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Inference on the Quantile Regression Process

Econometrica 2002 70(4), 1583-1612 open access
Tests based on the quantile regression process can be formulated like the classical Kolmogorov-Smirnov and Cramer-von-Mises tests of goodness-of-t employing the theory of Bessel processes as in Kiefer (1959). However, it is fre-quently desirable to formulate hypotheses involving unknown nuisance parameters, thereby jeopardizing the distribution free character of these tests. We characterize this situation as \ he Durbin problem " since it was posed in Durbin (1973), for parametric empirical processes. In this paper we consider an approach to the Durbin problem involving a mar-tingale transformation of the parametric empirical process suggested by Khmaladze (1981) and show that it can be adapted to a wide variety of inference problems involving the quantile regression process. In particular, we suggest new tests of the location shift and location-scale shift models that underlie much of classical econometric inference. The methods are illustrated with a reanalysis of data on unemployment durations from the Pennsylvania Reemployment Bonus Experiments. The Pennsylvania ex-periments, conducted in 1988-89, were designed to test the ecacy of cash bonuses paid for early reemployment in shortening the duration of insured unemployment spells. 1.

Architecture of Power Markets

Econometrica 2002 70(4), 1299-1340
Liberalization of infrastructure industries presents classic economic issues about how organization and procedure affect market performance. These issues are examined in wholesale power markets. The perspective from game theory complements standard economic theory to examine effects on efficiency and incentives.

Swapping the Nested Fixed Point Algorithm: A Class of Estimators for Discrete Markov Decision Models

Econometrica 2002 70(4), 1519-1543
This paper proposes a procedure for the estimation of discrete Markov decision models and studies its statistical and computational properties.Our Nested Pseudo-Likelihood method (NPL) is similar to Rust's Nested Fixed Point algorithm (NFXP), but the order of the two nested algorithms is swapped.First, we prove that NPL produces the Maximum Likelihood Estimator under the same conditions as NFXP.Our procedure requires fewer policy iterations at the expense of more likelihood-climbing iterations.We focus on a class of in…nite-horizon, partial likelihood problems for which NPL results in large computational gains.Second, based on this algorithm we de…ne a class of consistent and asymptotically equivalent Sequential Policy Iteration (PI) estimators, which encompasses both Hotz-Miller's CCP estimator and the partial Maximum Likekihood estimator.This presents the researcher with a "menu" of sequential estimators re ‡ecting a trade-o¤ between …nite-sample precision and computational cost.Using actual and simulated data we compare the relative performance of these estimators.In all our experiments the bene…ts in terms of precision of using a 2-stage PI estimator instead of 1-stage (i.e., Hotz-Miller) are very signi…cant.More interestingly, the bene…ts of MLE relative to 2-stage PI are small.

On the Internal Structure of Cities

Econometrica 2002 70(4), 1445-1476
We prove the existence of a symmetric equilibrium in a circular city in which businesses and housing can both be located anywhere in the city. In this equilibrium, firms balance the external benefits from locating near other producers against the costs of longer commutes for workers. An equilibrium city need not take the form of a central business district surrounded by a residential area. We propose a general algorithm for constructing equilibria, and use it to study the way land use is affected by changes in the model's underlying parameters. Copyright The Econometric Society 2002.

Spatial Price Competition: A Semiparametric Approach

Econometrica 2002 70(3), 1111-1153
We investigate the nature of price competition among firms that produce differentiated products and compete in markets that are limited in extent. We propose an instrumental variables series estimator for the matrix of cross price response coefficients, demonstrate that our estimator is consistent, and derive its asymptotic distribution. Our semiparametric approach allows us to discriminate among models of global competition, in which all products compete with all others, and local competition, in which products compete only with their neighbors. We apply our semiparametric estimator to data from U.S. wholesale gasoline markets and find that, in this market, competition is highly localized.