Knowledge that Transforms

We study some seemingly anomalous results that arise in possibly misspecified, reduced-rank linear asset-pricing models estimated by the continuously updated generalized method of moments. When a spurious factor (that is, a factor that is uncorrelated with the returns on the test assets) is present, the test for correct model specification has asymptotic power that is equal to the nominal size. In other words, applied researchers will erroneously conclude that the model is correctly specified even when the degree of misspecification is arbitrarily large.The rejection probability of the test for overidentifying restrictions typically decreases further in underidentified models where the dimension of the null space is larger than 1.

It is often argued that additional constraints on redistribution such as granting veto power to more players in society better protects property from expropriation. We use a model of multilateral bargaining to demonstrate that this intuition may be flawed. Increasing the number of veto players or raising the supermajority requirement for redistribution may reduce protection on the equilibrium path. The reason is the existence of two distinct mechanisms of property protection. One is formal constraints that allow individuals or groups to block any redistribution that is not in their favor. The other occurs in equilibrium where players without such powers protect each other from redistribution. Players without formal veto power anticipate that the expropriation of other similar players will ultimately hurt them and thus combine their influence to prevent redistributions. In a stable allocation, the society exhibits a “class” structure with class members having equal wealth and strategically protecting each other from redistribution.

We develop a continuum player timing game that subsumes standard wars of attrition and pre‐emption games, and introduces a new rushes phenomenon. Payoffs are continuous and single‐peaked functions of the stopping time and stopping quantile. We show that if payoffs are hump‐shaped in the quantile, then a sudden “rush” of players stops in any Nash or subgame perfect equilibrium. Fear relaxes the first mover advantage in pre‐emption games, asking that the least quantile beat the average; greed relaxes the last mover advantage in wars of attrition, asking just that the last quantile payoff exceed the average. With greed, play is inefficiently late: an accelerating war of attrition starting at optimal time, followed by a rush. With fear, play is inefficiently early: a slowing pre‐emption game, ending at the optimal time, preceded by a rush. The theory predicts the length, duration, and intensity of stopping, and the size and timing of rushes, and offers insights for many common timing games.

We develop a theory of intergenerational transmission of preferences that rationalizes the choice between alternative parenting styles (as set out in Baumrind1967). ParentsmaximizeanobjectivefunctionthatcombinesBeckerian 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.

The ill-posedness of the inverse problem of recovering a regression function in a 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 regression function is monotone and consider sieve estimators that enforce the monotonicity constraint.We define a restricted measure of ill-posedness that is relevant for the constrained estimators and show that under the monotone IV assumption and certain other conditions, our measure of ill-posedness is bounded uniformly over the dimension of the sieve space, in stark contrast with a well-known result that the unrestricted sieve measure of ill-posedness that is relevant for the unconstrained estimators 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 estimators.The bound gives a set of data-generating processes where the monotonicity constraint has a particularly strong regularization effect and considerably improves the performance of the estimators.The bound shows that the regularization effect can be strong even in large samples and for steep regression functions if the NPIV model is severely ill-posed -a finding that is confirmed by our simulation study.We apply the constrained estimator to the problem of estimating gasoline demand from U.S. data.

This paper extends the long-term factorization of the stochastic discount factor introduced and studied by Alvarez and Jermann (2005) in discrete-time ergodic environments and by Hansen and Scheinkman (2009) and Hansen (2012) in Markovian environments to general semimartingale environments. The transitory component discounts at the stochastic rate of return on the long bond and is factorized into discounting at the long-term yield and a positive semimartingale that extends the principal eigenfunction of Hansen and Scheinkman (2009) to the semimartingale setting. The permanent component is a martingale that accomplishes a change of probabilities to the long forward measure, the limit of T-forward measures. The change of probabilities from the data-generating to the long forward measure absorbs the long-term risk-return trade-off and interprets the latter as the long-term risk-neutral measure.

This paper examines the role of uncertainty shocks in a one-sector, representative-agent dynamic stochastic general-equilibrium model. When prices are exible, uncertainty shocks are not capable of producing business-cycle comovements among key macro variables. With countercyclical markups through sticky prices, however, uncertainty shocks can generate uctuations that are consistent with business cycles. Monetary policy usually plays a key role in osetting the negative impact of uncertainty shocks. If the central bank is constrained by the zero lower bound, then monetary policy can no longer perform its usual stabilizing function and higher uncertainty has even more negative eects on the economy. Calibrating the size of uncertainty shocks using uctuations in the VIX, we nd that increased uncertainty about the future may indeed have played a signicant role in worsening the Great Recession, which is consistent with statements by policymakers, economists, and the nancial press.

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.

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 o↵er 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.

This paper provides positive testability results for the identification condition in a nonparametric instrumental variable model, known as completeness, and it links the outcome of the test to properties of an estimator of the structural function. In particular, I show that the data can provide empirical evidence in favor of both an arbitrarily small identified set as well as an arbitrarily small asymptotic bias of the estimator. This is the case for a large class of complete distributions as well as certain incomplete distributions. As a byproduct, the results can be used to estimate an upper bound of the diameter of the identified set and to obtain an easy to report estimator of the identified set itself.