Knowledge that Transforms

This paper considers model averaging as a way to construct optimal instruments for the two-stage least squares (2SLS), limited information maximum likelihood (LIML), and Fuller estimators in the presence of many instruments. We propose averaging across least squares predictions of the endogenous variables obtained from many different choices of instruments and then use the average predicted value of the endogenous variables in the estimation stage. The weights for averaging are chosen to minimize the asymptotic mean squared error of the model averaging version of the 2SLS, LIML, or Fuller estimator. This can be done by solving a standard quadratic programming problem.

We consider a class of mechanism games in which there are multiple principals and three or more agents. For a mechanism game in this class, a sort of folk theorem holds: there is a threshold value for each of the principals such that an allocation is achieved at a pure-strategy sequential equilibrium of the game if and only if (i) it is incentive compatible and (ii) it attains an expected utility for each principal that is greater than or equal to the threshold value for the principal.

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 considers a panel data model for predicting a binary outcome. The conditional probability of a positive response is obtained by evaluating a given distribution function (F) at a linear combination of the predictor variables. One of the predictor variables is unobserved. It is a random effect that varies across individuals but is constant over time. The semiparametric aspect is that the conditional distribution of the random effect, given the predictor variables, is unrestricted.

This paper proposes a method to address the longstanding problem of lack of monotonicity in estimation of conditional and structural quantile functions, also known as the quantile crossing problem (Bassett and Koenker (1982)). The method consists in sorting or monotone rearranging the original estimated non-monotone curve into a monotone rearranged curve. We show that the rearranged curve is closer to the true quantile curve than the original curve in finite samples, establish a functional delta method for rearrangement-related operators, and derive functional limit theory for the entire rearranged curve and its functionals. We also establish validity of the bootstrap for estimating the limit law of the entire rearranged curve and its functionals. Our limit results are generic in that they apply to every estimator of a monotone function, provided that the estimator satisfies a functional central limit theorem and the function satisfies some smoothness conditions. Consequently, our results apply to estimation of other econometric functions with monotonicity restrictions, such as demand, production, distribution, and structural distribution functions. We illustrate the results with an application to estimation of structural distribution and quantile functions using data on Vietnam veteran status and earnings.

Much of the extensive empirical literature on insurance markets has focused on whether adverse selection can be detected. Once detected, however, there has been little attempt to quantify its welfare cost or to assess whether and what potential government interventions may reduce these costs. To do so, we develop a model of annuity contract choice and estimate it using data from the U.K. annuity market. The model allows for private information about mortality risk as well as heterogeneity in preferences over different contract options. We focus on the choice of length of guarantee among individuals who are required to buy annuities. The results suggest that asymmetric information along the guarantee margin reduces welfare relative to a first-best symmetric information benchmark by about £127 million per year or about 2 percent of annuitized wealth. We also find that by requiring that individuals choose the longest guarantee period allowed, mandates could achieve the first-best allocation. However, we estimate that other mandated guarantee lengths would have detrimental effects on welfare. Since determining the optimal mandate is empirically difficult, our findings suggest that achieving welfare gains through mandatory social insurance may be harder in practice than simple theory may suggest.

An emerging literature in time series econometrics concerns the modeling of potentially nonlinear temporal dependence in stationary Markov chains using copula functions. We obtain sufficient conditions for a geometric rate of mixing in models of this kind. Geometric β-mixing is established under a rather strong sufficient condition that rules out asymmetry and tail dependence in the copula function. Geometric ρ-mixing is obtained under a weaker condition that permits both asymmetry and tail dependence. We verify one or both of these conditions for a range of parametric copula functions that are popular in applied work.

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.

The coalitional Nash bargaining solution is defined to be the core allocation for which the product of players' payoffs is maximal. We consider a non-cooperative model with discounting in which one team may form and every player is randomly selected to make a proposal in every period. The grand team, consisting of all players, generates the largest surplus. But a smaller team may form. We show that as players get more patient if an efficient and stationary equilibrium exists, it must deliver payoffs that correspond to the coalitional Nash bargaining solution. We also characterize when an efficient and stationary equilibrium exists, which requires conditions that go beyond the nonemptiness of the core.