In the regression model indeniand 131 p2iniownpricej

Question

Quistion

In the regression model In(deniand) =13₁+ p₂Iniownpricej+ 3₃1n(competitorsprice)+ u how would you interpret the coefficient )32 7

A 1% increase in my own price will lead to a ^-132/100 unit drop in demand, taking into account my competitor's reaction to my price change.

A 1% increase in my own price will lead to a ^-132/100 unit drop in demand. assuming my competitor does not change her price.

A 1% increase in my own price will lead to a ^-132 % drop in demand. taking into account my competitor's reaction to my price change. A 1% increase in my own price will lead to a ^-132 % drop in demand. assuming my competitor does not change her price.

Quistion 1 Consider the regression model y_i=j3_i-F)3₂x_i+_j3₃X_i² + Lli . In which case does this model describe an inverted U-shaped relationship between X and Y?

If I3 < 0 no matter what 132 is. ... Only ii  0 and 132 > 0 .

If 133 > 0 no matter what132 is. ... Only 413₃ > 0 and13₂ <0 .

Question 3 Consider the Laffer curve revenue = 40rate - 0.4rate² + u : expressing how total tax revenues (in trillions of dollars) vary with the average income tax rate (in percent, so rate = 30 would correspond to a 30% tax rate). If taxes are currently at 30%, what is the marginal effect on revenues of a small change in the tax rate?

Question 4

Suppose we are trying to model y as a polynomial function of x. Which of the following is NOT a valid reason to pick a fourth-order polynomial over a third-order polynomial? 0 Adding the fourth-order term improved the BIC.

0 We actually believe that y behaves according to such a model.

0 The coefficient on the fourth-order term is significant.

e The R² is higher in the fourth-order model.

Question  5

In the regression model yi =_.13i +132Xi + f33 Z+ + P4XiZi+: what does the term "+54XiZi " capture? Assume all coefficients are positive.

X and Z both have a positive influence on Y.

If Z is higher_: the expected value of Y is higher, regardless of the value of X.

c, If Z is higher, the impact of an increase in X on the expected value of Y is greater. If 2 is higher_: X also tends to be higher.

Quistion 6

In the regression model v_i=0₁+13₂x_i+,6₃z_i+)3₄x_iz_i+ Lir_i: how do we assess the significance of Zr? Using a t test for Ho: 03 = 0 .

Using two t tests_: first for Ho: )33 = 0 : and if that one doesn't reject_: also for H0: )34 = 0 . Using two t tests_: first for H0: ,6₄ = 0 . and if that one doesn't reject_: also for H0: )33 = 0 . Using an F test for H0: )33 = )34 = .

Quistion 7 Suppose that a researcher, using wage data on randomly selected male and female workers, obtains the estimated regression model wagei = 12.52 + 2.12malei + ei, where wage is measured in dollars per hour and male is a dummy variable that is equal to 1 if the person is male and 0 if the person is female. Another researcher uses the same data_: but regresses wage on female, a dummy variable that is equal to 1 if the person is female and 0 if the person is male. What are the regression estimates obtained from this regression?

wagei = 10.40 -2.12femalei + wagei = 12.52 - 2.12females + wagei = 14.64 - 2 12femalei + 0 We don't have enough information to answer this question.

Question B

Finish the following sentence_ When using dummy variables to deal with a categorical variable that takes k values, one needs to fit a model with a constant term and

• ___ one dummy variable that takes In categorical values.
• In - 1 dummy variables that take the values zero and one
• In dummy variables that take the values zero and one_
• In + 1 dummy variables that take the values zero and one_

Question 9

Let d be a dummy variable, and x a regular regressor We assume that 1/ =131+132x + 1.1 for individuals with d= 0 and V= LYl + 0'2X + U for individuals with d = 1. We are interested in testing whether both regression lines are equal, so we run the Chow test regression V= 01+ 51d + 02X + 52d • X + U Which hypothesis do we need to test in this last regression?

0 52 = O.

/³2 - ⁵2 - ⁰.

5₁=5₂ = 0.

C..) ⁵1=02 = ⁵2 = O•

Question 10

In the Chow test regression model y = 5₁ + 5₁d + 3₂ X + 5₂ d • x + Li what would it mean if 5₂ = 0 ? ci The marginal effect of x on y is equal in both groups. 0 For individuals with d= 1_: x has no effect on y.rTh If x = 0_: both groups have the same expected value for y. 0 The average values of x are equal in both groups.

Question 11

Which of the following are measures of how heavily an outlier affects the estimated regression line? DFITS.

DFBETA.

• Both of the above.

m   None of the above.

Question 12

Finish the following sentence. Multicollinearity occurs when two or more explanatory variables are highly correlated with... each other.

m   their own lags.

• ___ the error term.
• the dependent variable. Question 13

Which of the following situations causes the least squares estimators to be biased in general?

Omitted variables. Redundant variables. Both of the above. None of the above.

Question 14

Suppose the RESET test rejects its null hypothesis. What should you do?

0 Continue working with the linear model.

m  Work with the unrestricted model that was estimated for the RESET test.

m  Add the squares and cubes of all explanatory variables to the model.

m  Search for appropriate nonlinear functions to be added as regressors.

Question 15

If we wish to test whether Cov[ii,x] = 0, what is wrong with using Cov[e.x] for that purpose?

Nothing. a simple test should work fine.

• Cov[e)4] is subject to too much sampling error to be practically useful in small samples. In large enough samples. there is no problem
• Cov[eA is not informative about Cov[t.r.x], even in very large samples.

m  Sample selection bias tends to make Cov[e,x] > 0 even if Cov[u_:x] = 0 in population.

Question 16

What is the effect of endogeneity on the least squares estimators?

§  They are still unbiased. consistent_; and BLUE: we just need to adjust the degrees of freedom.

They are still unbiased and consistent_; but not BLUE.

• They are still unbiased. but not consistent.
• They become biased. and lose their consistency as well.

Question 17

Which of the following problems would be visible on a residual plot of et versus t? _tV_a Heteroskedasticity.

Autocorrelation.

0 Both of the above.

0 None of the above.

Question 18

Which of the following statements is NOT true?

c, In the presence of heteroskedasticity, we can still use our usual t and F tests, as long as we adjust the degrees of freedom.

Multicollinearity among explanatory variables makes it harder to reject null hypotheses that the true parameters in a regression are zero.

If our sample is large enough, we can be confident that the t and F statistics have approximately the correct distributions, even if the disturbance terms are not normally distributed 4. In a regression model with 25 observations and three explanatory variables other than the intercept term_: we have 21 degrees of freedom.

Question 19

How does the Central Limit Theorem help us in regression models with non-normal errors? . It doesn't.

It tells us that the distribution of the disturbance terms will tend to normal as the sample size grows.

It tells us that the distribution of t and F statistics is correct even in small samples, despite the non-normality of the disturbance terms. It tells us that the distribution of t and F statistics tends to the correct one as the sample size grows.

Question 20

How would a 0-0 plot look if the disturbance terms have a kurtosis much smaller than three_: but no skewness? _ . Points would generally fall above the line in both tails.

_ . Points would generally fall below the line in both tails.

_ . Points would generally fall above the line in the left tail_; and below the line in the right tail. Points would generally fall below the line in the left tail_; and above the line in the right tail.