Problem $1.[90$ pts$]($Porter $(1983))$ During the $1880$s$,$ a cartel known as the Joint Executive

Committee $($JEC$)$ controlled the rail transport of grain from the Midwest to eastern cities in the

United States. The cartel preceded the Sherman Antitrust Act of $1890,$ and it legally operated to

increase the price of grain above what would have been the competitive price. From time to time,

cheating by members of the cartel brought about a temporary collapse of the collusive price$-$setting

agreement. In this exercise, you will use variations in supply associated with the cartel$$s collapses

to estimate the elasticity of demand for rail transport of grain. The data file JEC contains weekly

observations on the rail shipping price and other factors from $1880$ to $1886.$ A detailed description

of the data is contained in JEC$\_$Description.

Suppose that the demand curve for rail transport of grain is specified as:

ln Qi $=$ $0+$ $1$ ln Pi $+$ $2$Icei $+$

$12$

j$=1$

$2+$j Seasj,i $+$ ui

where Qi is the total tonnage of grain shipped in week i$,$ Pi is the price of shipping a ton of grain

by rail, Icei is a binary variable that is equal to $1$ if the Great Lakes are not navigable because of

ice, and Seasj,i is a binary variable that captures seasonal variation in demand. Ice is included

because grain could also be transported by ship when the Great Lakes were navigable.

$1.[10$ pts$]$ Estimate the demand equation by OLS. What is the estimated value of the demand

elasticity and its standard error?

$2.[20$ pts$]$ Explain why the interaction of supply and demand could make the OLS estimator of

the elasticity biased.

$3.[10$ pts$]$ Consider using the variable Cartel as an instrumental variable for ln P $.$ Use economic

reasoning to argue whether Cartel plausibly satisfies the two conditions for a valid instrument.

$4.[20$ pts$]$ Estimate the demand equation by instrumental variable regression. What is the

estimated demand elasticity and its standard error?

$5.[30$ pts$]$ Does the evidence suggest that the cartel was charging the profit$-$maximizing monopoly

price? Explain. $($Hint: What should a monopolist do if the price elasticity is less than $1?)$

Problem $2.[110$ pts$]($Cohen and Einav $(2003))$ Traffic crashes are the leading cause of death for

Americans between the ages of $5$ and $32.$ Through various spending policies, the federal government

$1$