计量经济分析（第六版）答案 Notes-22.docx

Econometrics IProfessor William GreeneNotes 22. Two Step ML and GMM EstimationI. Two step estimationA. Setting, fitting a model which contains parameter estimates from another model.B. Typical application, inserting a prediction from one model into another.C. Procedures: How it*s done.D. Asymptotic results:1. Consistency2. Getting an appropriate estimator of the asymptotic covariance matrix3. The Murphy - Topel result (Next page)E. Application: Equation 1: Number of children Equation 2: Labor force participationII. GMM estimationA. "Moment Equations11 Examples:1. From familiar estimation settings:a. Least squaresb. Instrumental variablesc. Maximum likelihood estimation2. From behavioral models:E(ct - some expectation) | some set of variables in an information set = 0 What does this imply?B. The Method of Moments. Solving the moment equations1. Exactly identified cases2. Overidentified casesC. Consistency. How do we know the method of moments is consistent?D. Asymptotic covariance matrix.E. Consistent vs. Efficient estimation1. A weighting matrix2. The minimum distance estimator3. What is the efficient weighting matrix?4. Estimating the weighting matrix.F. The Generalized method of moments estimator - how it is computed.G. Computing the appropriate asymptotic covariance matrixIII. Testing Hypotheses in the GMM framework.A. Testing hypotheses about the parameters:1. Wald Test2. A counterpart to the likelihood ratio testB. Testing the overidentifying restrictionsIV. Application (Monday)? Data transformations. Number of kids, scale income variables * Create ; Kids = kl6 + k618;income = faminc/10000 ;Wifeinc = ww*whrs/1000 $? Equation 1, number of kids. Standard Poisson fertility model.? Fit equation, collect parameters Thetal and covariance matrix VI ? compute fitted values. Namelist; Z = one,wa,we,income,wifeinc$ Poisson ; Lhs = kids;Rhs = Z $Matrix ; Thetal = b ;VI = VARB $Create ; ExpKids = Exp(Z1Thetal) $ ? Set up probit labor force participation model ? Compute probit model and collect results. Gamma = coefficient on ? fitted number of kids. Collect Theta2 and V2 as above.Namelist; X = one,wa,we,ha,he,income $Namelist; XF = X,ExpKids $ Probit ; Lhs = Ifp;Rhs = X,ExpKids $ Calc ; gamma = b(kreg) $ Matrix ; Theta2 = b;V2 = VARB $Create ; bxf = Xf1Theta2 $ *? Poisson log likelihood Zi (kidSiXZi10i - exp(Ziz0i) - logkidsi!)? Derivative of term with respect to 0 is (kidSi - exp (Zii) ) xzi *Create ; gl = Kids - ExpKids $ *? Probit, logL = 2 (lfp=0) log(-P* - y exp (Zi'Oi)?+E (lfp=l) log(+0'Xi + y exp(Zi。)? Obtain this with one term by using 2*lfp - 1 = -1 or +1 for 0 or 1.? This is the derivative with respect to the argument of .;g2 = (2*lfp-l)*N01(bxf)/Phi(2*lfp-l)*bxf) ? These are the terms that are used to compute R and C. ?* Typo in your text. Delete (1/n) in C-hat and R-hat on page 135.;vc = g2 * g2*gamma*ExpKids;vr = g2 * gl $? Compute matrix products and report resultsMatrix ; R = Xf1vrZ;C = Xf1vcZ;Q = C*Vl*Cf - R*Vl*Cf - C*Vl*Rf;V2s = V2 + V2*Q*V2;Stat(Theta2fV2s)$+I Poisson RegressionKIDS|ONE|250|7|-367.9654|-432.0402|128.1496|4|.0000000|RsqP= .2720|RsqD= .3108|+I Maximum Likelihood Estimates I Dependent variableI Weighting variableI Number of observationsI Iterations completedI Log likelihood functionI Restricted log likelihoodI Chi-squaredI Degrees of freedomI Significance levelI Chi- squared =263.00713I G - squared =284.19970+I Variable|Coefficient|Standard Error|b/St.Er. |P|Z|>z|Mean ofX|+Constant3.436586649.430037867.991.0000WA6765766674E-01.67769033E-02-9.984.0000WE1957100726E-01.27310844E-01-.717.4736INCOME.6461865674E-01.38825572E-011.664.0960WIFEINC4622239565E-01.14329665E-01-3.226.0013(Note: E+nnor E-nn meansmultiply by 10to + or -rm power.)42.92000012.3520002.30625403.1035352+I Binomial ProbitModel|I Maximum LikelihoodEstimates|IDependent variableLFP|IWeighting variableONE|INumber of observations250|IIterations completed6IILog likelihood function-132.0586|IRestricted log likelihood-168.2529|IChi-squared72.38862|IDegrees of freedom6IISignificance level.0000000|+I Variable | Coefficient | Standard Error |b/St.Er.|P|Z|>z | Mean of X| +Index function for probabilityConstant12.884250152.09230216.158.0000WA-.2114374146.37956821E-01-5.570.000042.920000WE.6868897361E-01.55472307E-011.238.215612.352000HA-.1926323530E-01.22665533E-01-.850.395445.024000HE-.1057757370E-01.37641934E-01-.281.778712.536000INCOME.1020796842.79918260E-011.277.20152.3062540EXPKIDS-2.197363852.31891089-6.890.00001.6000000-> Matrix ; R = Xf»vrZ;C = Xf'vcZ;Q = C*V1*C! - R*V1*C' - C*V1*R*;V2s = V2 + V2*Q*V2;Stat(Theta2zV2s)$Matrix statistical results: Coefficients=THETA2Variance=V2S+|Variable | Coefficient | Standard Error |b/St.Er.|P|Z|>z |+THETA_112.884250152.81455324.578.0000THETA12-.2114374146.43778989E-01-4.830.0000THETA13.6868897361E-01.93577162E-01.734.4629THETa14-.1926323530E-01.23485205E-01-.820.4121THETA5-.1057757370E-01.47240796E-01-.224.8228THETA6.1020796842.20901593.488.6253THETA_7-2.197363852.49750060-4.417.0000