Questions and Answers of Econometric

In the example in equation (7.29), suppose that we define outlf to be one if the woman is out of the labor force, and zero otherwise.(i) If we regress outlf on all of the independent variables in
Suppose you collect data from a survey on wages, education, experience, and gender. In addition, you ask for information about marijuana usage. The original question is: "On how many separate
Let d be a dummy (binary) variable and let z be a quantitative variable. Consider the modely = (0 + (0d + (1z + (1d (z + u;this is a general version of a model with an interaction between a dummy
Use the data GPA1.RAW for this exercise.(i) Add the variables mothcoll and fathcoll to the equation estimated in (7.6) and report the results in the usual form. What happens to the estimated effect
Use the data in NBASAL.RAW for this exercise.(i) Estimate a linear regression model relating points per game to experience in the league and position (guard, forward, or center). Include experience
Use the data in 401KSUBS.RAW for this exercise.(i) Compute the average, standard deviation, minimum, and maximum values of nettfa in the sample.(ii) Test the hypothesis that average nettfa does not
Use the data set in BEAUTY.RAW, which contains a subset of the variables (but more usable observations than in the regressions) reported by Hamermesh and Biddle (1994).(i) Find the separate fractions
Use the data in APPLE.RAW to answer this question.(i) Define a binary variable as ecobuy = 1 if ecolbs > 0 and ecobuy = 0 if ecolbs = 0. In other words, ecobuy indicates whether, at the prices
Use the data in CHARITY.RAW to answer this question. The variable respond is a dummy variable equal to one if a person responded with a contribution on the most recent mailing sent by a charitable
Use the data in WAGE2.RAW for this exercise.(i) Estimate the modeland report the results in the usual form. Holding other factors fixed, what is the approximate difference in monthly salary between
A model that allows major league baseball player salary to differ by position iswhere outfield is the base group.(i) State the null hypothesis that, controlling for other factors, catchers and
Use the data in GPA2.RAW for this exercise.(i) Consider the equationwhere colgpa is cumulative college grade point average, hsize is size of high school graduating class, in hundreds, hsperc is
In Problem 4.2, we added the return on the firm's stock, ros, to a model explaining CEO salary; ros turned out to be insignificant. Now, define a dummy variable, rosneg, which is equal to one if ros
Use the data in SLEEP75.RAW for this exercise. The equation of interest is sleep = (0 + (1 totwrk + (2educ + (3 age + (4age2 + (5 yngkid + u.(i) Estimate this equation separately for men and women
Use the data in WAGE 1 .RAW for this exercise.(i) Use equation (7.18) to estimate the gender differential when educ = 12.5. Compare this with the estimated differential when educ = 0.(ii) Run the
Use the data in LOANAPP.RAW for this exercise. The binary variable to be explained is approve, which is equal to one if a mortgage loan to an individual was approved. The key explanatory variable is
There has been much interest in whether the presence of 401(k) pension plans, available to many U.S. workers, increases net savings. The data set 401KSUBS.RAW contains information on net financial
Which of the following are consequences of heteroskedasticity? (i) The OLS estimators, j, are inconsistent. (ii) The usual F statistic no longer has an F distribution. (iii) The OLS estimators are
Consider a linear model to explain monthly beer consumption:beer = (0 + (1inc + (2 price + (3 educ + (4 female + u.E(u|inc, price, educ, female) = 0Var(u|inc, price, educ, female) = (2 inc2.Write the
True or False: WLS is preferred to OLS, when an important variable has been omitted from the model?
Using the data in GPA3.RAW, the following equation was estimated for the fall and second semester students:Here, trmgpa is term GPA, crsgpa is a weighted average of overall GPA in courses taken,
The variable smokes is a binary variable equal to one if a person smokes, and zero otherwise. Using the data in SMOKE.RAW, we estimate a linear probability model for smokes:The variable white equals
There are different ways to combine features of the Breusch-Pagan and White tests for heteroskedasticity. One possibility not covered in the text is to run the regressionon xi1, xi2, ...., xik,
Consider a model at the employee level,yi,e = (0 + (1xi,e,1 + (2xi,e,2 + ... + (kxi,e,k + fi + vi,e'where the unobserved variable fi is a "firm effect" to each employee at a given firm i. The error
Consider the following model to explain sleeping behavior:sleep = BQ + Bjotwrk + B2 educ + B1 age + B4 age2 + B5 yngkid + B6 male + u.(i) Write down a model that allows the variance of u to differ
Use the data set 401KSUBS.RAW for this exercise.(i) Using OLS, estimate a linear probability model for e401k, using as explanatory variables inc, inc2, age, age2, and male. Obtain both the usual OLS
Use the data in 401KSUBS.RAW for this question, restricting the sample to fsize = 1.(i) To the model estimated in Table 8.1, add the interaction term, e401k ( inc. Estimate the equation by OLS and
Use the data in MEAP00_01.RAW to answer this question.(i) Estimate the modelmathA = (0 + (1 lunch + (2 log(enroll) + (3log(exppp) + uby OLS and obtain the usual standard errors and the fully robust
(i) Use the data in HPRICE1.RAW to obtain the heteroskedasticity-robust standard errors for equation (8.17). Discuss any important differences with the usual standard errors.(ii) Repeat part (i) for
Apply the full White test for heteroskedasticity [see equation (8.19)] to equation (8.18). Using the chi-square form of the statistic, obtain the p-value. What do you conclude?
Use VOTE 1.RAW for this exercise.(i) Estimate a model with voteA as the dependent variable and prtystrA, democA, log(expendA), and log(expendB) as independent variables. Obtain the OLS residuals, u,
Use the data in PNTSPRD.RAW for this exercise.(i) The variable sprdcvr is a binary variable equal to one if the Las Vegas point spread for a college basketball game was covered. The expected value of
In Example 7.12, we estimated a linear probability model for whether a young man was arrested during 1986:arr86 - (0 + (1 pcnv + (2avgsen + (3 tot time + (4 ptime86 + (5 qemp86 + u.(i) Estimate this
Use the data in LOANAPP.RAW for this exercise.(i) Estimate the equation in part (iii) of Computer Exercise C7.8, computing the heteroskedasticity-robust standard errors. Compare the 95% confidence
Use the data set GPA 1.RAW for this exercise.(i) Use OLS to estimate a model relating colGPA to hsGPA, ACT, skipped, and PC. Obtain the OLS residuals.(ii) Compute the special case of the White test
In Example 8.7, we computed the OLS and a set of WLS estimates in a cigarette demand equation.(i) Obtain the OLS estimates in equation (8.35).(ii) Obtain the h. used in the WLS estimation of equation
In Problem 4.11, the R-squared from estimating the modellog(salary) = (0 + (1logi (sales) + (2 log(mktval) + (3 profmarg+ (4 ceoten + (5 fomten + u,Using the data in CEOSAL2.RAW, was R2 = .353 (n =
Let us modify Computer Exercise C8.4 by using voting outcomes in 1990 for incumbents who were elected in 1988. Candidate A was elected in 1988 and was seeking reelection in 1990; voteA90 is Candidate
Let mathl0 denote the percentage of students at a Michigan high school receiving a passing score on a standardized math test (see also Example 4.2). We are interested in estimating the effect of per
The following equation explains weekly hours of television viewing by a child in terms of the child's age, mother's education, father's education, and number of siblings: Tv hours* = (0 + (1 age +
In Example 4.4, we estimated a model relating number of campus crimes to student enrollment for a sample of colleges. The sample we used was not a random sample of colleges in the United States,
In the model (9.17), show that OLS consistently estimates a and ( if a1. is uncorrelated with xi. and bi. is uncorrelated with xi. and xi2, which are weaker assumptions than (9.19). [Write the
Consider the simple regression model with classical measurement error, y = (0 + (0x* + u, where we have m measures on x*. Write these as zh - x* + eh, h - 1, .... m. Assume that x* is uncorrelated
(i) Apply RESET from equation (9.3) to the model estimated in Computer Exercise C7.5. Is there evidence of functional form misspecification in the equation?(ii) Compute a heteroskedasticity-robust
You need to use two data sets for this exercise, JTRAIN2.RAW and JTRAIN3.RAW. The former is the outcome of a job training experiment. The file JTRAIN3.RAW contains observational data, where
Use the data for the year 1993 for this question, although you will need to first obtain the lagged murder rate, say mrdrte - 1.(i) Run the regression of mrdrte on exec, unem. What are the
Use the data in ELEM94_95 to answer this question. See also Computer Exercise C4.10.(i) Using all of the data, run the regression lavgsal on bs, lenrol, Istaff, and lunch. Report the coefficient on
Use the data set WAGE2.RAW for this exercise.(i) Use the variable KWW (the "knowledge of the world of work" test score) as a proxy for ability in place of IQ in Example 9.3. What is the estimated
Use the data from JTRAIN.RAW for this exercise, (i) Consider the simple regression model log(scrap) = (0 + (1 grant + u.where scrap is the firm scrap rate and grant is a dummy variable indicating
Use the data for the year 1990 in INFMRT.RAW for this exercise.(i) Reestimate equation (9.43), but now include a dummy variable for the observation on the District of Columbia (called DC). Interpret
Use the data in RDCHEM.RAW to further examine the effects of outliers on OLS estimates and to see how LAD is less sensitive to outliers. The model isrdintens = (0 + (1 sales + (2 sales2 + (3 profmarg
Redo Example 4.10 by dropping schools where teacher benefits are less than 1% of salary.(i) How many observations are lost?(ii) Does dropping these observations have any important effects on the
Use the data in LOANAPP.RAW for this exercise.(i) How many observations have obrat > 40, that is, other debt obligations more than 40% of total income?(ii) Reestimate the model in part (iii) of
Use the data in TWOYEAR.RAW for this exercise.(i) The variable stotal is a standardized test variable, which can act as a proxy variable for unobserved ability. Find the sample mean and standard
In this exercise, you are to compare OLS and LAD estimates of the effects of 401(k) plan eligibility on net financial assets. The model isnettfa = (0 + (1inc + B2inc2 + (3age + (4age2 + (5male +
Decide if you agree or disagree with each of the following statements and give a brief explanation of your decision: (i) Like cross-sectional observations, we can assume that most time series
Let gGDPt denote the annual percentage change in gross domestic product and let intt denote a short-term interest rate. Suppose that gGDPt is related to interest rates bygGDPt = a0 + (0intt, + (1int
When the three event indicators beftle6, qffile6, and afdec6 are dropped from equation (10.22), we obtain R2 = .281 and = .264. Are the event indicators jointly significant at the 10% level?
Suppose you have quarterly data on new housing starts, interest rates, and real per capita income. Specify a model for housing starts that accounts for possible trends and seasonality in the
In Example 10.4, we saw that our estimates of the individual lag coefficients in a distributed lag model were very imprecise. One way to alleviate the multicollinearity problem is to assume that the
In Example 10.4, we wrote the model that explicitly contains the long-run propensity, (0, as gfrt = a0 + (0pet + (1(pet-1 -pet) + (2(pet t-2 - pet) + ut, Where we omit the other explanatory variables
In the linear model given in equation (10.8), the explanatory variables xt = (xt1, ...., xtk) are said to be sequentially exogenous (sometimes called weakly exogenous) ifE(ut|xt, xt-1,_,, ...,x,) =
Decide if you agree or disagree with each of the following statements and give a brief explanation of your decision:(i) Like cross-sectional observations, we can assume that most time series
Consider the model estimated in (10.15); use the data in INTDEF.RAW.(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
The file TRAFFIC2.RAW contains 108 monthly observations on automobile accidents, traffic laws, and some other variables for California from January 1981 through December 1989. Use this data set to
(i) Estimate equation (10.2) using all the data in PHILLIPS.RAW 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
Use the data in MINWAGE.RAW for this exercise. In particular, use the employment and wage series for sector 232 (Men's and Boy's Furnishings). The variable gwage232 is the monthly growth (change in
Let gGDPt denote the annual percentage change in gross domestic product and let intt denote a short term interest rate. Suppose that gGDPt is related to interest rates bygGDPt = a0 + (0intt + (1
Suppose yt follows a second order FDL model:yt = a0 + (0zt + (1zt-1 + (2zt-2 + ut.Let z* denote the equilibrium value of zt and let y* be the equilibrium value of yt, such thaty* = a0 + (0z* + (1z* +
When the three event indicators beftle6, qffile6, and afdec6 are dropped from equation (10.22), we obtain R2 = .281 and = .264. Are the event indicators jointly significant at the 10% level?
Suppose you have quarterly data on new housing starts, interest rates, and real per capita income. Specify a model for housing starts that accounts for possible trends and seasonality in the
In Example 10.4, we saw that our estimates of the individual lag coefficients in a distributed lag model were very imprecise. One way to alleviate the multicollinearity problem is to assume that the
Use the data set CONSUMP.RAW for this exercise.(i) Estimate a simple regression model relating the growth in real per capita consumption (of nondurables and services) to the growth in real per capita
Use the data in FERTIL3.RAW for this exercise.(i) Add pe t-3 and pet-4 to equation (10.19). Test for joint significance of these lags.(ii) Find the estimated long-run propensity and its standard
Use the data in VOLAT.RAW 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
Let {ei: t = - 1, 0, 1, ...} be a sequence of independent, identically distributed random variables with mean zero and variance one. Define a stochastic process byx, = et - (l/2)e1-1 + (l/2)e1-2, t =
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 (2e. The random variable z does not change over
Let {y,: t = 1, 2, ...} follow a random walk, as in (11.20), with y0 = 0. Show that Corr(yt, yt+h) = /for t > 1, h > 0?
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:
Let hy6t denote the three-month holding yield (in percent) from buying a six-month T-bill at time (t - 1) and selling it at time t (three months hence) as a three month T-bill. Let hy3t-1 be the
A partial adjustment model isy*i = (0 + (1xt + etyt - y t-1 = ((y*t - yt-1) + at,Where yt* is the desired or optimal level of y, and yt is the actual (observed) level. For example, yt* is the desired
Suppose that the equationyt = a + (t + (1xt1 + ...+(kxtk + u,satisfies the sequential exogeneity assumption in equation (11.40).(i) Suppose you difference the equation to obtain(yt = ( + (1 (xt1 +
Use the data in HSEINV.RAW for this exercise.(i) Find the first order autocorrelation in log(mvpc). Now. find the autocorrelation after linearly detrending log(invpc). Do the same for log( price).
Use all the data in PHILLIPS.RAW 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
Okun's Law-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,
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 gwagelil is the monthly growth (change in logs) in
In Example 11.7, define the growth in hourly wage and output per hour as the change in the natural log: ghrwage - (log (hrwage) and goutphr = (log(outphr). Consider a simple extension of the model
(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 returnt-1. To check this possibility, use the data in NYSE.RAW to
Use the data in PHILLIPS.RAW 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
(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
Let inven, be the real value inventories in the United States during year t, let GDP, denote real gross domestic product, and let r3t denote the (ex post) real interest rate on three-month T-bills.
Use CONSUMP.RAW 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
Use the data in PHILLIPS.RAW 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
Use the data in TRAFFIC2.RAW for this exercise. Computer Exercise C10.11 previously asked for an analysis of these data.(i) Compute the first order autocorrelation coefficient for the variable
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 j? Is it always true that the OLS standard
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
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
True or false: "If the errors in a regression model contain ARCH, they must be serially correlated?
(i) In the enterprise zone event study in Computer Exercise CI0.5, a regression of the OLS residuals on the lagged residuals produces-= .841 and se() = .053. What implications does this have for
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

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