econometrics mcqs

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1 Multiple Choice Question Bank for BUEC 333 (copyright 2006, Peter Kennedy) This set of multiple choice questions has been prepared to supply you with a means of checking your command of the course material. For each week of the course I have tried to provide questions that cover the full range of material discussed during that week. I have also tried not to include “duplicate” questions, namely questions that are basically the same as other questions but, for example, just use different numbers. The questions range quite widely in character. Some check your knowledge of definitions, some address implications of concepts, some require finding numbers in tables, some ask you to do calculations, some are very easy, and some are very difficult. Because of this, not all questions are such that they are likely to appear on an exam, so how you score on these questions is not as important as how well you understand the logic of the answers. Spending quality time on these questions should help your efforts to learn this course material. My advice is to work through each chapter’s questions after you believe you have a good command of that chapter’s material, and then if there are any questions for which you don’t understand why the answer provided is the best answer, make sure you find out why. These questions have not been tested, so there may be problems with them. Some questions may be vague or defective, and some answers may be incorrect. Please bring to my attention any questions that are messed up. Week 1: Statistical Foundations I The next 10 questions refer to a variable x distributed as follows: x 1 2 3 Prob(x) .1 .2 k 1. The value of k is a) .3 b) .5 c) .7 d) indeterminate 2. The expected value of x is a) 2.0 b) 2.1 c) 2.6 d) indeterminate 3. The expected value of x squared is a) 4.0 b) 6.76 c) 7.2 d) indeterminate 4. The variance of x is a) 0.44 b) 0.66 c) 4.6 d) indeterminate 5. If all the x values were increased by 5 in this table, then the answer to question 2 would be a) unchanged b) increased by 5 c) multiplied by 5 d) indeterminate

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Page 1: Econometrics MCQS

1

Multiple Choice Question Bank for BUEC 333(copyright 2006, Peter Kennedy)

This set of multiple choice questions has been prepared to supply you with a means ofchecking your command of the course material. For each week of the course I have triedto provide questions that cover the full range of material discussed during that week. Ihave also tried not to include “duplicate” questions, namely questions that are basicallythe same as other questions but, for example, just use different numbers. The questionsrange quite widely in character. Some check your knowledge of definitions, some addressimplications of concepts, some require finding numbers in tables, some ask you to docalculations, some are very easy, and some are very difficult. Because of this, not allquestions are such that they are likely to appear on an exam, so how you score on thesequestions is not as important as how well you understand the logic of the answers.

Spending quality time on these questions should help your efforts to learn this coursematerial. My advice is to work through each chapter’s questions after you believe youhave a good command of that chapter’s material, and then if there are any questions forwhich you don’t understand why the answer provided is the best answer, make sure youfind out why.

These questions have not been tested, so there may be problems with them. Somequestions may be vague or defective, and some answers may be incorrect. Please bring tomy attention any questions that are messed up.

Week 1: Statistical Foundations I

The next 10 questions refer to a variable x distributed as follows:

x 1 2 3Prob(x) .1 .2 k

1. The value of k isa) .3 b) .5 c) .7 d) indeterminate

2. The expected value of x isa) 2.0 b) 2.1 c) 2.6 d) indeterminate

3. The expected value of x squared isa) 4.0 b) 6.76 c) 7.2 d) indeterminate

4. The variance of x isa) 0.44 b) 0.66 c) 4.6 d) indeterminate

5. If all the x values were increased by 5 in this table, then the answer to question 2would be

a) unchanged b) increased by 5 c) multiplied by 5 d) indeterminate

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6. If all the x values were increased by 5 in this table, then the answer to question 3would be

a) unchanged b) increased by 25 c) multiplied by 25 d) none of the above

7. If all the x values were increased by 5 in this table, then the answer to question 4would be

a) unchanged b) increased by 25 c) multiplied by 25 d) none of the above

8. If all the x values were multiplied by 5 in this table, then the answer to question 2would be

b) unchanged b) increased by 5 c) multiplied by 5 d) indeterminate

9. If all the x values were multiplied by 5 in this table, then the answer to question 3would be

b) unchanged b) increased by 25 c) multiplied by 25 d) none of the above

10. If all the x values were multiplied by 5 in this table, then the answer to question 4would be

a) unchanged b) increased by 25 c) multiplied by 25 d) none of the above

The next 17 questions refer to variables X and Y with the following joint distributionprob(X,Y)

Y=4 Y=5 Y=6X=1 .1 .05 kX=2 .05 .1 .1X=3 .1 .1 .4

11. The value of k isa) 0 b) .1 c) .2 d) indeterminate

12. If I know that Y=4, then the probability that X=3 isa) .1 b) .25 c) .4 d) .6

13. If I don’t know anything about the value of Y, then the probability that X=3 isa) .1 b) .2 c) .4 d) .6

14. If I know that Y=5, then the expected value of X isa) 0.55 b) 2.0 c) 2.2 d) 2.5

15. If I don’t know anything about Y, then the expected value of x isa) 2.0 b) 2.25 c) 2.45 d) indeterminate

16. If I know that Y=5, then the variance of X isa) .56 b) .75 c) 4.84 d) 5.4

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17. If I don’t know anything about Y, then the variance of x isa) .55 b) .74 c) 6.0 d) 6.55

18. The covariance between X and Y isa) 0.0 b) .09 c) .19 d) .29

19. The correlation between X and Y isa) 0.0 b) .29 c) .47 d) .54

20. If all the X values in the table above were increased by 8, then the answer to question18 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

21. If all the X values in the table above were increased by 8, then the answer to question19 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

22. If all the X values and all the Y values in the table above were increased by 8, thenthe answer to question 18 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

23. If all the X values and all the Y values in the table above were increased by 8, thenthe answer to question 19 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

24. If all the X values in the table above were multiplied by 8, then the answer to question18 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

25. If all the X values in the table above were multiplied by 8, then the answer to question19 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

26. If all the X values and all the Y values in the table above were multiplied by 8, thenthe answer to question 18 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

27. If all the X values and all the Y values in the table above were multiplied by 8, thenthe answer to question 19 would be

a) unchanged b) increased by 8 c) multiplied by 8 d) multiplied by 64

28. The distribution of X when Y is known is called the ________ distribution of X, andis written as ________. These blanks are best filled with

a) conditional, p(X) b) conditional, p(X |Y)c) marginal, p(X) d) marginal, p(X |Y)

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29. The distribution of X when Y is not known is called the ________ distribution of X,and is written as ________. These blanks are best filled with

a) conditional, p(X) b) conditional, p(X |Y)c) marginal, p(X) d) marginal, p(X |Y)

The next 5 questions refer to the following information. You have estimated the equationwage = alphahat + betahat*experience to predict a person’s wage using years ofexperience as an explanatory variable. Your results are that alphahat is 5.0 with standarderror 0.8, betahat is 1.2 with standard error 0.1, and the estimated covariance betweenalphahat and betahat is –0.005. What this means is that 5.0 is a realization of a randomvariable with unknown mean and standard error 1.0, and 1.2 is a realization of anotherrandom variable which has unknown mean and standard error 0.01.

30. The estimated variance of your forecast of the wage of a person with no experience isa) 0.64 b) 0.8 c) 0.81 d) none of these

31. The estimated variance of your forecast of the wage of a person with one year ofexperience is

a) 0.01 b) 0.64 c) 0.65 d) none of these

32. The estimated variance of your forecast of the wage of a person with two years ofexperience is

a) 0.64 b) 0.65 c) 0.66 d) 0.67

33. The estimate of the increase in wage enjoyed by a person with three additional yearsof experience is

a) 3.6 b) 8.6 c) 15 d) none of these

34. The estimated variance of the estimate of the increase in wage enjoyed by a personwith three additional years of experience is

a) 0.01 b) 0.03 c) 0.09 d) none of these

The next 9 questions refer to the following information. The percentage returns fromstocks A, B, and C are random variables with means 0.05, 0.08, and 0.12 respectively,and variances 0.04, 0.09, and 0.16, respectively. The covariance between A and B returnsis minus 0.01; the return from stock C is independent of the other two. A GIC is availablewith a guaranteed return of 0.03.

35. If you buy a thousand dollars each of A and B, your expected percentage return forthis portfolio is

a) 0.05 b) 0.065 c) 0.08 d) none of these

36. If you buy a thousand dollars each of A and B, the variance of your percentage returnfor this portfolio is

a) 0.11 b) 0.12 c) 0.13 d) none of these

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37. If you buy a thousand dollars of A and two thousand dollars of B, your expectedpercentage return for this portfolio is

a) 0.05 b) 0.07 c) 0.08 d) none of these

38. If you buy a thousand dollars of A and two thousand dollars of B, the variance ofyour percentage return for this portfolio is

a) 0.04 b) 0.044 c) 0.73 d) none of these

39. If you were to supplement either of the above portfolios with some of stock C yourexpected return should go ____ and if you were to supplement with some GIC yourexpected return should go ____. The best ways to fill these blanks are

a) up, up b) up, down c) down, up d) down, down

40. If you were to supplement either of the above portfolios with some GIC the varianceof your return should

a) increaseb) decreasec) remain unchangedd) can’t tell what will happen

41. If you were to supplement either of the above portfolios with some of stock C, thevariance of your return should

a) increaseb) decreasec) remain unchangedd) can’t tell what will happen

42. Suppose you bought a thousand dollars of each of A, B, C and GIC. The expectedreturn of this portfolio is

a) .0625 b) .07 c) .087 d) none of these

43. Suppose you bought a thousand dollars of each of A, B, C and GIC. The variance ofthe return of this portfolio is

a) .017 b) .068 c) .075 d) .27

44. Suppose we have a sample of size 100 from a random variable x with mean 3 andvariance 4. The standard deviation of xbar, the average of our sample values, isa) 0.04 b) 0.2 c) 2 d) 4

45. You have obtained the following data on the wages of randomly-obtainedobservationally-identical teenagers: 7, 8, 8, 7, 9, 8, 10, 8, 7, 8, 8. You calculate theaverage as 8 and intend to report this figure; you also want to provide a confidenceinterval but to do this you have to estimate the standard error of this average. Theestimated standard error you should use is approximately the square root of

a) 0.073 b) 0.08 c) 0.8 d) none of these

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46. From a sample of size 300 you have estimated the percentage of workers who haveexperienced an injury on the job last year to be six percent. You wish to report thisfigure but you also want to provide a confidence interval. To do this you need toestimate the standard error of this estimate. The estimated standard error you shoulduse is approximately

a) 0.0002 b) 0.014 c) 0.056 d) none of these

47. A negative covariance between x and y means that whenever we obtain an x valuethat is greater than the mean of x

a) we will obtain a corresponding y value smaller than the mean of yb) we will obtain a corresponding y value greater than the mean of yc) we have a greater than fifty percent chance of obtaining a corresponding y value

smaller than the mean of yd) we have a greater than fifty percent chance of obtaining a corresponding y value

greater than the mean of y

48. The central limit theorem assures us that the sampling distribution of the meana) is always normalb) is always normal for large sample sizesc) approaches normality as the sample size increasesd) appears normal only when the sample size exceeds 1,000

49. For a variable x the standard error of the sample mean is calculated as 20 whensamples of size 25 are taken and as 10 when samples of size 100 are taken. Aquadrupling of sample size has only halved the standard error. We can conclude thatincreasing sample size is

a) always cost effective b) sometimes cost effective c) never cost effective

50. In the preceding question, what must be the value of the standard error of x?a) 1000 b) 500 c) 377.5 d) 100

51. Suppose a random variable x has distribution given by f(x) = 2x, for 0 ≤ x ≤ 1 andzero elsewhere. The expected value of x isa) less than 0.5 b) equal to 0.5 c) greater than 0.5 d) indeterminate

52. Suppose a random variable x has distribution given by f(x) = kx, for 0 ≤ x ≤ 2 andzero elsewhere. The value of k is

a) 0.5 b) 1.0 c) 2.0 d) indeterminate

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Week 2: Statistical Foundations II

1. Suppose that if the null that beta equals one is true a test statistic you have calculatedis distributed as a t statistic with 17 degrees of freedom. What critical value cuts off5% of the upper tail of this distribution?

a) 1.65 b) 1.74 c) 1.96 d) 2.11

2. Suppose that in the previous question beta is equal to 1.2. Then the critical value fromthe previous question will cut off ______ of the upper tail of the distribution of yourtest statistic. The blank is best filled with

a) less than 5% b) 5% c) more than 5%

3. Suppose that if the null that alpha and beta both equal one is true a test statistic youhave calculated is distributed as a chi-square statistic with 2 degrees of freedom.What critical value cuts off 5% of the upper tail of this distribution?

a) 3.84 b) 5.02 c) 5.99 d) 7.38

4. Suppose that if the null that alpha and beta both equal one is true a test statistic youhave calculated is distributed as an F statistic with 2 and 22 degrees of freedom forthe numerator and denominator respectively. What critical value cuts off 5% of theupper tail of this distribution?

b) 3.00 b) 3.44 c) 4.30 d) 5.72

5. Suppose that if the null that beta equals one is true a test statistic you have calculatedis distributed as a z (standard normal) statistic. What critical value cuts off 5% of theupper tail of this distribution?

a) 0.31 b) 0.48 c) 1.65 b) 2.57

6. Suppose that if the null that beta equals one is true a test statistic you have calculatedis distributed as a z (standard normal) statistic. If you choose 1.75 as your criticalvalue, what is your (one-sided) type I error probability?

a) 4% b) 5% c) 6% d) 7%

7. Suppose that if the null that beta equals one is true a test statistic you have calculatedis distributed as a z (standard normal) statistic. If you choose 1.28 as your criticalvalue, what is your (two-sided) type I error probability?

a) 5% b) 10% c) 15% d) 20%

8. A type I error isa) failing to reject the null when it is falseb) rejecting the null when it is true

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9. The probability of a type I error is determined bya) the researcherb) the sample sizec) the degree of falsity of the null hypothesisd) both b) and c) above

10. A type II error isa) failing to reject the null when it is falseb) rejecting the null when it is true

11. The probability of a type II error is determined bya) the researcherb) the sample sizec) the degree of falsity of the null hypothesisd) both b) and c) above

12. Hypothesis testing is based ona) minimizing the type I errorb) minimizing the type II errorc) minimizing the sum of type I and type II errorsd) none of these

13. A power curve graphs the degree of falseness of the null againsta) the type I error probabilityb) the type II error probabilityc) one minus the type I error probabilityd) one minus the type II error probability

14. When the null is true the power curve measuresa) the type I error probabilityb) the type II error probabilityc) one minus the type I error probabilityd) one minus the type II error probability

15. Other things equal, when the sample size increases the power curvea) flattens outb) becomes steeperc) is unaffected

16. Other things equal, when the type I error probability is increased the power curvea) shifts up b) shifts down c) is unaffected

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17. The power of a test statistic should become larger as thea) sample size becomes largerb) type II error becomes largerc) null becomes closer to being trued) significance level becomes smaller

18. A manufacturer has had to recall several models due to problems not discovered withits random final inspection procedures. This is an example ofa) a type I error b) a type II error c) both types of error d) neither type of error

19. As the sample size becomes larger, the type I error probabilitya) increases b) decreases c) does not change d) can’t tell

20. Consider the following two statements: a) If you reject a null using a one-tailed test,then you will also reject it using a two-tailed test at the same significance level; b) For agiven level of significance, the critical value of t gets closer to zero as the sample sizeincreases.a) both statements are true b) neither statement is truec) only the first statement is true d) only the second statement is true

21. Power is the probability of making the right decision whena) the null is trueb) the null is falsec) the null is either true or falsed) the chosen significance level is 100%

22. The p value isa) the power b) one minus the power c) the type II error d) none of the above

23. After running a regression, the Eviews software containsa) the residuals in the resid vector and the constant (the intercept) in the c vectorb) the residuals in the resid vector and the parameter estimates in the c vectorc) the squared residuals in the resid vector and the constant in the c vectord) the squared residuals in the resid vector and the parameter estimates in the c vector

24. In the Eviews software, in the OLS output the intercept estimate by default isa) printed last and called “I” for “intercept”b) printed first and called “I”c) printed last and called “C” (for “constant”)d) printed first and called “C”

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25. A newspaper reports a poll estimating the proportion u of the adult population infavor of a proposition as 65%, but qualifies this result by saying that “this result isaccurate within plus or minus 3 percentage points, 19 times out of twenty.” What doesthis mean?a) the probablilty is 95% that u lies between 62% and 68%b) the probability is 95% that u is equal to 65%c) 95% of estimates calculated from samples of this size will lie between 62% and 68%d) none of the above

26. In the Eviews software, when you run an OLS regression by clicking on buttons, theparameter estimates are put in a vector calleda) c (for “coefficient vector”) with the first element in this vector the intercept estimateb) c (for “coefficient vector”) with the last element in this vector the intercept estimatec) b (for “beta vector”) with the first element in this vector the intercept estimated) b (for “beta vector”) with the last element in this vector the intercept estimate

27. A newspaper reports a poll of 400 people estimating the proportion u of the adultpopulation in favor of a proposition as 60%, but qualifies this result by saying that “thisresult is accurate within plus or minus x percentage points, 19 times out of twenty.” Thevalue of x in this case is abouta) 2 b) 3 c) 4 d) 5

28. In the Eviews software, in the OLS output the far right column reportsa) the coefficient estimate b) the standard error c) the t value d) none of these

29. A politician wants to estimate the proportion of people in favour of a proposal, aproportion he believes is about 60%. About what sample size is required to estimate thetrue proportion to within plus or minus 0.05 at the 95% confidence level?a) 10 b) 100 c) 200 d) 400

30. When you calculate a 95% confidence interval for an unknown parameter beta, theinterpretation of this interval is thata) the probability that the true value of beta lies in this interval is 95%b) 95% of repeated calculations of estimates of beta from different samples will lie in

this intervalc) 95% of intervals computed in this way will cover the true value of betad) none of the above

31. Suppose from a very large sample you have estimated a parameter beta as 2.80 withestimated variance 0.25. Your 90% confidence interval for beta is 2.80 plus or minusapproximatelya) 0.41 b) 0.49 c) 0. 82 d) 0.98

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The next 8 questions refer to the following information. You have an estimate 1.75 of aslope coefficient which you know is distributed normally with unknown mean beta andknown variance 0.25. You wish to test the null that beta = 1 against the alternative thatbeta > 1 at the 10% significance level.

32. The critical value to use here isa) 1.28 b) 1.65 c) 1.96 d) none of these

33. You should _____ the null. If you had used a 5% significance level you would______ the null. The blanks are best filled witha) accept; accept b) accept; reject c) reject; accept d) reject; reject

34. The p value (one-sided) for your test is approximatelya) 5% b) 7% c) 10% d) 23%

35. If the true value of beta is 1.01, the power of your test is approximatelya) 1% b) 5% c) 10% d) nowhere near these values

36. If the true value of beta is 10.01, the power of your test is approximatelya) 1% b) 5% c) 10% d) nowhere near these values

37. If the true value of beta is 1.75, the power of your test is approximatelya) 10% b) 40% c) 60% d) 90%

38. If the true value of beta is 1.65, the power of your test is approximatelya) 10% b) 50% c) 70% d) 90%

39. If the true value of beta is 1.25, the power of your test is approximatelya) 22% b) 40% c) 60% d) 78%

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Week 3: What is Regression Analysis?

1. In the regression specification y = α + βx + εa) y is called the dependent variable or the regressand, and x is called the regressorb) y is called the dependent variable or the regressor, and x is called the regressandc) y is called the independent variable or the regressand, and x is called the regressord) y is called the independent variable or the regressor, and x is called the regressand

2. In the regression specification y = α + βx + εa) α is called the intercept, β is called the slope, and ε is called the residualb) α is called the slope, β is called the intercept, and ε is called the residualc) α is called the intercept, β is called the slope, and ε is called the errord) α is called the slope, β is called the intercept, and ε is called the error

3. In the regression specification y = α + βx + ε which of the following is not ajustification for epsilon

a) it captures the influence of a million omitted explanatory variablesb) it incorporates measurement error in xc) it reflects human random behaviord) it accounts for nonlinearities in the functional form

4. In the regression specification y = α + βx + ε if the expected value of epsilon is afixed number but not zero

a) the regression cannot be runb) the regression is without a reasonable interpretationc) this non-zero value is accommodated by the βx termd) this non-zero value is incorporated into α

5. In the regression specification y = α + βx + ε the conditional expectation of y isa) the average of the sample y valuesb) the average of the sample y values corresponding to a specific x valuec) α + βx d) α + βx + ε

6. In the regression specification y = α + βx + ε the expected value of y conditional onx=1 is

a) the average of the sample y values corresponding to x=1b) α + β + ε c) β d) α + β

7. In the regression specification y = α + βx + δz + ε the parameter β is interpreted asthe amount by which y changes when x increases by one and

a) z does not changeb) z changes by onec) z changes by the amount it usually changes whenever x increases by oned) none of the above

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8. In the regression specification y = α + βx + δz + ε the parameter α is calleda) the slope coefficientb) the interceptc) the constant termd) both b) and c) above

9. The terminology ceteris paribus meansa) all else equalb) changing everything else by the amount by which they usually changec) changing everything else by equal amountsd) none of the above

The next 3 questions refer to the following information. Suppose the regressionspecification y = α + βx + δz + ε was estimated as y = 2 + 3x + 4z. We have a newobservation for which x = 5 and z = -2. For this new observation

10. the associated value of y isa) 7 b) 9 c) 25 d) impossible to determine

11. the expected value of y isa) 7 b) 9 c) 25 d) impossible to determine

12. our forecasted value of y isa) 7 b) 9 c) 25 d) impossible to determine

13. Suppose the regression specification y = α + βx + ε was estimated as y = 1 + 2x. Wehave a new observation for which x = 3 and y = 11. For this new observation the residualisa) zero b) 4 c) –4 d) unknown because the error is unknown

14. For the regression specification y = α + βx + ε the OLS estimates result fromminimizing the sum ofa) (α + βx)2

b) (α + βx + ε)2

c) (y - α + βx)2

d) none of these

15. For the regression specification y = α + βx + ε a computer search to find the OLSestimates would search over all values ofa) x b) α and β c) α, β, and x d) α, β, x, and y

16. R-square is the fraction ofa) the dependent variable explained by the independent variablesb) the variation in the dependent variable explained by the independent variablesc) the variation in the dependent variable explained linearly by the independent

variables

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17. Obtaining a negative R-square probably means thata) the computer made a calculation errorb) the true functional form is not linearc) an intercept was omitted from the specificationd) the explanatory variable ranged too widely

18. Maximizing R-square createsa) a better fit than minimizing the sum of squared errorsb) an equivalent fit to minimizing the sum of squared errorsc) a worse fit than minimizing the sum of squared errors

19. When there are more explanatory variables the adjustment of R-square to createadjusted R-square isa) bigger b) smaller c) unaffected

20. Compared to estimates obtained by minimizing the sum of absolute errors, OLSestimates are _______ to outliers. The blank is best filled with

a) more sensitive b) equally sensitive c) less sensitive

21. The popularity of OLS is due to the fact that ita) minimizes the sum of squared errorsb) maximizes R-squarec) creates the best fit to the datad) none of these

22. R-squared isa) The minimized sum of squared errors as a fraction of the total sum of squared errors.b) The sum of squared errors as a fraction of the total variation in the dependent

variable.c) One minus the answer in a).d) One minus the answer in b).

23. You have 46 observations on y (average value 15) and on x (average value 8) andfrom an OLS regression have estimated the slope of x to be 2.0. Your estimate of themean of y conditional on x isa) 15 b) 16 c) 17 d) none of the above

The following relates to the next two questions. Suppose we have obtained the followingregression results using observations on 87 individuals: yhat = 3 + 5x where the standarderrors of the intercept and slope are 1 and 2, respectively.

24. If an individual increases her x value by 4, what impact do you predict this will haveon her y value? Up by

a) 4 b) 5 c) 20 d) 23

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25. What is the variance of this prediction?a) 4 b) 16 c) 32 d) 64

26. Suppose wage = α + βage + ε and we have 100 observations on wage and age, withaverage values 70 and 30, respectively. We have run a regression to estimate the slope ofx as 2.0. Consider now a new individual whose age is 20. For this individual thepredicted wage from this regression isa) 40 b) 50 c) 60 d) impossible to predict without knowing the intercept estimate

27. After running an OLS regression, the reported R2 isa) never smaller than the “adjusted” R2

b) a number lying between minus one and plus onec) one minus the sum of squared errors divided by the variation in the independent

variablesd) none of the above

28. You have regressed y on x to obtain yhat = 3 + 4x. If x increases from 7 to 10, what isyour forecast of y?a) 12 b) 31 c) 40 d) 43

29. Suppose wage = α + βexp + ε and we have 50 observations on wage and exp, withaverage values 10 and 8, respectively. We have run a regression to estimate the interceptas 6.0. Consider now a new individual whose exp is 10. For this individual the predictedwage from this regression isa) 6 b) 10 c) 11 d) impossible to predict without knowing the slope estimate

30. If the expected value of the error term is 5, then after running an OLS regressiona) the average of the residuals should be approximately 5b) the average of the residuals should be exactly zeroc) the average of the residuals should be exactly fived) nothing can be said about the average of the residuals

31. Suppose we run a regression of y on x and save the residuals as e. If we now regress eon x the slope estimate should bea) zero b) one c) minus one d) nothing can be said about this estimate

32. Suppose your data produce the regression result y = 10 + 3x. Consider scaling thedata to express them in a different base year dollar, by multiplying observations by 0.9.If both y and x are scaled, the new intercept and slope estimates will be

a) 10 and 3 b) 9 and 3 c) 10 and 2.7 d) 9 and 2.7

33. You have used 60 observations to regress y on x, z, p, and q, obtaining slopeestimates 1.5, 2.3, -3.4, and 5.4, respectively. The minimized sum of squared errors is 88and the R-square is 0.58. The OLS estimate of the variance of the error term isa) 1.47 b) 1.57 c) 1.60 d) 1.72

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34. Suppose your data produce the regression result y = 10 + 3x. Consider scaling thedata to express them in a different base year dollar, by multiplying observations by 0.9. Ify is scaled but x is not (because y is measured in dollars and x is measured in physicalunits, for example), the new intercept and slope estimates will be

a) 10 and 3 b) 9 and 3 c) 10 and 2.7 d) 9 and 2.7

35. The variance of the error term in a regression isa) the average of the squared residualsb) the expected value of the squared error termc) SSE divided by the sample sized) none of these

36. The standard error of regression isa) the square root of the variance of the error termb) an estimate of the square root of the variance of the error termc) the square root of the variance of the dependent variabled) the square root of the variance of the predictions of the dependent variable

37. Asymptotics refers to what happens whena) the sample size becomes very largeb) the sample size becomes very smallc) the number of explanatory variables becomes very larged) the number of explanatory variables becomes very small

38. The first step in an econometric study should be toa) develop the specificationb) collect the datac) review the literatured) estimate the unknown parameters

39. Your data produce the regression result y = 8 + 5x. If the x values were scaled bymultiplying them by 0.5 the new intercept and slope estimates will be

a) 4 and 2.5 b) 8 and 2.5 c) 8 and 10 d) 16 and 10

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Week 4: The CLR Model

1. Whenever the dependent variable is a fraction we should use as our functional formthe

a) double log b) semi-log c) logarithmic d) none of these

2. Suppose y=AKαLβ. Then ceteris paribusa) α is the change in y per unit change in Kb) α is the percentage change in y per unit change in Kc) α is the percentage change in y per percentage change in Kd) α is none of the above because it is an elasticity

3. Suppose we are estimating the production function y=AeθtKαLβ. Then θ is interpretedas

a) the returns to scale parameterb) the rate of technical changec) an elasticityd) an intercept

4. Suppose you are estimating a Cobb-Douglas production function using first-differenced data. How would you interpret the intercept from this regression?a) the percentage increase in output per percentage increase in timeb) the average percentage increase in output each time periodc) the average percentage increase in output each time period above and beyond

output increases due to capital and labour incrementsd) there is no substantive interpretation because we are never interested in the

intercept estimate from a regression.

5. Suppose you regress y on x and the square of x.a) Estimates will be unreliableb) It doesn’t make sense to use the square of x as a regressorc) The regression will not run because these two regressors are perfectly correlatedd) There should be no problem with this.

6. The acronym CLR stands fora) constant linear regressionb) classical linear relationshipc) classical linear regressiond) none of these

7. The first assumption of the CLR model is thata) the functional form is linearb) all the relevant explanatory variables are includedc) the expected value of the error term is zerod) both a) and b) above

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8. Consider the two specifications y = α + βx-1 + ε and y = Axθ + ε.a) both specifications can be estimated by a linear regressionb) only the first specification can be estimated by a linear regressionc) only the second specification can be estimated by a linear regressiond) neither specification can be estimated by a linear regression

9. Suppose you are using the specification wage = α + βEducation + δMale +θEducation*Male + εIn this specification the influence of Education on wage is the same for both males andfemales ifa) δ = 0 b) θ = 0 c) δ = θ d) δ + θ = 0

10. The most common functional form for estimating wage equations isa) Linearb) Double logc) semilogarithmic with the dependent variable loggedd) semilogarithmic with the explanatory variables logged

11. As a general rule we should log variablesa) which vary a great dealb) which don’t change very muchc) for which changes are more meaningful in absolute termsd) for which changes are more meaningful in percentage terms

12. In the regression specification y = α + βx + δz + ε the parameter α is usuallyinterpreted as

a) the level of y whenever x and z are zerob) the increase in y whenever x and z increase by onec) a meaningless number that enables a linear functional form to provide a good

approximation to an unknown functional formd) none of the above

13. To estimate a logistic functional form we transform the dependent variable toa) its logarithm b) the odds ratio c) the log odds ratio d) none of these

14. The logistic functional forma) forces the dependent variable to lie between zero and oneb) is attractive whenever the dependent variable is a probabilityc) never allows the dependent variable to be equal to zero or oned) all of the above

15. Whenever the dependent variable is a fraction, using a linear functional form is OK ifa) most of the dependent variable values are close to oneb) most of the dependent variable values are close to zeroc) most of the dependent variable values are close to either zero or oned) none of the dependent variable values are close to either zero or one

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16. Violation of the CLR assumption that the expected value of the error is zero is aproblem only if this expected value is

a) negativeb) constantc) correlated with an explanatory variabled) uncorrelated with all explanatory variables

17. Nonspherical errors refers toa) heteroskedasticityb) autocorrelated errorsc) both a) and b)d) expected value of the error not equal to zero

18. Heteroskedasticity is abouta) errors having different variances across observationsb) explanatory variables having different variances across observationsc) different explanatory variables having different variancesd) none of these

19. Autocorrelated errors is abouta) the error associated with one observation not being independent of the error

associated with another observationb) an explanatory variable observation not being independent of another observation’s

value of that same explanatory variablec) an explanatory variable observation not being independent of observations on other

explanatory variablesd) the error is correlated with an explanatory variable

20. Suppose your specification is that y = α + βx + ε where β is positive. If x and ε arepositively correlated then OLS estimation will

a) probably produce an overestimation of βb) probably produce an underestimation of βc) be equally likely to overestimate or underestimate β

21. Correlation between the error term and an explanatory variable can arise becausea) of error in measuring the dependent variableb) of a constant non-zero expected errorc) the equation we are estimating is part of a system of simultaneous equationsd) of multicollinearity

22. Multicollinearity occurs whena) the dependent variable is highly correlated with all of the explanatory variablesb) an explanatory variable is highly correlated with another explanatory variablec) the error term is highly correlated with an explanatory variabled) the error term is highly correlated with the dependent variable

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23. In the specification wage = βEducation + δMale + θFemale + εa) there is perfect multicollinearityb) the computer will refuse to run this regressionc) both a) and b) aboved) none of the above

24. In the CNLR modela) the errors are distributed normallyb) the explanatory variables are distributed normallyc) the dependent variable is distributed normally

25. Suppose you are using the specification wage = α + βEducation + δMale +θExperience + ε. In your data the variables Education and Experience happen to behighly correlated because the observations with a lot of education happen not to havemuch experience. As a consequence of this negative correlation the OLS estimates

a) are likely to be better because the movement of one explanatory variable offsets theother, allowing the computer more easily to isolate the impact of each on thedependent variable

b) are likely to be better because the negative correlation reduces variance makingestimates more reliable

c) are likely to be worse because the computer can’t tell which variable is causingchanges in the dependent variable

d) are likely to be worse because compared to positive correlation the negativecorrelation increases variance, making estimates less reliable

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Week 5: Sampling Distributions

1. A statistic is said to be a random variable becausea) its value is determined in part by random eventsb) its variance is not zeroc) its value depends on random errorsd) all of the above

2. A statistic’s sampling distribution can be pictured by drawing aa) histogram of the sample datab) normal distribution matching the mean and variance of the sample datac) histogram of this statistic calculated from the sample datad) none of the above

3. An example of a statistic isa) a parameter estimate but not a t value or a forecastb) a parameter estimate or a t value, but not a forecastc) a parameter estimate, a t value, or a forecastd) a t value but not a parameter estimate or a forecast

4. The value of a statistic calculated from our sample can be viewed asa) the mean of that statistic’s sampling distributionb) the median of that statistic’s sampling distributionc) the mode of that statistic’s sampling distributiond) none of the above

5. Suppose we know that the CLR model applies to y = βx + ε, and that we estimateusing β* = Σy/Σx = β + Σε/Σx. This appears to be a good estimator because thesecond term is

a) zero because Eε = 0b) small because Σx is largec) small because Σε is smalld) is likely to be small because because Σε is likely to be small

6. A drawback of asymptotic algebra is thata) it is more difficult than regular algebrab) it only applies to very small sample sizesc) we have to assume that its results apply to small sample sizesd) we have to assume that its results apply to large sample sizes

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7. A Monte Carlo study isa) used to learn the properties of sampling distributionsb) undertaken by getting a computer to create data sets consistent with the econometric

specificationc) used to see how a statistic’s value is affected by different random drawings of the

error termd) all of the above

8. Knowing what a statistic’s sampling distribution looks like is important becausea) we can deduce the true value of an unknown parameterb) we can eliminate errors when testing hypothesesc) our sample value of this statistic is a random drawing out of this distributiond) none of the above

9. We should choose our parameter estimator based ona) how easy it is to calculateb) the attractiveness of its sampling distributionc) whether it calculates a parameter estimate that is close to the true parameter valued) none of the above

10. We should choose our test statistic based ona) how easy it is to calculateb) how closely its sampling distribution matches a distribution described in a statistical

tablec) how seldom it makes mistakes when testing hypothesesd) how small is the variance of its sampling distribution

11. An unbiased estimator is an estimator whose sampling distribution hasa) mean equal to the true parameter value being estimatedb) mean equal to the actual value of the parameter estimatec) a zero varianced) none of the above

12. Suppose we estimate an unknown parameter with the value 6.5, ignoring the data.This estimator

a) has minimum varianceb) has zero variancec) is biasedd) all of the above

13. MSE stands fora) minimum squared errorb) minimum sum of squared errorsc) mean squared errord) none of the above

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14. A minimum variance unbiased estimatora) is the same as the MSE estimatorb) has the smallest variance of all estimatorsc) has a very narrow sampling distributiond) none of the above

15. In the CLR model the OLS estimator is popular becausea) it minimizes the sum of squared errorsb) it maximizes R-squaredc) it is the best unbiased estimatord) none of the above

16. Betahat is the minimum MSE estimator if it minimizesa) the sum of bias and varianceb) the sum of bias squared and variance squaredc) the expected value of the square of the difference between betahat and the mean of

betahatd) the expected value of the square of the difference between betahat and the true

parameter value

17. A minimum MSE estimatora) trades off bias and varianceb) is used whenever it is not possible to find an unbiased estimator with a small variancec) is identical to the minimum variance estimator whenever we are considering only

unbiased estimatorsd) all of the above

18. Econometric theorists are trained toa) find estimators with good sampling distribution propertiesb) find test statistics with known sampling distributions when the null hypothesis is truec) use asymptotic algebrad) all of the above

19. The OLS estimator is not used for all estimating situations becausea) it is sometimes difficult to calculateb) it doesn’t always minimize R-squaredc) it doesn’t always have a good-looking sampling distributiond) sometimes other estimators have better looking sampling distributions

20. The traditional hypothesis testing methodology is based on whethera) the data support the null hypothesis more than the alternative hypothesisb) it is more likely that the test statistic value came from its null-is-true sampling

distribution or its null-is-false sampling distributionc) the test statistic value is in the tail of its null-is-true sampling distributiond) the test statistic value is in the tail of its null-is-false sampling distribution

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21. To create a random variable that is normally distributed with mean 6 and variance 9we should have the computer draw a value from a standard normal and then weshould

a) add 6 to it and multiply the result by 3b) add 6 to it and multiply the result by 9c) multiply it by 3 and add 6 to the resultd) multiply it by 9 and add 6 to the result

22. Suppose we have performed a Monte Carlo study to evaluate the samplingdistribution properties of an estimator betahat in a context in which we have chosenthe true parameter value beta to be 1.0. We have calculated 2000 values of betahatand found their average to be 1.3, and their sample standard error to be 0.5. Theestimated MSE of betahat is

a) 0.34 b) 0.59 c) 0.8 d) none of these

23. Suppose we have performed a Monte Carlo study to evaluate the samplingdistribution properties of a test statistic that is supposed to be distributed as a tstatistic with 17 degrees of freedom if the null hypothesis is true. Forcing the nullhypothesis to be true we have calculated 3000 values of this statistic. Approximately___ of these values should be greater than 1.333 and when ordered from smallest tolargest the 2850th value should be approximately ____. These blanks are best filledwith

a) 300, 1.74 b) 300, 2.11 c) 600, 1.74 d) 600, 2.11

For the next two questions, suppose you have programmed a computer as follows:i. Draw 50 x values from a distribution uniform between 10 and 20.ii. Count the number g of x values greater than 18.iii. Divide g by 50 to get h1.iv. Repeat this procedure to get 1000 h values h1 to h1000.v. Calculate the average hav and the variance hvar of the h values.

24. Hav should be approximatelya) 0.1 b) 0.2 c) 2 d) 20

25. Hvar should be approximatelya) 0.0002 b) 0.003 c) 8 d) 160

26. Suppose the CNLR model applies and you have used OLS to estimate a slope as 2.4.If the true value of this slope is 3.0, then the OLS estimatora) has bias of 0.6b) has bias of –0.6c) is unbiasedd) we cannot say anything about bias here

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For the next two questions, suppose you have programmed a computer as follows:i. Draw randomly 25 values from a standard normal distribution.ii. Multiply each of these values by 8 and add 5.iii. Take their average and call it A1.iv. Repeat this procedure to obtain 400 averages A1 through A400.v. Compute the average of these 400 A values. Call it Abar.vi. Compute the standard error of these 400 A values. Call it Asterr.

27. Abar should be approximatelya) 0.2 b) 5 c) 13 d) 125

28. Asterr should be approximatelya) 0.02 b) 0.4 c) 1.6 d) 8

29. Four econometricians have proposed four different estimates for an unknown slope.The estimators that have produced these estimates have bias 1, 2, 3, and 4,respectively, and variances 18, 14, 10, and 6, respectively. From what you have learnedin this course, which of these four should be preferred?a) first b) second c) third d) fourth

30. Suppose the CNLR model applies and you have used OLS to estimate beta as 1.3 andthe variance of this estimate as 0.25. The sampling distribution of the OLS estimator

a) has mean 1.3 and variance 0.25.b) has a normal distribution shapec) has a smaller variance than any other estimatord) has bias equal to the difference between 1.3 and the true value of beta

For the next three questions, suppose you have programmed a computer as follows:i. Draw 12 x values from a distribution uniform between 5 and 15.ii. Draw randomly 12 e values from a standard normal distribution.iii. Create 12 y values as y = 3*x + 2*e.iv. Calculate bhat1 as the sum of the y values divided by the sum of the x

values.v. Calculate bstar1 as the sum of the xy values divided by the sum of the x

squared values.vi. Repeat this procedure from ii above to obtain 4000 bhat values bhat1

through bhat4000 and 4000 bstar values bstar1 through bstar4000.vii. Compute the averages of these 4000 values. Call them bhatbar and

bstarbar.viii. Compute the variances of these 4000 values. Call them bhatv and bstarv.

31. In these resultsa) neither bhatbar nor bstarbar should be close to threeb) bhatbar and bstarbar should both be very close to threec) bhatbar should be noticeably closer to three than bstarbard) bstarbar should be noticeably closer to three than bhatbar

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32. In these resultsa) bhatv and bstarv should both be approximately equally close to zerob) bhatv should be noticeably closer to zero than bstarvc) bstarv should be noticeably closer to zero than bhatvd) nothing can be said about the relative magnitudes of bhatv and bstarv

33. In the previous question suppose you had subtracted three from each of the bhatvalues to get new numbers called q1 through q4000 and then ordered these numbersfrom smallest to largest. The 3600th of these q values should be

a) approximately equal to 1.29b) approximately equal to 1.36c) approximately equal to 1.80d) not very close to any of these values

34. Suppose you have programmed a computer to do the following.i. Draw 20 x values from a distribution uniform between 2 and 8.ii. Draw 20 z values from a normal distribution with mean 12 and variance 2.iii. Draw 20 e values from a standard normal distribution.iv. Create 20 y values using the formula y = 2 + 3x + 4z + 5e.v. Regress y on x and z, obtaining the estimate bz of the coefficient of z and the

estimate sebz of its standard error.vi. Subtract 4 from bz, divide this by sebz and call it w1.vii. Repeat the process described above from step iii until 5,000 w values have

been created, w1 through w5000.viii. Order the five thousand w values from smallest to largest.

The 4750th of these values should be approximatelya) 1.65 b) 1.74 c) 1.96 d) 2.11

35. Suppose you have a random sample of 100 observations on a variable x which isdistributed normally with mean 14 and variance 8. The sample average, xbar, is 15, andthe sample variance is 7. Then the mean of the sampling distribution of xbar is

a) 15 and its variance is 7b) 15 and its variance is 0.07c) 14 and its variance is 8d) 14 and its variance is 0.08

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Week 6: Dummy Variables

1. The dummy variable trap occurs whena) a dummy is not defined as zero or oneb) there is more than one type of category using dummiesc) the intercept is omittedd) none of the above

The next 13 questions are based on the following information. Suppose we specify that y= α + βx + δ1Male + δ2Female + θ1Left + θ2Center + θ3Right + ε where Left, Center,and Right refer to the three possible political orientations. A variable Fringe is created asthe sum of Left and Right, and a variable x*Male is created as the product of x and Male.

2. Which of the following creates a dummy variable trap? Regress y on an intercept, x,a) Male and Leftb) Male, Left, and Centerc) Left, Center, and Rightd) None of these

3. Which of the following creates a dummy variable trap? Regress y on an intercept, x,a) Male and Fringeb) Male, Center, and Fringe.c) Both of the aboved) None of the above

4. The variable Fringe is interpreted asa) being on the Left or on the Rightb) being on both the Left and the Rightc) being twice the value of being on the Left or being on the Rightd) none of these

5. Using Fringe instead of Left and Right separately in this specification is done to forcethe slopes of Left and Right to be

a) the sameb) half the slope of Centerc) twice the slope of Centerd) the same as the slope of Center

6. If we regress y on an intercept, x, Male, Left, and Center, the slope coefficient onMale is interpreted as the intercept difference between males and females

a) regardless of political orientationb) assuming a Right political orientationc) assuming a Left or Center political orientationd) none of the above

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7. If we regress y on an intercept, x, Male, and x*Male the slope coefficient on x*Maleis interpreted as

a) the difference between the male and female interceptb) the male slope coefficient estimatec) the difference between the male and female slope coefficient estimatesd) none of these

8. Suppose we regress y on an intercept, x, and Male, and then do another regression,regressing y on an intercept, x, and Female. The slope estimates on Male and onFemale should be

a) equal to one anotherb) equal but opposite in signc) bear no necessary relationship to one anotherd) none of these

9. Suppose we regress y on an intercept, x, Male, Left and Center and then do anotherregression, regressing y on an intercept, x, and Center and Right. The interpretation ofthe slope estimate on Center should be

a) the intercept for those from the political center in both regressionsb) the difference between the Center and Right intercepts in the first regression, and the

difference between the Center and Left intercepts in the second regressionc) the difference between the Center and Left intercepts in the first regression, and the

difference between the Center and Right intercepts in the second regressiond) none of these

10. Suppose we regress y on an intercept, x, Male, Left and Center and then do anotherregression, regressing y on an intercept, x, and Center and Right. The slope estimateon Center in the second regression should be

a) the same as the slope estimate on Center in the first regressionb) equal to the difference between the original Center coefficient and the Left coefficientc) equal to the difference between the original Center coefficient and the Right

coefficientd) unrelated to the first regression results

11. Suppose we regress y on an intercept, Male, Left, and Center. The base category isa) a male on the leftb) a female on the leftc) a male on the rightd) a female on the right

12. Suppose we regress y on an intercept, Male, Left, and Center. The intercept isinterpreted as the intercept of a

a) maleb) male on the rightc) femaled) female on the right

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13. Researcher A has used the specification: y = α + βx + γMLMaleLeft + γMCMaleCenter + γMRMaleRight + γFLFemaleLeft +

γFCFemaleCenter + εHere MaleLeft is a dummy representing a male on the left; other variables are defined insimilar fashion.Researcher B has used the specification:

y = αB + βBx + λMale + δLeft + κCenter + θMLMale*Left + θMCMale*Center + εHere Male*Left is a variable calculated as the product of Male and Left; other variablesare defined in similar fashion. These specifications are fundamentallya) differentb) the same so that the estimate of γML should be equal to the estimate of θMLc) the same so that the estimate of γML should be equal to the sum of the estimates of λ,

δ, and θML d) the same so that the sum of the estimates of γML, γMC, and γMR should be equal to the

estimate of λ.

14. In the preceding question, the base categories for specifications A and B are,respectively,

a) male on the right and female on the rightb) male on the right and female on the leftc) female on the right and female on the rightd) female on the right and male on the right

15. Analysis of variance is designed toa) estimate the influence of different categories on a dependent variableb) test whether a particular category has a nonzero influence on a dependent variablec) test whether the intercepts for all categories in an OLS regression are the samed) none of these

16. Suppose you have estimated wage = 5 + 3education + 2gender, where gender is onefor male and zero for female. If gender had been one for female and zero for male, thisresult would have beena) Unchangedb) wage = 5 + 3education - 2genderc) wage = 7 + 3education + 2genderd) wage = 7 + 3education - 2gender

17. Suppose we have estimated y = 10 + 1.5x + 4D where y is earnings, x is experienceand D is zero for females and one for males. If we had coded the dummy as minusone for females and one for males the results (10, 2, 3) would have been

a) 14, 1.5, -4 b) 18, 1.5, -4 c) 12, 1.5, 2 d) 12, 1.5, -2

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18. Suppose we have estimated y = 10 + 2x + 3D where y is earnings, x is experience andD is zero for females and one for males. If we had coded the dummy as one for femalesand two for males, the results (10, 2, 3) would have beena) 10, 2, 3 b) 10, 2, 1.5 c) 7, 2, 3 d) 7, 2, 1.5

The following relates to the next three questions. In a study investigating the effect of anew computer instructional technology for economics principles, a researcher taught acontrol class in the normal way and an experimental class using the new technology. Sheregressed student final exam numerical grade (out of 100) on GPA, Male, Age, Tech (adummy equaling unity for the experimental class), and interaction variables Tech*GPA,Tech*Male, and Tech*Age. Age and Tech*GPA had coefficients jointly insignificantlydifferent from zero, so she dropped them and ended up with

grade = 45 + 9*GPA + 5*Male + 10*Tech - 6*Tech*Male - 0.2*Tech*Agewith all coefficients significant. She concludes that a) age makes no difference in thecontrol group, but older students do not seem to benefit as much from the computertechnology, and that b) the effect of GPA is the same regardless of what group a studentis in.

19. These empirical results suggest thata) both conclusions are warrantedb) neither conclusion is warrantedc) only the first conclusion is warrantedd) only the second conclusion is warranted

20. These point estimates suggest that in the control classa) males and females perform equallyb) females outperform malesc) males outperform femalesd) we can only assess relative performance in the new technology group

21. These point estimates measure the impact of the new technology on male and femalescores, respectively, to bea) 5 and zero b) 4 and 10 c) –1 and 10 d) 9 and 10

22. The MLE is popular because ita) maximizes Rsquare

b) minimizes the sum of squared errorsc) has desirable sampling distribution propertiesd) maximizes both the likelihood and loglikelihood functions

23. To find the MLE we maximize thea) likelihoodb) log likelihoodc) probability of having obtained our sampled) all of these

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24. In a logit regression, to report the influence of an explanatory variable x on theprobability of observing a one for the dependent variable we report

a) the slope coefficient estimate for xb) the average of the slope coefficient estimates for x of all the observations in the

samplec) the slope coefficient estimate for x for the average observation in the sampled) none of these

25. The logit functional forma) is linear in the logarithms of the variablesb) has either zero or one on the left-hand sidec) forces the left-hand variable to lie between zero and oned) none of these

26. The logit model is employed whena) all the regressors are dummy variablesb) the dependent variable is a dummy variablec) we need a flexible functional formd) none of these

27. In the logit model the predicted value of the dependent variable is interpreted asa) the probability that the dependent variable is oneb) the probability that the dependent variable is zeroc) the fraction of the observations in the sample that are onesd) the fraction of the observations in the sample that are zeroes.

28. To find the maximum likelihood estimates the computer searches over all possiblevalues of the

a) dependent variableb) independent variablesc) coefficientsd) all of the above

29. The MLE is popular becausea) it maximizes R-square and so creates the best fit to the datab) it is unbiasedc) it is easily calculated with the help of a computerd) none of these

30. In large samples the MLE isa) unbiased b) efficient c) normally distributed d) all of these

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31. To predict the value of a dependent dummy variable for a new observation we shouldpredict it as a one if

a) the estimated probability of this observation’s dependent variable being a one isgreater than fifty percent

b) more than half of the observations are onesc) the expected payoff of doing so is greater than the expected payoff of predicting it as

a zerod) none of these

32. Which of the following is the best way to measure the prediction success of a logitspecification?

a) the percentage of correct predictions across all the datab) the average of the percent correct predictions in each categoryc) a weighted average of the percent correct predictions in each category, where the

weights are the fractions of the observations in each categoryd) the sum across all the observations of the net benefits from each observation’s

prediction

33. A negative coefficient on an explanatory variable x in a logit specification means thatan increase in x will, ceteris paribus,

a) increase the probability that an observation’s dependent variable is a oneb) decrease the probability that an observation’s dependent variable is a onec) the direction of change of the probability that an observation is a one cannot be

determined unequivocally from the sign of this slope coefficient

34. You have estimated a logit model and found for a new individual that the estimatedprobability of her being a one (as opposed to a zero) is 40%. The benefit of correctlyclassifying this person is $1,000, regardless of whether she is a one or a zero. Thecost of classifying this person as a one when she is actually a zero is $500. Youshould classify this person as a one when the other misclassification cost exceedswhat value?

a) $750 b) $1,000 c) $1250 d) $1500

35. You have estimated a logit model and found for a new individual that the estimatedprobability of her being a one (as opposed to a zero) is 40%. The benefit of correctlyclassifying this person is $2,000, regardless of whether she is a one or a zero. Thecost of classifying this person as a zero when she is actually a one is $1600. Youshould be indifferent to classifying this person as a one or a zero when the othermisclassification cost equals what value?

a) $100 b) $200 c) $300 d) $400

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36. You have estimated a logit model to determine the probability that an individual isearning more than ten dollars an hour, with observations earning more than tendollars an hour coded as ones; your estimated logit index function is

-22 + 2*Ed – 6*Female + 4*Expwhere Ed is years of education, Female is a dummy with value one for females, and Expis years of experience. You have been asked to classify a new observation with 10 yearsof education and 2 years of experience. You should classify her asa) a one b) a zero c) too close to calld) not enough information to make a classification

37. In the preceding question, suppose you believe that the influence of experiencedepends on gender. To incorporate this into your logit estimation procedure youshould

a) add an interaction variable defined as the product of Ed and Femaleb) estimate using only the female observations and again using only the male

observationsc) add a new explanatory variable coded as zero for the male observations and whatever

is the value of the experience variable for the female observationsd) none of the above

38. From estimating a logit model you have produced a slope estimate of 0.3 on theexplanatory variable x. This means that a unit increase in x will cause

a) an increase in the probability of being a y=1 observation of 0.3b) an increase in the probability of being a y=0 observation of 0.3c) an increase in the ratio of these two probabilities of 0.3d) none of the above

39. You have obtained the following regression results using data on law students fromthe class of 1980 at your university:

Income = 11 + .24GPA - .15Female + .14Married - .02Married*Femalewhere the variables are self-explanatory. Consider married individuals with equal GPAs.Your results suggest that compared to female income, male income is higher bya) 0.01 b) 0.02 c) 0.15 c) 0.17

Suppose you have run the following regression:y = α + βx + γUrban + θImmigrant + δUrban*Immigrant + εwhere Urban is a dummy indicating that an individual lives in a city rather than in a rural

area, and Immigrant is a dummy indicating that an individual is an immigrant ratherthan a native. The following three questions refer to this information.

40. The coefficient γ is interpreted as the ceteris paribus difference in y betweena) an urban person and a rural personb) an urban native and a rural nativec) an urban immigrant and a rural immigrantd) none of these

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41. The coefficient θ is interpreted as the ceteris paribus difference in y betweena) an immigrant and a nativeb) a rural immigrant and a rural nativec) an urban immigrant and an urban natived) none of these

42. The coefficient δ is interpreted as the ceteris paribus difference in y between an urbanimmigrant and

a) a rural nativeb) a rural immigrantc) an urban natived) none of these

43. You have estimated a logit model to determine the success of an advertising programin a town, with successes coded as ones; your estimated logit index function is -70 +2*PerCap + 3*South where PerCap is the per capita income in the town (measured inthousands of dollars), and South is a dummy with value one for towns in the southand zero for towns in the north, the only other region. If the advertising program is asuccess, you will make $5000; if it is a failure you will lose $3000. You areconsidering two towns, one in the south and one in the north, both with per capitaincomes of $35,000. You should undertake the advertising program

a) in both townsb) in neither townc) in only the south townd) in only the north town

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Week 7: Hypothesis Testing

1. The square root of an F statistic is distributed as a t statistic. This statement isa) true b) true only under special conditions c) false

2. To conduct a t test we need toa) divide a parameter estimate by its standard errorb) estimate something that is supposed to be zero and see if it is zeroc) estimate something that is supposed to be zero and divide it by its standard error

3. If a null hypothesis is true, when we impose the restrictions of this null the minimizedsum of squared errors

a) becomes smaller b) does not change c) becomes biggerd) changes in an indeterminate fashion

4. If a null hypothesis is false, when we impose the restrictions of this null theminimized sum of squared errors

a) becomes smaller b) does not change c) becomes biggere) changes in an indeterminate fashion

5. Suppose you have 25 years of quarterly data and specify that demand for yourproduct is a linear function of price, income, and quarter of the year, where quarter ofthe year affects only the intercept. You wish to test the null that ceteris paribusdemand is the same in spring, summer, and fall, against the alternative that demand isdifferent in all quarters. The degrees of freedom for your F test are

a) 2 and 19 b) 2 and 94 c) 3 and 19 d) 3 and 94

6. In the preceding question, suppose you wish to test the hypothesis that the entirerelationship (i.e., that the two slopes and the intercept) is the same for all quarters,versus the alternative that the relationship is completely different in all quarters. Thedegrees of freedom for your F test are

a) 3 and 94 b) 6 and 88 c) 9 and 82 d) none of these

7. In the preceding question, suppose you are certain that the intercepts are differentacross the quarters, and wish to test the hypothesis that both slopes are unchangedacross the quarters, against the alternative that the slopes are different in each quarter.The degrees of freedom for your F test are

a) 3 and 94 b) 6 and 88 c) 9 and 82 d) none of these

8. As the sample size becomes very large, the t distributiona) collapses to a spike because its variance becomes very smallb) collapses to normally-distributed spikec) approximates more and more closely a normal distribution with mean oned) approximates more and more closely a standard normal distribution

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9. Suppose we are using 35 observations to regress wage on an intercept, education,experience, gender, and dummies for black and hispanic (the base being white). Inaddition we are allowing the slope on education to be different for the three racecategories. When using a t test to test for discrimination against females, the degreesof freedom is

a) 26 b) 27 c) 28 d) 29

10. After running a regression, to find the covariance between the first and second slopecoefficient estimates we

a) calculate the square root of the product of their variancesb) look at the first off-diagonal element of the correlation matrixc) look at the first diagonal element of the variance-covariance matrixd) none of these

11. Suppose you have used Eviews to regress output on capital, labor, and a time trend byclicking on these variables in the order above, or, equivalently, using the command lsy cap lab time c. To test for constant returns to scale using the Wald – CoefficientRestrictions button you need to provide the software with the following information

a) cap+lab =1b) c(1)+c(2)=1c) c(2)+c(3) = 1d) none of these

12. When testing a joint null, an F test is used instead of several separate t tests becausea) the t tests may not agree with each otherb) the F test is easier to calculatec) the collective results of the t test could misleadd) the t tests are impossible to calculate in this case

13. The rationale behind the F test is that if the null hypothesis is true, by imposing thenull hypothesis restrictions on the OLS estimation the per restriction sum of squarederrors

a) falls by a significant amountb) rises by a significant amountc) falls by an insignificant amountd) rises by an insignificant amount

14. Suppose we are regressing wage on an intercept, education, experience, gender, anddummies for black and hispanic (the base being white). To find the restricted SSE tocalculate an F test to test the null hypothesis that the black and hispanic coefficientsare equal we should regress wage on an intercept, education, experience, gender, anda new variable constructed as the

a) sum of the black and hispanic dummiesb) difference between the black and hispanic dummiesc) product of the black and hispanic dummiesd) none of these

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15. In the preceding question, if the null hypothesis is true then, compared to theunrestricted SSE, the restricted SSE should be

a) smaller b) the same c) larger d) unpredictable

16. In question 14, if we regress wage on an intercept, education, experience, gender, anda dummy for white, compared to the restricted SSE in that question, the resulting sumof squared errors should be

a) smaller b) the same c) larger d) unpredictable

17. Suppose you have specified the demand for beer (measured in liters) asLnBeer = β0 + β1lnBeerprice + β2lnOthergoodsprice + β3lnIncome + εwhere the notation should be obvious. Economists will tell you that in theory thisrelationship should be homogeneous of degree zero, meaning that if income and prices allincrease by the same percent, demand should not change. Testing homogeneity of degreezero means testing the null thata) β1 = β2 = β3 = 0 b) β1 + β2 + β3 = 0 c) β1 + β2 + β3 = 1 d) none of these

Suppose you have run a logit regression in which defaulting on a credit card payment isrelated to people’s income, gender, education, and age, with the coefficients on incomeand age, but not education, allowed to be different for males versus females. The next 4questions relate to this information.

18. The degrees of freedom for the LR test of the null hypothesis that gender does notmatter is

a) 1 b) 2 c) 3 d) 4

19. To calculate the LR test statistic for this null we need to compute twice the differencebetween the

a) restricted and unrestricted maximized likelihoodsb) restricted and unrestricted maximized loglikelihoodsc) unrestricted and restricted maximized likelihoodsd) unrestricted and restricted maximized loglikelihoods

20. Suppose the null that the slopes on income and age are the same for males andfemales is true. Then compared to the unrestricted maximized likelihood, therestricted maximized likelihood should be

a) smaller b) the same c) bigger d) unpredictable

21. The coefficient on income can be interpreted as ceteris paribus the change in the______ resulting from a unit increase in income.

a) probability of defaultingb) odds ratio of defaulting versus not defaultingc) log odds ratio of defaulting versus not defaultingd) none of these

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Week 9: Specification

1. Specification refers to choice ofa) test statisticb) estimating procedurec) functional form and explanatory variablesd) none of these

2. Omitting a relevant explanatory variable when running a regressiona) never creates biasb) sometimes creates biasc) always creates bias

3. Omitting a relevant explanatory variable when running a regression usuallya) increases the variance of coefficient estimatesb) decreases the variance of coefficient estimatesc) does not affect the variance of coefficient estimates

4. Suppose that y = α + βx + δw + ε but that you have ignored w and regressed y ononly x. If x and w are negatively correlated in your data, the OLS estimate of β willbe biased downward if

a) β is positiveb) β is negativec) δ is positived) δ is negative

5. Suppose that y = α + βx + δw + ε but that you have ignored w and regressed y ononly x. The OLS estimate of β will be unbiased if x and w are

a) collinearb) orthogonalc) positively correlatedd) negatively correlated

6. Omitting an explanatory variable from a regression in which you know it belongscould be a legitimate decision if doing so

a) increases R-squareb) decreases the SSEc) decreases MSEd) decreases variance

7. In general, omitting a relevant explanatory variable createsa) bias and increases varianceb) bias and decreases variancec) no bias and increases varianced) no bias and decreases variance

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8. Suppose you know for sure that a variable does not belong in a regression as anexplanatory variable. If someone includes this variable in their regression, in generalthis will create

a) bias and increase varianceb) bias and decrease variancec) no bias and increase varianced) no bias and decrease variance

9. Adding an irrelevant explanatory variable which is orthogonal to the otherexplanatory variables causes

a) bias and no change in varianceb) bias and an increase in variancec) no bias and no change in varianced) no bias and an increase in variance

10. A good thing about data mining is that ita) avoids biasb) decreases MSEc) increases R-squared) may uncover an empirical regularity which causes you to improve your specification

11. A bad thing about data mining is that it is likely toa) create biasb) capitalize on chancec) both of the aboved) none of the above

12. The bad effects of data mining can be minimized bya) keeping variables in your specification that common sense tell you definitely belongb) setting aside some data to be used to check the specificationc) performing a sensitivity analysisd) all of the above

13. A sensitivity analysis is conducted by varying the specification to see what happensto

a) Biasb) MSEc) R-squared) the coefficient estimates

14. The RESET test is used mainly to check fora) collinearityb) orthogonalityc) functional formd) capitalization on chance

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15. To perform the RESET test we rerun the regression adding as regressors the squaresand cubes of the

a) dependent variableb) suspect explanatory variablec) forecasts of the dependent variabled) none of these

16. The RESET test isa) a z test b) a t test c) a chi-square test d) an F test

17. Regressing y on x using a distributed lag model specifies that y is determined bya) the lagged value of yb) the lagged value of xc) several lagged values of xd) several lagged values of x, with the coefficients on the lagged x’s decreasing as the

lag becomes longer

18. Selecting the lag length in a distributed lag model is usually done bya) minimizing the MSEb) maximizing R-squarec) maximizing the t valuesd) minimizing an information criterion

19. A major problem with distributed lag models is thata) R-square is lowb) coefficient estimates are biasedc) variances of coefficient estimates are larged) the lag length is impossible to determine

20. The rationale behind the Koyck distributed lag is that ita) eliminates biasb) increases the fit of the equationc) exploits an information criteriond) incorporates more information into estimation

21. In the Koyck distributed lag model, as the lag lengthens the coefficients on the laggedexplanatory variable

a) increase and then decrease b) decrease foreverc) decrease for awhile and then become zero d) none of these

22. Using the lagged value of the dependent variable as an explanatory variable is oftendone to

a) avoid biasb) reduce MSEc) improve the fit of a specificationd) facilitate estimation of some complicated models

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Week 10: Multicollinearity; Applied Econometrics

1. Multicollinearity occurs whenevera) the dependent variable is highly correlated with the independent variablesb) the independent variables are highly orthogonalc) there is a close linear relationship among the independent variablesd) there is a close nonlinear relationship among the independent variables

2. High collinearity is not a problem ifa) no bias is createdb) R-square is highc) the variance of the error term is smalld) none of these

3. The multicollinearity problem is very similar to the problems caused bya) nonlinearitiesb) omitted explanatory variablesc) a small sample sized) orthogonality

4. Multicollinearity causesa) low R-squaresb) biased coefficient estimatesc) biased coefficient variance estimatesd) none of these

5. A symptom of multicollinearity isa) estimates don’t change much when a regressor is omittedb) t values on important variables are quite bigc) the variance-covariance matrix contains small numbersd) none of these

6. Suppose your specification is y = βx + γMale + θFemale + δWeekday + λWeekend +ε

a) there is no problem with this specification because the intercept has been omittedb) there is high collinearity but not perfect collinearityc) there is perfect collinearityd) there is orthogonality

7. Suppose you regress y on x and the square of x.a) Estimates will be biased with large variancesb) It doesn’t make sense to use the square of x as a regressorc) The regression will not run because these two regressors are perfectly correlatedd) There should be no problem with this.

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8. A friend has told you that his multiple regression has a high R2 but all the estimates ofthe regression slopes are insignificantly different from zero on the basis of t tests ofsignificance. This has probably happened because thea) intercept has been omittedb) explanatory variables are highly collinearc) explanatory variables are highly orthogonald) dependent variable doesn’t vary by much

9. Dropping a variable can be a solution to a multicollinearity problem because ita) avoids biasb) increases t valuesc) eliminates the collinearityd) could decrease mean square error

10. The main way of dealing with a multicollinearity problem is toa) drop one of the offending regressorsb) increase the sample sizec) incorporate additional informationd) transform the regressors

11. A result of multicollinearity is thata) coefficient estimates are biasedb) t statistics are too smallc) the variance of the error is overestimatedd) variances of coefficient estimates are large

12. A result of multicollinearity is thata) OLS is no longer the BLUEb) Variances of coefficient estimates are overestimatedc) R-square is misleadingly smalld) Estimates are sensitive to small changes in the data

13. Suppose you are estimating y = α + βx + δz + θw + ε for which the CLR assumptionshold and x, z, and w are not orthogonal to one another. You estimate incorporatingthe information that β = δ. To do this you will regress

a) y on an intercept, 2x, and wb) y on an intercept, (x+z), and wc) y-x on an intercept, z, and wd) none of these

14. In the preceding question, suppose that in fact β is not equal to δ. Then in general,compared to regressing without this extra information, your estimate of θ

a) is unaffectedb) is still unbiasedc) has a smaller varianced) nothing can be said about what will happen to this estimate

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15. Economic theory tells us that when estimating the real demand for exports we shoulduse the ______ exchange rate and when estimating the real demand for money weshould use the _______ interest rate. The blanks should be filled with

a) real; realb) real; nominalc) nominal; reald) nominal; nominal

16. You have run a regression of the change in inflation on unemployment. Economictheory tells us that our estimate of the natural rate of unemployment is

a) the intercept estimateb) the slope estimatec) minus the intercept estimate divided by the slope estimated) minus the slope estimate divided by the intercept estimate

17. You have thirty observations from a major golf tournament in which the percentageof putts made was recorded for distances ranging from one foot to thirty feet, inincrements of one foot (i.e., you have 30 observations). You propose estimatingsuccess as a function of distance. What functional form should you use?

a) linearb) logisticc) quadraticd) exponential

18. Starting with a comprehensive model and testing down to find the best specificationhas the advantage that

a) complicated models are inherently betterb) testing down is guaranteed to find the best specificationc) testing should be unbiasedd) pretest bias is eliminated

19. Before estimating your chosen specification you shoulda) data mineb) check for multicollinearityc) look at the datad) test for zero coefficients

20. The interocular trauma test isa) a t test b) an F test c) a chi-square test d) none of the above

21. When the sample size is quite large, a researcher needs to pay special attention toa) coefficient magnitudesb) t statistic magnitudesc) statistical significanced) type I errors

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22. Your only measure of a key economic variable is unsatisfactory but you use itanyway. This is an example of

a) knowing the contextb) asking the right questionsc) compromisingd) a sensitivity analysis

23. “Asking the right question” meansa) selecting the appropriate null hypothesisb) looking for a lost item where you lost it instead of where the light is betterc) resisting the temptation to change a problem so that it has a mathematically elegant

solutiond) all of the above

24. A sensitivity analysis involvesa) avoiding type I errorsb) checking for multicollinearityc) omitting variables with low t valuesd) examining the impact of specification changes

25. When testing if a coefficient is zero it is traditional to use a type I error rate of 5%.When testing if a variable should remain in a specification we should

a) continue to use a type I error rate of 5%b) use a smaller type I error ratec) use a larger type I error rated) forget about the type I error rate and instead choose a type II error rate

26. An example of knowing the context is knowing thata) some months have five Sundaysb) only children from poor families are eligible for school lunch programsc) many auctions require a reserve price to be exceeded before an item is soldd) all of the above

27. A type III error occurs whena) you make a type I and a type II error simultaneouslyb) type I and type II errors are confusedc) the right answer is provided to the wrong questiond) the wrong functional form has been used

28. The adage that begins with “Graphs force you to notice ….” is completed witha) outliersb) incorrrect functional formsc) what you never expected to seed) the real relationships among data

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29. In econometrics, KISS stands fora) keeping it safely sane b) keep it simple, stupid c) keep it sensibly simpled) keep inference sophisticatedly simple

30. An advantage of simple models is that theya) do not place unrealistic demands on the datab) are less likely to lead to serious mistakesc) facilitate subjective insights d) all of the above

31. An example of the laugh test is thata) your coefficient estimates are of unreasonable magnitudeb) your functional form is very unusualc) your coefficient estimates are all negatived) some of your t values are negative

32. Hunting statistical significance with a shotgun meansa) avoiding multicollinearity by transforming datab) throwing every explanatory variable you can think of into your specificationc) using F tests rather than t testsd) using several different type I error rates

33. “Capitalizing on chance” means thata) by luck you have found the correct specificationb) you have found a specification that explains the peculiarities of your data setc) you have found the best way of incorporating capital into the production functiond) you have done the opposite of data mining

34. The adage that begins with “All models are wrong, ….” is completed witha) especially those with low R-squaresb) but some are usefulc) so it is impossible to find a correct specificationd) but that should not concern us

35. Those claiming that statistical significance is being misused are referring to theproblem that

a) there may be a type I errorb) there may be a type II errorc) the coefficient magnitude may not be of consequenced) there may be too much multicollinearity

36. Those worried that researchers are “using statistical significance to sanctify a result”suggest that statistical analysis be supplemented by

a) looking for corroborating evidenceb) looking for disconfirming evidencec) assessing the magnitude of coefficientsd) all of the above

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37. To deal with results tainted by subjective specification decisions undertaken duringthe heat of econometric battle it is suggested that researchers

a) eliminate multicollinearityb) report a senstitivity analysisc) use F tests instead of t testsd) use larger type I error rates

38. You have regressed yt on xt and xt-1, obtaining a positive coefficient estimate on xt, asexpected, but a negative coefficient estimate on lagged x. This

a) indicates that something is wrong with the regressionb) implies that the short-run effect of x is smaller than its long-run effectc) implies that the short-run effect of x is larger than its long-run effectd) is due to high collinearity

39. Outliers shoulda) be deleted from the datab) be set equal to the sample averagec) prompt an investigation into their legitimacyd) be neutralized somehow

40. Influential observationsa) can be responsible for a wrong signb) is another name for outliersc) require use of an unusual specificationd) all of the above

41. Suppose you are estimating the returns to education and so regress wage on years ofeducation and some other explanatory variables. One problem with this is that peoplewith higher general ability levels, for which you have no measure, tend to opt formore years of education, creating bias in your estimation. This bias is referred to as

a) multicollinearity biasb) pretest biasc) self-selection biasd) omitted variable bias

42. A wrong sign could result froma) a theoretical oversightb) an interpretation errorc) a data problemd) all of the above

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Week 11: Autocorrelated errors; heteroskedasticity

1. If errors are nonspherical it means that they area) autocorrelatedb) heteroskedasticc) autocorrelated or heteroskedasticd) autocorrelated or heteroskedastic, or both

2. The most important consequence of nonspherical errors is thata) coefficient estimates are biasedb) inference is biasedc) OLS is no longer BLUEd) none of these

3. Upon discovering via a test that you have nonspherical errors you shoulda) use generalized least squaresb) find the appropriate transformation of the variablesc) double-check your specificationd) use an autocorrelation- or heteroskedasticity-consistent variance covariance matrix

estimate

4. GLS can be performed by running OLS on variables transformed so that the errorterm in the transformed relationship is

a) homoskedasticb) sphericalc) serially uncorrelatedd) eliminated

5. Second-order autocorrelated errors means that the current error εt is a linear functionof

a) εt-1 b) εt-1 squared c) εt-2 d) εt-1 and εt-2

6. Suppose you have an autocorrelated error with rho equal to 0.4. You should transformeach variable xt to become

a) .4xt b) .6xt c) xt - .4xt-1 d) .6xt - .4xt-1

7. Pushing the autocorrelation- or heteroskedasticity-consistent variance-covariancematrix button in econometrics software when running OLS causes

a) the GLS estimation procedure to be usedb) the usual OLS coefficient estimates to be produced, but with corrected estimated

variances of these coefficient estimatesc) new OLS coefficient estimates to be produced, along with corrected estimated

variances of these coefficient estimatesd) the observations automatically to be weighted to remove the bias in the coefficient

estimates

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8. A “too-big” t statistic could come about because ofa) a very large sample sizeb) multicollinearityc) upward bias in our variance estimatesd) downward bias in our variance estimates

9. A “too-big” t statistic could come about because ofa) Multicollinearity b) a small sample size c) orthogonality d) none of these

10. The DW test isa) called the Durbin-Watson testb) should be close to 2.0 when the null is truec) defective whenever the lagged value of the dependent variable appears as a regressord) all of the above

11. The Breusch-Godfrey test isa) used to test the null of no autocorrelationb) is valid even when the lagged value of the dependent variable appears as a regressorc) is a chi-square testd) all of the above

12. To use the Breusch-Godfrey statistic to test the null of no autocorrelation against thealternative of second order autocorrelated errors, we need to regress the OLSresiduals on ________ and use _____ degrees of freedom for our test statistic. Theblanks are best filled with

a) two lags of the OLS residuals; 2b) the original explanatory variables and one lag of the OLS residuals; 1c) the original explanatory variables and two lags of the OLS residuals; 2d) the original explanatory variables, their lags, and one lag of the OLS residuals; 1

13. With heteroskedasticity we should use weighted least squares wherea) by doing so we maximize R-squareb) use bigger weights on those observations with error terms that have bigger variancesc) we use bigger weights on those observations with error terms that have smaller

variancesd) the weights are bigger whenever the coefficient estimates are more reliable

14. Suppose you are estimating y = α + βx + δz + ε but that the variance of ε isproportional to the square of x. Then to find the GLS estimate we should regress

a) y on an intercept, 1/x, and z/xb) y/x on 1/x and z/xc) y/x on an intercept, 1/x, and z/xd) not possible because we don’t know the factor of proportionalitye) none of these

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15. Pushing the heteroskedasticity-consistent variance-covariance matrix button ineconometric software

a) removes the coefficient estimate bias from using OLSb) does not change the OLS coefficient estimatesc) increases the t valuesd) none of these

16. Suppose your dependent variable is aggregate household demand for electricity forvarious cities. To correct for heteroskedasticity you should

a) multiply observations by the city sizeb) divide observations by the city sizec) multiply observations by the square root of the city sized) divide observations by the square root of the city sizee) none of these

17. Suppose your dependent variable is crime rates for various cities. To correct forheteroskedasticity you should

a) multiply observations by the city sizeb) divide observations by the city sizec) multiply observations by the square root of the city sized) divide observations by the square root of the city sizee) none of these

18. When using the eyeball test for heteroskedasticity, under the null we would expect therelationship between the squared residuals and the explanatory variable to be suchthat

a) as the explanatory variable gets bigger the squared residual gets biggerb) as the explanatory variable gets bigger the squared residual gets smallerc) when the explanatory variable is quite small or quite large the squared residual will

be large relative to its value otherwised) there is no evident relationship

19. Suppose you are estimating the relationship y = α + βx + δz + ε but you suspect thatthe 50 male observations have a different error variance than the 40 femaleobservations. The degrees of freedom for the Goldfeld-Quandt test are

a) 50 and 40 b) 49 and 39 c) 48 and 38 d) 47 and 37

20. In the previous question, suppose you had chosen to use the studentized BP test. Thedegrees of freedom would then have been

a) 1 b) 2 c) 3 d) 4

21. In the previous question, to conduct the studentized BP test you would have regressedthe squared residuals on an intercept and

a) x b) z c) x and z d) a dummy for gender

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22. Suppose you are estimating demand for electricity using aggregated data onhousehold income and on electricity demand across 30 cities of differing sizes Ni.Your specification is that household demand is a linear function of household incomeand city price. To estimate using GLS you should regress

a) per capita demand on an intercept, price and per capita incomeb) aggregate demand on an intercept, price, and aggregate incomec) per capita demand on the inverse of Ni, price divided by Ni, and per capita incomed) none of these

23. Suppose you are estimating student performance on an economics exam, regressingexam score on an intercept, GPA, and a dummy MALE. The CLR model assumptionsapply except that you have determined that the error variance for the maleobservations is eight but for females it is only two. To estimate using GLS you shouldtransform by

a) dividing the male observations by 8 and the female observations by 2b) multiplying the male observations by 2 and the female observations by 8c) dividing the male observations by 2d) multiplying the female observations by 8

24. Suppose the CLR model applies except that the errors are nonspherical of knownform so that you can calculate the GLS estimator. Then

a) the R-square calculated using the GLS estimates is smaller than the OLS R-squareb) the R-square calculated using the GLS estimates is equal to the OLS R-squarec) the R-square calculated using the GLS estimates is larger than the OLS R-squared) nothing can be said about the relative magnitudes of R-square

Consider a case in which there is a nonspherical error of known form so that you cancalculate the GLS estimator. You have conducted a Monte Carlo study to investigate thedifference between OLS and GLS, using the computer to generate 2000 samples withnonspherical errors, from which you calculate the following.a) 2000 OLS estimates and their average betaolsbarb) 2000 estimated variances of these OLS estimates and their average betaolsvarbarc) the estimated variance of the 2000 OLS estimates, varbetaols.d) 2000 corresponding GLS estimates and their average betaglsbare) 2000 estimated variances of these GLS estimates and their average betaglsvarbarf) the estimated variance of the 2000 GLS estimates, varbetaglsThe following six questions refer to this information.

25. You should find that betaolsbar and betaglsbar area) approximately equal, and varbetaols and varbetagls are also approximately equalb) not approximately equal, and varbetaols and varbetagls are also not approximately

equalc) approximately equal, but varbetaols and varbetagls are not approximately equald) not approximately equal, but varbetaols and varbetagls are approximately equal

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26. You should expect thata) betaolsbar and betaglsbar are approximately equalb) betaolsbar is bigger than betaglsbarc) betaolsbar is smaller than betaglsbard) not possible to determine relative size here

27. You should expect thata) Varbetaols and Varbetagls are approximately equalb) Varbetaols is bigger than Varbetaglsc) Varbetaols is smaller than Varbetaglsd) not possible to determine relative size here

28. You should expect that varbetaols and betaolsvarbar area) approximately equal and varbetagls and betaglsvarbar are also approximately equalb) not approximately equal but varbetagls and betaglsvarbar are approximately equalc) approximately equal but varbetagls and betaglsvarbar are not approximately equald) not approximately equal and varbetagls and betaglsvarbar are also not approximately

equal

29. You should expect thata) varbetaols and betaolsvarbar are approximately equalb) varbetaols is bigger than betaolsvarbarc) varbetaols is smaller than betaolsvarbard) not possible to determine relative size here

30. You should expect thata) varbetagls and betaglsvarbar are approximately equalb) varbetagls is bigger than betaglsvarbarc) varbetagls is smaller than betaglsvarbard) not possible to determine relative size here

31. Suppose the CLR model holds but the presence of nonspherical errors causes thevariance estimates of the OLS estimator to be an underestimate. Because of this,when testing for the significance of a slope coefficient using for our large sample thecritical t value 1.96, the type I error rate

a) is higher than 5%b) is lower than 5%c) remains fixed at 5%d) not possible to tell what happens to the type I error rate

32. Suppose you want to undertake a Monte Carlo study to examine the impact ofheteroskedastic errors of the form V(ε) = 4 + 9x2 where x is one of the explanatoryvariables in your specification. After getting the computer to draw errors from astandard normal, to create the desired heteroskedasticity you need to multiply the itherror by

a) 3xi b) 2 + 3xi c) 4 + 9xi2 d) none of these

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33. Suppose the CLR model assumptions apply to y = α + βx + θz + ε except that thevariance of the error is proportional to x squared. To produce the GLS estimator youshould regress y/x on

a) an intercept, 1/x, and z/xb) an intercept and z/xc) 1/x and z/xd) not possible to produce GLS because the factor of proportionality is not known

34. Suppose the CLR model assumptions apply to y = α + βx + θz + ε. You mistakenlythink that the variance of the error is proportional to x squared and so transform thedata appropriately and run OLS. If x and z are positively correlated in the data, thenyour estimate of θ is

a) biased upwardb) biased downwardc) unbiasedd) not possible to determine the nature of the bias here

35. Suppose income is the dependent variable in a regression and contains errors ofmeasurement (i) caused by people rounding their income to the nearest $100, or (ii)caused by people not knowing their exact income but always guessing within 5% ofthe true value. In case (i) there is

a) heteroskedasticity and the same for case (ii)b) heteroskedasticity but not for case (ii)c) no heteroskedasticity but heteroskedasiticity for case (ii)d) no heteroskedasticity and the same for case (ii)

36. Suppose you have regressed score on an economics exam on GPA for 50 individuals,ordered from smallest to largest GPA. The DW statistic is 1.5; you should concludethat

a) the errors are autocorrelatedb) there is heteroskedasticityc) there is multicollinearityd) there is a functional form misspecification

37. A regression using the specification y = α + βx + θz + ε produced SSE =14 usingannual data for 1961-1970, and SSE = 45 using data for 1971-1988. The Goldfeld-Quant test statistic for a change in error variance beginning in 1971 is

a) 3.2 b) 1.8 c) 1.5 d) none of these

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Week 12: Bayesian Statistics

1. The main difference between Bayesian and classical statisticians isa) their choice of priorb) their definitions of probabilityc) their views of the type I error rated) the formulas for probability used in calculations

2. Suppose a classical statistician estimates via OLS an unknown parameter beta andbecause the CLR model assumptions hold declares the resulting estimate’s samplingdistribution to be such that it is unbiased and has minimum variance among all linearunbiased estimators. For the Bayesian the sampling distribution

a) is also unbiasedb) is biased because of the priorc) has a smaller varianced) does not exist

Suppose the CNLR model applies and with a very large sample size the classicalstatistician produces an estimate betahat = 6, with variance 4. With the same data, usingan ignorance prior, a Bayesian produces a normal posterior distribution with mean 6 andvariance 4. The next ten questions refer to this information.

3. The sampling distribution of betahata) has mean 6b) has mean betac) is graphed with beta on the horizontal axisd) has the same interpretation as the posterior distribution

4. The posterior distribution of betaa) has mean 6b) has mean betac) is graphed with betahat on the horizontal axisd) has the same interpretation as the sampling distribution

5. In this example the Bayesian estimate of beta would be the same as the classicalestimate if the loss function were

a) all-or-nothing b) absolute c) quadratic d) all of the above

6. If the Bayesian had used an informative prior instead of an ignorance prior theposterior would have had

a) the same mean but a smaller varianceb) the same mean but a larger variancec) a different mean and a smaller varianced) a different mean and a larger variance

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7. For the Bayesian, the probability that beta is greater than 7 isa) 40% b) 31% c) 16% d) not a meaningful question

8. For the classical statistician, the probability that beta is greater than 7 isa) 40% b) 31% c) 16% d) not a meaningful question

9. Suppose we want to test the null hypothesis that beta is equal to 4, against thealternative that beta is greater than 4. The classical statistician’s p value isapproximately

a) .16 b) .31 c) .32 d) none of these

10. Suppose we want to test the null hypothesis that beta is less than or equal to 4, againstthe alternative that beta is greater than 4. The Bayesian statistician’s probability thatthe null is true is approximately

a) .16 b) .69 c) .84 d) none of these

11. The Bayesian would interpret the interval from 2.7 to 9.3 asa) an interval which if calculated in repeated samples would cover the true value of beta

90% of the timeb) a range containing the true value of beta with 90% probabilityc) an interval that the Bayesian would bet contains the true value of beta

12. Consider the interval from 2.7 to 9.3. For the Bayesian the probability that the truevalue of beta is not in this interval is

a) approximately equal to the probability that beta is less than 3.4b) a lot greater than the probability that beta is less than 3.4c) a lot less than the probability that beta is less than 3.4d) not a meaningful question

13. Bayes theorem says that the posterior isa) equal to the likelihoodb) proportional to the likelihoodc) equal to the prior times the likelihoodd) proportional to the prior times the likelihood

14. The subjective element in a Bayesian analysis comes about through use ofa) an ignorance priorb) an informative priorc) the likelihoodd) the posterior

15. The Bayesian loss function tells usa) the loss incurred by using a particular point estimateb) the expected loss incurred by using a particular point estimatec) the loss associated with a posterior distributiond) the expected loss associated with a posterior distribution

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16. The usual “Bayesian point estimate” is the mean of the posterior distribution. Thisassumes

a) a quadratic loss functionb) an absolute loss functionc) an all-or-nothing loss functiond) no particular loss function

17. The Bayesian point estimate is chosen bya) minimizing the lossb) minimizing expected lossc) finding the mean of the posterior distributiond) all of the above

18. From the Bayesian perspective a sensitivity analysis checks to see by how much theresults change when a different

a) loss function is usedb) prior is usedc) posterior is usedd) data set is used

19. The main output from a Bayesian analysis isa) the likelihoodb) the prior distributionc) the posterior distributiond) a point estimate

20. When hypothesis testing in a Bayesian framework the type I errora) is fixedb) is irrelevantc) is set equal to the type II errord) none of the above

21. The Bayesian accepts/rejects a null hypothesis based ona) minimizing the type I errorb) minimizing the type II errorc) maximizing the benefit from this decisiond) maximizing the expected benefit from this decision

22. Suppose you are a Bayesian and your posterior distribution for next month’sunemployment rate is a normal distribution with mean 8.0 and variance 0.25. If thismonth’s unemployment rate is 8.1 percent, what would you say is the probability thatunemployment will increase from this month to next month?a) 50% b) 42% c) 5% d) 2.3%

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23. If a Bayesian has a quadratic loss function, his/her preferred point estimate isa) the mean of the posterior distributionb) the median of the posterior distributionc) the mode of the posterior distributiond) cannot be determined unless the specific quadratic loss function is known

24. Suppose the net cost to a firm of undertaking a venture is $1800 if beta is less than orequal to one and its net profit is $Q if beta is greater than one. Your posteriordistribution for beta is normal with mean 2.28 and variance unity. Any value of Qbigger than what number entices you to undertake this venture?

a) 100 b) 200 c) 300 d) 450

25. A Bayesian has a client with a loss function equal to the absolute value of thedifference between the true value of beta and the point estimate of beta. The posteriordistribution is f(beta) = 2*beta for beta between zero and one, with f(beta) zeroelsewhere. (This distribution has mean two-thirds and variance one-eighteenth.)Approximately what point estimate should be given to this client?

a) 0.50 b) 0.66 c) 0.71 d) 0.75

26. A Bayesian has a client with a quadratic loss function. The posterior distribution isbeta = 1, 2, and 3 with probabilities 0.1, 0.3 and 0.6, respectively. What pointestimate should be given to this client?

a) 1 b) 2 c) 3 d) none of these

27. A Bayesian has a client with an all-or-nothing loss function. The posteriordistribution is beta = 1, 2, and 3 with probabilities 0.1, 0.3 and 0.6, respectively. Whatpoint estimate should be given to this client?

a) 1 b) 2 c) 3 d) none of these

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Answers

Week 1: Statistical Foundations I 1c, 2c, 3c, 4a, 5b, 6d, 7a, 8c, 9c, 10c, 11a, 12c, 13d,14c, 15c, 16a, 17a, 18d, 19c, 20a, 21a, 22a, 23a, 24c, 25a, 26d, 27a, 28b, 29c, 30a, 31b,32c, 33a, 34c, 35b, 36d, 37b, 38a, 39b, 40b, 41d, 42b, 43a, 44b, 45a, 46b, 47c, 48c, 49b,50d, 51c, 52a

Week 2: Statistical Foundations II 1b, 2c, 3c, 4b, 5c, 6a, 7d, 8b, 9a, 10a, 11d, 12d, 13d,14a, 15b, 16a, 17a, 18b, 19c, 20d, 21b, 22d, 23b, 24c, 25d, 26b, 27d, 28d, 29d, 30c, 31c,32a, 33c, 34b, 35c, 36d, 37c, 38b, 39a

Week 3: What is Regression Analysis? 1a, 2c, 3b, 4d, 5c, 6d, 7a, 8d, 9a, 10d, 11b, 12b,13b, 14d, 15b, 16c, 17c, 18b, 19a, 20a, 21d, 22d, 23d, 24c, 25d, 26b, 27a, 28d, 29c, 30b,31a, 32b, 33c, 34d, 35b, 36b, 37a, 38c, 39c

Week 4: The CLR Model 1d, 2c, 3b, 4c, 5d, 6c, 7d, 8b, 9b, 10c, 11d, 12c, 13c, 14d, 15d,16c, 17c, 18a, 19a, 20a, 21c, 22b, 23d, 24a, 25c

Week 5: Sampling Distributions 1d, 2d, 3c, 4d, 5d, 6c, 7d, 8c, 9b, 10c, 11a, 12d, 13c,14d, 15d, 16d, 17d, 18d, 19d, 20c, 21c, 22a, 23a, 24b, 25b, 26c, 27b, 28c, 29b, 30b, 31b,32c, 33d, 34b, 35d

Week 6: Dummy Variables 1d, 2c, 3b, 4a, 5a, 6a, 7c, 8b, 9b, 10b, 11d, 12d, 13c, 14c,15c, 16d, 17c, 18c, 19a, 20c, 21b, 22c, 23d, 24d, 25c, 26b, 27a, 28c, 29d, 30d, 31c, 32d,33b, 34c, 35d, 36d, 37c, 38d, 39d, 40b, 41b, 42d, 43a

Week 7: Hypothesis Testing 1b, 2c, 3c, 4c, 5b, 6d, 7b, 8d, 9b, 10d, 11b, 12c, 13d, 14a,15c, 16b, 17b, 18c, 19d, 20a, 21c

Week 9: Specification 1c, 2b, 3b, 4c, 5b, 6c, 7b, 8c, 9c, 10d, 11b, 12d, 13d, 14c, 15d,16d, 17c, 18d, 19c, 20d, 21b, 22d

Week 10: Multicollinearity; Applied Econometrics 1c, 2d, 3c, 4d, 5d, 6c, 7d, 8b, 9d,10c, 11d, 12d, 13b, 14c, 15b, 16c, 17b, 18c, 19c, 20d, 21a, 22c, 23d, 24d, 25c, 26d, 27c,28c, 29c, 30d, 31a, 32b, 33b, 34b, 35c, 36d, 37b, 38c, 39c, 40a, 41c, 42d

Week 11: Nonspherical Errors 1d, 2b, 3c, 4b, 5d, 6c, 7b, 8d, 9d, 10d, 11d, 12c, 13c,14c, 15b, 16d, 17c, 18d, 19d, 20a, 21d, 22d, 23c, 24a, 25c, 26a, 27b, 28b, 29d, 30a, 31a,32d, 33a, 34c, 35c, 36d, 37c

Week 12: Bayesian Statistics 1b, 2d, 3b, 4a, 5d, 6c, 7b, 8d, 9a, 10a, 11b, 12a, 13d, 14b,15a, 16a, 17b, 18b, 19c, 20d, 21d, 22b, 23a, 24b, 25c, 26d, 27c