Question: Let invent be the real value inventories

> 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 otherwi

> 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: where PC is a binary variable indicating PC ownership. (i) Why might PC ownership be co

> 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 wit

> 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, {vit: t = 1, ….., ,T}—are

> Suppose that, for one semester, you can collect the following data on a random sample of college juniors and seniors for each class taken: a standardized final exam score, percentage of lectures attended, a dummy variable indicating whether the class is

> 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

> 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? Wha

> In a random effects model, define the composite error vit =

> With a single explanatory variable, the equation used to obtain the between estimator is where the overbar represents the average over time. We can assume that E(ai) = 0 because we have included an intercept in the equation. Suppose that ui is uncorrelat

> Suppose that the idiosyncratic errors in (14.4), {

> Using the data in INJURY for Kentucky, we find the estimated equation when afchnge is dropped from (13.12) is Is it surprising that the estimate on the interaction is fairly close to that in (13.12)? Explain. (ii) When afchnge is included but highearn is

> 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

> 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

> 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? crmrtet Во + 8od87, + Biunem, + a, + lis [13.14]

> Using the data in KIELMC, the following equations were estimated using the years 1978 and 1981: And Compare the estimates on the interaction term y81·nearinc with those from equation (13.9). Why are the estimates so different? log(price

> 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 aver

> Use the data in TRAFFIC2 for this exercise. (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 rate. (ii) Estimate a multiple regression m

> Consider a standard multiple linear regression model with time series data: Assume that Assumptions TS.1, TS.2, TS.3, and TS.4 all hold. (i) Suppose we think that the errors {ut} follow an AR(1) model with parameter r and so we apply the Prais-Winsten me

> 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: What does using the heteroskedasticity-robust t statistic do to the significa

> (i) A regression of the OLS residuals on the lagged residuals produces

> True or false: “If the errors in a regression model contain ARCH, they must be serially correlated.”

> Estimate 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?)

> Explain what is wrong with the following statement: “The Cochrane-Orcutt and Prais-Winsten methods are both used to obtain valid standard errors for the OLS estimates when there is a serial correlation.”

> 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

> 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. (i) Use a 2SLS routine to estimate the equation where sibs is the I

> Use the data in 401KSUBS for this exercise. The equation of interest is a linear probability model: The goal is to test whether there is a tradeoff between participating in a 401(k) plan and having an individual retirement account (IRA). Therefore, we wa

> Use the data in PHILLIPS for this exercise. (i) In Example 11.5, we estimated an expectations augmented Phillips curve of the form where ∆inft = inft – inft-1. In estimating this equation by OLS, we assumed that the su

> 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 r

> 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 unempl

> 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,

> 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 (i) Estimate this equation by OLS, omitting the first time period for later comparisons.

> Use the data in CARD for this exercise. (i) The equation is as 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. Could nearc4 be correlated with things

> 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 by OLS and interpret the estimates. In particular, holding age

> Use the data in CATHOLIC to answer this question. The model of interest is where cathhs is a binary indicator for whether a student attends a Catholic high school. (i) How many students are in the sample? What percentage of these students attend a Cathol

> The data set in VOUCHER, 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 tho

> Use the data in HTV 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

> Use the data in WAGE2 for this exercise. (i) 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

> The file PENSION 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 t

> 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. Let gct = log(ct) – log(ct-

> 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 where the first available year (the base year) is 1993 because of the lagged spe

> Use the state-level data on murder rates and executions in MURDER for the following exercise. (i) Consider the unobserved effects model where mrdrte = 1 + Biexec, + Bzunem, + a; + Uj, %3D

> Add the interaction term unionit ·t to the equation estimated in Table 14.2 to see if wage growth depends on union status. Estimate the equation by random and fixed effects and compare the results. TABLE 14.2 Three Different Estimators

> (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 y

> Papke also uses a model that allows each city to have its own time trend: where ai and ci are both unobserved effects. This allows for more heterogeneity across cities. (i) Show that, when the previous equation is first differenced, we obtain Notice that

> 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 (i) Estimate the equation using fixed effects. How many firms are used in the FE estimation?

> Use CRIME4 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?

> 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) Consider the model where θt represents a different intercept for each time pe

> 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

> 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 leg

> 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 sc

> 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 er

> Use the data in AIRFARE for this exercise. We are interested in estimating the model where log(fare) = n, + Biconcen + Bzlog(dist;) + B3[log(dist;) ]P + a; + uj, t = 1,..., 4,

> 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 wh

> 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 w

> 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 incumbentâ

> 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

> Use CRIME3 for this exercise. (i) In the model of Example 13.6, test the hypothesis H0:

> 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 w

> 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

> 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 signifi

> 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 If building the incinerator reduces the value of homes closer to the site, what is the sign of d1? What do

> 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? (ii) Holding other factors fixed, what is the estimated percent increase in nominal wage for a ma

> 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 dev

> 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 variabl

> Use the data in JTRAIN3 for this question. (i) Estimate the simple regression model re78 =

> Use the data in WAGEPAN for this exercise. (i) Consider the unobserved effects model where ai is allowed to be correlated with educi and unionit. Which parameters can you estimate using first differencing? (ii) Estimate the equation from part (i) by FD,

> Use the data in MURDER for this exercise. (i) Using the years 1990 and 1993, estimate the equation 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 presence of ai. Do

> 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 percen

> 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 (i) Estimate the equation using first differencing. How many firms are used in the estimation

> 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

> Use the data in PHILLIPS for this exercise, but only through 1996. (i) 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 pas

> 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 b

> 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 equ

> (i) Use 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 tes

> 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 binar

> (i) Use NYSE to estimate equation (12.48). Let â„Ž t be the fitted values from this equation (the estimates of the conditional variance). How many â„Ž t are negative? (ii) Add return2t21 to (12.48) and again compute the

> (i) In part (1) 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. 1) Use the data in INVEN to estimate the accelerator model. Report the resu

> (i) Using the data in WAGEPRC, estimate the distributed lag model by Using regression given below 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 propen

> Use the data in MINWAGE for this exercise, focusing on sector 232. (i) Estimate the equation 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 =

> It may be that the expected value of the return at time t, given past returns, is a quadratic function of return-1. To check this possibility, use the data in NYSE to estimate report the results in standard form. (ii) State and test the null hypothesis t

> 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 ∆invent =

> 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

> Use the data in PHILLIPS to answer these questions. (i) Using the entire data set, estimate the static Phillips curve equation inft =

> we estimated a finite DL model in first differences (changes): Use the data in FERTIL3 to test whether there is AR(1) serial correlation in the errors. cgfr, 3 Yo + dосре, + бусре, -1 + бәсре, -2 + и,.

> Use the data in APPROVAL to answer the following questions. See also Computer Exercise C14 in Chapter 11. (i) Estimate the equation using first differencing and test the errors in the first-differenced (FD) equation for AR(1) serial correlation. In par

> 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

> Use the data in APPROVAL to answer the following questions. (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 where the first two

> 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. Woul

> 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

> Suppose that the equation satisfies the sequential exogeneity assumption in equation (11.40). (i) Suppose you difference the equation to obtain How come applying OLS on the differenced equation does not generally result in consistent estimators of the

> 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 se

> A partial adjustment model is where y*t is the desired or optimal level of y and yt is the actual (observed) level. For example, y*t is the desired growth in firm inventories, and xt is growth in firm sales. The parameter g1 measures the effect of xt on

> 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 hy3t-1 be the three month holding yield from buying a three-month T-bill

> 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 = ∆log(price) and gwage = â&#

> Let {yt: t = 1, 2,….} follow a random walk, as in (11.20), with y0 = 0. Show that for t ≥ 1, h > 0. Corr(y, Yt+h) = /(t + h) Y: = yt-1 + e, t = 1, 2, ..., [11.20]

> Suppose that a time series process {yt} is generated by yt = z + et, for all t = 1, 2,…. , where {et} is an i.i.d. sequence with mean zero and variance σ2e. The random variable z does not change over time; it has mean zero and variance σ2e. Assume that e

> Let {et: t = -1, 0, 1, ……} be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a stochastic process by xt = et – (1/2)et-1 + (1/2)et-2, t = 1, 2,……. (i) Find E(xt) and Var(xt). Do either of these

> Let {xt: t = 1, 2,…….} be a covariance stationary process and define