Professor Hayes' second response is posted here.
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
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
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
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.