Berk–Nash Equilibrium: A Framework for Modeling Agents With Misspecified Models

We develop an equilibrium framework that relaxes the standard assumption that people have a correctly specified view of their environment. Each player is characterized by a (possibly misspecified) subjective model, which describes the set of feasible beliefs over payoff‐relevant consequences as a function of actions. We introduce the notion of a Berk–Nash equilibrium: Each player follows a strategy that is optimal given her belief, and her belief is restricted to be the best fit among the set of beliefs she considers possible. The notion of best fit is formalized in terms of minimizing the Kullback–Leibler divergence, which is endogenous and depends on the equilibrium strategy profile. Standard solution concepts such as Nash equilibrium and self‐confirming equilibrium constitute special cases where players have correctly specified models. We provide a learning foundation for Berk–Nash equilibrium by extending and combining results from the statistics literature on misspecified learning and the economics literature on learning in games.     

Uncertainty and Unemployment

This paper studies the impact of time‐varying idiosyncratic risk at the establishment level on unemployment fluctuations over 1972–2009. I build a tractable directed search model with firm dynamics and time‐varying idiosyncratic volatility. The model allows for endogenous separations, entry and exit, and job‐to‐job transitions. I show that the model can replicate salient features of the microeconomic behavior of firms and that the introduction of volatility improves the fit of the model for standard business cycle moments. In a series of counterfactual experiments, I show that time‐varying risk is important to account for the magnitude of fluctuations in aggregate unemployment for past U.S. recessions. Though the model can account for about 40% of the total increase in unemployment for the 2007–2009 recession, uncertainty alone is not sufficient to explain the magnitude and persistence of unemployment during that episode.     

Communication With Unknown Perspectives

Consider a group of individuals with unobservable perspectives (subjective prior beliefs) about a sequence of states. In each period, each individual receives private information about the current state and forms an opinion (a posterior belief). She also chooses a target individual and observes the target's opinion. This choice involves a trade‐off between well‐informed targets, whose signals are precise, and well‐understood targets, whose perspectives are well known. Opinions are informative about the target's perspective, so observed individuals become better understood over time. We identify a simple condition under which long‐run behavior is history independent. When this fails, each individual restricts attention to a small set of experts and observes the most informed among these. A broad range of observational patterns can arise with positive probability, including opinion leadership and information segregation. In an application to areas of expertise, we show how these mechanisms generate own field bias and large field dominance.     

A Dynamic Reinterpretation of Nash Bargaining With Endogenous Threats

This paper concerns the two‐stage game introduced in Nash (1953). It formalizes a suggestion made (but not pursued) by Nash regarding equilibrium selection in that game, and hence offers an arguably more solid foundation for the “Nash bargaining with endogenous threats” solution. Analogous reasoning is then applied to an infinite horizon game to provide equilibrium selection in two‐person repeated games with contracts. In this setting, issues about enforcement of threats are much less problematic than in Nash's static setting. The analysis can be extended to stochastic games with contracts.     

Robust Contracts in Continuous Time

We study a continuous‐time contracting problem under hidden action, where the principal has ambiguous beliefs about the project cash flows. The principal designs a robust contract that maximizes his utility under the worst‐case scenario subject to the agent's incentive and participation constraints. Robustness generates endogenous belief heterogeneity and induces a tradeoff between incentives and ambiguity sharing so that the incentive constraint does not always bind. We implement the optimal contract by cash reserves, debt, and equity. In addition to receiving ordinary dividends when cash reserves reach a threshold, outside equity holders also receive special dividends or inject cash in the cash reserves to hedge against model uncertainty and smooth dividends. The equity premium and the credit yield spread generated by ambiguity aversion are state dependent and high for distressed firms with low cash reserves.     

Identification of Nonseparable Models Using Instruments With Small Support

I consider nonparametric identification of nonseparable instrumental variables models with continuous endogenous variables. If both the outcome and first stage equations are strictly increasing in a scalar unobservable, then many kinds of continuous, discrete, and even binary instruments can be used to point‐identify the levels of the outcome equation. This contrasts sharply with related work by Imbens and Newey, 2009 that requires continuous instruments with large support. One implication is that assumptions about the dimension of heterogeneity can provide nonparametric point‐identification of the distribution of treatment response for a continuous treatment in a randomized controlled experiment with partial compliance.     

Female Labor Supply,Human Capital,and Welfare Reform

We estimate a dynamic model of employment, human capital accumulation—including education, and savings for women in the United Kingdom, exploiting tax and benefit reforms, and use it to analyze the effects of welfare policy. We find substantial elasticities for labor supply and particularly for lone mothers. Returns to experience, which are important in determining the longer‐term effects of policy, increase with education, but experience mainly accumulates when in full‐time employment. Tax credits are welfare improving in the U.K., increase lone‐mother labor supply and marginally reduce educational attainment, but the employment effects do not extend beyond the period of eligibility. Marginal increases in tax credits improve welfare more than equally costly increases in income support or tax cuts.     

Sales Force and Competition in Financial Product Markets: The Case of Mexico's Social Security Privatization

This paper examines how sales force impacts competition and equilibrium prices in the context of a privatized pension market. We use detailed administrative data on fund manager choices and worker characteristics at the inception of Mexico's privatized social security system, where fund managers had to set prices (management fees) at the national level, but could select sales force levels by local geographic areas. We develop and estimate a model of fund manager choice where sales force can increase or decrease customer price sensitivity. We find exposure to sales force lowered price sensitivity, leading to inelastic demand and high equilibrium fees. We simulate oft proposed policy solutions: a supply‐side policy with a competitive government player and a demand‐side policy that increases price elasticity. We find that demand‐side policies are necessary to foster competition in social safety net markets with large segments of inelastic consumers.     

Innovation Strategy,Human Resource Policy,and Firms' Revenue Growth: The Roles of Environmental Uncertainty and Innovation Performance*

This study investigates the interactions of innovation strategy execution and innovation‐focused human resource (HR) policy adoption on innovation performance and revenue growth. In addition, we investigate the moderating role of environmental uncertainty on the effects of innovation strategy execution and innovation‐focused HR policy on innovation performance. Results show that the interaction of innovation strategy execution and innovation‐focused HR policy is positively related to innovation performance. Results also show that environmental uncertainty positively moderates the innovation strategy execution–innovation performance relationship. Finally, innovation performance mediates the interaction of innovation strategy execution and environmental uncertainty on firms’ revenue growth. Implications of these findings for theory and practice are discussed.     

Information Frictions in Trade

It is costly to learn about market conditions elsewhere, especially in developing countries. This paper examines how such information frictions affect trade. Using data on regional agricultural trade in the Philippines, I first document a number of observed patterns in trade flows and prices that suggest the presence of information frictions. I then incorporate information frictions into a perfect competition trade model by embedding a process whereby heterogeneous producers engage in a costly sequential search process to determine where to sell their produce. I show that introducing information frictions reconciles the theory with the observed patterns in the data. Structural estimation of the model finds that information frictions are quantitatively important: roughly half the observed regional price dispersion is due to information frictions. Furthermore, incorporating information frictions improves the out‐of‐sample predictive power of the model.     

An Empirical Equilibrium Model of a Decentralized Asset Market

I estimate a search‐and‐bargaining model of a decentralized market to quantify the effects of trading frictions on asset allocations, asset prices, and welfare, and to quantify the effects of intermediaries that facilitate trade. Using business‐aircraft data, I find that, relative to the Walrasian benchmark, 18.3 percent of the assets are misallocated; prices are 19.2 percent lower; and the aggregate welfare losses equal 23.9 percent. Dealers play an important role in reducing trading frictions: In a market with no dealers, a larger fraction of assets would be misallocated, and prices would be higher. However, dealers reduce aggregate welfare because their operations are costly, and they impose a negative externality by decreasing the number of agents' direct transactions.     

The Value of Free Water: Analyzing South Africa's Free Basic Water Policy

This paper analyzes South Africa's Free Basic Water Policy, under which households receive a free water allowance equal to the World Health Organization's recommended minimum. I estimate residential water demand, evaluate the welfare effects of free water, and provide optimal price schedules derived from a social planner's problem. I use a data set of monthly metered billing data for 60,000 households for 2002–2009 from a particularly disadvantaged suburb of Pretoria, with rich price variation across 20 different nonlinear tariff schedules. I find that the free allowance acts as a lump‐sum subsidy, without large effects on water consumption. However, it is possible to reallocate the current subsidy to form an optimal tariff without a free allowance, which would increase welfare while leaving the water provider's profit unchanged. This optimal tariff would also reduce the number of households consuming low quantities of water, a desirable policy goal according to the WHO.     

The Evolution of Culture and Institutions: Evidence From the Kuba Kingdom

We use variation in historical state centralization to examine the long‐term impact of institutions on cultural norms. The Kuba Kingdom, established in Central Africa in the early 17th century by King Shyaam, had more developed state institutions than the other independent villages and chieftaincies in the region. It had an unwritten constitution, separation of political powers, a judicial system with courts and juries, a police force, a military, taxation, and significant public goods provision. Comparing individuals from the Kuba Kingdom to those from just outside the Kingdom, we find that centralized formal institutions are associated with weaker norms of rule following and a greater propensity to cheat for material gain. This finding is consistent with recent models where endogenous investments to inculcate values in children decline when there is an increase in the effectiveness of formal institutions that enforce socially desirable behavior. Consistent with such a mechanism, we find that Kuba parents believe it is less important to teach children values related to rule‐following behaviors.     

IV Quantile Regression for Group‐Level Treatments,With an Application to the Distributional Effects of Trade

We present a methodology for estimating the distributional effects of an endogenous treatment that varies at the group level when there are group‐level unobservables, a quantile extension of Hausman and Taylor, 1981. Because of the presence of group‐level unobservables, standard quantile regression techniques are inconsistent in our setting even if the treatment is independent of unobservables. In contrast, our estimation technique is consistent as well as computationally simple, consisting of group‐by‐group quantile regression followed by two‐stage least squares. Using the Bahadur representation of quantile estimators, we derive weak conditions on the growth of the number of observations per group that are sufficient for consistency and asymptotic zero‐mean normality of our estimator. As in Hausman and Taylor, 1981, micro‐level covariates can be used as internal instruments for the endogenous group‐level treatment if they satisfy relevance and exogeneity conditions. Our approach applies to a broad range of settings including labor, public finance, industrial organization, urban economics, and development; we illustrate its usefulness with several such examples. Finally, an empirical application of our estimator finds that low‐wage earners in the United States from 1990 to 2007 were significantly more affected by increased Chinese import competition than high‐wage earners.     

Promotion,Turnover, and Compensation in the Executive Labor Market

This paper develops a generalized Roy model with human capital accumulation, moral hazard, and career concerns. We identify and estimate the model with a large panel that matches data on publicly listed firms to information on their executives. The structural estimates obtained are used to decompose the firm‐size pay gap. We find that although total compensation and incentive pay increase with firm size, certainty‐equivalent pay decreases with firm size. In larger firms, and for more highly ranked executives, weaker signal quality about effort results in higher risk premiums. This risk premium accounts for roughly 80 percent of the firm‐size gap in total compensation. Larger firms are also willing to pay more than smaller ones to attract executives. Finally, the estimated coefficients on human capital accumulation from formal education and experience gained from different firms are individually significant, but their collective effect on firm‐size pay differentials nets out.     

Bayesian Learning,Smooth Approximate Optimal Behavior,and Convergence to ε‐Nash Equilibrium

In this paper, I construct players' prior beliefs and show that these prior beliefs lead the players to learn to play an approximate Nash equilibrium uniformly in any infinitely repeated slightly perturbed game with discounting and perfect monitoring. That is, given any ε > 0, there exists a (single) profile of players' prior beliefs that leads play to almost surely converge to an ε‐Nash equilibrium uniformly for any (finite normal form) stage game with slight payoff perturbation and any discount factor less than 1.     

Consumption Dynamics During Recessions

Are there times when durable spending is less responsive to economic stimulus? We argue that aggregate durable expenditures respond more sluggishly to economic shocks during recessions because microeconomic frictions lead to declines in the frequency of households' durable adjustment. We show this by first using indirect inference to estimate a heterogeneous agent incomplete markets model with fixed costs of durable adjustment to match consumption dynamics in PSID microdata. We then show that aggregating this model delivers an extremely procyclical Impulse Response Function (IRF) of durable spending to aggregate shocks. For example, the response of durable spending to an income shock in 1999 is estimated to be almost twice as large as if it occurred in 2009. This procyclical IRF holds in response to standard business cycle shocks as well as in response to various policy shocks, and it is robust to general equilibrium. After estimating this robust theoretical implication of micro frictions, we provide additional direct empirical evidence for its importance using both cross‐sectional and time‐series data.     

Forecasting With Model Uncertainty: Representations and Risk Reduction

We consider forecasting with uncertainty about the choice of predictor variables. The researcher wants to select a model, estimate the parameters, and use the parameter estimates for forecasting. We investigate the distributional properties of a number of different schemes for model choice and parameter estimation, including: in‐sample model selection using the Akaike information criterion; out‐of‐sample model selection; and splitting the data into subsamples for model selection and parameter estimation. Using a weak‐predictor local asymptotic scheme, we provide a representation result that facilitates comparison of the distributional properties of the procedures and their associated forecast risks. This representation isolates the source of inefficiency in some of these procedures. We develop a simulation procedure that improves the accuracy of the out‐of‐sample and split‐sample methods uniformly over the local parameter space. We also examine how bootstrap aggregation (bagging) affects the local asymptotic risk of the estimators and their associated forecasts. Numerically, we find that for many values of the local parameter, the out‐of‐sample and split‐sample schemes perform poorly if implemented in the conventional way. But they perform well, if implemented in conjunction with our risk‐reduction method or bagging.     

Fiscal Rules and Discretion Under Persistent Shocks

This paper studies the optimal level of discretion in policymaking. We consider a fiscal policy model where the government has time‐inconsistent preferences with a present bias toward public spending. The government chooses a fiscal rule to trade off its desire to commit to not overspend against its desire to have flexibility to react to privately observed shocks to the value of spending. We analyze the optimal fiscal rule when the shocks are persistent. Unlike under independent and identically distributed shocks, we show that the ex ante optimal rule is not sequentially optimal, as it provides dynamic incentives. The ex ante optimal rule exhibits history dependence, with high shocks leading to an erosion of future fiscal discipline compared to low shocks, which lead to the reinstatement of discipline. The implied policy distortions oscillate over time given a sequence of high shocks, and can force the government to accumulate maximal debt and become immiserated in the long run.     

Inferring Labor Income Risk and Partial Insurance From Economic Choices

This paper uses the information contained in the joint dynamics of individuals' labor earnings and consumption‐choice decisions to quantify both the amount of income risk that individuals face and the extent to which they have access to informal insurance against this risk. We accomplish this task by using indirect inference to estimate a structural consumption–savings model, in which individuals both learn about the nature of their income process and partly insure shocks via informal mechanisms. In this framework, we estimate (i) the degree of partial insurance, (ii) the extent of systematic differences in income growth rates, (iii) the precision with which individuals know their own income growth rates when they begin their working lives, (iv) the persistence of typical labor income shocks, (v) the tightness of borrowing constraints, and (vi) the amount of measurement error in the data. In implementing indirect inference, we find that an auxiliary model that approximates the true structural equations of the model (which are not estimable) works very well, with negligible small sample bias. The main substantive findings are that income shocks are moderately persistent, systematic differences in income growth rates are large, individuals have substantial amounts of information about their income growth rates, and about one‐half of income shocks are smoothed via partial insurance. Putting these findings together, the amount of uninsurable lifetime income risk that individuals perceive is substantially smaller than what is typically assumed in calibrated macroeconomic models with incomplete markets.