Large deviations and multinomial probit choice

We consider a discrete choice model in which the payoffs to each of an agent?s n actions are subjected to the average of m i.i.d. shocks, and use tools from large deviations theory to characterize the rate of decay of the probability of choosing a given suboptimal action as m approaches infinity. Our model includes the multinomial probit model of Myatt and Wallace (2003) [5] as a special case. We show that their formula describing the rates of decay of choice probabilities is incorrect, provide the correct formula, and use our large deviations analysis to provide intuition for the difference between the two.     

Macroeconomic implications of financial policy

This paper studies the effects of financial policy in a model with heterogeneous agents, incomplete markets and portfolio restrictions. For an economy calibrated to replicate key aspects of the U.S. wealth distribution, we find that the quantitative effects of financial policy are relatively small. The reason is that the households determining aggregate behavior are relatively well insured and can therefore offset the actions of the firm by modifying their portfolio allocations. However, financial policy has important effects on asset prices. Whereas a higher level of debt in the capital structure of the firm introduces more risk into the economy by increasing the volatility of the equity return, it enhances the liquidity of households by increasing the supply of bonds. In an economy with a substantial amount of heterogeneity, this last effect dominates and leverage leads to a decrease in the equity premium. This is in contrast to the findings in representative agent models, in which leverage unambiguously increases the premium through a higher equity return volatility.     

Equilibrium portfolios in the neoclassical growth model

This paper studies equilibrium portfolios in the standard neoclassical growth model under uncertainty with heterogeneous agents and dynamically complete markets. Preferences are purposely restricted to be quasi-homothetic. The main source of heterogeneity across agents is due to different endowments of shares of the representative firm at date 0. Fixing portfolios is the optimal equilibrium strategy in stationary endowment economies with dynamically complete markets. However, when the environment displays changing degrees of heterogeneity across agents, the trading strategy of fixed portfolios cannot be optimal in equilibrium. Very importantly, our framework can generate changing heterogeneity if and only if either minimum consumption requirements are not zero or labor income is not zero and the value of human and non-human wealth are linearly independent.     

Optimal risk sharing and borrowing constraints in a continuous-time model with limited commitment

We study a continuous-time version of the optimal risk-sharing problem with one-sided commitment. In the optimal contract, the agent?s consumption is a time-invariant, strictly increasing function of a single state variable: the maximal level of the agent?s income realized to date. We characterize this function in terms of the agent?s outside option value function and the discounted amount of time in which the agent?s income process is expected to reach a new to-date maximum. Under constant relative risk aversion we solve the model in closed-form: optimal consumption of the agent equals a constant fraction of his maximal income realized to date. In the complete-markets implementation of the optimal contract, the Alvarez–Jermann solvency constraints take the form of a simple borrowing constraint familiar from the Bewley–Aiyagari incomplete-markets models.     

Heterogeneous quantal response equilibrium and cognitive hierarchies

We explore an equilibrium model of games where behavior is given by logit response functions, but payoff responsiveness and beliefs about others' responsiveness are heterogeneous. We study two substantively different ways of extending quantal response equilibrium (QRE) to this setting: (1) Heterogeneus QRE, where players share identical correct beliefs about the distribution of payoff responsiveness; and (2) Truncated QRE, where players have downward looking beliefs, systematically underestimating others' responsiveness. We show that the cognitive hierarchy model is a special case of Truncated QRE. We conduct experiments designed to differentiate these approaches. We find significant evidence of payoff responsive stochastic choice, and of heterogeneity and downward looking beliefs in some games.     

Aggregate information cascades

We introduce a new model of aggregate information cascades where only one of two possible actions is observable to others. Agents make a binary decision in sequence. The order is random and agents are not aware of their own position in the sequence. When called upon, they are only informed about the total number of others who have chosen the observable action before them. This informational structure arises naturally in many applications. Our most important result is that only one type of cascade arises in equilibrium, the aggregate cascade on the observable action. A cascade on the unobservable action never arises.     

Heterogeneous beliefs and learning in forward looking economic models*

We study a class of forward looking economic models with heterogeneous agents in a bounded rationality setting. The agents employ the same recursive learning rule to update beliefs but are characterized by different memory parameters. The peculiarity of the learning mechanism is that the learning rate is not vanishing in the limit. Differently from what is obtained in the case of a vanishing learning step, i.e., the stability conditions in the heterogeneous agents case are those of the representative agent model, we show that heterogeneity matters for the expectational stability of a stationary perfect foresight equilibrium and that the stability parameter restrictions with heterogeneous agents are stronger than in the case of homogeneous agents.     

How noise matters

Recent advances in evolutionary game theory have introduced noise into decisionmaking to select in favor of certain equilibria in coordination games. Noisy decisionmaking is justified on bounded rationality grounds, and consequently the sources of noise are left unmodelled. This methodological approach can only be successful if the results do not depend too much on the nature of the noise process. This paper investigates invariance to noise of these results, both for the random matching paradigm that has characterized much of the recent literature and for a larger class of two-strategy population games where payoffs may vary non-linearly with the distribution of strategies among the population. Several parametrizations of noise reduction are investigated. The results show that a symmetry property of the noise process and, in the case of non-linear payoffs, bounds on the asymmetry of the payoff functions suffice to preserve the known stochastic stability results.     

Learning from private information in noisy repeated games

We study the perfect type-contingently public ex-post equilibrium (PTXE) of repeated games where players observe imperfect public signals of the actions played, and both the payoff functions and the map from actions to signal distributions depend on an unknown state. The PTXE payoffs when players are patient are determined by the solutions to a family of linear programming problems. Using this characterization, we develop conditions under which play can be as if the players have learned the state. We provide a sufficient condition for the folk theorem, and a characterization of the PTXE payoffs in games with a known monitoring structure.     

Calibrating spatial models of trade

Empirical spatial models of trade that are based on a mathematical programming specification often exhibit a large discrepancy between the equilibrium solution and the observed demand, supply and levels of trade flows among countries. This discrepancy may be due to several causes. Assuming, however, that a trade model is not misspecified – in the sense that behavior of the economic agents involved in the specific commodity markets has been included in the study and that the relevant policy instruments have been properly taken into account – the cause of discrepancy may be traced either to imprecision of unit transaction costs or to imprecision in the measurement of the demand and supply functions' parameters, or both. Policy assessments based on this type of imprecise models are distorted. This paper presents a methodology for calibrating mathematical programming spatial trade models of increasing complexity, from the one-commodity case to a multi-commodity model with asymmetric slope matrices of demand and supply functions. The proposed calibration procedure identifies corrections of imperfectly measured parameters. The calibrated models generate solutions that exactly reproduce quantities produced and consumed in all countries, as well as trade flows among all pairs of countries, observed in a given base year. Such models may then serve as a springboard for assessing the impact of various policy changes on economic agents in the countries under study.     

Fiscal Policy in a Growing Economy with Financial Frictions and Firm Heterogeneity

This paper constructs a tractable model of endogenous growth with financial frictions and firm heterogeneity. We introduce factor income tax, consumption tax as well as the government consumption into the base model and explore the growth effect of fiscal policy. We show that from the qualitative perspective, the long‐run effects of fiscal actions in our model are similar to those obtained in the representative agent models. However, the quantitative impacts of fiscal policy on long‐run growth in our setting can be substantially different from those established in the model where agents are homogeneous and there is no financial frictions.     

Quantal Response Equilibria for Extensive Form Games

This article investigates the use of standard econometric models for quantal choice to study equilibria of extensive form games. Players make choices based on a quantal-choice model and assume other players do so as well. We define an agent quantal response equilibrium (AQRE), which applies QRE to the agent normal form of an extensive form game and imposes a statistical version of sequential rationality. We also define a parametric specification, called logit-AQRE, in which quantal-choice probabilities are given by logit response functions. AQRE makes predictions that contradict the invariance principle in systematic ways. We show that these predictions match up with some experimental findings by Schotter et al. (1994) about the play of games that differ only with respect to inessential transformations of the extensive form. The logit-AQRE also implies a unique selection from the set of sequential equilibria in generic extensive form games. We examine data from signaling game experiments by Banks et al. (1994) and Brandts and Holt (1993). We find that the logit-AQRE selection applied to these games succeeds in predicting patterns of behavior observed in these experiments, even when our prediction conflicts with more standard equilibrium refinements, such as the intuitive criterion. We also reexamine data from the McKelvey and Palfrey (1992) centipede experiment and find that the AQRE model can account for behavior that had previously been explained in terms of altruistic behavior. This revised version was published online in August 2006 with corrections to the Cover Date.     

Comment on “Correlated information, mechanism design and informational rents” [J. Econ. Theory 123 (2) (2005) 210–217]

We amend an error in [S. Parreiras, Correlated information, mechanism design and informational rents, J. Econ. Theory 123 (2005) 210–217]. Consequently, it is in general not possible to reinterpret a mechanism design model that violates the spanning condition of Crémer and McLean [J. Crémer, R. McLean, Full extraction of the surplus in bayesian, dominant strategy auctions, Econometrica 56 (1988) 1247–1258] as one in which agents hold private information about the informativeness of their signals about other agents? types. Instead, such an interpretation is warranted only when the weights used to span an agent?s set of beliefs stand in a singular relation with the prior type distribution that is known as an alternative characterization of Blackwell dominance.     

Gender differences in the volatility of work hours and labor demand

This paper examines the role of heterogeneity in a real business cycle model, which traditionally has not fully captured the relative volatility of hours to output. Men and women have different cyclical volatilities in hours worked, which is robust to different filtering methods. This empirical regularity is used to motivate a standard RBC model augmented to allow for two different agents following Jaimovich et al. (2013). These two agents have identical utility functions, but face different elasticities of labor demand due to their different complementarities with capital. These estimated elasticities find that women are more complementary to capital. The calibrated model generates the cyclical volatility of work hours by gender and for the total hours worked that matches the U.S. data better than the traditional representative agent model. I then explore other extensions to this model including investigating the stability of the estimated labor demand elasticities and allowing for various Frisch elasticities of labor supply. This paper demonstrates that allowing for even broad levels of heterogeneity in a simple framework can increase the model’s tractability with the data. Since gender is important to explain U.S. business cycle dynamics, we need to carefully consider heterogeneity when analyzing counter-cyclical economic policy, as it may not have symmetric effects across assorted groups.     

Business cycle amplification with heterogeneous expectations

This paper studies the implications for business cycle dynamics of heterogeneous expectations in a stochastic growth model. The assumption of homogeneous, rational expectations is replaced with a heterogeneous expectations model where a fraction of agents hold rational expectations and the remaining fraction adopt parsimonious forecasting models that are, in equilibrium, optimal within a restricted class. Our approach nests the literature on rational expectations in business cycle models with a recent approach based on adaptive learning. We demonstrate that (i.) heterogeneous expectations can lead to substantial improvement in the internal propagation of equilibrium business cycle models and (ii.) the internal propagation depends on the degree of heterogeneity. A calibrated model with heterogeneity provides a closer fit to business cycle data than its representative agent, rational expectations counterpart.     

On Ramsey's conjecture: efficient allocations in the neoclassical growth model with private information

In his seminal paper of 1928, Ramsey conjectured that if agents discounted the future differently, in the long run all agents except the most patient would live at the subsistence level. The validity of this conjecture was investigated in different environments. In particular, it has been confirmed in the neoclassical growth model with dynamically complete markets. This paper studies this conjecture in a version of this model that includes private information and heterogeneous agents. A version of Bayesian implementation is introduced and a recursive formulation of the original allocation problem is established. Efficient allocations are renegotiation-proof and the expected utility of any agent cannot go to zero with positive probability if the economy does not collapse. If the economy collapses all agents will get zero consumption forever. Thus, including any degree of private information in the neoclassical growth model will deny Ramsey's conjecture, if efficient allocations are considered.     

Wealth distribution and output fluctuations

We explore the link between wealth inequality and output fluctuations in a general two-sector neoclassical growth model with endogenous labor and heterogeneous agents. When agents have homogeneous CRRA preferences and individual wealth is Pareto distributed, a sufficiently large rise in the Gini index typically leads to an increase in endogenous fluctuations of output. For general economies, we show that under plausible conditions on the fundamentals, wealth inequality is still a destabilizing factor.     

Heterogeneity and convergence of regional inflation (prices)

It is generally thought that members in a monetary union experience a similar level of inflation. This paper verifies this conventional belief. Using regional data, we present statistical evidence of heterogeneous inflation in Japan. Not only does the average inflation differ significantly across regions, but regional inflation responds differently to common economic and monetary factors. Furthermore, we show no evidence of price convergence in the entire group of regions although there is some evidence of convergence in subgroups. These results suggest that diversified regional inflation can exist within a monetary union.     

Public goods,voting, and growth

We study a parametric politico‐economic model of economic growth with productive public goods and public consumption goods. The provision of public goods is funded by a proportional tax. Agents are heterogeneous in their initial capital endowments, discount factors, and the relative weights of public consumption in overall private utility. They vote on the shares of public goods in gross domestic products (GDP). We propose a definition of voting equilibrium, prove the existence and provide a characterization of voting equilibria, and obtain a closed‐form solution for the voting outcomes. Also we introduce a “fictitious” representative agent and interpret the outcome of voting as a choice made by a central planner for his benefit. Finally, we undertake comparative static analysis of the shares of public goods in GDP and of the rate of balanced growth with respect to the discount factors and the preferences for public consumption. The results of this analysis suggest that the representative‐agent version of our model is capable of capturing the interaction between many voting heterogeneous agents only if the heterogeneity is one‐dimensional.