Questions and Answers of Introductory Econometrics Modern

In Example 16.14, we described an ordinal probit model for postsecondary education choice, and estimated a simple model in which the choice depended simply on the student's GRADES. Expand the ordered
In Example 16.15, we considered a count data model for the number of doctor visits by an individual as a function of a few explanatory variables. In this exercise, we expand the analysis using a
The data file ozconfn contains quarterly data on Australian real consumption expenditure (CONS) and real net national disposable income (INC) from 1975Q1 to 2010Q4.a. Create the series \(L C O N
The data file inter 2 contains 300 observations of a generated $\mathrm{I}(2)$ process shown in Figure 12.10. Show that the variable called inter 2 is indeed an $\mathrm{I}(2)$ variable by
In the post-World War II period, monetary policy effects and the supply and demand for money were important topics. Consider the following model, where $M$ is the money stock, $R$ is short-term
Reconsider Example 11.2 on the supply and demand for fish at the Fulton Fish Market. The data are in the file fultonfish.a. Obtain OLS estimates of the supply equation. Comment on the coefficient
Reconsider Example 11.2 on the supply and demand for fish at the Fulton Fish Market. The data are in the file fultonfish.a. Add the variable MIXED, which indicates poor but not STORMY weather
Reconsider Example 11.2 on the supply and demand for fish at the Fulton Fish Market. The data are in the file fultonfish. In this exercise, we explore the behavior of the market on days in which
In Examples 16.2 and 16.4, we presented the linear probability and probit model estimates using an example of transportation choice. The logit model for the same example is \(P(A U T
In Appendix 16A.1, we illustrate the calculation of a standard error for the marginal effect in a probit model of transportation, Example 16.4. In the appendix, the calculation is for the marginal
In Example 16.3, we illustrate the calculation of the likelihood function for the probit model in a small example.a. Calculate the probability that $y=1$ if $x=1.5$, given the values of the
In Example 16.3, we illustrate the calculation of the likelihood function for the probit model in a small example. In this exercise, we will repeat that example using logit instead of probit. The
We are given three observations on binary choice with $y_{1}=1, y_{2}=1, y_{3}=0$. Consider a logit model with only an intercept, $P(y=1)=\Lambda\left(\gamma_{1}\right)$, where
In this exercise, we generalize the results in Exercise 16.5. Consider a logit model with only an intercept, $P(y=1)=\Lambda\left(\gamma_{1}\right)$, where $\Lambda(\bullet)$ is the logistic \(c
Exercise 16.5 shows that given the three observations on binary choice with $y_{1}=1, y_{2}=1, y_{3}=0$ the maximum likelihood estimator of the logit model $P(y=1)=\Lambda\left(\gamma_{1}\right)$
Consider a probit model designed to explain the choice by homebuyers of fixed versus adjustable rate mortgages. The explanatory variables, with sample means in parentheses, are FIXRATE (13.25) =
Consider a probit model explaining the choice to attend college by high-school graduates. Define $C O L L E G E=1$ if a high-school graduate chooses either a 2-year or 4-year college, and zero
Consider a probit model explaining the choice to attend a 4-year college rather than a 2 -year college by high-school graduates who chose to attend a postsecondary school. Define $F O U R Y R=1$ if
Using data on $N=4,642$ infant births, we estimate a probit model with dependent variable $L B W E I G H T=1$ if it is a low birthweight baby and 0 otherwise, MAGE is the mother's age, PRENATAL1
This exercise is an extension of Example 16.12 using the larger data set nels with 6,649 observations. Two estimated multinomial logit models are reported in Table 16.11. In addition to the variable
This exercise is an extension of Example 16.13. It is a conditional logit model of choice among 3 brands of soda: Coke, Pepsi, and 7-Up. The data are in the data file cola. As in the example, we
Consider a Poisson regression explaining the number of Olympic Games medals won using data from 1988 (in Seoul, South Korea) and 1992 (in Barcelona, Spain) by various countries as a function of \(L P
Consider a regression explaining the share of Olympic Games medals won by each country in 1988 (in Seoul, South Korea), 1992 (in Barcelona, Spain), and 1996 (in Atlanta, GA, USA) as a function of \(L
In Chapter 7, we examined the Tennessee's Project STAR. In the experiment, children were randomly assigned within schools into three types of classes: small classes with 13-17 students, regular sized
Mortgage lenders are interested in determining borrower and loan characteristics that may lead to delinquency or foreclosure. In the data file lasvegas are 1000 observations on mortgages for single
Mortgage lenders are interested in determining borrower and loan factors that may lead to delinquency or foreclosure. In the data file vegas5_small are 1000 observations on mortgages for single
This exercise deals with the loan data in the data file lasvegas described in Exercise 6.18. The "Chow" test was introduced in Section 7.2.3 for testing the equality of coefficients in two
Data on 1500 purchases of canned lite tuna are in the data file tunafish. There are four brands of tuna (Starkist - water, Starkist - oil, Chicken of the Sea - water, Chicken of the Sea - oil). The
How do age, education, and other personal characteristics predict our assessment of our health status? Use the data file $r w m 88$ to answer the following.a. Tabulate the values of the variable
How well do age, education, and other personal characteristics predict our assessment of our health status? Use the data file rwm88 to answer the following.a. Tabulate the variable HSAT3, which is a
Consider household expenditures per person on apparel. Use the data file cex 5 for this exercise.a. What percentage of the households spent nothing on apparel in the previous quarter?b. Estimate a
Consider using data file mroz to estimate a model explaining a married woman's hours of work, $H O U R S$, as a function of her education, EDUC, her experience, EXPER, and her husband's hours of
In Example 7.11, we used the linear probability model to check whether students were assigned randomly to small classes in Project STAR. In this exercise, we use multinomial logit and the data file
We have used Ray Fair's voting data, (data file fair5, throughout the book to predict presidential election outcomes with the linear regression model. Here we apply probit to predict the outcome of
In this exercise, we illustrate some features of instrumental variables estimation, and two-stage least squares, when the potential endogenous variable is binary. Use the data file $r w m 88$ for
In this exercise, we use multinomial logit to describe factors leading an individual to fall into one of three categories. Use data file $r w m 88$ for this exercise.a. Create a variable called
Explain the differences between stationary and nonstationary time-series processes.
Describe the general behavior of an autoregressive process and a random walk process.
Explain why we need "unit root" tests, and state implications of the null and alternative hypotheses.
Explain what is meant by the statement that a series is "integrated of order one" or I(1).
Perform Dickey-Fuller and augmented Dickey-Fuller tests for stationarity.
Explain the meaning of a "spurious regression."
Explain the concept of cointegration and test whether two series are cointegrated.
Explain how to choose an appropriate model for regression analysis with time-series data.
Consider the $\operatorname{AR}(2)$ model $y_{t}=\delta+\theta_{1} y_{t-1}+\theta_{2} y_{t-2}+v_{t}$. Suppose that\[1-\theta_{1} z-\theta_{2} z^{2}=\left(1-c_{1} z\right)\left(1-c_{2}
a. Consider the stationary $\operatorname{AR}(1)$ model $y_{t}=ho y_{t-1}+v_{t},|ho|)=ho^{s}$. Given $ho=0.9$, find the autocorrelations for observations 1 period apart, 2 periods apart, etc.,
Figure 12.8 shows plots of four time series that are stored in the data file unit.a. The results from Dickey-Fuller test equations for these four variables are given below. Explain why these
A time-series process of the form $y_{t}=\alpha+y_{t-1}+v_{t}, v_{t} \sim N\left(0, \sigma^{2}\right)$ can be rearranged as $y_{t}-y_{t-1}=$ $\Delta y_{t}=\alpha+v_{t}$. This shows that
In Chapter 9, we found that, given a time series of observations, $I_{T}=\left\{\left(y_{1}, x_{1}\right),\left(y_{2}, x_{2}\right), \ldots,\left(y_{T}, x_{T}\right)\right\}$, the best one-period
Increases in the mortgage interest rate increase the cost of owning a house and lower the demand for houses. In this question we investigate the properties of two time series that could be used to
The data file usmacro contains quarterly observations on the U.S. unemployment rate $(U)$, the U.S. GDP growth rate (G), and the U.S. inflation rate (INF) from 1948Q1 to 2016Q1. Plot these series
The data file okun5_aus contains quarterly observations on the Australian unemployment rate $(U)$, and the Australian GDP growth rate $(G)$ from 1978Q2 to 2016Q2. Plot these series and perform
The data file phillips 5_aus contains quarterly observations on the Australian unemployment rate $(U)$, and the Australian inflation rate (INF) from 1987Q1 to 2016Q1. Plot these series and perform
The data file oil5 contains quarterly observations on the price of oil from 1980Q1 to 2016Q1.a. Plot the observations.b. Using data from 1980Q1 to $2015 \mathrm{Q} 2$, test whether the series is
The data file freddiel contains a monthly housing price index for the price of houses in Beckley, West Virginia (BEKLY), and the monthly value of Australian exports to China (XCHINA), from 1988M1 to
The data file freddie 2 contains monthly housing price indices for the prices of houses in ChampaignUrbana, Illinois (CHURB), and Charlottesville, Virginia (CHARV) from 1982M1 to 2015M12.a. Plot the
The data file $g d p 5$ contains the data on $G D P$ displayed in Figure 12.1.a. Is $G D P$ stationary or nonstationary? Explain your choice of test equation.b. What is the order of integration
The data file usdata5 contains the data on inflation displayed in Figure 12.1.a. Is inflation stationary or nonstationary? Explain your choice of test equation.b. What is the order of integration of
In Example 12.2, using data from the data file toody 5, we estimated the model\[\ln \left(Y_{I E L D_{t}}\right)=\alpha_{1}+\alpha_{2} t+\beta_{1} \text { RAIN }_{t}+\beta_{2} \text { RAIN
a. Using data from the data file toody 5 , estimate the following model. Comment on the results.\[\text { YIELD }_{t}=\alpha_{1}+\alpha_{2} t+\beta_{1} \text { RAIN
Consider the ARDL modelAssume that $y_{t}$ and $x_{t}$ are I(1) and cointegrated. Let the cointegrating relationship be described by the equation $y_{t}=\beta_{1}+\beta_{2} x_{t}+e_{t}$.a. Show
When we estimated an error correction model for the bond and federal funds rates in Example 12.9, we estimated the coefficients of the cointegrating relationship \(B R_{t}=\beta_{1}+\beta_{2} F F
The data file canada6 contains monthly Canadian/U.S. exchange rates for the period 1971M1 to 2017M3. Split the observations into two sample periods-a 1971M1-1987M12 sample period and a 1988M1-2017M3
The data file csi contains the Consumer Sentiment Index (CSI) produced by the University of Michigan for the sample period 1978M1-2006M12.a. Perform all three Dickey-Fuller tests. Are the results
The data file mexico contains real GDP for Mexico and the United States from the first quarter of 1980 to the third quarter of 2006 . Both series have been standardized so that the average value in
Prices around the world tend to move together. The data file $u k p i$ contains information about the price indices in the United Kingdom and in the Euro Area (the United Kingdom is a member of the
The data file nasa contains annual data on sunspots and the rate of growth in real GDP in the U.S. for the period 1950-2014. Jevons, a 19th century economist, suggested that there might be a
The data file shiller contains the stock market data in the book "Irrational Exuberance" by Robert Shiller. ${ }^{10}$ They comprise the monthly price and dividends of the S\&P Index (in logs) for
How easy is it to forecast the Australian/U.S. dollar exchange rate? The data file iron contains monthly data on the iron ore price and the exchange rate from 2010M1 to 2016M12. In the questions that
The data file inflation contains quarterly observations on the inflation rates in Germany and France from 1990Q1 to 2014Q4. For any hypothesis tests in the following questions, use a 5\% significance
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 data are stored in the data file steel. The
Explain why economic variables are dynamically interdependent.
Explain the VEC model.
Explain the importance of error correction.
Explain the VAR model.
Explain the relationship between a VEC model and a VAR model.
Explain how to estimate the VEC and VAR models for the bivariate case.
Explain how to generate impulse response functions and variance decompositions for the simple case when the variables are not contemporaneously interdependent and the shocks are not correlated.
Consider the following first-order VAR model of stationary variables:\[\begin{aligned}& y_{t}=\delta_{11} y_{t-1}+\delta_{12} x_{t-1}+v_{t}^{y} \\& x_{t}=\delta_{21} y_{t-1}+\delta_{22}
Consider the first-order VAR model in Exercise 13.1. Under the assumption that there is no contemporaneous dependence, determinea. the contribution of a shock to $y$ on the variance of the
The VEC model is a special form of the VAR for I(1) variables that are cointegrated. Consider the following VEC model:\[\begin{aligned}& \Delta
VAR and VEC models are popular forecasting models because they rely on the past history of observed outcomes to predict the expected future values.a. Consider the following estimated VAR
The data file $g d p$ contains quarterly data on the real GDP of Australia (AUS) and real GDP of the United States (USA) for the sample period 1970Q1 to 2000Q4.a. Are the series stationary or
The data file fred 5 contains the $\log$ of RPDI $(Y)$ and the log of RPCE $(C)$ for the U.S. economy over the period 1986Q1 to 2015Q2.a. Are the series stationary, or nonstationary? In
Consider again the data file fred5 used in Example 13.2 and Exercise 13.6.a. Estimate a VAR model for $\left\{\Delta C_{t}, \Delta Y_{t}\right\}$ with three lags of each variable included. Comment
The data file vec contains 100 observations on two generated series of data, $x$ and $y$. The variables are nonstationary and cointegrated without a constant term. Save the cointegrating
The data file var contains 100 observations on two generated series of data, $w$ and $z$. The variables are nonstationary but not cointegrated. Estimate a VAR model of changes in the variables.
The quantity theory of money says that there is a direct relationship between the quantity of money in the economy and the aggregate price level. Put simply, if the quantity of money doubles, then
Research into the Phillips curve is concerned with providing empirical evidence of a tradeoff between inflation and unemployment. Can an economy experience lower unemployment if it is prepared to
Figure 13.8 shows the time series for two exchange rates-the EURO per $$US$ and the STERLING per $$US$ (data file sterling). Both the levels and the changes in the data are shown.a. Which set of
Financial analysts often debate the role of dividends $(D V)$ in the determination of share prices $(S P)$. Figure 13.9 shows plots of the rate of change in $D V$ and $S P$ computed aswhere
The file $g f c$ contains data about economic activity in two major economies: the United States and the Euro Area (the group of countries in Europe where the Euro currency is the legal tender).
The file precious contains monthly data on the prices of gold and silver (in logs) for the period 1970M1 to $2014 \mathrm{M} 2$.a. Plot the two series and comment on the graph. Do the two prices
Explain the difference between a constant and a time-varying variance of the error term.
Explain the term "conditionally normal."
Perform a test for ARCH effects.
Estimate an ARCH model.
Forecast volatility.
Explain the difference between ARCH and GARCH specifications.
Explain the distinctive features of a T-GARCH model and a GARCH-in-mean model.

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