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introductory econometrics modern

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

C1 Use all the data in PHILLIPS.RAW to answer this question. You should now us 56 years of data. (i) Reestimate equation (11.19) and report the results in the usual form. Do the intercept and slope estimates change notably when you add the recent years of data? (ii) Obtain a new estimate of the
C Use the data in TRAFFIC2.RAW for this exercise. Computer Exercise C11 in Chapter 1 previously asked for an analysis of these data. (i) Compute the first order autocorrelation coefficient for the variable prcfat. Are you concerned that prcfat contains a unit root? Do the same for the unemployment
C8 Use the data in PHILLIPS.RAW for this exercis (i) Estimate an AR(1) model for the unemployment rate. Use this equation to predict the unemployment rate for 2004. Compare this with the actual unemployment rate for 2004. (You can find this information in a recent Economic Report of the President.)
C Use CONSUMP.RAW for this exercise. One version of the permanent income hypothes (PIH) of consumption is that the growth in consumption is unpredictable. [Another version is that the change in consumption itself is unpredictable; see Mankiw (1994, Chapter 15) for discussion of the PIH.] Let gct 5
C Let inve be the real value inventories in the United States during year t, let GDPt denote real gross domestic product, and let r3t denote the (ex post) real interest rate on threemonth T-bills. The ex post real interest rate is (approximately) r3t 5 i3t – inft , where i3t is the rate on
C5 (i Add a linear time trend to equation (11.27). Is a time trend necessary in the firstdifference equatio (ii) Drop the time trend and add the variables ww2 and pill to (11.27) (do not difference these dummy variables). Are these variables jointly significant at the 5% level? (iii) Add the
C4 Use the data in PHILLIPS.RAW for this exercise, but only through 199 (i) In Example 11.5, we assumed that the natural rate of unemployment is constant. An alternative form of the expectations augmented Phillips curve allows the natural rate of unemployment to depend on past levels of
C3 (i In Example 11.4, it may be that the expected value of the return at time t, give past returns, is a quadratic function of returnt21. To check this possibility, use the data in NYSE.RAW to estimate returnt 5 b0 1 b1returnt21 1 b2returnt 2 21 1 ut ; report the results in standard form. (ii)
C In Example 11.7, define the growth in hourly wage and output per hour as the chang in the natural log: ghrwage 5 Dlog(hrwage) and goutphr 5 Dlog(outphr). Consider a simple extension of the model estimated in (11.29): ghrwaget 5 b0 1 b1goutphrt 1 b2goutphrt21 1 ut . This allows an increase in
C1 Use the data in HSEINV.RAW for this exercis (i) Find the first order autocorrelation in log(invpc). Now, find the autocorrelation after linearly detrending log(invpc). Do the same for log( price). Which of the two series may have a unit root? (ii) Based on your findings in part (i), estimate the
8 Suppose that the equation yt 5 a 1 dt 1 b1xt1 1 … 1 bk xtk 1 ut satisfies the sequential exogeneity assumption in equation (11.40). (i) Suppose you difference the equation to obtain Dyt 5 d 1 b1Dxt1 1 … 1 bkDxtk 1 Dut . How come applying OLS on the differenced equation does not generally
7 A partial adjustment model is yt * 5 g0 1 g1xt 1 et yt 2 yt21 5 l(yt * 2 yt21) 1 at , where yt * is the desired or optimal level of y, and yt is the actual (observed) level. For example, yt * is the desired growth in firm inventories, and xt is growth in firm sales. The parameter g1 measures the
6 Let hy6t denote the three-month holding yield (in percent) from buying a six-month T-bill at time (t – 1) and selling it at time t (three months hence) as a three-month T-bill. Let hy3t21 be the three-month holding yield from buying a three-month T-bill at time (t – 1). At time (t – 1),
5 For the U.S. economy, let gprice denote the monthly growth in the overall price level and let gwage be the monthly growth in hourly wages. [These are both obtained as differences of logarithms: gprice 5 Dlog( price) and gwage 5 Dlog(wage).] Using the monthly data in WAGEPRC.RAW, we estimate the
4 Let {yt: t 5 1, 2, …} follow a random walk, as in (11.20), with y0 5 0. Show that Corr(yt , yt1h) 5  _______ t/(t 1 h)for t  1, h 0
3 Suppose that a time series process {yt } is generated by yt 5 z 1 et , for all t 5 1, 2, …, where {et } is an i.i.d. sequence with mean zero and variance se 2 . The random variable z does not change over time; it has mean zero and variance sz 2 . Assume that each et is uncorrelated with z. (i)
2 Let {et : t 5 21, 0, 1, …} be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a stochastic process by xt 5 et 2 (1/2)et21 1 (1/2)et22, t 5 1, 2, …. (i) Find E(xt ) and Var(xt ). Do either of these depend on t? (ii) Show that Corr(xt
1 Let {xt : t 5 1, 2, …} be a covariance stationary process and define gh 5 Cov(xt , xt1h) for h  0. [Therefore, g0 5 Var(xt ).] Show that Corr(xt , xt1h) 5 gh /g0.
C1 Use the data in MINWAGE.RAW for this exercise. In particular, use the employmen and wage series for sector 232 (Men’s and Boys’ Furnishings). The variable gwage232 is the monthly growth (change in logs) in the average wage in sector 232, gemp232 is the growth in employment in sector 232,
C12 (i Estimate equation (10.2) using all the data in PHILLIPS.RAW and report th results in the usual form. How many observations do you have now? (ii) Compare the estimates from part (i) with those in equation (10.14). In particular, does adding the extra years help in obtaining an estimated
C1 The file TRAFFIC2.RAW contains 108 monthly observations on automobile accidents traffic laws, and some other variables for California from January 1981 through December 1989. Use this data set to answer the following questions. (i) During what month and year did California’s seat belt law take
C10 Consider the model estimated in (10.15); use the data in INTDEF.RA (i) Find the correlation between inf and def over this sample period and comment. (ii) Add a single lag of inf and def to the equation and report the results in the usual form. (iii) Compare the estimated LRP for the effect of
C Use the data in VOLAT.RAW for this exercise. The variable rsp500 is the monthl return on the Standard & Poor’s 500 stock market index, at an annual rate. (This includes price changes as well as dividends.) The variable i3 is the return on three-month T-bills, and pcip is the percentage change
C7 Use the data set CONSUMP.RAW for this exercis (i) Estimate a simple regression model relating the growth in real per capita consumption (of nondurables and services) to the growth in real per capita disposable income. Use the change in the logarithms in both cases. Report the results in the
C6 Use the data in FERTIL3.RAW for this exercis (i) Regress gfrt on t and t 2 and save the residuals. This gives a detrended gfrt , say, gf ·· t . (ii) Regress gf ·· t on all of the variables in equation (10.35), including t and t 2 . Compare the R-squared with that from (10.35). What do you
C Use the data in EZANDERS.RAW for this exercise. The data are on monthly unemployment claims in Anderson Township in Indiana, from January 1980 through Novembe 1988. In 1984, an enterprise zone (EZ) was located in Anderson (as well as other cities in Indiana). [See Papke (1994) for details.] (i)
C Use the data in FERTIL3.RAW to verify that the standard error for the LRP in equatio (10.19) is about .030.
C Add the variable log( prgnp) to the minimum wage equation in (10.38). Is this variabl significant? Interpret the coefficient. How does adding log( prgnp) affect the estimated minimum wage effect?
C2 Use the data in BARIUM.RAW for this exercis (i) Add a linear time trend to equation (10.22). Are any variables, other than the trend, statistically significant? (ii) In the equation estimated in part (i), test for joint significance of all variables except the time trend. What do you conclude?
C In October 1979, the Federal Reserve changed its policy of using finely tuned interes rate adjustments and instead began targeting the money supply. Using the data in INTDEF.RAW, define a dummy variable equal to 1 for years after 1979. Include this dummy in equation (10.15) to see if there is a
8 In the linear model given in equation (10.8), the explanatory variables xt 5 (xt1, ..., xtk) are said to be sequentially exogenous (sometimes called weakly exogenous) if E(ut uxt , xt21, …, x1) 5 0, t 5 1, 2, …, so that the errors are unpredictable given current and all past values of the
7 In Example 10.4, we wrote the model that explicitly contains the long-run propensity, u0, as gfrt 5 a0 1 u0 pet 1 d1( pet21 2 pet ) 1 d2( pet22 2 pet ) 1 ut , where we omit the other explanatory variables for simplicity. As always with multiple regression analysis, u0 should have a ceteris
6 In Example 10.4, we saw that our estimates of the individual lag coefficients in a distributed lag model were very imprecise. One way to alleviate the multicollinearity problem is to assume that the dj follow a relatively simple pattern. For concreteness, consider a model with four lags: yt 5 a0
5 Suppose you have quarterly data on new housing starts, interest rates, and real per capita income. Specify a model for housing starts that accounts for possible trends and seasonality in the variables.
4 When the three event indicators befile6, affile6, and afdec6 are dropped from equation (10.22), we obtain R2 5 .281 and - R2 5 .264. Are the event indicators jointly significant at the 10% level?
3 Suppose yt follows a second order FDL model: yt 5 a0 1 d0zt 1 d1zt21 1 d2zt22 1 ut . Let z * denote the equilibrium value of zt and let y* be the equilibrium value of yt , such that y* 5 a0 1 d0z * 1 d1z * 1 d2z * . Show that the change in y* , due to a change in z * , equals the long-run
2 Let gGDPt denote the annual percentage change in gross domestic product and let intt denote a short-term interest rate. Suppose that gGDPt is related to interest rates by gGDPt 5 a0 1 d0intt 1 d1intt21 1 ut , where ut is uncorrelated with intt , intt21, and all other past values of interest
1 Decide if you agree or disagree with each of the following statements and give a brief explanation of your decision: (i) Like cross-sectional observations, we can assume that most time series observations are independently distributed. (ii) The OLS estimator in a time series regression is
C13 Use the data in CEOSAL2.RAW to answer this question (i) Estimate the model lsalary 5 b0 1 b1lsales 1 b2lmktval 1 b3ceoten 1 b4ceoten2 1 u by OLS using all of the observations, where lsalary, lsales, and lmktvale are all natural logarithms. Report the results in the usual form with the usual OLS
C1 Use the data in ELEM94_95 to answer this question. See also Computer Exercise C10 i Chapter 4. (i) Using all of the data, run the regression lavgsal on bs, lenrol, lstaff, and lunch. Report the coefficient on bs along with its usual and heteroskedasticity-robust standard errors. What do you
C1 Use the data in MURDER.RAW only for the year 1993 for this question, although yo will need to first obtain the lagged murder rate, say mrdrte21. (i) Run the regression of mrdrte on exec, unem. What are the coefficient and t statistic on exec? Does this regression provide any evidence for a
C1 You need to use two data sets for this exercise, JTRAIN2.RAW and JTRAIN3.RAW The former is the outcome of a job training experiment. The file JTRAIN3.RAW contains observational data, where individuals themselves largely determine whether they participate in job training. The data sets cover the
C In this exercise, you are to compare OLS and LAD estimates of the effects of 401(k plan eligibility on net financial assets. The model is nettfa 5 b0 1 b1inc 1 b2inc2 1 b3age 1 b4age2 1 b5male 1 b6e401k 1 u. (i) Use the data in 401KSUBS.RAW to estimate the equation by OLS and report the results
C8 Use the data in TWOYEAR.RAW for this exercis (i) The variable stotal is a standardized test variable, which can act as a proxy variable for unobserved ability. Find the sample mean and standard deviation of stotal. (ii) Run simple regressions of jc and univ on stotal. Are both college education
C7 Use the data in LOANAPP.RAW for this exercis (i) How many observations have obrat  40, that is, other debt obligations more than 40% of total income?(ii) Reestimate the model in part (iii) of Computer Exercise C8, excluding observations with obrat  40. What happens to the estimate and t
C Redo Example 4.10 by dropping schools where teacher benefits are less than 1% o salary. (i) How many observations are lost? (ii) Does dropping these observations have any important effects on the estimated tradeoff?
C Use the data in RDCHEM.RAW to further examine the effects of outliers on OLS estimates and to see how LAD is less sensitive to outliers. The model rdintens 5 b0 1 b1sales 1 b2sales2 1 b3 profmarg 1 u, where you should first change sales to be in billions of dollars to make the estimates easier
C4 Use the data for the year 1990 in INFMRT.RAW for this exercis (i) Reestimate equation (9.43), but now include a dummy variable for the observation on the District of Columbia (called DC). Interpret the coefficient on DC and comment on its size and significance. (ii) Compare the estimates and
C3 Use the data from JTRAIN.RAW for this exercis (i) Consider the simple regression model log(scrap) 5 b0 1 b1grant 1 u, where scrap is the firm scrap rate and grant is a dummy variable indicating whether a firm received a job training grant. Can you think of some reasons why the unobserved factors
C2 Use the data set WAGE2.RAW for this exercise. (i) Use the variable KWW (the “knowledge of the world of work” test score) as a proxy for ability in place of IQ in Example 9.3. What is the estimated return to education in this case? (ii) Now, use IQ and KWW together as proxy variables. What
C1 (i) Apply RESET from equation (9.3) to the model estimated in Computer Exercise C5 in Chapter 7. Is there evidence of functional form misspecification in the equation? (ii) Compute a heteroskedasticity-robust form of RESET. Does your conclusion from part (i) change?
9 Suppose that log(y) follows a linear model with a linear form of heteroskedasticity. We write this as log(y) 5 b0 1 xb 1 u u|x ~ Normal(0,h(x)), so that, conditional on x, u has a normal distribution with mean (and median) zero but with variance h(x) that depends on x. Because Med(u|x) 5 0,
8 The point of this exercise is to show that tests for functional form cannot be relied on as a general test for omitted variables. Suppose that, conditional on the explanatory variables x1 and x2, a linear model relating y to x1 and x2 satisfies the Gauss-Markov assumptions: y 5 b0 1 b1x1 1 b2x2 1
7 Consider the simple regression model with classical measurement error, y 5 b0 1 b1x* 1 u, where we have m measures on x*. Write these as zh 5 x* 1 eh, h 5 1, …, m. Assume that x* is uncorrelated with u, e1, ...., em, that the measurement errors are pairwise uncorrelated, and have the same
6 In the model (9.17), show that OLS consistently estimates a and b if ai is uncorrelated with xi and bi is uncorrelated with xi and x2 i , which are weaker assumptions than (9.19). [Hint: Write the equation as in (9.18) and recall from Chapter 5 that sufficient for consistency of OLS for the
5 In Example 4.4, we estimated a model relating number of campus crimes to student enrollment for a sample of colleges. The sample we used was not a random sample of colleges in the United States, because many schools in 1992 did not report campus crimes. Do you think that college failure to
4 The following equation explains weekly hours of television viewing by a child in terms of the child’s age, mother’s education, father’s education, and number of siblings: tvhours* 5 b0 1 b1age 1 b2age2 1 b3motheduc 1 b4 fatheduc 1 b5sibs 1 u. We are worried that tvhours* is measured with
3 Let math10 denote the percentage of students at a Michigan high school receiving a passing score on a standardized math test (see also Example 4.2). We are interested in estimating the effect of per student spending on math performance. A simple model is math10 5 b0 1 b1log(expend) 1
2 Let us modify Computer Exercise C4 in Chapter 8 by using voting outcomes in 1990 for incumbents who were elected in 1988. Candidate A was elected in 1988 and was seeking reelection in 1990; voteA90 is Candidate A’s share of the two-party vote in 1990. The 1988 voting share of Candidate A is
1 In Problem 11 in Chapter 4, the R-squared from estimating the model log(salary) 5 b0 1 b1log(sales) 1 b2log(mktval) 1 b3 profmarg 1 b4ceoten 1 b5comten 1 u, using the data in CEOSAL2.RAW, was R2 5 .353 (n 5 177). When ceoten2 and comten2 are added, R2 5 .375. Is there evidence of functional form
C14 Use the data in BEAUTY.RAW for this question. (i) Using the data pooled for men and women, estimate the equation lwage 5 b0 1 b1belavg 1 b2abvavg 1 b3female 1 b4educ 1 b5exper 1 b5exper2 1 u, and report the results using heteroskedasticity-robust standard errors below coefficients. Are any of
C13 Use the data in FERTIL2.RAW to answer this question. (i) Estimate the model children 5 b0 1 b1age 1 b2age2 1 b3educ 1 b4electric 1 b5urban 1 u and report the usual and heteroskedasticity-robust standard errors. Are the robust standard errors always bigger than the nonrobust ones? (ii) Add the
C12 Use the data in MEAP00.RAW to answer this question. (i) Estimate the model math4 5 b0 1 b1lunch 1 b2log(enroll) 1 b3log(exppp) 1 u by OLS and obtain the usual standard errors and the fully robust standard errors. How do they generally compare? (ii) Apply the special case of the White test for
C1 Use the data in 401KSUBS.RAW for this question, restricting the sample to fsize 5 (i) To the model estimated in Table 8.1, add the interaction term, e401k inc. Estimate the equation by OLS and obtain the usual and robust standard errors. What do you conclude about the statistical significance
C10 Use the data set 401KSUBS.RAW for this exercis (i) Using OLS, estimate a linear probability model for e401k, using as explanatory variables inc, inc2 , age, age2 , and male. Obtain both the usual OLS standard errors and the heteroskedasticity-robust versions. Are there any important
C In Example 8.7, we computed the OLS and a set of WLS estimates in a cigarette demand equatio (i) Obtain the OLS estimates in equation (8.35). (ii) Obtain the ˆ hi used in the WLS estimation of equation (8.36) and reproduce equation (8.36). From this equation, obtain the unweighted residuals
C8 Use the data set GPA1.RAW for this exercis (i) Use OLS to estimate a model relating colGPA to hsGPA, ACT, skipped, and PC. Obtain the OLS residuals. (ii) Compute the special case of the White test for heteroskedasticity. In the regression of û2 i on colGPAi , colGPA2 i , obtain the
C7 Use the data in LOANAPP.RAW for this exercis (i) Estimate the equation in part (iii) of Computer Exercise C8 in Chapter 7, computing the heteroskedasticity-robust standard errors. Compare the 95% confidence interval on bwhite with the nonrobust confidence interval. (ii) Obtain the fitted values
C In Example 7.12, we estimated a linear probability model for whether a young ma was arrested during 1986: arr86 5 b0 1 b1pcnv 1 b2avgsen 1 b3tottime 1 b4 ptime86 1 b5qemp86 1 u. (i) Using the data in CRIME1.RAW, estimate this model by OLS and verify that all fitted values are strictly between
C5 Use the data in PNTSPRD.RAW for this exercis (i) The variable sprdcvr is a binary variable equal to one if the Las Vegas point spread for a college basketball game was covered. The expected value of sprdcvr, say m, is the probability that the spread is covered in a randomly selected game. Test
C4 Use VOTE1.RAW for this exercise. (i) Estimate a model with voteA as the dependent variable and prtystrA, democA, log(expendA), and log(expendB) as independent variables. Obtain the OLS residuals, uˆi , and regress these on all of the independent variables. Explain why you obtain R2 5 0. (ii)
C3 Apply the full White test for heteroskedasticity [see equation (8.19)] to equation (8.18). Using the chi-square form of the statistic, obtain the p-value. What do you conclude?
C2 (i) Use the data in HPRICE1.RAW to obtain the heteroskedasticity-robust standard errors for equation (8.17). Discuss any important differences with the usual standard errors. (ii) Repeat part (i) for equation (8.18). (iii) What does this example suggest about heteroskedasticity and the
C1 Consider the following model to explain sleeping behavior: sleep 5 b0 1 b1totwrk 1 b2educ 1 b3age 1 b4age2 1 b5 yngkid 1 b6male 1 u. (i) Write down a model that allows the variance of u to differ between men and women. The variance should not depend on other factors. (ii) Use the data in
7 Consider a model at the employee level, yi,e 5 b0 1 b1xi,e,1 1 b2xi,e,2 1 … 1 bkxi,e,k 1 fi 1 vi,e, where the unobserved variable fi is a “firm effect” to each employee at a given firm i. The error term vi,e is specific to employee e at firm i. The composite error is ui,e 5 fi 1 vi,e, such
6 There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedasticity. One possibility not covered in the text is to run the regression uˆi 2 on xi1, xi2, …, xik, yˆi 2 , i 5 1, …, n, where the uˆi are the OLS residuals and the yˆi are the OLS fitted
5 The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. Using the data in SMOKE.RAW, we estimate a linear probability model for smokes: smokes 5 .656 2 .069 log(cigpric) 1 .012 log(income) 2 .029 educ (.855) (.204) (.026) (.006) [.856] [.207] [.026]
4 Using the data in GPA3.RAW, the following equation was estimated for the fall and second semester students: trmgpa 5 22.12 1 .900 crsgpa 1 .193 cumgpa 1 .0014 tothrs (.55) (.175) (.064) (.0012) [.55] [.166] [.074] [.0012] 1 .0018 sat 2 .0039 hsperc 1 .351 female 2 .157 season (.0002) (.0018)
3 True or False: WLS is preferred to OLS when an important variable has been omitted from the model.
2 Consider a linear model to explain monthly beer consumption: beer 5 b0 1 b1inc 1 b2price 1 b3educ 1 b4 female 1 u E(uuinc,price, educ, female) 5 0 Var(uuinc,price, educ, female) 5 s2 inc2 . Write the transformed equation that has a homoskedastic error term.
1 Which of the following are consequences of heteroskedasticity? (i) The OLS estimators, b ˆ j , are inconsistent. (ii) The usual F statistic no longer has an F distribution. (iii) The OLS estimators are no longer BLUE.
C15 Use the data in FERTIL2.RAW to answer this questio (i) Find the smallest and largest values of children in the sample. What is the average of children? Does any woman have exactly the average number of children? (ii) What percentage of women have electricity in the home? (iii) Compute the
C1 Use the data in CHARITY.RAW to answer this question. The variable respond is dummy variable equal to one if a person responded with a contribution on the most recent mailing sent by a charitable organization. The variable resplast is a dummy variable equal to one if the person responded to the
C13 Use the data in APPLE.RAW to answer this questio (i) Define a binary variable as ecobuy 5 1 if ecolbs  0 and ecobuy 5 0 if ecolbs 5 0. In other words, ecobuy indicates whether, at the prices given, a family would buy any ecologically friendly apples. What fraction of families claim they
C1 Use the data set in BEAUTY.RAW, which contains a subset of the variables (but mor usable observations than in the regressions) reported by Hamermesh and Biddle (1994). (i) Find the separate fractions of men and women that are classified as having above average looks. Are more people rated as
C11 Use the data in 401KSUBS.RAW for this exercis (i) Compute the average, standard deviation, minimum, and maximum values of nettfa in the sample. (ii) Test the hypothesis that average nettfa does not differ by 401(k) eligibility status; use a two-sided alternative. What is the dollar amount of
C10 Use the data in NBASAL.RAW for this exercis (i) Estimate a linear regression model relating points per game to experience in the league and position (guard, forward, or center). Include experience in quadratic form and use centers as the base group. Report the results in the usual form.
C There has been much interest in whether the presence of 401(k) pension plans, availabl to many U.S. workers, increases net savings. The data set 401KSUBS.RAW contains information on net financial assets (nettfa), family income (inc), a binary variable for eligibility in a 401(k) plan (e401k), and
C Use the data in LOANAPP.RAW for this exercise. The binary variable to be explaine is approve, which is equal to one if a mortgage loan to an individual was approved. The key explanatory variable is white, a dummy variable equal to one if the applicant was white. The other applicants in the data
C7 Use the data in WAGE1.RAW for this exercis (i) Use equation (7.18) to estimate the gender differential when educ 5 12.5. Compare this with the estimated differential when educ 5 0. (ii) Run the regression used to obtain (7.18), but with female?(educ 2 12.5) replacing female?educ. How do you
C6 Use the data in SLEEP75.RAW for this exercise. The equation of interest sleep 5 b0 1 b1totwrk 1 b2educ 1 b3age 1 b4age2 1 b5yngkid 1 u. (i) Estimate this equation separately for men and women and report the results in the usual form. Are there notable differences in the two estimated equations?
C4 Use the data in GPA2.RAW for this exercis (i) Consider the equation colgpa 5 b0 1 b1hsize 1 b2hsize2 1 b3hsperc 1 b4sat 1 b5 female 1 b6athlete 1 u, where colgpa is cumulative college grade point average, hsize is size of high school graduating class, in hundreds, hsperc is academic percentile
C3 A model that allows major league baseball player salary to differ by position log(salary) 5 b0 1 b1years 1 b2gamesyr 1 b3bavg 1 b4hrunsyr 1 b5rbisyr 1 b6runsyr 1 b7 fldperc 1 b8allstar 1 b9 frstbase 1 b10scndbase 1 b11thrdbase 1 b12shrtstop 1 b13catcher 1 u, where outfield is the base group. (i)
C2 Use the data in WAGE2.RAW for this exercis (i) Estimate the model log(wage) 5 b0 1 b1educ 1 b2exper 1 b3tenure 1 b4married 1 b5black 1 b6south 1 b7urban 1 u and report the results in the usual form. Holding other factors fixed, what is the approximate difference in monthly salary between blacks
C1 Use the data in GPA1.RAW for this exercis (i) Add the variables mothcoll and fathcoll to the equation estimated in (7.6) and report the results in the usual form. What happens to the estimated effect of PC ownership? Is PC still statistically significant? (ii) Test for joint significance of
10 For a child i living in a particular school district, let voucheri be a dummy variable equal to one if a child is selected to participate in a school voucher program, and let scorei be that child’s score on a subsequent standardized exam. Suppose that the participation variable, voucheri , is
9 Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the model y 5 b0 1 d0d 1 b1z 1 d1d ? z 1 u; this is a general version of a model with an interaction between a dummy variable and a quantitative variable. [An example is in equation (7.17).] (i) Since it changes
8 Suppose you collect data from a survey on wages, education, experience, and gender. In addition, you ask for information about marijuana usage. The original question is: “On how many separate occasions last month did you smoke marijuana?” (i) Write an equation that would allow you to estimate
7 In the example in equation (7.29), suppose that we define outlf to be one if the woman is out of the labor force, and zero otherwise. (i) If we regress outlf on all of the independent variables in equation (7.29), what will happen to the intercept and slope estimates? (Hint: inlf 5 1 2 outlf.
6 To test the effectiveness of a job training program on the subsequent wages of workers, we specify the model log(wage) 5 b0 1 b1train 1 b2educ 1 b3exper 1 u, where train is a binary variable equal to unity if a worker participated in the program. Think of the error term u as containing unobserved

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