Questions and Answers of Introductory Econometrics Modern

Consider the simple regression model $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$ where we hypothesize heteroskedasticity of the form $\sigma_{i}^{2}=\sigma^{2} x_{i}^{2}$. We have $N=4$
Consider the simple regression model $y_{i}=\beta_{1}+\beta_{2} x_{i 2}+e_{i}$. Suppose $N=5$ and the values of $x_{i 2}$ are $(1,2,3,4,5)$. Let the true values of the parameters be
Consider the wage equationwhere wage is measured in dollars per hour, education and experience are in years, and METRO $=1$ if the person lives in a metropolitan area. We have $N=1000$
Consider the simple treatment effect model $y_{i}=\beta_{1}+\beta_{2} d_{i}+e_{i}$. Suppose that $d_{i}=1$ or $d_{i}=0$ indicating that a treatment is given to randomly selected individuals or
It can be shown that the theoretically useful form of the OLS estimator of $\beta_{1}$ in the simple linear regression model $y_{i}=\beta_{1}+\beta_{2} x_{i 2}+e_{i}$ is
We wish to estimate the hedonic regression modelThe variables are PRICE (\$$1000),$ SQFT (100s), CLOSE = 1 if located near a major university, 0 otherwise, AGE (years), FIREPLACE, POOL, TWOSTORY
Does having more children drive parents to drink more alcohol? We have data on the following variables: $W A L C=$ budget share (percent of income spent) for alcohol expenditure; INCOME = total net
We are interested in the relationship between rice production, inputs of labor and fertilizer, and the area planted using data on $N=44$ farms.a. We observe the least squares residuals,
An econometrician wishes to study the properties of an estimator using simulated data. Suppose the sample size $N$ is set to be 100 . The intercept and slope parameters are 100 , and 10 ,
A researcher has 1100 observations on household expenditures on entertainment (per person in the previous quarter, \$) ENTERT. The researcher wants to explain these expenditures as a function of
Using data on 1000 home loan borrowers, we estimate the linear probability modelwhere $D E F A U L T=1$ if the borrower has made a mortgage payment more than 90 days late, $L T V=100$ (loan
We have $N=396$ observations on employment at fast-food restaurants in two neighboring states, New Jersey and Pennsylvania. In Pennsylvania, the control group $d_{i}=0$, there is no minimum wage
A sample of 200 Chicago households was taken to investigate how far American households tend to travel when they take a vacation. Consider the modelMILES is miles driven per year, INCOME is measured
In this exercise, we explore the relationship between total household expenditures and expenditures on clothing. Use the data file malawi_small (malawi has more observations) and observations for
Consider the wage equation,where WAGE is measured in dollars per hour, education and experience are in years, and $M E T R O=1$ if the person lives in a metropolitan area. Use the data file cps 5
In this exercise we explore the relationship between total household expenditures and expenditures on telephone services. Use the data file malawi_small (malawi has more observations).a. Using
The data file $b r 2$ contains data on 1080 houses sold in Baton Rouge, Louisiana, during mid-2005. We will be concerned with the selling price (PRICE), the size of the house in square feet (SQFT),
In Example 8.9 we estimated the linear probability modelwhere $C O K E=1$ if a shopper purchased Coke and $C O K E=0$ if a shopper purchased Pepsi. The variable PRATIO was the relative price
Use data file cps 5 for this exercise.a. Estimate the following wage equation by OLS and use heteroskedasticity robust standard errors:Discuss the results.b. Add MARRIED to the equation and
Using the data in cps 5 obtain OLS estimates of the wage equationa. Interpret the coefficient of UNION. Test the null hypothesis that the coefficient of UNION is less than or equal to zero, against
In this exercise, we will explore some of the factors predicting costs at American universities using the data file poolcoll2. Let $T C=$ the real (2008 dollars) total cost per student, \(F T U
What effect does having public health insurance have on the number of doctor visits a person has during a year? Using 1988 data, in the data file rwm88_small, from Germany, we will explore this
In the STAR experiment, Example 7.8, children were randomly assigned within schools into three types of classes: small classes with 13-17 students, regular-sized classes with 22-25 students, and
There were 64 countries who competed in the 1992 Olympics and won at least one medal. For each of these countries, let MEDALTOT be the total number of medals won, $P O P$ be population in millions,
In this exercise you will create some simulated data and try out estimation and testing methods. Use your software to create a new data set, or "workfile," with $N=100$ observations. All modern
The data file mexican contains data collected in 2001 from the transactions of 754 Mexican sex workers.a. Using OLS, estimate the hedonic log-linear model with LNPRICE as the dependent variable and
The data file grunfeld 2 contains annual data on the gross investment, capital stock, and the value of the firm, measured by the value of common and preferred stock for General Electric and
Explain why lags are important in models that use time-series data, and the ways in which lags can be included in dynamic econometric models.
Explain what is meant by a serially correlated time series and how we measure serial correlation.
Compute the autocorrelations for a time series, graph the corresponding correlogram, and use it to test for serial correlation.
Explain the nature of regressions that involve lagged variables and the number of observations that are available.
Use autoregressive (AR) and autoregressive distributed lag (ARDL) models to compute forecasts, standard errors of forecasts, and forecast intervals.
Explain the assumptions required for $A R$ and ARDL forecasting.
Specify and estimate ARDL models. Use serial correlation checks, significance of coefficients, and model selection criteria to choose lag lengths.
Test for Granger causality.
Use a correlogram of residuals to test for serially correlated errors.
Use a Lagrange multiplier test for serially correlated errors.
Explain the differences between time-series models for forecasting and time-series models for policy analysis.
Estimate and interpret the estimates from finite and infinite distributed lag models.
Compute HAC standard errors for least squares estimates. Explain why they are used.
Compute nonlinear least squares and generalized least squares estimates for a model with an $A R(1)$ error.
Contrast the exogeneity assumption required for HAC standard errors with that required for estimating an $\mathrm{AR}(1)$ error model.
Compute delay, interim, and total multipliers for finite and infinite distributed lag models.
Test for consistency of least squares in the ARDL representation of an infinite distributed lag model.
Contrast the assumptions for a finite distributed lag model with those for an infinite distributed lag model.
Test for misspecification using RESET.
a. Show that the mean-squared forecast error $E\left[\left(\hat{y}_{T+1}-y_{T+1}\right)^{2} \mid I_{T}\right]$ for a forecast $\hat{y}_{T+1}$, that depends only on past information $I_{T}$, can
Consider the AR(1) model $y_{t}=\delta+\theta y_{t-1}+e_{t}$ where $|\theta|)=0$ and $\operatorname{var}\left(e_{t} \mid I_{t-1}\right)=\sigma^{2}$. Let \(\bar{y}_{-1}=\sum_{t=2}^{T} y_{t}
Consider a stationary model that combines the $\operatorname{AR}(2)$ model $y_{t}=\delta+\theta_{1} y_{t-1}+\theta_{2} y_{t-2}+e_{t}$ with an $\mathrm{AR}(1)$ error model \(e_{t}=ho
In Example 9.13, the following finite distributed lag model was estimated for Okun's Law using the data file okun5_aus.a. Find the correlogram of the least squares residuals for this model. Is there
Using the data file phillips5_aus, estimate the equationa. Find the first eight lag weights (delay multipliers) of the infinite distributed lag representation that corresponds to this model. What is
Using the data file phillips5_aus, estimate the equationa. Find the first eight lag weights (delay multipliers) of the infinite distributed lag representation that corresponds to this model. What is
In Example 9.16, we considered a geometrically declining infinite distributed lag model to describe the relationship between the change in consumption $D C_{t}=C_{t}-C_{t-1}$ and the change in
a. Using observations on the change in consumption $D C_{t}=C_{t}-C_{t-1}$ and the change in income $D Y_{t}=$ $Y_{t}-Y_{t-1}$ from 1959Q3 to 2015Q4, obtained from the data file cons_inc,
Using time series data on five different countries, Atkinson and Leigh ${ }^{17}$ examine changes in inequality measured as the percentage income share (SHARE) held by those with the top $1 \%$
Consider the following model where a dependent variable $y$ depends on infinite distributed lags of the two variables $x$ and $z$.Suppose that both sets of lag weights decline geometrically,
In this exercise, we use a subset of the data compiled by Everaert and Pozzi ${ }^{18}$ to forecast growth in per capita private consumption (CONSN) and growth in per capita real disposable income
In Examples 9.14 and 9.15, we considered the Phillips curvewhere inflationary expectations are assumed to be constant, $I N F_{t}^{E}=\alpha$, and $\beta_{0}=-\gamma$. In Example 9.15, we used
One way of modeling supply response for an agricultural crop is to specify a model in which area planted AREA depends on expected price, PRICE*. A log-log (constant elasticity) version of this model
In this exercise, we consider a partial adjustment model as an alternative to the model used in Exercise 9.29 for modeling sugar cane area response in Bangladesh. The data are in the file bangla5. In
Using data on the Maltese economy, Apap and Gravino ${ }^{19}$ estimate a number of versions of Okun's Law. Their quarterly data run from 1999Q1 to 2012Q4 and can be found in the data file apap.
In their paper referred to in Exercise 9.31, Apap and Gravino examine the separate effects of output growth in the manufacturing and services sectors on changes in the unemployment rate. Their
The data file xrate contains monthly observations from 1986M1 to 2008 M12 on the following variables $^{20}$ :$N E R=$ the nominal exchange rate for the Australian dollar in terms of U.S.
In the new Keynesian Phillips curve (NKPC), inflation at time $t\left(I N F_{t}\right)$ depends on inflationary expectations formed at time $t$ for time $t+1\left(\right.$ INFEX
Do lags of the variables in the new Keynesian Phillips curve provide a good basis for forecasting quarterly inflation? In this exercise, we investigate this question using the French data from
Using state level data, a researcher wishes to examine the relationship between the median rent paid (RENT) as a function of median house values (MDHOUSE in \$$1000).$ The percentage of the state
Give an intuitive explanation of why correlation between a random $x$ and the error term causes the least squares estimator to be inconsistent.
The labor supply of married women has been a subject of a great deal of economic research. Consider the following supply equation specificationwhere HOURS is the supply of labor, WAGE is hourly wage,
Describe the "errors-in-variables" problem in econometrics and its consequences for the least squares estimator.
In the regression model $y=\beta_{1}+\beta_{2} x+e$, assume $x$ is endogenous and that $z$ is a valid instrument. In Section 10.3.5, we saw that \(\beta_{2}=\operatorname{cov}(z, y) /
Describe the properties of a good instrumental variable.
Suppose that $x$ is endogenous in the regression $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$. Suppose that $z_{i}$ is an instrumental variable that takes two values, one and zero; it is an
Discuss how the method of moments can be used to derive the least squares and instrumental variables estimators, paying particular attention to the assumptions upon which the derivations are based.
Suppose that $x_{i}$ is endogenous in the regression $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$. Suppose that $z_{i}$ is an instrumental variable that takes two values, one and zero with
Explain why it is important for an instrumental variable to be highly correlated with the random explanatory variable for which it is an instrument.
Suppose that $x_{i}$ is endogenous in the regression $y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}$. Suppose that $z_{i}$ is an instrumental variable that takes two values, one and zero.a. Let
Describe how instrumental variables estimation is carried out in the case of surplus instruments.
Angrist and Krueger (1991) use quarter of birth as an instrumental variable to estimate the returns to schooling, using a sample of 327,509 from the 1980 census. The model of interest is \(\ln (W A G
State the approximate large-sample distribution of the instrumental variables estimator for the simple linear regression model, and how it can be used for the construction of interval estimates and
Knowledge is Power Program (KIPP) Schools are charter schools with largely minority students. These schools differ in a number of ways from public schools, but emphasize longer days and more time
Consider the model in Example 10.5. Suppose we have the idea that the effect of education may differ for individuals who have siblings. Suppose SIBS = number of siblings, which we assume is
Describe a test for the existence of contemporaneous correlation between the error term and the contemporaneous explanatory variables in a model, explaining the null and alternative hypotheses, and
Consider the wage equation in Example 10.5.a. Two possible instruments for EDUC are NEARC4 and NEARC2, where these are dummy variables indicating whether the individual lived near a 4-year college or
Estimating cost and production functions for industrial plants is important. Decisions are based on estimated average and marginal cost, and average and marginal products. Suppose a manufacturing
Households plan consumption expenditures and saving with consideration of their long-run income. We wish to estimate SAVING $=\beta_{1}+\beta_{2}$ LRINCOME $+e$, where LRINCOME is long-run
The Capital Asset Pricing Model (CAPM) says that the risk premium on security $j$ is related to the risk premium on the market portfolio, that iswhere $r_{j}$ and $r_{f}$ are the returns to
Consider the simple wage model in Example 10.2. Use the 428 observations on married women who participate in the labor force.a. Using the instrumental variables estimator in equation (10.17), divide
Consider the wage model in Example 10.5 and the 428 observations on married women who participate in the labor force. Use only MOTHEREDUC as an instrument in this exercise.a. Estimate the first-stage
Consider the wage model in Example 10.5 and the 428 observations on married women who participate in the labor force. Use only MOTHEREDUC as an instrument in this exercise.a. Estimate the first-stage
Using tha data file usmacro, estimate the ARDL $(2,1)$ modelYour estimates should agree with the results given in equation (9.42). Use these estimates to verify the forecast results given in Table
Using the data file usmacro, estimate the $\operatorname{AR}(1)$ model $G_{t}=\alpha+\phi G_{t-1}+v_{t}$. From these estimates and those obtained in Exercise 9.16, use the results from Exercise
Consider the $\operatorname{ARDL}(p, q)$ equationand the data in the file usmacro. For $p=2$ and $q=1$, results from the LM test for serially correlated errors were reported in Table 9.6 for
Consider the $\operatorname{ARDL}(p, q)$ equationand the data in the file usmacro. For $p=2$ and $q=1$, results from the LM test for serially correlated errors were reported in Table 9.6 for
Consider the data file $m r o z$ on working wives. Use the 428 observations on married women who participate in the labor force. In this exercise, we examine the effectiveness of a parent's college
Consider the data file $m r o z$ on working wives. Use the 428 observations on married women who participate in the labor force. In this exercise, we examine the effectiveness of a parent's college
The CAPM says that the risk premium on security $j$ is related to the risk premium on the market portfolio. That iswhere $r_{j}$ and $r_{f}$ are the returns to security $j$ and the risk-free
This question is an extension of Exercise 10.22. Consider the data file $m r o z$ on working wives and the model $\ln (W A G E)=\beta_{1}+\beta_{2} E D U C+\beta_{3} E X P E R+e$. Use the 428
Consider the data file $m r o z$ on working wives. Use the 428 observations on married women who participate in the labor force. In this exercise, we examine the effectiveness of alternative
To examine the quantity theory of money, Brumm (2005) ["Money Growth, Output Growth, and Inflation: A Reexamination of the Modern Quantity Theory's Linchpin Prediction," Southern Economic Journal,
Consider the data file mroz on working wives and the model $\ln (W A G E)=\beta_{1}+\beta_{2} E D U C+$ $\beta_{3} E X P E R+e$. Use the 428 observations on married women who participate in the

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