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Decision-Making under Strong Uncertainty: Five Applications to Sunspot Theory and neo-Schumpeterian Growth Theory

Paolo Giordani

PhD Programme in Economics
University of Rome La Sapienza, Department of Public Economics

Internal Advisor: Prof. Guido Cozzi
External Advisor: Prof. Karl Shell

March 2005

Abstract
The goal of this work is to shed some light on the role of (strong) uncertainty in the decision-making process carried out by economic agents in two distinct branches of economic theory: 'general equilibrium theory with sunspots' and 'neo-Schumpeterian growth theory'. According to the classical de'nition proposed by Frank Knight (Knight (1921)), uncertainty - as opposed to risk - refers to situations in which the decision-maker cannot assign an objective probability distribution to the ran- domness with which she is faced. The focus on those two fields is respectively motivated by the two following claims. On the one hand, sunspot theory has formalized the idea that, in some circustances, economic fundamentals are not sufficient to pin down univocally the equilibrium allocation, and that the Keynesian 'animal spirits' can eventually matter. In this framework, strong uncertainty seems a promising way to qualify purely 'extrinsic uncertainty' (that is, uncertainty not related to fundamentals), and to represent the possibility of an agent's 'fuzzy perception 'of the sunspot activity. On the other hand, in Schumpeterian growth theory, the Schumpeter's view of economic development, as spurred by incessant R&D races aimed at gaining monopoly profits, is incorporated into an Arrow-Debreu dynamic general equilibrium framework with 'measurable uncertainty' (risk). The assumption of a perfectly assessable investment horizon - that is, the idea that transparent and well-organized 'nancial markets allow savers to 'nance R&D activity in the light of an expected discounted value of future returns 'revealed'by an efficient stock market - is standard along these models. However, the innovation process is, by definition, an intrinsically uncertain economic activity. Causal empiricism suggests that investors are not generally able to evaluate exactly the expected returns from R&D activity. This idea is quite close to the Schumpeter's original view of the innovative process as the breaking of a stationary equilibrium brought about by 'resourceful' entrepreneurs and, hence, as a process characterized by some intrinsically unpredictable aspect (Schumpeter (1934) and (1939)).

The thesis is structured as follows. Preceded by an introductory chapter, the work is divided in two parts: the first part (Strong Uncertainty in Sunspot Theory) is composed of two chapters and focuses on the theoretical relationship between uncertainty and the existence of sunspot equilibria; the second part (Strong Uncertainty in neo-Schumpeterian Growth Theory) is composed of three chapters and is meant to bring about a stricter adherence to reality in the Schumpeterian framework by introducing explicitely a role for non-probabilistic uncertainty. In what follows I will briefly sum up the content of each chapter.

Chapter 0 (Decision Making under Uncertainty: a Macro User Guide) is intended to provide the basic decision-making tools useful for the next chapters. It 'rst reviews the four classical criteria under complete ignorance (Luce and Rai¤a (1958)): the 'maximin return criterion', the 'minimax regret criterion', the 'optimism-pessimism index criterion'and the Laplace's 'principle of insufficient reason'. Afterwards it gives an 'operational'introduction to the more recent axiomatic approaches to decision making under uncertainty 'rst developed by Gilboa and Schmeidler: the Choquet expected utility (CEU) theory (Schmeidler (1989)), and the maximin expected utility (MEU) theory (Gilboa and Schmeidler (1989)). Technically both of them are generalizations of the subjective expected utility (SEU) theory (de Finetti (1931), Savage(1954)), though capable of revitalizing the classical Knightian distinction.

Chapter 1 (Do Sunspots Matter under Complete Ignorance') considers a two-period, sunspot, pure-exchange economy a là Cass and Shell (1983), and analyzes the possibility that agents do not have a probabilistic knowledge of the 'sunspot activity'. Two generations, each of which is made up of identical agents, populate this economy. The participation in the Arrow securities market is restricted, and the generation, which is allowed to trade in assets, can alternatively confront the uncertainty via the 'maxmin return criterion'or the 'minimax regret criterion'. When the former is used, then sunspots do never matter. When the latter is used, sunspots can matter: in particular, I prove that, if the economy admits two Walrasian equilibria, then a unique sunspot equilibrium always exists; I pin down this equilibrium, determine the prices of the Arrow securities and show that, at these prices, no trade in securities takes place.

In Chapter 2 (Uncertainty-Averse Bank-Runners) I provide an application of the Gilboa-Schmeidler's MEU decision rule to the standard literature on 'bank runs', as started with the seminal Diamond and Dybvig (1983). I consider the banking model elaborated by Peck and Shell (2003), in which a broad class of feasible contractual arrangements is allowed and which admits a run equilibrium, and stress the assumption that depositors are uncertain of their position in the queue when expecting a run. Given MEU maximizing depositors, I prove that there exists a positive measure set of subjective prior beliefs, obtained from the minimization over the set of admissible priors, for which the bank run equilibrium disappears. The implication is that 'suspension schemes'are valuable since, in addition to improving risk-sharing among agents, they may undermine panic-driven bank runs.

In Chapter 3 (Is Strong Uncertainty Harmful for Schumpeterian Growth') I begin to explore the theoretical implications of the - rather realistic - possibility that investment decisions on R&D activity be taken under conditions of strong uncertainty on their possible returns. In the standard neo- Schumpeterian growth theory the arrival of innovation in the economy is governed by a Poisson process, whose parameter , representing the 'ow probability of innovation, is assumed to be perfectly known by investors. In the framework developed by Aghion and Howitt (1992), I remove the hypothesis of a perfectly known, and assume that neither its exact value nor a prior distribution over its potential values is known by investors when deciding upon R&D investments. The investment decision process under complete ignorance is then alternatively modeled via the four distribution-free choice criteria reviewed in chapter 0. The steady state equilibrium R&D efforts (determined under all these decision rules) reveal the direct connection between the attitude towards uncertainty of the investors and the overall economic performance. Comparative statics and welfare analysis are also carried out, and provide results in accordance with the original model. The contribution of this chapter is twofold: 'rst, it proves the robustness of the Schumpeterian theoretical framework to the investors' strong uncertainty; second, it stresses that, coeteris paribus, economies characterized by more uncertainty- seeking investors grow relatively faster than the others.

Chapter 4 (An Uncertainty-Based Explanation of Symmetric Growth in neo-Schumpeterian Growth Models) provides a re-foundation of the symmetric growth equilibrium characterizing the research sector of all vertical R&D-driven growth models. This result does not rely on the usual assumption of a symmetric expectation on the future per-sector R&D expenditure. Indeed, with this structure of expecations, returns in R&D are equalized, and agents turn out to be indi¤erent as to where targeting research: hence, the problem of the allocation of R&D investments across sectors is indeterminate. In line with the 'true'Schumpeterian perspective, I solve this indeterminacy by allowing for decision makers strictly uncertain about the future per-sector distribution of R&D e¤orts. By using the Gilboa- Schmeidler's MEU decision rule, I prove that the symmetric structure of R&D investment is the unique rational expectations (RE) equilibrium compatible with uncertainty-averse agents adopting a maximin strategy.

Finally in Chapter 5 (Uncertainty-Averse Agents in a Quality-Ladder Growth Model with Asymmetric Fundamentals), I first develop an extension of the standard symmetric quality-ladder growth model (Grossman-Helpman (1991), Segerstrom (1998) and others) to encompass an economy with asymmetric fundamentals - i.e. heterogenous quality-jumps, arrival rates and so on. The new steady- state equilibrium is shown to be characterized by an asymmetric composition of actual and expected R&D e¤orts. Since in equilibrium returns are equalized across sectors once again, the problem of inde- terminacy in the allocation of R&D investments emerges analogously to what it did in the symmetric version of chapter 4. I then allow for the agents'beliefs on the future composition of R&D efforts to be strictly uncertain, and formalize their attitude towards uncertainty once again via the MEU model. With this assumption I provide a re-foundation of the RE equilibrium, in which actual and expected R&D efforts are equal among each others, and are such that returns are equalized across sectors.

Information on the author
Paolo Giordani is Research Fellow at the European University Institute of Florence, Department of Economics. His PhD Thesis has won the SIE award for the "Best Italian PhD Thesis in Economics 2005", assigned by the Italian Economic Society (Società Italiana degli Economisti).

Contact details
Dr Paolo Giordani
Research Fellow
Department of Economics
European University Institute
Email: Paolo.Giordani@iue.it

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Additional information
This thesis is listed also in sections Economics and English.

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