = α + + it i x β y i X β ε X i T i 0 t 1 i i i , E( | ) 0. w Not a regression. Changes with next period's data.  Viewed as the   of   on  (1, , ,,..., ) . = α α = α + Σ + α = i it t i1 i2 iT X x δ projection x x x x
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Chamberlain (3) - Data 11 12 1T 11 12 1T                        Period                      Period                    t=  1     2  ...    T          1     2  ...    T Individual i= 1    y   y   ...  y                ...   Individual x x x 21 22 2T 21 22 2T 11 12 1T 11 12 1T  i=2    y   y   ...  y                ...                    ...                ...                            ... Individual i= N    y   y   ...  y                ...            x x x x x x it it i i                       y                       K variables                         T variables           = TK variables                           =  NxT matrix           = N x TK matrix = = x y x Y X
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Chamberlain (4) Model = = = α + + ε ε = ε ε = ϖ α = α + Σ + = α + Σ + + ε + α + + = = ϖ σ σ π it i it it i it is i ts T i 0 t 1 i T it 0 t 1 it i 2 0 i t it it i it is i ts w 2 w y ,  E[ | ] 0,  E[ | ]  unrestricted w y w     =  v ,  E[v | ] 0,  E[v v | ] +  still unrestricted =   +    is a it it t it t it x x x β x δ x x δ β x x x     I Σ Ω = α + + = α + + π π i1 0 i 1 i1 i2 0 i 2 i2 n unrestricted TxT covariance matrix. SEEMINGLY UNRELATED REGRESSIONS y v     Equation uses year 1 data, N observations y v    Each equation has y for that year regressed on     .. x x = α + + π iT 0 i T iT .                       the x's from all years.  There is a constant term y v    plus TxK variables in each equation. x
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Chamberlain (5) SUR Model = α + + = α + + = α + + α α α α + + π π π π π π Π i1 0 i 1 i1 i2 0 i
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