423 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
Network and panel quantile effects via distribution regression
This paper provides a method to construct simultaneous con fidence bands for quantile functions and quantile effects in nonlinear network and panel models with unobserved two-way effects, strictly exogenous covariates, and possibly discrete outcome variables. The method is based upon projection of simultaneous confi dence bands for distribution functions constructed from fixed effects distribution regression estimators. These fi xed effects estimators are bias corrected to deal with the incidental parameter problem. Under asymptotic sequences where both dimensions of the data set grow at the same rate, the confi dence bands for the quantile functions and effects have correct joint coverage in large samples. An empirical application to gravity models of trade illustrates the applicability of the methods to network data.https://arxiv.org/abs/1803.08154First author draf
The Sorted Effects Method: Discovering Heterogeneous Effects Beyond Their Averages
The partial (ceteris paribus) effects of interest in nonlinear and
interactive linear models are heterogeneous as they can vary dramatically with
the underlying observed or unobserved covariates. Despite the apparent
importance of heterogeneity, a common practice in modern empirical work is to
largely ignore it by reporting average partial effects (or, at best, average
effects for some groups). While average effects provide very convenient scalar
summaries of typical effects, by definition they fail to reflect the entire
variety of the heterogeneous effects. In order to discover these effects much
more fully, we propose to estimate and report sorted effects -- a collection of
estimated partial effects sorted in increasing order and indexed by
percentiles. By construction the sorted effect curves completely represent and
help visualize the range of the heterogeneous effects in one plot. They are as
convenient and easy to report in practice as the conventional average partial
effects. They also serve as a basis for classification analysis, where we
divide the observational units into most or least affected groups and summarize
their characteristics. We provide a quantification of uncertainty (standard
errors and confidence bands) for the estimated sorted effects and related
classification analysis, and provide confidence sets for the most and least
affected groups. The derived statistical results rely on establishing key, new
mathematical results on Hadamard differentiability of a multivariate sorting
operator and a related classification operator, which are of independent
interest. We apply the sorted effects method and classification analysis to
demonstrate several striking patterns in the gender wage gap.Comment: 62 pages, 9 figures, 8 tables, includes appendix with supplementary
material
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
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
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
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