(a) Estimate the price elasticity of demand by using OLS to regress the log of the quantity of grain shipped on the log of the price and the full set of monthly binary indicators. What is the estimated value of the demand elasticity and its standard error? (b) Explain why the interaction of supply and demand could make the OLS estimator of the elasticity obtained in (a) biased. (c) Consider using the variable cartel as instrumental variable for In(P). Use economic reasoning to argue whether cartel plausibly satisfies the two conditions for a valid instrument. (d) One of the reasons for price fluctuations was that the Great Lakes periodically froze, making shipping grain by boat impossible and temporarily increasing the demand for rail. Ice; is a binary variable that is equal to 1 if the Great Lakes are not navigable because of ice. Consider using the variable Ice as instrumental variable for In (P). Use economic reasoning to argue whether Ice plausibly satisfies the two conditions for a valid instrument