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introductory econometrics modern

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

C11 A common method for estimating Engel curves is to model expenditure shares as a function of total expenditure, and possibly demographic variables. A common specification has the form sgood  b0 b1ltotexpend1 demographic 1 where sgood is the fraction of spending on a particular good out of
C10 Use the entire panel data set in AIRFARE.RAW for this exercise. The demand equation in a simultaneous equations unobserved effects model is log(passenit)  ut1  a1log(fareit)  ai1  uit1, where we absorb the distance variables into ai1. (i) Estimate the demand function using fixed
C9 For this exercise, use the data in AIRFARE.RAW, but only for the year 1997. (i) A simple demand function for airline seats on routes in the United States is log(passen)  b10  a1log(fare)  b11log(dist)  b12[log(dist)]2  u1,where passen average passengers per day fare average
C8 Use the data set in FISH.RAW, which comes from Graddy (1995), to do this exercise. The data set is also used in Computer Exercise C9 in Chapter 12. Now, we will use it to estimate a demand function for fish. (i) Assume that the demand equation can be written, in equilibrium for each time period,
C7 Refer to Example 13.9 and the data in CRIME4.RAW. (i) Suppose that, after differencing to remove the unobserved effect, you think log(polpc) is simultaneously determined with log(crmrte); in particular, increases in crime are associated with increases in police officers. How does this help
C6 Use the data in CEMENT.RAW for this exercise. (i) A static (inverse) supply function for the monthly growth in cement price (gprc) as a function of growth in quantity (gcem) is gprct  a1gcemt  b0  b1gprcpet  b2 febt  …  b12dect  ut s , where gprcpet (growth in the price of
C5 Use the Economic Report of the President (2005 or later) to update the data in CONSUMP.RAW, at least through 2003. Reestimate equation (16.35). Do any important conclusions change?
C4 Use the data in CONSUMP.RAW for this exercise. (i) In Example 16.7, use the method from Section 15.5 to test the single overidentifying restriction in estimating (16.35). What do you conclude? (ii) Campbell and Mankiw (1990) use second lags of all variables as IVs because of potential data
C3 Use the data in OPENNESS.RAW for this exercise. (i) Because log(pcinc) is insignificant in both (16.22) and the reduced form for open, drop it from the analysis. Estimate (16.22) by OLS and IV without log(pcinc). Do any important conclusions change? (ii) Still leaving log(pcinc) out of the
C2 Use MROZ.RAW for this exercise. (i) Reestimate the labor supply function in Example 16.5, using log(hours) as the dependent variable. Compare the estimated elasticity (which is now constant) to the estimate obtained from equation (16.24) at the average hours worked.(ii) In the labor supply
C1 Use SMOKE.RAW for this exercise. (i) A model to estimate the effects of smoking on annual income (perhaps through lost work days due to illness, or productivity effects) is log(income)  b0  b1cigs  b2educ  b3age  b4age2  u1, where cigs is number of cigarettes smoked per day, on
8 How big is the effect of per-student school expenditures on local housing values? Let HPRICE be the median housing price in a school district and let EXPEND be per-student expenditures. Using panel data for the years 1992, 1994, and 1996, we postulate the model lHPRICEit  ut  b1lEXPENDit
change the estimated equation? (vi) If some games are sold out, what problems does this cause for estimating the demand function? (Hint: If a game is sold out, do you necessarily observe the true demand?)
7 For a large university, you are asked to estimate the demand for tickets to women’s basketball games. You can collect time series data over 10 seasons, for a total of about 150 observations. One possible model is lATTENDt  b0  b1lPRICEt  b2WINPERCt  b3RIVALt  b4WEEKENDt  b5t
6 Consider a linear probability model for whether employers offer a pension plan based on the percentage of workers belonging to a union, as well as other factors: pension  b0  b1percunion  b2avgage  b3avgeduc  b4 percmale  b5percmarr  u1. (i) Why might percunion be jointly
5 A simple model to determine the effectiveness of condom usage on reducing sexually transmitted diseases among sexually active high school students is infrate  b0  b1conuse  b2percmale  b3avginc  b4city  u1, where infrate the percentage of sexually active students who have
4 Suppose that annual earnings and alcohol consumption are determined by the SEM log(earnings)  b0  b1alcohol  b2educ  u1 alcohol  g0  g1log(earnings)  g2educ  g3log(price)  u2, where price is a local price index for alcohol, which includes state and local taxes. Assume
3 In Problem 3 of Chapter 3, we estimated an equation to test for a tradeoff between minutes per week spent sleeping (sleep) and minutes per week spent working (totwrk) for a random sample of individuals. We also included education and age in the equation. Because sleep and totwrk are jointly
2 Let corn denote per capita consumption of corn in bushels at the county level, let price be the price per bushel of corn, let income denote per capita county income, and let rainfall be inches of rainfall during the last corn-growing season. The following simultaneous equations model imposes the
1 Write a two-equation system in “supply and demand form,” that is, with the same variable y1 (typically, “quantity”) appearing on the left-hand side: y1  a1y2  b1z1  u1 y1  a2y2  b2z2  u2. (i) If a1  0 or a2  0, explain why a reduced form exists for y1. (Remember, a
C11 The data set in VOUCHER.DTA, which is a subset of the data used in Rouse (1998), can be used to estimate the effect of school choice on academic achievement. Attendance at a choice school was paid for by a voucher, which was determined by a lottery among those who applied. The data subset was
C10 Use the data in HTV.RAW for this exercise. (i) Run a simple OLS regression of log(wage) on educ. Without controlling for other factors, what is the 95% confidence interval for the return to another year of education? (ii) The variable ctuit, in thousands of dollars, is the change in college
C9 The purpose of this exercise is to compare the estimates and standard errors obtained by correctly using 2SLS with those obtained using inappropriate procedures. Use the data file WAGE2.RAW. (i) Use a 2SLS routine to estimate the equation log(wage) 5 b0 1 b1educ 1 b2exper 1 b3tenure 1 b4black 1
C8 Use the data in 401KSUBS.RAW 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
C7 Use the data in PHILLIPS.RAW 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 .
C6 Use the data in MURDER.RAW 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
C5 Use the data in CARD.RAW 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, vˆ2, from the reduced form regression educ on nearc4, exper, exper2 , black, smsa, south,
C4 Use the data in INTDEF.RAW for this exercise. A simple equation relating the threemonth 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
C3 Use the data in CARD.RAW for this exercise. (i) The equation we estimated in Example 15.4 can be written as log(wage) 5 b0 1 b1educ 1 b2exper 1 … 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
C2 The data in FERTIL2.RAW 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,
C1 Use the data in WAGE2.RAW 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,
11 Consider a simple time series model where the explanatory variable has classical measurement error: yt 5 b0 1 b1x* t 1 ut [15.58] xt 5 x* t 1 et , where ut has zero mean and is uncorrelated with x* t and et . We observe yt and xt only. Assume that et has zero mean and is uncorrelated with x* t
10 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
9 Suppose that, in equation (15.8), you do not have a good instrumental variable candidate for skipped. But you have two other pieces of information on students: combined SAT score and cumulative GPA prior to the semester. What would you do instead of IV estimation?
8 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
7 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 b2 faminc 1 u1, where score is the score on a
6 (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
5 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: Corr(z,u) 5 .1. Suppose also that z and x have a somewhat stronger correlation:
4 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
3 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 ˆ 1 can be written as bˆ 1 5 ( - y1 2 - y0)/(- x1 2 - x0), where - y0 and - x0 are the sample averages of yi and xi over the part of the sample
2 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 b2 priGPA 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
1 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)
C14 Use the data set in AIRFARE.RAW 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
C13 The data set DRIVING.RAW 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
C12 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
C11 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
C10 Use the data in AIRFARE.RAW for this exercise. We are interested in estimating the model log( fareit)  t  1concenit  2log )  3[log(dis )]2  ai  uit, t 1, where t means that we allow for different year intercepts.(i) Estimate the above equation by pooled OLS,
C9 The file PENSION.RAW contains information on participant-directed pension plans for U.S. workers. Some of the observations are for couples within the same family, so this data set constitutes a small cluster sample (with cluster sizes of two). (i) Ignoring the clustering by family, use OLS to
C5 (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
C4 In Example 13.8, we used the unemployment claims data from Papke (1994) to estimate the effect of enterprise zones on unemployment claims. Papke also uses a model that allows each city to have its own time trend: log(uclmsit) ai ci  1ezt  where ai and ci are both unobserved effects.
C3 For this exercise, we use JTRAIN.RAW 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 0 1d8t  289t  1grntit  2gra  3log(employit) a  u (i) Estimate the equation using
C2 Use CRIME4.RAW for this exercise. (i) Reestimate the unobserved effects model for crime in Example 13.9 but use fixed effects rather than differencing. Are there any notable sign or magnitude changes in the coefficients? What about statistical significance? (ii) Add the logs of each wage
C1 Use the data in RENTAL.RAW 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 log(rent) = Bo+8y90, + Blog(pop) +
C15 The data set HAPPINESS.RAW 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
C14 Use the data in JTRAIN3.RAW 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
C13 Use the data in WAGEPAN.RAW for this exercise. (i) Consider the unobserved effects model lwageit 5 b0 1 d1d81t 1 … 1 d7d87t 1 b1educi 1 g1d81t educi 1 … 1 d7 d87t educi 1 b2unionit 1 ai 1 uit, where ai is allowed to be correlated with educi and unionit. Which parameters can you estimate
C12 Use the data in MURDER.RAW 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
C11 The file MATHPNL.RAW 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
C10 For this exercise, we use JTRAIN.RAW 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 b3log(employit) 1 ai 1 uit. (i) Estimate the equation using first
C9 Use CRIME4.RAW 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
C8 VOTE2.RAW 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
C7 Use GPA3.RAW 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
C6 Use CRIME3.RAW 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
C5 Use the data in RENTAL.RAW 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 log(rentit) 5 b0 1 d0y90t 1
C4 Use the data in INJURY.RAW 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
C3 Use the data in KIELMC.RAW for this exercise. (i) The variable dist is the distance from each home to the incinerator site, in feet. Consider the model log(price) 5 b0 1 d0 y81 1 b1log(dist) 1 d1y81?log(dist) 1 u. If building the incinerator reduces the value of homes closer to the site, what is
C2 Use the data in CPS78_85.RAW 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
C1 Use the data in FERTIL1.RAW 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
7 (i) Using the data in INJURY.RAW for Kentucky, we find the estimated equation when afchnge is dropped from (13.12) is log(durat) 5 1.129 1 .253 highearn 1 .198 afchnge·highearn (0.022) (.042) (.052) n 5 5,626, R2 5 .021. Is it surprising that the estimate on the interaction is fairly close to
6 In 1985, neither Florida nor Georgia had laws banning open alcohol containers in vehicle passenger compartments. By 1990, Florida had passed such a law, but Georgia had not. (i) Suppose you can collect random samples of the driving-age population in both states, for 1985 and 1990. Let arrest be a
5 Suppose that we want to estimate the effect of several variables on annual saving and that we have a panel data set on individuals collected on January 31, 1990, and January 31, 1992. If we include a year dummy for 1992 and use first differencing, can we also include age in the original model?
4 If we think that b1 is positive in (13.14) and that ∆ui and ∆unemi are negatively correlated, what is the bias in the OLS estimator of b1 in the first-differenced equation? [Hint: Review equation (5.4).]
3 Why can we not use first differences when we have independent cross sections in two years (as opposed to panel data)?
2 Using the data in KIELMC.RAW, the following equations were estimated using the years 1978 and 1981: log(price) 5 11.49 2 .547 nearinc 1 .394 y81?nearinc (.26) (.058) (.080) n 5 321, R2 5 .220 and log(price) 5 11.18 1 .563 y81 2 .403 y81?nearinc (.27) (.044) (.067) n 5 321, R2 5 .337.
1 In Example 13.1, assume that the averages of all factors other than educ have remained constant over time and that the average level of education is 12.2 for the 1972 sample and 13.3 in the 1984 sample. Using the estimates in Table 13.1, find the estimated change in average fertility between 1972
C15 Use the data in BARIUM.RAW 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 erorrs is flawed. (ii) Reestimate the equation
C14 Use the data in MINWAGE.RAW 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
C13 Use the data in OKUN.RAW 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 {cunemt : t 5 1, 2, …} is strictly exogenous. What do you conclude? (ii)
C12 Use the data in INVEN.RAW for this exercise; see also Computer Exercise C6 in Chapter 11. (i) Obtain the OLS residuals from the accelerator model ∆invent 5 b0 1 b1∆GDPt 1 ut and use the regression ût on ût21 to test for serial correlation. What is the estimate of r? How big a problem does
C11 Use the data in NYSE.RAW 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 û2 t over the sample.(ii) Use the squared OLS residuals to estimate the following model of heteroskedasticity:
C10 Use the data in PHILLIPS.RAW 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), ût , and obtain r from the regression ût
C9 The file FISH.RAW 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
C8 Use the data in TRAFFIC2.RAW 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
C7 (i) For Example 12.4, using the data in BARIUM.RAW, obtain the iterative CochraneOrcutt estimates.(ii) Are the Prais-Winsten and Cochrane-Orcutt estimates similar? Did you expect them to be?
C6 (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.RAW). (ii) In Computer Exercise C7 in Chapter 11, you tested the permanent income hypothesis
C5 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
C4 (i) Use NYSE.RAW to estimate equation (12.48). Let ˆ ht be the fitted values from this equation (the estimates of the conditional variance). How many ˆ ht are negative? (ii) Add return2 t21 to (12.48) and again compute the fitted values, ˆ ht . Are any ˆ ht negative? (iii) Use the ˆ ht from
C3 (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 CochraneOrcutt and compare the results.
C2 (i) Using the data in WAGEPRC.RAW, 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? (iii) Using
C1 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.RAW to test whether there is AR(1) serial correlation in the errors.
7 Consider a standard multiple linear regression model with time series data:
6 In Example 12.8, we found evidence of heteroskedasticity in ut in equation (12.47). Thus, we compute the heteroskedasticity-robust standard errors (in [?]) along with the usual standard errors: returnt 5 .180 1 .059 returnt21 (.081) (.038) [.085] [.069] n 5 689, R2 5 .0035, - R2 5 .0020. What
5 (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 ˆ 5 .841 and se( r ˆ) 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
4 True or false: “If the errors in a regression model contain ARCH, they must be serially correlated.”
3 In Example 10.6, we estimated a variant on Fair’s model for predicting presidential election outcomes in the United States. (i) What argument can be made for the error term in this equation being serially uncorrelated? (Hint: How often do presidential elections take place?)(ii) When the OLS
2 Explain what is wrong with the following statement: “The Cochrane-Orcutt and PraisWinsten methods are both used to obtain valid standard errors for the OLS estimates when there is a serial correlation.”
1 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 ˆ j ? Is it always true that the OLS standard errors are too small?
C13 Use the data in BEVERIDGE.RAW to answer this question. The data set includes monthly observations on vacancy rates and unemployment rates for the U.S. from December 2000 through February 2012. (i) Find the correlation beween urate and urate_1. Would you say the correlation points more toward a
C1 Use the data in MINWAGE.RAW for this exercise, focusing on the wage and employment series for sector 232 (Men’s and Boys’ Furnishings). The variable gwage232 i the monthly growth (change in logs) in the average wage in sector 232; gemp232 is the growth in employment in sector 232; gmwage is
C1 Okun’s Law—see, for example, Mankiw (1994, Chapter 2)—implies the followin 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%

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