Presentation on theme: "Econometric Analysis of Panel Data"— Presentation transcript:
1Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business
2Dear Professor Greene, I have to apply multiplicative heteroscedastic models, that I studied in your book, to the analysis of trade data. Since I have not found any Matlab implementations, I am starting to write the method from scratch. I was wondering if you are aware of reliable implementations in Matlab or any other language, which I can use as a reference.
3a “multi-level” modelling feature along the following lines a “multi-level” modelling feature along the following lines? My data has a “two level” hierarchical structure: I'd like to perform an ordered probit analysis such that we allow for random effects pertaining to individuals and the organisations they work for.
12Instrumental Variables Instrumental variable associated with changes in x, not with εdy/dx = β dx/dx + dε /dx = β + dε /dx. Second term is not 0.dy/dz = β dx/dz + dε /dz. The second term is 0.β =cov(y,z)/cov(x,z) This is the “IV estimator”Example: Corporate earnings in year t Earnings(t) = β R&D(t) + ε(t) R&D(t) responds directly to Earnings(t) thus ε(t) A likely valid instrumental variable would be R&D(t-1) which probably does not respond to current year shocks to earnings.
16Cornwell and Rupert Data Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 Years Variables in the file areEXP = 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 wage set by unioin contract ED = years of education LWAGE = log of wage = dependent variable in regressionsThese data were analyzed in Cornwell, C. and Rupert, P., "Efficient Estimation with Panel Data: An Empirical Comparison of Instrumental Variable Estimators," Journal of Applied Econometrics, 3, 1988, pp See Baltagi, page 122 for further analysis. The data were downloaded from the website for Baltagi's text.
17Wage Equation with Endogenous Weeks logWage=β1+ β2 Exp + β3 ExpSq + β4OCC + β5 South + β6 SMSA + β7 WKS + εWeeks worked is believed to be endogenous in this equation.We use the Marital Status dummy variable MS as an exogenous variable.Wooldridge Condition (5.3) Cov[MS, ε] = 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 projection interpretation: In the projectionXitK =θ1 x1it + θ2 x2it + … + θK-1 xK-1,it + θK zit , θK ≠ 0.(One normally doesn’t “check” the variables in this fashion.
18Auxiliary Projection| Ordinary least squares regression || LHS=WKS Mean = ||Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X|ConstantEXPEXPSQOCCSOUTHSMSAMS
19Application: IV for WKS in Rupert | Ordinary least squares regression || Residuals Sum of squares = || Fit R-squared = || Adjusted R-squared = ||Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] |ConstantEXPEXPSQ DOCCSOUTHSMSAWKS
20Application: IV for wks in Rupert | LHS=LWAGE Mean = || Standard deviation = || Residuals Sum of squares = || Standard error of e = || Fit R-squared = || Adjusted R-squared = || Not using OLS or no constant. Rsqd & F may be < 0. ||Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] |ConstantEXPEXPSQ DOCCSOUTHSMSAWKSOLSWKS
28A General Result for IVWe defined a class of IV estimators by the set of variablesThe minimum variance (most efficient) member in this class is 2SLS (Brundy and Jorgenson(1971)) (rediscovered JW, 2000, p )