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2017 | OriginalPaper | Buchkapitel

12. Uncertainty and Sentiment-Driven Equilibria

verfasst von : Jess Benhabib, Pengfei Wang, Yi Wen

Erschienen in: Sunspots and Non-Linear Dynamics

Verlag: Springer International Publishing

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Abstract

We construct a simple neoclassical model to capture the Keynesian idea that equilibrium aggregate supply is determined by aggregate demand and thus influenced by consumer sentiments about aggregate income. This result is nontrivial because in a standard neoclassical setting it is the aggregate supply (productive capacity) that determines aggregate demand, instead of the other way around, through factor-income shares and market-clearing mechanisms. However, we show that when firms’ production and employment decisions must be based on expectations of aggregate demand and that realized demand follows from firms’ production and employment decisions through market-clearing mechanisms, rational expectations about aggregate demand can lead to stochastic sentiment-driven equilibria despite the absence of production externalities, incomplete financial markets, strategic complementarity or any non-convexities in the model. The key is imperfect information arising naturally from the fact that production and employment decisions by firms, and consumption and labor supply decisions by households, are all made prior to goods being produced and exchanged, and before market clearing prices are realized. The sentiment-driven equilibria in our model are not based on randomizations over multiple fundamental equilibria as in many sunspot-driven business cycle models.

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Fußnoten
1
For the classical work on extrinsic uncertainty and sunspots, see Cass and Shell (1983).
 
2
In the island model where agents on each island face a signal extraction problem Lucas (1972) showed that there is a unique fundamental equilibrium as realized prices reveal the ratio of the monetary shock to the the island-specific (population) shock. In a private communication to Lucas, Jean-Michel Grandmont noted a flaw in the uniqueness proof, which is acknowledged and discussed by Lucas (1983). For an extensive follow-up analysis see Chiappori and Guesnerie (1991).
 
3
We can also interpret the preference shock as an aggregate productivity shock to the production of the aggregate final good.
 
4
See Cass and Shell (1983) for the classical case of sunspot equilibrium that is not based on randomizations over fundamental equilibria. Peck and Shell (1991) also show the existence of sunspot equilibria in a finite economy with a unique fundamental equilibrium by allowing non-Walrasian trades prior to trading on the post-sunspot spot markets. Spear (1989) shows the possibility of an equilibrium for an OLG model with two islands where sunspot driven prices in one island act as sunspots for the other and vice versa. The equilibrium in each of the two islands depend on prices on both islands with sunspot variables eliminated, and the equilibrium is non-trivially stochastic.
 
5
The correlated sentiments induce correlated optimal choices for firms to generate additional stochastic equilibria, similar to correlated equilibria in games where the introduction of correlations in players’ strategies can enlarge a game’s equilibrium possibilities beyond the set of Nash equilibria. See Aumann (1974, 1987), Maskin and Tirole (1987); Aumann et al. (1988); Peck and Shell (1991); Bergemann and Morris (2013, 2015); Bergemann et al. (2015).
 
6
At this point, since goods markets have not opened and goods prices have not yet been realized, there is no guarantee that labor demand should magically (automatically) equal labor supply. We will show, however, that in equilibrium, where the distribution of sentiments is pinned down, labor supply will always equal labor demand.
 
7
The quasi-linear utility function is assumed for simplicity without loss of generality.
 
8
In Benhabib et al. (2015), where firms that produce intermediate goods face idiosyncratic demand shocks as opposed to aggregate demand shocks, there also are sentiment-driven stochastic equilibria, but the fundamental equilibrium is always unique.
 
9
In typical calibrations \(\theta =10\) implies a markup of about 11 %.
 
10
So the sentiment equilibria collapse to the fundamental one as \(\sigma _{z}^{2}\) goes to zero. In a different context Manuelli and Peck (1994) show that in an OLG model with two islands, as in Spear (1989), that shocks to fundamentals may also act as sunspots thyat amplify fluctuations, even as these shocks get arbitrarily small.
 
11
It is easy to see that the fundamental equilibrium is not affected by sentiments: if the aggregate price depends only on the aggregate preference shock, the sentiment shocks will not affect the consumption decision of the households.
 
Literatur
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Metadaten
Titel
Uncertainty and Sentiment-Driven Equilibria
verfasst von
Jess Benhabib
Pengfei Wang
Yi Wen
Copyright-Jahr
2017
DOI
https://doi.org/10.1007/978-3-319-44076-7_12