计量经济学实证练习答案

1、PART TWOSolutions to EmpiricalExercisesChapter 3Review of Statistics1.Solutions to Empirical Exercises(a)Average Hourly Earnings, Nominal $sMeanSE(Mean)95% Confidence Interval11.50 11.7516.58 16.9695% Confidence Interval 4.91 5.37AHE1992AHE200411.6316.77Difference 5.140.0640.098SE(Difference) 0.117A

2、HE2004 AHE1992(b)Average Hourly Earnings, Real $2004MeanSE(Mean)95% Confidence IntervalAHE1992AHE200415.6616.77Difference 1.110.0860.098SE(Difference) 0.13015.49 15.8216.58 16.9695% Confidence Interval 0.85 1.37AHE2004 AHE1992(c)(d)The results from part (b) adjust for changes in purchasing power. Th

3、ese results should be used.Average Hourly Earnings in 2004MeanSE(Mean)95% Confidence IntervalHigh SchoolCollege13.8120.31Difference 6.500.1020.158SE(Difference) 0.18813.61 14.0120.00 20.6295% Confidence Interval 6.13 6.87College High SchoolSolutions to Empirical Exercises in Chapter 3109(e)Average H

4、ourly Earnings in 1992 (in $2004)MeanSE(Mean)95% Confidence IntervalHigh SchoolCollege13.4819.07Difference 5.590.0910.148SE(Difference) 0.17313.30 13.6518.78 19.3695% Confidence Interval 5.25 5.93College High School(f)Average Hourly Earnings in 2004MeanSE(Mean)95% Confidence IntervalAHEHS,2004 AHEHS

5、,1992AHECol,2004 AHECol,19920.06 0.600.330.1371.240.2170.82 1.665.25 5.936.13 6.8795% Confidence Interval 0.41 1.41ColHS Gap (1992)ColHS Gap (2004)5.596.50Difference 0.910.1730.188SE(Difference) 0.256Gap2004 Gap1992Wages of high school graduates increased by an estimated 0.33 dollars per hour (with

6、a 95% confidence interval of 0.06 0.60); Wages of college graduates increased by an estimated 1.24 dollars per hour (with a 95% confidence interval of 0.82 1.66). The College High School gap increased by an estimated 0.91 dollars per hour.(g)Gender Gap in Earnings for High School GraduatesYearsmnmsw

7、nwYm YwSE( Ym Yw )95% CIYmYw1992200414.5714.886.557.162770277211.8611.925.215.39187015742.712.960.1730.1922.37 3.052.59 3.34There is a large and statistically significant gender gap in earnings for high school graduates. In 2004 the estimated gap was $2.96 per hour; in 1992 the estimated gap was $2.

8、71 per hour(in $2004). The increase in t it is for college graduates.der gap is somewhat smaller for high school graduates thanChapter 4Linear Regression with One RegressorSolutions to Empirical Exercises·AHE 3.32 0.45 u AgeEarnings increase, o1.(a)age, by 0.45 dollars per hour when workers age

9、 by 1 year.Bobs predicted earnings 3.32 0.45 u 26 $11.70 Alexiss predicted earnings 3.32 0.45 u 30 $13.70The R2 is 0.02.This mean that age explains a small fraction of the variability in earnings across individuals.(b)(c)2.(a)5432-2-10Beauty Index12There appears to be a weak positive relationship be

10、tween course evaluation and the beauty index. C·ourse _ Eval 4.00 0.133 u Beauty. The variable Beauty has a mean that is equal to 0; the estimated intercept is the mean of the dependent variable (Course_Eval) minus the estimated slope (0.133) times the mean of the regressor (Beauty). Thus, the

11、estimated intercept is equalto the mean of Course_Eval.The standard deviation of Beauty is 0.789. ThusProfessor Watsons predicted course evaluations 4.00 0.133 u 0 u 0.789 4.00Professor Stocks predicted course evaluations 4.00 0.133 u 1 u 0.789 4.105(b)(c)Course EvaluationSolutions to Empirical Exer

12、cises in Chapter 4111(d)The standard deviation of course evaluations is 0.55 and the standard deviation of beauty is 0.789. A one standard deviation increase in beauty is expected to increase course evaluation by0.133 u 0.789 0.105, or 1/5 of a standard deviation of course evaluations. The effect is

13、 small. The regression R2 is 0.036, so that Beauty explains only 3.6% of the variance in course evaluations.(e)E¶d 13.96 0.073 u Dist. The regression predicts that if colleges are built 103.(a)rto wheres go to high school, average years of college will increase by 0.073 years.Bobs predicted yea

14、rs of completed education 13.96 0.073 u 2 13.81(b)from college 13.96 0.073 uBobs predicted years of completed education if he was 10 1 13.89The regression R2 is 0.0074, so that distance explains only a very small fraction of years of(c)completed education. SER 1.8074 years.(d)(a)4.105Growth0-50.51Tr

15、ade Share1.52Yes, there appears to be a weak positive relationship. Malta is the “outlying” observation with a trade share of 2. G·rowth 0.64 2.31 u TradesharePredicted growth 0.64 2.31 u 1 2.95 G·rowth 0.96 1.68 u Tradeshare Predicted growth 0.96 1.68 u 1 2.74Malta is an island nation in

16、the Mediterranean Sea, south of Sicily. Malta is a freight transport(b)(c)(d)(e)site, which explains its large “trade share”. Many goods cointo Malta (imports into Malta)and immediately transported to other countries (as exports from Malta). Thus, Maltas importsand exports and unlike the imports and

17、 exports of most other countries. Malta should not be included in the analysis.Chapter 5Regression with a Single Regressor: Hypothesis Tests and Confidence IntervalsSolutions to Empirical Exercises(a) ·AHE 3.32 0.45 u Age(0.97) (0.03)The t-statistic is 0.45/ 0.03 13.71, which has a p-value of 0

18、.000, so the null hypothesis can be rejected at the 1% level (and thus, also at the 10% and 5% levels).1.0.45 r 1.96 u 0.03 0.387 to 0.517·AHE 6.20 0.26 u Age(1.02) (0.03)The t-statistic is 0.26/ 0.03 7.43, which has a p-value of 0.000, so the null hypothesis can be rejected at the 1% level (an

19、d thus, also at the 10% and 5% levels).·AHE 0.23 0.69 u Age(1.54) (0.05)The t-statistic is 0.69/ 0.05 13.06, which has a p-value of 0.000, so the null hypothesis can be rejected at the 1% level (and thus, also at the 10% and 5% levels).(b)(c)(d)E- EThe difference in the estimated E1 coefficient

20、s is 0.69 0.26 0.43. The(e)1,College1,HighScoolstandard error of for the estimated difference is SE (E- E) (0.032 0.052)1/2 1,College1,HighScool0.06, so that a 95% confidence interval for the difference is 0.43 r 1.96 u 0.06 0.32 to 0.54(dollars per hour).C·ourse _ Eval 4.00 0.13u Beauty(0.03)

21、(0.03)The t-statistic is 0.13/ 0.03 4.12, which has a p-value of 0.000, so the null hypothesis can be rejected at the 1% level (and thus, also at the 10% and 5% levels).2.(a) E¶d 13.96 0.073 u Dist(0.04) (0.013)The t-statistic is 0.073/0.013 5.46, which has a p-value of 0.000, so the null hypot

22、hesis can be rejected at the 1% level (and thus, also at the 10% and 5% levels).(b) The 95% confidence interval is 0.073 r 1.96 u 0.013 or 0.100 to 0.047.(c) E¶d 13.94 0.064 u Dist(0.05) (0.018)3.Solutions to Empirical Exercises in Chapter 5113(d) E¶d 13.98 0.084 u Dist(0.06) (0.013)E- E(e

23、) The difference in the estimated E1 coefficients is 0.064 ( 0.084) 0.020.1,Female1,MaleThe standard error of for the estimated difference is SE (E- E) (0.0182 0.0132)1/2 1,Female1,Male0.022, so that a 95% confidence interval for the difference is 0.020 r 1.96 u 0.022 or 0.022 to0.064. The differenc

24、e is not statistically different.Chapter 6Linear Regression with Multiple Regressors1.Solutions to Empirical ExercisesRegressions used in (a) and (b)MabRegressorBeauty Intro OneCredit Female Minority NNEnglish Intercept0.1330.1660.0110.634 0.173 0.167 0.244 4.074.00SERR20.5450.0360.5130.155(a)(b)The

25、 estimated slope is 0.133The estimated slope is 0.166. The coefficient does not change by an large amount. Thus, there does not appear to be large omitted variable bias.Professor Smiths predicted course evaluation (0.166 u 0) 0.011 u 0) (0.634 u 0) (0.173 u0) (0.167 u 1) (0.244 u 0) 4.068 3.901(c)2.

26、Estimated regressions used in question MRegressora 0.073b 0.032dist bytest female black hispanic incomehi ownhome dadcoll cue80 stwmfg80 intercept0.0930.1450.3670.3980.3950.1520.6960.023 0.051 8.82713.956SER R2R21.810.0070.0071.840.2790.277Solutions to Empirical Exercises in Chapter 6115 0.073 0.032

27、The coefficient has fallen by more than 50%. Thus, it seems that result in (a) did suffer from omitted variable bias.The regression in (b) fits the data much better as indicated by the R2, R2, and SER. The R2 and(a)(b)(c)(d)R2are similar because the number of observations is large (n 3796).s with a

28、“dadcoll 1” (so that the(e)s father went to college) complete 0.696 mores with “dadcoll 0” (so that theyears of education, o not go to college).age, thans father did(f)These terms capture the opportucost of attending college. As STWMFG increases, forgonewages increase, so that, oage, college attenda

29、nce declines. The negative sign on thecoefficient is consistent with this. As CUE80 increases, it is more difficult to find a job, whichlowers the opportucost of attending college, so that college attendance increases. Thepositive sign on the coefficient is consistent with this.Bobs predicted years

30、of education 0.0315 u 2 0.093 u 58 0.145 u 0 0.367 u 1 0.398 u0 0.395 u 1 0.152 u 1 0.696 u 0 0.023 u 7.5 0.051 u 9.75 8.827 14.75Jims expected years of education is 2 u 0.0315 0.0630 less than Bobs. Thus, Jims expected years of education is 14.75 0.063 14.69.(g)(h)3.Standard DeviationVariableMeanUn

31、itsgrowth rgdp60 tradeshare yearsschool rev_coups assasinations1.8631310.5423.950.1700.2811.8225230.2292.550.2250.494Percentage Points$1960unit yearscoups per year assasinations per yearoil0001 indicator variable (b)Estimated Regression (in table format):RegressorCoefficient tradeshare1.34(0.88)0.56

32、* (0.13) 2.15* (0.87)0.32(0.38) 0.00046* (0.00012)0.626(0.869)1.590.290.23yearsschoolrev_coupsassasinationsrgdp60interceptSER R2R2116Stock/Watson - Introduction to Econometrics - Second EditionThe coefficient on Rev_Coups is í2.15. An additional coup in a five year period, reduces the average y

33、ear growth rate by (2.15/5) = 0.43% over this 25 year period. This means the GPD in 1995 is expected to be approximately .43×25 = 10.75% lower. This is a large effect.(c) The 95% confidence interval is 1.34 r 1.96 u 0.88 or 0.42 to 3.10. The coefficient is not statistically significant at the 5

34、% level.(d) The F-statistic is 8.18 which is larger than 1% critical value of 3.32.Chapter 7Hypothesis Tests and Confidence Intervals in Multiple RegressionSolutions to Empirical ExercisesEstimated Regressions1.MRegressorabAge0.45(0.03)0.44(0.03) 3.17 (0.18)6.87(0.19)FemaleBachelorIntercept3.32(0.97

35、)SER R2R28.660.0230.0227.880.1900.190(a)(b)The estimated slope is 0.45The estimated marginal effect of Age on AHE is 0.44 dollars per year. The 95% confidence interval is 0.44 r 1.96 u 0.03 or 0.38 to 0.50.The results are quite similar. Evidently the regression in (a) does not suffer from important

36、omitted variable bias.Bobs predicted average hourly earnings 0.44 u 26 3.17 u 0 6.87 u 0 3.32 $11.44Alexiss predicted average hourly earnings 0.44 u 30 3.17 u 1 6.87 u 1 3.32 $20.22 The regression in (b) fits the data much better. Gender and education are important predictors of(c)(d)(e)earnings. Th

37、e R2 andare similar because the sample size is large (n 7986).R2(f)Gender and education are important. The F-statistic is 752, which is (much) larger than the 1% critical value of 4.61.The omitted variables must have non-zero coefficients and must correlated with the included regressor. From (f) Fem

38、ale and Bachelor have non-zero coefficients; yet there does not seemto be important omitted variable bias, suggesting that the correlation of Age and Female and Ageand Bachelor is small. (The sample correlations are C· or (Age, Female) 0.03 andCor (Age,Bachelor) 0.00).(g)118Stock/Watson - Intro

39、duction to Econometrics - Second Edition2.MRegressorabcBeauty0.13* (0.03)0.17* (0.03)0.01(0.06)0.63* (0.11) 0.17* (0.05) 0.17* (0.07) 0.24* (0.09)4.07* (0.04)0.17(0.03)IntroOneCredit0.64* (0.10) 0.17* (0.05) 0.16* (0.07) 0.25* (0.09)4.07* (0.04)FemaleMinorityNNEnglishIntercept4.00* (0.03)SER R2R20.5

40、450.0360.0340.5130.1550.1440.5130.1550.1450.13 r 0.03 u 1.96 or 0.07 to 0.20See the table above. Intro is not signific(a)(b)n (b), but the other variables are significant.A reasonable 95% confidence interval is 0.17 r 1.96 u 0.03 or 0.11 to 0.23.Solutions to Empirical Exercises in Chapter 71193.MReg

41、ressor(a)(b)(c)dist 0.073* (0.013) 0.031* (0.012)0.092* (0.003)0.143* (0.050)0.354* (0.067)0.402* (0.074)0.367* (0.062)0.146* (0.065)0.570* (0.076)0.379* (0.084)0.024* (0.009) 0.050* (0.020) 0.033* (0.013)0.093* (.003)0.144* (0.050)0.338* (0.069)0.349* (0.077)0.374* (0.062)0.143* (0.065)0.574* (0.07

42、6)0.379* (0.084)0.028* (0.010) 0.043* (0.020)0.0652(0.063) 0.184 (0.099)8.893* (0.243)bytestfemaleblackhispanicincomehiownhomedadcollmomcollcue80stwmfg80urbantuitionintercept13.956* (0.038)8.861* (0.241)F-statitisticfor urban and tuition SERR2R21.810.0070.0071.540.2820.2811.540.2840.281(a) The group

43、s claim is that the coefficient on Dist is 0.075 ( 0.15/2). The 95% confidence forEDist from column (a) is 0.073 r 1.96 u 0.013 or 0.099 to 0.046. The groups claim is included in the 95% confidence interval so that it is consistent with the estimated regression.120Stock/Watson - Introduction to Econ

44、ometrics - Second Edition(b) Column (b) shows the base specification controlling for other important factors. Here the coefficient on Dist is 0.031, much different than the results from the simple regression in (a);when additional variables aded (column (c), the coefficient on Dist changes little fr

45、om theresult in (b). From the base specification (b), the 95% confidence interval for EDist is 0.031 r1.96 u 0.012 or 0.055 to 0.008. Similar results are obtained from the regression in (c).(c) Yes, the estimated coefficients EBlack and EHispanic are positive, large, and statistically significant.Ch

46、apter 8Nonlinear Regression Functions1.Solutions to Empirical ExercisesThis table contains the results from seven regressions that are referenced in these answers.Data from 2004(1)(2)(3)(4)(5)(6)(7)(8)Dependent VariableAHEln(AHE)ln(AHE)ln(AHE)ln(AHE)ln(AHE)ln(AHE)ln(AHE)Age0.439* (0.030)0.024* (0.00

47、2)0.147* (0.042) 0.0021* (0.0007)0.146* (0.042) 0.0021* (0.0007)0.190* (0.056) 0.0027* (0.0009)0.117* (0.056) 0.0017 (0.0009)0.160(0.064) 0.0023 (0.0011)Age2ln(Age)0.725* (0.052)Female u Age 0.097 (0.084)0.0015(0.0014) 0.123 (0.084)0.0019(0.0014)0.091(0.084) 0.0013 (0.0014)1.764(1.239)Female u Age2B

48、achelor u Age0.064(0.083) 0.0009 (0.0014) 0.210* (0.014)Bachelor u Age2 3.158* (0.176)6.865* (0.185) 0.180* (0.010) 0.180* (0.010) 0.180* (0.010) 0.210* (0.014)Female1.358* (1.230)Bachelor0.405* (0.010)0.405* (0.010)0.405* (0.010)0.378* (0.014)0.064* (0.021)0.078(0.612)0.378* (0.014)0.063* (0.021) 0

49、.633 (0.819) 0.769 (1.228)0.066* (0.021)0.604(0.819) 1.186 (1.239)0.066* (0.021) 0.095 (0.945)Female u BachelorIntercept1.884(0.897)1.856* (0.053)0.128(0.177)0.059(0.613)F-statistic and p-values on joint hypotheses(a) F-statistic on terms involving Age(b) Interaction terms with Age and Age2SERR 298.

50、54(0.00)100.30(0.00)51.42(0.00)4.12(0.02)0.4560.194353.04(0.00)7.15(0.00)0.4560.195036.72(0.00)6.43(0.00)0.4560.19597.8840.18970.4570.19210.4570.19240.4570.19290.4570.1937Significant at the *5% and *1% significance level.122Stock/Watson - Introduction to Econometrics - Second Edition(a)The regressio

51、n results for this question are shown in column (1) of the table. If Age increases from 25 to 26, earnings are predicted to increase by $0.439 per hour. If Age increases from 33 to 34, earnings are predicted to increase by $0.439 per hour. These values are the same because the regression is a linear

52、 function relating AHE and Age.The regression results for this question are shown in column (2) of the table. If Age increases from 25 to 26, ln(AHE) is predicted to increase by 0.024. This means that earnings are predicted to increase by 2.4%. If Age increases from 34 to 35, ln(AHE) is predicted to

53、 increase by 0.024. This means that earnings are predicted to increase by 2.4%. These values, in percentage terms, are the same because the regression is a linear function relating ln(AHE) and Age.The regression results for this question are shown in column (3) of the table. If Age increases from 25 to 26, then ln(Age) has increased by ln(26) ln(25) 0.0392 (or 3.92%). The predicted increase in ln(AHE) is 0.725 u (.0392) 0.0284. This means that earnings are predicted to increa