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Introductory Econometrics A Modern Approach 6th Edition Jeffrey M. Wooldridge - Solutions

Use the data in 401KSUBS for this exercise. The equation of interest is a linear probability model:pira 5 b0 1 b1p401k 1 b2inc 1 b3inc2 1 b4age 1 b5age2 1 u.The goal is to test whether there is a tradeoff between participating in a 401(k) plan and having an individual retirement account (IRA).
Use the data in PHILLIPS for this exercise.(i) In Example 11.5, we estimated an expectations augmented Phillips curve of the form Dinft 5 b0 1 b1unemt 1 et, where Dinft 5 inft 2 inft21. In estimating this equation by OLS, we assumed that the supply shock, et, was uncorrelated with unemt. If this is
Use the data in MURDER for this exercise. The variable mrdrte is the murder rate, that is, the number of murders per 100,000 people. The variable exec is the total number of prisoners executed for the current and prior two years; unem is the state unemployment rate.(i) How many states executed at
Use the data in CARD for this exercise.(i) In Table 15.1, the difference between the IV and OLS estimates of the return to education is economically important. Obtain the reduced form residuals, v^ 2, from the reduced form regression educ on nearc4, exper, exper2, black, smsa, south, smsa66,
Use the data in INTDEF for this exercise. A simple equation relating the three-month T-bill rate to the inflation rate (constructed from the Consumer Price Index) is i3t 5 b0 1 b1inft 1 ut.(i) Estimate this equation by OLS, omitting the first time period for later comparisons. Report the results in
Use the data in CARD for this exercise.(i) The equation we estimated in Example 15.4 can be written as log1wage2 5 b0 1 b1educ 1 b2exper 1 p 1 u,where the other explanatory variables are listed in Table 15.1. In order for IV to be consistent, the IV for educ, nearc4, must be uncorrelated with u.
The data in FERTIL2 include, for women in Botswana during 1988, information on number of children, years of education, age, and religious and economic status variables.(i) Estimate the model children 5 b0 1 b1educ 1 b2age 1 b3age2 1 u by OLS and interpret the estimates. In particular, holding age
Use the data in WAGE2 for this exercise.(i) In Example 15.2, if sibs is used as an instrument for educ, the IV estimate of the return to education is .122. To convince yourself that using sibs as an IV for educ is not the same as just plugging sibs in for educ and running an OLS regression, run the
Consider a simple time series model where the explanatory variable has classical measurement error:yt 5 b0 1 b1xp t 1 ut [15.58]xt 5 xp t 1 et, where ut has zero mean and is uncorrelated with xp t and et. We observe yt and xt only. Assume that et has zero mean and is uncorrelated with xp t and that
In a recent article, Evans and Schwab (1995) studied the effects of attending a Catholic high school on the probability of attending college. For concreteness, let college be a binary variable equal to unity if a student attends college, and zero otherwise. Let CathHS be a binary variable equal to
Suppose you want to test whether girls who attend a girls’ high school do better in math than girls who attend coed schools. You have a random sample of senior high school girls from a state in the United States, and score is the score on a standardized math test. Let girlhs be a dummy variable
The following is a simple model to measure the effect of a school choice program on standardized test performance [see Rouse (1998) for motivation and Computer Exercise C11 for an analysis of a subset of Rouse’s data]:score 5 b0 1 b1choice 1 b2faminc 1 u1, where score is the score on a statewide
(i) In the model with one endogenous explanatory variable, one exogenous explanatory variable, and one extra exogenous variable, take the reduced form for y2 (15.26), and plug it into the structural equation (15.22). This gives the reduced form for y1:y1 5 a0 1 a1z1 1 a2z2 1 v1.Find the aj in terms
Refer to equations (15.19) and (15.20). Assume that su 5 sx, so that the population variation in the error term is the same as it is in x. Suppose that the instrumental variable, z, is slightly correlated with u: Corr1z, u2 5 .1. Suppose also that z and x have a somewhat stronger correlation:
Suppose that, for a given state in the United States, you wish to use annual time series data to estimate the effect of the state-level minimum wage on the employment of those 18 to 25 years old (EMP). A simple model is gEMPt 5 b0 1 b1gMINt 1 b2gPOPt 1 b3gGSPt 1 b4gGDPt 1 ut, where MINt is the
Consider the simple regression model y 5 b0 1 b1x 1 u and let z be a binary instrumental variable for x. Use (15.10) to show that the IV estimator b^1 can be written as b^1 5 1y1 2 y0 2/1x1 2 x0 2, where y0 and x0 are the sample averages of yi and xi over the part of the sample with zi 5 0, and
Suppose that you wish to estimate the effect of class attendance on student performance, as in Example 6.3. A basic model is stndfnl 5 b0 1 b1atndrte 1 b2priGPA 1 b3ACT 1 u, where the variables are defined as in Chapter 6.(i) Let dist be the distance from the students’ living quarters to the
Consider a simple model to estimate the effect of personal computer (PC) ownership on college grade point average for graduating seniors at a large public university:GPA 5 b0 1 b1PC 1 u, where PC is a binary variable indicating PC ownership.(i) Why might PC ownership be correlated with u?(ii)
Use the data in COUNTYMURDERS to answer this question. The data set covers murders and executions (capital punishment) for 2,197 counties in the United States. See also Computer Exercise C16 in Chapter 13.(i) Consider the model murdrateit 5 ut 1 d0execsit 1 d1execsi,t21 1 d2execsi,t22 1
Use the data set in AIRFARE to answer this question. The estimates can be compared with those in Computer Exercise 10, in this Chapter.(i) Compute the time averages of the variable concen; call these concenbar. How many different time averages can there be? Report the smallest and the largest.(ii)
The data set DRIVING includes state-level panel data (for the 48 continental U.S. states) from 1980 through 2004, for a total of 25 years. Various driving laws are indicated in the data set, including the alcohol level at which drivers are considered legally intoxicated. There are also indicators
Use the data in ELEM94_95 to answer this question. The data are on elementary schools in Michigan. In this exercise, we view the data as a cluster sample, where each school is part of a district cluster.(i) What are the smallest and largest number of schools in a district? What is the average
This question assumes that you have access to a statistical package that computes standard errors robust to arbitrary serial correlation and heteroskedasticity for panel data methods.(i) For the pooled OLS estimates in Table 14.1, obtain the standard errors that allow for arbitrary serial
Use the data in AIRFARE for this exercise. We are interested in estimating the model log1 fareit 2 5 ht 1 b1concenit 1 b2log1disti 2 1 b3 3log1disti 2 42 1 ai 1 uit, t 5 1, p, 4, where ht means that we allow for different year intercepts.(i) Estimate the above equation by pooled OLS, being sure to
Use the data in MATHPNL for this exercise. You will do a fixed effects version of the first differencing done in Computer Exercise 11 in Chapter 13. The model of interest is math4it 5 d1y94t 1 p 1 d5y98t 1 g1log1rexppit 2 1 g2log1rexppi,t21 2 1 c1log1enrolit 2 1 c2lunchit 1 ai 1 uit, where the
Use the state-level data on murder rates and executions in MURDER for the following exercise.(i) Consider the unobserved effects model mrdrteit 5 ht 1 b1execit 1 b2unemit 1 ai 1 uit, where ht simply denotes different year intercepts and ai is the unobserved state effect. If past executions of
(i) In the wage equation in Example 14.4, explain why dummy variables for occupation might be important omitted variables for estimating the union wage premium.(ii) If every man in the sample stayed in the same occupation from 1981 through 1987, would you need to include the occupation dummies in a
For this exercise, we use JTRAIN to determine the effect of the job training grant on hours of job training per employee. The basic model for the three years is hrsempit 5 b0 1 d1d88t 1 d2d89t 1 b1grantit 1 b2granti,t2l 1 b3log1employit 2 1 ai 1 uit.(i) Estimate the equation using fixed effects.
Use the data in RENTAL for this exercise. The data on rental prices and other variables for college towns are for the years 1980 and 1990. The idea is to see whether a stronger presence of students affects rental rates. The unobserved effects model is log1rentit 2 5 b0 1 d0y90t 1 b1log1popit 2 1
The data in CENSUS2000 is a random sample of individuals from the United States. Here we are interested in estimating a simple regression model relating the log of weekly income, lweekinc, to schooling, educ. There are 29,501 observations. Associated with each individual is a state
Using the “cluster” option in the econometrics package Stata® 11, the fully robust standard errors for the pooled OLS estimates in Table 14.2—that is, robust to serial correlation and heteroskedasticity in the composite errors, 5vit: t 5 1, p , T6—are obtained as se1b^educ 2 5 .011,
In order to determine the effects of collegiate athletic performance on applicants, you collect data on applications for a sample of Division I colleges for 1985, 1990, and 1995.(i) What measures of athletic success would you include in an equation? What are some of the timing issues?(ii) What
Use the data in COUNTYMURDERS to answer this question. The data set covers murders and executions (capital punishment) for 2,197 counties in the United States.(i) Find the average value of murdrate across all counties and years. What is the standard deviation? For what percentage of the sample is
The data set HAPPINESS contains independently pooled cross sections for the even years from 1994 through 2006, obtained from the General Social Survey. The dependent variable for this problem is a measure of “happiness,” vhappy, which is a binary variable equal to one if the person reports
Use the data in JTRAIN3 for this question.(i) Estimate the simple regression model re78 5 b0 1 b1train 1 u, and report the results in the usual form. Based on this regression, does it appear that job training, which took place in 1976 and 1977, had a positive effect on real labor earnings in
Use the data in WAGEPAN for this exercise.(i) Consider the unobserved effects model lwageit 5 b0 1 d1d81t 1 p 1 d7d87t 1 b1educi 1 g1d81teduci 1 p 1 d7d87teduci 1 b2unionit 1 ai 1 uit, where ai is allowed to be correlated with educi and unionit. Which parameters can you estimate using first
Use the data in MURDER for this exercise.(i) Using the years 1990 and 1993, estimate the equation mrdrteit 5 d0 1 d1d93t 1 b1execit 1 b2unemit 1 ai 1 uit, t 5 1, 2 by pooled OLS and report the results in the usual form. Do not worry that the usual OLS standard errors are inappropriate because of
The file MATHPNL contains panel data on school districts in Michigan for the years 1992 through 1998. It is the district-level analogue of the school-level data used by Papke (2005). The response variable of interest in this question is math4, the percentage of fourth graders in a district
For this exercise, we use JTRAIN to determine the effect of the job training grant on hours of job training per employee. The basic model for the three years is hrsempit 5 b0 1 d1d88t 1 d2d89t 1 b1grantit 1 b2granti, t21 1 b3log1employit 2 1 ai 1 uit.(i) Estimate the equation using first
Use CRIME4 for this exercise.(i) Add the logs of each wage variable in the data set and estimate the model by first differencing.How does including these variables affect the coefficients on the criminal justice variables in Example 13.9?(ii) Do the wage variables in (i) all have the expected sign?
VOTE2 includes panel data on House of Representatives elections in 1988 and 1990. Only winners from 1988 who are also running in 1990 appear in the sample; these are the incumbents. An unobserved effects model explaining the share of the incumbent’s vote in terms of expenditures by both
Use GPA3 for this exercise. The data set is for 366 student-athletes from a large university for fall and spring semesters. [A similar analysis is in Maloney and McCormick (1993), but here we use a true panel data set.] Because you have two terms of data for each student, an unobserved effects
Use CRIME3 for this exercise.(i) In the model of Example 13.6, test the hypothesis H0: b1 5 b2. (Hint: Define u1 5 b1 2 b2 and write b1 in terms of u1 and b2. Substitute this into the equation and then rearrange. Do a t test on u1.)(ii) If b1 5 b2, show that the differenced equation can be written
Use the data in RENTAL for this exercise. The data for the years 1980 and 1990 include rental prices and other variables for college towns. The idea is to see whether a stronger presence of students affects rental rates. The unobserved effects model is log1rentit 2 5 b0 1 d0y90t 1 b1log1popit 2 1
Use the data in INJURY for this exercise.(i) Using the data for Kentucky, reestimate equation (13.12), adding as explanatory variables male, married, and a full set of industry and injury type dummy variables. How does the estimate on afchnge#highearn change when these other factors are controlled
Use the data in KIELMC for this exercise.(i) The variable dist is the distance from each home to the incinerator site, in feet. Consider the model log1price2 5 b0 1 d0y81 1 b1log1dist2 1 d1y81#log1dist2 1 u.If building the incinerator reduces the value of homes closer to the site, what is the sign
Use the data in CPS78_85 for this exercise.(i) How do you interpret the coefficient on y85 in equation (13.2)? Does it have an interesting interpretation? (Be careful here; you must account for the interaction terms y85#educ and y85#female.)(ii) Holding other factors fixed, what is the estimated
Use the data in FERTIL1 for this exercise.(i) In the equation estimated in Example 13.1, test whether living environment at age 16 has an effect on fertility. (The base group is large city.) Report the value of the F statistic and the p-value.(ii) Test whether region of the country at age 16 (South
(i) Using the data in INJURY for Kentucky, we find the estimated equation when afchnge is dropped from (13.12) is log1durat2 5 1.129 1 .253 highearn 1 .198 afchnge#highearn 10.0222 1.0422 1.0522 n 5 5,626, R2 5 .021.Is it surprising that the estimate on the interaction is fairly close to that in
If we think that b1 is positive in (13.14) and that Dui and Dunemi are negatively correlated, what is the bias in the OLS estimator of b1 in the first-differenced equation? [Hint: Review equation (5.4).]
Using the data in KIELMC, the following equations were estimated using the years 1978 and 1981:log1price2 5 11.49 2 .547 nearinc 1 .394 y81#nearinc 1.262 1.0582 1.0802 n 5 321, R2 5 .220 and log1price2 5 11.18 1 .563 y81 2 .403 y81#nearinc 1.272 1.0442 1.0672 n 5 321, R2 5 .337.Compare the
Use the data in APPROVAL to answer the following questions. See also Computer Exercise C14 in Chapter 11.(i) Estimate the equation approvet 5 b0 1 b1lcpifoodt 1 b2lrgaspricet 1 b3unemployt 1 b4sep11t 1 b5iraqinvadet 1 ut using first differencing and test the errors in the first-differenced (FD)
Use the data in BARIUM to answer this question.(i) In Table 12.1 the reported standard errors for OLS are uniformly below those of the corresponding standard errors for GLS (Prais-Winsten). Explain why comparing the OLS and GLS standard errors is flawed.(ii) Reestimate the equation represented by
Use the data in MINWAGE for this exercise, focusing on sector 232.(i) Estimate the equation gwage232t 5 b0 1 b1gmwaget 1 b2gcpii 1 ut, and test the errors for AR(1) serial correlation. Does it matter whether you assume gmwaget and gcpit are strictly exogenous? What do you conclude overall?(ii)
Use the data in OKUN to answer this question; see also Computer Exercise C11 in Chapter 11.(i) Estimate the equation pcrgdpt 5 b0 1 b1cunemt 1 ut and test the errors for AR(1) serial correlation, without assuming 5cunemt: t 5 1, 2, p6 is strictly exogenous. What do you conclude?(ii) Regress the
Use the data in INVEN for this exercise; see also Computer Exercise C6 in Chapter 11.(i) Obtain the OLS residuals from the accelerator model Dinvent 5 b0 1 b1DGDPt 1 ut and use the regression u^t on u^t21 to test for serial correlation. What is the estimate of r? How big a problem does serial
Use the data in NYSE to answer these questions.(i) Estimate the model in equation (12.47) and obtain the squared OLS residuals. Find the average, minimum, and maximum values of u^2 t over the sample.(ii) Use the squared OLS residuals to estimate the following model of heteroskedasticity:Var1ut
Use the data in PHILLIPS to answer these questions.(i) Using the entire data set, estimate the static Phillips curve equation inft 5 b0 1 b1 unemt 1 ut by OLS and report the results in the usual form.(ii) Obtain the OLS residuals from part (i), u^t, and obtain r from the regression u^t on u^t21.
The file FISH contains 97 daily price and quantity observations on fish prices at the Fulton Fish Market in New York City. Use the variable log(avgprc) as the dependent variable.(i) Regress log(avgprc) on four daily dummy variables, with Friday as the base. Include a linear time trend. Is there
Use the data in TRAFFIC2 for this exercise.(i) Run an OLS regression of prcfat on a linear time trend, monthly dummy variables, and the variables wkends, unem, spdlaw, and beltlaw. Test the errors for AR(1) serial correlation using the regression in equation (12.14). Does it make sense to use the
(i) For Example 12.4, using the data in BARIUM, obtain the iterative Cochrane-Orcutt estimates.(ii) Are the Prais-Winsten and Cochrane-Orcutt estimates similar? Did you expect them to be?
(i) In Computer Exercise C7 in Chapter 10, you estimated a simple relationship between consumption growth and growth in disposable income. Test the equation for AR(1) serial correlation(using CONSUMP).(ii) In Computer Exercise C7 in Chapter 11, you tested the permanent income hypothesis by
Consider the version of Fair’s model in Example 10.6. Now, rather than predicting the proportion of the two-party vote received by the Democrat, estimate a linear probability model for whether or not the Democrat wins.(i) Use the binary variable demwins in place of demvote in (10.23) and report
(i) Use NYSE to estimate equation (12.48). Let h^t be the fitted values from this equation (the estimates of the conditional variance). How many h^t are negative?(ii) Add return2 t21 to (12.48) and again compute the fitted values, h^t. Are any h^t negative?(iii) Use the h^t from part (ii) to
(i) In part (i) of Computer Exercise C6 in Chapter 11, you were asked to estimate the accelerator model for inventory investment. Test this equation for AR(1) serial correlation.(ii) If you find evidence of serial correlation, reestimate the equation by Cochrane-Orcutt and compare the results.
(i) Using the data in WAGEPRC, estimate the distributed lag model from Problem 5 in Chapter 11.Use regression (12.14) to test for AR(1) serial correlation.(ii) Reestimate the model using iterated Cochrane-Orcutt estimation. What is your new estimate of the long-run propensity?
In Example 11.6, we estimated a finite DL model in first differences (changes):cgfrt 5 g0 1 d0cpet 1 d1cpet21 1 d2cpet22 1 ut.Use the data in FERTIL3 to test whether there is AR(1) serial correlation in the errors.
follow an AR(1) model with parameter r and so we apply the Prais-Winsten method. If the errors do not follow an AR(1) model–for example, suppose they follow an AR(2) model, or an MA(1) model–why will the usual Prais-Winsten standard errors be incorrect?(ii) Can you think of a way to use the
Consider a standard multiple linear regression model with time series data:yt 5 b0 1 b1xt1 1 p 1 bkxtk 1 ut.Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold.(i) Suppose we think that the errors 5ut
In Example 12.8, we found evidence of heteroskedasticity in ut in equation (12.47). Thus, we compute the heteroskedasticity-robust standard errors (in 3# 4) along with the usual standard errors:returnt 5 .180 1 .059 returnt2l 1.0812 1.0382 3.0854 3.0694 n 5 689, R2 5 .0035, R2 5 .0020.What does
(i) In the enterprise zone event study in Computer Exercise C5 in Chapter 10, a regression of the OLS residuals on the lagged residuals produces r^ 5 .841 and se1r^ 2 5 .053. What implications does this have for OLS?(ii) If you want to use OLS but also want to obtain a valid standard error for the
In Example 10.6, we used the data in FAIR to estimate a variant on Fair’s model for predicting presidential election outcomes in the United States.
When the errors in a regression model have AR(1) serial correlation, why do the OLS standard errors tend to underestimate the sampling variation in the b^j? Is it always true that the OLS standard errors are too small?
Use the data in APPROVAL to answer the following questions. See also Computer Exercise C14 in Chapter 10.(i) Compute the first order autocorrelations for the variables approve and lrgasprice. Do they seem close enough to unity to worry about unit roots?(ii) Consider the model approvet 5 b0 1
Use the data in BEVERIDGE to answer this question. The data set includes monthly observations on vacancy rates and unemployment rates for the United States from December 2000 through February 2012.(i) Find the correlation between urate and urate_1. Would you say the correlation points more toward a
Use the data in MINWAGE for this exercise, focusing on the wage and employment 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; gmwage is the
Okun’s Law—see, for example, Mankiw (1994, Chapter 2)—implies the following relationship between the annual percentage change in real GDP, pcrgdp, and the change in the annual unemployment rate, cunem:pcrgdp 5 3 2 2 ? cunem.If the unemployment rate is stable, real GDP grows at 3% annually.
Use all the data in PHILLIPS to answer this question. You should now use 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 natural
Use the data in TRAFFIC2 for this exercise. Computer Exercise C11 in Chapter 10 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
Use the data in PHILLIPS for this exercise.(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.)(ii)
Use CONSUMP for this exercise. One version of the permanent income hypothesis (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
Let invent 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 three-month T-bills. The ex post real interest rate is (approximately) r3t 5 i3t 2 inft, where i3t is the rate on
(i) Add a linear time trend to equation (11.27). Is a time trend necessary in the first-difference equation?(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 linear
Use the data in PHILLIPS for this exercise, but only through 1996.(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 unemployment. In
(i) In Example 11.4, it may be that the expected value of the return at time t, given past returns, is a quadratic function of returnt21. To check this possibility, use the data in NYSE to estimate returnt 5b0 1b1returnt21 1b2returnt21 2 1ut;report the results in standard form.(ii) State and test
In Example 11.7, define the growth in hourly wage and output per hour as the change in the natural log: ghrwage 5 Dlog1hrwage2 and goutphr 5 Dlog1outphr2. 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
Use the data in HSEINV for this exercise.(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
A partial adjustment model is yp t 5 g0 1 g1xt 1 et yt 2 yt21 5 l1yp t 2 yt21 2 1 at, where yp t is the desired or optimal level of y and yt is the actual (observed) level. For example, yp t is the desired growth in firm inventories, and xt is growth in firm sales. The parameter g1 measures the
Let hy6t denote the three-month holding yield (in percent) from buying a six-month T-bill at time 1t 2 12 and selling it at time t (three months hence) as a three-month T-bill. Let hy3t21 be the threemonth holding yield from buying a three-month T-bill at time 1t 2 12. At time 1t 2 12, hy3t21 is
Let 5yt: t 5 1, 2, p6 follow a random walk, as in (11.20), with y0 5 0. Show that Corr1yt, yt1h 2 5 "t/1t 1 h2 for t $ 1, h . 0.
Suppose that a time series process 5yt 6 is generated by yt 5 z 1 et, for all t 5 1, 2, p, where 5et 6 is an i.i.d. sequence with mean zero and variance s2e. The random variable z does not change over time; it has mean zero and variance s2 z. Assume that each et is uncorrelated with z.(i) Find the
Let 5et: t 5 21, 0, 1, p6 be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a stochastic process by xt 5 et 2 11/22et21 1 11/22et22, t 5 1, 2, p.(i) Find E1xt 2 and Var1xt 2. Do either of these depend on t?(ii) Show that Corr1xt, xt11 2 5
Let 5xt: t 5 1, 2, p6 be a covariance stationary process and define gh 5 Cov1xt, xt1h 2 for h $ 0.[Therefore, g0 5 Var1xt 2.] Show that Corr1xt, xt1h 2 5 gh/g0.
Use the data in APPROVAL to answer the following questions. The data set consists of 78 months of data during the presidency of George W. Bush. (The data end in July 2007, before Bush left office.)In addition to economic variables and binary indicators of various events, it includes an approval
Use the data in MINWAGE for this exercise. In particular, use the employment 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, gmwage is
(i) Estimate equation (10.2) using all the data in PHILLIPS and report the 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 tradeoff
The file TRAFFIC2 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
Consider the model estimated in (10.15); use the data in INTDEF.(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 inflation
Use the data in VOLAT for this exercise. The variable rsp500 is the monthly 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 in
Use the data in FERTIL3 for this exercise.(i) Add pet23 and pet24 to equation (10.19). Test for joint significance of these lags.(ii) Find the estimated long-run propensity and its standard error in the model from part (i). Compare these with those obtained from equation (10.19).(iii) Estimate the

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