Casey Rothschild

Adversarial Risk Analysis with Incomplete Information: A Level-k Approach

This article proposes, develops, and illustrates the application of level-k game theory to adversarial risk analysis. Level-k reasoning, which assumes that players play strategically but have bounded rationality, is useful for operationalizing a Bayesian approach to adversarial risk analysis. It can be applied in a broad class of settings, including settings with asynchronous play and partial but incomplete revelation of early moves. Its computational and elicitation requirements are modest. We illustrate the approach with an application to a simple defend-attack model in which the defenders countermeasures are revealed with a probability less than one to the attacker before he decides on how or whether to attack.

The Efficiency of Categorical Discrimination in Insurance Markets

Crocker and Snow (1986) show that banning categorization based on risk-related characteristics such as gender or race in pricing insurance policies is inefficient whenever categorization is costless. Their analysis, by contrast, suggests ambiguous welfare effects of banningcostlycategorization. I show that this latter conclusion is incorrect: categorical pricing bans are inefficient even when categorization is costly. Whenever the ban-imposing government can instead provide breakeven partial social insurance, it can remove its ban in such a way that the insurance market will choose to employ the categorizing technology only when doing so is Pareto improving.

Robust Adversarial Risk Analysis: A Level-k Approach

Adversarial risk analysis is an active and important area of decision analytic research. Both single-actor decision analysis and multiple-actor game theory have been applied to this problem, with game theoretic methods being particularly popular. Although game theory models do explicitly capture strategic interactions between attackers and defenders, two of the key assumptions---decision making based on subjective expected utility maximization and common knowledge of rationality---are known to be descriptively inaccurate in some situations. This paper addresses these shortcomings by proposing, formulating, and illustrating the application of robust optimization methodologies to a level-k game theory model for adversarial risk analysis. Level-k game theory provides a practical method for modeling bounded rationality. Robust optimization provides an alternative way to model the actions of conservative players facing “deep” uncertainties about their environment---uncertainties that are possible to bound but that are difficult or impossible to represent using probability distributions. Our approach thus combines level-k and robust optimization insights to provide a computationally tractable model of boundedly rational players who are faced with significant and difficult to quantify uncertainties.

Enhancing Retirement Security Through the Tax Code: The Efficacy of Tax-Based Subsidies in Life Annuity Markets

The under-development of existing annuity markets coupled with the secular trend away from traditional pensions towards defined contribution accounts in the U.S. raises significant concerns about the adequacy of retirement income for future retirees. We develop dynamic programming techniques to evaluate the efficacy of policies designed to address this concern by encouraging annuitization. Our analysis suggests that policies providing monetary incentives through the tax code can indeed significantly enhance annuitization among retirees: our central estimates suggest that tax-exemption based policies which have been recently proposed in Congress have the potential to increase annuitization by as much as

Screening with Endogenous Preferences

50,000 for each retired household, at a relatively modest revenue cost to the government. Similar sized policies based instead on refundable tax credits may be more desirable from both efficiency and distributional perspectives.

Risk Classification and Health Insurance

A general framework is developed for studying screening in many-agent discrete type environments wherein each agent’s preferences depend endogenously on the allocations received by the other agents. Applications include optimal income taxation, performance contracting with across-worker externalities, and insurance with endogenous risks. The solution to the principal’s problem is analyzed by decomposing it, a la Rothschild and Scheuer (2013, 2014b), into an inner problem with fixed preferences and an outer problem with varying preferences. The outer problem is typically discontinuous at points where the preferences of two or more types endogenously coincide. As a result, the principal will frequently find it optimal to select allocations which involve two or more types with endogenously coinciding preferences, even though such allocations may appear, ex-ante, to be highly unusual. Assuming that types are strictly ordered by their single-crossing preferences is, therefore, not innocuous in endogenous preference environments.

Risk Classification in Insurance Contracting

Risk classification refers to the use of observable characteristics by insurers to group individuals with similar expected claims, compute the corresponding premiums, and thereby reduce asymmetric information. With perfect risk classification, premiums fully reflect the expected cost associated with each class of risk characteristics and yield efficient outcomes. In the health sector, risk classification is also subject to concerns about social equity and potential discrimination. We present an analytical framework that illustrates the potential trade-off between efficient insurance provision and social equity. We also review empirical studies on risk classification and residual asymmetric information that inform this trade-off.

A Guide for “JEE Content” Submissions

Risk classification refers to the use of observable characteristics by insurers to group individuals with similar expected claims, compute the corresponding premiums, and thereby reduce asymmetric information. An efficient risk classification system generates premiums that fully reflect the expected cost associated with each class of risk characteristics. This is known as financial equity. In the health sector, risk classification is also subject to concerns about social equity and potential discrimination. We present different theoretical frameworks that illustrate the potential trade-off between efficient insurance provision and social equity. We also review empirical studies on risk classification and residual asymmetric information.

Complexity and Macro Pedagogy: The Complexity Vision as a Bridge between Graduate and Undergraduate Macro

This is an update of a guide to the thinking of the editorial collective for the Content section of the Journal of Economic Education (JEE). The authors discuss the type of papers they are looking for, what in their view constitutes a good paper, and how their review process works. They specifically discuss their reviewing process, the content they are looking for, and their view of the structure of a good paper. Although they focus specifically on Content articles for the JEE, many of the general issues discussed may carry over to other sections of the JEE and to journals more generally.

A Guide for Submissions to the JEE Content Section

The macro economy is complex; everyone knows that. Complex systems are difficult to analyze and manage; everyone knows that too. The best approach to teaching and describing the complex macro economy is something we know much less well. Currently, in teaching macro to both graduate and undergraduate students, we don’t stress just how complex the economy really is. The argument in this paper is that we should emphasize that complexity to frame the macro question.1 Having done that, we can get on with what we do, and much of the structure of both the graduate and undergraduate macro can be taught as it currently is. But instead of seeing the approaches at the two levels as substitutes for one another, complexity helps to frame as what they really are: complementary approaches to addressing a challenging set of questions.