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1、Econometric Analysis of Panel Data,William Greene Department of Economics Stern School of Business,Econometric Analysis of Panel Data,8. Instrumental Variables Estimation,Structure and Regression,Agenda,Single equation instrumental variable estimation Exogeneity Instrumental Variable (IV) Estimation
2、 Two Stage Least Squares (2SLS) Generalized Method of Moments (GMM) Panel data Hausman and Taylors formulation Application Arellano/Bond/Bover framework,Exogeneity,The Effect of Education on LWAGE,What Influences LWAGE?,An Exogenous Influence,An Experimental Treatment Effect,The Measurement Error Pr
3、oblem,How general is this result?,The Endogeneity Problem,Regression: y = x + Changes in x are associated with changes in y, but not dy/dx is measured by Cov(x,y), “dx/dx” is measured by Var(x) dy/dx = dx/dx + d/dx = = Cov(x,y)/Var(x) If x is correlated with , then changes in x are associated with c
4、hanges in . There are now two sources of change in y, direct change in x, change in associated with change in x dy/dx measured in the data is not equal to dx/dx = . dy/dx = dx/dx + d/dx = + d/dx,Instrumental Variables,Instrumental variable associated with changes in x, not with dy/dz = dx/dz + d /dz
5、. The second term is 0. =cov(y,z)/cov(x,z) This is the “IV estimator” Example: Corporate earnings in year t Earnings(t) = R&D(t) + (t) R&D(t) responds directly to Earnings(t) thus (t) A likely valid instrumental variable would be R&D(t-1) which probably does not respond to current year shocks to ear
6、nings.,The First IV Study (Snow, J., On the Mode of Communication of Cholera, 1855),London Cholera epidemic, ca 1853-4 Cholera = f(Water Purity,u)+. Effect of water purity on cholera? Purity=f(cholera prone environment (poor, garbage in streets, rodents, etc.). Regression does not work.Two London wa
7、ter companiesLambeth Southwark =|=Main sewage discharge,Paul Grootendorst: A Review of Instrumental Variables Estimation of Treatment Effects http:/individual.utoronto.ca/grootendorst/pdf/IV_Paper_Sept6_2007.pdf,IV Estimation,Cholera=f(Purity,u)+ Z = water company Cov(Cholera,Z)=Cov(Purity,Z) Z is r
8、andomly mixed in the population (two full sets of pipes) and uncorrelated with behavioral unobservables, u) Cholera=+Purity+u+ Purity = Mean+random variation+u Cov(Cholera,Z)= Cov(Purity,Z),Instrumental Variable Estimation,One “problem” variable the “last” one yit = 1x1it + 2x2it + + KxKit + it Eit|
9、xKit 0. (0 for all others) There exists a variable zit such that ExKit| x1it, x2it, xK-1,it,zit = g(x1it, x2it, xK-1,it,zit)In the presence of the other variables, zit “explains” xit Eit| x1it, x2it, xK-1,it,zit = 0In the presence of the other variables, zit and it are uncorrelated. A projection int
10、erpretation: In the projectionXkt =1x1it,+ 2x2it + + k-1xK-1,it + K zit, K 0.,Least Squares,The IV Estimator,A Moment Based Estimator,Consistency and Asymptotic Normality of the IV Estimator,Least Squares Revisited,Comparing OLS and IV,Cornwell and Rupert Data,Cornwell and Rupert Returns to Schoolin
11、g Data, 595 Individuals, 7 Years Variables in the file are EXP = work experience, EXPSQ = EXP2 WKS = weeks worked OCC = occupation, 1 if blue collar, IND = 1 if manufacturing industry SOUTH = 1 if resides in south SMSA = 1 if resides in a city (SMSA) MS = 1 if married FEM = 1 if female UNION = 1 if
12、wage set by unioin contract ED = years of education BLK = 1 if individual is black LWAGE = log of wage = dependent variable in regressions These data were analyzed in Cornwell, C. and Rupert, P., “Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators,“ Jou
13、rnal of Applied Econometrics, 3, 1988, pp. 149-155. See Baltagi, page 122 for further analysis. The data were downloaded from the website for Baltagis text.,Wage Equation with Endogenous Weeks,logWage=1+ 2 Exp + 3 ExpSq + 4OCC + 5 South + 6 SMSA + 7 WKS + Weeks worked is believed to be endogenous in
14、 this equation. We use the Marital Status dummy variable MS as an exogenous variable. Wooldridge Condition (5.3) CovMS, = 0 is assumed. Auxiliary regression: For MS to be a valid instrumental variable, In the regression of WKS on 1,EXP,EXPSQ,OCC,South,SMSA,MS, MS significantly “explains” WKS. A proj
15、ection interpretation: In the projection XitK =1 x1it + 2 x2it + + K-1 xK-1,it + K zit , K 0.(One normally doesnt “check” the variables in this fashion.,Auxiliary Projection (5.5),+-+ | Ordinary least squares regression | | LHS=WKS Mean = 46.81152 | +-+ +-+-+-+-+-+-+ |Variable | Coefficient | Standa
16、rd Error |b/St.Er.|P|Z|z | Mean of X| +-+-+-+-+-+-+Constant 45.4842872 .36908158 123.236 .0000EXP .05354484 .03139904 1.705 .0881 19.8537815EXPSQ -.00169664 .00069138 -2.454 .0141 514.405042OCC .01294854 .16266435 .080 .9366 .51116447SOUTH .38537223 .17645815 2.184 .0290 .29027611SMSA .36777247 .17284574 2.128 .0334 .65378151MS .95530115 .20846241 4.583 .0000 .81440576,
