Rich Nations, Poor Nations: How much can multiple equilibria explain?

The idea that income differences between rich and poor nations arise through multiple equilibria or 'poverty traps' is as intuitive as it is difficult to verify. In this paper, we explore the empirical relevance of such models. We calibrate a simple two sector model for 127 countries, and use the results to analyze the international prevalence of poverty traps and their consequences for productivity. We also examine the possible effects of multiplicity on the world distribution of income, and identify events in the data that may correspond to equilibrium switching.

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 a large number of countries. Under the assumptions of the model, around a quarter of the world’s economies are found to be in a low output equilibrium. The output gains associated with an equilibrium switch are sizeable, but well short of the vast income disparity observed in the data.poverty traps, multiple equilibria, TFP differences,calibration

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.

Scenario Sampling for Large Supermodular Games

This paper introduces a simulation algorithm for evaluating the log-likelihood function of a large supermodular binary-action game. Covered examples include (certain types of) peer effect, technology adoption, strategic network formation, and multi-market entry games. More generally, the algorithm facilitates simulated maximum likelihood (SML) estimation of games with large numbers of players, $T$, and/or many binary actions per player, $M$ (e.g., games with tens of thousands of strategic actions, $TM=O(10^4)$). In such cases the likelihood of the observed pure strategy combination is typically (i) very small and (ii) a $TM$-fold integral who region of integration has a complicated geometry. Direct numerical integration, as well as accept-reject Monte Carlo integration, are computationally impractical in such settings. In contrast, we introduce a novel importance sampling algorithm which allows for accurate likelihood simulation with modest numbers of simulation draws.Comment: 40 pages, 2 Figures and an 8 page Appendi

Identification and Estimation of 'Irregular' Correlated Random Coefficient Models

In this paper we study identification and estimation of a correlated random coefficients (CRC) panel data model. The outcome of interest varies linearly with a vector of endogenous regressors. The coefficients on these regressors are heterogenous across units and may covary with them. We consider the average partial effect (APE) of a small change in the regressor vector on the outcome (cf., Chamberlain, 1984; Wooldridge, 2005a). Chamberlain (1992) calculates the semiparametric efficiency bound for the APE in our model and proposes a √ N consistent estimator. Nonsingularity of the APEâs information bound, and hence the appropriateness of Chamberlainâs (1992) estimator, requires (i) the time dimension of the panel ( T) to strictly exceed the number of random coefficients ( p) and (ii) strong conditions on the time series properties of the regressor vector. We demonstrate irregular identification of the APE when T = p and for more persistent regressor processes. Our approach exploits the different identifying information in the subpopulations of âstayersâ â or units whose regressor values change little across periods â and âmoversâ â or units whose regressor values change substantially across periods. We propose a feasible estimator based on our identification result and characterize its large sample properties. While irregularity precludes our estimator from attaining parametric rates of convergence, it limiting distribution is normal and inference is straightforward to conduct. Standard software may be used to compute point estimates and standard errors. We use our methods to estimate the average elasticity of calorie consumption with respect to total outlay for a sample of poor Nicaraguan households.

Identification in a Binary Choice Panel Data Model with a Predetermined Covariate

We study identification in a binary choice panel data model with a single \emph{predetermined} binary covariate (i.e., a covariate sequentially exogenous conditional on lagged outcomes and covariates). The choice model is indexed by a scalar parameter $\theta$, whereas the distribution of unit-specific heterogeneity, as well as the feedback process that maps lagged outcomes into future covariate realizations, are left unrestricted. We provide a simple condition under which $\theta$ is never point-identified, no matter the number of time periods available. This condition is satisfied in most models, including the logit one. We also characterize the identified set of $\theta$ and show how to compute it using linear programming techniques. While $\theta$ is not generally point-identified, its identified set is informative in the examples we analyze numerically, suggesting that meaningful learning about $\theta$ may be possible even in short panels with feedback. As a complement, we report calculations of identified sets for an average partial effect, and find informative sets in this case as well.Comment: 41 pages, 4 figures. Initial draft prepared for a conference in honor of Manuel Arellano at the Bank of Spain (July 2022