HW 6: Due April 11, 23:59:59
Problem 1
A researcher is interested in the effect of more secure property rights on income across countries.
He collects recent data form 60 countries and runs the OLS regression
Yi = β0 + β1Xi + ui,
where Yi is a country’s GDP per capita and Xi is an index taking values between 0 and 10 reflect-
ing the protection against expropriation where a higher value indicates greater protection against
expropriation, that is, more secure property rights.
(1) Explain why the OLS estimates are likely to be unreliable in this regression model.
(2) All of the countries in the researcher’s sample were former colonies. Institutions securing
property rights could originate from early institutions established alongside European settlements.
The decision for Europeans to settle or otherwise could reflect concerns for mortality among settlers.
Explain how settler mortality might be used as an instrument to estimate the effect of more secure
property rights on income across countries.
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Problem 2
Consider the regression model with a single regressor: Yi = β0+β1Xi+ui. Suppose the LSA#1 ∼
LSA#3 hold.
(1) Does Zi = Xi satisfy the conditions to be a valid instrument variable? (i.e., does it satisfy IV1
and IV2?)
(2) Show that the IV estimator constructed using Zi = Xi is identical to the OLS estimator.
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Problem 3
Consider a product market with a supply function:
Qsi = β0 + β1Pi + u
s
i ,
and with the demand function:
Qdi = γ0 + u
d
i ,
where usi and u
d
i are mutually independent i.i.d. random variables. Naturally, the market clears
when Qsi = Q
d
i .
(1) Are Pi and u
s
i are correlated or uncorrelated? Explain.
(2) Is OLS estimator β1 unbiased? Explain.
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Problem 4
Consider the instrumental variable regression model
Yi = β0 + β1Xi + β2Wi + ui
whereXi is correlated with ui and Zi is an instrument. Which IV assumption is NOT satisfied when:
(1) Zi is independent of (Yi, Xi,Wi)?
(2) Zi = Xi?
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Problem 5
A researcher is interested in the effect of military service on human capital. He collects data from
a random sample of 4000 workers aged 40 and runs the OLS regression
Yi = β0 + β1Xi + ui,
where Yi is a worker’s annual earnings and Xi is a binary variable that is equal to 1 if the person
served in the military and is equal to 0 otherwise.
(1) Explain why the OLS estimates are likely to be unreliable. (Hint. Which variables are omited
from the regression? Are they correlated with military service?)
(2) During the Vietnam War there was a draft in which priority for the draft was determined by
a national lottery. (The days of the year were randomly reordered 1 through 365. Those with
birthdates ordered first were drafted before those with birthdates reordered second, and so forth.)
Explain how the lottery might be used as an instrument to estimate the effect of military service
on earnings.