I avoided reading it because I already knew his error.
To obtain this estimate this out, consider the relationship between the log price of gold and the nominal Fed funds rate, estimated over the 1968M03-2019M02 period.
pgold = 6.423 – 10.210 fedfunds
The bold face is mine. He is missing part of that assumption, he also has to assume that we were on the gold standard during that time. He is assuming a Godot that has placed permanent, infinitely divisible markets in the gold pits. His other error, thus, is not obtaining a complete sequence, of which we have two, From the Roosevelt gold repricing to the Nixon repricing to today.
If you fix my first objection, then his set of gold prices and fund rates will both be binomial, with the fund rate as a risk equalizer. The sequence is observable by all traders, not just Menzie ex post. His target rate becomes move toward typical rate in the middle of the binomial coin flips, not the starting rate, he needs to take an N/2 root at least.
The second completes the sequence, we know the peak to peak default rate.
I do not mind his use of log as long as he has the complete sequence. Using logs simply means the traders were infinitely fast, the problem is still bounded at the boundaries.
The difference is the Lucas criteria. I did it right in the previous post.
Technically there are two rates, the interest swaps. But the probability of default so small that the other rate is close to one and gets eliminated within the bounded uncertainty. The solution is the instantenous probability of default, with a compounding charge. The longer you continuously loan gold to Treasury, the more your interest gain compounds.
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