计量经济分析（第六版）答案 final07.docx

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1、NYUtSTERNDepartment of EconomicsNEW YORK UNIVERSITY LEONARD N. STERN SCHOOL OF BUSINESSECONOMETRICS ITake Home Final ExaminationFall 2007Professor William GreenePhone: 212.998.0876Office: KMC 7-78Home page:ww.stern.nyu.edu/-wgreene e-mail: wgreenestern.nyu.eduURL for course web page:www.stern.nyu.ed

2、u/wgreene/Econometrics/Econometrics.htmToday is Tuesday, December 4, 2007. This exam is due by 3PM, Monday, December 17, 2007. You may submit your answers to me electronically as an attachment to an e-mail if you wish.Please do not include a copy of the exam questions with your submission; submit on

3、ly your answers to the questions.Your submission for this examination is to be a single authored project - you are assumed to be working alone.NOTE: In the empirical results below, a number of the form .nnnnnnE+aa means multiply the number .nnnnnn by 1() to the aa power. E-aa implies multiply 1() to

4、 the minus aa power. Thus, .123456E- 04 is 0.0000123456.This test comprises 150 points in two parts. Part I contains 10 questions, allocated 10 points per part, based on general econometric methods and theory as discussed in class. Part II asks you to dissect a recently published article that was do

5、cumented in the popular press.This course is governed by the Stern honor code:I will not lie, cheat or steal to gain an academic advantage, or tolerate those who do.Signature 6. We now return to the panel data set examined in question 2. The results below show OLS, fixed effects and random effects e

6、stimates.a. Test the hypothesis of no effects5 vs. some effects9 using the results given below.b. Explain in precise detail the difference between the fixed and random effects model.c. Carry out the Hausman test for fixed effects and report your conclusion. Carefully explain what you are doing in th

7、is test.d. In the context of the fixed effects model, test the hypothesis that there are no effects - i.e., that all ndividuals have the same constant term. (The statistics you need to carry out the test are given in the results.)OLS WithoutGroup Dummy VariablesOrdinaryleast squares regressionLHS=WA

8、GEMean2.296821Standard deviation=.5282364WTS=noneNumber of observs.17919Model sizeParameters=5Degrees of freedom=17914ResidualsSum of squares4120.874Standard error of e.4796212FitR-squared=.1757801Adjusted R-squared.1755961Model testF 4, 17914 (prob)955.12 (.0000)DiagnosticLog likelihood-12257.32Res

9、tricted(b=0)-13989.35Chi-sq 4 (prob)=3464.06 (.0000)Info criter.LogAmemiya Prd. Crt.=-1.469238Akaike Info. Criter.-1.469238+Panel DataAnalysis ofWAGEONE wayUnconditionalANOVA (Noregressors)SourceVariationDeg. Free.Mean SquareBetween2795.692177.1.28419Residual2204.0415741.140019Total4999.7317918.2790

10、34+I Variable I Coefficient | Standard Error |b/St.Er.|P|Z|z | Mean of X|+EXP|.03961671.0008969244.170.00008.36268765EDUC|.19746165.0171855011.490.000012.6760422EDSQ|-.00470726.00063536-7.409.0000164.377588EDAB|.00674776.0003773817.880.00001.60372621Constant|.22543337.115913271.945.0518+I Least Squa

11、res with Group Dummy Variables|Ordinaryleast squares regressionLHS=WAGEMean=2.296821Standard deviation =.5282364WTS=noneNumber of observs.=17919Model sizeParameters=2182Degrees of freedom =15737ResidualsSum of squares=1769.553Standard error of e =.3353287FitR-squared=.6460701Adjusted R-squared =.597

12、0187Model testF*z 15737 (prob)=13.17 (.0000)DiagnosticLog likelihood=-4683.510Restricted(b=0)=-13989.35Chi-sq *(prob) =* (. 0000)Info criter.LogAmemiya Prd. Crt.=-2.070380Akaike Info. Criter.=-2.071594Estd. Autocorrelation of e (i,t).226821+4-I Panel:Groups Empty0,Valid data2178 |ISmallest1,Largest1

13、5 IIAverage group size8.23 |+I Variable I Coefficient | Standard Error |b/St.Er.|P|Z|z | Mean of X|+EXP|.03865572.0007603850.838.00008.36268765EDUC|.23258879.047513254.895.000012.6760422EDSQ|-.00470394.00176606-2.664.0077164.377588EDAB|.02854571.008468803.371.00071.60372621+ITest Statistics for the

14、Classical Model|+I (1)I (2)I (3)I (4)ModelConstant term Group effects X - variablesLog-Likelihood only -13989.35052 only -6650 . 69444 only -12257.31866X and group effects-4683.50926Sum of Squares.4999725975D+04.2204037620D+04.4120873648D+04.1769552677D+04R-squared .0000000 .5591683 .1757801 .646070

15、1Hypothesis TestsLikelihood Ratio TestF Tests1Chi-squaredd.f.Prob.Fnum.denom.P value1 (2)vs (1) 14677.3122177.000009.172217715741.000001 (3)vs (1)3464.0644.00000955.123417914.000001 (4)vs (1) 18611.6832181.0000013.171218115737.000001 (4)vs (2)3934.3704.00000965.991415737.000001 (4)vs (3) 15147.61921

16、77.000009.605217715737.00000+I Random Effects Model: v (iz t) = e (i,t) + u (i)|IEstimates:Vare=.112445D+00|IVaru=.117591D+00|ICorrv(i,t),v(i,s)=.511185|I Lagrange Multiplier Test vs. Model (3) =17670.62 |I( 1 df, prob value=. 000000)|(High values of LMfavor FEM/REM overCRmodel.)|IBaltagi-Li form of

17、LMStatistic =7310.10|I Fixed vs. Random Effects (Hausman) =54.58 |I( 4 dfz prob value=. 000000)|I(High (low) valuesofH favor FEM(REM).)|ISum of Squares.417038D+04 |IR-squared.170935D+00 |+I Variable| Coefficient|Standard Error|b/St.Er. |P|Z|z |Mean ofX|+EXP|.03941919.0007205154.710.00008.36268765EDU

18、C|.18291694.028186366.490.000012.6760422EDSQ|-.00335822.00102860-3.265.0011164.377588EDAB|.00567682.000779907.279.00001.60372621Constant|.15385761.19080450.806.42007 The data listed on the next two pages of this exam are the Burnett data that are discussed in Section 21.6.6 in the 5th edition of you

19、r text and 23.8.4 in the 6th edition. The variable of interest in this part of this exam is y2, “presence of a womens studies program. Other variables are z2 = ranking, z3 二 size of the economics faculty, z4 = percent of the economics faculty that is female, z5 = religious affilitation and z6 二 perc

20、ent of women on the college faculty. Ignore the region dummy variables, z7 - zlO. (To transport the data to a statistical package, you can copy/paste them right out of this document into any other place as ASCII test. Of, you can download the data file from the website for the text. If you have prob

21、lems managing the data, get in touch with me and well work it out.)1. Your assigment is to estimate a binary choice model using these data. (You may fit a probit model or a logit model - your choice. Indicate in your report which form you used.) You are going to decide what variables are to be in th

22、e equation. Report your results. As part of your analysis, compute the partial effect on the probability of having a womens study program of having one more economist on the faculty. Report your result, and interpret it. Compute the partial effect of having a religious affiliation. Explain your comp

23、utations.8. Notice that the academic reputation variable suddenly jumps from 44 to 160. This is actually two groups of colleges. Your first model pools the full sample. Now, split the sample based on this variable, and compute the two probit models for the subsamples. Carry out a likelihood ratio te

24、st of the hypothesis that pooling is valid versus the alternative that separate models apply to the two subsamples. (Hint: The statistic is 2lnL(l) + lnL(2) - InL(pooled) and the number of degrees of freedom is the number of coefficients in the model.)z4z5z6z7z8z9Z10.20000.29120010.11000.27270010.20

25、000.30320010.37500.55090010.12500. 34690100.20000. 33890010.07100.28450010.09000.26750010.16600.31860010.31000.45520010.50000.45940010.11000.29330001.22000.42000010.25000.37300001.27000.31250010.06000.15380100.18700.25510010.14201.21101000.33000.39760010.12500.36840001.20000.32090010.00000.14701000.

26、25000.30770010.18000.29710010.33001.24700010.40000.54330010.25000.36990010.06601.28020010.31000.28340100.16600.36000010.37500.30000010.16700.34400100.66000.48600010.11000.24240010.20001.15731000.25000.34280010.50001.47360010.40000. 44400010.75001.88800010.18750.51360010.33000.31410010.00001.18050010

27、.42800.54540010.50001.60000010.16601.46370010.66001.68600010.14300.29400010.00001.13720010.20001.57690010.00000.460000101.00001.76590010.55001.47500010.66000.50770010.00001.25000010.00000.11900100.62501.64800100.00000.67000100.22000.37000100.27001.27000100.00001.20000100.00001.50000100.33001.5880010

28、0.40001.70370100.30001.41050100.20000.33680100.20001.28570100.00001.34480100.00001.13150100.11001.29480100.50001.30350100.37501.20330001.66000.73070001.28500.45760001.50001. 44000001309068041 z 2 1 1 11198o12yl y2 z2111111113113118118115111501511801801501131113112011201117011511171181129002411201124

29、01361120112401361129113301330129113611441044001600015201145101520014100162011520114500149001420114900143001520115201145001450014900162001440014711152001791114200156001430014700156011430014700145001470016400156011410014600147001440118100181000000000010000000000000000000001640 1901164017401520 1901159

30、01590145014311450147016411520 2131152015201521159016411420152014701470181115211740147114101500176oooooooooooooooooloooooo5 5 3 56 8 5 6loooooollooooool0000000015011410161017601530165014111.09001.276300012.50001.636000017.28501.556700014.25001.280000011.00001.310800014.00001.297300014.00000. 29500001

31、3.11001.246100017.14281.271100018.12500.210000015.20001.342800016.16601.145800015.40001.222000016.16600.196900015.40001.673900016.16600.200000012.00001.184600017.00001.208300015.00001.396000015.20001.163200018.12501.340900018.75001.666000016.66001.309000017.00000.183900018.25001.314800016.00000.2967

32、00013.33001.514700017.42801.161300016.16701.257100017.14301.231010004.50001.1818100014.42800.223510009.22001.335010004.75001.573710006.50000.288410008.12501. 476210006.16601.250010003.00001.297210004.25001.365010004.25001.222010006.16601.360010005.40001.372010005.20001.3804100021.00001.471410002.500

33、00.418610004.00000.228010008.25001.185710003.00001.413710003.00001.373610003.00001.646110006.67000.5604100010.10001.218010007.28501.2950100010.30001.315710003.00001.138810001.00001.483810005.20001.320710004.00001.150010008. This question involves a small amount of “library“ research. (You can do it

34、on the web, of course.) Locate an empirical (applied) paper (study) in any field (political science, economics, finance, management, accounting, pharmacology, environment, etc.) that is an application of the “sample selection (or “selectivity or “Heckmans” model. Report (a) what empirical issue the

35、study was about; (b) what the model was; (c) what estimation technique the author used; (d) (briefly) what results they obtained. In part (d), describe the actual statistics that the author reported, and what conclusion they drew. This entire essay should not exceed one double spaced page.9. In the

36、paper Convenient Estimators for the Panel Probit Model J the authors Michael Lechner and Irene Bertschuk propose to “simplify“ estimation of a binary choice model by making use of the relationshipEy|x= F(Pi + p2x).where y is a binary variable (such as Womens study program in the earlier question), x

37、 is an independent variable and F(.) is the probability model used for the binary choice. They suggest an instrumental variable style estimator, based on the set of orthogonality conditions suggested by1zlz2z3where zl, z2, and z3 are three instrumental variables.a. Explain how to use this model to o

38、btain GMM estimators of the model parameters. Be precise and detailed on the computations that you will do. Include in your description exactly what computations you will do to obtain the estimator and also how you will estimate the asymptotic covariance matrix of for your estimatorb. Note that there are two unknown parameters and 4 mome