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Part 8: IV and GMM Estimation [ 1/48] Econometric Analysis of Panel Data William Greene Department of Economics Stern School of Business

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Part 8: IV and GMM Estimation [ 2/48] Dear 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.

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Part 8: IV and GMM Estimation [ 3/48] 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.

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Part 8: IV and GMM Estimation [ 4/48]

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Part 8: IV and GMM Estimation [ 5/48]

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Part 8: IV and GMM Estimation [ 6/48]

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Part 8: IV and GMM Estimation [ 7/48] Random Coefficients OrdProbs Model Dependent variable HSAT Log likelihood function Estimation based on N = 947, K = 14 Inf.Cr.AIC = AIC/N = Unbalanced panel has 250 individuals Ordered probit (normal) model LHS variable = values 0,1,...,10 Simulation based on 200 Halton draws | Standard Prob. 95% Confidence HSAT| Coefficient Error z |z|>Z* Interval |Nonrandom parameters Constant| *** AGE| *** EDUC|.05835*** |Scale parameters for dists. of random parameters Constant| *** |Standard Deviations of Random Effects R.E.(01)|.05759* |Threshold parameters for probabilities Mu(01)|.13522** Mu(09)| ***

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Part 8: IV and GMM Estimation [ 8/48] Agenda Single equation instrumental variable estimation Exogeneity Instrumental Variable (IV) Estimation Two Stage Least Squares (2SLS) Generalized Method of Moments (GMM) Panel data Fixed effects Hausman and Taylor’s formulation Application Arellano/Bond/Bover framework

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Part 8: IV and GMM Estimation [ 9/48] Structure and Regression

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Part 8: IV and GMM Estimation [ 10/48] Exogeneity

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Part 8: IV and GMM Estimation [ 11/48] An Experimental Treatment Effect

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Part 8: IV and GMM Estimation [ 12/48] Instrumental Variables Instrumental variable associated with changes in x, not with ε dy/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.

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Part 8: IV and GMM Estimation [ 13/48] Least Squares

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Part 8: IV and GMM Estimation [ 14/48] The IV Estimator

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Part 8: IV and GMM Estimation [ 15/48] A Moment Based Estimator

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Part 8: IV and GMM Estimation [ 16/48] Cornwell and Rupert Data Cornwell and Rupert Returns to Schooling Data, 595 Individuals, 7 Years Variables in the file are EXP = work experience, EXPSQ = EXP 2 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 regressions These 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.

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Part 8: IV and GMM Estimation [ 17/48] Wage Equation with Endogenous Weeks logWage=β 1 + β 2 Exp + β 3 ExpSq + β 4 OCC + β 5 South + β 6 SMSA + β 7 WKS + ε Weeks 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 projection X itK =θ 1 x 1it + θ 2 x 2it + … + θ K-1 x K-1,it + θ K z it, θ K ≠ 0. (One normally doesn’t “check” the variables in this fashion.

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Part 8: IV and GMM Estimation [ 18/48] Auxiliary Projection | Ordinary least squares regression | | LHS=WKS Mean = | |Variable | Coefficient | Standard Error |b/St.Er.|P[|Z|>z] | Mean of X| Constant EXP EXPSQ OCC SOUTH SMSA MS

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Part 8: IV and GMM Estimation [ 19/48] Application: 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] | Constant EXP EXPSQ D OCC SOUTH SMSA WKS

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Part 8: IV and GMM Estimation [ 20/48] Application: 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] | Constant EXP EXPSQ D OCC SOUTH SMSA WKS OLS WKS

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Part 8: IV and GMM Estimation [ 21/48] Generalizing the IV Estimator-1

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Part 8: IV and GMM Estimation [ 22/48] Generalizing the IV Estimator - 2

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Part 8: IV and GMM Estimation [ 23/48] Generalizing the IV Estimator

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Part 8: IV and GMM Estimation [ 24/48] The Best Set of Instruments

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Part 8: IV and GMM Estimation [ 25/48] Two Stage Least Squares

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Part 8: IV and GMM Estimation [ 26/48] 2SLS Estimator

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Part 8: IV and GMM Estimation [ 27/48] 2SLS Algebra

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Part 8: IV and GMM Estimation [ 28/48] A General Result for IV We defined a class of IV estimators by the set of variables The minimum variance (most efficient) member in this class is 2SLS (Brundy and Jorgenson(1971)) (rediscovered JW, 2000, p )

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Part 8: IV and GMM Estimation [ 29/48] GMM Estimation – Orthogonality Conditions

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Part 8: IV and GMM Estimation [ 30/48] GMM Estimation - 1

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Part 8: IV and GMM Estimation [ 31/48] GMM Estimation - 2

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Part 8: IV and GMM Estimation [ 32/48] IV Estimation

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Part 8: IV and GMM Estimation [ 33/48] An Optimal Weighting Matrix

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Part 8: IV and GMM Estimation [ 34/48] The GMM Estimator

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Part 8: IV and GMM Estimation [ 35/48] GMM Estimation

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Part 8: IV and GMM Estimation [ 36/48] Application - GMM NAMELIST; x = one,exp,expsq,occ,south,smsa,wks$ NAMELIST ; z = one,exp,expsq,occ,south,smsa,ms,union,ed$ 2SLS ; lhs = lwage ; RHS = X ; INST = Z $ NLSQ ; fcn = lwage-b1'x ; labels = b1,b2,b3,b4,b5,b6,b7 ; start = b ; inst = Z ; pds = 0$

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Part 8: IV and GMM Estimation [ 37/48] Application - 2SLS

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Part 8: IV and GMM Estimation [ 38/48] GMM Estimates

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Part 8: IV and GMM Estimation [ 39/48] 2SLS GMM with Heteroscedasticity

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Part 8: IV and GMM Estimation [ 40/48] Testing the Overidentifying Restrictions

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Part 8: IV and GMM Estimation [ 41/48] Inference About the Parameters

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Part 8: IV and GMM Estimation [ 42/48] Specification Test Based on the Criterion

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Part 8: IV and GMM Estimation [ 43/48] Extending the Form of the GMM Estimator to Nonlinear Models

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Part 8: IV and GMM Estimation [ 44/48] A Nonlinear Conditional Mean

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Part 8: IV and GMM Estimation [ 45/48] Nonlinear Regression/GMM NAMELIST; x = one,exp,expsq,occ,south,smsa,wks$ NAMELIST ; z = one,exp,expsq,occ,south,smsa,ms,union,ed$ ? Get initial values to use for optimal weighting matrix NLSQ ; lhs = lwage ; fcn=exp(b1'x) ; inst = z ; labels=b1,b2,b3,b4,b5,b6,b7 ; start=7_0$ ? GMM using previous estimates to compute weighting matrix NLSQ (GMM) ; fcn = lwage-exp(b1'x) ; inst = Z ; labels = b1,b2,b3,b4,b5,b6,b7 ; start = b ; pds = 0 $ (Means use White style estimator)

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Part 8: IV and GMM Estimation [ 46/48] Nonlinear Wage Equation Estimates NLSQ Initial Values

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Part 8: IV and GMM Estimation [ 47/48] Nonlinear Wage Equation Estimates 2 nd Step GMM

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Part 8: IV and GMM Estimation [ 48/48] IV for Panel Data

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