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Department of Economics
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RESEARCH
ABSTRACTS (BY TOPIC) To
return to the main page, click here COMPARATIVE STATICS Beyond Correlation: Measuring Interdependence Through
Complementarities with Margaret Meyer Given two sets
of random variables, how can one determine whether the former variables are more
interdependent than the latter? This question is of major importance to
economists, for example, in comparing how various policies affect systemic
risk or income inequality. Moreover, correlation is ill-suited to this task
as it is typically not justified by any economic objective. Economists'
interest in interdependence often stems from complementarities (or substitutabilities) in the environment they analyze. This
paper studies interdependence using supermodular objective functions: these
functions treat their variables as complements, and their expectation
increases as the realizations of the variables become more aligned. The
supermodular ordering has a linear structure, which we exploit to obtain
tractable characterizations and methods for comparing multivariate
distributions, and extend when objective functions are also monotonic or
symmetric. We also provide sufficient conditions for comparing random
variables generated by common and idiosyncratic shocks or by heterogeneous
lotteries, and illustrate our methods with several applications. Discounting,
Values, and Decisions with
John Quah,
Journal of Political Economy, October 2013 How do
discount rates affect agents' decisions and valuations? This paper provides a
common methodology and a systematic analysis of this question, considering stochastic
and managed cash-flows, stochastic discount rates, time inconsistency, and
including arbitrary learning and payoff or utility processes. We show that
some of these features can lead to counter-intuitive answers (e.g., “a more
patient agent stops earlier”), but we also establish, under simple
conditions, theorems yielding robust and unifying answers on the impact of
discount rates on control and stopping decisions and on valuations. We apply
our theory to models of search, experimentation, bankruptcy, optimal growth,
investment, and social learning. Aggregating the Single Crossing Property with John Quah, Econometrica, September 2012. The single
crossing property plays a crucial role in economic theory, yet there are
important instances where the property cannot be directly assumed or easily
derived. Difficulties often arise because the property cannot be aggregated:
the sum or convex combination of two functions with the single crossing
property need not have that property. We introduce a new condition
characterizing when the single crossing property is stable under aggregation,
and also identify sufficient conditions for the preservation of the single
crossing property under multidimensional aggregation. We use our results to
establish properties of objective functions (convexity, logsupermodularity),
the monotonicity of optimal decisions under uncertainty, and the existence of
monotone equilibria in Bayesian games. Increasing
Interdependence of Multivariate Distributions with Meg Meyer, Journal
of Economic Theory, Symposium on Inequality and Risk, July 2012. Orderings of
interdependence are useful in many economic contexts: in assessing ex post
inequality under uncertainty; in comparing multidimensional inequality; in
valuing portfolios of assets or insurance policies; and in assessing systemic
risk. We explore five orderings of interdependence for multivariate
distributions: greater weak association, the supermodular ordering, the
convex-modular ordering, the dispersion ordering, and the concordance
ordering. For two dimensions, all five are equivalent, whereas for three
dimensions, the first four are strictly ranked and the last two are
equivalent, and for four or more dimensions, all five are strictly ranked.
For the special case of binary random variables, we establish some
equivalences among the orderings. Generalized Monotonicity Analysis with Thomas Weber, Economic Theory, June 2010 Complex economic
models often lack the structure for the application of standard techniques in
monotone comparative statics. Generalized Monotonicity Analysis (GMA) extends
the available methods in several directions. First, it provides a way of
finding parameter moves that yield monotonicity of model solutions. Second,
it allows studying the monotonicity of functions or subsets of variables.
Third, GMA naturally provides bounds on the sensitivity of variables to
parameter changes. Fourth, GMA may be used to derive conditions under which
monotonicity obtains with respect to functions of parameters, corresponding
to imposed parameter moves. Fifth, GMA contributes
insights into the theory of comparative statics, for example, with respect to
dealing with constraints or exploiting additional information about the model
structure. Several applications of GMA are presented, including constrained
optimization, non-supermodular games, aggregation, robust inference, and
monotone comparative dynamics. Comparative Statics, Informativeness, and the Interval Dominance Order
with John Quah, Econometrica, November 2009. We identify a
natural way of ordering functions, which we call the interval dominance order
and develop a theory of monotone comparative statics based on this order.
This way of ordering functions is weaker than the standard one based on the
single crossing property (Milgrom and Shannon,
1994) and so our results apply in some settings where the single crossing
property does not hold. For example, they are useful when examining the
comparative statics of optimal stopping time problems. We also show that
certain basic results in statistical decision theory which are important in
economics - specifically, the complete class theorem of Karlin
and Rubin (1956) and the results connected with Lehmann’s (1988) concept of Informativeness - generalize to payoff functions obeying
the interval dominance order. DECISION THEORY From Anticipations to
Present Bias: A Theory of Forward-Looking Preferences with Simone Galperti
Forward-looking
agents are influenced by their future well-being and preferences, but how
does this influence shape their current well-being and preferences? Our
theory addresses this question, producing a new class of tractable models
which capture and explain phenomena such as present bias, consumption
interdependence, sign effects in discounting, and the desire to space out
consumption. Agents manifest impatience toward the current period, but not
necessarily toward the earlier of two future periods. The theory
characterizes the well-known quasi-hyperbolic discounting model as the unique
model of our class which does not display consumption interdependence.
Finally, it provides a rigorous approach for analyzing the welfare of agents
with time-inconsistent preferences. DYNAMIC METHODS On
the Smoothness of Value Functions and the Existence of Optimal Strategies in
Diffusion Models with Martin Szydlowski, Forthcoming, Journal of Economic Theory, Symposium on Dynamic
Contracts and Mechanism Design Studies of
dynamic economic models often rely on each agent having a smooth value function
and a well-defined optimal strategy. For time-homogeneous optimal control
problems with a one-dimensional diffusion, we prove that the corresponding
value function must be twice continuously differentiable under Lipschitz,
growth, and non-vanishing-volatility conditions. Under similar conditions,
the value function of any optimal stopping problem is shown to be (once)
continuously differentiable. We also provide sufficient conditions, based on
comparative statics and differential methods, for the existence of an optimal
control in the sense of strong solutions. The results are applied to growth,
experimentation, and dynamic contracting settings. FINANCE Capital
Mobility and Asset Pricing with Darrell Duffie, Econometrica, November 2012. We present a
model for the equilibrium movement of capital between asset markets that are
distinguished only by the levels of capital invested in each. Investment in
that market with the greatest amount of capital earns the lowest risk
premium. Intermediaries optimally trade off the costs of intermediation
against fees that depend on the gain they can offer to investors for moving
their capital to the market with the higher mean return. The bargaining power
of an investor depends on potential access to alternative intermediaries. In
equilibrium, the speeds of adjustment of mean returns and of capital between
the two markets are increasing in the degree to which capital is imbalanced
between the two markets, and can be reduced by competition among
intermediaries Supplement to "Capital
Mobility and Asset Pricing" Performance Sensitive Debt with Gustavo Manso and Alexei
Tchistyi, Review of Financial Studies (winner of the Young Researcher Award, 2009), May 2010. This paper studies performance-sensitive debt (PSD), the
class of debt obligations whose interest payments depend on some measure of
the borrowers’ performance. We demonstrate that the existence of PSD
obligations cannot be explained by the trade-off theory of capital structure,
as PSD leads to earlier default and lower equity value compared to fixed-rate
debt of the same market value. We show that, consistent with the pecking
order theory, PSD can be used as an inexpensive screening device and find
empirical ly that firms choosing PSD loans are more
likely to improve their credit ratings than firms choosing fixed-interest
loans. We also develop a method to value PSD obligations allowing for general
payment profiles and obtain closed-form pricing formulas for step-up bonds
and linear PSD. LAW AND ECONOMICS On the Design of Criminal Trials: the Benefit of Three-Verdict Systems
with
Ron Siegel We propose adding a third, intermediate, verdict
to the two-verdict system used in criminal trials. We show that the
additional verdict can be used to distinguish between convicted defendants,
based on the residual doubt regarding their guilt at the end of the trial, in
a way that improves welfare and does not increase the set of innocent
defendants who are wrongly convicted. It can also be guaranteed that
wrongfully convicted defendants do not serve longer sentences, provided that
the sentence in the two-verdict system was not too inefficiently low. Since
even acquitted defendants may face a social stigma, we also consider using
the additional verdict to distinguish between acquitted defendants, and
provide conditions under which this improves welfare. Generalizations to
multi-verdict systems with a larger number of verdicts are also explored. We
also consider plea bargains, and show that a properly chosen plea in a
two-verdict system leads to higher welfare than any multi-verdict system, and
is in fact the optimal mechanism. Finally, we consider the impact of multiple
verdicts on the incentives to gather evidence, and show that the effect is
generally positive. POLITICAL ECONOMY Collective Commitment with
Christian Roessler and Sandro Shelegia We consider collective decisions made by agents whose preferences
and power depend on past events and decisions. Faced with an inefficient
equilibrium and an opportunity to commit to a policy, can the agents reach an
agreement on such a policy? Under an intuitive condition linking power
structures in the dynamic setting and at the commitment stage, the answer is
negative: when the condition holds, the only agreement that may be reached at
the outset, if any, coincides with the equilibrium without commitment. The
condition is also necessary: when it fails, as in the case of a single
time-inconsistent agent, commitment is valuable for some payoffs. We apply
our result to explain inefficient collective decisions in the contexts of
investment in a public good, hiring, and reform. The Hidden Cost of Direct
Democracy: How Ballot Initiatives Affect Politicians’ Selection and
Incentives with Carlo Prato Citizen
initiatives and referendums play an important role in modern democracies,
from treaty ratifications in the European Union to gay marriage in
California, to the control of foreign workers in Switzerland. Departing from
the classic opposition between direct and representative democracy, we study
the equilibrium effects of direct democracy institutions on the incentives
and selection of elected officials. We find that facilitating direct
democracy induces a negative spiral on politicians’ role and contribution to
society, which may dominate any direct benefit. The theory offers predictions
on reelection probabilities and politicians’ performance consistent with
recent evidence from the U.S. states. Learning
While Voting: Determinants of Collective Experimentation Econometrica, May 2010. This paper combines dynamic social choice and strategic
experimentation to study the following question: how does a society, a
committee, or, more generally, a group of individuals with potentially
heterogeneous preferences, experiment with new opportunities? Each voter
recognizes that, during experimentation, other voters also learn about their
preferences. As a result, pivotal voters today are biased against
experimentation because it reduces their likelihood of remaining pivotal.
This phenomenon reduces equilibrium experimentation below the socially
efficient level, and may even result in a negative option value of
experimentation. However, one can restore efficiency by designing a voting
rule that depends deterministically on time. Another main result is that,
even when payoffs of a reform are independently distributed across the population,
good news about any individual’s payoff increases other individuals’
incentives to experiment with that reform, due to a positive voting
externality. Extension: Voting and Experimentation with Correlated
Types Working paper version ( This version includes the “Singaporean
Restaurant” example RENEGOTIATION AND BARGAINING Explicit
Renegotiation in Repeated Games
with Mikhail Safronov (New/Updated) Cooperative concepts of renegotiation in repeated games
have typically assumed that Pareto-ranked equilibria could not coexist within
the same renegotiation-proof set. With explicit renegotiation, however, a
proposal to move to a Pareto-superior equilibrium can be deterred by a different continuation equilibrium which harms the proposer
and rewards the rejecter. This paper introduces a simple protocol of
renegotiation for repeated games and defines the stability of social norms
and renegotiation-proof outcomes in terms of a simple equilibrium refinement.
We provide distinct necessary and sufficient conditions for renegotiation-proofness, which converge to each other as renegotiation
frictions become negligible. Renegotiation-proof outcomes always exist and
can be all included within a single, most permissive social norm that is
straightforward to characterize graphically. Contract
Negotiation and the Coase Conjecture
This paper analyzes an explicit protocol of contract
negotiation between a principal who has all the bargaining power and an agent
with a privately known type, and provides a foundation for renegotiation-proof
contracts in such environments. The model extends the framework of the Coase
conjecture to situations in which the seller and the buyer must determine the
quantity or the quality of the good being sold. All equilibria converge to
the same type-specific contracts as renegotiation frictions become
negligible. Those contracts are efficient and the principal extracts a
strictly positive share of the gain from negotiation. Contracts, Information Persistence,
and Renegotiation, November
2011 This paper studies how renegotiation and information
persistence shape long-term contracts in principal-agent relationships.
Truthful contracts that are renegotiation-proof, according to a concept
tailored to account for persistence in the agent's type, are characterized by
their sensitivity to the reports of the agent. The sensitivity of the optimal
renegotiation-proof contract is increasing in information persistence and in
the discount rate of the agent, and causes immiserization.
Renegotiation-proof contracts are self-correcting off the equilibrium path.
These results still hold when the agent is also subject to moral hazard. In
that case, a lower cost of effort of the agent can reduce the payoff of the
principal by increasing the severity of the agency problem. SOCIAL LEARNING AND EXPERIMENTATION Social Experimentation with
Interdependent and Expanding Technologies with Umberto
Garfagnini, Revise & Resubmit,
Review of Economic of Studies How do successive, forward-looking agents experiment with
interdependent and endogenous technologies? In this paper, trying a radically
new technology is not only informative about the value of similar
technologies, but also reduces the cost of experimenting with them, in effect
expanding the space of feasible technologies. Successful radical
experimentation has mixed consequences on subsequent experimentation: It
improves the immediate outlook of radical experimentation but also reduces
both the value and marginal value of experimentation in the longer term,
resulting in less ambitious, `incremental' experimentation and a reduced size
of radical experimentation. Incremental experimentation lowers the option
value of similar technologies, which may spur a return to radical
experimentation. However, we find that radical experimentation stagnates in
the long run for all parameters of the model. Learning While Voting: Determinants
of Collective Experimentation Econometrica, May 2010. This paper combines dynamic social choice and strategic
experimentation to study the following question: how does a society, a
committee, or, more generally, a group of individuals with potentially
heterogeneous preferences, experiment with new opportunities? Each voter
recognizes that, during experimentation, other voters also learn about their
preferences. As a result, pivotal voters today are biased against
experimentation because it reduces their likelihood of remaining pivotal.
This phenomenon reduces equilibrium experimentation below the socially
efficient level, and may even result in a negative option value of
experimentation. However, one can restore efficiency by designing a voting
rule that depends deterministically on time. Another main result is that,
even when payoffs of a reform are independently distributed across the
population, good news about any individual’s payoff increases other individuals’
incentives to experiment with that reform, due to a positive voting
externality. AUCTIONS AND CONSUMER THEORY Substitute Goods, Auctions, and Equilibrium
with Paul Milgrom, Journal of Economic Theory, January 2009. This paper
identifies two notions of substitutes for auction and equilibrium analysis.
Weak substitutes, which is the usual price-theory notion, guarantees
monotonicity of tâtonnement processes and
convergence of clock auctions to a pseudo-equilibrium, but only strong
substitutes, which treats each unit traded as a distinct good with its own
price, guarantees that every pseudo-equilibrium is a Walrasian
equilibrium, that the Vickrey outcome is in the
core, and that the “law of aggregate demand” is satisfied. The paper provides
several primal and dual characterizations and properties of weak and strong
substitutes. When goods are divisible, weak substitutes along with concavity
guarantees all of the above properties, except for the law of aggregate
demand. PUBLICATIONS IN OPERATIONS RESEARCH Additive
Envelopes of Continuous Functions with Thomas Weber, Operations
Research Letters, May 2010. We present an
iterative method for constructing additive envelopes of continuous functions
on a compact set, with contact at a specified point. For elements of a class
of submodular functions we provide closed-form expressions for such additive
envelopes. Monotone Comparative Statics: A Geometric Approach with Thomas Weber, Journal of Optimization Theory and
Applications, June 2008. We consider the comparative statics of solutions to
parameterized optimization problems. A geometric method is developed for
finding a vector field that, at each point in the parameter space, indicates a direction
in which monotone comparative statics obtains. Given such a vector field, we
provide sufficient conditions under which the problem can be re-parameterized
on the parameter space (or a subset thereof) in a way that guarantees
monotone comparative statics. A key feature of our method is that it does not
require the feasible set to be a lattice and works in the absence of the
standard quasi-supermodularity and single-crossing assumptions on the objective
function. We illustrate our approach with a variety of applications. |
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