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Econometrica, Vol. 68, No. 6 November, 2000 , 1541᎐1548
INDETERMINACY UNDER CONSTANT RETURNS TO SCALE IN
MULTISECTOR ECONOMIES
1
BY JESS BENHABIB, QINGLAI MENG, AND KAZUO NISHIMURA
1. INTRODUCTION
RECENTLY THERE HAS BEEN a renewed interest in indeterminacy, or alternatively put, in
the existence of a continuum of equilibria in dynamic economies that exhibit some
market imperfections.2 One of the primary concerns of this literature has been the
empirical plausibility of indeterminacy, which arises in markets with external effects or
with monopolistic competition, often coupled with some degree of increasing returns.
While the early results on indeterminacy relied on relatively large increasing returns and
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high markups, more recently Benhabib and Farmer 1996 showed that indeterminacy
can also occur in two-sector models with small sector-specific external effects and very
mild increasing returns. Nevertheless, a number of empirical researchers, refining the
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earlier findings of Hall 1990 on disaggregated US data, have concluded that returns to
scale seem to be roughly constant, if not decreasing.3 While one can argue whether the
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degree of increasing returns required for indeterminacy in Benhabib and Farmer 1996
falls within the standard errors of the recent empirical estimates, one may also inquire
whether increasing returns are at all needed for indeterminacy to arise in a plausible
manner.
In this paper we argue that in multisector models indeterminacy can arise as a type of
coordination problem, even without increasing returns, if there is a small wedge between
private and social returns. In simple one-sector models increasing returns, sustained in a
market context by external effects or monopolistic competition, can create a coordination
problem. In such a setting, if all agents were to simultaneously increase their investment
in an asset above the level associated with the initial equilibrium, the rate of return on
that asset would tend to increase, justifying the higher level of investment. In a
multisector model however, the rates of return and marginal products depend not only
on the stocks of assets, but also on the composition of output across sectors. The rate of
return on an asset can increase with the stock of the asset even in the absence of
increasing returns. For example, consider a two-sector model with a pure consumption
and a pure capital good. Increasing the relative price and hence the output of the capital
good by moving along the production possibility frontier will increase the marginal
product of the capital good if it is relatively more capital intensive. When combined with
market distortions and external effects, the consequent rise in the stock of capital may
not be enough to offset the initial increase of its marginal product. Both the stock and
the marginal product of the capital good would rise simultaneously, mimicking the effect
1We wish to thank a co-editor, Danyang Xie, and anonymous referees for very useful comments.
Support from the C. V. Starr Center for Applied Economics at New York University is gratefully
acknowledged.
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See, for example, Benhabib, and Farmer 1994 , Benhabib and Perli 1994 , Benhabib, Perli, and
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Xie 1994 , Boldrin and Rustichini 1994 , Bond, Wang, and Yip 1996 , Schmitt-Grohe 1997 , or
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Xie 1994 .
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See Basu and Fernald 1997 .
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