哈佛大学计量经济学考试题-期末05.pdf

Department of Economics Economics 1123 Harvard University Fall 2005 Final Exam 2 15 p m Saturday January 21 2006 Instructions 1 Do not turn this page until so instructed 2 This exam is three hours long 3 The exam has five parts for a total of 100 points 4 Please put each question in a separate blue book five blue books total Put your name and Harvard ID number on the cover of each blue book 5 You are permitted one two sided 8 x 11 sheet of notes plus a calculator Computers and wireless devices are not permitted without prior permission You may not share resources with anyone else 6 Turn in this exam when you finish An electronic copy of the exam with answers will be posted on the course Web site in a few days and hard copies of the exam will be available when you pick up your graded blue books 7 Some questions ask you to draw a real world judgment in a problem of practical importance The quality of that judgment counts For example consider the question It is 10oF outside In your judgment why are so many people wearing heavy coats The answer To stay warm would receive more points than the answer Because they are fashion conscious 1 Background for Parts I and II Voting on Women s Issues Parts I and II examine the relationship between the gender of a U S representative s children and his her voting record on women s issues The data pertain to votes taken during the 105th Congress 1997 1998 each Congress lasts two years The observational unit is a U S representative House of Representatives only no senators There are 435 representatives but the study focuses on the 371 who have at least one child regressions with fewer than n 371 reflect some missing opinion survey data Among these 371 representatives with at least one child 89 are men and the mean age is 53 Two voting measures are considered The first Teen contraceptive is binary whether the representative voted to support a specific bill that would increase teenagers access to contraceptives The second NOW is a score ranging from 0 to 100 based on votes on multiple bills related to women s issues computed by the National Organization of Women NOW measuring the agreement between the representative s votes and the voting recommendations made by NOW 0 to 100 with 100 perfect agreement The data set contains variables that measure the characteristics of the representative s district and the results of a political opinion survey administered to voters in his her district Variables in the Voting Data Set Variable Definition Teen contraceptive 1 if the representative voted in favor of a specific bill increasing teen access to contraception 0 otherwise NOW Composite NOW voting score 0 complete disagreement with NOW s positions 100 complete agreement with NOW s positions Fraction daughters fraction of the representative s children who are female range is 0 to 1 District characteristics Registered Democrat proportion of voters registered as Democratic Party 0 to 1 District income median income in district thousands of dollars Fraction white fraction of district voters who are white 0 to 1 Fraction college grads fraction of district voters who are college graduates 0 to 1 District opinions Abortion should be legal fraction of survey respondents in district who agree 0 to 1 Women are equal to men fraction of survey respondents in district who agree 0 to 1 Anti crime spending should increase fraction of survey respondents in district who agree 0 to 1 Social service spending should increase fraction of survey respondents in district who agree 0 to 1 Should be laws to protect homosexuals from discrimination fraction of survey respondents in district who agree 0 to 1 2 The questions in Parts I and II refer to Table 1 Table 1 The Effect of Having Daughters on Representatives Votes 1 2 3 4 5 Dependent variable Teen contra ceptives Teen contra ceptives NOW NOW Fract daughters Estimation method Probit OLS OLS OLS OLS Regressors Intercept 0 51 0 10 0 38 0 06 40 2 4 1 38 6 2 3 0 07 0 29 Fraction daughters 0 36 0 12 0 13 0 05 6 18 2 67 6 01 2 86 District characteristics Registered Democrat 0 71 0 28 0 23 0 09 84 27 11 57 82 1 15 8 0 20 0 26 District income 0 21 0 20 0 00 0 00 Fraction white 8 6 9 5 0 08 0 19 Fraction college grads 108 5 77 7 1 72 1 58 District opinions Abortion should be legal 41 0 20 6 0 32 0 40 Women are equal to men 20 6 23 1 0 25 0 29 Anti crime spending should increase 30 2 18 7 0 82 0 52 Social service spending should increase 14 8 16 8 1 53 0 47 Should be laws to protect homosexuals from discrimination 10 2 13 9 0 06 0 36 N 371 371 371 331 331 F statistics testing that the coefficients on variables in a group are all zero District characteristics 0 93 0 46 1 10 0 36 District opinions 1 98 0 081 1 41 0 220 Notes Heteroskedasticity robust standard errors appear in parentheses under regression coefficients and p values appear in parentheses under F statistics The regressions are estimated using data on U S representatives during the 105th Congress 1997 1998 Significant at the 1 5 significance level 3 Questions for Part I 18 points Please answer these questions in Blue Book I 1 Interpret the coefficient on Fraction daughters in regression 2 3 points 2 Consider a representative with 2 daughters and 1 son from a district in which 55 of voters are registered Democrats a Using regression 1 compute the probability that this representative voted in favor of the bill on teen access to contraception 3 points b Using regression 2 compute the probability that this representative voted in favor of the bill on teen access to contraception 3 points 3 Does the coefficient on Fraction daughters change substantially in a real world sense from regression 3 to regression 4 What does this tell you about the additional variables that were included in regression 4 3 points 4 A critic asserts that a shortfall of this study is that it focuses exclusively on daughters indicating gender bias by the author The critic suggests adding one more regressor to regression 4 specifically Fraction sons which is the fraction of males among the representative s children What would be learned from this regression Be specific 3 points 5 Another critic suggests that more conservative districts might elect representatives with fewer daughters so that Fraction daughters is endogenous The author responds that regression 5 provides evidence against this hypothesis because Fraction daughters is with only one exception unpredictable by the other regressors and thus is exogenous Do you agree or disagree with the author s response Why Be precise 3 points 4 Questions for Part II 24 points Please answer these questions in Blue Book II 1 The following questions concern regression 4 a Provide a potential reason why the coefficient on district income in 4 is subject to omitted variable bias 2 points b Comment on the following statement Your answer to the previous question implies that the conditional mean of the error term in 4 is nonzero given the regressors in 4 Therefore the first least squares assumption is violated and the coefficient on Fraction daughters in 4 does not have a causal interpretation 3 points For the remaining questions suppose hypothetically that the data set is extended to be panel data for T 3 Congresses the 105th 1997 1998 106th 1999 2000 and 107th 2001 2002 Congresses The observational unit would be a representative his her votes children and district in a given Congressional session The data set would consist of all representatives who were elected to Congress for all three sessions Suppose n 300 so there is a total of 900 observations representatives are elected for two year terms and almost all who run for reelection are reelected 2 Representatives in the 105th Congress who retire are not reelected or die would be in the cross sectional data set used in Table 1 but would not be in the panel data set Would this introduce sample selection bias into the panel data estimate of the effect of Fraction daughters 3 points Regardless of your answer to question 2 for the rest of these questions ignore the possibility of sample selection bias 3 To what extent would including representative fixed effects address the endogeneity criticism Explain 3 points 4 Would it be appropriate to include time fixed effects in addition to representative fixed effects in the panel data regression Explain 3 points 5 Consider a hypothetical panel data version of regression 4 in Table 1 in which both representative fixed effects and time fixed effects are included Call this hypothetical regression P4 P for panel a What is the problem that is solved by clustered or HAC standard errors and how do clustered standard errors solve that problem 3 points b In regression P4 which would you recommend using conventional heteroskedasticity robust standard errors or clustered standard errors Explain with specific reference to regression P4 3 points c Suppose that the author estimated regression P4 using the standard errors you recommended in part b Using your judgment do you think that these standard errors in hypothetical panel regression P4 would be smaller larger or about the same as those in the cross section regression 4 in Table 1 Explain 3 points 5 Background to Parts III and IV Female Labor Supply Harvard economist Claudia Goldin attributes much of the rise of professional women in the U S labor force to their ability to engage in family planning after the introduction of the birth control pill In developing countries early childbearing is associated with lower levels of education and more dependency of women on their husband s earnings This question examines the effect of family size on female labor supply The data set consists of n 254 654 married women aged 21 35 as reported in the 1980 U S Census of the Population the data pertain to the full calendar year of 1979 Variables in the Female Labor Supply Data Set Variable Definition Wife s weeks worked No of weeks wife worked for pay in 1979 Husband s weeks worked No of weeks husband worked for pay in 1979 Same sex 1 if first two children have same sex 0 otherwise 2 boys 1 if first two children are boys 0 otherwise 2 girls 1 if first two children are girls 0 otherwise Kids 2 1 if family has more than 2 children 0 otherwise Boy first 1 if first child is a boy 0 otherwise Current age of mother age of mother in 1979 Age of mother at 1st birth age of mother at birth of first child Black 1 if black Hispanic 1 if Hispanic Other race 1 if nonwhite nonblack nonHispanic 6 The questions in Parts III and IV refer to Table 2 Table 2 Child Sex Composition Family Size and Labor Supply 1 2 3 4 5 6 Dependent variable Kids 2 Kids 2 Wife s weeks worked Wife s weeks worked Wife s weeks worked Husband s weeks worked Estimation method OLS OLS OLS TSLS TSLS TSLS Instruments Same sex 2 boys 2 girls Same sex Regressors Same sex 0694 0018 2 boys 0599 0026 2 girls 0789 0026 Kids 2 8 04 0 09 5 40 1 21 5 16 1 20 1 01 0 63 Boy first 0011 0019 0015 0026 0 05 0 08 0 02 0 08 0 02 0 08 0 03 0 08 Current age of mother 0304 0003 0304 0003 1 33 0 01 1 25 0 04 1 25 0 04 0 10 0 04 Age of mother at 1st birth 0436 0003 0436 0003 1 36 0 17 1 24 0 05 1 24 0 05 0 21 0 06 Black 0680 0042 0680 0042 10 83 0 19 10 66 0 21 10 64 0 21 4 10 0 26 Hispanic 1260 0039 1260 0039 0 04 0 18 0 38 0 23 0 41 0 23 2 61 0 23 Other race 0480 0044 0480 0044 2 82 0 20 2 70 0 21 2 69 0 21 2 02 0 18 N 254 654 254 654 254 654 254 654 254 654 254 654 F statistic on Same sex 1413 0 F statistic on 2 boys 2 girls 725 9 J statistic 3 24 Notes Regressions 4 5 and 6 are estimated by two stage least squares TSLS regression in which the included endogenous variable is Kids 2 Heteroskedasticity robust standard errors appear in parentheses under regression coefficients and p values appear in parentheses under F statistics All regressions include an estimated intercept which is not reported Regressions 1 5 are estimated using data on married women for 1979 regression 6 is estimated using data for the husbands of those married women Significant at the 1 5 significance level 7 Questions for Part III 21 points Please answer these questions in Blue Book III 1 Give the best reason you can why the OLS estimator of the coefficient on Kids 2 in Table 2 column 3 might be biased 3 points 2 Consider the hypothesis that on average U S parents want to have children of both genders that is they prefer at least one girl and one boy to all girls or all boys Does Table 2 provide evidence in favor of this hypothesis against this hypothesis or neither Explain 3 points 3 Consider the following potential instrumental variables for Kids 2 in regression 3 a Whether wife came from large family binary 3 points b The teen pregnancy rate in the wife s city or town of residence 3 points For each proposed instrument is the variable arguably a valid instrument variable Briefly explain 4 Based on a combination of your judgment and the empirical results in Table 2 a Is Same sex a valid instrument in regression 4 3 points b Is the pair of variables 2 boys and 2 girls a valid set of instruments in regression 5 3 points 5 The estimated coefficient on Kids 2 differs in regressions 3 and 4 the OLS estimate is more negative than the TSLS estimate Provide a real world explanation an interpretation of the results that explains why the OLS estimate is more negative than the TSLS estimate 3 points 8 Questions for Part IV 17 points Please answer these questions in Blue Book IV 1 Consider a hypothetical regression 7 Wife s weeks workedi 0 1Kids 2 ui 7 which would be estimated by TSLS using Same sex as an instrument so regression 7 is regression 4 without the variables Boy first Other race For this question assume that Same sex is a valid instrument in regression 4 and in addition that Same sex is distributed independently of all the control variables in regression 4 so E Boy first Same sex 0 E Other race Same sex 0 a Explain why Same sex would be a valid instrument in regression 7 3 points b Provide a reason why despite the validity of Same sex as an instrument in regression 7 you would still prefer regression 4 3 points 2 Some women are more ambitious professionally than others Suppose that the effect on labor force participation of having a large family is not the same for every woman specifically the more ambitious the woman the smaller is the effect the most ambitious women will work whether or not they have a large family How if at all would this change your interpretation of the results in regressions 4 and 5 Explain your reasoning 5 points Use Table 2 to comment on the following statements For each statement do you agree or disagree with the statement and explain why be specific 3 Families with large numbers of children tend to be unusual in certain ways in some cases coming from certain religious ethnic backgrounds traditional Catholic families Mormons etc So the analysis in regressions 4 and 5 is not providing a valid estimate of the effect of family size on labor supply it is just reflects this religious ethnic effect 3 points 4 Even though having large families reduces female labor force participation this is only half of the story because their husbands will work more to compensate for the loss of the wife s earnings 3 points 9 Background to Part V The Term Spread and Output Growth The U S Treasury issues bonds of different maturities A 10 year bond is debt that is paid off over 10 years A one year bond is debt that is paid off over one year Usually the rate of interest on a 10 year bond exceeds the rate of interest on a one year bond If short term interest rates are unusually high however then the rate of interest on a one year bond can exceed the rate of interest on a 10 year bond The difference between the rate of interest on a long term bond here the 10 year bond and the rate of interest a short term bond here the one year bond is called the Term Spread If the 10 year rate is 4 5 percent and the 1 year rate is 3 5 percent then the spread is 1 0 percentage points The Term Spread is often viewed as a measure of monetary policy If monetary policy is especially tight then short term interest rates are high relative to long term interest rates and the term spread is negative Over the past few months the Term Spread in the U S has fallen and just recently it became negative for the first time since the onset of the recession in 2000 The Term Spread data set contains quarterly time series data for the U S from the first quarter of 1960 1960 I through the third quarter of 2005 2005 III The data are plotted in Figure 1 Variables in Term Spread Data Set Variable Definition GDP growth quarterly growth rate of GDP expressed in percent at an annual rate computed using the logarithmic approximation GDP growth 400ln GDPt GDPt 1 where GDPt is the real Gross Domestic Product of the U S in quarter t Quarterly GDP is the total value of final goods and services produced in the United States in that quarter Term Spread the interest rate on a 10 year U S Treasury bill minus the interest rate on a 1 year U S Treasury bill Quarterly GDP growth at an annual rate time 1960q11972q31985q11997q32010q1 10 0 10 20 Term Spread 10 year minus 1 year time 1960q11972q31985q11997q32010q1 4 2 0 2 4 Figure 1 Time series plots of quarterly GDP growth and Term Spread 1960 I 2005 III 10 11 The questions in Part V refer to Table 3 Table 3 GDP Growth and the Term Spread Dependent variable GDP growtht 1 2 3 4 5 Sample period 1960 I 2005 III 1960 I 2005 III 1960 I 2005 III 1960 I 1984 IV 1985 I 2005 III Regressors Intercept 2 42 0 38 2 04 0 52 1 85 0 45 2 05 0 56 2 07 0 57 GDP growtht 1 0 27 0 08 0 24 0 08 0 26 0 07 0 23 0 10 0 25 0 12 GDP growtht 2 0 18 0 14 GDP growtht 3 0 06 0 08 GDP growtht 4 0 01 0 10 Term Spreadt 1 0 67 0 25 1 56 0 44 0 18 0 20 Quandt Likelihood Ratio QLR statistic p value in parentheses 1 18 0 41 1 71 0 32 5 37 0 03 2 59 0 26 2 88 0 24 T 183 183 183 100 83 SER 3 3 3 2 3 1 3 8 1 93 F statistic testing zero coefficients on GDP growtht 2 GDP growt