SUMMER TERM 2021
DEPARTMENTALLY ARRANGED 24-HOUR ONLINE EXAMINATION COVER SHEET
ECON0019 QUANTITATIVE ECONOMICS AND ECONOMETRICS
ASSESSMENT COMPONENT: 40% 24-hour online examination
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SUMMER TERM 2021
DEPARTMENTALLY ARRANGED 24-HOUR ONLINE EXAMINATION
ECON0019: QUANTITATIVE ECONOMICS AND ECONOMETRICS
Answer BOTH questions.
1. In “Does Trade Cause Growth?” (American Economic Review, 1999), Je↵rey Frankel and David
Romer study the e↵ect of trade on income. Their simple specification is
log Yi = ↵+ Ti + Wi + "i,
where Yi is per capita income of country i, Ti is international trade, Wi is within-country trade,
and "i reflects other determinants of income. Since "i is likely to be correlated with the trade
variables, Frankel and Romer decide to use instrumental variables to estimate the coecients
and . As instruments, they use a measure of country’s geographic position (its proximity to
other countries) Pi and the country size Si.
(a) Explain in detail (step by step) how one can construct the instrumental variable estimates
ˆ and ˆ when one has data on Yi, Ti, Wi, Pi, and Si for a random sample of countries.
(b) Provide formal conditions for these estimates to be consistent. Which of them can be tested?
(c) Explain the economic intuition why the conditions from Question 1(b) may be satisfied in
this context. Also give at least one economic justification why at least one of them may be
(d) Suppose that, unfortunately, data on within-country trade Wi are not available. In order
to be able to estimate , the researchers add another assumption (on top of those you
proposed in item (b)): that Wi follows the model
Wi = ⌘ + Si + ⌫i,
and Pi is uncorrelated with ⌫i. Explain in detail (step by step) how one can estimate
from the data on Yi, Ti, Pi, and Si only and why that estimator will be consistent.
ECON0019 1 TURN OVER
(e) Suppose now it is known that = 0. Further, the true e↵ects of international trade on
income are heterogeneous across countries, denoted i, such that the true model for per
capita income is
log Yi = ↵+ iTi + "i.
Suppose the researchers estimate the regression of log Yi on Ti (and a constant), using Pi
as the single instrument. Under what condition would they asymptotically recover the
average causal e↵ect E[i]? Provide an economic justification for why this condition may
be violated in this context. Explain how to interpret the estimand of this IV procedure in
that case and the direction in which it may di↵er from the average causal e↵ect.
2. The transmission of human capital across generations has drawn attention for many decades
in Economics. Mikael Linhdahl, Marten Palme, Sofia Sadgren-Massih and Anna Sjogren (“A
Test of the Becker-Tomes Model of Human Capital Transmission Using Microdata on Four
Generations”, Journal of Human Capital, 2014) use Swedish data to examine this question
across several generations employing years of schooling as a measure for human capital.
(a) A simple version for the model entertained in their article, focussing on particular family,
St = 0 + 1St1 + Et
where St is years of schooling for generation t and Et is “ability” for that generation. As-
sume that |1| < 1 so that stationarity and weak dependence hold. How would you test
whether Et is serially correlated in this particular context?
(b) Their model also postulates that ability is transmitted across generations according to:
Et = ↵0 + ↵1Et1 + Vt.
Assume that Vt is iid across generations, with mean zero and variance given by 2 > 0. If
↵1 6= 0 is contemporaneous exogeneity satisfied? Justify your answer. If one has data on
T generations, suggest a consistent estimator for ↵1 ⇥ 1 and a test for the null hypothesis
that ↵1 ⇥ 1 = 0. Explain your answer.
(c) Assume now that one has data on a cross-section with only two generations (“parent”
and “child”). Suppose that the data on years of schooling for the child only provides the
number of years when those are less than 12 years and, otherwise, one can only know that
an individual had 12 or more years of schooling. The data on years of schooling for the
parent is nonetheless complete, i.e., one observes the number of schooling years without the
restriction above. Let HEC be equal to 1 if the child has 12 or more years of education, and
ECON0019 2 CONTINUED
zero otherwise. Denote by SP the years of schooling for the parent. Consider the following
HEC = 1(0 + 1 lnS
P + U 0).
Assume that U ⇠ N (0, 1) and notice that the regressor is the logarithm of SP . Write down
the log-likelihood function for the model above and a random sample of N families. How
would you estimate
E[@P(HEC = 1|SP )/@SP ]?
(d) Under the data scenario above (i.e., years of schooling for the child is censored at 12 years),
let SC be the child’s years of schooling. A friend is interested in the following regression:
SC = 0 + 1S
P + E
using this cross-sectional data. She suggests using only the uncensored observations (i.e.,
those for which SC < 12) and estimate the regression above with OLS. Will the estimator
consistently estimate 0 and 1? Explain your answer.
(e) Still on the regression from question 2(d), another friend instead suggests using a selection
model to estimate 0 and 1. Explain how you would construct such an estimator in this
ECON0019 3 END OF PAPER学霸联盟