TITLE:
A Study on Lucas’ “Expectations and the Neutrality of Money”—II
AUTHORS:
Masayuki Otaki
KEYWORDS:
Signal Extraction Problem Compatible with the Market Equilibrium; Transformation of the Joint Distribution Function; One-to-One Correspondence from the Environmental Variable to the Equilibrium Price
JOURNAL NAME:
Theoretical Economics Letters,
Vol.3 No.3,
June
7,
2013
ABSTRACT: My preceding paper on this topic (Otaki
[1]) explored whether the equilibrium existence proof in Lucas [2] is truly
complete. We showed that the proof is incomplete that some additional
conditions are required to complete the job. In this paper, we explore another
ambiguity in Lucas’s model, which has been pointed out by Grammond (see Lucas
[3]): can the model transform the joint probability density function of the
exogenous environment into one that which includes market equilibrium information?
This problem is peculiar to the signal extraction problem compatible with the
market equilibrium condition. The result indicates that although Lucas [3]
was fundamentally correct in refuting Grammond’s critique, the model contains
another crucial assumption concerning the property of the equilibrium function,
namely, one-to-one correspondence from the environmental variable to the
equilibrium price, which has not been proved by Lucas [2] to date.