Economics

We study conditions for the existence of stable and group-strategy-proof mechanisms in a many-to-one matching model with contracts if students' preferences are monotone in contract terms. We show that "equivalence", properly defined, to a choice profile under which contracts are substitutes and the law of aggregate holds is a necessary and sufficient condition for the existence of a stable and group-strategy-proof mechanism. Our result can be interpreted as a (weak) embedding result for choice functions under which contracts are observable substitutes and the observable law of aggregate demand holds.

Plurality and approval voting are two well-known voting systems with different strengths and weaknesses. In this paper we consider a new voting system we call beta(k) which allows voters to select a single first-choice candidate and approve of any other number of candidates, where k denotes the relative weight given to a first choice; this system is essentially a hybrid of plurality and approval. Our primary goal is to characterize the behavior of beta(k) for any value of k. Under certain reasonable assumptions, beta(k) can be made to mimic plurality or approval voting in the event of a single winner while potentially breaking ties otherwise. Under the assumption that voters are honest, we show that it is possible to find the values of k for which a given candidate will win the election if the respective approval and plurality votes are known. Finally, we show how some of the commonly used voting system criteria are satisfied by beta(k).

Our understanding of risk preferences can be sharpened by considering their evolutionary basis. The existing literature has focused on two sources of risk: idiosyncratic risk and aggregate risk. We introduce a new source of risk, heritable risk, in which there is a positive correlation between the fitness of a newborn agent and the fitness of her parent. Heritable risk was plausibly common in our evolutionary past and it leads to a strictly higher growth rate than the other sources of risk. We show that the presence of heritable risk in the evolutionary past may explain the tendency of people to exhibit skewness loving today.

We introduce an evolutionary framework to evaluate competing (mis)specifications in strategic situations, focusing on which misspecifications can persist over a correct specification. Agents with heterogeneous specifications coexist in a society and repeatedly match against random opponents to play a stage game. They draw Bayesian inferences about the environment based on personal experience, so their learning depends on the distribution of specifications and matching assortativity in the society. One specification is evolutionarily stable against another if, whenever sufficiently prevalent, its adherents obtain higher expected objective payoffs than their counterparts. The learning channel leads to novel stability phenomena compared to frameworks where the heritable unit of cultural transmission is a single belief instead of a specification (i.e., set of feasible beliefs). We apply the framework to linear-quadratic-normal games where players receive correlated signals but possibly misperceive the information structure. The correct specification is not evolutionarily stable against a correlational error, whose direction depends on matching assortativity. As another application, the framework also endogenizes coarse analogy classes in centipede games.

The potential benefits of portfolio diversification have been known to investors for a long time. Markowitz (1952) suggested the seminal approach for optimizing the portfolio problem based on finding the weights as budget shares that minimize the variance of the underlying portfolio. Hatemi-J and El-Khatib (2015) suggested finding the weights that will result in maximizing the risk adjusted return of the portfolio. This approach seems to be preferred by the rational investors since it combines risk and return when the optimal budget shares are sought for. The current paper provides a general solution for this risk adjusted return problem that can be utilized for any potential number of assets that are included in the portfolio.

The Solow-Swan model is shortly reviewed from a mathematical point of view. By considering non-constant returns to scale, we obtain a general solution strategy. We then compute the exact solution for the Cobb-Douglas production function, for both the classical model and the von Bertalanffy model. Numerical simulations are provided.

The principle that rational agents should maximize expected utility or choiceworthiness is intuitively plausible in many ordinary cases of decision-making under uncertainty. But it is less plausible in cases of extreme, low-probability risk (like Pascal's Mugging), and intolerably paradoxical in cases like the St. Petersburg and Pasadena games. In this paper I show that, under certain conditions, stochastic dominance reasoning can capture most of the plausible implications of expectational reasoning while avoiding most of its pitfalls. Specifically, given sufficient background uncertainty about the choiceworthiness of one's options, many expectation-maximizing gambles that do not stochastically dominate their alternatives "in a vacuum" become stochastically dominant in virtue of that background uncertainty. But, even under these conditions, stochastic dominance will not require agents to accept options whose expectational superiority depends on sufficiently small probabilities of extreme payoffs. The sort of background uncertainty on which these results depend looks unavoidable for any agent who measures the choiceworthiness of her options in part by the total amount of value in the resulting world. At least for such agents, then, stochastic dominance offers a plausible general principle of choice under uncertainty that can explain more of the apparent rational constraints on such choices than has previously been recognized.

Recursive preferences, of the sort developed by Epstein and Zin (1989), play an integral role in modern macroeconomics and asset pricing theory. Unfortunately, it is non-trivial to establish the unique existence of a solution to recursive utility models. We show that the tightest known existence and uniqueness conditions can be extended to (i) Schorfheide, Song and Yaron (2018) recursive utilities and (ii) recursive utilities with `narrow framing'. Further, we sharpen the solution space of Borovicka and Stachurski (2019) from L 1 to L p so that the results apply to a broader class of modern asset pricing models. For example, using L 2 Hilbert space theory, we find the class of parameters which generate a unique L 2 solution to the Bansal and Yaron (2004) and Schorfheide, Song and Yaron (2018) models.

In this paper we develop a general framework to analyze stochastic dynamic problems with unbounded utility functions and correlated and unbounded shocks. We obtain new results of the existence and uniqueness of solutions to the Bellman equation through a general fixed point theorem that generalizes known results for Banach contractions and local contractions. We study an endogenous growth model as well as the Lucas asset pricing model in an exchange economy, significantly expanding their range of applicability.

This paper derives primitive, easily verifiable sufficient conditions for existence and uniqueness of (stochastic) recursive utilities for several important classes of preferences. In order to accommodate models commonly used in practice, we allow both the state-space and per-period utilities to be unbounded. For many of the models we study, existence and uniqueness is established under a single, primitive "thin tail" condition on the distribution of growth in per-period utilities. We present several applications to robust preferences, models of ambiguity aversion and learning about hidden states, and Epstein-Zin preferences.