Download Due Dec. 5 Homework 4 These data were collected at the Fulton

Due Dec. 5
Homework 4
These data were collected at the Fulton Fish Market in New York City to analyze a model of supply
and demand for fish. The buyers of fish in this market were restaurant owners and fried-fish stand
operators who bought fish between Monday and Friday, while the sellers received their daily stock of
fish directly from boats that caught the fish in the ocean off the coast of New York and returned to the
market. You can find the original paper, data and an accompanying data description on Kathryn Graddy’s
website (paper here and data here labeled “daily data”), but the relevant variables are available in a
.csv file on the course website.
In this homework you should use the simple Cobb-Douglas demand model
log q t = β0 + β1 log p t + δ>
d Dt + u t
(1)
where q t is total quantity sold in a day (log-quantity is qty in the data), p t is average transaction price
(log-price is price) and Dt is a vector of indicator variables denoting which day of the week it is (in
the data, columns day1 (= Monday) through day4 (= Thursday)). Wt is a vector of weather readings
that include the variables stormy and mixed. The stormy variable is an indicator that is equal to 1
when waves on the ocean near New York are greater than 4.5 feet high and wind speed is higher than
18 knots. The mixed variable is an indicator that is equal to 1 when wave height is above 3.8 feet and
wind speed is higher than 13 knots.
As a theoretical tool in your analysis of the demand equation (1), imagine that an equation linking
price and quantity supplied by fisherman is
log q t = γ1 log p t + Z t> γ2 + Wt> γ3 + vt
where Z are variables that might affect supply — Z may contain D and/or other variables.
1. For this and the next two questions, assume that endogeneity is not a problem. Estimate demand
model (1) using OLS and summarize the results in a way a non-economist could understand.
2. Estimate robust standard errors for the model and compare them to the standard errors produced
automatically by the least squares algorithm. Discuss and explain their differences or similarities
in plain English.
3. Use this estimate to conduct a test that the price elasticity of the quantity of fish demanded is
negative. Conduct your test so that it is robust to heteroskedasticity.
4. Explain why you might be worried that your estimate in part 1 could be incorrect. What feature(s)
of the model is/are the cause and what effect might this have on your estimates?
5. Discuss what makes W a good instrument for estimating this demand function. As part of your
answer, address why is important that W is in the supply equation and not the demand equation.
Check statistically that W are relevant as instruments.
6. Now re-estimate the model using two-stage least squares. Discuss the relative magnitudes of the
price elasticities you find using your two methods of estimation. Check statistically whether the
moment conditions underlying this estimation strategy seem to be satisfied.
Extra credit. Using your final estimate, test the hypothesis that there is no significant fluctuation in demand
over the days of the week. Conduct your test so that it is robust to heteroskedasticity.
1