Economics 421/521

Winter 2006

Homework #4

[PDF FILE]

1. Using the data set on non-borrowed bank reserves and the federal funds rate (monthly from 1959:1 – 2005:12), estimate. (a) Regress the federal funds rate on non-borrowed reserves for the entire sample. How well does the model fit? (b) Split the sample at 1982 and use a dummy variable specification to allow both the slope and the intercept to change at the break point (1959:1-1981:12 and 1982:1-2005:12). (c) Estimate a piecewise linear model with a break at 1982. (d) Which of the three models do you prefer? Can you think of any omitted variables that might bias the results? Explain.

2. Consider the following equation for the annual consumption of chicken in the United States:

Y_{t} = a +
b_{1}PC_{t} +b_{2}PB_{t}
+ b_{3}YD_{t}+
u_{t}

where, Y_{t} = per capita chicken consumption (in
pounds) in year t, PC_{t} = the price of chicken (in cents per pound) in
year t, PB_{t} = the price of beef (in cents per pound) in year t, and
YD_{t} = U.S. per capita disposable income (in hundreds of dollars) in
year t. (a) Using the data set on chicken consumption, estimate the equation
using OLS and test the hypothesis that the price of beef has a positive impact
on the per capita chicken consumption at the 10% level of significance. (b) Is
the coefficient of the per capita disposable income variable statistically
significant at the 10% level? (c) Estimate the equation without YD_{t}.
Which model do you prefer, the model with YD_{t} or the model without YD_{t}.
Why? (e) Regress on Y_{t} on PC_{t}. Is the coefficient on PC_{t}
unbiased? Explain. (f) Estimate the following equation:

lnY_{t} = a +
b_{1}lnPC_{t} +
b_{2}lnPB_{t} + b_{3}lnYD_{t}
+ u_{t}

where ln is the natural logarithm. What is the interpretation
of the coefficient on lnYD_{t}? Which model do you prefer, the linear
model or the double-log model?

3. Assume that you’ve been hired by the surgeon general of the United States to study the determinants of smoking behavior and that you estimate the following cross-sectional model based on data for 1988 from all 50 states (standard errors in parentheses):

Ĉ_{i} = 100 – 9.0E_{i} + 1.0I_{i}
-0.04T_{i} – 3.0V_{i} + 1.5R_{i
}(36.) (3.5) (.75) (0.05) (.90) (0.3)

R^{2} = .57 n = 50 (states)

where C_{i} = the number of cigarettes consumed per
day per person in the ith state, E_{i} = the average years of education
for persons over 21 in the ith state, I_{i} = the average income in the
ith state (thousands of dollars), T_{i} = the tax per package of
cigarettes in the ith state (cents), V_{i} = the number of video ads
against smoking aired on the three major networks in the ith state, and R_{i}
= the number of radio ads against smoking aired on the five largest radio
networks in the ith state. (a) Develop and test (at the 5% level) appropriate
hypotheses for the coefficients of the variables in this equation. (b) Do you
appear to have any irrelevant variables? Do you appear to have any omitted
variables? Explain. (c) Assume your answer to part (b) was yes to both. Which
problem is generally more troublesome, irrelevant variables or omitted
variables? Why? (d) One of the purposes of estimating this equation was to
determine the effectiveness of antismoking advertising on television and radio.
What is your conclusion?

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