Knowledge that Transforms

This paper studies the econometrics of computed dynamic models. Since these models generally lack a closed-form solution, their policy functions are approximated by numerical methods. Hence, the researcher can only evaluate an approximated likelihood associated with the approximated policy function rather than the exact likelihood implied by the exact policy function. What are the consequences for inference of the use of approximated likelihoods? First, we find conditions under which, as the approximated policy function converges to the exact policy, the approximated likelihood also converges to the exact likelihood. Second, we show that second order approximation errors in the policy function, which almost always are ignored by researchers, have first order effects on the likelihood function. Third, we discuss convergence of Bayesian and classical estimates. Finally, we propose to use a likelihood ratio test as a diagnostic device for problems derived from the use of approximated likelihoods.

The Lemke–Howson algorithm is the classical method for finding one Nash equilibrium of a bimatrix game. This paper presents a class of square bimatrix games for which this algorithm takes, even in the best case, an exponential number of steps in the dimension d of the game. Using polytope theory, the games are constructed using pairs of dual cyclic polytopes with 2d suitably labeled facets in d-space. The construction is extended to nonsquare games where, in addition to exponentially long Lemke–Howson computations, finding an equilibrium by support enumeration takes on average exponential time.

A number of studies, most notably Crémer and McLean (1985, 1988), have shown that in generic type spaces that admit a common prior and are of a fixed finite size, an uninformed seller can design mechanisms that extract all the surplus from privately informed bidders. We show that this result hinges on the nonconvexity of such a family of priors. When the ambient family of priors is convex, generic priors do not allow for full surplus extraction provided that for at least one prior in this family, players' beliefs about other players' types do not pin down the players' own preferences. In particular, full surplus extraction is generically impossible in finite type spaces with a common prior. Similarly, generic priors on the universal type space do not allow for full surplus extraction.

In this paper, we introduce a kernel-based estimation principle for nonparametric models named local partitioned regression (LPR). This principle is a nonparametric generalization of the familiar partition regression in linear models. It has several key advantages: First, it generates estimators for a very large class of semi- and nonparametric models. A number of examples that are particularly relevant for economic applications will be discussed in this paper. This class contains the additive, partially linear, and varying coefficient models as well as several other models that have not been discussed in the literature. Second, LPR-based estimators achieve optimality criteria: They have optimal speed of convergence and are oracle-efficient. Moreover, they are simple in structure, widely applicable, and computationally inexpensive. A Monte Carlo simulation highlights these advantages. Copyright The Econometric Society 2006.

We consider the situation when there is a large number of series, N, each with T observations, and each series has some predictive ability for some variable of interest. A methodology of growing interest is first to estimate common factors from the panel of data by the method of principal components and then to augment an otherwise standard regression with the estimated factors. In this paper, we show that the least squares estimates obtained from these factor-augmented regressions are consistent and asymptotically normal if . The conditional mean predicted by the estimated factors is consistent and asymptotically normal. Except when T/N goes to zero, inference should take into account the effect of “estimated regressors” on the estimated conditional mean. We present analytical formulas for prediction intervals that are valid regardless of the magnitude of N/T and that can also be used when the factors are nonstationary.

Building upon a continuous-time model of search with Nash bargaining in a stationary environment, we analyze the effect of changes in minimum wages on labor market outcomes and welfare. Although minimum wage increases may or may not lead to increases in unemployment in our model, they can be welfare-improving to labor market participants on both the supply and demand sides of the labor market. We discuss identification of the model using Current Population Survey data on accepted wages and unemployment durations, and show that by incorporating a limited amount of information from the demand side of the market it is possible to obtain credible and precise estimates of all primitive parameters. We show that the optimal minimum wage in 1996 depends critically on whether or not contact rates can be considered to be exogenous and we note that the limited variation in minimum wages makes testing this assumption problematic. Copyright The Econometric Society 2006.

This note revisits the identification theorems of Brown (1983) and Roehrig (1988). We describe an error in the proofs of the main identification theorems in these papers, and provide an important counterexample to the theorems on the identification of the reduced form. Specifically, the reduced form of a nonseparable simultaneous equations model is not identified even under the assumptions of these papers. We provide conditions under which the reduced form is identified and is recoverable using the distribution of the endogenous variables conditional on the exogenous variables. However, these conditions place substantial limitations on the structural model. We conclude the note with a conjecture that it may be possible to use classical exclusion restrictions to recover some of the key implications of the theorems in more general settings.

FLWIN

A convex, compact, and possibly discontinuous better reply secure game has a Nash equilibrium. We introduce a very weak notion of continuity that can be used to establish that a game is better reply secure and we show that this notion of continuity is satisfied by a large class of games.

School choice has become an increasingly prominent strategy for enhancing academic achievement. To evaluate the impact on participants, we exploit randomized lotteries that determine high school admission in the Chicago Public Schools. Compared to those students who lose lotteries, students who win attend high schools that are better in a number of dimensions, including peer achievement and attainment levels. Nonetheless, we find little evidence that winning a lottery provides any systematic benefit across a wide variety of traditional academic measures. Lottery winners do, however, experience improvements on a subset of nontraditional outcome measures, such as self-reported disciplinary incidents and arrest rates.