TABLE OF CONTENTS Volume 86, Issue 1 (January 2018)
James J. Heckman, Rodrigo Pinto
This paper defines and analyzes a new monotonicity condition for the identification of counterfactuals and treatment effects in unordered discrete choice models with multiple treatments, heterogeneous agents, and discrete‐valued instruments. Unordered monotonicity implies and is implied by additive separability of choice of treatment equations in terms of observed and unobserved variables. These results follow from properties of binary matrices developed in this paper. We investigate conditions under which unordered monotonicity arises as a consequence of choice behavior. We characterize IV estimators of counterfactuals as solutions to discrete mixture problems.
Growth, Trade, and Inequality
Gene M. Grossman, Elhanan Helpman
We introduce firm and worker heterogeneity into a model of innovation‐driven endogenous growth. Individuals who differ in ability sort into either a research activity or a manufacturing sector. Research projects generate new varieties of a differentiated product. Projects differ in quality and the resulting technologies differ in productivity. In both sectors, there is a complementarity between firm quality and worker ability. We study the co‐determination of growth and income inequality in both the closed and open economy, as well as the spillover effects of policy in one country to outcomes in others.
Assortative Matching with Large Firms
Jan Eeckhout, Philipp Kircher
Two cornerstones of empirical and policy analysis of firms, in macro, labor and industrial organization, are the determinants of the firm size distribution and the determinants of sorting between workers and firms. We propose a unifying theory of production where management resolves a tradeoff between hiring more versus better workers. The span of control or size is therefore intimately intertwined with the sorting pattern. We provide a condition for sorting that captures this tradeoff between the quantity and quality of workers and that generalizes Becker's sorting condition. A system of differential equations determines the equilibrium allocation, the firm size, and wages, and allows us to characterize the allocation of the quality and quantity of labor to firms of different productivity. We show that our model nests a large number of widely used existing models. We also augment the model to incorporate labor market frictions in the presence of sorting with large firms.
The Dual Approach to Recursive Optimization: Theory and Examples
Nicola Pavoni, Christopher Sleet, Matthias Messner
We develop a recursive dual method for solving dynamic economic problems. The method uses a Lagrangian to pair a dynamic recursive economic problem with a dual problem. We show that such dual problems can be recursively decomposed with costates (i.e., Lagrange multipliers on laws of motion) functioning as state variables. In dynamic contracting and policy settings, the method often replaces an endogenous state space of forward‐looking utilities with an exogenously given state space of costates. We provide a principle of optimality for dual problems and give conditions under which the dual Bellman operator is a contraction with the optimal dual value function its unique fixed point. We relate economic problems to their duals, address computational issues, and give examples.
Time Preferences and Bargaining
This paper presents an analysis of general time preferences in the canonical Rubinstein (1982) model of bargaining, allowing for arbitrarily history‐dependent strategies. I derive a simple sufficient structure for optimal punishments and thereby fully characterize (i) the set of equilibrium outcomes for any given preference profile, and (ii) the set of preference profiles for which equilibrium is unique. Based on this characterization, I establish that a weak notion of present bias—implied, for example, by any hyperbolic or quasi‐hyperbolic discounting—is sufficient for equilibrium to be unique, stationary, and efficient. Conversely, I demonstrate how certain violations of present bias give rise to multiple (non‐stationary) equilibria that feature delayed agreement under gradually increasing offers.
Equilibrium Selection in Auctions and High Stakes Games
Paul Milgrom, Joshua Mollner
We introduce the test-set equilibrium refinement of Nash equilibrium to formalize the idea that players contemplate only deviations from equilibrium play in which a single competitor plays a non‐equilibrium best response. We then apply this refinement to three well‐known auction games, comparing our findings to similar ones previously obtained by specialized equilibrium selections. We also introduce a theory of high stakes versions of games, in which strategies are first proposed and then subjected to a potentially costly review‐and‐revise process. We demonstrate a sense in which the test‐set equilibria emerge from such processes when the cost of revision is small.
Identifying Preferences in Networks with Bounded Degree
Áureo de Paula, Seth Richards‐Shubik, Elie Tamer
This paper provides a framework for identifying preferences in a large network where links are pairwise stable. Network formation models present difficulties for identification, especially when links can be interdependent, for example, when indirect connections matter. We show how one can use the observed proportions of various local network structures to learn about the underlying preference parameters. The key assumption for our approach restricts individuals to have bounded degree in equilibrium, implying a finite number of payoff‐relevant local structures. Our main result provides necessary conditions for parameters to belong to the identified set. We then develop a quadratic programming algorithm that can be used to construct this set. With further restrictions on preferences, we show that our conditions are also sufficient for pairwise stability and therefore characterize the identified set precisely. Overall, the use of both the economic model along with pairwise stability allows us to obtain effective dimension reduction.
Identification of Nonparametric Simultaneous Equations Models with a Residual Index Structure
Steven T. Berry, Philip A. Haile
We present new identification results for a class of nonseparable nonparametric simultaneous equations models introduced by Matzkin (2008). These models combine traditional exclusion restrictions with a requirement that each structural error enter through a “residual index.” Our identification results are constructive and encompass a range of special cases with varying demands on the exogenous variation provided by instruments and the shape of the joint density of the structural errors. The most important results demonstrate identification when instruments have only limited variation. Even when instruments vary only over a small open ball, relatively mild conditions on the joint density suffice. We also show that the primary sufficient conditions for identification are verifiable and that the maintained hypotheses of the model are falsifiable.
Identification of Treatment Effects under Conditional Partial Independence
Matthew A. Masten, Alexandre Poirier
Conditional independence of treatment assignment from potential outcomes is a commonly used but nonrefutable assumption. We derive identified sets for various treatment effect parameters under nonparametric deviations from this conditional independence assumption. These deviations are defined via a conditional treatment assignment probability, which makes it straightforward to interpret. Our results can be used to assess the robustness of empirical conclusions obtained under the baseline conditional independence assumption.