It is difficult to say anything about the results Allin claims. He
doesn't provide nearly enough information about his methods. It is
impossible to attempt to replicate his results. It is impossible to
evaluate the appropriateness of the procedures.
His post thus leaves one only two choices. Either accept his
conclusions on faith or refuse to do so. I cannot in good
conscience accept things on faith. So, until sufficient information
is provided, I must reject his conclusions.
I do suspect that an error has crept in somehow, somewhere. That is
because it is a simple matter of algebra that, if it were true that
Yj = Xj*exp(Uj)
then it would also be true that
Yj/Zj = (Xj/Zj)*exp(Uj).
Hence, if the labor theory of relative prices were true, the
regression coefficients would have to have the same "true" values
whichever equational form was specified and whatever Zj (not equal
to Xj or Yj) were chosen. That's what the algebra says and that's
what my simulations verify.
Andrew Kliman