110 research outputs found
On the Effect of Bias Estimation on Coverage Accuracy in Nonparametric Inference
Nonparametric methods play a central role in modern empirical work. While
they provide inference procedures that are more robust to parametric
misspecification bias, they may be quite sensitive to tuning parameter choices.
We study the effects of bias correction on confidence interval coverage in the
context of kernel density and local polynomial regression estimation, and prove
that bias correction can be preferred to undersmoothing for minimizing coverage
error and increasing robustness to tuning parameter choice. This is achieved
using a novel, yet simple, Studentization, which leads to a new way of
constructing kernel-based bias-corrected confidence intervals. In addition, for
practical cases, we derive coverage error optimal bandwidths and discuss
easy-to-implement bandwidth selectors. For interior points, we show that the
MSE-optimal bandwidth for the original point estimator (before bias correction)
delivers the fastest coverage error decay rate after bias correction when
second-order (equivalent) kernels are employed, but is otherwise suboptimal
because it is too "large". Finally, for odd-degree local polynomial regression,
we show that, as with point estimation, coverage error adapts to boundary
points automatically when appropriate Studentization is used; however, the
MSE-optimal bandwidth for the original point estimator is suboptimal. All the
results are established using valid Edgeworth expansions and illustrated with
simulated data. Our findings have important consequences for empirical work as
they indicate that bias-corrected confidence intervals, coupled with
appropriate standard errors, have smaller coverage error and are less sensitive
to tuning parameter choices in practically relevant cases where additional
smoothness is available
Regression Discontinuity Designs Using Covariates
We study regression discontinuity designs when covariates are included in the
estimation. We examine local polynomial estimators that include discrete or
continuous covariates in an additive separable way, but without imposing any
parametric restrictions on the underlying population regression functions. We
recommend a covariate-adjustment approach that retains consistency under
intuitive conditions, and characterize the potential for estimation and
inference improvements. We also present new covariate-adjusted mean squared
error expansions and robust bias-corrected inference procedures, with
heteroskedasticity-consistent and cluster-robust standard errors. An empirical
illustration and an extensive simulation study is presented. All methods are
implemented in \texttt{R} and \texttt{Stata} software packages
Binscatter Regressions
We introduce the \texttt{Stata} (and \texttt{R}) package \textsf{Binsreg},
which implements the binscatter methods developed in
\citet*{Cattaneo-Crump-Farrell-Feng_2019_Binscatter}. The package includes the
commands \texttt{binsreg}, \texttt{binsregtest}, and \texttt{binsregselect}.
The first command (\texttt{binsreg}) implements binscatter for the regression
function and its derivatives, offering several point estimation, confidence
intervals and confidence bands procedures, with particular focus on
constructing binned scatter plots. The second command (\texttt{binsregtest})
implements hypothesis testing procedures for parametric specification and for
nonparametric shape restrictions of the unknown regression function. Finally,
the third command (\texttt{binsregselect}) implements data-driven number of
bins selectors for binscatter implementation using either quantile-spaced or
evenly-spaced binning/partitioning. All the commands allow for covariate
adjustment, smoothness restrictions, weighting and clustering, among other
features. A companion \texttt{R} package with the same capabilities is also
available
On Binscatter
Binscatter is very popular in applied microeconomics. It provides a flexible,
yet parsimonious way of visualizing and summarizing large data sets in
regression settings, and it is often used for informal evaluation of
substantive hypotheses such as linearity or monotonicity of the regression
function. This paper presents a foundational, thorough analysis of binscatter:
we give an array of theoretical and practical results that aid both in
understanding current practices (i.e., their validity or lack thereof) and in
offering theory-based guidance for future applications. Our main results
include principled number of bins selection, confidence intervals and bands,
hypothesis tests for parametric and shape restrictions of the regression
function, and several other new methods, applicable to canonical binscatter as
well as higher-order polynomial, covariate-adjusted and smoothness-restricted
extensions thereof. In particular, we highlight important methodological
problems related to covariate adjustment methods used in current practice. We
also discuss extensions to clustered data. Our results are illustrated with
simulated and real data throughout. Companion general-purpose software packages
for \texttt{Stata} and \texttt{R} are provided. Finally, from a technical
perspective, new theoretical results for partitioning-based series estimation
are obtained that may be of independent interest
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