Knowledge that Transforms

We discuss the identification and estimation of discrete games of complete information. Following Bresnahan and Reiss (1990, 1991), a discrete game is a generalization of a standard discrete choice model where utility depends on the actions of other players. Using recent algorithms to compute all of the Nash equilibria to a game, we propose simulation-based estimators for static, discrete games. We demonstrate that the model is identified under weak functional form assumptions using exclusion restrictions and an identification at infinity approach. Monte Carlo evidence demonstrates that the estimator can perform well in moderately sized samples. As an application, we study entry decisions by construction contractors to bid on highway projects in California. We find that an equilibrium is more likely to be observed if it maximizes joint profits, has a higher Nash product, uses mixed strategies, and is not Pareto dominated by another equilibrium.

This paper provides computationally intensive, yet feasible methods for inference in a very general class of partially identified econometric models. Let P denote the distribution of the observed data. The class of models we consider is defined by a population objective function Q(θ, P) for θ∈Θ. The point of departure from the classical extremum estimation framework is that it is not assumed that Q(θ, P) has a unique minimizer in the parameter space Θ. The goal may be either to draw inferences about some unknown point in the set of minimizers of the population objective function or to draw inferences about the set of minimizers itself. In this paper, the object of interest is Θ0(P)=argminθ∈ΘQ(θ, P), and so we seek random sets that contain this set with at least some prespecified probability asymptotically. We also consider situations where the object of interest is the image of Θ0(P) under a known function. Random sets that satisfy the desired coverage property are constructed under weak assumptions. Conditions are provided under which the confidence regions are asymptotically valid not only pointwise in P, but also uniformly in P. We illustrate the use of our methods with an empirical study of the impact of top-coding outcomes on inferences about the parameters of a linear regression. Finally, a modest simulation study sheds some light on the finite-sample behavior of our procedure.

We use a second-price common-value auction, called the maximal game, to experimentally study whether the winner's curse (WC) can be explained by models which retain best-response behavior but allow for inconsistent beliefs. We compare behavior in a regular version of the maximal game, where the WC can be explained by inconsistent beliefs, to behavior in versions where such explanations are less plausible. We find little evidence of differences in behavior. Overall, our study casts a serious doubt on theories that posit the WC is driven by beliefs.

A unifying framework to test for causal effects in nonlinear models is proposed. We consider a generalized linear-index regression model with endogenous regressors and no parametric assumptions on the error disturbances. To test the significance of the effect of an endogenous regressor, we propose a statistic that is a kernel-weighted version of the rank correlation statistic (tau) of Kendall (1938). The semiparametric model encompasses previous cases considered in the literature (continuous endogenous regressors (Blundell and Powell (2003)) and a single binary endogenous regressor (Vytlacil and Yildiz (2007))), but the testing approach is the first to allow for (i) multiple discrete endogenous regressors, (ii) endogenous regressors that are neither discrete nor continuous (e.g., a censored variable), and (iii) an arbitrary “mix” of endogenous regressors (e.g., one binary regressor and one continuous regressor).

The absence of state capacities to raise revenue and to support markets is a key factor in explaining the persistence of weak states. This paper reports on an on-going project to investigate the incentive to invest in such capacities. The paper sets out a simple analytical structure in which state capacities are modeled as forward looking investments by government. The approach highlights some determinants of state building including the risk of external or internal conflict, the degree of political instability, and dependence on natural resources. Throughout, we link these state capacity investments to patterns of development and growth.

This paper extends the static analysis of oligopoly structure into an infinite-horizon setting with sunk costs and demand uncertainty. The observation that exit rates decline with firm age motivates the assumption of last-in first-out dynamics: An entrant expects to produce no longer than any incumbent. This selects an essentially unique Markov-perfect equilibrium. With mild restrictions on the demand shocks, sequences of thresholds describe firms' equilibrium entry and survival decisions. Bresnahan and Reiss' (1993) empirical analysis of oligopolists' entry and exit assumes that such thresholds govern the evolution of the number of competitors. Our analysis provides an infinite-horizon game-theoretic foundation for that structure.

We study a continuous-time principal–agent model in which a risk-neutral agent with limited liability must exert unobservable effort to reduce the likelihood of large but relatively infrequent losses. Firm size can be decreased at no cost or increased subject to adjustment costs. In the optimal contract, investment takes place only if a long enough period of time elapses with no losses occurring. Then, if good performance continues, the agent is paid. As soon as a loss occurs, payments to the agent are suspended, and so is investment if further losses occur. Accumulated bad performance leads to downsizing. We derive explicit formulae for the dynamics of firm size and its asymptotic growth rate, and we provide conditions under which firm size eventually goes to zero or grows without bounds.

This paper formulates and estimates multistage production functions for child cognitive and noncognitive skills. Output is determined by parental environments and investments at different stages of childhood. We estimate the elasticity of substitution between investments in one period and stocks of skills in that period to assess the benefits of early investment in children compared to later remediation. We establish nonparametric identification of a general class of nonlinear factor models. A by-product of our approach is a framework for evaluating childhood interventions that does not rely on arbitrarily scaled test scores as outputs and recognizes the differential effects of skills in different tasks. Using the estimated technology, we determine optimal targeting of interventions to children with different parental and personal birth endowments. Substitutability decreases in later stages of the life cycle for the production of cognitive skills. It increases in later stages of the life cycle for the production of noncognitive skills. This finding has important implications for the design of policies that target the disadvantaged. For some configurations of disadvantage and outcomes, it is optimal to invest relatively more in the later stages of childhood.

We prove the generic existence of a recursive equilibrium for overlapping-generations economies with uncertainty. “Generic” here means in a residual set of utilities and endowments. The result holds provided there is a sufficient number of potentially different individuals within each cohort.

Behavioral choice models generate inequalities which, when combined with additional assumptions, can be used as a basis for estimation. This paper considers two sets of such assumptions and uses them in two empirical examples. The second example examines the structure of payments resulting from the upstream interactions in a vertical market. I then mimic the empirical setting for this example in a numerical analysis which computes actual equilibria, examines how their characteristics vary with the market setting, and compares them to the empirical results. The final section uses the numerical results in a Monte Carlo analysis of the robustness of the two approaches to estimation to their underlying assumptions.