38,263 research outputs found
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
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
Program Evaluation and Causal Inference with High-Dimensional Data
In this paper, we provide efficient estimators and honest confidence bands
for a variety of treatment effects including local average (LATE) and local
quantile treatment effects (LQTE) in data-rich environments. We can handle very
many control variables, endogenous receipt of treatment, heterogeneous
treatment effects, and function-valued outcomes. Our framework covers the
special case of exogenous receipt of treatment, either conditional on controls
or unconditionally as in randomized control trials. In the latter case, our
approach produces efficient estimators and honest bands for (functional)
average treatment effects (ATE) and quantile treatment effects (QTE). To make
informative inference possible, we assume that key reduced form predictive
relationships are approximately sparse. This assumption allows the use of
regularization and selection methods to estimate those relations, and we
provide methods for post-regularization and post-selection inference that are
uniformly valid (honest) across a wide-range of models. We show that a key
ingredient enabling honest inference is the use of orthogonal or doubly robust
moment conditions in estimating certain reduced form functional parameters. We
illustrate the use of the proposed methods with an application to estimating
the effect of 401(k) eligibility and participation on accumulated assets.Comment: 118 pages, 3 tables, 11 figures, includes supplementary appendix.
This version corrects some typos in Example 2 of the published versio
Multiplier bootstrap of tail copulas with applications
For the problem of estimating lower tail and upper tail copulas, we propose
two bootstrap procedures for approximating the distribution of the
corresponding empirical tail copulas. The first method uses a multiplier
bootstrap of the empirical tail copula process and requires estimation of the
partial derivatives of the tail copula. The second method avoids this
estimation problem and uses multipliers in the two-dimensional empirical
distribution function and in the estimates of the marginal distributions. For
both multiplier bootstrap procedures, we prove consistency. For these
investigations, we demonstrate that the common assumption of the existence of
continuous partial derivatives in the the literature on tail copula estimation
is so restrictive, such that the tail copula corresponding to tail independence
is the only tail copula with this property. Moreover, we are able to solve this
problem and prove weak convergence of the empirical tail copula process under
nonrestrictive smoothness assumptions that are satisfied for many commonly used
models. These results are applied in several statistical problems, including
minimum distance estimation and goodness-of-fit testing.Comment: Published in at http://dx.doi.org/10.3150/12-BEJ425 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
Optimal Sup-norm Rates and Uniform Inference on Nonlinear Functionals of Nonparametric IV Regression
This paper makes several important contributions to the literature about
nonparametric instrumental variables (NPIV) estimation and inference on a
structural function and its functionals. First, we derive sup-norm
convergence rates for computationally simple sieve NPIV (series 2SLS)
estimators of and its derivatives. Second, we derive a lower bound that
describes the best possible (minimax) sup-norm rates of estimating and
its derivatives, and show that the sieve NPIV estimator can attain the minimax
rates when is approximated via a spline or wavelet sieve. Our optimal
sup-norm rates surprisingly coincide with the optimal root-mean-squared rates
for severely ill-posed problems, and are only a logarithmic factor slower than
the optimal root-mean-squared rates for mildly ill-posed problems. Third, we
use our sup-norm rates to establish the uniform Gaussian process strong
approximations and the score bootstrap uniform confidence bands (UCBs) for
collections of nonlinear functionals of under primitive conditions,
allowing for mildly and severely ill-posed problems. Fourth, as applications,
we obtain the first asymptotic pointwise and uniform inference results for
plug-in sieve t-statistics of exact consumer surplus (CS) and deadweight loss
(DL) welfare functionals under low-level conditions when demand is estimated
via sieve NPIV. Empiricists could read our real data application of UCBs for
exact CS and DL functionals of gasoline demand that reveals interesting
patterns and is applicable to other markets.Comment: This paper is a major extension of Sections 2 and 3 of our Cowles
Foundation Discussion Paper CFDP1923, Cemmap Working Paper CWP56/13 and arXiv
preprint arXiv:1311.0412 [math.ST]. Section 3 of the previous version of this
paper (dealing with data-driven choice of sieve dimension) is currently being
revised as a separate pape
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