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Giordani
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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