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introductory econometrics modern
Questions and Answers of
Introductory Econometrics Modern
In Section 9.5.3, we described how a generalized least squares (GLS) estimator for \(\alpha\) and \(\beta_{0}\) in the regression model \(y_{t}=\alpha+\beta_{0} x_{t}+e_{t}\), with
Consider the following distributed lag model relating the percentage growth in private investment (INVGWTH) to the federal funds rate of interest (FFRATE).a. Suppose \(F F R A T E=1 \%\) for
Using 157 weekly observations on sales revenue (SALES) and advertising expenditure (ADV) in millions of dollars for a large department store, the following relationship was estimateda. How many
Consider the following time series sample of size \(T=10\) on a random variable \(y_{t}\) whose sample mean is \(\bar{y}=0\).a. Use a hand calculator or spreadsheet to compute the sample
Using 250 quarterly observations on U.S. GDP growth \((G)\) from 1947Q2 to 2009Q3, we calculate the following quantities.a. Compute the first three autocorrelations \(\left(r_{1}, r_{2}\right.\), and
Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for houses. In this question, we use three equations to forecast the monthly change in the number of
Consider the infinite lag representation \(y_{t}=\alpha+\sum_{s=0}^{\infty} \beta_{s} x_{t-s}+e_{t}\) for the ARDL modela. Show that \(\alpha=\delta /\left(1-\theta_{1}-\theta_{3}\right),
Inflationary expectations play an important role in wage negotiations between employers and employees. In this exercise, we examine how inflationary expectations of Australian businesses, collected
a. Write the \(\mathrm{AR}(1)\) error model \(e_{t}=ho e_{t-1}+v_{t}\) in lag operator notation.b. Show thatand hence that (1pL)=1+ pL + pL + pL +... -
Reconsider the data file inequality used in Exercise 9.26 and the model in part (a) of that exercise but include the median marginal tax rate for the upper \(1 \%\) of incomes (TAX). We are
Consider the wage equation used in Example 10.5. Suppose we have a variable designed to measure ABILITY. This variable is an index created using 10 different tests of cognitive ability. Using data on
Consider the data file mroz 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 standard
When using \(N=50\) observations to estimate the model \(y_{i}=\beta_{1}+\beta_{2} x_{i}+\beta_{3} z_{i}+e_{i}\), you obtain \(S S E=2132.65\) and \(s_{y}=9.8355\).a. Find \(R^{2}\).b. Find the value
Consider the following model that relates the percentage of a household's budget spent on alcohol WALC to total expenditure TOTEXP, age of the household head \(A G E\), and the number of children in
Consider the regression model \(y_{i}=\beta_{1}+\beta_{2} x_{i}+\beta_{3} z_{i}+e_{i}\), where \(E\left(e_{i} \mid \mathbf{X}\right)=0, \operatorname{var}\left(e_{i} \mid
Consider the regression model \(y_{i}=\beta_{1}+\beta_{2} x_{i}+\beta_{3} z_{i}+\beta_{4} q_{i}+e_{i}\), where \(E\left(e_{i} \mid \mathbf{X}\right)=0\), with \(\mathbf{X}\) representing all
Consider the following wage equation where \(E D U C=\) years of education and \(E X P E R=\) years of experience:Suppose that observations on EXPER are not available, and so you decide to use the
Use an \(F\)-test to jointly test the relevance of the two variables \(X T R A \_X 5\) and \(X T R A \_X 6\) for the family income equation in Example 6.12 and Table 6.1.Data From Example 6.12:-To
The standard error of the forecast error is \(\operatorname{se}(f)=\) \(\sqrt{22.4208}=4.7351\), and the relevant \(t\)-value is \(t_{(0.975,71)}=\) 1.9939 , giving a \(95 \%\) prediction interval
Consider the wage equationwhere the explanatory variables are years of education \((E D U C)\) and years of experience (EXPER). Estimation results for this equation, and for modified versions of it
RESET suggests augmenting an existing model with the squares or the squares and higher powers of the predictions \(\hat{y}_{i}\). For example, \(\left(\hat{y}_{i}^{2}\right)\) or
Reconsider Example 6.19 where we used nonlinear least squares to estimate the model \(y_{i}=\beta x_{i 1}+\) \(\beta^{2} x_{i 2}+e_{i}\) by minimizing the sum of squares function
In Example 6.7 we tested the joint null hypothesisin the modelBy substituting the restrictions into the model and rearranging variables, show how the model can be written in a form where least
This exercise uses data on 850 houses sold in Baton Rouge, Louisiana during mid-2005. We will be concerned with the selling price in thousands of dollars (PRICE), the size of the house in hundreds of
Do gun buybacks save lives? Following the "Port Arthur massacre" in 1996, the Australian government introduced a gun buyback scheme in 1997. The success of that scheme has been investigated by Leigh
Do gun buybacks save lives? Following the "Port Arthur massacre" in 1996, the Australian government introduced a gun buyback scheme in 1997. As mentioned in Exercise 6.13, the success of that scheme
The following equation estimates the dependence of CANS (the weekly number of cans of brand A tuna sold in thousands) on the price of brand \(\mathrm{A}\) in dollars (PRA) and the prices of two
Using 28 annual observations on output \((Y)\), capital \((K)\), labor \((L)\) and intermediate materials \((M)\) for the U.S manufacturing sector, to estimate the Cobb-Douglas production
Reconsider Example 6.16 in the text. In that example a number of models were assessed on their within-sample and out-of-sample predictive ability using data in the file \(b r 5\). Of the models
Consider Example 6.17 where the rice production functionwas estimated using data from the file rice 5.a. Using data from 1994 only, contrast the outcomes of the following hypothesis tests.i. \(H_{0}:
Consider the following expenditure share equation where WFOOD is the proportion of household total expenditure allocated to food, TOTEXP is total weekly household expenditure in British pounds (
In Example 6.18, using 900 observations from the data file \(b r 5\), we identified three potentially influential observations in the estimation of the modelThose observations were numbers 150,411
Reconsider Example 6.20 where a logistic growth curve for the share of U.S. steel produced by electric arc furnace (EAF) technology was estimated. The curve is given by the equationa. Find \(95 \%\)
To examine the quantity theory of money, Brumm \({ }^{15}\) specifies the equationwhere INFLAT is the growth rate of the general price level, MONEY is the growth rate of the money supply, and OUTPUT
For two inputs \(X_{1}\) and \(X_{2}\) and output \(Y\), a constant elasticity of substitution (CES) production function is given bywhere \(\alpha>0\) is an efficiency parameter, \(\eta>0\) is
Using the data in the file \(b r 5\), find least squares estimates of the following house-price relationships for houses sold in Baton Rouge during 2005.a. Report the coefficient estimates and their
Using the data in the file \(b r 5\), estimate the equationwhere PRICE is the selling price in thousands of dollars for houses sold in Baton Rouge, Louisiana, in 2005, SQFT is the size of each house
Each morning between 6:30 Am and 8:00Am Bill leaves the Melbourne suburb of Carnegie to drive to work at the University of Melbourne. The time it takes Bill to drive to work (TIME), depends on the
It has been claimed that an extra year of experience increases wage by \(0.8 \%\) and that an extra year of education is worth 14 extra years of experience. Doing the calculation, this would mean an
Using time-series data on five different countries, Atkinson and Leigh \({ }^{18}\) investigate the impact of the marginal tax rate paid by high-income earners on the level of inequality. A subset of
Using time-series data on five different countries, Atkinson and Leigh investigate the impact of the marginal tax rate paid by high-income earners on the level of inequality. A subset of their data
Consider a translog production function where output is measured as firm sales and there are three inputs: capital, labor, and materials. This function can be written aswhere LSALES is the log of
Everaert and Pozzi \({ }^{20}\) develop a model to examine the predictability of consumption growth in 15 OECD countries. Their data is stored in the file oecd. The variables used are growth in real
In their study of the prices of Californian and Washington red wines, Costanigro, Mittelhammer and McCluskey \(^{21}\) categorize the wines into commercial, semipremium, premium, and ultrapremium.
In this exercise we reconsider the premium wine data in the file wine 1. Please see Exercise 6.32 and wine1.def for details.a. Estimate the following equation using (i) only cabernet wines, (ii) only
The difference between qualitative and quantitative economic variables.
How to include a \(0-1\) indicator variable on the right-hand side of a regression, how this affects model interpretation, and give an example.
How to interpret the coefficient on an indicator variable in a log-linear equation.
How to include a slope-indicator variable in a regression, how this affects model interpretation, and give an example.
How to include a product of two indicator variables in a regression, and how this affects model interpretation, giving an example.
How to model qualitative factors with more than two categories (similar to region of the country), and how to interpret the resulting model, giving an example.
The consequences of ignoring a structural change in parameters during part of the sample.
How to test the equivalence of two regression equations using indicator variables.
How to estimate and interpret a regression with an indicator dependent variable.
The difference between a randomized controlled experiment and a natural experiment.
The difference between the average treatment effect (ATE) and the average treatment effect on the treated (ATT).
How to use a regression discontinuity design (RDD), and explain when it is useful.
Suppose we are able to collect a random sample of data on economics majors at a large university. Further suppose that, for those entering the workforce, we observe their employment status and salary
In September of 1998, a local TV station contacted an econometrician to analyze some data for them. They were going to do a Halloween story on the legend of full moons affecting behavior in strange
One of the key problems regarding housing prices in a region concerns construction of "price indexes." That is, holding other factors constant, have prices increased, decreased or stayed relatively
Angrist and Pischke \({ }^{29}\) report estimation results of log-earnings equations using a large sample of college graduates. The predictors of interest (there are others included in their model)
In 1985, the state of Tennessee carried out a statewide experiment with primary school students. Teachers and students were randomly assigned to be in a regular-sized class or a small class. The
In 1985, the state of Tennessee carried out a statewide experiment with primary school students. Teachers and students were randomly assigned to be in a regular-sized class or a small class. The
Can monetary policy reduce the impact of a severe recession? A natural experiment is provided by the State of Mississippi. In December of 1930, there were a series of bank failures in the southern
Using \(N=2005\) observations, we examine the relationship between food expenditures away from home per person in the past month as a function of household monthly income, the highest level of
Suppose we wish to estimate a model of household expenditures on alcohol ( \(A L C\), in dollars per month) as a function of household income (INCOME, \\($100's\) per month), and some other
Suppose we wish to estimate a model of household expenditures on alcohol ( \(A L C\), in dollars per month) as a function of household income (INCOME, \(\$ 100\) 's per month), and some other
Consider the log-linear regression model \(\ln (y)=\beta_{1}+\beta_{2} x+\delta_{1} D+\delta_{2}(x \times D)+e\). If the regression errors are normally distributed \(N\left(0, \sigma^{2}\right)\),
Consider the log-linear regression model \(\ln (y)=\beta_{1}+\beta_{2} x+\delta_{1} D+\delta_{2}(x \times D)+e\). If the regression errors are normally distributed \(N\left(0, \sigma^{2}\right)\),
Many cities in California have passed Inclusionary Zoning policies (also known as below-market housing mandates) as an attempt to make housing more affordable. These policies require developers to
Consider a model explaining the weekly sales ( \(S A L E S=100\) 's cans sold) of a popular brand (the "target" brand) of canned tuna as a function of its price ( \(P R I C E=\) average price in
Mortgage lenders are interested in determining borrower and loan characteristics that may lead to delinquency or foreclosure. We estimate a regression model using 1000 observations and the following
In this exercise, we examine the hours of market work by married women as a function of their education and number of children. Use data file cps5mw_small for this exercise. The data file cps5mw
Does a mother's smoking affect the birthweight of her child? Using data in the file bweight_small taken from Cattaneo (2010), \({ }^{31}\) we explore this question. The file bweight contains more
Does a mother's smoking affect the birthweight of her child? Using the data file bweight_small, we explore this question. The file bweight contains more observations.a. Estimate the regression model
Does a mother's smoking affect the birthweight of her child? Using the data file bweight_small we explore this question. The file bweight contains more observations. The variable MSMOKE is the number
In this exercise, we will explore some of the factors predicting costs at American universities using the data file poolcoll2 and observations outside the great recession. Let \(T C=\) the real
In this exercise, we explore some of the factors predicting costs at American public universities using the data file pubcoll. Let \(T C=\) the real \((\$ 2008)\) total cost per student, \(F T U G=\)
In this exercise, we explore some of the factors predicting costs at American public universities using the data file pubcoll. Let \(T C=\) the real \((\$ 2008)\) total cost per student, \(F T U G=\)
In the STAR experiment (Section 7.5.3), 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
Many cities in California have passed Inclusionary Zoning policies (also known as below-market housing mandates) as an attempt to make housing more affordable. These policies require developers to
Professor Ray C. Fair's voting model was introduced in Exercise 2.23. He builds models that explain and predict the U.S. presidential elections. See his website at
The data file \(b r 2\) contains data on 1080 house sales in Baton Rouge, Louisiana, during July and August 2005. The variables are: PRICE (\\($)\), SQFT (total square feet), BEDROOMS (number), BATHS
The three most important words in real estate are "location, location, location!" We explore this question using 500, single-family home sales in Baton Rouge, LA from 2009 to 2013 in the data file
How much of an incumbency advantage do winners in U.S. House elections enjoy? This is the topic of a paper by David S. Lee (2008) "Randomized experiments from nonrandom selection in U.S. House
How much of an incumbency advantage do winners in U.S. Senate elections enjoy? This issue is examined by Matias D. Cattaneo, Brigham R. Frandsen and Rocío Titiunik (2015) "Randomization Inference in
What effect does having public health insurance have on the number of doctor visits a person has during a year? Using 1988 data,rwm88_small, from Germany we will explore this question. The data file
Explain the meaning of heteroskedasticity and give examples of data sets likely to exhibit heteroskedasticity.
Explain how and why plots of least squares residuals can reveal heteroskedasticity.
Specify a variance function and use it to test for heteroskedasticity with (a) a Breusch-Pagan test and (b) a White test.
Test for heteroskedasticity using a Goldfeld-Quandt test applied to (a) two subsamples with potentially different variances and (b) a model where the variance is hypothesized to depend on an
Describe and compare the properties of the least squares and generalized least squares estimators when heteroskedasticity exists.
Compute heteroskedasticity-consistent standard errors for least squares.
Describe how to transform a model to eliminate heteroskedasticity.
Compute generalized least squares estimates for heteroskedastic models where (a) the variance is known except for the proportionality constant \(\sigma^{2}\), (b) the variance is a function of
Explain why the linear probability model exhibits heteroskedasticity.
Compute generalized least squares estimates of the linear probability model.
For the simple regression model with heteroskedasticity, \(y_{i}=\beta_{1}+\beta_{2} x_{i}+e_{i}\) and \(\operatorname{var}\left(e_{i} \mid \mathbf{x}_{i}\right)=\sigma_{i}^{2}\) show that the
Consider the regression model \(y_{i}=\beta_{1} x_{i 1}+\beta_{2} x_{i 2}+e_{i}\) with two explanatory variables, \(x_{i 1}\) and \(x_{i 2}\), but no constant term.a. The sum of squares function is
Suppose that an outcome variable \(y_{i j}=\beta_{1}+\beta_{2} x_{i j}+e_{i j}, i=1, \ldots, N ; j=1, \ldots, N_{i}\). Assume \(E\left(e_{i j} \mid \mathbf{X}\right)=0\) and
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