Knowledge that Transforms

To study intertemporal decisions under risk, we develop a new recursive model of non‐expected‐utility preferences. The main axiom of our analysis is called mixture aversion, as it captures a dislike of probabilistic mixtures of lotteries. Our representation for mixture‐averse preferences can be interpreted as if an individual optimally selects her risk attitude from some feasible set. We describe some useful parametric examples of our representation and provide comparative statics that tightly link decreases in risk aversion to larger sets of feasible risk attitudes. We then present several applications of the model. In an insurance problem, mixture‐averse preferences can produce a marginal willingness to pay for insurance coverage that increases in the level of existing coverage. In investment decisions, our model can generate endogenous heterogeneity in equilibrium stock market participation, even when consumers have identical preferences. Finally, we demonstrate that our model can address the Rabin paradox even in the presence of reasonable levels of background risk.

We document that consumption growth rates are far from i.i.d. and have a highly persistent component. First, we estimate univariate and multivariate models of cash‐flow (consumption, output, dividends) growth that feature measurement errors, time‐varying volatilities, and mixed‐frequency observations. Monthly consumption data are important for identifying the stochastic volatility process; yet the data are contaminated, which makes the inclusion of measurement errors essential for identifying the predictable component. Second, we develop a novel state‐space model for cash flows and asset prices that imposes the pricing restrictions of a representative‐agent endowment economy with recursive preferences. To estimate this model, we use a particle MCMC approach that exploits the conditional linear structure of the approximate equilibrium. Once asset return data are included in the estimation, we find even stronger evidence for the persistent component and are able to identify three volatility processes: the one for the predictable cash‐flow component is crucial for asset pricing, whereas the other two are important for tracking the data. Our model generates asset prices that are largely consistent with the data in terms of sample moments and predictability features. The state‐space approach allows us to track over time the evolution of the predictable component, the volatility processes, the decomposition of the equity premium into risk factors, and the variance decomposition of asset prices.

We develop inference methods about long†run comovement of two time series. The parameters of interest are defined in terms of population second moments of low†frequency transformations (“low†pass†filtered versions) of the data. We numerically determine confidence sets that control coverage over a wide range of potential bivariate persistence patterns, which include arbitrary linear combinations of I(0), I(1), near unit roots, and fractionally integrated processes. In an application to U.S. economic data, we quantify the long†run covariability of a variety of series, such as those giving rise to balanced growth, nominal exchange rates and relative nominal prices, the unemployment rate and inflation, money growth and inflation, earnings and stock prices, etc.

Multivalued treatment models have typically been studied under restrictive assumptions: ordered choice, and more recently, unordered monotonicity. We show how treatment effects can be identified in a more general class of models that allows for multidimensional unobserved heterogeneity. Our results rely on two main assumptions: treatment assignment must be a measurable function of threshold‐crossing rules, and enough continuous instruments must be available. We illustrate our approach for several classes of models.

Is the standard hyperbolic†discounting model capable of robust qualitative predictions for savings behavior? Despite results suggesting a negative answer, we provide a positive one. We give conditions under which all Markov equilibria display either saving at all wealth levels or dissaving at all wealth levels. Moreover, saving versus dissaving is determined by a simple condition comparing the interest rate to a threshold made up of impatience parameters only. Our robustness results illustrate a well†behaved side of the model and imply that qualitative behavior is determinate, dissipating indeterminacy concerns to the contrary (Krusell and Smith, 2003). We prove by construction that equilibria always exist and that multiplicity is present in some cases, highlighting that our robust predictions are not due to uniqueness. Similar results may be obtainable in related dynamic games, such as political economy models of public spending.

In French parliamentary and local elections, candidates ranked first and second in the first round automatically qualify for the second round, while a third candidate qualifies only when selected by more than 12.5 percent of registered citizens. Using a fuzzy RDD around this threshold, we find that the third candidate's presence substantially increases the share of registered citizens who vote for any candidate and reduces the vote share of the top two candidates. It disproportionately harms the candidate ideologically closest to the third and causes her defeat in one fifth of the races. Additional evidence suggests that these results are driven by voters who value voting expressively over voting strategically for the top‐two candidate they dislike the least to ensure her victory; and by third candidates who, absent party‐level agreements leading to their dropping out, value the benefits associated with competing in the second round more than influencing its outcome.

We explore the learning process and behavior of an individual with unrealistically high expectations (overconfidence) when outcomes also depend on an external fundamental that affects the optimal action. Moving beyond existing results in the literature, we show that the agent's beliefs regarding the fundamental converge under weak conditions. Furthermore, we identify a broad class of situations in which “learning” about the fundamental is self‐defeating: it leads the individual systematically away from the correct belief and toward lower performance. Due to his overconfidence, the agent—even if initially correct—becomes too pessimistic about the fundamental. As he adjusts his behavior in response, he lowers outcomes and hence becomes even more pessimistic about the fundamental, perpetuating the misdirected learning. The greater is the loss from choosing a suboptimal action, the further the agent's action ends up from optimal. We partially characterize environments in which self‐defeating learning occurs, and show that the decisionmaker learns to take the optimal action if, and in a sense only if, a specific non‐identifiability condition is satisfied. In contrast to an overconfident agent, an underconfident agent's misdirected learning is self‐limiting and therefore not very harmful. We argue that the decision situations in question are common in economic settings, including delegation, organizational, effort, and public‐policy choices.

We develop a tractable method for augmenting macroeconomic models with autonomous variation in higher‐order beliefs. We use this to accommodate a certain type of waves of optimism and pessimism that can be interpreted as the product of frictional coordination and, unlike the one featured in the news literature, regards the short‐term economic outlook rather than the medium‐ to long‐run prospects. We show that this enrichment provides a parsimonious explanation of salient features of the data; it accounts for a significant fraction of the business‐cycle volatility in estimated models that allow for various competing structural shocks; and it captures a type of fluctuations that have a Keynesian flavor but do not rely on nominal rigidities.

Several school districts use assignment systems that give students an incentive to misrepresent their preferences. We find evidence consistent with strategic behavior in Cambridge. Such strategizing can complicate preference analysis. This paper develops empirical methods for studying random utility models in a new and large class of school choice mechanisms. We show that preferences are nonparametrically identified under either sufficient variation in choice environments or a preference shifter. We then develop a tractable estimation procedure and apply it to Cambridge. Estimates suggest that while 83% of students are assigned to their stated first choice, only 72% are assigned to their true first choice because students avoid ranking competitive schools. Assuming that students behave optimally, the Immediate Acceptance mechanism is preferred by the average student to the Deferred Acceptance mechanism by an equivalent of 0.08 miles. The estimated difference is smaller if beliefs are biased, and reversed if students report preferences truthfully.

We develop an aggregative games approach to study oligopolistic price competition with multiproduct firms. We introduce a new class of IIA demand systems, derived from discrete/continuous choice, and nesting CES and logit demands. The associated pricing game with multiproduct firms is aggregative and a firm's optimal price vector can be summarized by a uni‐dimensional sufficient statistic, the ι‐markup. We prove existence of equilibrium using a nested fixed‐point argument, and provide conditions for equilibrium uniqueness. In equilibrium, firms may choose not to offer some products. We analyze the pricing distortions and provide monotone comparative statics. Under (nested) CES and logit demands, another aggregation property obtains: All relevant information for determining a firm's performance and competitive impact is contained in that firm's uni‐dimensional type. We extend the model to nonlinear pricing, quantity competition, general equilibrium, and demand systems with a nest structure. Finally, we discuss applications to merger analysis and international trade.