Knowledge that Transforms

The accepted manuscript version (last revised 5 Jan 2018 (v8)) has 118 pages, 3 tables, 11 figures, and includes supplementary appendix. This version corrects some typos in Example 2 of the published version. This supplement contains 11 appendices with additional results and some omitted proofs. Appendices F-J include additional results for Sections 2-7, respectively. Appendix K gathers auxiliary results on algebra of covering entropies. Appendices L and M contain the proofs of Sections 4 and 5 omitted from the main text. Appendix N contains the proofs of Sections 6 omitted from the main text, together with the proofs of the additional results for Section 6 in Appendix I. Appendix O reports the results of a simulation experiment.

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.

We propose a method to correct for sample selection in quantile regression models. Selection is modeled via the cumulative distribution function, or copula, of the percentile error in the outcome equation and the error in the participation decision. Copula parameters are estimated by minimizing a method‐of‐moments criterion. Given these parameter estimates, the percentile levels of the outcome are readjusted to correct for selection, and quantile parameters are estimated by minimizing a rotated “check” function. We apply the method to correct wage percentiles for selection into employment, using data for the UK for the period 1978–2000. We also extend the method to account for the presence of equilibrium effects when performing counterfactual exercises.

This paper proposes a perfectly competitive model of a market with adverse selection. Prices are determined by zero-profit conditions, and the set of traded contracts is determined by free entry. Crucially for applications, contract characteristics are endogenously determined, consumers may have multiple dimensions of private information, and an equilibrium always exists. Equilibrium corresponds to the limit of a differentiated products Bertrand game. We apply the model to establish theoretical results on the equilibrium effects of mandates. Mandates can increase efficiency but have unintended consequences. With adverse selection, an insurance mandate reduces the price of low-coverage policies, which necessarily has indirect effects such as increasing adverse selection on the intensive margin and causing some consumers to purchase less coverage.

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.

This paper develops a theory in which society-wide economic outcomes shape individual aspira-tions, which affect the investment incentives of individuals. Through its impact on investments, aspirations in turn affect ambient social outcomes. We explore this two-way link. A central feature is that aspirations that are moderately above an individual’s current standard of living tend to encourage investment, while still higher aspirations may lead to frustration and lower investment. When integrated with the feedback effect from investment, we are led to a the-ory in which aspirations and income evolve jointly, and the social determinants of preferences play an important role. We examine conditions under which growth is compatible with long-run equality in the distribution of income. More generally, we describe steady state income distri-butions, which are typically clustered around local poles. Finally, the theory has predictions for the growth rates along the cross-section of income. We use these predictions to calibrate the model so that it fits growth data by income percentile for 43 countries, and back out the implicit aspirations-formation process that underlies these observations.

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 develop a theory that rationalizes the use of a dominant unit of account in an economy. Agents enter into non-contingent contracts with a variety of business partners. Trade unfolds sequentially in credit chains and is subject to random matching. By using a dominant unit of account, agents can lower their exposure to relative price risk, avoid costly default, and create more total surplus. We discuss conditions under which it is optimal to adopt circulating government paper as the dominant unit of account, and the optimal choice of ?currency areas? when there is variation in the intensity of trade within and across regions.

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.