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[ECON2300] Introductory Econometrics (St Lucia & external). Semester 2, 2022 ECON2300S_7260_62727

Assessment Quizzes: Problem Solving Exercises

Take Test: ECON2300 Quiz 5 (Semester 2, 2022)

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Due date: 4pm, Friday, October 21, 2022

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QUESTION 1 0.5 points Save Answer

Question Completion Status: Welcome Organisations Help

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1. Within each Factory, products are assigned randomly to

Process A or Process B.

2. Production costs for each product are recorded.

Suppose a manufacturing firm has two factories (Factory 1 and

Factory 2), and a single production process (Process A) that is used

in both factories. A new process (Process B) is developed that

potentially reduces production costs. To test whether Process B is

less costly than Process A, an experiment is designed where:

Note that resources (i.e. materials, workers, equipment) are not

reassigned across factories.

Let Yi be the cost of producing product i, let Xi be 1 if Process B is

used to produce i and 0 if Process A is used, and let Wi be 1 if

product i is produced in Factory 1 and 0 if it is produced in Factory 2.

In a regression of Yi on X, it is advisable to:

Exclude Wi as products are randomly assigned and including

Wi would increase standard errors

Exclude Wi as it is uncorrelated with Xi

Include Wi as E(ui | Xi) ≠ 0, but E(Xi | Wi) = 0

Include Wi as E(ui | Xi) ≠ 0, but E(ui | Xi, Wi) = E(ui | Wi

QUESTION 2

Continue to use the example from Question 1.

Suppose each product is randomly assigned to a process by a

computer program, but some products get reassigned on the factory

floor (for practical reasons). Let Zi denote the original assignment and

Xi the actual process used to produce i. In a regression of Yi

on Xi and Wi, OLS is:

Potentially biased because Wi should not be included

Potentially biased, but an IV regression using Zi as an

instrument can be used to obtain a consistent estimator

Unbiased because the products were randomly assigned in the

beginning

Unbiased as long as Zi is also included as a control variable

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QUESTION 3 0.5 points Save Answer

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Questions 3-6 require information from the following table.

Suppose that the Federal Government is considering a new tax on

cigarettes that is estimated to increase the retail price by $0.25 per

pack. If the current price per pack is $6.75, use the regression in

column (2) to predict the change in demand.

What is the (approximate) predicted percentage change in the

quantity of cigarettes? Report your answer as a percentage to two

decimal places without a percentage sign.

QUESTION 4

Continue to use the information in column (2) from Question 3.

Is there evidence that the instrument in this column is weak?

What is the relevant test statistic? (Report

the number as it appears in the table).

Therefore, does this suggest that the instrument is weak? (Type Yes

or No)

1 points Save Answer

a.

b.

c.

d.

QUESTION 5

For this question use information in column (3) from Question 3.

From the information provided, what can we conclude about the

exogeneity of the instruments? Use a 5% level of significance.

Both the instruments are exogenous.

Neither of the instruments are exogenous.

At least one of the instruments is exogenous.

At least one of the instruments is endogenous.

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a.

b.

c.

d.

QUESTION 6

For this question use information in column (2) of question 3.

Can you test for the exogeneity of the instrument in this model?

Yes, I can use a t-test.

I don't need to test, instruments are always exogeneous.

Yes, I can use a J-test, even if it is not reported in the table.

No, in order to test for exogeneity, the model must be

overidentified, with the number of instruments strictly larger

than the number of endogenous variables.

0.5 points Save Answer

a.

b.

c.

d.

e.

f.

QUESTION 7

Estimation of the IV regression model:

is possible if the number of instruments is equal to the

number of endogenous variables.

is possible if the model is over-identified.

is possible if the number of instruments is larger than the

number of endogenous variables.

is possible if there is exact identification.

All of the above.

None of the above.

0.5 points Save Answer

a.

b.

c.

d.

e.

f.

QUESTION 8

Which one of the following statements is true:

If E(u|X)≠ 0, OLS is an inconsistent estimator.

If E(u|Z)=0 and Corr(X,Z)≠ 0, then Z is a valid instrument.

If E(u|X)=0, you don’t need to look for instruments.

If E(u|X)≠ 0 and Corr(X,Z) = 0, then Z is not a valid

instrument.

All of the above.

None of the above.

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a.

b.

c.

d.

e.

f.

QUESTION 9

When calculating the TSLS estimator:

you regress X on Z and then Y on the predicted values of the

first regression.

you regress X on Z and then Y on Z.

you regress Y on X and then regress Y on Z.

you regress Z on X and then Y on the predicted values of the

first regression.

you regress Y on Z and then X on the predicted values of Y.

None of the above.

0.5 points Save Answer

a.

b.

c.

d.

e.

f.

QUESTION 10

Having many relevant instruments:

is good because they provide more information.

leads to underidentification.

typically results in larger standard errors for the TSLS

estimator.

means that we will have more than one first stage regression.

All of the above.

None of the above.

0.5 points Save Answer

a.

b.

c.

d.

e.

f.

QUESTION 11

Assume that data are available on other characteristics of the

subjects that are relevant to determining the randomized

experimental outcome. Then not including these determinants

explicitly results in:

the limited dependent variable model.

omitted variable bias.

the multiple regression model.

large scale equilibrium effects.

All of the above.

None of the above.

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a.

b.

c.

d.

e.

f.

QUESTION 12

Causal effects that depend on the value of an observable variable,

say W : i

cannot be estimated.

can be estimated by interacting the treatment variable

with W .i

result in the OLS estimator being inefficient.

requires use of homoskedasticity-only standard errors.

All of the above.

None of the above.

0.5 points Save Answer

a.

b.

c.

d.

e.

f.

QUESTION 13

In the context of a controlled experiment, consider the simple linear

regression formulation Y = β + β X + u . Let the Y be the

outcome, X the treatment level when the treatment is binary,

and u contain all the additional determinants of the outcome. Then:

i 0 1 i i i

i

i

the OLS estimator of the slope will be inconsistent in the

case of a randomly assigned X since there are omitted

variables present.

i

X and u will not be independently distributed if the X are

randomly assigned.

i i i

β represents the causal effect of X on Y when X is zero.0

E(Y|X= 1) is the expected value for the treatment group.

All of the above.

None of the above.

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