The agent is modeled as a current self that optimally incurs a cognitive cost of empathizing with future selves. The model unifies well‐known experimental and empirical findings in intertemporal choice and enriches the multiple selves model with a notion of self‐control. The defining feature of the model is magnitude‐decreasing impatience: greater patience toward larger rewards. Two behavioral definitions of magnitude‐decreasing impatience are provided and the model is characterized under each of them.
We evaluate and partially challenge the household leverage view of the Great Recession. In the data, employment and consumption declined more in U.S. states where household debt declined more. We study a model of a monetary union composed of many regions in which liquidity constraints shape the response of employment and consumption to changes in debt. We estimate the model with Bayesian methods combining state and aggregate data. Changes in household credit explain 40% of the differential rise and fall of employment across states, but a small fraction of the aggregate employment decline in 2007–2010. Nevertheless, since household deleveraging was gradual, credit shocks greatly slowed the recovery.
Smooth ambiguity preferences (Klibanoff, Marinacci, and Mukerji (2005)) describe a decision maker who evaluates each act f according to the twofold expectation <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"> <a:mi>V</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>f</a:mi> <a:mo stretchy="false">)</a:mo> <a:mo>=</a:mo> <a:msub> <a:mrow> <a:mo>∫</a:mo> </a:mrow> <a:mrow> <a:mi mathvariant="script">P</a:mi> </a:mrow> </a:msub> <a:mi>ϕ</a:mi> <a:mo stretchy="true" maxsize="5.2ex" minsize="5.2ex">(</a:mo> <a:msub> <a:mrow> <a:mo>∫</a:mo> </a:mrow> <a:mrow> <a:mi mathvariant="normal">Ω</a:mi> </a:mrow> </a:msub> <a:mi>u</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>f</a:mi> <a:mo stretchy="false">)</a:mo> <a:mspace width="0.2em"/> <a:mi mathvariant="normal">d</a:mi> <a:mi>p</a:mi> <a:mo stretchy="true" maxsize="5.2ex" minsize="5.2ex">)</a:mo> <a:mspace width="0.2em"/> <a:mi mathvariant="normal">d</a:mi> <a:mi>μ</a:mi> <a:mo stretchy="false">(</a:mo> <a:mi>p</a:mi> <a:mo stretchy="false">)</a:mo> </a:math> defined by a utility function u , an ambiguity index ϕ , and a belief μ over a set <u:math xmlns:u="http://www.w3.org/1998/Math/MathML" display="inline"> <u:mi mathvariant="script">P</u:mi> </u:math> of probabilities. We provide an axiomatic foundation for the representation, taking as a primitive a preference over Anscombe–Aumann acts. We study a special case where <x:math xmlns:x="http://www.w3.org/1998/Math/MathML" display="inline"> <x:mi mathvariant="script">P</x:mi> </x:math> is a subjective statistical model that is point identified, that is, the decision maker believes that the true law <ab:math xmlns:ab="http://www.w3.org/1998/Math/MathML" display="inline"> <ab:mi>p</ab:mi> <ab:mo>∈</ab:mo> <ab:mi mathvariant="script">P</ab:mi> </ab:math> can be recovered empirically. Our main axiom is a joint weakening of Savage's sure‐thing principle and Anscombe–Aumann's mixture independence. In addition, we show that the parameters of the representation can be uniquely recovered from preferences, thereby making operational the separation between ambiguity attitude and perception, a hallmark feature of the smooth ambiguity representation.
If experiment A is Blackwell more informative than experiment B , it is always possible that A and B are induced by signals A′ and B′ such that A′ is a refinement of B′, that is, A′ entails observing B′ plus some additional information. We first show that this result does not extend beyond pairs of experiments: There exist collections of experiments that cannot be induced by a collection of signals so that whenever two experiments are Blackwell ordered, the associated signals are refinement ordered. In other words, sometimes it is impossible for more informed agents to know everything that less informed agents know. More broadly, define an information hierarchy to be a partially ordered set that ranks experiments in terms of informativeness. Is it the case that for any choice of experiments indexed on the hierarchy such that higher experiments are Blackwell more informative, there are signals that induce these experiments with higher signals being refinements of lower signals? We show that the answer is affirmative if and only if the undirected graph of the information hierarchy is a forest.
Discrete location, occupation, skill, and hours choices of workers underpin their incomes. This paper analyzes the optimal taxation of discrete income‐generating choice. It derives optimal tax equations and Pareto test inequalities for mixed logit choice environments that can accommodate discrete and unstructured choice sets, rich preference heterogeneity, and complex aggregate cross‐substitution patterns between choices. These equations explicitly connect optimal taxes to societal redistributive goals and private substitution behavior, with the latter encoded as a substitution matrix that describes cross‐sensitivities of choice distributions to tax‐induced utility variation. In repeated mixed logit settings, the substitution matrix is exactly the Markov matrix of shock‐induced agent transitions across choices. We describe implications of this equivalence for evaluation of prevailing tax designs and the structural estimation of optimal policy mixed logit models. We apply our results to two salient examples: spatial taxation and taxation of couples.
We document that between 50% and 70% of changes in the U.S. wage structure over the last four decades are accounted for by relative wage declines of worker groups specialized in routine tasks in industries experiencing rapid automation. We develop a conceptual framework where tasks across industries are allocated to different types of labor and capital. Automation technologies expand the set of tasks performed by capital, displacing certain worker groups from jobs for which they have comparative advantage. This framework yields a simple equation linking wage changes of a demographic group to the task displacement it experiences. We report robust evidence in favor of this relationship and show that regression models incorporating task displacement explain much of the changes in education wage differentials between 1980 and 2016. The negative relationship between wage changes and task displacement is unaffected when we control for changes in market power, deunionization, and other forms of capital deepening and technology unrelated to automation. We also propose a methodology for evaluating the full general equilibrium effects of automation, which incorporate induced changes in industry composition and ripple effects due to task reallocation across different groups. Our quantitative evaluation explains how major changes in wage inequality can go hand‐in‐hand with modest productivity gains.
How can one determine whether a treatment, such as the introduction of a social program or trade shock, alters agents' incentives to form links in a network? This paper proposes analogs of a two‐sample Kolmogorov–Smirnov test, widely used in the literature to test the null hypothesis of no treatment effects, for network data. It first specifies a testing problem in which the null hypothesis is that two networks are drawn from the same random graph model. It then describes two randomization tests based on the magnitude of the difference between the networks' adjacency matrices as measured by the 2 → 2 and ∞ → 1 operator norms. Power properties of the tests are examined analytically, in simulation, and through two real‐world applications. A key finding is that the test based on the ∞ → 1 norm can be much more powerful for the kinds of sparse and degree‐heterogeneous networks common in economics.
United States households' consumption expenditures and car purchases collapsed during the Great Recession and more so than income changes would have predicted. Using CEX data, we show that both the extensive and the intensive car spending margins contracted sharply in the Great Recession. We also document significant cross‐cohort differences in the impact of the Great Recession including a stronger reduction in car spending by younger cohorts. We draw inference on the sources of the Great Recession by investigating which shocks can explain household choices in a 60 period life‐cycle model with idiosyncratic and aggregate shocks fitted to aggregate and life‐cycle moments. We find that the Great Recession was caused by a combination of large aggregate income and wealth shocks, while cross‐cohort adjustment patterns imply a role for life‐cycle income profile shocks. We also find a role for car loan premia shocks in accounting for car spending and car loans.
Airfares fluctuate due to demand shocks and intertemporal variation in willingness to pay. I estimate a model of dynamic airline pricing accounting for both sources of price adjustments using flight‐level data. I use the model estimates to evaluate the welfare effects of dynamic airline pricing. Relative to uniform pricing, dynamic pricing benefits early‐arriving, leisure consumers at the expense of late‐arriving, business travelers. Although dynamic pricing ensures seat availability for business travelers, these consumers are then charged higher prices. When aggregated over markets, welfare is higher under dynamic pricing than under uniform pricing. The direction of the welfare effect at the market level depends on whether dynamic price adjustments are mainly driven by demand shocks or by changes in the overall demand elasticity.
In this paper, we argue that a large class of recursive contracts can be studied by means of the conventional Negishi method. A planner is responsible for prescribing current actions along with a distribution of future utility values to all agents, so as to maximize their weighted sum of utilities. Under convexity, the method yields the exact efficient frontier. Otherwise, the implementation requires contracts be contingent on publicly observable random signals uncorrelated to fundamentals. We also provide operational first‐order conditions for the characterization of efficient contracts. Finally, we compare extensively our approach with the dual method established in the literature.