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Questions and Answers of Econometrics

From a sample of 10 observations, the following results were obtained:ΣYi = 1,110 ΣXi = 1,700 ΣXiYi = 205,500ΣXi2 = 322,000
The following table gives data on gold prices, the Consumer Price Index (CPI), and the New York Stock Exchange (NYSE) Index for the United States for the period 1974 €“2006. The NYSE Index
If X1, X2, and X3 are uncorrelated variables each having the same standard deviation, show that the coefficient of correlation between X1 + X2 and X2 + X3 is equal to 1/2. Why is the correlation
Show that the estimates Î²Ì‚1= 1.572 and Î²Ì‚2= 1.357 used in the first experiment of Table 3.1 are in fact the OLS estimators.Table 3.1 Y2i (6) Y; X¢
According to Malinvaud (see footnote 11), the assumption that E(ui | Xi) = 0 is quite important. To see this, consider the PRF: Y = β1 + β2Xi + ui . Now consider two situations:(i) β1 = 0, β2 =
Table 3.8 gives data on gross domestic product (GDP) for the United States for the years 1959 2005.a. Plot the GDP data in current and constant (i.e., 2000) dollars against time.b. Letting Y denote
Consider the sample regressionYi = β̂1 + β̂2Xi + ûiImposing the restrictions (i) Σûi = 0 and (ii) Σ ûiXi = 0, obtain the estimators β̂1 and β̂2 and show that they are identical
In the regression Yi = β1 + β2Xi + ui suppose we multiply each X value by a constant, say, 2. Will it change the residuals and fitted values of Y? Explain. What if we add a constant value, say, 2,
Show that r2 defined in (3.5.5) ranges between 0 and 1. You may use the Cauchy–Schwarz inequality, which states that for any random variables X and Y the following relationship holds true:[E (XY)]2
Let β̂YX and β̂XY represent the slopes in the regression of Y on X and X on Y, respectively. Show thatβ̂YX β̂XY = r2Where r is the coefficient of correlation between X and Y.
Spearman’s rank correlation coefficient rs is defined as follows:rs = 1 – 6 Σd2 / n(n2 – 1)Where d = difference in the ranks assigned to the same individual or phenomenon and n = number of
Suppose in Exercise 3.6 that β̂YX β̂XY = 1. Does it matter then if we regress Y on X or X on Y? Explain carefully.
For the SAT example given in Exercise 2.16 do the following:In exerciseTable 2.9 gives data on mean Scholastic Aptitude Test (SAT) scores for collegebound seniors for 1972€“2007. These data
Show that Eq. (3.5.14) in fact measures the coefficient of determination.Apply the definition of r given in Eq. (3.5.13) and recall that Î£yiyÌ‚i =
Table 3.6 gives data on indexes of output per hour (X) and real compensation per hour (Y) for the business and nonfarm business sectors of the U.S. economy for 1960€“2005. The base year of
The relationship between nominal exchange rate and relative prices. From annual observations from 1985 to 2005, the following regression results were obtained, where Y = exchange rate of the
In Table 3.5, you are given the ranks of 10 students in midterm and final examinations in statistics. Compute Spearman€™s coefficient of rank correlation and interpret it. Student Rank E D
Regression without any regressor. Suppose you are given the model: Yi = β1 + ui.Use OLS to find the estimator of β1. What is its variance and the RSS? Does the estimated β1 make intuitive sense?
Explain with reason whether the following statements are true, false, or uncertain:a. Since the correlation between two variables, Y and X, can range from −1 to +1, this also means that cov (Y, X)
What is meant by an intrinsically linear regression model? If β2 in Exercise 2.7d were 0.8, would it be a linear or nonlinear regression model?
Are the following models linear regression models? Why or why not?a. Yi = eβ1 + β2Xi + uib. Yi = 1 / 1 + eβ1 + β2Xi + uic. ln Yi = β1 + β2 (1/Xi) + uid. Yi = β1 + (0.75-β1)e-β2(Xi-2) +uie.
Determine whether the following models are linear in the parameters, or the variables, or both. Which of these models are linear regression models? Descriptive Title Model Reciprocal Semilogarithmic
What do we mean by a linear regression model?
Why do we need regression analysis? Why not simply use the mean value of the regressand as its best value?
What is the role of the stochastic error term ui in regression analysis? What is the difference between the stochastic error term and the residual, ûi?
What is the difference between the population and sample regression functions? Is this a distinction without difference?
What is the conditional expectation function or the population regression function?
Table 2.10 presents data on mean SAT reasoning test scores classified by income for three kinds of tests: critical reading, mathematics, and writing. In Example 2.2, we presented Figure 2.7, which
Table 2.9 gives data on mean Scholastic Aptitude Test (SAT) scores for collegebound seniors for 1972€“2007. These data represent the critical reading and mathematics test scores for both
Table 2.8 gives data on expenditure on food and total expenditure, measured in rupees, for a sample of 55 rural households from India. (In early 2000, a U.S. dollar was about 40 Indian rupees.)a.
You are given the data in Table 2.7 for the United States for years 1980€“2006.a. Plot the male civilian labor force participation rate against male civilian unemployment rate. Eyeball a
Is the regression line shown in Figure I.3 of the Introduction the PRF or the SRF? Why? How would you interpret the scatterpoints around the regression line? Besides GDP, what other factors, or
What does the scattergram in Figure 2.10 reveal? On the basis of this diagram, would you argue that minimum wage laws are good for economic well being? Ratio of one year's salary at minimum wage to
You are given the scattergram in Figure 2.8 along with the regression line. What general conclusion do you draw from this diagram? Is the regression line sketched in the diagram a population
Consider the following nonstochastic models (i.e., models without the stochastic error term). Are they linear regression models? If not, is it possible, by suitable algebraic manipulations, to
The data presented in Table 1.6 were published in the March 1, 1984, issue of The Wall Street Journal. They relate to the advertising budget (in millions of dollars) of 21 firms for 1983 and millions
Controlled experiments in economics: On April 7, 2000, President Clinton signed into law a bill passed by both Houses of the U.S. Congress that lifted earnings limitations on Social Security
Suppose you were to develop an economic model of criminal activities, say, the hours spent in criminal activities (e.g., selling illegal drugs). What variables would you consider in developing such a
The data behind the M1 money supply in Figure 1.5 are given in Table 1.5. Can you give reasons why the money supply has been increasing over the time period shown in the table?Table 1.5 Seasonally
a. Using Table 1.3, plot the inflation rate of Canada, France, Germany, Italy, Japan, and the United Kingdom against the United States inflation rate.b. Comment generally about the behavior of the
Table 1.3 gives data on the Consumer Price Index (CPI) for seven industrialized countries with 1982€“1984 = 100 as the base of the index.a. From the given data, compute the inflation rate
Calculating VIFs typically involves running sets of auxiliary regressions, one regression for each independent variable in an equation. To get practice with this procedure, calculate the following:a.
Simultaneous equations make sense in cross-sectional as well as time-series applications. For example, James Ragan examined the effects of unemployment insurance (hereafter UI) eligibility standards
As an exercise to gain familiarity with the 2SLS program on your computer, take the data provided for the simple Keynesian model in Section 14.3, and:a. Estimate the investment function with OLS.b.
The word recursive is used to describe an equation that has an impact on a simultaneous system without any feedback from the system to the equation. Which of the equations in the following systems
In 2008, Goldman and Romley studied hospital demand by analyzing how 8,721 Medicare-covered pneumonia patients chose from among 117 hospitals in the greater Los Angeles area. The authors concluded
Because their college had just upgraded its residence halls, two seniors decided to build a model of the decision to live on campus. They collected data from 533 upper-class students (first-year
In 2001, Heo and Tan published an article in which they used the Granger causality model to test the relationship between economic growth and democracy. For years, political scientists have noted a
Some farmers were interested in predicting inches of growth of corn as a function of rainfall on a monthly basis, so they collected data from the growing season and estimated an equation of the
You€™ve been hired to determine the impact of advertising on gross sales revenue for €œFour Musketeers€ candy bars. Four Musketeers has the same price and more or less
Let's investigate the possibility of heteroskedasticity in time-series data by looking at a model of the black market for U.S. dollars in Brazil that was studied by R. Dornbusch and C. Pechman. In
Suppose that you€™re interested in the effect of price on the demand for a €œsalon€ haircut and that you collect the following data for four U.S. cities for 2003:and
The discussion of random assignment experiments in Section 16.1 includes models both with (Equation 16.2) and without (Equation 16.1) two additional observable factors (X1 and X2). In contrast, the
James Stock and Mark Watson suggest a quite different approach to heteroskedasticity. They state that “economic theory rarely gives any reason to believe that the errors are homoskedastic. It
As an example of impure serial correlation caused by an incorrect functional form, let€™s return to the equation for the percentage of putts made (Pi) as a function of the length of the
Your friend is just finishing a study of attendance at Los Angeles Laker regular-season home basketball games when she hears that you€™ve read a chapter on serial correlation and asks your
Recall from Section 9.5 that switching the order of a data set will not change its coefficient estimates. A revised order will change the Durbin€“Watson statistic, however. To see both
In 1998, Mark McGwire hit 70 homers to break Roger Maris€™s old record of 61, and yet McGwire wasn€™t voted the Most Valuable Player (MVP) in his league. To try to understand how
A researcher once attempted to estimate an asset demand equation that included the following three explanatory variables: current wealth Wt, wealth in the previous quarter Wt-1, and the change in
V. N. Murti and V. K. Sastri investigated the production characteristics of various Indian industries, including cotton and sugar. They specified Cobbâ€“Douglas production functions for output
In an effort to explain regional wage differentials, you collect wage data from 7,338 unskilled workers, divide the country into four regions (Northeast, South, Midwest, and West), and estimate the
Look over the following equations and decide whether they are linear in the variables, linear in the coefficients, both, or neither:a. Yi = β0 + β1X3i + εib. Yi = β0 + β1ln Xi + εic. ln Yi =
Let€™s return to the model of Exercises 3-7 and 5-8 of the auction price of iPods on eBay. In that model, we used datafile IPOD3 to estimate the following equation:Where:PRICEi = the price
Let’s return to the model of financial aid awards at a liberal arts college that was first introduced in Section 2.2. In that section, we estimated the following equation (standard errors in
Consider the following annual model of the death rate (per million population) due to coronary heart disease in the United States (Yt):Where:Ct = per capita cigarette consumption (pounds of tobacco)
Frederick Schut and Peter VanBergeijk16 published an article in which they attempted to see if the pharmaceutical industry practiced international price discrimination by estimating a model of the
Suppose that you€™ve been asked by the San Diego Padres baseball team to evaluate the economic impact of their new stadium by analyzing the team€™s attendance per game in the last
Using the techniques of Section 5.3, test the following two-sided hypotheses:a. For Equation 5.8, test the hypothesis that:H0: 2 = 160.0HA: 2 ≠ 160.0at the 5-percent level of significance.b.
Create null and alternative hypotheses for the following coefficients:a. The impact of height on weightb. All the coefficients in Equation A in Exercise 5, Chapter 2c. All the coefficients in Y = β0
In Hollywood, most nightclubs hire €œpromoters,€ or people who walk around near the nightclub and try to convince passersby to enter the club. One of the nightclub owners asked a
Which of the following pairs of independent variables would violate Assumption VI? (That is, which pairs of variables are perfect linear functions of each other?)a. Right shoe size and left shoe size
Let’s get some more experience with the six steps in applied regression. Suppose that you’re interested in buying an Apple iPod (either new or used) on eBay (the auction website) but you want to
The Graduate Record Examination (GRE) subject test in economics was a multiple-choice measure of knowledge and analytical ability in economics that was used mainly as an entrance criterion for
Do liberal arts colleges pay economists more than they pay other professors? To find out, we looked at a sample of 2,929 small-college faculty members and built a model of their salaries that
Suppose that you work in the admissions office of a college that doesn€™t allow prospective students to apply by using the Common Application.9 How might you go about estimating the number
Suppose that you have been asked to estimate a regression model to explain the number of people jogging a mile or more on the school track to help decide whether to build a second track to handle all
Consider the following two least-squares estimates of the relationship between interest rates and the federal budget deficit in the United States:Model A: Ŷ1 = 0.103 - 0.079X1 R2 = .00Where:Y1 =
Let’s return to the wage determination example of Section 1.2. In that example, we built a model of the wage of the ith worker in a particular field as a function of the work experience, education,
If an equation has more than one independent variable, we have to be careful when we interpret the regression coefficients of that equation. Think, for example, about how you might build an equation

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