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Economics 120C

Winter 2012

Dr. Maria Cndido

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Student Name:_____________________________________

Student ID:________________________________________

Name of Student to your right:_______________________________________

Name of Student to your left: ________________________________________

Economics 120C Midterm Examination

Winter Quarter

February 17th

, 2012

Version A

Instructions:

a.

You have 50 minutes to finish your exam. Write your name and student ID number on theupper left corner of this page.

b. Confirm that your test has 9 pages. Make sure you find a sheet with two tables of critical

values, as well as the standard normal distribution table, in the pages of your exam. The last

page can be used as scratch paper.

c. There are two parts to this exam multiple-choice questions (Part I) and problems (Part II).

You do not need to justify your answers for the multiple-choice questions. Show ALL yourwork for the Part II questions.

d. Use a pen to write your answers. You give up your right to a regrade if you choose to use a

pencil.

e. The table below indicates how points will be allocated on the exam. You can answer the

questions in any order you like. Use your time carefully and efficiently.

f. With you, you should only have a pen, and a basic calculator.

g.

You will NOT be allowed to leave the room during the exam. Turn off your cell phone andyour IPod, and good luck!

Question Points

Part I 24

Part II

1. 24

2. 52

Exam Total 100


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PART I: Multiple-Choice Questions(4 points each, 24 points total)

You do NOT need to justify your answers for the multiple choice questions. Please, fill your answers here.

1. ________ 2. ________ 3. ________

4. _________ 5. ________ 6. ________

1) Which of the following models cannot be estimated using the OLS method?

a. Yi =

"0+ "

1X

i

3+ ui

b. ln(Yi) = "0 + "1 ln(Xi) + ui

c. Yi= "

0+ "

1X

i

"2+ u

i

d. None of the above models can be estimated by OLS.

2) Consider a competitive market where the demand and the supply depend on the current price of the good.

Then fitting a line through the quantity-price outcomes willa. give you an estimate of the demand curve.

b. estimate neither a demand curve nor a supply curve.

c. enable you to calculate the price elasticity of supply.

d. give you the exogenous part of the demand in the first stage of TSLS.

3) You plot the estimated regression function produced by the probit regression of participation in the

workforce by women on years of education. The estimated probit regression function has a stretched Sshape given that the coefficient on education is positive. Consider a probit regression function with a

negative coefficient. The shape would

a. resemble an inverted S shape (for low values of X, the predicted probability of Y = 1 would

approach 1)

b.

not exist since probabilities cannot be negativec. remain the S shape as with a positive slope coefficient

d. would have to be estimated with a logit function

4) The interpretation of the estimated slope coefficient in the model ln(Y) = "2.07+ 0.442X is as follows:

a. a 1% change inXis associated with a 0.442% change in Y.

b. a 1% change inXis associated with a change in Yof 0.01 .0.442.

c. a change inXby one unit is associated with a 44.2% change in Y.

d. a change inXby one unit is associated with a 0.442% change in Y.

5) The rule-of-thumb for checking for weak instruments is as follows: for the case of a single endogenous

regressor,a. a first stageFmust be statistically significant to indicate a strong instrument.

b. a first stageF> 1.96 indicates that the instruments are weak.

c. the t-statistic on each of the instruments must exceed at least 1.64.

d. a first stageF< 10 indicates that the instruments are weak.

6) In the probit regression, the coefficient "1on the regressor X indicates

a. the change in the probability of Y = 1 given a unit change in Xb. the change in the probability of Y = 1 given a percent change in X

c. the change in the z- value associated with a unit change in X

d. none of the above


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PART II: Problems (76 points total)

Note: Assume throughout the exam that, if not specified otherwise, the significance level for any hypothesis

test is 5%.

1) (24 points) You have data on educational attainment (S) for 540 randomly selected people. Your datasetalso has information about other characteristics such as gender, race, marital status and so on. You want to

study the determinants of educational attainment. You start by estimating the following model:

S= "0+ "

1male+ "

2black+ "

3hisp +otherfactors

where other factors include mother and fathers education, score on a standardized high school test, and

others you found relevant to explain educational attainment.

maleis a binary variable that takes the value 1 if person is a man, blackis a binary variable that takes value

1 if person is black and hispis a binary variable that takes the value 1 if the person is Hispanic.

You think more deeply about the problem and you decide instead to estimate the following regression:

S= "0 + "1male+ "2black+ "3hisp + "4 (male*black) + "5 (male* hisp) + otherfactors

a.

What is the idea behind the introduction of those two interaction terms?

b. Consider the second model:

S= "0 + "1male+ "2black+ "3hisp + "4 (male*black) + "5 (male* hisp) +otherfactors

How do you interpret the coefficients "1and "

2?

c. Consider the second model:S= "0 + "1male+ "2black+ "3hisp + "4 (male*black) + "5 (male* hisp) +otherfactors

According to this model, what is the expected gender gap in educational attainment for Hispanics(keeping all the other variables constant)?


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2) (52 points) Your textbook website has a dataset that contains information on health insurance, employment

type and other individual characteristics such as educational attainment, age, marital status, race and family

size for randomly selected workers in the US. The number of workers in your sample is 8,000. The specific

variables in the dataset are:

Variable Description

insured =1 if individual has health insurance

selfemp =1 if individual is self employed

age age in years

deg_hs =1 if highest degree obtained is a high-school degree

deg_ba =1 if highest degree obtained is a bachelor degree

deg_ma =1 if highest degree obtained is a masters degree

deg_phd = 1 if highest degree obtain is a PhD degree

familysize = number of members in the workers household

race_wh = 1 if individual is white

married = 1 if individual is married

male = 1 if individual is male

a. You start by regressing a simple regression of the binary variable insuredonselfemp. The results are

below:

Interpret the coefficient on selfemp. Is the estimated coefficient large in a real-world sense? Is it

statistically significant?


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b. You realize that the selfemployed might systematically differ from wage earners in their age,

education, family size, etc. You decide to control for those other factors and you obtain the following

regression results:

Is the result you obtained in part a. robust to adding additional control variables?

c.

How does the likelihood of being insured vary with educational achievement? Explain. What do you

think are the reasons for this relationship?

d.

How does health insurance status vary with age? In this sample, age varies between 18 and 62 years-old. Compute the difference in probability of being insured between a 60 year old and a 20-year old

(keeping all the other variables constant).


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e. You decide to add the interaction term age_self = agex selfempto the above regression. Explain the

rationale behind including this variable. The estimated coefficient for that variable is 0.0006349 with a

standard error of 0.0015196. What do you conclude?

f. Thinking about the potential problems with the linear probability model, you decide to estimate a

probit model using the same regressors as in part b. (no interaction term). According to this probit

model, does the effect ofselfempon the likelihood of having insurance depend on age? Briefly explain.

g. Below are the estimation results from your probit model:

Ms. Rosen is a 30-year old single Asian female, with no dependents. She has a college degree and she

works for a corporation. What is the chance that Ms. Rosen has health insurance?


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=======================================================================

Appendix: Tables and Formulas

=======================================================================

Large Sample Critical Values for the t-statistic from the Standard Normal

Distribution

Significance Level

10% 5% 1%

2-Sided Test 1.64 1.96 2.58

1-Sided Test (>) 1.28 1.64 2.33

1-Sided Test (


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