Questions and Answers of Econometrics

13.5 Consider a study to evaluate the effect on college student grades of dorm room Internet connections. In a large dorm, half the rooms are randomly wired for high-speed Internet connections (the
13.4 Read the box “What Is the Effect on Employment of the Minimum Wage?” in Section 13.4. Suppose, for concreteness, that Card and Krueger collected their data in 1991 (before the change in the
13.3 Suppose in a randomized controlled experiment of the effect of a SAT preparatory course on SAT scores, the following results are reported:a. Estimate the average treatment effect on test
13.2 For the following calculations, use the results in column (3) of Table 13.2.Consider two classrooms, A and B, with identical values of the regressors in column (3) of Table 13.2, except that:a.
13.1 How would you calculate the small class treatment effect from the results in Table 13.1. Can you distinguish this treatment effect from the aide treatment effect? How would you change the
13.5 Consider the quasi-experiment described in Section 13.4 involving the draft lottery, military service, and civilian earnings. Explain why there might be heterogeneous effects of military service
13.4 What are experimental effects? How can they create biased treatment effects and what can a researcher do to reduce the bias?
13.3 Researchers studying the STAR data report anecdotal evidence that school principals were pressured by some parents to place their children in the small classes. Suppose that some principals
13.2 A clinical trial is carried out for a new cholesterol-lowering drug. The drug is given to 500 patients, and a placebo is given to another 500 patients, using random assignment of the patients.
13.1 A researcher studying the effects of a new fertilizer on crop yields plans to carry out an experiment in which different amounts of the fertilizer are applied to 100 different 1-acre parcels of
E12.3 (This requires Appendix 12.5) On the textbook website, www.pearsonglobaleditions.com/Stock_Watson, you will find the data set WeakInstrument which contains 200 observations on (Yi, Xi, Zi) for
E12.2 Does viewing a violent movie lead to violent behavior? If so, the incidence of violent crimes, such as assaults, should rise following the release of a violent movie that attracts many viewers.
E12.1 How does fertility affect labor supply? That is, how much does a woman’s labor supply fall when she has an additional child? In this exercise you will estimate this effect using data for
12.10 Consider the instrumental variable regression model Yi = b0 + b1Xi +b2Wi + ui, where Zi is an instrument. Suppose that data on Wi are not available and the model is estimated omitting Wi from
12.9 A researcher is interested in the effect of military service on human capital.He collects data from a random sample of 4000 workers aged 40 and runs the OLS regression Yi = b0 + b1Xi + ui, where
12.8 Consider a product market with a supply function Qsi= b0 + b1Pi + usi, a demand function Qdi= g0 + udi, and a market equilibrium condition Qsi= Qdi, where usi and udi are mutually independent
12.7 In an instrumental variable regression model with one regressor, Xi, and two instruments, Z1i and Z2i, the value of the J-statistic is J = 2.2.a. Does this suggest that E(ui 0Z1i, Z 2i) 0?
12.6 In an instrumental variable regression model with one regressor, Xi, and one instrument, Zi, the regression of Xi onto Zi has R2 = 0.1 and n = 50.Is Zi a strong instrument? [Hint: See Equation
12.5 Consider the instrumental variable regression model Yi = b0 + b1Xi + b2Wi + ui, where Xi is correlated with ui and Zi is an instrument. Suppose that the first three assumptions in Key Concept
12.4 Consider TSLS estimation with a single included endogenous variable and a single instrument. Then the predicted value from the first-stage regression is X ni = pn 0 + pn 1Zi. Use the definition
12.3 A classmate is interested in estimating the variance of the error term in Equation (12.1).a. Suppose that she uses the estimator from the second-stage regression of TSLS: sn 2a= 1 n - 2gni= 1(Yi
12.2 Consider the regression model with a single regressor: Yi = b0 + b1Xi + ui.Suppose that the least squares assumptions in Key Concept 4.3 are satisfied.a. Show that Xi is a valid instrument. That
12.1 This question refers to the panel data regressions summarized in Table 12.1.a. Suppose that the Federal Government is considering a new tax on cigarettes that is estimated to increase the retail
12.4 In their study of the effectiveness of cardiac catheterization, McClellan, McNeil, and Newhouse (1994) used as an instrument the difference in distance to cardiac catheterization and regular
12.3 In his study of the effect of incarceration on crime rates, suppose that Levitt had used the number of lawyers per capita as an instrument. Would this instrument be relevant? Would it be
12.2 Describe the key characteristics of a valid instrument. If you were a researcher, how would you determine if the variable you have selected as an instrument for an endogenous regressor is valid
12.1 In the demand curve regression model of Equation (12.3), is ln(Pbutter i )positively or negatively correlated with the error, ui? If b1 is estimated by OLS, would you expect the estimated value
E11.2 Believe it or not, workers used to be able to smoke inside office buildings.Smoking bans were introduced in several areas during the 1990s. In addition to eliminating the externality of
E11.1 In April 2008 the unemployment rate in the United States stood at 5.0%.By April 2009 it had increased to 9.0%, and it had increased further, to 10.0%, by October 2009. Were some groups of
11.11 (Refer to Appendix 11.3) Which model would you use for:a. A study explaining the number of hours spent by a person working for income during a week.b. A study explaining the level of
11.10 (Requires Section 11.3 and calculus) Suppose that a random variable Y has the following probability distribution: Pr(Y = 1) = p, Pr(Y = 2) = q, and Pr(Y = 3) = 1 - p - q. A random sample of
11.9 Use the estimated linear probability model shown in column (1) of Table 11.2 to answer the following:a. Two applicants—one self-employed and one salaried—apply for a mortgage. They have the
11.8 Consider the linear probability model Yi = b0 + b1Xi + ui, where Pr(Yi = 1Xi) = b0 + b1Xi.a. Show that E(ui Xi) = 0.b. Show that var(ui Xi) = (b0 + b1Xi)[1 - (b0 + b1Xi)]. [Hint: Review
11.7 Repeat Exercise 11.6 using the logit model in Equation (11.10). Are the logit and probit results similar? Explain.
11.6 Use the estimated probit model in Equation (11.8) to answer the following questions:a. A black mortgage applicant has a P/I ratio of 0.35. What is the probability that his application will be
11.5 Using the results in column (7):a. Akira is a man with 10 years of schooling. What is the probability that the government will employ him?b. Jane is a woman with 12 years of schooling. What is
11.4 Using the results in columns (4) through (6):a. Compute the estimated probability of passing the test for men and for women.b. Are the models in (4) through (6) different? Why or why not?
11.3a. Answer (a) through (c) from Exercise 11.1 using the results in column (3).b. Sketch the predicted probabilities from the probit and linear probability in columns (1) and (3) as a function of
11.2a. Answer (a) through (c) from Exercise 11.1 using the results in column (2).b. Sketch the predicted probabilities from the probit and logit in columns(1) and (2) for values of Schooling between
11.1 Using the results in column (1):a. Does the probability of working in the government depend on Schooling? Explain.b. Matthew has 16 years of schooling. What is the probability that he will pass
11.4 What measures of fit are typically used to assess binary dependent variable regression models?
11.3 What is a maximum likelihood estimation? What are the advantages of using maximum likelihood estimators such as the probit and the logit, instead of the linear probability model? How would you
11.2 In Table 11.2 the estimated coefficient on black is 0.084 in column (1), 0.688 in column (2), and 0.389 in column (3). In spite of these large differences, all three models yield similar
11.1 Suppose that a linear probability model yields a predicted value of Y that is equal to 1.3. Explain why this is nonsensical.
E10.2 Do citizens demand more democracy and political freedom as their incomes grow? That is, is democracy a normal good? On the textbook website, www.pearsonglobaleditions.com/Stock_Watson, you will
E10.1 Some U.S. states have enacted laws that allow citizens to carry concealed weapons. These laws are known as “shall-issue” laws because they instruct local authorities to issue a concealed
10.11 Let b nDM 1 denote the entity-demeaned estimator given in Equation (10.22), and let b nBA 1 denote the “before and after” estimator without an intercept, so that b nBA 1 = 3ni= 1(Xi2 -
10.10 A researcher wants to estimate the determinants of annual earnings: age, gender, schooling, union status, occupation, and sector of employment.The researcher has been told that if they collect
10.9a. In the fixed effects regression model, are the fixed entity effects, ai, consistently estimated as n¡ with T fixed? (Hint: Analyze the model with no X’s: Yit = ai + uit.)b. If n is large
10.8 Consider observations (Yit, Xit) from the linear panel data model Yit = Xitb1 + ai + lit + uit, where t = 1,c, T; i = 1,c, n; and ai + lit is an unobserved entityspecific time trend. How would
10.7 Suppose a researcher believes that the occurrence of natural disasters, such as earthquakes, leads to increased activity in the construction industry.The researcher decides to collect
10.6 Do the fixed effects regression assumptions in Key Concept 10.3 imply that cov(v it,v is) = 0 for t s in Equation (10.28)? Explain.
10.5 Consider the model with a single regressor Yit = b1X1,it + ai + lt + uit.This model also can be written as Yit = b0 + b1X1,it + d2B2t + g+ dTBTt + g2D2i + g+ gnDni + uit, where B2t = 1 if t = 2
10.4 Using the regression in Equation (10.11), what is the slope and intercept fora. Entity 1 in time period 1?b. Entity 1 in time period 3?c. Entity 3 in time period 1?d. Entity 3 in time period 3?
10.3 Section 9.2 gave a list of five potential threats to the internal validity of a regression study. Apply that list to the empirical analysis in Section 10.6 and thereby draw conclusions about its
10.2 Consider the binary variable version of the fixed effects model in Equation(10.11), except with an additional regressor, D1i; that is, let Yit = b0 + b1Xit + g1D1i + g2D2i + g+ gnDni + uit.a.
10.1 This exercise refers to the drunk driving panel data regression, summarized in Table 10.1.a. New Jersey has a population of 8.85 million people. Suppose that New Jersey increased the tax on a
10.4 In the context of the regression you suggested for Question 10.2, explain why the regression error for a given individual might be serially correlated.
10.3 Can the regression that you suggested in response to Question 10.2 be used to estimate the effect of gender on an individual’s earnings? Can that regression be used to estimate the effect of
10.2 A researcher is using a panel data set on n = 1000 workers over T = 10 years (from 2001 through 2010) that contains the workers’ earnings, gender, education, and age. The researcher is
10.1 Define panel data. What is the advantage of using such data to make statistical and economic inferences? Why is it necessary to use two subscripts, i and t, to describe panel data? What does i
E9.2 Use the data set Birthweight_Smoking introduced in Empirical Exercise 5.1 to answer the following questions.a. In Empirical Exercise 7.1(f), you estimated several regressions and were asked:
E9.1 Use the data set CPS12, described in Empirical Exercise 8.2, to answer the following questions.a. Discuss the internal validity of the regressions that you used to answer Empirical Exercise
9.13 Assume that the regression model Yi = b0 + b1Xi + ui satisfies the least squares assumptions in Key Concept 4.3 in Section 4.4. You and a friend collect a random sample of 300 observations on Y
9.12 Consider the one-variable regression model Yi = b0 + b1Xi + ui and suppose that it satisfies the least squares assumptions in Key Concept 4.3. The regressor Xi is missing, but data on a related
9.11 Read the box “The Demand for Economics Journals” in Section 8.3. Discuss the internal and external validity of the estimated effect of price per citation on subscriptions.
9.10 Read the box “The Return to Education and the Gender Gap” in Section 8.3. Discuss the internal and external validity of the estimated effect of education on earnings.
9.9 Consider the linear regression of TestScore on Income shown in Figure 8.2 and the nonlinear regression in Equation (8.18). Would either of these regressions provide a reliable estimate of the
9.8 Would the regression in Equation (9.5) be useful for predicting test scores in a school district in Massachusetts? Why or why not?
9.7 Are the following statements true or false? Explain your answer.a. “An ordinary least squares regression of Y onto X will not be internally valid if Y is correlated with the error term.”b.
9.6 Suppose that n = 50, i.i.d. observations for (Yi, Xi) yield the following regression results:Another researcher is interested in the same regression, but makes an error when entering the data
9.5 The demand for a commodity is given by Q = b0 + b1P + u, where Q denotes quantity, P denotes price, and u denotes factors other than price that determine demand. Supply for the commodity is given
9.4 Using the regressions shown in columns (2) of Table 8.3 and 9.3, and column(2) of Table 9.2, construct a table like Table 9.3 to compare the estimated effects of a 10 percentage point increase in
9.3 Labor economists studying the determinants of women’s earnings discovered a puzzling empirical result. Using randomly selected employed women, they regressed earnings on the women’s number of
9.2 Consider the one-variable regression model Yi = b0 + b1Xi + ui and suppose that it satisfies the least squares assumptions in Key Concept 4.3. Suppose that Yi is measured with error, so the data
9.1 Suppose you just read a careful statistical study of the effect of improved health of children on their test scores at school. Using data from a project in a West African district, in 2000, the
9.6 A researcher estimates a regression using two different software packages.The first uses the homoskedasticity-only formula for standard errors. The second uses the heteroskedasticity-robust
9.5 Define simultaneous causality bias. Explain the potential for simultaneous causality in a study of the effects of high levels of bureaucratic corruption on national income.
9.4 What is sample selection bias? Suppose you read a study using data on college graduates of the effects of an additional year of schooling on earnings.What is the potential sample selection bias?
9.3 What is the effect of measurement error in Y? How is this different from the effect of measurement error in X?
9.2 Key Concept 9.2 describes the problem of variable selection in terms of a trade-off between bias and variance. What is this trade-off? Why could including an additional regressor decrease bias?
9.1 Is it possible for an econometric study to have internal validity but not external validity?
E8.2 On the text website www.pearsonglobaleditions.com/Stock_Watson you will find a data file CPS12, which contains data for full-time, full-year workers, ages 25–34, with a high school diploma or
E8.1 Lead is toxic, particularly for young children, and for this reason government regulations severely restrict the amount of lead in our environment.But this was not always the case. In the early
8.12 The discussion following Equation (8.28) interprets the coefficient on interacted binary variables using the conditional mean zero assumption.This exercise shows that interpretation also applies
8.11 Derive the expressions for the elasticities given in Appendix 8.2 for the linear and log-log models. (Hint: For the log-log model, assume that u and X are independent, as is done in Appendix 8.2
8.10 Consider the regression model Yi = b0 + b1X1i + b2X2i + b3(X1i * X2i) +ui. Use Key Concept 8.1 to show:a. Y>X1 = b1 + b3X2 (effect of change in X1, holding X2 constant).b. Y>X2 = b2 + b3X1
8.9 Explain how you would use Approach #2 from Section 7.3 to calculate the confidence interval discussed below Equation (8.8). [Hint: This requires estimating a new regression using a different
8.8 X is a continuous variable that takes on values between 5 and 100. Z is a binary variable. Sketch the following regression functions (with values of X between 5 and 100 on the horizontal axis and
8.7 This problem is inspired by a study of the “gender gap” in earnings in top corporate jobs [Bertrand and Hallock (2001)]. The study compares total compensation among top executives in a large
8.6 Refer to Table 8.3.a. A researcher suspects that the effect of %Eligible for subsidized lunch has a nonlinear effect on test scores. In particular, he conjectures that increases in this variable
8.5 Read the box “The Demand for Economics Journals” in Section 8.3.a. The box reaches three conclusions. Looking at the results in the table, what is the basis for each of these conclusions?b.
8.4 Read the box “The Return to Education and the Gender Gap” in Section 8.3.a. Consider a man with 16 years of education and 2 years of experience who is from a western state. Use the results
8.3 After reading this chapter’s analysis of test scores and class size, an educator comments, “In my experience, student performance depends on class size, but not in the way your regressions
8.2 Suppose a researcher collects data on houses that have been sold in a particular neighborhood over the past year, and obtains the regression results in the table shown below.a. Using the results
8.1 Sales of a company is $243 million in 2013, and it increases to $250 million in 2014.a. Compute the percentage increase in sales, using the usual formula 100 * (Sales2014 - Sales2013)Sales2013 .
8.6 What types of independent variables—binary or continuous—may interact with one another in a regression? How do you interpret the coefficient on the interaction between two continuous
8.5 Suppose that in Exercise 8.2 you thought that the value of b2 was not constant but rather increased when K increased. How could you use an interaction term to capture this effect?
8.4 Suppose the regression in Equation (8.30) is estimated using LoSTR and LoEL in place of HiSTR and HiEL, where LoSTR = 1 - HiSTR is an indicator for a low-class-size district and LoEL = 1 - HiEL
8.3 How is the slope coefficient interpreted in a log-linear model, where the dependent variable is (i) in logarithms but the independent variable is not, (ii)in a linear-log model, (iii) in a

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