Bryan S. Graham

Rich Nations, Poor Nations: How Much Can Multiple Equilibria Explain?

This paper asks whether the income gap between rich and poor nations can be explained by multiple equilibria. We explore the quantitative implications of a simple two-sector general equilibrium model that gives rise to multiplicity, and calibrate the model for 127 countries. Under the assumptions of the model, around a quarter of the world’s economies are found to be in a low output equilibrium. We also find that, since the output gains associated with an equilibrium switch are sizeable, the model can explain between 15 and 25% of the variation in the logarithm of GDP per worker across countries.

Econometric methods for the analysis of assignment problems in the presence of complementarity and social spillovers 1

Abstract Concern over the distributional effects of policies which induce changes in peer group structure, or ‘associational redistributions’ (Durlauf, 1996c), motivates a substantial body of theoretical and empirical research in economics, sociology, psychology, and education. A growing collection of econometric methods for characterizing the effects of such policies are now available. This chapter surveys these methods. I discuss the identification and estimation of the distributional effects of partner reassignment in one-on-one matching models, the average outcome and inequality effects of segregation, and treatment response in the presence of spillovers.

Efficiency Bounds for Missing Data Models with Semiparametric Restrictions

This paper shows that the semiparametric efficiency bound for a parameter identified by an unconditional moment restriction with data missing at random (MAR) coincides with that of a particular augmented moment condition problem. The augmented system consists of the inverse probability weighted (IPW) original moment restriction and an additional conditional moment restriction which exhausts all other implications of the MAR assumption. The paper also investigates the value of additional semiparametric restrictions on the conditional expectation function (CEF) of the original moment function given always- observed covariates. In the program evaluation context, for example, such restrictions are implied by semiparametric models for the potential outcome CEFs given baseline covariates. The efficiency bound associated with this model is shown to also coincide with that of a particular moment condition problem. Some implications of these results for estimation are briefly discussed.

An Econometric Model of Link Formation with Degree Heterogeneity

I introduce a model of undirected dyadic link formation which allows for assortative matching on observed agent characteristics (homophily) as well as unrestricted agent level heterogeneity in link surplus (degree heterogeneity). Like in fixed effects panel data analyses, the joint distribution of observed and unobserved agent-level characteristics is left unrestricted. Two estimators for the (common) homophily parameter, β0, are developed and their properties studied under an asymptotic sequence involving a single network growing large. The first, tetrad logit (TL), estimator conditions on a sufficient statistic for the degree heterogeneity. The second, joint maximum likelihood (JML), estimator treats the degree heterogeneity {Ai0}Ni=1 as additional (incidental) parameters to be estimated. The TL estimate is consistent under both sparse and dense graph sequences, whereas consistency of the JML estimate is shown only under dense graph sequences. JEL Codes: C31, C33, C35

Comparative Static and Computational Methods for an Empirical One-to-one Transferable Utility Matching Model

I show that the equilibrium distribution of matches associated with the empirical transferable utility one-to-one matching (TUM) model introduced by Choo and Siow (2006a, 2006b) corresponds to the fixed point of system of K + L nonlinear equations; with K and L respectively equal to the number of discrete types of women and men. I use this representation to derive new comparative static results, showing how the match distribution varies with match surplus and the marginal distributions of agent types.

Redistributive Effects for Discretely-Valued Inputs

In this paper we study the effect of reallocating an indivisible input across a population of production units on average output. We define the Average Redistributive Effect (ARE) as the effect of such a reallocation on average output. We consider the case where inputs are discretely-valued, studying the case where they take two or three levels in detail. In these cases the set of feasible reallocations are respectively indexed by one and four parameters. With two input levels the ARE is a linear function with a slope coefficient equal to a measure of input complementarity. The average output maximizing allocation is completely determined by the production technology. With three input levels the optimal allocation depends on both the form of the production function and the availability of inputs at each level in potentially complicated ways. We provide conditions under which the ARE is identified and consider some non-standard aspects of inference. We relate the ARE to the average treatment effect (ATE) estimand and our constrained input allocation problem to the unconstrained treatment assignment problem considered by Manski (2004) and Dehejia (2005).

Identification and efficiency bounds for the average match function under conditionally exogenous matching

ABSTRACT Consider two heterogenous populations of agents who, when matched, jointly produce an output, Y. For example, teachers and classrooms of students together produce achievement, parents raise children, whose life outcomes vary in adulthood, assembly plant managers and workers produce a certain number of cars per month, and lieutenants and their platoons vary in unit effectiveness. Let and denote agent types in the two populations. Consider the following matching mechanism: take a random draw from the W = wj subgroup of the first population and match her with an independent random draw from the X = xk subgroup of the second population. Let β(wj, xk), the average match function (AMF), denote the expected output associated with this match. We show that (i) the AMF is identified when matching is conditionally exogenous, (ii) conditionally exogenous matching is compatible with a pairwise stable aggregate matching equilibrium under specific informational assumptions, and (iii) we calculate the AMF’s semiparametric efficiency bound.