Professor Hayes' second response is posted here. The main gist of this response is that if one were to instrument for oil prices in the crack-ratio regressions, using natural gas prices as the instrument, then the coefficient associated with ethanol increases and becomes statistically significant.

Aaron and I have decided not write a detailed response for a number of reasons, not the least of which is that it should be clear that Professor Hayes' proposed instrument for crude oil prices---natural gas prices---violates the exclusion restriction and is therefore an INvalid instrument. Professor Hayes' most recent response may be the basis of a nice undergraduate econometrics exam question. Some proposed wording is:

1. Consider an econometric model of the crack ratio---the ratio of gasoline to oil prices. Imagine you were convinced by a scatter plot of the crack ratio to oil prices showing a clear negative relationship between the two, and therefore felt the need to control for oil prices in the econometric model. Further, suppose you were concerned that oil prices were endogenous. You consider an instrumental variables approach. Recall that a valid instrument is BOTH correlated with the endogenous regressor and uncorrelated with the residual (the latter is known as the exclusion restriction). A fellow student proposes using natural gas prices as the instrument.

A. Give at least two reasons why natural gas prices fail the exclusion restriction and are therefore an invalid instrument.
B. In response to your answer regarding violations of the exclusion restriction, your fellow student provides evidence that natural gas prices have a high first-stage F-stat---they are highly correlated. Discuss why this is not relevant to your answer in A.
C. Discuss why the estimates from a two-stage least squares regression that uses an invalid instrument are themselves invald.