# A MODEL OF THE DISTRIBUTION OF PRICES1

 Publication Date 01 February 1994 DOI http://doi.org/10.1111/j.1468-0084.1994.mp56001005.x Date 01 February 1994 Author Vance L. Martin,John Creedy
OXFORD BULLETIN OF ECONOMICS AND STATISTICS. 56, 1 (1994)
0305-9049
A MODEL OF THE DISTRIBUTION OF PRICES1
John Creedy and Vance L. Martin
I. INTRODUCTION
This paper shows how the distribution of prices can be derived explicitly from
an economic model. The approach generates a generalized gamma distribu-
tion which belongs to the generalized exponential family (see Cobb, Kopp-
stein and Chen, 1983; Cobb and Zacks, 1985; and Lye and Martin, 1993a).
This distribution is extremely flexible as it contains the gamma, Rayleigh, and
exponential distribution as special cases, and is related to the generalized
gamma distribution studied by McDonald (1984). This flexibility is important
in empirical work as the use of the generalized gamma distribution provides a
consistent framework for estimating and testing alternative distributional
models. A feature of this approach is that distributional characteristics such
as skewness and kurtosis can be explicitly related to the parameters of the
economic model and thus given economic interpretations. Furthermore, it is
shown that when there are multiple equilibria, the distribution of relative
prices is multimodal: the (deterministic) stable equilibrium relative prices
correspond to the modes of the distribution whilst the (deterministic)
unstable equilibrium relative prices correspond to the antimodes of the
distribution.
The paper proceeds as follows. A simple model is introduced in Section II,
along with the introduction of stochastics. The distributional implications are
analysed in Section III. In this section, two types of distribution are distin-
guished; these are the transitional and stationary distributions respectively.
The transitional distributions provide information on the changing distribu-
tion of prices resulting from exogenous changes to the system when prices do
not adjust instantaneously. The stationary distribution describes the long-run
properties of the sequence of transitional distributions; this represents the
stochastic analogue of long-run equilibrium. Conclusions and implications of
the price distribution model are given in Section IV.
'We are grateful to the editor and a referee for helpful suggestions.
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