Knowledge that Transforms

This paper studies a shape-invariant Engel curve system with endogenous total expenditure, in which the shape-invariant specification involves a common shift parameter for each demographic group in a pooled system of nonparametric Engel curves. We focus on the identification and estimation of both the nonparametric shapes of the Engel curves and the parametric specification of the demographic scaling parameters. The identification condition relates to the bounded completeness and the estimation procedure applies the sieve minimum distance estimation of conditional moment restrictions, allowing for endogeneity. We establish a new root mean squared convergence rate for the nonparametric instrumental variable regression when the endogenous regressor could have unbounded support. Root-n asymptotic normality and semiparametric efficiency of the parametric components are also given under a set of “low-level” sufficient conditions. Our empirical application using the U.K. Family Expenditure Survey shows the importance of adjusting for endogeneity in terms of both the nonparametric curvatures and the demographic parameters of systems of Engel curves.

We study, theoretically and quantitatively, the general equilibrium of an economy in which households smooth consumption by means of both a riskless asset and unsecured loans with the option to default. The default option resembles a bankruptcy filing under Chapter 7 of the U.S. Bankruptcy Code. Competitive financial intermediaries offer a menu of loan sizes and interest rates wherein each loan makes zero profits. We prove the existence of a steady-state equilibrium and characterize the circumstances under which a household defaults on its loans. We show that our model accounts for the main statistics regarding bankruptcy and unsecured credit while matching key macroeconomic aggregates, and the earnings and wealth distributions. We use this model to address the implications of a recent policy change that introduces a form of “means testing” for households contemplating a Chapter 7 bankruptcy filing. We find that this policy change yields large welfare gains.

We consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression “error” conditional on an instrumental variable to be zero. The resulting estimating equation is a nonlinear integral equation of the first kind, which generates an ill-posed inverse problem. The integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically. We show that the estimator is mean-square consistent, derive its rate of convergence in probability, and give conditions under which this rate is optimal in a minimax sense. The results of Monte Carlo experiments show that the estimator behaves well in finite samples.

We present sufficient conditions for monotone matching in environments where utility is not fully transferable between partners. These conditions involve not only complementarity in types of the total payoff to a match, as in the transferable utility case, but also monotonicity in type of the degree of transferability between partners. We apply our conditions to study some models of risk sharing and incentive problems, deriving new results for predicted matching patterns in those contexts.

This paper investigates a new class of two-player games in continuous time, in which the players' observations of each other's actions are distorted by Brownian motions. These games are analogous to repeated games with imperfect monitoring in which the players take actions frequently. Using a differential equation, we find the set ℰ(r) of payoff pairs achievable by all public perfect equilibria of the continuous-time game, where r is the discount rate. The same differential equation allows us to find public perfect equilibria that achieve any value pair on the boundary of the set ℰ(r). These public perfect equilibria are based on a pair of continuation values as a state variable, which moves along the boundary of ℰ(r) during the course of the game. In order to give players incentives to take actions that are not static best responses, the pair of continuation values is stochastically driven by the players' observations of each other's actions along the boundary of the set ℰ(r). Copyright The Econometric Society 2007.

The Role of Labor Market Intermittency in Explaining Gender Wage Differentials by Julie L. Hotchkiss and M. Melinda Pitts. Published in volume 97, issue 2, pages 417-421 of American Economic Review, May 2007

Where do preferences come from? What determines their properties? Though traditionally reluctant to ask such questions, economists have recently turned to evolutionary models for answers. We focus on intertemporal preferences here, arising out of the evolutionary implications of different reproductive strategies or life histories. An agent’s life history specifies the agent’s number and timing (and in a richer model, quality) of offspring. Evolution will select the life history that maximizes the growth rate of the associated group of individuals. We begin with the simplest possible biological life history, that of a semelparous agent that, if it survives a fixed number of years, reproduces and then dies. We show the evolutionary criterion for success in this case entails hyperbolic time discounting of the log of the number of offspring produced. The rate of time preference is a function of age, however, not of time relative to the present, and there are no preference reversals in the sense of behavioral economics. At the same time, the optimal strategy maximizes the exponentially discounted number of offspring, provided we discount at the sum of the death rate and the maximal growth rate. Conventional discounting thus suffices to induce optimal choices from the agent. More generally, if the animal is iteroparous, that is, has a nondegenerate profile of offspring, we show the evolutionary indifference curves over offspring of various ages are hyperplanes that are not parallel, but tilt to reflect greater impatience as the growth rate increases. There is no additively separable function of the age profile of expected offspring that is globally equivalent to this basic biological growth-rate The Evolution of Intertemporal Preferences

We present a dynamic model of network formation where nodes find other nodes with whom to form links in two ways: some are found uniformly at random, while others are found by searching locally through the current structure of the network (e.g., meeting friends of friends). This combination of meeting processes results in a spectrum of features exhibited by large social networks, including the presence of more high- and low-degree nodes than when links are formed independently at random, having low distances between nodes in the network, and having high clustering of links on a local level. We fit the model to data from six networks and impute the relative ratio of random to network-based meetings in link formation, which turns out to vary dramatically across applications. We show that as the random/network-based meeting ratio varies, the resulting degree distributions can be ordered in the sense of stochastic dominance, which allows us to infer how the formation process affects average utility in the network.

We extend William Rogerson's (2003) intriguing analysis of simple procurement contracts to settings where the supplier's innate production cost is not necessarily distributed uniformly. Although the simple contract that Rogerson analyzes performs remarkably well when the smaller cost realizations are relatively likely, it can perform poorly when the larger cost realizations are relatively likely. We show that in all settings under consideration, a simple pair of contracts – one that involves linear cost sharing and one that involves full cost reimbursement – can always secure more than 73 percent of the gain achieved with a fully optimal contract.

Economists have recently argued recessions play a useful role in fostering growth. Yet a major source of growth, R&D, is procyclical. This paper argues one reason for procyclical R&D is a dynamic externality inherent in R&D that makes entrepreneurs short-sighted and concentrate their innovation in booms, even when it is optimal to concentrate it in recessions. Additional forces may imply that procyclical R&D is desirable, but equilibrium R&D is likely to be too procyclical, and macroeconomic shocks are likely to have overly persistent effects on output and make growth more costly than in the absence of such shocks.