Nonparametric Stochastic Discount Factor Decomposition

Stochastic discount factor (SDF) processes in dynamic economies admit a permanent‐transitory decomposition in which the permanent component characterizes pricing over long investment horizons. This paper introduces an empirical framework to analyze the permanent‐transitory decomposition of SDF processes. Specifically, we show how to estimate nonparametrically the solution to the Perron–Frobenius eigenfunction problem of Hansen and Scheinkman, 2009. Our empirical framework allows researchers to (i) construct time series of the estimated permanent and transitory components and (ii) estimate the yield and the change of measure which characterize pricing over long investment horizons. We also introduce nonparametric estimators of the continuation value function in a class of models with recursive preferences by reinterpreting the value function recursion as a nonlinear Perron–Frobenius problem. We establish consistency and convergence rates of the eigenfunction estimators and asymptotic normality of the eigenvalue estimator and estimators of related functionals. As an application, we study an economy where the representative agent is endowed with recursive preferences, allowing for general (nonlinear) consumption and earnings growth dynamics.     

Single‐Crossing Random Utility Models

We propose a novel model of stochastic choice: the single‐crossing random utility model (SCRUM). This is a random utility model in which the collection of preferences satisfies the single‐crossing property. We offer a characterization of SCRUMs based on two easy‐to‐check properties: the classic Monotonicity property and a novel condition, Centrality. The identified collection of preferences and associated probabilities is unique. We show that SCRUMs nest both single‐peaked and single‐dipped random utility models and establish a stochastic monotone comparative result for the case of SCRUMs.     

The Effect of Changes in Risk Attitude on Strategic Behavior

We study families of normal‐form games with fixed preferences over pure action profiles but varied preferences over lotteries. That is, we subject players' utilities to monotone but nonlinear transformations and examine changes in the rationalizable set and set of equilibria. Among our results: The rationalizable set always grows under concave transformations (risk aversion) and shrinks under convex transformations (risk love). The rationalizable set reaches an upper bound under extreme risk aversion, and lower bound under risk love, and both of these bounds are characterized by elimination processes. For generic two‐player games, under extreme risk love or aversion, all Nash equilibria are close to pure and the limiting set of equilibria can be described using preferences over pure action profiles.     

Consistency of Higher Order Risk Preferences

Risk aversion (a second‐order risk preference) is a time‐proven concept in economic models of choice under risk. More recently, the higher order risk preferences of prudence (third‐order) and temperance (fourth‐order) also have been shown to be quite important. While a majority of the population seems to exhibit both risk aversion and these higher order risk preferences, a significant minority does not. We show how both risk‐averse and risk‐loving behaviors might be generated by a simple type of basic lottery preference for either (1) combining “good” outcomes with “bad” ones, or (2) combining “good with good” and “bad with bad,” respectively. We further show that this dichotomy is fairly robust at explaining higher order risk attitudes in the laboratory. In addition to our own experimental evidence, we take a second look at the extant laboratory experiments that measure higher order risk preferences and we find a fair amount of support for this dichotomy. Our own experiment also is the first to look beyond fourth‐order risk preferences, and we examine risk attitudes at even higher orders.     

A Theory of Intergenerational Altruism

Modeling intergenerational altruism is crucial to evaluate the long‐term consequences of current decisions, and requires a set of principles guiding such altruism. We axiomatically develop a theory of pure, direct altruism: Altruism is pure if it concerns the total utility (rather than the mere consumption utility) of future generations, and direct if it directly incorporates the utility of all future generations. Our axioms deliver a new class of altruistic, forward‐looking preferences, whose weight put on the consumption of a future generation generally depends on the consumption of other generations. The only preferences lacking this dependence correspond to the quasi‐hyperbolic discounting model, which our theory characterizes. Our approach provides a framework to analyze welfare in the presence of altruistic preferences and addresses technical challenges stemming from the interdependent nature of such preferences.     

Farms,Families, and Markets: New Evidence on Completeness of Markets in Agricultural Settings

The farm household model has played a central role in improving the understanding of small‐scale agricultural households and non‐farm enterprises. Under the assumptions that all current and future markets exist and that farmers treat all prices as given, the model simplifies households' simultaneous production and consumption decisions into a recursive form in which production can be treated as independent of preferences of household members. These assumptions, which are the foundation of a large literature in labor and development, have been tested and not rejected in several important studies including Benjamin (1992). Using multiple waves of longitudinal survey data from Central Java, Indonesia, this paper tests a key prediction of the recursive model: demand for farm labor is unrelated to the demographic composition of the farm household. The prediction is unambiguously rejected. The rejection cannot be explained by contamination due to unobserved heterogeneity that is fixed at the farm level, local area shocks, or farm‐specific shocks that affect changes in household composition and farm labor demand. We conclude that the recursive form of the farm household model is not consistent with the data. Developing empirically tractable models of farm households when markets are incomplete remains an important challenge.     

Competitive Division of a Mixed Manna

A mixed manna contains goods (that everyone likes) and bads (that everyone dislikes), as well as items that are goods to some agents, but bads or satiated to others. If all items are goods and utility functions are homogeneous of degree 1 and concave (and monotone), the competitive division maximizes the Nash product of utilities (Gale–Eisenberg): hence it is welfarist (determined by the set of feasible utility profiles), unique, continuous, and easy to compute. We show that the competitive division of a mixed manna is still welfarist. If the zero utility profile is Pareto dominated, the competitive profile is strictly positive and still uniquely maximizes the product of utilities. If the zero profile is unfeasible (for instance, if all items are bads), the competitive profiles are strictly negative and are the critical points of the product of disutilities on the efficiency frontier. The latter allows for multiple competitive utility profiles, from which no single‐valued selection can be continuous or resource monotonic. Thus the implementation of competitive fairness under linear preferences in interactive platforms like SPLIDDIT will be more difficult when the manna contains bads that overwhelm the goods.     

Leverage and Default in Binomial Economies: A Complete Characterization

Our paper provides a complete characterization of leverage and default in binomial economies with financial assets serving as collateral. Our Binomial No‐Default Theorem states that any equilibrium is equivalent (in real allocations and prices) to another equilibrium in which there is no default. Thus actual default is irrelevant, though the potential for default drives the equilibrium and limits borrowing. This result is valid with arbitrary preferences and endowments, contingent or noncontingent promises, many assets and consumption goods, production, and multiple periods. We also show that only no‐default equilibria would be selected if there were the slightest cost of using collateral or handling default. Our Binomial Leverage Theorem shows that equilibrium Loan to Value (LTV) for noncontingent debt contracts is the ratio of the worst‐case return of the asset to the riskless gross rate of interest. In binomial economies, leverage is determined by down risk and not by volatility.     

Nonparametric Instrumental Variable Estimation Under Monotonicity

The ill‐posedness of the nonparametric instrumental variable (NPIV) model leads to estimators that may suffer from poor statistical performance. In this paper, we explore the possibility of imposing shape restrictions to improve the performance of the NPIV estimators. We assume that the function to be estimated is monotone and consider a sieve estimator that enforces this monotonicity constraint. We define a constrained measure of ill‐posedness that is relevant for the constrained estimator and show that, under a monotone IV assumption and certain other mild regularity conditions, this measure is bounded uniformly over the dimension of the sieve space. This finding is in stark contrast to the well‐known result that the unconstrained sieve measure of ill‐posedness that is relevant for the unconstrained estimator grows to infinity with the dimension of the sieve space. Based on this result, we derive a novel non‐asymptotic error bound for the constrained estimator. The bound gives a set of data‐generating processes for which the monotonicity constraint has a particularly strong regularization effect and considerably improves the performance of the estimator. The form of the bound implies that the regularization effect can be strong even in large samples and even if the function to be estimated is steep, particularly so if the NPIV model is severely ill‐posed. Our simulation study confirms these findings and reveals the potential for large performance gains from imposing the monotonicity constraint.     

Sharing Rule Identification for General Collective Consumption Models

We propose a method to set identify bounds on the sharing rule for a general collective household consumption model. Unlike the effects of distribution factors, the level of the sharing rule cannot be uniquely identified without strong assumptions on preferences across households. Our new results show that, though not point identified without these assumptions, strong bounds on the sharing rule can be obtained. We get these bounds by applying revealed preference restrictions implied by the collective model to the household's continuous aggregate demand functions. We obtain informative bounds even if nothing is known about whether each good is public, private, or assignable within the household, though having such information tightens the bounds. We apply our method to US PSID data, obtaining narrow bounds that yield useful conclusions regarding the effects of income and wages on intrahousehold resource sharing, and on the prevalence of individual (as opposed to household level) poverty.     

Cautious Expected Utility and the Certainty Effect

Many violations of the independence axiom of expected utility can be traced to subjects' attraction to risk‐free prospects. The key axiom in this paper, negative certainty independence ([Dillenberger, 2010]), formalizes this tendency. Our main result is a utility representation of all preferences over monetary lotteries that satisfy negative certainty independence together with basic rationality postulates. Such preferences can be represented as if the agent were unsure of how to evaluate a given lottery p; instead, she has in mind a set of possible utility functions over outcomes and displays a cautious behavior: she computes the certainty equivalent of p with respect to each possible function in the set and picks the smallest one. The set of utilities is unique in a well defined sense. We show that our representation can also be derived from a “cautious” completion of an incomplete preference relation.     

Research Design Meets Market Design: Using Centralized Assignment for Impact Evaluation

A growing number of school districts use centralized assignment mechanisms to allocate school seats in a manner that reflects student preferences and school priorities. Many of these assignment schemes use lotteries to ration seats when schools are oversubscribed. The resulting random assignment opens the door to credible quasi‐experimental research designs for the evaluation of school effectiveness. Yet the question of how best to separate the lottery‐generated randomization integral to such designs from non‐random preferences and priorities remains open. This paper develops easily‐implemented empirical strategies that fully exploit the random assignment embedded in a wide class of mechanisms, while also revealing why seats are randomized at one school but not another. We use these methods to evaluate charter schools in Denver, one of a growing number of districts that combine charter and traditional public schools in a unified assignment system. The resulting estimates show large achievement gains from charter school attendance. Our approach generates efficiency gains over ad hoc methods, such as those that focus on schools ranked first, while also identifying a more representative average causal effect. We also show how to use centralized assignment mechanisms to identify causal effects in models with multiple school sectors.     

Parenting With Style: Altruism and Paternalism in Intergenerational Preference Transmission

We develop a theory of parent‐child relations that rationalizes the choice between alternative parenting styles (as set out in Baumrind, 1967). Parents maximize an objective function that combines Beckerian altruism and paternalism towards children. They can affect their children's choices via two channels: either by influencing children's preferences or by imposing direct restrictions on their choice sets. Different parenting styles (authoritarian, authoritative, and permissive) emerge as equilibrium outcomes and are affected both by parental preferences and by the socioeconomic environment. Parenting style, in turn, feeds back into the children's welfare and economic success. The theory is consistent with the decline of authoritarian parenting observed in industrialized countries and with the greater prevalence of more permissive parenting in countries characterized by low inequality.     

Robustness and Separation in Multidimensional Screening

A principal wishes to screen an agent along several dimensions of private information simultaneously. The agent has quasilinear preferences that are additively separable across the various components. We consider a robust version of the principal's problem, in which she knows the marginal distribution of each component of the agent's type, but does not know the joint distribution. Any mechanism is evaluated by its worst‐case expected profit, over all joint distributions consistent with the known marginals. We show that the optimum for the principal is simply to screen along each component separately. This result does not require any assumptions (such as single crossing) on the structure of preferences within each component. The proof technique involves a generalization of the concept of virtual values to arbitrary screening problems. Sample applications include monopoly pricing and a stylized dynamic taxation model.     

Recursive Equilibria in Dynamic Economies With Stochastic Production

In this paper, we prove the existence of recursive equilibria in a dynamic stochastic model with infinitely lived heterogeneous agents, several commodities, and general inter‐ and intratemporal production. We illustrate the usefulness of our result by providing sufficient conditions for the existence of recursive equilibria in heterogeneous agent versions of both the Lucas asset pricing model and the neoclassical stochastic growth model.     

Perceived Ambiguity and Relevant Measures

We axiomatize preferences that can be represented by a monotonic aggregation of subjective expected utilities generated by a utility function and some set of i.i.d. probability measures over a product state space, S^∞. For such preferences, we define relevant measures, show that they are treated as if they were the only marginals possibly governing the state space, and connect them with the measures appearing in the aforementioned representation. These results allow us to interpret relevant measures as reflecting part of perceived ambiguity, meaning subjective uncertainty about probabilities over states. Under mild conditions, we show that increases or decreases in ambiguity aversion cannot affect the relevant measures. This property, necessary for the conclusion that these measures reflect only perceived ambiguity, distinguishes the set of relevant measures from the leading alternative in the literature. We apply our findings to a number of well‐known models of ambiguity‐sensitive preferences. For each model, we identify the set of relevant measures and the implications of comparative ambiguity aversion.     

Poverty and Self‐Control

We argue that poverty can perpetuate itself by undermining the capacity for self‐control. In line with a distinguished psychological literature, we consider modes of self‐control that involve the self‐imposed use of contingent punishments and rewards. We study settings in which consumers with quasi‐hyperbolic preferences confront an otherwise standard intertemporal allocation problem with credit constraints. Our main result demonstrates that low initial assets can limit self‐control, trapping people in poverty, while individuals with high initial assets can accumulate indefinitely. Thus, even temporary policies that initiate accumulation among the poor may be effective. We examine implications concerning the effect of access to credit on saving, the demand for commitment devices, the design of financial accounts to promote accumulation, and the variation of the marginal propensity to consume across income from different sources. We also explore the nature of optimal self‐control, demonstrating that it has a simple and behaviorally plausible structure that is immune to self‐renegotiation.     

Marriage,Labor Supply,and Home Production

We develop a search model of marriage where men and women draw utility from private consumption and leisure, and from a non‐market good that is produced in the home using time resources. We condition individual decisions on wages, education, and an index of family attitudes. A match‐specific, stochastic bliss shock induces variation in matching given wages, education, and family values, and triggers renegotiation and divorce. Using BHPS (1991–2008) data, we take as given changes in wages, education, and family values by gender, and study their impact on marriage decisions and intrahousehold resource allocation. The model allows to evaluate how much of the observed gender differences in labor supply results from wages, education, and family attitudes. We find that family attitudes are a strong determinant of comparative advantages in home production of men and women, whereas education complementarities induce assortative mating through preferences.     

Nonparametric Welfare Analysis for Discrete Choice

We consider empirical measurement of equivalent variation (EV) and compensating variation (CV) resulting from price change of a discrete good using individual‐level data when there is unobserved heterogeneity in preferences. We show that for binary and unordered multinomial choice, the marginal distributions of EV and CV can be expressed as simple closed‐form functionals of conditional choice probabilities under essentially unrestricted preference distributions. These results hold even when the distribution and dimension of unobserved heterogeneity are neither known nor identified, and utilities are neither quasilinear nor parametrically specified. The welfare distributions take simple forms that are easy to compute in applications. In particular, average EV for a price rise equals the change in average Marshallian consumer surplus and is smaller than average CV for a normal good. These nonparametric point‐identification results fail for ordered choice if the unit price is identical for all alternatives, thereby providing a connection to Hausman–Newey's (2014) partial identification results for the limiting case of continuous choice.     

Investment and Competitive Matching

We study markets in which agents first make investments and are then matched into potentially productive partnerships. Equilibrium investments and the equilibrium matching will be efficient if agents can simultaneously negotiate investments and matches, but we focus on markets in which agents must first sink their investments before matching. Additional equilibria may arise in this sunk‐investment setting, even though our matching market is competitive. These equilibria exhibit inefficiencies that we can interpret as coordination failures. All allocations satisfying a constrained efficiency property are equilibria, and the converse holds if preferences satisfy a separability condition. We identify sufficient conditions (most notably, quasiconcave utilities) for the investments of matched agents to satisfy an exchange efficiency property as well as sufficient conditions (most notably, a single crossing property) for agents to be matched positive assortatively, with these conditions then forming the core of sufficient conditions for the efficiency of equilibrium allocations.