Introductory Econometrics A Modern Approach 5th Edition Jeffrey M. Wooldridge - Solutions

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2.5 Show that the coefficient of determination, R2, can also be obtained as the squared correlation between actual Yvalues and the Yvalues estimated from the regression model 2;), where Y is the dependent variable. Note that the coefficient of correlation between variables Yand X is defined as: r
2.4 Would it make sense to standardize variables in the log-linear Cobb-Douglas production function and estimate the regression using standardized variables? Why or why not? Show the necessary calculations.
2.3 For the food expenditure data given in Table 2.6, see if the following model fits the data well: SFDHOi = Bl + B2 Expendi + B3 Expendr and compare your results with those discussed in the text.
2.2 How would you compute the output-labor and output-capital elasticities for the linear production function given in Table 2.3?
2.1 Consider the following production function, known in the literature as the transcendental production function (TPF). Q. = BILB2 K B3 I I I where Q, L, and K represent output, labor, and capital, respectively. (a) How would you linearize this function? (Hint: logarithms.) 24 See Christiaan
1.1 Consider the regression results given in Table 1.2. (a) Suppose you want to test the hypothesis that the true or population regression coefficient of the education variable is 1. How would you test this hypothesis? Show the necessary calculations.(b) Would you reject or not reject the
18 In Chapter 19, the final chapter, we discusses a topic that has received considerable attention in the literature, namely, the method of Instrumental Variables (IV), The bulk of this book has been devoted to the case of nonstochastic or fixed regressors, but there are situations where we have
17 In Chapter 18 we discuss the topic of duration or survival analysis. Duration of a marriage, duration of a strike, duration of an illness, and duration of unemployment are some examples of duration data.
16 The models discussed in the preceding chapters dealt with cross-sectional or time series data. Chapter 17 deals with models that combine cross-sectional and time series data. These models are known as panel data regression models. We show in this chapter how such models are estimated and
15 we show how we find this out and what happens if the variables are not co integrated. 15 Forecasting is a specialized field in time series econometrics. In Chapter 16 we discuss the topic of economic forecasting using the LRM as well as two prominently used methods of forecasting, namely, ARIMA
14 If you regress a nonstationary time series on one or more nonstationary time series, it might lead to the so-called spurious or nonsense regression phenomenon. However, if there is a stable long-term relationship between variables, that is if the variables are cointegrated, there need not be
13 Although heteroscedasticity is generally associated with cross-sectional data, it can also arise in time series data in the so-called volatility clustering phenomenon observed in financial time series. The ARCH and GARCH models discussed in Chapter 14 will show how we model volatility clustering.
12 In cases oftime series data, an underlying assumption of the CLRM is that the time series are stationary. If that is not the case, is the usual OLS methodology still applicable? What are the alternatives? We discuss this topic in Chapter 13.
11 Occasionally we come across data that is of the count type, such as the number of visits to a doctor, the number of patents received by a firm, the number customers passing through a check-out counter in a span of 15 minutes, and so on. To model such count data, the Poisson probability
10 Sometimes the regressand is restricted in the values it takes because of the design of the problem under study. Suppose we want to study expenditure on housing by families making income under $50,000 a year. Obviously, this excludes families with income over this limit. The censored sample and
9 Although nominal scale variables cannot be readily quantified, they can sometimes be ordered or ranked. Ordered logit and ordered probit models, discussed in Chapter 10, show how ordered or ranked models can be estimated.
8 Chapter 9 extends the bivariate logit and probit models to multi-category nominal scale variables, where the regress and has more than two nominal values. For example, consider the means of transportation to work. Suppose we have three choices: private car, public bus, or train. How do we decide
7 Suppose the dependent variable is not a ratio or interval scale variable but is a nominal scale variable, taking values of 1 and O. Can we still apply the usual OLS techniques to estimate such models? If not, what are the alternatives? The answer to these questions can be found in Chapter 8,
6 One of the assumptions of the CLRM is that the model used in empirical analysis is "correctly specified" in the sense that all relevant variables are included in the model, no superfluous variables are included in the model, the probability distribution of the error term is correctly specified,
5 In time series data the assumption of no autocorrelation in the error term is unlikely to be fulfilled. How do we find that out? What are the consequences of autocorrelation? How do we correct for autocorrelation? We will answer these questions in Chapter 6.
4 In cross-sectional data the error variance may be heteroscedastic rather than homoscedastic. How do we find that out? And what are the consequences of heteroscedasticity? Are OLS estimators still BLUE? How do we correct for heteroscedastidty? We answer these questions in Chapter 5.
3 If we have several regressors in a regression model, how do we find out that we do not have the problem of multicollinearity? If we have that problem, what are the consequences? And how do we deal with them? We discuss this topic in Chapter 4.
2 Suppose some of the regressors are quantitative and some are qualitative or nominal scale variables, also called dummy variables. Are there special problems in dealing with dummy variables? How do we handle the interaction between quantitative and dummy variables in a given situation? In our
1 The wage model given in Table 1.2 is linear in variables as well as parameters. Could the wage variable, for instance, be in logarithmic form? Could the variables for education and experience be also in logarithmic form? Since wages are not expected to grow linearly with experience forever,
31 Following Hamermesh and Parker (2005), try to establish a link between the physical appearance of college instructors and student evaluations. This can be done on campus via a survey. Somewhat crude data can be obtained from websites that allow students to rank their professors and provide some
30 Do your own “audit” study to test for race or gender discrimination in hiring. (One such study is described in Example C.3 of Appendix C.) Have pairs of equally qualified friends, say, one male and one female, apply for job openings in local bars or restaurants. You can provide them with
29 Test whether stores or restaurants practice price discrimination based on race or ethnicity. Graddy (1997) used data on fast-food restaurants in New Jersey and Pennsylvania, along with zip code-level characteristics, to see whether prices vary by characteristics of the local population. She
28 What factors affect election outcomes? Does spending matter? Do votes on specific issues matter? Does the state of the local economy matter? See, for example, Levitt (1994) and the data sets VOTE1.RAW and VOTE2.RAW. Fair (1996) performed a time series analysis of U.S. presidential elections.
27 Do differences in tax codes across states affect the amount of foreign direct investment? Hines (1996) studied the effects of state corporate taxes, along with the ability to apply foreign tax credits, on investment from outside the United States.
26 What factors affect chief executive officer salaries? The files CEOSAL1.RAW and CEOSAL2.RAW are data sets that have various firm performance measures as well as information such as tenure and education. You can certainly update these data files and look for other interesting factors. Rose and
25 Are there aggregate productivity effects of computer usage? You would need to obtain time series data, perhaps at the national level, on productivity, percentage of employees using computers, and other factors. What about spending (probably as a fraction of total sales) on research and
24 At the city level, estimate a time series model for crime. An example is Cloninger and Sartorius (1979). As a twist, you might estimate the effects of community policing or midnight basketball programs, relatively new innovations in fighting crime. Inferring causality is tricky. Including a
23 Obtain monthly or quarterly data on teenage employment rates, the minimum wage, and factors that affect teen employment to estimate the effects of the minimum wage on teen employment. Solon (1985) used quarterly U.S. data, while Castillo-Freeman and Freeman (1992) used annual data on Puerto
22 What factors might explain racial and gender differences in employment and wages? For example, Holzer (1991) reviewed the evidence on the “spatial mismatch hypothesis” to explain differences in employment rates between blacks and whites. Korenman and Neumark (1992) examined the effects of
21 What is the behavior of mergers in the U.S. economy (or some other economy)? Shughart and Tollison (1984) characterize (the log of) annual mergers in the U.S. economy as a random walk by showing that the difference in logs—roughly, the growth rate—is unpredictable given past growth rates.
20 What factors affect output growth? Two factors of interest are inflation and investment [for example, Blomström, Lipsey, and Zejan (1996)]. You might use time series data on a country you find interesting. Or you could use a cross section of countries, as in De Long and Summers (1991). Friedman
19 What are the effects of state regulations, such as motorcycle helmet laws, on motorcycle fatalities? Or do differences in boating laws—such as minimum operating age—help to explain boating accident rates? The U.S. Department of Transportation compiles such information. This can be merged
18 Use state- or county-level data or, if possible, school district–level data to look at the factors that affect education spending per pupil. An interesting question is: Other things being equal (such as income and education levels of residents), do districts with a larger percentage of
17 What factors affect manufacturing productivity at the state level? In addition to levels of capital and worker education, you could look at degree of unionization. A panel data analysis would be most convincing here, using multiple years of census data, say 1980, 1990, 2000, and 2010. Clark
16 Collect murder rates for a sample of counties (say, from the FBI Uniform Crime Reports) for two years. Make the latter year such that economic and demographic variables are easy to obtain from the County and City Data Book. You can obtain the total number of people on death row plus executions
15 What effect, if any, does success in college athletics have on other aspects of the university (applications, quality of students, quality of nonathletic departments)? McCormick and Tinsley (1987) looked at the effects of athletic success at major colleges on changes in SAT scores of entering
14 You can test whether the market for gambling on sports is efficient. For example, does the spread on football or basketball games contain all usable information for picking against the spread? The data set PNTSPRD.RAW contains information on men’s college basketball games. The outcome
13 Is there racial discrimination in the market for baseball cards? This involves relating the prices of baseball cards to factors that should affect their prices, such as career statistics, whether the player is in the Hall of Fame, and so on. Holding other factors fixed, do cards of black or
12 Can excess returns on a stock, or a stock index, be predicted by the lagged price/dividend ratio? Or by lagged interest rates or weekly monetary policy? It would be interesting to pick a foreign stock index, or one of the less well-known U.S. indexes. Cochrane (1997) provides a nice survey of
11 What factors affect student performance at public schools? It is fairly easy to get schoollevel or at least district-level data in most states. Does spending per student matter? Do student-teacher ratios have any effects? It is difficult to estimate ceteris paribus effects because spending is
10 Do minimum wages alleviate poverty? You can use state or county data to answer this question. The idea is that the minimum wage varies across states because some states have higher minimums than the federal minimum. Further, there are changes over time in the nominal minimum within a state, some
9 Answer this question: Are cigarette smokers less productive? A variant on this is: Do workers who smoke take more sick days (everything else being equal)? Mullahy and Portney (1990) use individual-level data to evaluate this question. You could use data at, say, the metropolitan level. Something
8 Is there a marriage premium for professional athletes? Korenman and Neumark (1991) found a significant wage premium for married men after using a variety of econometric methods, but their analysis is limited because they cannot directly observe productivity. (Plus, Korenman and Neumark used men
7 Are blacks discriminated against in the lending market? Hunter and Walker (1996) looked at this question; in fact, we used their data in Computer Exercises C.8 in Chapter 7 and C.2 in Chapter 17.
6 Do changes in traffic laws affect traffic fatalities? McCarthy (1994) contains an analysis of monthly time series data for the state of California. A set of dummy variables can be used to indicate the months in which certain laws were in effect. The file TRAFFIC2.RAW contains the data used by
5 Do parental consent laws increase the teenage birthrate? You can use state level data for this: either a time series for a given state or, even better, a panel data set of states. Do the same laws reduce abortion rates among teenagers? The Statistical Abstract of the United States contains all
4 Low and McPheters (1983) used city cross-sectional data on wage rates and estimates of risk of death for police officers, along with other controls. The idea is to determine whether police officers are compensated for working in cities with a higher risk of on-the-job injury or death.
3 Do gun control laws at the city level reduce violent crimes? Such questions can be difficult to answer with a single cross section because city and state laws are often endogenous. [See Kleck and Patterson (1993) for an example. They used cross-sectional data and instrumental variables methods,
2 There are many variants on the preceding topic. You can study the effects of drug or alcohol usage, or of living in a fraternity, on grade point average. You would want to control for many family background variables, as well as previous performance variables.
1 Do your own campus survey to answer a question of interest at your university. For example: What is the effect of working on college GPA? You can ask students about high school GPA, college GPA, ACT or SAT scores, hours worked per week, participation in athletics, major, gender, race, and so on.
C15 This question asks you to study the so-called Beveridge Curve from the perspective of cointegration analysis. The U.S. monthly data from December 2000 through February 2012 are in BEVERIDGE.RAW. (i) Test for a unit root in urate using the usual Dickey-Fuller test (with a constant) and the
C14 Use the data in MINWAGE.DTA for sector 232 to answer the following questions. (i) Confirm that lwage232t and lemp232t are best characterized as I(1) processes. Use the augmented DF test with one lag of gwage232 and gemp232, respectively, and a linear time trend. Is there any doubt that these
C13 Use the data in TRAFFIC2.RAW for this exercise. These monthly data, on traffic accidents in California over the years 1981 to 1989, were used in Computer Exercise C11 in Chapter 10. (i) Using the standard Dickey-Fuller regression, test whether ltotacct has a unit root. Can you reject a unit
C12 This exercise also uses the data from VOLAT.RAW. Computer Exercise C11 studies the long-run relationship between stock prices and industrial production. Here, you will study the question of Granger causality using the percentage changes. (i) Estimate an AR(3) model for pcipt , the percentage
C11 Use the data in VOLAT.RAW for this exercise. (i) Confirm that lsp500  log(sp500) and lip  log(ip) appear to contain unit roots. Use Dickey-Fuller tests with four lagged changes and do the tests with and without a linear time trend. (ii) Run a simple regression of lsp500 on lip. Comment
C10 Use the data in INTQRT.RAW for this exercise. (i) Using the data from all but the last four years (16 quarters), estimate an AR(1) model for r6t . (We use the difference because it appears that r6t has a unit root.) Find the RMSE of the one-step-ahead forecasts for r6, using the last 16
C9 Use CONSUMP.RAW for this exercise. (i) Let yt be real per capita disposable income. Use the data through 1989 to estimate the model yt    t  yt1  ut and report the results in the usual form. (ii) Use the estimated equation from part (i) to forecast y in 1990. What is the
C8 Use the data in FERTIL3.RAW for this exercise. (i) Graph gfr against time. Does it contain a clear upward or downward trend over the entire sample period? (ii) Using the data through 1979, estimate a cubic time trend model for gfr (that is, regress gfr on t, t 2 , and t 3 , along with an
C7 Use the data in BARIUM.RAW for this exercise. (i) Estimate the linear trend model chnimpt    t  ut, using the first 119 observations (this excludes the last 12 months of observations for 1988). What is the standard error of the regression? (ii) Now, estimate an AR(1) model for
C6 Use the data in PHILLIPS.RAW to answer these questions. (i) Estimate the models in (18.48) and (18.49) using the data through 1997. Do the parameter estimates change much compared with (18.48) and (18.49)? (ii) Use the new equations to forecast unem1998; round to two places after the decimal.
C5 Use INTQRT.RAW for this exercise. (i) In Example 18.7, we estimated an error correction model for the holding yield on six-month T-bills, where one lag of the holding yield on three-month T-bills is the explanatory variable. We assumed that the cointegration parameter was one in the equation
C4 In testing for cointegration between gfr and pe in Example 18.5, add t 2 to equation (18.32) to obtain the OLS residuals. Include one lag in the augmented DF test. The 5% critical value for the test is 4.15.
C3 Use the data in VOLAT.RAW for this exercise. (i) Estimate an AR(3) model for pcip. Now, add a fourth lag and verify that it is very insignificant. (ii) To the AR(3) model from part (i), add three lags of pcsp to test whether pcsp Granger causes pcip. Carefully, state your conclusion. (iii) To
C2 Use the data in HSEINV.RAW for this exercise. (i) Test for a unit root in log(invpc), including a linear time trend and two lags of log(invpct ). Use a 5% significance level. (ii) Use the approach from part (i) to test for a unit root in log(price). (iii) Given the outcomes in parts (i) and
C1 Use the data in WAGEPRC.RAW for this exercise. Problem 5 in Chapter 11 gave estimates of a finite distributed lag model of gprice on gwage, where 12 lags of gwage are used. (i) Estimate a simple geometric DL model of gprice on gwage. In particular, estimate equation (18.11) by OLS. What are the
9 Let {yt} be an I(1) sequence. Suppose that gˆn is the one-step-ahead forecast of yn1 and let ˆfn  gˆn  yn be the one-step-ahead forecast of yn1. Explain why the forecast errors for forecasting yn1 and yn1 are identical.
8 Suppose that yt follows the model yt    1zt1  ut ut  ut1  et E(etIt1)  0, where It1 contains y and z dated at t  1 and earlier. (i) Show that E(yt1It)  (1  )  yt  1zt  1zt1. (Hint: Write ut1  yt1 
7 Let gMt be the annual growth in the money supply and let unemt be the unemployment rate. Assuming that unemt follows a stable AR(1) process, explain in detail how you would test whether gM Granger causes unem.
6 Using the monthly data in VOLAT.RAW, the following model was estimated: pcip (1.54)(.344)pcip1 (.074)pcip2 (.073)pcip3 (.031)pcsp1 pciˆp 0(.56)(.042) (.045) (.042) (.013) n  554, R2  .174, - R2  .168, where pcip is the percentage change in monthly
5 Suppose the process {(xt, yt): t  0, 1, 2, …} satisfies the equations yt  xt  ut and xt  xt1  vt, where E(utIt1)  E(vtIt1)  0, It1 contains information on x and y dated at time t  1 and earlier,   0, and   1 [so that xt,
4 Consider the error correction model in equation (18.37). Show that if you add another lag of the error correction term, yt2  xt2, the equation suffers from perfect collinearity. (Hint: Show that yt2  xt2 is a perfect linear function of yt1  xt1, xt1, and
3 Suppose that {yt} and {zt} are I(1) series, but yt  zt is I(0) for some   0. Show that for any   , yt  zt must be I(1).
2. Using the IV approach to estimating the h and , what would you use as instruments for yt1? 2 An interesting economic model that leads to an econometric model with a lagged dependent variable relates yt to the expected value of xt, say, xt *, where the expectation is based on all
1 Consider equation (18.15) with k 
C15 Use the data set in ALCOHOL.RAW, obtained from Terza (2002), to answer this question. The data, on 9,822 men, includes labor market information, whether the man abuses alcohol, and demographic and background variables. In this question you will study the effects of alcohol abuse on employ,
C14 Use the data in HAPPINESS.RAW for this question. See also Computer Exercise C15 in Chapter 13. (i) Estimate a probit probability model relating vhappy to occattend and regattend, and include a full set of year dummies. Find the average partial effects for occattend and regattend. How do these
C13 Use the data in HTV.RAW to answer this question. (i) Using OLS on the full sample, estimate a model for log(wage) using explanatory variables educ, abil, exper, nc, west, south, and urban. Report the estimated return to education and its standard error. (ii) Now estimate the equation from part
C12 Use the data in CHARITY.RAW to answer these questions. (i) The variable respond is a binary variable equal to one if an individual responded with a donation to the most recent request. The database consists only of people who have responded at least once in the past. What fraction of people
C11 Use the data in CPS91.RAW for this exercise. These data are for married women, where we also have information on each husband’s income and demographics. (i) What fraction of the women report being in the labor force? (ii) Using only the data for working women—you have no choice—estimate
C10 Use the data in SMOKE.RAW for this exercise. (i) The variable cigs is the number of cigarettes smoked per day. How many people in the sample do not smoke at all? What fraction of people claim to smoke 20 cigarettes a day? Why do you think there is a pileup of people at 20 cigarettes? (ii) Given
C9 Use the data in APPLE.RAW for this exercise. These are telephone survey data attempting to elicit the demand for a (fictional) “ecologically friendly” apple. Each family was (randomly) presented with a set of prices for regular apples and the eco-labeled apples. They were asked how many
C8 The file JTRAIN2.RAW contains data on a job training experiment for a group of men. Men could enter the program starting in January 1976 through about mid-1977. The program ended in December 1977. The idea is to test whether participation in thejob training program had an effect on unemployment
C7 Use the MROZ.RAW data for this exercise. (i) Using the 428 women who were in the workforce, estimate the return to education by OLS including exper, exper2 , nwifeinc, age, kidslt6, and kidsge6 as explanatory variables. Report your estimate on educ and its standard error. (ii) Now, estimate the
C6 Use the data in RECID.RAW to estimate the model from Example 17.4 by OLS, using only the 552 uncensored durations. Comment generally on how these estimates compare with those in Table 17.4.
C4 In Example 9.1, we added the quadratic terms pcnv2 , ptime862 , and inc862 to a linear model for narr86. (i) Use the data in CRIME1.RAW to add these same terms to the Poisson regression in Example 17.3. (ii) Compute the estimate of 2 given by ˆ2  (n  k  1)1 n i1 ˆ u2 i
C3 Use the data in FRINGE.RAW for this exercise. (i) For what percentage of the workers in the sample is pension equal to zero? What is the range of pension for workers with nonzero pension benefits? Why is a Tobit model appropriate for modeling pension? (ii) Estimate a Tobit model explaining
C2 Use the data in LOANAPP.RAW for this exercise; see also Computer Exercise C8 in Chapter 7. (i) Estimate a probit model of approve on white. Find the estimated probability of loan approval for both whites and nonwhites. How do these compare with the linear probability estimates? (ii) Now, add the
C1 Use the data in PNTSPRD.RAW for this exercise. (i) The variable favwin is a binary variable if the team favored by the Las Vegas point spread wins. A linear probability model to estimate the probability that the favored team wins is P( favwin  1spread)  0  1spread. Explain why,
7 Suppose you are hired by a university to study the factors that determine whether students admitted to the university actually come to the university. You are given a large random sample of students who were admitted the previous year. You have information on whether each student chose to attend,
6 Consider a family saving function for the population of all families in the United States: sav  0  1inc  2hhsize  3educ  4age  u, where hhsize is household size, educ is years of education of the household head, and age is age of the household head. Assume that
5 (Requires calculus) Let patents be the number of patents applied for by a firm during a given year. Assume that the conditional expectation of patents given sales and RD is E(patentssales,RD)  exp[0  1log(sales)  2RD  3RD2 ], where sales is annual firm sales and RD is
4 Let mvpi be the marginal value product for worker i, which is the price of a firm’s good multiplied by the marginal product of the worker. Assume that log(mvpi )  0  1xi1  …  kxik  ui wagei  max(mvpi ,minwagei ), where the explanatory variables include education,
3 (Requires calculus) (i) Suppose in the Tobit model that x1  log(z1), and this is the only place z1 appears in x. Show that ∂E(yy  0,x) _____________ ∂z1  (1/z1){1  (x/)[x/  (x/)]}, [17.52] where b1 is the coefficient on log(z1) (ii) If x1  z1,
2 Let grad be a dummy variable for whether a student-athlete at a large university graduates in five years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study be the number of hours spent per week in an organized study hall. Suppose that, using data on 420
1 (i) For a binary response y, let - y be the proportion of ones in the sample (which is equal to the sample average of the yi ). Let qˆ0 be the percent correctly predicted for the outcome y  0 and let qˆ1 be the percent correctly predicted for the outcome y  1. If pˆ is the overall

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Introductory Econometrics A Modern Approach 5th Edition Jeffrey M. Wooldridge - Solutions

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