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introductory econometrics modern

Questions and Answers of Introductory Econometrics Modern

Consider the analysis in Computer Exercise C11 in Chapter 4 using the data in HTV, where educ is the dependent variable in a regression.(i) How many different values are taken on by educ in the
In the potential outcomes framework with heterogeneous (nonconstant) treatment effect, write the error asui = (1 – xi)ui(0) + xiui(1).Let s20 = Var[ui(0)] and s21 Var[ui(1)]. Assume random
In the potential outcomes framework, suppose that program eligibility is randomly assigned but participation cannot be enforced. To formally describe this situation, for each person i, zi is the
Consider the potential outcomes framework from Section 2.7a, where yi(0) and yi(1) are the potential outcomes in each treatment state.(i) Show that if we could observe yi(0) and yi(1) for all i then
In the context of Problem 2.13, suppose yi is also binary. For concreteness, yi indicates whether worker i is employed after a job training program, where yi = 1 means has a job, yi = 0 means does
Let y be any response variable and x a binary explanatory variable. Let {(xi, yi): i = 1, ... , n} be a sample of size n. Let n0 be the number of observations with xi = 0 and n1 the number of
Consider the problem described at the end of Section 2-6, running a regression and only estimating an intercept.(i) Given a sample {yi: i 5 1, 2,c, n}, let β́0 be the solution toShow that β̅0 =
Use the data in GPA1 to answer these questions. It is a sample of Michigan State University undergraduates from the mid-1990s, and includes current college GPA, colGPA, and a binary variable
The data set in CATHOLIC includes test score information on over 7,000 students in the United States who were in eighth grade in 1988. The variables math12 and read12 are scores on twelfth grade
Let β̂0 and β̂1 be the OLS intercept and slope estimators, respectively, and let u be the sample average of the errors (not the residuals!).(i) Show that β̂2 can be written as
Use the data in COUNTYMURDERS to answer these questions. Use only the data for 1996.(i) How many counties had zero murders in 1996? How many counties had at least one execution? What is the largest
To complete this exercise you need a software package that allows you to generate data from the uniform and normal distributions.(i) Start by generating 500 observations on xi—the explanatory
The data in ECONMATH were obtained on students from a large university course in introductory microeconomics. For this problem, we are interested in two variables: score, which is the final course
The data set in ALCOHOL contains information on a sample of men in the United States. Two key variables are self-reported employment status and alcohol abuse (along with many other variables). The
Use the data in COUNTYMURDERS to answer this question. Use only the year 1996. The variable murders is the number of murders reported in the county. The variable execs is the number of executions
The data in FERTIL2 were collected on women living in the Republic of Botswana in 1988. The variable children refers to the number of living children. The variable electric is a binary indicator
Use the data in WAGE1 for this exercise.(i) Find the average education level in the sample. What are the lowest and highest years of education?(ii) Find the average hourly wage in the sample. Does it
Let x be a binary explanatory variable and suppose P(x = 1) = ρ for 0 < ρ < 1.(i) If you draw a random sample of size n, find the probability—call it γn—that Assumption SLR.3 fails.(ii)
Use the data in HTV to answer this question. The data set includes information on wages, education, parents’ education, and several other variables for 1,230 working men in 1991.(i) What is the
Use the data in MEAPSINGLE to study the effects of single-parent households on student math performance. These data are for a subset of schools in southeast Michigan for the year 2000. The
Suppose that the population model determining y isy = β0 + β1x1 + β2x2 + β3x3 + u,and this model satisfies Assumptions MLR.1 through MLR.4. However, we estimate the model that omits x3. Let
The data in ECONMATH contain grade point averages and standardized test scores, along with performance in an introductory economics course, for students at a large public university. The variable to
Use the data in GPA1 to answer this question. We can compare multiple regression estimates, where we control for student achievement and background variables, and compare our findings with the
(i) Consider the simple regression model y = β0 + β1x + u under the first four Gauss-Markov assumptions. For some function g(x), for example g(x) = x2 or g(x) = log(1 + x2) , define zi = g(xi).
Suppose you have a sample of size n on three variables, y, x1, and x2, and you are primarily interested in the effect of x1 on y. Let β̇1 be the coefficient on x1 from the simple regression
The following estimated equations use the data in MLB1, which contains information on major league baseball salaries. The dependent variable, lsalary, is the log of salary. The two explanatory
The following equations were estimated using the data in LAWSCH85: Isalary = 9.90 .0041 rank + .294 GPA (.24) (.0003) (.069) n = 142, R = .8238 Isalary 9.86 - .0038 rank + .295 GPA + .00017 age
Consider an estimated equation for workers earning an hourly wage, wage,where educ, years of schooling, and exper, actual years in the workforce, are measured in years. The dependent variable is
The potential outcomes framework in Section 3-7e can be extended to more than two potential outcomes. In fact, we can think of the policy variable, w, as taking on many different values, and then
Consider the estimated equation from Example 4.3, which can be used to study the effects of skipping class on college GPA:(i) Using the standard normal approximation, find the 95% confidence interval
Use the data in HTV to answer this question. See also Computer Exercise C10 in Chapter 3.(i) Estimate the regression modeleduc = β0 + β1motheduc + β2fatheduc + β3abil + β4abil2 + uby OLS and
The following analysis was obtained using data in MEAP93, which contains school-level pass rates (as a percent) on a tenth-grade math test.(i) The variable expend is expenditures per student, in
Use the data in ECONMATH to answer the following questions.(i) Estimate a model explaining colgpa to hsgpa, actmth, and acteng. Report the results in the usual form. Are all explanatory variables
The data in MEAPSINGLE were used to estimate the following equations relating school-level performance on a fourth-grade math test to socioeconomic characteristics of students attending school. The
Use the data set GPA1 to answer this question. It was used in Computer Exercise C13 in Chapter 3 to estimate the effect of PC ownership on college GPA.(i) Run the regression colGPA on PC, hsGPA, and
Use the data set JTRAIN98 to answer this question.(i) Add the unemployment indicator unem96 to the regression reported in equation (4.52). Interpret its coefficient and discuss whether its sign and
Suppose that the modelpctstck = β0 + β1funds + β2risktol + usatisfies the first four Gauss-Markov assumptions, where pctstck is the percentage of a worker’s pension invested in the stock market,
Several statistics are commonly used to detect nonnormality in underlying population distributions. Here we will study one that measures the amount of skewness in a distribution. Recall that any
The following histogram was created using the variable score in the data file ECONMATH. Thirty bins were used to create the histogram, and the height of each cell is the proportion of observations
Consider the equationy = β0 + β1x + β2x2 + uE(u|x) = 0where the explanatory variable x has a standard normal distribution in the population. In particular, E(x) = 0, E(x2) = Var (x) = 1, and E(x3)
Use the data in ECONMATH to answer this question.(i) Logically, what are the smallest and largest values that can be taken on by the variable score? What are the smallest and largest values in the
Let β̂0, β̂1, . . . , β̂k be the OLS estimates from the regression of yi on xi1, . . . , xik, i = 1, 2, . . . , n. For nonzero constants c1, . . . , ck, argue that the OLS intercept and slopes
If we start with (6.38) under the CLM assumptions, assume large n, and ignore the estimation error in the β̂j, a 95% prediction interval for ŷ0 is [exp(–1.96ŝ) exp(logy0), exp(1.96ŝ)
The following two equations were estimated using the data in MEAPSINGLE. The key explanatory variable is lexppp, the log of expenditures per student at the school level.(i) If you are a policy maker
Consider the equationwhere the explanatory variable x has a standard normal distribution in the population. In particular,E(x) = 0, E(x2) = Var(x) = 1, and E(x3) = 0. This last condition holds
Use the data in BENEFITS to answer this question. It is a school-level data set at the K–5 level on average teacher salary and benefits. See Example 4.10 for background.(i) Regress lavgsal on bs
The following equations were estimated using the data in ECONMATH, with standard errors reported under coefficients. The average class score, measured as a percentage, is about 72.2; exactly 50% of
Consider Example 7.11, where, prior to computing the interaction between the race/ethnicity of a player and the city’s racial composition, we center the city composition variables about the sample
(i) In the context of potential outcomes with a sample of size n, let [yi(0), yi(1)] denote the pair of potential outcomes for unit i. Define the averages
Use the data in FERTIL2 to answer this question.(i) Find the smallest and largest values of children in the sample. What is the average of children? Does any woman have exactly the average number of
Use the data in CATHOLIC to answer this question.(i) In the entire sample, what percentage of the students attend a Catholic high school? What is the average of math12 in the entire sample?(ii) Run a
Use the data in JTRAIN98 to answer this question. The variable unem98 is a binary variable indicating whether a worker was unemployed in 1998. It can be used to measure the effectiveness of the job
The following equations were estimated using the data in ECONMATH. The first equation is for men and the second is for women. The third and fourth equations combine men and women.(i) Compute the
Consider the potential outcomes framework, where w is a binary treatment indicator and the potential outcomes are y(0) and y(1). Assume that w is randomly assigned, so that w is independent of
Use the data in FERTIL2 to answer this question.(i) Estimate the modeland report the usual and heteroskedasticity-robust standard errors. Are the robust standard errors always bigger than the
Use the data in BEAUTY for this question.(i) Using the data pooled for men and women, estimate the equationand report the results using heteroskedasticity-robust standard errors below coefficients.
The point of this exercise is to show that tests for functional form cannot be relied on as a general test for omitted variables. Suppose that, conditional on the explanatory variables x1 and x2, a
Suppose that log(y0 follows a linear model with a linear form of heteroskedasticity. We write this asso that, conditional on x, u has a normal distribution with mean (and median) zero but with
This exercise shows that in a simple regression model, adding a dummy variable for missing data on the explanatory variable produces a consistent estimator of the slope coefficient if the
(i) In column (3) of Table 9.2, the coefficient on educ is .018 and it is statistically insignificant, and that on IQ is actually negative, – .0009, and also statistically insignificant. Explain
Use the data in CEOSAL2 to answer this question.(i) Estimate the modellsalary = β0 + β1lsales + β2lmktval + β3ceoten + β4ceoten2 + uby OLS using all of the observations, where lsalary, lsales,
Use the data in ECONMATH to answer this question. The population model isscore = β0 + β1act + u.(i) For how many students is the ACT score missing? What is the fraction of the sample? Define a new
In October 1979, the Federal Reserve changed its policy of using finely tuned interest rate adjustments and instead began targeting the money supply. Using the data in INTDEF, define a dummy variable
Use the data in BARIUM for this exercise.(i) Add a linear time trend to equation (10.22). Are any variables, other than the trend, statistically significant?(ii) In the equation estimated in part
Add the variable log(prgnp) to the minimum wage equation in (10.38). Is this variable significant? Interpret the coefficient. How does adding log(prgnp) affect the estimated minimum wage effect?
Use the data in FERTIL3 to verify that the standard error for the LRP in equation (10.19) is about .030.
Use the data in EZANDERS for this exercise. The data are on monthly unemployment claims in Anderson Township in Indiana, from January 1980 through November 1988. In 1984, an enterprise zone (EZ) was
Use the data in FERTIL3 for this exercise.(i) Regress gfrt on t and t2 and save the residuals. This gives a detrended gfrt, say, gf̈t.(ii) Regress gf̈t on all of the variables in equation (10.35),
(i) Estimate equation (10.2) using all observations 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
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.)
Let {5xt: t = 1, 2, . . .) be a covariance stationary process and define γh = Cov(xt, xt+h) for h ≥ 0. [Therefore, γ0 = Var (xt).] Show that Corr (xt, xt+h) = γh/γ0.
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
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
Suppose in a static or distributed lag time series regression, you are able to use n = 280 quarterly observations. What would be some reasonable values for the lag g in the Newey-West estimator?
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
Use the data in APPROVAL to answer the following questions. (i) Estimate the equationusing first differencing and test the errors in the first-differenced (FD) equation for AR(1) serial
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
Use the data in COUNTYMURDERS for this exercise. 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
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
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
Consider the unobserved effects panel data model for a random draw i, where at denotes different year intercepts:Assuming a balanced panel, write down, for a given i, the CRE equation that you would
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,
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
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
Use the data in WAGEPAN.DTA to answer the following questions. (i) Using lwage as the dependent variable, estimate a model that only contains an intercept and the year dummies d81 through d87.
Use the data in SCHOOL93_98 to answer the following questions. Use the command xtset schid year to set the cross section and time dimensions.(i) How many schools are there. Does each school have a
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
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
Use the data in CATHOLIC to answer this question. The model of interest iswhere cathhs is a binary indicator for whether a student attends a Catholic high school.(i) How many students are in the
Use the data in LABSUP to answer the following questions. These are data on almost 32,000 black or Hispanic women. Every woman in the sample is married. It is a subset of the data used in Angrist and

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