ECON 599: B1,B2
Assignment #1
Due Date: Friday Feb 17* (by 4pm)
D.Young
*Assignments will be accepted without penalty until Wednesday Feb. 22 at 3pm. Only
assignments submitted by 4pm Feb 17 will be returned before the midterm. The instructor will
not be available to answer questions regarding the assignment after Feb. 17.
Question 1: 50 marks (NO MARKS will be awarded if your answers are not accompanied
by programs and output files that clearly show how your answers were obtained. Clearly
indicate where the various components of your answers can be found in your output files. NO
MARKS will be awarded if the answers to each part of the question are not written up
separately from your output files.)
Consider the following set of Euler equations that arise from a simple consumption-beta asset
pricing model for a resource-based economy:
Et [ 
U (Ct 1 )(1  rt )
 1]  0
U (Ct )
Et [ 
U (Ct 1 )( pt 1 )
 1]  0
U (Ct )( pt )
where pt = price of an exhaustible resource at time t;
U′(Ct ) = marginal utility of per capita consumption at time t;
δ = is a parameter that represents the discount factor for future utility;
rt = rate of return on a risk-free asset (such as US treasury bills) at time t;
For this assignment, we will consider the case of Chile, the world’s largest producer of copper.
Data on a few of aspects of Chile’s economy, the 3-month US treasury bill rate, and on the price
of copper (measured in US dollars) are available in a series of excel spreadsheets that have been
posted on the course web page. Information on exchange rates has not been provided, but can be
found, for example, at: http://fx.sauder.ubc.ca/data.html
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(a) First: Use these various data sources to build a quarterly data set for the following variables:
CON
= private consumption
RPLUS1
= 1 plus the rate of return on a risk-free asset
EXCH
= US / Chilean Exchange rate
PCOPUS
= Price of copper expressed in US dollars per metric tonne.
PCOPCH
= Price of copper expressed in Chilean Pesos per metric tonne.
CONPC
= private consumption per capita
GDPPC
= GDP per capita (measured in Chilean Pesos)
CLEARLY explain how each of these variables was constructed from the data provided (or that
you collected).
Then: Present a Table* of summary statistics for all of the variables constructed in (a) using the
time period for which there are no missing values for any of these variables. Clearly state the
units of measurement for each variable. Attach (on paper or via e-mail) (i) a Stata program and
associated output file and (ii) a TSP program and associated output file that reproduces the
results presented in your table.
*Report your summary statistics in a clearly labelled table of YOUR OWN design. I.e., don’t
just cut and paste output from your program,
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(c) Based on a constant relative risk aversion utility function for per capita consumption, and
using a constant, the first and second lags of the local currency resource price, the first and
second lags of per capita GDP, the first and second lags of the exchange rate, and the first and
second lags of per capita consumption as instruments, estimate and test the significance of the
parameters of the model. Test the overall model via a J test.
(i) (4 marks) Write out the formulae for the utility function and the corresponding marginal
utility function.
(ii) (14 marks) Report your parameter estimates, their standard errors, and the J test statistic in a
clearly labelled table of YOUR OWN design. Do not simply cut and paste from your output file.
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(d) Repeat (c)-(ii) using a subset of the instruments employed in (c). The subset chosen must be
large enough to allow for a valid J test of the overall model.
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(e) Compare the results from (c) and (d), either in detailed point form (using full sentences) or in
a clearly written paragraph.
Question 2: (20 marks)
Some people claim that university student abilities follow a normal distribution, and therefore final grades
for university courses should fall along ‘a curve.’ The file a1q2W12.xls contains observations on raw
(uncurved) final grades for 2 classes. Class 1 is a large introductory course that attracts a wide variety of
students. Class 2 is a 3rd year specialized course that is only taken by those majoring in the discipline.
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(a) Before looking at the data, what would be your a priori expectations on which of these classes is most
likely to have student abilities that follow a normal distribution? What distributions might be considered
for the other class (provide at least 2 distributions)? Explain the reasoning behind your answer.
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(b) For Class 1 use the method of moments to estimate the parameters of the underlying distribution,
under the assumption of normality. Then perform a test to determine whether or not abilities are normally
distributed.
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(c) For Class 2, use a reasonable candidate distributions of your choice as the basis of a test for whether or
not the data are random draws from that distribution.
FOR ALL TESTS, clearly set out all steps in the testing procedure including a clear statement of the null
hypothesis, the alternative hypothesis, the test statistic employed, the ‘critical value’ for your test, your
decision to reject or not reject, and a brief verbal interpretation of these results in the context of the
problem at hand.
Question 3: (15 marks)
Find a paper written within the past 5 years that uses a GMM estimation approach. Provide
(i) (2 marks) a full bibliographical reference for the paper;
(ii) (6 marks) a brief description of the economic problem addressed in the paper (65 to 100
words);
(iii) (4 marks) the set of population moment conditions underlying the estimation performed in
the paper;
(iv) (3 marks) the source(s) of the data used in the paper.
a 3 mark bonus will be awarded if the paper you select is not selected by anybody else in the
course
Question 4 (15 marks)
An agricultural economist has proposed two non-linear growth models for the size (weight) of
turkeys at age t:
(i)
(ii)
a Logistic model Wt = β/(1 + α exp(-γt)) + ut ;
a Richards model: Wt = β/[(1 + α exp(-γt))1/δ] + vt ;
where W is the weight of a turkey and t is a time trend (measured in days).
(a) (1 mark) What restriction(s) on the Richards model lead to a Logistic model?
(b) (4 marks) Show what the “Xo” matrix looks like for the Richards model. Clearly indicate
the exact formula for the typical element in each column of this matrix.
(c) (3 marks) Show what the “Xo” matrix looks like when evaluated at the ‘restricted’
parameter values from (a). Clearly indicate the exact formula for the typical element in
each column of the restricted Xo matrix.
(d) (4 marks) Explain in detail how you would conduct an LM test for testing the
restriction(s) in (a). Clearly show the exact form of every element in the formula for this
test statistic in the context of the specific model under consideration.
(e) (3 marks) Estimation of the Richards model yielded an estimated value of 0.003 for δ
with a corresponding standard error of 0.035. Use a Wald test to determine whether or
not a Logistic model should be used in this context.