4,797 research outputs found
Panel Data Models with Nonadditive Unobserved Heterogeneity: Estimation and Inference
This paper considers fixed effects estimation and inference in linear and
nonlinear panel data models with random coefficients and endogenous regressors.
The quantities of interest -- means, variances, and other moments of the random
coefficients -- are estimated by cross sectional sample moments of GMM
estimators applied separately to the time series of each individual. To deal
with the incidental parameter problem introduced by the noise of the
within-individual estimators in short panels, we develop bias corrections.
These corrections are based on higher-order asymptotic expansions of the GMM
estimators and produce improved point and interval estimates in moderately long
panels. Under asymptotic sequences where the cross sectional and time series
dimensions of the panel pass to infinity at the same rate, the uncorrected
estimator has an asymptotic bias of the same order as the asymptotic variance.
The bias corrections remove the bias without increasing variance. An empirical
example on cigarette demand based on Becker, Grossman and Murphy (1994) shows
significant heterogeneity in the price effect across U.S. states.Comment: 51 pages, 4 tables, 1 figure, it includes supplementary appendi
Inference for Extremal Conditional Quantile Models, with an Application to Market and Birthweight Risks
Quantile regression is an increasingly important empirical tool in economics
and other sciences for analyzing the impact of a set of regressors on the
conditional distribution of an outcome. Extremal quantile regression, or
quantile regression applied to the tails, is of interest in many economic and
financial applications, such as conditional value-at-risk, production
efficiency, and adjustment bands in (S,s) models. In this paper we provide
feasible inference tools for extremal conditional quantile models that rely
upon extreme value approximations to the distribution of self-normalized
quantile regression statistics. The methods are simple to implement and can be
of independent interest even in the non-regression case. We illustrate the
results with two empirical examples analyzing extreme fluctuations of a stock
return and extremely low percentiles of live infants' birthweights in the range
between 250 and 1500 grams.Comment: 41 pages, 9 figure
On the dynamic toroidal multipoles from localized electric current distributions
We analyze the dynamic toroidal multipoles and prove that they do not have an
independent physical meaning with respect to their interaction with
electromagnetic waves. We analytically show how the split into electric and
toroidal parts causes the appearance of non-radiative components in each of the
two parts. These non-radiative components, which cancel each other when both
parts are summed, preclude the separate determination of each part by means of
measurements of the radiation from the source or of its coupling to external
electromagnetic waves. In other words, there is no toroidal radiation or
independent toroidal electromagnetic coupling. The formal meaning of the
toroidal multipoles is clear in our derivations. They are the higher order
terms of an expansion of the multipolar coefficients of electric parity with
respect to the electromagnetic size of the source
Improving Point and Interval Estimates of Monotone Functions by Rearrangement
Suppose that a target function is monotonic, namely, weakly increasing, and
an available original estimate of this target function is not weakly
increasing. Rearrangements, univariate and multivariate, transform the original
estimate to a monotonic estimate that always lies closer in common metrics to
the target function. Furthermore, suppose an original simultaneous confidence
interval, which covers the target function with probability at least
, is defined by an upper and lower end-point functions that are not
weakly increasing. Then the rearranged confidence interval, defined by the
rearranged upper and lower end-point functions, is shorter in length in common
norms than the original interval and also covers the target function with
probability at least . We demonstrate the utility of the improved
point and interval estimates with an age-height growth chart example.Comment: 24 pages, 4 figures, 3 table
Dual and chiral objects for optical activity in general scattering directions
Optically active artificial structures have attracted tremendous research
attention. Such structures must meet two requirements: Lack of spatial
inversion symmetries and, a condition usually not explicitly considered, the
structure shall preserve the helicity of light, which implies that there must
be a vanishing coupling between the states of opposite polarization handedness
among incident and scattered plane waves. Here, we put forward and demonstrate
that a unit cell made from chiraly arranged electromagnetically dual scatterers
serves exactly this purpose. We prove this by demonstrating optical activity of
such unit cell in general scattering directions.Comment: This document is the unedited Authors version of a Submitted Work
that was subsequently accepted for publication in ACS Photonics, copyright
American Chemical Society after peer review. To access the final edited and
published work see
http://pubs.acs.org/articlesonrequest/AOR-3yvzAibCIU6wdTuzx9c
Quantile and Probability Curves Without Crossing
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. 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 in finite samples than the original curve, 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
the entire rearranged curve and its functionals. Our limit results are generic
in that they apply to every estimator of a monotone econometric 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 quantile functions using data on Vietnam veteran
status and earnings.Comment: 29 pages, 4 figure
Inference on Counterfactual Distributions
Counterfactual distributions are important ingredients for policy analysis
and decomposition analysis in empirical economics. In this article we develop
modeling and inference tools for counterfactual distributions based on
regression methods. The counterfactual scenarios that we consider consist of
ceteris paribus changes in either the distribution of covariates related to the
outcome of interest or the conditional distribution of the outcome given
covariates. For either of these scenarios we derive joint functional central
limit theorems and bootstrap validity results for regression-based estimators
of the status quo and counterfactual outcome distributions. These results allow
us to construct simultaneous confidence sets for function-valued effects of the
counterfactual changes, including the effects on the entire distribution and
quantile functions of the outcome as well as on related functionals. These
confidence sets can be used to test functional hypotheses such as no-effect,
positive effect, or stochastic dominance. Our theory applies to general
counterfactual changes and covers the main regression methods including
classical, quantile, duration, and distribution regressions. We illustrate the
results with an empirical application to wage decompositions using data for the
United States.
As a part of developing the main results, we introduce distribution
regression as a comprehensive and flexible tool for modeling and estimating the
\textit{entire} conditional distribution. We show that distribution regression
encompasses the Cox duration regression and represents a useful alternative to
quantile regression. We establish functional central limit theorems and
bootstrap validity results for the empirical distribution regression process
and various related functionals.Comment: 55 pages, 1 table, 3 figures, supplementary appendix with additional
results available from the authors' web site
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