Econometrics Problem Set 3
Section 1
Q1: Consider any continuous outcome (or dependent) variable of interest, Yi that follows a
normal distribution. For a sample of sufficient size n, we could plot the probability density of
Yi as
Without running any regressions, which raw data relationship would we care about to
describe the variation in the outcome variable Yi?
(d) All of the above
Q2: A scatter plot takes n combinations of two random variables, Xi and Yi, and plots the
paired values in the sample as (Xi,Yi) on a two dimensional graph. Sketch a scatter plot (you
choose the direction of the correlation), and a prediction line from the model:
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Yi = β0 + β1Xi + ϵi.
(1)
Label the line of best fit by writing the prediction equation from (1). Based on the way your
graph is drawn, what is the hypothesized sign of βˆ1?
Q3: For the regression
Yi = β0 + β1Xi + ϵi.
(2)
which of the following explains variation in Yi that is predicted by the model specified above?
(e) All of the above
Q4: Consider the expression
.
When R2 → 1, it is assumed that ESS → ? (Choose 1 from below).
(c) 0
(d) ∞
(e) None of the above
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(3)
Q5: As R2 → 1, more of the variation in Yi is explained by the model. Hence the term explained
sum of squares. This implies that ESS increases as R2 increases. Why does ESS not approach
infinity? Discuss the upper limit of ESS, using words, math, or a visual sketch to explain the
decomposition of the variation in Yi.
Section 2
Consider a market for poultry in a small island nation like Costa Rica. Imagine for starters
that Costa Rica is closed to the import and export of chicken. The poultry sector employs 1215% of all Costa Ricans in any given year. The largest employer is the tourism sector, which
employs 67% of citizens.
If we wanted to estimate the supply curve for chicken production, we might try to estimate
log(quantityi) = α0 + α1log(pricei) + ϵi,
(4)
where, for each firm i:
• price : the per-pound market price of chicken in the prior month
• quantity : quantity of chicken supplied in the current month
Q6: What is the hypothesized sign for ˆα1? Given the model specification, what is the
economic interpretation of ˆα1?
Q7: From the perspective of a microeconomist, discuss the possible range of values for your
estimate ˆα1. Sketch two supply and demand diagrams to demonstrate the different ranges
of ˆα1, and explain in words what your graphs show.
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Q8: From the perspective of a macroeconomist, discuss the policy implications of Costa Rica
opening trade of poultry to the rest of the world. Assume that the world price is above the
domestic equilibrium price, and the trade relationship between Costa Rica and the US is
healthy. Use 2-3 paragraphs taking into consideration your findings in 6 &7, along with the
employment demographics mentioned in the start of this section. Use additional visuals as
you deem appropriate.
Q9: A reckless econometrician decides to estimate a complicated regression with many
additional variables that have little to do with the quantity of chicken produced in Costa Rica.
The model takes the form:
log(quantityi) = α0 + α1log(pricei) + X′β + ϵi,
(5)
where all variables are the same as equation 4, except X′β is common notation used to denote
a vector of additional variables included in the regression aside from our independent
variable of interest (price). Our coefficient of interest is ˆα1, and βˆ represents a set of
coefficients for each X variable that we are less interested in.
If the X variables have no relationship with Costa Rican chicken production, what will happen
if we use the unadjusted R2 to measure the model fit? How might we remedy this issue?
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