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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 4. Fixed Effects Estimation with Fixed Effects The fixed effects model c i is arbitrarily correlated with x it but E[ ε it  X i ,c i ]=0 Dummy variable representation it it i it i i i i i i i i i i i i N i= 1 i 1 2 N y = + c + , observation for person i at time ε t = + c + , T observations in group i = + + , note (c ,c ,...,c ) = + + , T observations in the sample c= ( , ,... ) , ′ ′ = Σ ′ ′ ′ ′ x β y X i β ε X c c β ε y X c β ε c c c N i= 1 i T by 1 vector Σ N it it j= 1 j ijt it ijt y = + d + , d = (i=j) ε ′ Σ α x 1 β Assumptions for the FE Model y i = X i β + d i α i + ε i , for each individual 1 1 2 2 N = = N ÷ ÷ = + ÷ ÷ ÷ ÷ + ÷ + 1 2 N y X d y X d β ε α y X d β [X,D] ε α Z δ ε M M M M O M E[c i  X i ] = g( X i ); Effects are correlated with included variables. Common: Cov[ x it ,c i ] ≠ Useful Analysis of Variance Notation i i 2 T T N 2 N 2 N i=1 t=1 it i=1 t=1 it i i=1 i i Decomposition of Total variation: (z z) (z z.) T z. z Σ Σ Σ Σ Σ  = + Total variation = Within groups variation + Between groups variation 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, 19601978 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 Application of Pooling and Testing Procedures," European Economic Review, 22, 1983, pp. 117137. The data were downloaded from the website for Baltagi's text. Analysis of Variance Per Capita G asoline U se for 18 O EC D C ountries COUNTRY 3.50 4.00 4.50 5.00 5.50 6.00 6.50 3.00 2 4 6 8 10 12 14 16 18 LGASPCAR Analysis of Variance REGRESS;Lhs=lgaspcar ; Rhs=one ; Panel ; Str = Country $ + +  Analysis of Variance for LGASPCAR   Stratification Variable COUNTRY   Observations weighted by ONE   Total Sample Size 342   Number of Groups 18   Number of groups with no data 0   Overall Sample Mean 4.2962420   Sample Standard Deviation .5489071   Total Sample Variance .3012990     Source of Variation...
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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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