Questions and Answers of Econometric

In Example 11.6, we estimated a finite DL model in first differences:(g/rt = (0 + (0(pet + (1(pet-1 + 82(pett-2 + ut.Use the data in FERTIL3.RAW to test whether there is AR(1) serial correlation in
Use the data in PHILLIPS.RAW to answer these questions.(i) Using the entire data set, estimate the static Phillips curve equation inft = (0 + (1 unemt + ut by OLS and report the results in the usual
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 u] over the
Use the data in INVEN.RAW for this exercise; see also Computer Exercise CI 1.6.(i) Obtain the OLS residuals from the accelerator model (inventt - (0 + (1(GDPi + ut and use the regression t on t-1
Use the data in OKUN.RAW to answer this question; see also Computer Exercise 11.11.(i) Estimate the equation pcrgdpt = (0 + (1 (unemt + ut and test the errors for AR(1) serial correlation, without
Use the data in MINWAGE.RAW for this exercise, focusing on sector 232.(i) Estimate the equationgwage232t = (0 + (1 ygmwaget + (2 gcpi i+ ut,and test the errors for AR( 1) serial correlation. Does it
(i) Using the data in WAGEPRC.RAW, estimate the distributed lag model from Problem 11.5. Use regression (12.14) to test for AR(1) serial correlation.(ii) Reestimate the model using iterated
(i) In part (i) of Computer Exercise CI 1.6, 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
(i) Use NYSE.RAW to estimate equation (12.48). Let t be the fitted values from this equation (the estimates of the conditional variance). How many t are negative?(ii) Add return2t-1 to (12.48) and
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
In Computer Exercise C10.7, 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)
(i) For Example 12.4, using the data in BARIUM.RAW, obtain the iterative Cochrane-Orcutt estimates, (ii) Are the Prais-Winsten and Cochrane-Orcutt estimates similar? Did you expect them to be?
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
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
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
Using the data in KIELMC.RAW, 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
Why can we not use first differences when we have independent cross sections in two years (as opposed to panel data)?
If we think that (1 is positive in (13.14) and that (ui. and (unemi are negatively correlated, what is the bias in the OLS estimator of (1, in the first-differenced equation? [Review equation (5.4).]
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
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
(i) Using the data in INJURY.RAW for Kentucky, the estimated equation when afchnge is dropped from (13.12) isIs it surprising that the estimate on the interaction is fairly close to that in (13.12)?
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.)
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 ishrsempit = (0 + (1td88t + (2d89, +
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
Use the data in MURDER.RAW for this exercise.(i) Using the years 1990 and 1993, estimate the equationmrdrteit = (0 + (1d93t + (1execit + (2unemit + ai + uit,t = 1, 2By pooled OLS and report the
Use the data in WAGEPAN.RAW for this exercise.(i) Consider the unobserved effects modelIwage it = (0 + (1d81t+ ... + (7d87t + (1educi+ (1d81t, educi + ... + (7dx87t educi + (2 unionit + ai +
Use the data in JTRAIN3.RAW for this question.(i) Estimate the simple regression model re78 = (0 + (1 Strain + u, and report the results in the usual form. Based on this regression, does it appear
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
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 modellog(price) = (0 + (0y81 + (1 log(dist) + (0y81 (
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
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
Use CRIME3.RAW for this exercise.(i) In the model of Example 13.6, test the hypothesis H0 : (1 = (2 (Define (1 = (1 - (2 and write, (1 in terms of (1 and (2. Substitute this into the equation and
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
VOTE2.RAW includes panel data on House of Representative 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
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
Suppose that the idiosyncratic errors in (14.4), {uit: t = 1, 2,....,T}, are serially uncorrelated with constant variance,σit2. Show that the correlation between adjacent differences, Δuit and
With a single explanatory variable, the equation used to obtain the between estimator iswhere the overbar represents the average over time. We can assume that E(a.) = 0 because we have included an
In a random effects model, define the composite error vit = ai + uit, where ai is uncorrelated with uit and the uit have constant variance σ2it and are serially uncorrelated. Define eit = vit (λi,
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
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
Suing the "cluster" option in the econometrics package Stata®, the fully robust standard errors for pooled OLS estimates in Table 14.2--that is, robust to serial correlation and heteroskedasticity
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
Use the data in AIRFARE.RAW for this exercise. We are interested in estimating the modelwhere 6t means that we allow for different year intercepts.(i) Estimate the above equation by pooled OLS, being
This question assumes that you have access to a statistical package the computes standard errors robust to arbitrary serial correlation and heteroskedasticity for panel data methods. (i) For the
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
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
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(i) Estimate the equation using
In Example 13.8, we used the unemployment claims data from Papke (1994) to esti¬mate the effect of enterprise zones on unemployment claims. Papke also uses a model that allows each city to have its
(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
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.
Use the state-level data on murder rates and executions in MURDER.RAW for the following exercise.(i) Consider the unobserved effects modelwhere 6, simply denotes different year intercepts and a is
Use the data in MATHPNL.RAW for this exercise. You will do a fixed effects version of the first differencing done in Computer Exercise C13.11. The model of interest iswhere the first available year
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
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 = β0 + β1PC + u, where PC
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
Consider a simple time series model where the explanatory variable has classical measurement error:where ut has zero mean and is uncorrelated with x*t, and et. We observe yt and xt only. Assume that
Suppose that you wish to estimate the effect of class attendance on student performance, as in Example 6.3. A basic model is Stndfnl = β0 + β1 atndrte + β2 priGPA + β3 ACT + u, where the
Consider the simple regression modelY = Î²0 + Î²1 x + uand let z be a binary instrumental variable for x. Use (15.10) to show that the IV estimator 1, can be written aswhere 0 and 0 are the
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
Refer to equations (15.19) and (15.20). Assume that σit = σx, 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
(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
The following is a simple model to measure the effect of a school choice program on standardized test performance [see Rouse (1998) for motivation]: Score = β0 + β1 choice + β2 faminc + u1, where
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
Use the data in WAGE2.RAW for this exercise.(i) In Example 15.2, using sibs as an instrument for educ, the IV estimate of the return to education is . 122. To convince yourself that using sibs as an
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
The data in FERTIL2.RAW includes, for women in Botswana during 1988, information on number of children, years of education, age, and religious and economic status variables.(i) Estimate the
Use the data in CARD.RAW for this exercise.(i) The equation we estimated in Example 15.4 can be written aslog(wage) = β0 + β1 educ + β2 exper + ... + u,where the other explanatory variables are
Use the data in INTDEF.RAW for this exercise. A simple equation relating the three-month T-bill rate to the inflation rate (constructed from the Consumer Price Index) isi3t = β0 + β1inft + ut,(i)
Use the data in CARD.RAW for this exercise.(ii) Estimate the equation by 2SLS, adding nearc2 as an instrument. Does the coefficient on educ change much?(iii) Test the single over identifying
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
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
Use the data in PHILLIPS.RAW for this exercise.(i) In Example 11.5, we estimated an expectations augmented Phillips curve of the formΔinft = β0 + β1 unemt + et,where Δinft = inft - inft-1. In
Use the data in 401 KSUBS.RAW for this exercise. The equation of interest is a linear probability model:pira = β0 + β 1p401k + β2jnc + β3Jnc2 + β4 age + β5 age2 + u.The goal is to test whether
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
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: (i) If Î±, = 0 or Î±2 = 0, explain why a
In Problem 3.3 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
Suppose that annual earnings and alcohol consumption are determined by the SEM log(earnings) = β0 + β1 alcohol + β2 educ + ux alcohol - y0 + y1 log(earnings) + y2educ + y3 log(price) + u2, where
A simple model to determine the effectiveness of condom usage on reducing sexually transmitted diseases among sexually active high school students isinfrate = β0 + β1 conuse + β2 percmale + β3
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 = β0 + β1percunion +
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
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
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) islog{income) = β0 + β1cigs
Use the entire panel data set in AIRFARE.RAW for this exercise. The demand equation in a simultaneous equations unobserved effects model isLog(passenit) = θit + α1 log(fareit) + ait + uit,where we
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
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
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)
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?
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) isgprct = αtgcemt + β0 +
Refer to Example 13.9 and the data in CRIME4.RAW.(i) Suppose that, after differencing to remove the unobserved effect, you think Δlog(polpc) is simultaneously determined with Δlog(crmrte); in
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 C12.9. Now, we will use it to estimate a demand function for fish.(i)
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 isLog(passen) = β10 + α1 log(fare) + β11
(i) For a binary response y, let y be the proportion of ones in the sample (which is equal to the sample average of the y.). Let 0 be the percent correctly predicted for the outcome y = 0 and let 1
Let grad be a dummy variable for whether a student-athlete at a large university graduates in five years. Let hsGPA and SAT be high school grade point average and SAT score, respectively. Let study
(Requires calculus)(i) Suppose in the Tobit model that x1 = log(z1), and this is the only place z1 appears in x. Shows thatWhere Î²1 is the coefficient on log(z1).(ii) If x1 = z1, and x2 = z21,
Let mvpi be the marginal value product for worker i, which is the price of a firm's good multiplied by the marginal product of the worker. Assume that log(mvpi) = β0 + β1 xi1 + ... + βk xik +
(Requires calculus) Let patents be the number of patents applied for by a firm during a given year. Assume that the conditional expectation of patents given sales and RD is E(patents | sales, RD) =
Consider a family saving function for the population of all families in the United States: sav = β0 + β1inc + β2hhsize + β3educ + β4age + u, where hhsize is household size, educ is years of
Suppose you are hired by a university to study the factors that determine whether students admitted to the university actually come to the university. You are given a large random sample of students
Use the data in PNTSPRD.RAW for this exercise.(i) The variable favwin is a binary variable if the team favored by the Las Vegas point spread wins. A linear probability model to estimate the
Use the data in SMOKE.RAW for this exercise.(i) The variable cigs is the number of cigarettes smoked per day. How many people in the sample do not smoke at all? What fraction of people claim to smoke

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