Yale
University
Carl Arvid Anderson Fellowship, 2002-2003
Yale Dissertation Fellowship, Spring 2002
Cowles Foundation Prize, Summer 2001
Cowles Foundation Prize, Summer 2000
Cowles Foundation Prize, Summer 1999
Yale University Fellowship, 1998-2002
University of California-Berkeley
Phi Beta Kappa, 1997
Golden Key, 1997
Summer Research Opportunity Program, Summer 1997
Dean’s List, Spring 1996
Carnegie Mellon University
NSF-Research Experience for Undergraduates, Mathematics,
Summer 1996
Stanford University
AEA Summer Economics Program, Summer 1995 |
"Pareto
Improving Taxation in Incomplete Markets," Yale University, 2003
"Welfare Impact of Financial Innovation in Incomplete Markets," Yale University,
2003
"Theory of Demand in Incomplete Markets", Yale University, 2003. Presented on
May 31, 2003 at the 12th European Workshop on General Equilibrium Theory.
"The Transfer Paradox in Incomplete Markets: Characterization and Existence with
Multiple Countries and Goods," Yale University, 2002
"Extension of the Incomplete Markets APT to Nontradeable Endowments and Multiple
Commodities," Yale University, 2002 |
Incomplete asset
markets play a central role in Macroeconomics and Finance. When asset markets are
incomplete, there are almost always many Pareto improving policy interventions, provided
there are multiple commodities and households. Remarkably, these policies do not involve
adding any new markets.
I create a framework for proving the existence of Pareto improving policy interventions,
and for computing them. The framework requires knowledge of how interventions and prices
affect aggregate, but not individual, supply and demand.
Pareto improving policy is possible without adding new markets only because intervention
causes a price adjustment, whose effect is to redistribute wealth across states, beyond
the span of the original assets. I prove that if the equilibrium price adjustment to the
intervention is itself sufficiently sensitive to risk aversion, then for almost all
utilities (risk aversions) and endowments, Pareto improving policy interventions exist,
and can be computed. I show how to verify the sensitivity of the equilibrium price
adjustment with standard demand theory, which I extend from complete to incomplete
markets.
Interventions can cause a paradoxical welfare impact along with the equilibrium price
adjustment. For example, the addition of an asset can hurt everyone, and the gift of real
commodities can hurt the recipient and help the donor. My framework shows how this
happens, and when it happens.
Chapter 1 develops the theory of demand for commodities and for assets in incomplete
markets. First, I decompose the derivative of demand with respect to commodity prices,
asset prices, and asset payoffs into an income effect matrix and a Slutsky substitution
effect matrix. Next, I identify the properties every Slutsky matrix must satisfy, and
prove conversely that any matrix satisfying these properties must be the Slutsky matrix of
some demand. Finally, I show that the Slutsky matrix can be perturbed arbitrarily, subject
only to maintaining these properties, by perturbing the second derivative (risk aversion)
of the utility generating the Slutsky matrix, while preserving demand and the income
effect matrix. These results for incomplete markets demand mirror exactly those for
complete markets demand derived by Geanakoplos and Polemarchakis (1980).
For some economies, the price adjustment function does not admit a single intervention
that makes everyone better off. By taking Slutsky perturbations of demand, I show that for
almost all nearby economies the price adjustment function does admit one. Slutsky
perturbations are thus the key to why there exist almost always Pareto improving
interventions.
Geanakoplos and Polemarchakis (1986) began the study of generic improvements with
incomplete markets, and introduced the idea of Slutsky perturbations from quadratic
utility perturbations. But since they allowed the central planner to decide the
agents’ asset portfolios, they did not need to go beyond perturbations to the Slutsky
matrices of demand in spot markets. To show why weaker interventions can improve welfare,
such as anonymous taxes and changes in asset payoffs, it is necessary to know how
agents’ decisions about their asset portfolios cause a price adjustment, and then to
perturb the Slutsky matrices of demand in asset markets as well as in spot markets. The
literature following Geanakoplos and Polemarchakis (1986) has dealt with this problem by
analyzing the first order conditions of every agent. This approach has the disadvantage
that the policymaker needs to know the second derivative of every agent’s utility. I
work at the aggregate level. In my approach the policymaker needs to know only how
interventions and prices affect aggregate demand.
My approach simplifies also the theory of equilibrium welfare. It is easier, for stressing
intuitive notions of demand theory, and shorter, for not reworking demand theory
implicitly every time.
Chapter 2 distills the reason why so many policies generically admit Pareto improving
interventions, when markets are incomplete. I formulate a model of policies, general
enough to include several types of taxation and financial innovation, and then prove the
existence of Pareto improving interventions. The sole condition on the intervention is
that the equilibrium price adjustment is sufficiently sensitive to risk aversion. I show
that various policies meet the condition, using the Slutsky perturbations from chapter 1.
These policies include (a) tax rates on asset purchases, as in Citanna, Polemarchakis, and
Tirelli (2001), (b) lump-sum taxes on present incomes plus one flat tax rate on asset
purchases, (c) asset measurable tax rates on capital gains, (d) financial innovation in an
existing asset, (e) financial innovation in a new unwanted asset, as in Elul (1995) and
Cass and Citanna (1998). I give a formula for the welfare impact of intervention,
identifying the Pareto improving interventions. My formula requires fine information about
individual marginal utilities and net trades, and about the derivative of aggregate
demand, but not individual demand, with respect to prices and intervention. To assess the
rate of Pareto improvement, I define an agent’s equilibrium insurance deficit,
which is zero when her commodity demand is as though asset markets were complete. I find
that the rate of Pareto improvement is quadratic in the insurance deficits, and affine in
the level of trade and in the proximity to price crashes.
Chapter 3 studies the transfer paradox discovered by Leontief (1936), extending the work
of Samuelson (1947), Dixit (1983) and Safra (1983) to incomplete markets and multiple
commodities. I derive a formula for the welfare impact of donations, generalizing
Dixit’s formula from two commodities to multiple commodities and incomplete markets.
The formula shows that the paradox is present only at equilibria where net trade positions
are sufficiently large and marginal propensities to demand are sufficiently different. It
quantifies how much larger the net trades need to be, the more similar the marginal
propensities to consume become. Conversely, the formula allows me to give a constructive
proof of Safra’s theorem that for any utilities, and almost every Pareto efficient
allocation, there are endowments generating the allocation as an equilibrium at which the
transfer paradox is present. |