### Sample Chapter

**INSTANT DOWNLOAD COMPLETE TEST BANK WITH ANSWERS**

**ISBN-10:** 0470626739

**ISBN-13:** 9780470626733

** **

**Principles of Econometrics 4th Edition by R. Carter Hill –**

**Test Bank**

**Sample Questions**

File**: Ch01, Chapter 1, An Introduction to Econometrics**

Multiple Choice

- Which of the following is NOT generally included in the study of econometrics?

a.) using economic data to estimate relationships

b.) testing economic hypotheses

c.) predicting economic outcomes

d.) developing new economic relationships.

Section: 1.1

2.Consider the following model:

*Q ^{d}* = f(

*P, P*)

^{s}, P^{c}, INCwhere *Q ^{d }*is quantity demanded of a particular product per month,

*P*is the price of the product,

*P*is the price of substitutes,

^{s}*P*is the price of complements, and

^{c}*INC*is monthly income.

This equation represents

a.) a non-linear model

b.) an economic model

c.) an econometric model

d.) a challenge to the law of demand.

Section: 1.2

- Economic theory provides a basis for which variables are relevant and should be included in an econometric model. But econometrics provides tools to estimate ____________________ which tells us ________________________________.

a.) a model, the functional form that should be used.

b.) causality, why it happens that way

c.) a parameter, how much or to what degree things change.

d.) variables, the probability of a specific outcome.

Section: 1.2

- Why is a random error term included in an econometric model?

a.) because many economic models have not been well developed yet and need to allow for inaccuracies

b.) because some people are irrational

c.) because there is intrinsic uncertainty in any economic activity due to individual decision making

d.) because most estimating techniques are not well suited to work with a deterministic model.

Section: 1.3

- Refer to the following equation:

*Q ^{s}* = b

_{1}+ b

_{2}

*P*+ b

_{3}

*P*+ b

^{r}_{4}

*P*+ b

^{s}_{5}

*TAX*+

*e*

where *Q ^{s}* is annual quantity supplied,

*P*is the price of the product,

*P*is the price of resources,

^{r}*P*is the price of goods that are substitutes in production, and

^{s}*TAX*is the excise tax on the product. This equation is

a.) an economic model

b.) an econometric model

c.) a market model

d.) a non-linear model

Section: 1.3

- Refer to the following equation:

*Q ^{s}* = b

_{1}+ b

_{2}

*P*+ b

_{3}

*P*+ b

^{r}_{4}

*P*+ b

^{s}_{5}

*TAX*+

*e*

where *Q ^{s}* is annual quantity supplied,

*P*is the price of the product,

*P*is the price of resources,

^{r}*P*is the price of goods that are substitutes in production, and

^{s}*TAX*is the excise tax on the product. In this equation b

_{1 }represents

a.) a parameter to be estimated

b.) the random error term

c.) the predicted quantity supplied

d.) the equilibrium quantity

Section: 1.3

- The parameters estimated using econometric methods are generally used for ___________________ or _____________________.

a.) testing hypotheses, predicting

b.) confirming, denying effects of policy.

c.) validation, repudiation.

d.) generating data, probability distributions.

Section: 1.3

- Suppose you stand outside a store and randomly give some shoppers coupons as they enter while other shoppers receive none. You then record how much each shopper spends in the store. The data you collect are

a.) survey data

b.) random data

c.) experimental data

d.) selective data

Section: 1.4

- A data set that has observations on one entity at multiple points in time is classified as

a). time series data

b.) cross-section data

c.) panel data

d.) flow data

Section: 1.5

10: A data set containing the number of adults with college degrees in each of the US states in 2009 is

a). time series data.

b.) cross-section data.

c.) panel data.

d.) flow data.

Section: 1.5

- Which of the following variables is
*most*likely to be quantitative?

a.) gender

b.) education

c.) income

d.) employment

Section: 1.5

12: Which of the following variables is *least* likely to be quantitative?

a.) age

b.) GDP growth

c.) marital status

d.) inflation

Section: 1.5

- What does it mean for a panel data set to be balanced?

a.) males and females are equally represented in the sample

b.) the observations are equally split before and after the event being studied

c.) the number of observations in the treatment and control group are equal

d.) each unit of observation is observed for the same number of time periods

/Difficult

Section: 1.5

- Of the following steps in conducting empirical economic research, which one should be performed last?

a.) find appropriate data that can be used for estimation

b.) build an economic model guided by economic theory

c.) evaluate and analyze the consequences and implications of the results

d.) estimate parameters and test hypotheses

Section: 1.6

- Which of the following sections usually comes first in a research report?

a.) state of problem

b.) description of data

c.) review of literature on the topic

d.) economic model

Section: 1.7

- What does NBER stand for?

a.) Northern Banks Emergency Reserves

b.) Normally Balanced Econometric Regression

c.) National Bureau of Economic Research

d.) National Business and Economic Regulators

Section: 1.8

- Which regional Federal Reserve Bank provides access to large amounts of economic data through FRED?

a.) Boston

b.) New York

c.) San Francisco

d.) St. Louis

Section: 1.8

File: Ch-Prob, Probability Primer, Probability Primer

Multiple Choice

- A measure of the daily change in the closing value of the DJIA is a ____________ variable and a variable indicating whether it moved up or down is a ______________ variable.

a.) continuous, discrete

b.) flow, stock

c.) random, determined

d.) discrete, continuous

Section: P.1

- If (P(X=x|Y=y) = P(X=x), then

a.) Y is the dependent variable

b.) X and Y are positively correlated

c.) X and Y are statistically independent

c.) Y must be a discrete random variable

Section: P.3

- The expected value of a random variable is

a.) the probability weighted mean

b.) a measure of central tendency of the pdf

c.) average value that occurs in many repeated trial of an experiment

d.) all of the above

Section: P.5

- Which of the following is NOT equal to cov(X,Y)?

a.) s_{xy}

b.) E[(x-m_{x})(y-m_{y})]

c.) E(xy)-m_{x}m_{y}

d.) r_{xy}

/Difficult

Section: P.5

- If Z is a random variable generated by adding together X and Y which are also random variables, what do we know about var(Z) if X and Y are positively correlated.?

a.) var(Z) = var(X) + var(Y)

b.) var(Z) < var(X) + var(Y)

c.) var(Z) > var(X) + var(Y)

d.) var(Z) = var(X) * var(Y)

/Difficult

Section: P.5

- Which of the following statements about the standard normal distribution is NOT true?

a.) m=0 , s^{2} = 1

b.) it can be used to find probability intervals for any normal distribution

c.) it is symmetric

d.) it is derived from repeated sampling of naturally occurring phenomena

Section: P.6

- Which of the following statements is true of the standard normal distribution, but not other normal probability distributions?

a.) P(X<0)=0.5

b.) it is symmetric

c.) P(X<(m_{x}-1)) = P(X>(m_{x}+1))

d.) it is often referred to as a “bell” curve

Section: P.6

Short Answer

1.) The difference between a pdf and cdf is ___________________________.

- How would you write the following expression using summation notation?

Q_{1} + Q_{2} + Q_{3} + Q_{4} + ………….. + Q_{29}

- Final grades in Professor Pickle’s course are calculated as a weighted average of the midterm and final exam. The midterm is weighted at 0.4 and the final is weighted as 0.6. This semester grades on the midterm exam were normally distributed with m
_{m}= 63 and s^{2}_{m}= 14. Grades on the final exam were also normally distributed with m_{f}= 75 and s^{2}_{f}= 20.

a.) Calculate the average final grade in Professor Pickle’s course?

b.) What do you expect the variance of the distribution of final grades to be? Why?

Section: P.5

File: Ch02, Chapter 2, The Simple Linear Regression Model

Multiple Choice

- In an economic model that uses income to predict monthly expenditures on entertainment, what is the dependent variable?

a.) income

b.) monthly expenditures on entertainment

c.) income elasticity

d.) demand for entertainment

Section: 2.1

- In an economic model that uses income to predict monthly expenditures on entertainment, what is the independent or explanatory variable?

a.) income

b.) monthly expenditures on entertainment

c.) income elasticity

d.) demand for entertainment

Section: 2.1

- Which of the following is NOT an assumption of the Simple Linear Regression Model?

a.) The value of y, for each value of x, is

y = b_{1} + b_{2}x + *e*

b.)The variance of the random error *e* is

var(*e*)= s^{2}

c.) The covariance between any pair of random errors *e*_{i} and *e*_{j} is zero

d.) The parameter estimate of b_{1 }is unbiased.

Section: 2.2

- The OLS estimators for b
_{1 }and b_{2 }are formulas derived by minimizing _____________.

a.) the sum of the error terms or residuals

b.) the sum of the squared residuals

c.) the slope of the regression line

d.) the fit of the regression line to the observed data.

Section: 2.3

- Applying the OLS model to our data give us the following regression equation:

ŷ = 3.41 + 12.89 x.

What would the forecast value be when the independent variable is 15.0?

a.) 196.76

b.) 16.30

c.) 244.50

d.) 32.19

Section: 2.3

- In the OLS model, what happens to var(
*b*_{1}) as the sample size (N) increases?

a.) it also increases

b.) it decreases

c.) it does not change

d.) cannot be determined without more information

/Difficult

Section: 2.4

- If
*b*_{1 }is an estimator for b_{1 }such that E(*b*_{1}) = b_{1}, then it must be the case that

a.) * b*_{1 }is an efficient estimator

b.) *b*_{1 }is an unbiased estimator

c.) *b*_{1 }is a linear estimator

d.) *b*_{1 }is a preferred estimator

Section: 2.4 & 2.5

- Under the Gauss-Markov Theorem when assumptions SR1 – SR5 are met, what estimators of b
_{1}and b_{2}may have smaller variances than*b*_{1}and*b*_{2}?

a.) none

b.) a non-linear estimator

c.) a normally distributed estimator

d.) an estimator derived from economic theory

Section: 2.5

- What mathematical theorem allows for normally distributed least squares estimators when assumptions SR1 – SR5 hold but the error term is NOT normally distributed?

a.) Central Limit Theorem

b.) Gauss-Markov Theorem

c.) Law of Large Numbers

d.) the Least Squares Principle

Section: 2.6

- If we use as an estimator of s
^{2}it is _______________, but it can be corrected by _______________.

a.) biased, changing the numerator to

b.) non-linear, changing the denominator to N – 2

c.) biased, changing the denominator to N-2

d.) non-linear, taking the log of each term.

Section: 2.7

- Which of the following non-linear adjustments CANNOT be accommodated using OLS?

a.) including an independent variable that has been raised to a power

b.) taking a logarithmic transformation of the dependent variable

c.) including a binary indicator variable

d.) raising parameters to a power

Section: 2.8

- How do you interpret the estimated value of g
_{1}in the following equation:

ln(*ENT_EXP*) = g_{1} + g_{2} (*INCOME*) + e

where *INCOME *is annual household income (in thousands) and *ENT_EXP * is annual entertainment expenses?

a.) the income elasticity of entertainment

b.) when multiplied by 100 it is the percentage increase in entertainment expenses associated with an additional $1000 in income

c.) the increase in entertain expenses associated with a 1% increase in income

d.) the average of the logarithm of entertainment expenses for a household with zero income

Section: 2.8

- How do you interpret the estimated value of g
_{2}in the following equation:

ln(*ENT_EXP*) = g_{1} + g_{2} (*INCOME*) + e

where* INCOME* is annual household income (in thousands) and *ENT_EXP* is annual entertainment expenses?

a.) the income elasticity of entertainment

b.) .) when multiplied by 100 it is the percentage increase in entertainment expenses associated with an additional $1000 in income

c.) the increase in entertain expenses associated with a 1% increase in income

d.) the average of the logarithm of entertainment expenses for a household with zero income

Section: 2.8

- You have estimated the following equation using OLS:

ŷ = 33.75 + 1.45 *MALE*

where y is annual income in thousands and *MALE* is an indicator variable such that it is 1 for males and 0 for females. According to this model, what is the average income for females?

a.) $33,750

b.) $35,200

c.) $32,300

d.) cannot be determined

Section: 2.9

- You have estimated the following equation using OLS:

ŷ = 33.75 + 1.45 *MALE*

where y is annual income in thousands and *MALE* is an indicator variable such that it is 1 for males and 0 for females. According to this model, what is the average income for males?

a.) $33,750

b.) $35,200

c.) $32,300

d.) cannot be determined

Section: 2.9

File: Ch03, Chapter 3, Interval Estimation and Hypothesis Testing

Multiple Choice

- You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

** y = 97.25 + 33.74 *x**

** (3.86) (9.42)**

What are the endpoints of the interval estimator for b_{2} with a 95% interval estimate?

a.) (14.90, 52.58)

b.) (24.32, 43.16)

c.) (-3.58, 3.58)

d.) (30.16,37.32)

Section: 3.1

- You estimate a simple linear regression model using a sample of 25 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

** y = 97.25 + 19.74* x**

** (3.86) (3.42)**

What are the endpoints of the interval estimator for b_{2} with a 98% interval estimate?

a.) (-5.77, 25.51)

b.) ( 16.32 , 23.16)

c.) (11.19, 28.29)

d.) (12.90, 26.58)

Section: 3.1

- You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

** y = 97.25 + 33.74* x**

** (3.86) (9.42)**

You want to test the following hypothesis: **H _{0}: **

**b**

_{2}**= 12, H1:**

**b**

_{2 }**≠12.**If you choose to reject the null hypothesis based on these results, what is the probability you have committed a Type I error?

a.) between .05 and .10

b.) between .01 and .025

c.) between .02 and .05

d.) It is impossible to determine without knowing the true value of b_{2}

Section: 3.2

- You estimate a simple linear regression model using a sample of 62 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

** y = 97.25 + 33.74* x**

** (3.86) (9.42)**

You want to test the following hypothesis: **H _{0}: **

**b**

_{2}**= 12, H**

_{1}:**b**

_{2 }**≠12.**If you choose to reject the null hypothesis based on these results, what is the probability you have committed a Type II error?

a.) between .05 and .10

b.) between .01 and .025

c.) between .02 and .05

d.) It is impossible to determine without knowing the true value of b_{2}

Section: 3.2

- You estimate a simple linear regression model using a sample of 25 observations and obtain the following results (estimated standard errors in parentheses below coefficient estimates):

** y = 97.25 + 19.74 *x**

** (3.86) (3.42)**

You want to test the following hypothesis: **H _{0}: **

**b**

_{2}**= 1, H**

_{1}:**b**

_{2 }**>12.**If you choose to reject the null hypothesis based on these results, what is the probability you have committed a Type I error?

a.)between .01 and .02

b.)between .02 and .05

c.)less than .005

d.) It is impossible to determine without knowing the true value of b_{2}

Section: 3.2

- Which of the following is not a component of a hypothesis tes?

a.) null hypothesis

b.) goodness-of-fit

c.) test statistic

d.) rejection region

Section: 3.2

7.) Which of the following cannot be an alternative hypothesis?

a.) b_{k} = 0

b.) b_{k} ≠ 0

c.) b_{k} > 0

d.) b_{k} < 0

Section: 3.2

8.) Rejecting a true null hypothesis

a.) is a Type I error.

b.) is a Type II error.

c.) should not happen if a valid statistical test is used.

d.) depends on the size of the estimation sample.

Section: 3.2

9.) For which alternative hypothesis do you reject H_{0} if t≤t _{(}_{a}_{,N-2)}?

a.) b_{k} = c

b.) b_{k} ≠ c

c.) b_{k} > c

d.) b_{k} < c

Section: 3.3

10.) For which alternative hypothesis do you reject H_{0} if |t| ≤t _{(}_{a/2}_{,N-2)}?

a.) b_{k} = c

b.) b_{k} ≠ c

c.) b_{k} > c

d.) b_{k} < c

Section: 3.3

11.) How do you reduce the probability of committing a Type I error?

a.) reduce a

b.) increase a

c.) use a two-tailed test

d.) increase the rejection region

Section: 3.3

12.) In which case would testing the null hypothesis involve a two-tailed statistical test?

a.) H_{1}: Incentive pay for teachers does affect student achievement

b.) H_{1}: Higher sales tax rates does not reduce state tax revenues

c.) H_{1}: Extending the duration of unemployment benefits does not increase the length of joblessness

d.) H_{1}: Smoking does not reduce life expectancy

Section: 3.4

13.) In testing H_{0}: b_{2} = c using a .05 probability of a Type I error, you find a p-value of .38. What should you conclude?

a.) H_{0} is true, b_{2} = c.

b.) H_{0} should be rejected and is unlikely to be true since the p-value < .50.

c.) It is impossible to know for sure, but there is a .38 probability that b_{2} = c.

d.) There is not sufficient evidence to reject H_{0}, so we accept the hypothesis by default.

Section: 3.5

- What does a p-value NOT tell you?

a.) The size of the largest rejection region that would not contain the observed test statistic

b.) The probability that the null hypothesis is true and you would observe a test statistic more extreme than the one observed

c.) The highest value of a for which you cannot reject the null hypothesis based on the data

d.) The probability that the null hypothesis is true

Section: 3.5

- You want to test the hypothesis

** H _{0}: (c_{1} **

**b**

_{1}**+ c**

_{2}**b**

_{2}**) – c**

_{0}= 0 and H_{1}: (c_{1}**b**

_{1}**+ c**

_{2}**b**

_{2}**) – c**

_{0}≠ 0What test statistic should you use for the test?

a.)

b.)

c.)

d.) c^{2}=(b_{1} – b_{2})/se(b_{1} + b_{2})

Section: 3.6

- You want to test the hypothesis

** H _{0}: (c_{1} **

**b**

_{1}**+ c**

_{2}**b**

_{2}**) – c**

_{0}= 0 and H_{1}: (c_{1}**b**

_{1}**+ c**

_{2}**b**

_{2}**) – c**

_{0}≠ 0If the null hypothesis is true, how will the test statistic be distributed?

a.) t_{(}_{a}_{/2)}

b.) N(0,1)

c.) t_{(N-2)}

d.) c^{2}_{(3 , N-2)}

Section: 3.6

- If you are performing a two-tailed test of significance and you find that the area to the left of |t
_{c}| is .975, what is the p-value?

a.).025

b.) .050

c.) .975

d.) .950

Section: 3.5

- If you are performing a left-tailed significance test and find the area to the left of |t
_{c}| is .99, what is the p-value?

a.) .01

b.) .99

c.) .02

d.) .05

Section: 3.5

- When should a left-tailed significance test be used?

a.) When economic theory suggests the coefficient should be positive

b.) When it allows you to reject the null hypothesis at a lower p-value

c.) When economic theory suggests the coefficient should be negative

d.) When you know the true value of b_{2} is positive.

Section: 3.5

File: Ch04, Chapter 4, Prediction, Goodness-of-Fit, and Modeling Issues

Multiple Choice

- Which of the following leads to large forecast errors?

a.) larger sample size, N

b.) variation in the explanatory variable, x, is large

c.) overall uncertainty in the model, as measured by s^{2}, is smaller

d.) the value of (x_{0} – x̄) ^{2} is larger

Section: 4.1

- At what values of x
_{0}will the standard error of the forecast be smallest?

a.) x_{0} = 0

b.) x_{0} =x̅

c.) x_{0}^{2} = ŝ^{2}

d.) x_{0} = t_{c} se(f)

Section: 4.1

- Which of the following expressions is NOT equal to Ʃ(y
_{i}– y̅)^{2}?

a.) Ʃ(ŷ_{i}-y̅)^{2}+ Ʃe_{i}^{2}

b.) SSR + SSE

c.) SSR/SSE

d.) SST

Section: 4.2

- What does R2, the coefficient of determination, measure?

a.) the probability of the true value falling within the forecast interval

b.) the p-value on the coefficient we are using to test our hypothesis of interest

c.) the confidence interval of the error terms as determined by the coefficients

d.) the proportion of the variation in y explained by x within the regression model

Section: 4.2

- You have estimated a regression model and your printout includes the following information

**s _{xy}= 3614.00**

**s _{x} = 12.72**

**s _{y} = 394.61**

**SST = 758912.00.**

What is R^{2} for this regression model?

a.) .72

b.) .11

c.) .03

d.) .53

Section: 4.2

- You have estimated a regression model and your printout includes the following information

**s _{xy}= 3614.00**

**s _{x} = 12.72**

**s _{y} = 394.61**

**SST = 758912.00**.

Use this information to calculate SSE.

a.) 546,416.64

b.) 212,495.36

c.) 381.89

d.) 5019.44

Section: 4.2

- Which of the following will change if you scale the dependent variable in a simple regression model?

a.) p-value

b.) t-value of b_{2}

c.) R^{2}

d.) b_{1}

Section: 4.3

- When should a researcher consider transforming the explanatory variable in a simple linear regression model?

a.) when a data plot suggests there is a non-linear functional form

b.) to get a coefficient estimate with the sign predicted by economic theory

c.) to reduce the variation in the explanatory variable

d.) to maximize SSR

Section: 4.3

- When should a researcher consider transforming the explanatory variable in the simple linear regression model?

a.) to estimate a coefficient on the dependent variable that matches economic theory

b.) to allow non-constant marginal effects

c.) to reduce variance in the dependent variable

d.) to reduce (Note: the “hat” should be over the whole expression, but I can’t accomplish that in my software right now)

Section: 4.3

- How do you interpret the estimated value of b
_{2}in the following model?

** ln(y) = ****b**_{1}** + ****b**_{2}** * ln(x) **

a.) the slope of the line representing the relationship between y and x

- b) the elasticity of y with respect to x

c.) cannot be determined without more information

d.) the mean value of ln(y) when ln(x) = 0.

Section: 4.3

- You have estimated the following simple regression model

**y = 379 + 1.44 x ^{3}**

What does this model predict y to be when x = 8.49?

a.) 415.68

b.) 690.39

c.) 1260.22

d.) 2205.47

Section: 4.4

- You have estimated the following simple regression model

y = 379 + 1.44 x^{3}

What is the elasticity when x = 8.49?

a.) 263.19

b.) 311.39

c.) 2.10

d.) -24.7

Section: 4.4

- You have estimated a model of two variables related such that

**ln(y) = 17.3 – .04 x**

If x decreases by 2 units, what is the expected change in y?

a.) y decreases by .08 units.

b.) y increases by 8 percent.

c.) y increases by 4 units

d.) y decreases by 8 percent.

Section: 4.5

- While working with the sales manager of your firm you have estimated the following model of sales volume as a function of monthly household income:

(0.781) (0.392)

Where Q is monthly sales volume, I is monthly household income in thousands, and standard errors are listed below the parameter estimates.

What is the income elasticity of your firm’s product?

a.) 1.212

b.) 2.206

c.) 3.418

d.) 4.630

Section: 4.6

- While working with the sales manager of your firm you have estimated the following model of sales volume as a function of monthly household income:

** ** (0.781) (0.392)

Where Q is monthly sales volume, I is monthly household income in thousands, and standard errors are listed below the parameter estimates.

What does the model predict sales volume to be if using the corrected predictor when income is $4000 per month?

a.) 708,133.68

b.) 723,146.11

c.) 163.73

d.) 167.20

Level: Difficult

Section: 4.6

- What hypothesis is tested when using the Jarque-Berra test ?

a.) H_{0}: The model is correctly specified as estimated

b.) H_{0}: The error terms are normally distributed

c.) H_{0}: The error terms are uncorrelated with x

d.) H_{0}: The error terms are random

Section: 4.3

Short Answer

- When the residuals from a simple regression model appear to be correlated with x, this is known as_______________________________.

- If a scatter plot of the data reveals an inverted U shape, what data transformation would allow it to be estimated with simple linear regression?

- A measure of the symmetry of a distribution is ________________________.

- What is the skewness of the normal distribution?

- What about the distribution of a random variable does kurtosis measure?

- What is the kurtosis measure of the normal distribution?

File: Ch05, Chapter 5, The Multiple Regression Model

Multiple Choice

- When an error term is added to an economic model and assumptions about the distribution of the error term are made, the resulting model is ______________.

a.) fallacious, you should not make assumptions about error terms.

b.) an econometric model that can be estimated and used for inference.

c.) misspecified due to missing information.

d.) heteroskedastic since error terms are no longer random.

Section: 5.1

2.) How should b_{k} in the general multiple regression model be interpreted?

a.) The number of units of change in the expected value of y for a 1 unit increase in x_{k} when all remaining variables are unchanged

b.) the magnitude by which x_{k} varies in the model

c.) the amount of variation in y explained by x_{k} in the model

d.) the number of variables used in the model.

Section: 5.1

3.) Which of the following is not an assumption of the multiple regression model?

a.) The values of each x_{ik} are not random and are not exact linear functions of the other explanatory variables.

b.) var(y_{i}.) = var(e_{i}) = s^{2}

c.) The least squares estimators are BLUE.

d.) cov(y_{i}, y_{j}) = cov(e_{i}, e_{j}) = 0; (i≠j)

/Difficult

Section: 5.1

4.) What is the unbiased estimator of s^{2} in the multiple regression model?

a.)

b.)

c.)

d.)

/Difficult

Section: 5.2

5.) Why does the denominator of ŝ_{2} need to be the same as the degrees of freedom in the model?

a.) so we will know how the estimate is distributed if H_{o} is true

b.) so we can extrapolate the results to other values of x

c.) so that the root MSE will be a positive number

d.) so the estimator will be unbiased

Section: 5.2

6.) In the multiple regression model which of the following does NOT lead to larger variances of the least squares estimators b_{2} and var(b_{2})?

a.) larger error variances, s^{2}

b.) larger correlation between x_{2} and x_{3}

c.) smaller values of Ʃ(x_{i2} – x̅_{2})^{2}

d.) larger correlation between x_{2} and y

Section: 5.3

7.) The matrix below represents the variance-covariance matrix estimated from the multiple regression model:

Which 2 elements of the matrix should always be equal?

a.) A & I

b.) B & H

c.) C & G

d.) D & F

Section: 5.3

8.) The matrix below represents the variance-covariance matrix estimated from the multiple regression model:

Which element of the matrix cannot be negative?

a.) A

b.) B

c.) C

d.) D

Section: 5.3

9.) You have estimated a multiple regression model with 6 explanatory variables and an intercept from a sample with 46 observations. What is t_{c} if you want to perform a right-tailed hypothesis test at the .01 level of significance?

a.) 2.426

b.) 2.708

c.) 2.423

d.) 2.704

Section: 5.3

10.) You estimate a model with 5 explanatory variables and an intercept from a data set with 247 observations. To test hypotheses on this model you should use a t distribution with how many degrees of freedom?

a.) 242

b.) 120

c.) ∞

d.) 241

- A model estimated using a dataset with 125 observations generates the following results.

Variable | b | Std. Error | t | P>|t| | ||||

x_{2} |
-0.01264 | 0.005519 | -2.28937 | 0.022 | ||||

x_{3} |
0.595792 | 0.014482 | 41.13934 | 0.000 | ||||

x_{4} |
1.124589 | 0.877192 | 1.282032 | 0.200 | ||||

x_{5} |
0.323742 | 0.060709 | 5.332661 | 0.000 | ||||

Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | ||||

What are the endpoints for the 95% confidence interval for b_{3}?

a.)(-0.6842, 1.8758)

b.)(-1.3842, 2.5758)

c.)(.5672, 6245)

d.)(-40.5435 , 41.7251)

Section: 5.4

12.) A model estimated using a dataset with 65 observations generates the following results.

Variable | b | Std. Error | t | P>|t| | ||||

x_{2} |
-0.01264 | 0.005519 | -2.28937 | 0.022 | ||||

x_{3} |
0.595792 | 0.014482 | 41.13934 | 0.000 | ||||

x_{4} |
1.124589 | 0.877192 | 1.282032 | 0.200 | ||||

x_{5} |
0.323742 | 0.060709 | 5.332661 | 0.000 | ||||

Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | ||||

What are the endpoints for the 99% confidence interval for b_{5}?

a.) (0.1623, 0.4852)

b.) (-5.0089 , 5.6564)

c.) (0.2630 , 0.3845)

d.) (0.1786 , 0.4688)

Section: 5.4

14.) A model estimated using a dataset with 65 observations generates the following results.

Variable | b | Std. Error | t | P>|t| | ||||

x_{2} |
-0.01264 | 0.005519 | -2.28937 | 0.022 | ||||

x_{3} |
0.595792 | 0.014482 | 41.13934 | 0.000 | ||||

x_{4} |
1.124589 | 0.877192 | 1.282032 | 0.200 | ||||

x_{5} |
0.323742 | 0.060709 | 5.332661 | 0.000 | ||||

Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | ||||

If you want to test the hypothesis that b_{3 }=0.45, what is the test statistic from this sample?

a.) 41.139

b.)10.067

c.)31.072

d.)0.000

Section: 5.5

- A model estimated using a dataset with 125 observations generates the following results.

Variable | b | Std. Error | t | P>|t| | ||||

x_{2} |
-0.01264 | 0.005519 | -2.28937 | 0.022 | ||||

x_{3} |
0.595792 | 0.014482 | 41.13934 | 0.000 | ||||

x_{4} |
1.124589 | 0.877192 | 1.282032 | 0.200 | ||||

x_{5} |
0.323742 | 0.060709 | 5.332661 | 0.000 | ||||

Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | ||||

If you want to test the hypothesis b_{5} = .47. What p-value does this test statistic generate if you are performing a two-tailed test?

a.) 0.000

b.) ≃0.02

c.) ≃0.01

d.) 0.05

/Difficult

Section: 5.5

15.) A model estimated using a dataset with 125 observations generates the following results.

Variable | b | Std. Error | t | P>|t| | ||||

x_{2} |
-0.01264 | 0.005519 | -2.28937 | 0.022 | ||||

x_{3} |
0.595792 | 0.014482 | 41.13934 | 0.000 | ||||

x_{4} |
1.124589 | 0.877192 | 1.282032 | 0.200 | ||||

x_{5} |
0.323742 | 0.060709 | 5.332661 | 0.000 | ||||

Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | ||||

What test statistic would you use to test the hypothesis b_{5}≥.25?

a.) 1.2147

b.) 5.3327

c.) 1.2948

d.) 0.0607

Section: 5.5

16.) How can you estimate non-linear function forms using least squares?

a.) estimate the linear approximation over small ranges at a time

b.) transform, such as squaring or cubing, some explanatory variables.

c.) use a very large sample so you do not have to assume the error terms are normally distributed

d.) It cannot be done. You need to use another estimation technique.

Section: 5.6

17.) If you have the following economic model

y = b_{1} + b_{2}x – b_{3}x^{2}

What is dy/dx?

a.) b_{2}

b.) b_{3}+b_{2}

c.) b_{2} – 2b_{3}x

d.) b_{1 }+ 2b_{2}

_{ }

Section: 5.6

- You have the following economic model

** y = ****b**_{1}** + ****b**_{2}**x + ****b**_{3}**x ^{2}**

If b_{2} is positive and b_{3} is negative what is the general shape of F(x)?

a.) U-shape

b.) Inverted U

c.) Sigmoid

d.) rectangular hyperbola

Section: 5.6

- What is an interaction term?

a.) an additional variable that is the product of 2 other explanatory variables

b.) a variable indicating 2 observations are related

c.) a variable indicating an observation may be in the dataset multiple times

d.) the expected value formed by multiplying a variable by its estimated coefficient.

Section: 5.7

19.) A model estimated using a dataset with 125 observations generates the following results.

SS | df | MS | ||||||

Regression | 919587.543 | 4 | 229896.9 | |||||

Error | 2590390.62 | 121 | 534.2113 | |||||

Variable | b | Std. Error | t | P>|t| | ||||

x_{2} |
-0.0126355 | 0.005519 | -2.28937 | 0.022 | ||||

x_{3} |
0.5957923 | 0.014482 | 41.13934 | 0.000 | ||||

x_{4} |
1.124589 | 0.877192 | 1.282032 | 0.200 | ||||

x_{5} |
0.3237421 | 0.060709 | 5.332661 | 0.000 | ||||

constant | 8.86016 | 1.766116 | 5.016749 | 0.000 |

What is the R^{2} for this sample?

a.) .2620

b.) .3550

c.) .0888

d.) .2172

Section: 5.8

File: Ch06, Chapter 6, Further Inference in the Multiple Regression Model

Multiple Choice

- The following model has been estimated using a dataset with 4854 observations.

SS | df | MS | |||||||

Regression | 919587.543 | 4 | 229896.9 | ||||||

Error | 2590390.62 | 121 | 534.2113 | ||||||

Variable | b | Std. Error | t | P>|t| | |||||

x2 | -0.0126355 | 0.005519 | -2.28937 | 0.022 | |||||

x3 | 0.5957923 | 0.014482 | 41.13934 | 0.000 | |||||

x4 | 1.124589 | 0.877192 | 1.282032 | 0.200 | |||||

x5 | 0.3237421 | 0.060709 | 5.332661 | 0.000 | |||||

Constant | 8.86016 | 1.766116 | 5.016749 | 0.000 | |||||

Calculate the F-statistic to test **H _{0}: **

**b**

_{2}**=**

**b**

_{3}**=-**

**b**

_{4}**=**

**b**

_{5}**= 0**

a.) 430.35

b.) .2620

c.) 76.80

d.) 2.8169

Section: 6.1

- The critical value for a given p-value in the F-distribution depends on the degrees of freedom in the numerator and denominator. How do you find the degrees of freedom in the numerator?

a.) It is the number of observations minus the number of coefficients estimated (N-K)

b.) It is the number of hypotheses being tested simultaneously (J)

c.) It is the number of coefficients being estimated (K)

d.) It is the number of observations minus the number of hypotheses tested (N-J)

Section: 6.1

- The critical value for a given p-value in the F-distribution depends on the degrees of freedom in the numerator and denominator. How do you find the degrees of freedom in the denominator?

a.) It is the number of observations minus the number of coefficients estimated (N-K)

b.) It is the number of hypotheses being tested simultaneously (J)

c.) It is the number of coefficients being estimated (K)

d.) It is the number of observations minus the number of hypotheses tested (N-J)

Section: 6.1

- When performing an F-test, if the null hypothesis is
**H**_{0}:**b**_{2}**=****b**_{3}**= 0**what is the alternative hypothesis?

a.) b_{2} ≠0 and b_{3}≠0

b.) b_{2} ≠0 or b_{3}≠0

c.) (b_{2} ≠0 and b_{3}=0) or (b_{2} =0 and b_{3}≠0)

d.) (b_{2} <0 and b_{3}>0) or (b_{2} >0 and b_{3}<0)

Section: 6.1

- The F
_{(1,218)}distribution is equivalent to what distribution?

a.) N (1,218)

b.) F_{(2, 114)}

c.) t_{(218)}

d.) c^{2}_{(2,114)}

Section: 6.1

- What statistical test allows joint hypotheses to be tested?

a.) Breusch-Pagan Test

b.) t-test

c.) Gauss-Markov

d.) F-test

Section: 6.1

- If your computer printout includes an F-statistic and p-value for the overall model, how should you interpret the p-value?

a.) the probability that all of the coefficients are actually equal to zero

b.) the probability that all of the coefficients other than the intercept are actually zero and we would observe the estimated results

c.) the probability that the model is completely invalid

d.) the probability that the model is incorrectly specified

Section: 6.1

- Why should
__good__non-sample information be incorporated into an econometric model via restricted least squares?

a.) it reduces the variance of estimated coefficients without introducing bias

b.) it allows more precise hypotheses testing to be done

c.) it reduces the degrees of freedom in the denominator of an F-test

d.) It reduces the probability of rejecting a true null hypothesis

Section: 6.2

- How does omitting a relevant variable from a regression model affect the estimated coefficient of other variables in the model?

a.) they are biased downward and have smaller standard errors

b.) they are biased upward and have larger standard errors

c.) they are biased and the bias can be negative or positive

d.) they are unbiased but have larger standard errors

.

Section: 6.3

- How does including an irrelevant variable in a regression model affect the estimated coefficient of other variables in the model?

a.) they are biased downward and have smaller standard errors

b.) they are biased upward and have larger standard errors

c.) they are biased and the bias can be negative or positive

d.) they are unbiased but have larger standard errors

Section: 6.3

- Which of the following measures is NOT used to evaluate model specification?

a.) adj R^{2}

b.) Akiake Information Criterion (AIC)

c.) Bayesian Information Criterion (BIC)

d.) Jarque-Bera Test

Section: 6.3

- When are R
^{2}and adjusted R^{2}equal?

a.) when the model is correctly specified

b.) when K = 1

c.) when the error terms are normally distributed

d.) when an unrestricted model is estimated

Section: 6.3

- You estimate 4 different specifications of an econometric model by adding a variable each time and get the following results

R^{2} |
adj R^{2} |
AIC | ||

Model A | 0.3458 | 0.3285 | 22.56 | |

Model B | 0.3689 | 0.3394 | 22.37 | |

Model C | 0.4256 | 0.3916 | 21.21 | |

Model D | 0.4299 | 0.3911 | 21.79 | |

Which model appears to be correctly specified?

a.)A

b.)B

c.)C

d.)D

Section: 6.3

- If you reject the null hypothesis when performing a RESET test, what should you conclude?

a.) at least one of the original coefficients is not equal to zero

b.) the original model is incorrectly specified and can be improved upon

c.) relevant variable are omitted and the coefficient estimates of included variables are biased

d.) an incorrect functional form was used

(the misspecification does not have to be an omitted variable)

/Difficult

Section: 6.3

- When collinear variables are included in an econometric model coefficient estimates are

a.) biased downward and have smaller standard errors

b.) biased upward and have larger standard errors

c.) biased and the bias can be negative or positive

d.) unbiased but have larger standard errors

Section: 6.4

- When a set of variables with exact collinearity is included in an econometric model coefficient estimates are

a.) undefined

b.) unbiased

c.) biased upward

d.) biased, but the direction is unclear

Section: 6.4

- If your regression results show a high R
^{2}, adj R^{2}, and a significant F-test, but low t values for the coefficients, what is the most likely cause?

a.) omitted relevant variables

b.) irrelevant variables included

c.) collinearity

d.) heteroskedasiticity

Section: 6.4

- Running auxillary regressions where each explanatory variable is estimated as a function of eth remaining explanatory variables can help detect

a.) omitted relevant variables

b.) irrelevant variables included

c.) collinearity

d.) heteroskedasiticity

Section: 6.4

- Why is the variance of the forecast y larger than the variance of the expected value of y?

a.) the estimated forecast variance includes an estimate of ŝ^{2}

b.) the estimated forecast variance includes weighted covariance terms of all paired variables

c.) the Gauss-Markov theorem does not apply to forecast of a single observation

d.) the expected value of confidence intervals rely on the standard normal distribution while forecast use a t distribution.

Section: 6.5

Short Answer

- For what does RESET test?

- When two or more variables move together in systematic ways they are said to be ________________?

File: **Ch07, Chapter 7, Using Indicator Variables**

Multiple Choice

- Which of the following terms is NOT commonly used to refer to an indicator variable?

a.) dummy

b.) binary

c.) dichotomous

d.) digital

- Which of the following wage premia is modeled with an indicator variable that shifts the intercept?

a.) height

b.) gender

c.) education

d.) weight

Section: 7.1

- The following Mincer equation has been used to estimate wages:

ln (*Y*) = ln (*Y*_{o}) + b_{2}*EDU* + b_{3}*EXPER* + b_{4 }*EXPER*^{2} + *e*

where *Y* is income, *Y*_{0} is income of someone with no education or experience, *EDU* is years of education and *EXPER* is experience in the field. If you suspect males earn higher wages than females and that the wage difference increases with education how would you adjust the econometric model to estimate wages?

a.) include a binary variable for gender, *MALE*

b.) include an interaction term equal to *MALE* EXPER*

c.) include an indicator variable for *MALE* and one for *FEMALE*

d.) include a binary variable for *MALE* and an interaction term equal to *MALE * EXPER*

* *

Section: 7.1

- The Chow test is a specific application of a(n)

a.) z-test

b.) c^{2} test

c.) F-test

d.) t-test

Section 7.2

- A large company is accused of gender discrimination in wages. The following model has been estimated from the company’s human resource information

**ln( WAGE) = 1.439 + .0834 EDU + .0512 EXPER + .1932 MALE**

* *

Where WAGE is hourly wage, EDU is years of education, EXPER is years of relevant experience, and MALE indicates the employee is male. How much more do men at the firm earn, on average?

a.) $1.21 per hour more than females

b.) 19.32% more than females

c.) $19.32 per hour

d.) $19,320 more per year than females

Section: 7.3

[highlighted term should have a “hat” over]

- . A large company is accused of gender discrimination in wages. The following model has been estimated from the company’s human resource information

**ln( WAGE) = 1.439 + .0834 EDU + .0512 EXPER + .1932 MALE**

* *

Where WAGE is hourly wage, EDU is years of education, EXPER is years of relevant experience, and MALE indicates the employee is male. What hypothesis would you test to determine if the discrimination claim is valid?

a.) H_{0}:b_{MALE} = 0 ; H_{1}: b_{MALE} ≥ 0

b.) H_{0}:b_{MALE} = b_{EDU} = b_{EXPER }= 0 ; H_{1}: b_{MALE} ≠ 0 and b_{EDU} ≠ 0 and b_{EXPER }≠ 0

c.) H_{0}:b_{MALE} = b_{EDU} = b_{EXPER }= 0 ; H_{1}: b_{MALE} ≠ 0 or b_{EDU} ≠ 0 or b_{EXPER }≠ 0

d.) H_{0}:b_{MALE} ≤ b_{EDU} or b_{MALE }≤ b_{EXPER } ; H_{1}: b_{MALE} > b_{EDU} or b_{MALE }> b_{EXPER}

Section: 7.3

[highlighted term should have a “hat” over]

- When you have a multiple regression model with a binary dependent variable it is a __________.

a.) dichotomous model

b.) Bernoulli model

c.) Linear Probability model

d.) prediction model

Level: Easy

Section: 7.4

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise,

*MALE* = 1 if the voter is a male,

*PARTY* indicates the voter is registered with the same political party as the incumbent,

*MARRIED *= 1 for married voters, 0 otherwise, and

*KIDS *is the number of school age kids living with the voter.

What is the probability that a married female without kids who is not registered with a political party will vote for the incumbent?

a.) b_{1} + b_{4}

b.) b_{1}

c.) b_{1 }+ b_{2} + b_{3 }+ b_{5}

d.) b_{2} + b_{3} + b_{5}

Section: 7.4

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise,

*MALE* = 1 if the voter is a male,

*PARTY* indicates the voter is registered with the same political party as the incumbent,

*MARRIED *= 1 for married voters, 0 otherwise, and

*KIDS *is the number of school age kids living in the voter’s house.

How should we interpret b_{4}?

a.) the likelihood the incumbent candidate is married

b.) the percentage of married voters who vote for the incumbent

c.) the probability a married person is registered to vote

d.) the difference in probability a married voter will vote for the incumbent as opposed to an unmarried voter

Section: 7.4

- Treatment effects are
*best*estimated using data from

a.) randomized, controlled experiments.

b.) subjects that have already undergone the risky treatment.

c.) people most in need of the treatments.

d.) natural or quasi-experiments.

Section: 7.5

- Randomized, controlled experiments are needed to accurately measure treatment effects without

a.) the expense of having to treat everyone.

b.) the risk of discrimination bias.

c.) exposing everyone to untested treatments.

d.) selection bias.

Section: 7.5

- When certain characteristics cause a person to choose to be in a treatment group, selection bias can be overcome by using

a.) conditional randomization and fixed effects.

b.) difference in differences estimation.

c.) larger sample sizes.

d.) quasi-experiments.

Section: 7.5

- Treatment effects can be estimated from natural or quasi-experiments using which estimator?

a.) Restricted least squares

b.) Difference-in-differences estimator

c.) Fixed effects

d.) Quasi-Likelihood

Section: 7.5

- Which of the following variables is not necessary in order to estimate treatment effects using difference-in-differences?

a.) a treatment/control indicator

b.) pre-treatment / post-treatment indicator

c.) treatment group * treatment time interaction term

d.) post-treatment performance

Section: 7.5

- Estimating treatment effects using difference-in-differences requires what kind of data?

a.) aggregate measures over time

b.) time-series data spanning the treatment length

c.) paired, panel data

d.) cross-section spanning the treated population

Section: 7.5

- What benefit is gained by estimating treatment effects with fixed effects using panel data?

a.) it controls for unobserved, individual characteristics

b.) it controls for changes in individuals over time

c.) it allows the treatment effect to vary with the length of treatment

d.) it “fixes” the treatment to the same time for each individual

Section: 7.5

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise,

*MALE* = 1 if the voter is a male,

*PARTY* indicates the voter is registered with the same political party as the incumbent,

*MARRIED *= 1 for married voters, 0 otherwise, and

*KIDS *is the number of school age kids living in the voter’s house.

If you hypothesize males and females might have a different willingness to vote for a candidate registered with a different political party, which variable should you add to the economic model to allow you to test the hypothesis?

a.) MALE * PARTY

b.) MALE * MARRIED

c.) MARRIED * KIDS

d.) MARRIED * PARTY

Section: 7.2

- The following economic model predicts whether a voter will vote for an incumbent school board member

*INCUMBENT* = b_{1} + b_{2} *MALE* + b_{3 }*PARTY* + b_{4 }*MARRIED *+ b_{5 }*KIDS *

where

*INCUMBENT* = 1 if the voter votes for them, 0 otherwise.

*MALE* = 1 if the voter is a male.

*PARTY* indicates the voter is registered with the same political party as the incumbent.

*MARRIED *= 1 for married voters, 0 otherwise.

*KIDS *is the number of school age kids living in the voter’s house.

If you believe marriage affects male and female voters differently, which variable should you add to the economic model to allow you to test the hypothesis?

a.) MALE * PARTY

b.) MALE * MARRIED

c.) MARRIED * KIDS

d.) MARRIED * PARTY

Section: 7.2

- If you perform a Chow test to compare two regressions and reject the null hypothesis, what should you conclude?

a.) there is not sufficient evidence that the regressions are significantly different

b.) the regression equations are statistically different

c.) the regression equations are equivalent

d.) it depends on how you set up the null hypothesis

Section: 7.2

File: **Ch08, Chapter 8, Heteroskedasticity**

Multiple Choice

- Heteroskedasticity is a violation of which assumption of the MR model?

a.) The values of each x_{ik} are not random and are not exact linear functions of the other explanatory variables

b.) var(*y*_{i}.) = var(*e*_{i}) = s^{2}

c.) E(*y*_{i}) = b_{1} + b_{2}*x*_{i2} + b_{3}*x*_{i3} + ……. + b_{k}*x*_{ik}, ⟺E(*e*_{i}) = 0

d.) cov(*y*_{i}, *y*_{j}) = cov(*e*_{i}, *e*_{j}) = 0; (i≠j)

Section: 8.1

- What are the consequences of using least squares when heteroskedasticity is present?

a.) no consequences, coefficient estimates are still unbiased

b.) confidence intervals and hypothesis testing are inaccurate due to inflated standard errors

c.) all coefficient estimates are biased for variables correlated with the error term

d.) it requires very large sample sizes to get efficient estimates

Section: 8.1

- If heteroskedasticity is suspected, all of the following could be used to test for it EXCEPT

a.) Lagrange Multiplier test

b.) Jarque-Bera test

c.) Breusch-Pagan test

d.) White test

Section: 8.2

- The LM (Lagrange Multiplier) test generates a test statistic N * R
^{2}~c^{2}_{(S-1)}. Where is the R^{2 }in the test statistic measured?

a.) the original econometric model when estimated using the White correction technique

b.) the average from all the auxiliary regressions estimated with each explanatory variable as a function of the other explanatory variables

c.) the original econometric model before any test of heteroskedasticity has been performed

d.) the auxiliary regression of residuals as a function of the explanatory variables generating the heteroskedasticity

/Difficult

Section: 8.2

- The LM (Lagrange Multiplier) test generates a test statistic N * R
^{2}~c^{2}_{(S-1)}. To what does the S in this distribution refer?

a.) the number of explanatory variables in the auxiliary regression

b.) the number of explanatory variables in the initial model

c.) N-K—the degrees of freedom in econometric model of interest

d.) the statistical significance level chosen for the LM test

/Difficult

Section: 8.2

- If you run a LM test for heteroskedasiticity and reject the null hypothesis, what should you conclude?

a.) at least one coefficients in the auxiliary regression is significantly different from zero, the assumption var(*y*_{i}.) = var(*e*_{i}) = s^{2 }is unlikely to be true

b.) there is no evidence of heteroskedasticity, the assumption var(*y*_{i}.) = var(*e*_{i}) = s^{2 }is most likely true

c.) there is heteroskedasticity present and it is correctly specified as tested

d.) there is heteroskedasticity, but it is not linear in the explanatory variables

/Difficult

Section: 8.2

- Which test for heteroskedasticity should you use if you suspect different variances of the error term for different groups of observations?

a.) White test

b.) Lagrange Multiplier test

c.) Goldfeld-Quandt test

d.) Chow Test

Section: 8.2

- If you model has heteroskedastic error terms, but you do not know the functional form of the variance equation, what should be done?

a.) use White’s Robust Estimator

b.) use weighted least squares

c.) try different functional forms for the variance until the Lagrange Multiplier falls 10%

d.) add observations to the dataset and estimate again

Section: 8.3

- How should you estimate a model with heteroskedasticity when you are confident the error variance is a function of one continuous variable?

a.) WLS or GLS

b.) White Robust

c.) FGLS

d.) Quasi-Least Squares

Secton: 8.4

- When using WLS to correct for heteroskedasticity, what weight should be used?

a.) whatever weight scales all variables and creates a homoskedastic error variance

b.) the inverse of the error variance at x̄

c.) whatever weight is determined by the Goldfeld-Quandt test

d.) the residuals from the initial regression model

Section: 8.4

- If you have heteroskedasticity such that the sample can be divided into groups with each group having a different error variance, what estimation technique should be used?

a.) FGLS—feasible generalized least squares

b.) WLS—Weighted least squares

c.) White’s robust estimator

d.) log-linear least squares

Section: 8.4

- How are coefficient estimates from WLS (weighted least squares) interpreted?

a.) they must be scaled up by the weight used in order to calculate marginal effects

b.) there is no difference in interpretation since each observation is scaled by the same divisor

c.) take the inverse of the natural logarithm of the coefficient to find marginal effects

d.) They should only be used for hypothesis testing. Coefficient estimates from the un-weighted, original model should be used for prediction.

Section: 8.4/8.5

- What is the tradeoff researchers face when deciding how to deal with heteroskedasticity?

a.) Goldfeld-Quandt overstates heteroskedasticity but LM leads to more Type I errors

b.) White’s robust estimator should be used for hypothesis testing, but GLS is better for interval estimation

c.) GLS gives minimum variance, but results are more difficult to interpret

d.) White’s robust estimator requires no assumptions about the structure of the variance, but it is not as efficient as GLS estimates when the right structure is imposed on the variance

Section: 8.5

- A linear probability model is likely to violate which assumption of MR most of the time?

a.) The values of each x_{ik} are not random and are not exact linear functions of the other explanatory variables

b.) var(*y*_{i}.) = var(*e*_{i}) = s^{2}

c.) E(*y*_{i}) = b_{1} + b_{2}*x*_{i2} + b_{3}*x*_{i3} + ……. + b_{k}*x*_{ik}, ⟺E(*e*_{i}) = 0

d.) cov(*y*_{i}, *y*_{j}) = cov(*e*_{i}, *e*_{j}) = 0; (i≠j)

Section: 8.6

- (See graphs of Model A – D) The scatterplots show the estimated residuals plotted against predicted values of the dependent variable. Which model is LEAST likely to have violated the assumption var(
*y*_{i}) = var(*e*_{i}) = s^{2}?

a.) Model A

b.) Model B

c.) Model C

d.) Model D

Section: 8.1/8.2

- (See graphs of Model A – D) The scatterplots show the estimated residuals plotted against predicted values of the dependent variable. Which model is MOST likely to have violated the assumption var(
*y*_{i}) = var(*e*_{i}) = s^{2}?

a.) Model A

b.) Model B

c.) Model C

d.) Model D

Section: 8.1/8.2

- (See graphs of Model A – D) The scatterplots show the estimated residuals plotted against predicted values of the dependent variable. In which model is WLS LEAST likely to be an effective solution for the heteroskedasticity?

a.) Model A

b.) Model B

c.) Model C

d.) Model D

Section: 8.4

Short Answer

- If your initial econometric model has heteroskedastic error terms, which estimator allows unbiased coefficient estimates without imposing a structure on the heteroskedasticity?

- What test for heteroskedasticity should be used if you suspect the error terms have different variances by category?

**File: Ch09, Chapter 9, Regression With Time-Series Data: Stationary Variables**

Multiple Choice

- Which of the following is an example of a distributed lag model?

a.) y_{t} = f(x_{t}, x_{t-1}, x_{t-2}…….)

b.) y_{t} = f(y_{t-1}, x_{t}, x_{t-1}, x_{t-2}…)

c.) y_{t} = f(x_{t}, x^{2}_{t}, x^{3}_{t})

d.) y_{t} = f(x_{t}) + g(e_{t-1})

- Which of the following is an example of an autoregressive distributed lag model?

a.) y_{t} = f(x_{t}, x_{t-1}, x_{t-2}…….)

b.) y_{t} = f(y_{t-1}, x_{t}, x_{t-1}, x_{t-2}…)

c.) y_{t} = f(x_{t}, x^{2}_{t}, x^{3}_{t})

d.) y_{t} = f(x_{t}) + g(e_{t-1})

Section: 9.1

- Which model below has an autocorrelated error term?

a.) y_{t} = f(x_{t}, x_{t-1}, x_{t-2}…….)

b.) y_{t} = f(y_{t-1}, x_{t}, x_{t-1}, x_{t-2}…)

c.) y_{t} = f(x_{t}, x^{2}_{t}, x^{3}_{t})

d.) y_{t} = f(x_{t}) + g(e_{t-1})

Section: 9.1

- Which assumption is most likely to be violated with times series data:

a.) E(*e*_{t})=0

b.) var (*e*_{t})=s^{2}

c.) cov(*e*_{t}, *e*_{s}) =0, t≠s

d.) *e*_{t} N(0, s^{2})

Section: 9.1

- Finite distributed lag models are most useful for

a.) forecasting and economic policy analysis

b.) testing hypotheses and measuring economic dynamics

c.) measuring impacts and optimizing economic outcomes

d.) measuring autocorrelation and autoregressive dynamics

Section: 9.2

- How do you calculate the total multiplier for a finite distributed lag model where
*q*is the number of lags?

a.) b_{q}

b.)

c.)

d.) b_{q}– b_{0}

_{ }

Level: M

Section: 9.2

- If you use a times series data set with 100 years worth of data to estimate a distributed lag model of order 5, how many observations will you have for estimation?

a.) 100

b.) 5

c.) 95

d.) 105

/Moderate

Section: 9.2

- If you have a times series data set with 100 years worth of data that you use to estimate a distributed lag model of order 3, how many degrees of freedom will you have for hypothesis testing on estimated coefficients?

a.) 93

b.) 95

c.) 99

d.) 100

/Difficult

Section: 9.2

- When autocorrelation is present, which assumption of the linear regression model is incorrect?

a.) E(*e*_{t})=0

b.) var (*e*_{t})=s^{2}

c.) cov(*e*_{t}, *e*_{s}) =0, t≠s

d.) *e*_{t} N(0, s^{2})

Section: 9.3

- What is second order sample autocorrelation?

a.) correlation between a mean and the second moment of the sample distribution

b.) a test statistic distributed N(0, )

c.) correlation between observations that are two time periods apart

d.) correlation between the dependent variable and a squared explanatory variable

Section: 9.3

- When using the LM test for serial correlation, what is the null hypothesis?

a.) it depends on the model specification

b.) no serial correlation is present

c.) statistically significant serial correlation with the first lag

d.) statistically significant serial correlation with unspecified lag

Section: 9.4

- When performing a LM test for serial correlation, how is the test statistic distributed when the null hypothesis is true?

a.) c^{2}

b.) t_{n-1}

c.) F

d.) z

Section: 9.4

- When a lagged dependent variable is included as a regressor, we must use a weaker form of assumption TSMR2 that allows the error term to be correlated with future values of explanatory variables, but not present or past values. What implications does this weaker assumption have for our regressors?

a.) biased, but consistent

b.) unbiased, but no longer BLUE

c.) unbiased, but no longer linear

d.) biased, but with minimum variance

Section: 9.5

- What are the consequences of ignoring or failing to recognize serial correlation?

a.) biased, but consistent

b.) unbiased, but no longer BLUE

c.) unbiased, but no longer linear

d.) biased, but with minimum variance

Section: 9.5

- Which of the following is NOT true of Newey-West standard errors?

a.) allows valid inference despite the presence of serial correlation

b.) does not require knowledge of structure of serial correlation

c.) valid when estimated using stationary data

d.) always produce smaller standard error estimates, which makes them the BLUE estimator

Section: 9.5

- Which of the following is NOT a reason nonlinear least squares is used to estimate an AR(1) model?

a.) linear least squares is not possible since the transformation that allows the new error term to be uncorrelated is no longer linear in parameters

b.) using OLS to estimate the untransformed model provides incorrect standard errors

c.) the algorithmic nonlinear optimization is less complicated to compute when error terms are correlated

d.) minimizing the sum of squares of uncorrelated error terms produces an estimator that is unbiased and consistent

Section: 9.5

- Using the notation ARDL(
*p,q*) what does*p*represent?

a.) the number of lagged dependent variables included as explanatory variables

b.) the number of lagged explanatory variables included

c.) the frequency of the time series

d.) the degree or integration in the error term

Section: 9.6

- Using the notation ARDL(
*p,q*) what does*q*represent?

a.) the number of lagged dependent variables included as explanatory variables

b.) the number of lagged explanatory variables included

c.) the frequency of the time series

d.) the degree or integration in the error term

Section: 9.6

- Which of the following is not a valid criterion for choosing
*p*and*q*in an ARDL model?

a.) fewest number of lags that eliminates serial correlation

b.) statistical significance of coefficient estimates

c.) minimization of AIC and SC

d.) maximization of R^{2}

^{ }

/Moderate

Section: 9.6

- Which of the following is an ARDL (1,3) model?

a.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

b.) *y*_{t} = d + q_{1}*y*_{t-1}+ d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

c.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ *v*_{t}

d.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + *v*_{t}

_{ }

Section: 9.6

- Which of the following is an AR(3) model?

a.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

b.) *y*_{t} = d + q_{1}*y*_{t-1}+ d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

c.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ *v*_{t}

d.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + *v*_{t}

Level: Easy

Section: 9.6/9.7

- Which of the following is an ARDL(3,3) model?

a.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

b.) *y*_{t} = d + q_{1}*y*_{t-1}+ d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

c.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ *v*_{t}

d.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + *v*_{t}

Section: 9.6

- Which of the following is an ARDL(2,0) model?

*y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

*y*_{t} = d + q_{1}*y*_{t-1}+ d_{0}*x*_{t} + d_{1}*x*_{t-1}+ d_{2}*x*_{t-2}+ d_{3}*x*_{t-3 }+ *v*_{t}

*y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + d_{1}*x*_{t-1}+ *v*_{t}

d.) *y*_{t} = d + q_{1}*y*_{t-1}+q_{2}*y*_{t-2} +q_{3}*y*_{t-3} + d_{0}*x*_{t} + *v*_{t}

Section: 9.6

- AR models are primarily used for

a.) forecasting

b.) smoothing data over time

c.) policy evaluation

d.) hypothesis testing

/Moderate

Section: 9.6/9.7

- How are AR and exponential smoothing models similar?

a.) both use only previous observations of the same variable for forecasting future values

b.) both incorporate past information in the form of moving averages of multiple varaibles over time

c.) both incorporate information on current values of all relevant variables

d.) they generate forecasts with identically distributed expected values

Section: 9.7

- Which of the following is equivalent to L
^{3}*y*_{t}?

a.) *y *_{t-3}

b.) 3L^{2} *y* _{t}

c.) L*y*_{t} L^{2}*y*_{t}

d.) L*y*^{3}_{t}

_{ }

Section: 9.8

**File: Ch10, Chapter 10, Random Regressors and Moment-Based Estimation**

Multiple Choice

- If you are estimating

*y* = b_{1} + b_{2}*x* + *e*

and realize *x *and *y* are both random variables, what condition must be true for simple regression estimators to be BLUE?

a.) the data have been collected via random sampling

b.) the data are time series data

c.) *e* is normally distributed

d.) *x *is normally distributed

Section: 10.1

- Which assumption must be true when E(
*e*|*x*) = 0?

a.) E(*e*) = 0 and var(*e*) = s^{2}

b.) *e* = 0

c.) E(*e*) = 0 and cov(*x,e*) = 0.

d.) E(*e*) = *e*|*x* if *x*≠0

Section: 10.1

- If, for estimator it is true that p then is

a.) efficient

b.) consistent

c.) accurate

d.) independent

Section: 10.1

- If the assumption E(
*e*) = 0 and cov(*x*,*e*) = 0 holds, what are the implications of least squares estimators?

a.) still BLUE for all sample sizes

b.) consistent and normally distributed in very large sample sizes

c.) unbiased, but not BLUE for small samples

d.) inconsistent and parameter estimates do not converge to true values regardless of sample size.

Section: 10.1

- If the assumption that cov(
*x*,*e*) = 0 is not true, what are the implications of least squares estimators?

a.) still BLUE for all sample sizes

b.) consistent and normally distributed in very large sample sizes

c.) unbiased, but not BLUE for small samples

d.) inconsistent; parameter estimates do not converge to true values regardless of sample size.

Section: 10.1

- What does it mean for a variable to be endogenous?

a.) it is determined within the system or model

b.) it is measured after all other variables are observed

c.) it is determined outside the system or model

d.) it is measured before all other variables are observed

Section: 10.2

- Which of the following is
*not*a common cause of endogeneity?

a.) measurement error

b.) simultaneous equations

c.) omitted variables

d.) continuous variables

Section: 10.2

- What is the 4
^{th}moment of random variable*x*?

a.) E(*x*)^{4}

b.) S *x */ 4

c.) E(*x*^{4})

d.) (E(*x*^{4})-*x*^{4})/N

Section: 10.3

- Which of the following is
*not*a desirable characteristic in an instrumental variable,*z*, to be used in IV/2SLS estimation?

a.) cov (*z,e*) = 0

b.) *z* is unrelated to *y*

c.) high correlation between *z* & *x*

d.) normally distributed *z*

* *

Level: Easy/Moderate

Section: 10.3

- When an exogenous instrument is used, IV estimators are

a.) consistent and approximately normally distributed in large samples

b.) unbiased and BLUE in all sample sizes

c.) consistent if z is normally distributed

d.) normally distributed in all sample sizes and consistent in large sample sizes

Section: 10.3

- Which of the following statements is true regarding varwhen estimated by IV using
*z*as an instrument for*x*?

a.) instrumental variable estimation leads to larger variance of estimates compared to OLS

b.) instrumental variable estimation leads to smaller variance estimates compared to OLS

c.) the variance of the IV estimates can be larger or smaller than OLS, depending on r^{2}_{xz}

d.) there is no way to know which estimator leads to estimates with a larger variance, it depends on the data

Section: 10.3

- In 2SLS, how should the strength of an instrument be measured?

a.) an F-test on the first stage regression equation

b.) the p-value of the instrument’s coefficient in the second stage regression

c.) the R^{2} in the first stage regression equation

d.) an F-test on the second stage regression equation

Section: 10.3

- What is the null hypothesis when performing an F-test to test the strength of an instrument?

a.) the instrument is weak, with no q different from 0.

b.) it is a strong instrument with all q significantly different from 0.

c.) the instrument is sufficiently strong with at least 1 q significantly different from 0.

d.) the instrument is weak with all q different from 0.

Section: 10.3

- What should you conclude if you get an F-statistic of 8.3 when testing the strength of an instrument?

a.) it depends on the degrees of freedom and critical value of F

b.) do not reject H_{0}; conclude that the instrument is weak and should not be used in 2SLS.

c.) reject H_{0}; conclude the instrument is strong and proceed with 2SLS

d.) do not reject H_{0}; conclude the instrument is strong and use it in 2SLS

Sectoin: 10.3

- If L is the number of exogenous instruments and B is the number of endogenous regressors in the model, when L > B the model is

a.) just identified

b.) over identified

c.) under identified

d.) perfectly identified

Section: 10.3

- If L is the number of exogenous instruments and B is the number of endogenous regressors in the model, when L < B the model is

a.) just identified

b.) over identified

c.) under identified

d.) perfectly identified

Section: 10.3

- If L is the number of exogenous instruments and B is the number of endogenous regressors in the model, when L = B the model is

a.) just identified

b.) over identified

c.) under identified

d.) precisely identified

Section: 10.3

- What is the null hypothesis for a Hausman test for endogeneity?

a.) cov (z,x) > 0

b.) cov(x,e) > 0

c.) cov(x,e) = 0

d.) e is normally distributed

Section: 10.4

- If you reject the null hypothesis when performing a Hausman test, what should you conclude?

a.) at least one of the explanatory variables is endogenous

b.) there are no endogenous variables

c.) the 2SLS estimation has corrected the endogeneity in the initial model

d.) the 2SLS second stage equation still has endogenous variables

Section: 10.4

File: **Ch11, Chapter 11, Simultaneous Equations Models**

Multiple Choice

- In a multi-equation model the jointly determined variables are referred to as____________.

a.) exogenous

b.) explanatory

c.) regressors

d.) endogenous

Section: 11.1

- How does the least squares estimator perform on a simultaneous equation model with an endogenous regressor?

a.) unbiased and consistent in large samples

b.) unbiased but inconsistent in all sample sizes

c.) biased but consistent in large samples

d.) biased and inconsistent for structural equations, but unbiased and consistent for reduced form equations

Section: 11.1 / 11.2

- How does the least squares estimator perform on a simultaneous equation model with an endogenous regressor?

a.) unbiased and consistent in large samples

b.) biased and inconsistent in all sample sizes

c.) biased but consistent in large samples

d.) unbiased but inconsistent unless collected through random sampling

Section: 11.1

- What are reduced form equations in a system of equations?

a.) the structural equations rewritten with endogenous variables as a function of exogenous variables

b.) the structural equations without the endogenous regressors

c.) the exogenous variables reworked as a function of the other exogenous variables

d.) the equations remaining when the parameters of structural equations are reduced to generate additional degrees of freedom

Section: 11.2

- When estimating the structural parameters of simultaneous equation models, how do least squares estimates, compare to the true value of ?

a.) <

b.) >

c.) =

d.) The direction of the bias depends on the sample correlation.

.

Section: 11.3

- What estimation technique should be used to estimated parameters in an unidentified structural equation?

a.) none—no techniques exist

b.) OLS

c.) 2SLS

d.) GLS

Section: 11.4

- If a structural model has M simultaneous equations, what is the necessary condition for a unique parameter value to be consistently estimated for each variable in the equation?

a.) The number of endogenous variables excluded from the equation must be at least as large as M-1

b.) the number of endogenous variables excluded must be at least M/2

c.) the number of exogenous variables in the equation must be greater than the number of endogenous variables in the equation

d.) the sample size must be large enough to allow M * (M-1) degrees of freedom

Section: 11.4

- What does it mean for a structural equation to be unidentified?

a.) too many endogenous variables are included in the equation to estimate a unique parameter value

b.) the sample size is not large enough to rely on asymptotic estimator properties

c.) the simultaneous nature of the equations makes random samples impossible to obtain

d.) the sample size is not large enough to allow M*(M-1) degrees of freedom

/Moderate

Section: 11.4

- What does 2SLS abbreviate?

a.) twice squared linear series

b.) second summed linear sample

c.) second order stationary logical sequence

d.) two stage least squares

Section: 11.5

- What is the first stage of 2SLS?

a.) estimate parameters of reduced form equations and find predicted values

b.) find a random sample large enough to divide into 2 separate samples for the two stages

c.) estimate parameters of the structural equations using OLS

d.) use reduced form parameter estimates as explanatory variables

Section: 11.5

- What is the 2
^{nd}stage of 2SLS?

a.) estimate parameters of reduced form equations and find predicted values

b.) find a random sample large enough to divide into 2 separate samples for the two stages

c.) estimate parameters of the structural equations using predicted values from reduced form equations

d.) use reduced form parameter estimates as explanatory variables

Section: 11.5

- In a system of 4 simultaneous equations, how many endogenous variables must be excluded from an equation in the system for the parameters to be identified?

a.) 1

b.) 2

c.) 3

d.) 4

Section: 11.4

- Why is it best to use specialized software to estimate 2SLS?

a.) specialized t-values are needed for inference and hypothesis testing

b.) the t distribution is not widely available otherwise

c.) it is algebraically difficult to find structural parameter estimates from reduced form estimates, so the software needs to use specialized algorithms when algebra does not work

d.) it is too easy to make a data handling mistake when capturing predicted values to use as regressors in the second stage

/Difficult

Section: 11.5

- What are the implications for 2SLS estimators if reduced form parameter estimates are statistically insignificant?

a.) still consistent in large samples, but no longer BLUE

b.) there will be correlation in the structural equations, causing estimators to be inconsistent

c.) there are no consequences, only structural parameters matter

d.) small sample properties no longer hold, but asymptotic properties still apply

/Difficult

Section: 11.7

- In a system of M simultaneous equations, at least M-1 variables must be excluded from each equation for the equation to be identified. What does it mean if the equation is not identified?

a.) unique coefficient estimates for each variable cannot be identified using least squares

b.) the economic value of the predicted value cannot be identified

c.) the economic relationships are unclear and the equation should be dropped form the system

d.) the exogenous variables have been incorrectly identified

/Moderate

Section: 11.6

**File: Ch12, Chapter 12, Regression with Time-Series Data: Nonstationary Variables**

Multiple Choice

- How do you find the first difference in y
_{t}?

a.) y_{t}– y_{t-1}

b.) dy/ dt

c.) y_{t} –

d.) (y_{t} – ^{2}

Section: 12.1

- Which of the following is not a necessary condition for a variable to be stationary?

a.) E(y_{t}) = m

b.) var(y_{t}) = s^{2}

c.) cov(y_{t}, y_{t+s}) = cov(y_{t}, y_{t-s}) = g_{s}

d.) E(y_{t} – y_{t-1}) = p

Section: 12.1

- A stochastic process is best described as

a.) deterministic

b.) theoretical

c.) random

d.) mean reverting

Section: 12.1

- Which non-stationary time series has a constant mean but non-constant variance?

a.) random walk

b.) AR(1) with linear trent

c.) random walk with drift

d.) deterministic trend

Section: 12.1

- What is a spurious regression?

a.) statistically significant but meaningless results generated by regression analysis of non-stationary data

b.) the results generated by regression analysis of a station variable dependent on a non-stationary series

c.) regression analysis where endogenous and exogenous variables are reversed

d.) regression analysis that is impossible due to lack of identification

Level: M

Section: 12.2

- What is the null hypothesis of the Dickey-Fuller Test 1?

a.) the series is non-stationary over time

b.) the series is stationary

c.) the series is first order integrated

d.) the series are cointegrated

Level: E

Section: 12.3

- What is the null hypothesis of the Dickey-Fuller Test 2?

a.) the series is non-stationary over time

b.) the series is stationary

c.) the series is first order integrated

d.) the series are cointegrated

Level: E

Section: 12.3

- What is the null hypothesis of the Dickey-Fuller Test 2?

a.) the series is non-stationary over time

b.) the series is stationary

c.) the series is first order integrated

d.) the series are cointegrated

Level: E

Section: 12.3

- What is the difference between the Dickey-Fuller Tests 1, 2, and 3?

a.) they test for stationarity around zero, stationarity around a constant, and stationarity around a trend line, respectively

b.) they test r <1, r>1, and r=1, respectively

c.) they use t, t, and F tests, respectively

d.) they test for integration of orders 1, 2 and 3 respectively.

Section: 12.3

- Why should augmented Dickey-Fuller tests always be used when performing econometric analysis?

a.) the augmented tests allow for more degrees of freedom

b.) so we can test hypotheses using a t-distribution

c.) since no assumptions about the sign of r are needed to perform a one-tailed test

d.) to confirm that error terms are not autocorrelated

Section: 12.3

- What does it mean for a series to have a unit root?

a.) it has a constant mean equal to 1

b.) it has a constant variance equal to 1

c.) it is stationary

d.) it is integrated of order 1

Section: 12.3

- The minimum number of times a series must be differenced to generate a stationary series is the

a.) unit root

b.) order of integration

c.) trend coefficient

d.) spurious regression degree

Section: 12.3

- If series y and z have similar stochastic trends, but are otherwise unrelated, they are said to be

a.) cointegrated

b.) cotrending

c.) converging

d.) jointly stationary

Section: 12.4

14: How do you check for cointegration of two series?

a.) estimate a regression of one series as fuction of the other, then perform an augmented Dickey-Fuller test on estimated residuals

b.) estimate a regression of one as a function of the other and test the significance of the parameter estimates

c.) test the significance of the covariance between the two series

d.) subtract one series from the other and check of stationarity of the difference

Section: 12.4

- An ARDL model with nonstationary variables is a(n)

a.) error correction model

b.) VEC

c.) VAR

d.) variance decomposition

Section: 12.4

- Which of the following is a common way to convert a nonstationary series to a stationary series?

a.) first differencing

b.) cointegrating

c.) running a spurious regression

d.) estimating distributed lags

Section: 12.5

- Which of the following is a common way to convert a nonstationary series to a stationary series?

a.) detrending

b.) autoregression

c.) estimating distributed lags

d.) cointegrating

Section: 12.5

**File: Ch 13, Chapter 13, Vector Error Correction and Vector Autoregressive Models**

Multiple Choice

- What does VEC abbreviate?

a.) vector error correction

b.) variable error correction

c.) vector economic cointegration

d.) variable econometric condition

Section: 13.1

- What does VAR abbreviate?

a.) variance auto reduction

b.) vector autoregressive

c.) variance active regression

d.) vector alpha reduction

Section: 13.1

- What is the difference between a VEC and a VAR?

a.) The VAR model is for only 2 series and VEC models accommodate 3 or more variables.

b.) The VAR model is a special form of the VEC model and should be used for nonstationary series.

c.) The VEC model is a special form of the VAR and should be used with cointegrated series.

d.) The VAR model deals with stationary series while the VEC allows for dynamic series.

Section: 13.1

- When estimating a VEC model using a two step least squares process, what is the first step?

a.) use least squares to estimate the cointegrating relationship

b.) use least squares to estimate first differences as a function of estimated residuals

c.) use least squares to estimated residuals as a function of first differences

d.) use least squares to estimate first differences as a function of lagged differences

Section: 13.2

- When estimating a VEC model using a two step least squares process, what is the second step?

a.) use least squares to estimate the cointegrating relationship

b.) use least squares to estimate first differences as a function of estimated residuals

c.) use least squares to estimated residuals as a function of first differences

d.) use least squares to estimate first differences as a function of lagged differences

Section: 13.2

- In which case should a VAR model be used rather than a VEC model?

a.) the series are I(1)

b.) all series are stationary

c.) the series are not cointegrated

d.) you have more than 2 series

Section: 13.3

- Functions that show how variables adjust to shocks over time are known as

a.) adjustment functions

b.) system dynamic functions

c.) impulse response functions

d.) expansion paths

Section: 13.4

- Impulse response funcitons can be difficult to identify as a result of

a.) interdependent dynamics and unobserved data

b.) violations of the ceteris paribus assumption

c.) unobserved data and violations of the ceteris paribus assumption

d.) interdependent dynamics and innovation

Section: 13.4

- What type of model tells you whether two series are significantly related to each other?

a.) a VAR model

b.) an impulse response function

c.) variance decomposition

d.) an ARDL model

Section: 13.3

- What type of model shows how series react dynamically to shocks?

a.) a VAR model

b.) an impulse response function

c.) variance decomposition

d.) an ARDL model

Section: 13.4

- What type of model provides information about sources of volatility?

a.) a VAR model

b.) an impulse response function

c.) variance decomposition

d.) an ARDL model

Section: 13.4

**File: Ch14, Chapter 14, Time-Varying Volatility and ARCH Models**

Multiple Choice

- What does ARCH abbreviate?

a.) autoregressive conditional heteroskedastic

b.) alternative regression creating homoscedasticity

c.) all regression characteristic hierarchy

d.) abbreviated regular consistent hypothesis

Section: 14.1

- Suppose there is a series, Y
_{t}, modeled by the following three equations:

y_{t} = f + e_{t}

e_{t}|I_{t-1} N(0, h_{t})

h_{t} = a_{0} + a_{1}e^{2}_{t-1}, a_{0}>0, 0 ≤a_{1}<1

This model is classified as a(n)

a.) ARCH(1)

b.) ECM

c.) ARDL(1)

d.) VAR

Section: 14.1

- Suppose there is a series, Y
_{t}, modeled by the following three equations:

y_{t} = f + e_{t } (1)

e_{t}|I_{t-1} N(0, h_{t}) (2)

h_{t} = a_{0} + a_{1}e^{2}_{t-1}, a_{0}>0, 0 ≤a_{1}<1 (3)

Equation 2 indicates the error term is

a.) normally distributed

b.) conditionally normal

c.) bi-modally distributed

d.) binomially distributed

Section: 14.1

- When compared to a normal distribution, what does it mean for a distribution to be leptokuric?

a.) flatter around the mean and fatter tails

b.) more peaked around mean and fatter tails

c.) more peaked around mean and larger variance

d.) flatter around mean and larger variance

Section: 14.2

- What type of model is most useful for modeling volatility of financial data?

a.) VEC

b.) VAR

c.) ARCH(1)

d.) ARDL(1)

Level: Easy

Section: 14.2

- In an ARCH(1) model E(y
_{t}|x_{t-1}) has a _____________ distribution while E(y_{t}) has a ____________ distribution.

a.) leptokuric, normal

b.) binomial, leptokuric

c.) normal, binomial

d.) normal, leptokuric

Section: 14.2

- Which test is commonly performed to check for the presence of ARCH effects?

a.) Chow test

b.) Wald test

c.) LM

d.) F-test

Section: 14.3

- If you reject the null hypothesis when testing for ARCH effects, what should you conclude?

a.) the variance changes over time

b.) the variance is constant

c.) the mean is constant

d.) the mean varies over time

Section: 14.3

- How are ARCH models estimated?

a.) OLS

b.) 2SLS

c.) GLS

d.) ML

Section: 14.3

- A model with the following conditional variance function is what type of model?

h_{t}= a_{0} + a_{1}e^{2}_{t-1} + a_{2}e^{2}_{t-2} + a_{3}e^{2}_{t-3}

a.) ARCH(3)

b.) ARDL(2)

c.) ARDL(3)

d.) VAR

Section: 14.4

- In a GARCH(
*p,q*) model, what does the*p*indicate?

a.) the number of lagged *h* terms

b.) the number of lagged *e ^{2}* terms

c.) the number of endogenous variables in a system

d.) the number of excluded exogenous variables that can be instruments

Section: 14.4

- In a GARCH(
*p,q*) model, what does the*q*indicate?

a.) the number of lagged *h* terms

b.) the number of lagged *e ^{2}* terms

c.) the number of endogenous variables in a system

d.) the number of excluded exogenous variables that can be instruments

Section: 14.4

- What is the primary advantage of a GARCH model rather than an ARCH model?

a.) fewer parameters to be estimated

b.) fewer assumptions required

c.) normally distributed estimators

d.) lower variance of estimates

Section: 14.4

- What does the T in T-ARCH stand for and when is it used?

a.) threshold, used to model asymmetric effects

b.) two stage, used to model indirect effects

c.) time, used to model time varying heteroskedasticity

d.) total, used to model total variance

Section: 14.4

- What does it mean for a model to be GARCH-in-mean?

a.) the mean and variance both move over time but are independent

b.) the mean is constant but variance changes over time

c.) the mean increases while variance is constant

d.) the mean increases with the variance

Section: 14.4

**File: Ch15, Chapter 15, Panel Data Models**

Multiple Choice

- What is the primary advantage of using panel data rather than a large cross- section data set collected over time?

a.) it allow you to control for individual heterogeneity

b.) it allows the effects of legislation to be estimated

c.) it gives you more degrees of freedom

d.) it allow coefficients to vary over time

Section: 15.1

- If N is the number of individuals observed in each of T time periods, what is generally true of a “short, wide” panel?

a.) T > N

b.) N > T

c.) N = T

d.) N^{1/2 }< T^{2}

Section: 15.1

- If N is the number of individuals observed in each of T time periods, what is generally true of a “long, narrow” panel?

a.) T > N

b.) N > T

c.) N = T

d.) N^{1/2 }< T^{2}

^{ }

Section: 15.1

- What is the difference between balanced and unbalanced panels?

a.) unbalanced panels have some observations missing, balanced do not

b.) balanced panels are demographically representative of the population being studied, unbalanced are not

c.) balanced panels have an equal number of observations above and below the mean of the dependent variable, unbalanced panels are skewed

d.) a balanced panel has T = N, an unbalanced panel has N>T or N<T

Section: 15.1

- Which of the following is
*not*an estimation technique utilizing panel data? - ) a pooled model

b.) fixed effects

c.) random effects

d.) probit

Section: 15.2/ 15.3/ 15.4

- Which type of model does
*not*have a coefficient that varies with*t*or*i*?

a.) a pooled model

b.) fixed effects

c.) random effects

d.) none of these

Section: 15.2

- Which of the following assumptions must be made in order to use the pooled least squares estimator, but is relaxed in the cluster robust model?

a.) E(*e*_{it}) = 0

b.) var(*e*_{it}) = E(*e*^{2}_{it}) = s^{2}

c.) cov(*e*_{it}, *e*_{js}) = E(*e*_{it}, *e*_{js}) = 0 for i j or t s

d.) cov(*e*_{it}, *x*_{2it}) = 0, cov(*e*_{it}, *x*_{3it})

Section: 15.2

- Which of these assumptions indicates homoskedasticity?

a.) E(*e*_{it}) = 0

b.) var(*e*_{it}) = E(*e*^{2}_{it}) = s^{2}

c.) cov(*e*_{it}, *e*_{js}) = E(*e*_{it}, *e*_{js}) = 0 for i j or t s

d.) cov(*e*_{it}, *x*_{2it}) = 0, cov(*e*_{it}, *x*_{3it})

Section: 15.2

- Which of these assumptions means all error terms are uncorrelated?

a.) E(*e*_{it}) = 0

b.) var(*e*_{it}) = E(*e*^{2}_{it}) = s^{2}

c.) cov(*e*_{it}, *e*_{js}) = E(*e*_{it}, *e*_{js}) = 0 for i j or t s

d.) cov(*e*_{it}, *x*_{2it}) = 0, cov(*e*_{it}, *x*_{3it})

Section: 15.2

- Which of these assumptions means the errors are uncorrelated with all
*x*’s?

a.) E(*e*_{it}) = 0

b.) var(*e*_{it}) = E(*e*^{2}_{it}) = s^{2}

c.) cov(*e*_{it}, *e*_{js}) = E(*e*_{it}, *e*_{js}) = 0 for i j or t s

d.) cov(*e*_{it}, *x*_{2it}) = 0, cov(*e*_{it}, *x*_{3it})

Section: 15.2

- Which type of model has coefficients that vary with
*i,*but are constant with*t*?

a.) pooled model

b.) fixed effects

c.) random effects

d.) none of these

Section: 15.3

- Which type of model has coefficients that vary with
*i*and*t*?

a.) pooled model

b.) fixed effects

c.) random effects

d.) none of these

Section: 15.2/ 15.3/ 15.4

- In which model are coefficient estimates determined by variation within individuals rather than variation across individuals?

a.) pooled model

b.) fixed effects

c.) random effects

d.) none of these

Section: 15.3

- Which model is also called an error components model?

a.) pooled model

b.) fixed effects

c.) random effects

d.) none of these

Section: 15.4

- For a random effects model the least squares estimator is unbiased and consistent. The errors can be corrected for potential heterogeneity using _________________, but the estimator with minimum variance is _______________.

a.) cluster-robust standard errors, GLS

b.) White’s correction, ML

c.) 2SLS, fixed effects

d.) cluster-robust standard errors, pooled

/Difficult

Section: 15.4

- Which of the following is
*not*a reason random effects (RE) results may be preferred to fixed effects (FE) ?

a.) RE accounts for the random sampling process that generated the data

b.) RE is a GLS estimator so in large samples it has a smaller variance than FE which is a least squares estimator

c.) RE produces a coefficient for race, gender, or other individual characteristics that are constant over time

d.) RE estimates are more robust in the case of endogenous regressors

/Difficult

Section: 15.4

- How do you test for endogenous regressors, or correlation between the error term and any regressor in a random effects model?

a.) estimate coefficients with RE and FE, then perform a Hausman test of equality

b.) estimate the model capturing estimated residuals, then regress residuals on all regressors and perform an F-test

c.) estimate RE model capturing estimated residuals, then estimate coefficients of correlation with each regressor

d.) estimate RE and FE models and perform an F test on each model individually. If the difference between the F statistics is significant, conclude endogeneity.

Section: 15.5

- If you perform a Hausman test on a random effects model and have a test statistic that exceeds your critical value, what should you conclude?

a.) all of the regressors in the RE model are exogenous

b.) none of the common RE and FE coefficients are significantly different

c.) at least one of the coefficients is significantly different from zero

d.) at least one of the regressors in the RE model is endogenous

Section: 15.5

- If you perform a Hausman test on a random effects model and have a test statistic that exceeds your critical value, which of the following is
*not*correct?

a.) at least one of the regressors in the RE model is endogenous

b.) none of the common coefficient estimates in the RE model will be significantly different in the FE model

c.) FE may be the preferred estimation technique

d.) this model may be better estimated using the Hausman-Taylor estimator

Section: 15.5/ 15.6

- When should the Hausman-Taylor estimator be used?

a.) when a RE model has some endogenous regressors

b.) when FE is statistically insignificant

c.) when you do not have any information as to which regressors are endogenous

d.) when you want to estimate RE on a long, narrow data set

Section: 15.6

- Suppose you have a long, narrow panel of data and estimate a single equation with indicator variables and interaction terms for the individuals. In doing this what assumption from the pooled model have you maintained?

a.) coefficients on variables are equal across individuals

b.) errors are uncorrelated with any *x*’s

c.) expected value of errors are zero

d.) variances of error terms are equal across individuals

Section: 15.7

- Suppose you have a long, narrow panel of data and estimate a single equation with indicator variables and interaction terms for the individuals. In doing this what assumption from the pooled model have you relaxed?

a.) coefficients on variables are equal across individuals

b.) errors are uncorrelated with any *x*’s

c.) expected value of errors are zero

d.) variances of error terms are equal across individuals

Section: 15.7

- When an equation is estimated for each individual jointly, taking into account contemporaneous correlation the resulting model is a(n)

a.) Hausman-Taylor model

b.) SUR

c.) ECM

d.) VEC

Section: 15.7

**File: Ch16, Chapter 16, Qualitative and Limited Dependent Variable Models**

Multiple Choice

- When a decision maker has to choose between two mutually exclusive outcomes an econometrician may choose to use a(n)

a.) binary choice model

b.) ECM

c.) random effects model

d.) fixed effects model

Section: 16.1

- Which of the following is
*not*a problem with the linear probability model?

a.) assumes constant marginal effects

b.) generates predictions outside the (0,1) interval

c.) heteroskedastic error term

d.) coefficient estimates are biased

Section: 16.1

- When should a probit model be used?

a.) when you need a binary choice model that allows for varying marginal effects

b.) when you need to model the heteroskedasticity in the linear probability model

c.) to allow for endogenous regressors in a binary choice model

d.) to allow for multiple explanatory variables in a binary choice model

Section: 16.1

- How are choices predicted in a binary choice model?

a.)

b.)

c.)

d.)

Section: 16.1

- How is the average marginal effect calculated for a probit or logit model?

a.) taking the marginal effect at the mean of the sample

b.) mean marginal effects are always .5 in a binary choice model

c.) calculate the marginal effects for each observation, then take the mean

d.) take the mean of the marginal effects at the 5^{th} and 95^{th} percentile

Section: 16.1

- How are logit and probit models different?

a.) probit is estimated by least squares, logit by maximum likelihood

b.) probit uses the cumulative density function (cdf) of the standard normal distribution and logit uses the cdf of the logistic function

c.) logit is for binary choice models and probit is used when there are two or more choices

d.) probit allows for endogenous regressors, logit does not

Section: 16.2

- Which of the following statements is
*not*true regarding a logit model?

a.) it allows for marginal effects that vary with explanatory variables

b.) it is estimated by maximum likelihood

c.) it can be adjusted to accommodate more than 2 choice options

d.) it always generates larger marginal effects than a probit model

Section: 16.3

- When testing hypotheses of probit or logit coefficients, what 2 statistical tests are generally used?

a.) Wald and Likelihood Ratio

b.) z-test and t-test

c.) LM and Hausman

d.) F-test and R^{2}

Section: 16.2

- For which type of model does the researcher have to assume independence of irrelevant alternatives?

a.) probit

b.) multinomial logit

c.) linear probability

d.) latent variable model

Section:. 16.3

- Which model requires the assumption of independence of irrelevant alternatives?

a.) conditional logit

b.) nested logit

c.) multinomial probit

d.) mixed logit

Section: 16.4

- What is the difference between multinomial logit and conditional logit?

a.) conditional logit allows for variables to vary by individual and choice while multinomial logit only allows them to vary by individual

b.) multinomial logit allow for 3+ choices, conditional logit only accommodates 2

c.) multinomial logit is estimated with least squares, conditional logit by maximum likelihood

d.) multinomial logit has different coefficients for each choice equation, conditional logit has equal coefficients across choice equations on common variables

Section: 16.4

- Unobservable variables that enter into decisions are called

a.) latent variables

b.) endogenous variables

c.) heterogeneity

d.) count data

Section: 16.5

- What is the primary difference between ordered probit and ordered logit?

a.) ordered logit requires assumption of independence of irrelevant alternatives, ordered probit does not

b.) they make different assumptions about the distribution of coefficient estimates

c.) ordered logit allows variables to vary by choice, ordered probit does not

d.) they make different assumptions about the distribution of the error term

Section: 16.5

- For what dependent variable should a Poisson regression model be considered?

a.) satisfaction with job

b.) GPA (grade point average)

c.) number of mobile phones owned by a household

d.) level of education completed

/Difficult

Section: 16.6

- What is the difference between count data and ordered data?

a.) there is no difference, they are two names for the same thing

b.) in count data the dependent variable is an integer that represent a measurement, in ordered data it represents a rank

c.) ordered data can be continuous while count data are discrete

d.) count data indicate ranking while ordered data are categorical

Section: 16.6

- For which distribution is the mean equal to the variance?

a.) standard normal

b.) binomial

c.) Poisson

d.) chi-square

Section: 16.6

- When using least squares to estimate a model with a censored dependent variable, the results are

a.) biased and inconsistent

b.) unbiased, but not minimum variance

c.) unbiased and consistent

d.) biased but consistent

Section: 16.7

- When a substantial proportion of the observations for a dependent variable take on a limiting value, such as zero, the data are said to be

a.) truncated

b.) qualitative

c.) categorical

d.) censored

Section: 16.7

- When is a Tobit model used?

a.) when you have censored data

b.) for categorical data with a normally distributed error term

c.) when you want to combine a probit and multinomial logit

d.) to estimate varying marginal effects in a binary choice model

Section: 16.7

- What is accomplished by using a Tobit model rather than the least squares estimator?

a.) it generate unbiased and consistent estimates on censored data

b.) it corrects sample selection bias

c.) it allows for choice models to be estimated using GLS

d.) it generates the same unbiased coefficient estimates, but with smaller variances

/Difficult

Section: 16.7

- When should a Heckit model be used?

a.) when the sample was not randomly selected

b.) when the sample is small and error terms are not normally distributed

c.) as the alternative model to run a Hausman test on a Tobit model

d.) to minimize the variance of the error term when the sample selection process is suspect

/Difficult

Section: 16.7

- What type of model consists of a two stage process where the first stage is a binary choice model of sample selection and the second stage is the linear model of interest?

a.) Tobit

b.) Heckit

c.) multinomial logit

d.) probit

Section: 16.7

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