36 research outputs found
Asymptotically Efficient Estimation of Weighted Average Derivatives with an Interval Censored Variable
This paper studies the identification and estimation of weighted average
derivatives of conditional location functionals including conditional mean and
conditional quantiles in settings where either the outcome variable or a
regressor is interval-valued. Building on Manski and Tamer (2002) who study
nonparametric bounds for mean regression with interval data, we characterize
the identified set of weighted average derivatives of regression functions.
Since the weighted average derivatives do not rely on parametric specifications
for the regression functions, the identified set is well-defined without any
parametric assumptions. Under general conditions, the identified set is compact
and convex and hence admits characterization by its support function. Using
this characterization, we derive the semiparametric efficiency bound of the
support function when the outcome variable is interval-valued. We illustrate
efficient estimation by constructing an efficient estimator of the support
function for the case of mean regression with an interval censored outcome
Decentralization Estimators for Instrumental Variable Quantile Regression Models
The instrumental variable quantile regression (IVQR) model (Chernozhukov and
Hansen, 2005) is a popular tool for estimating causal quantile effects with
endogenous covariates. However, estimation is complicated by the non-smoothness
and non-convexity of the IVQR GMM objective function. This paper shows that the
IVQR estimation problem can be decomposed into a set of conventional quantile
regression sub-problems which are convex and can be solved efficiently. This
reformulation leads to new identification results and to fast, easy to
implement, and tuning-free estimators that do not require the availability of
high-level "black box" optimization routines
Moment Inequalities in the Context of Simulated and Predicted Variables
This paper explores the effects of simulated moments on the performance of
inference methods based on moment inequalities. Commonly used confidence sets
for parameters are level sets of criterion functions whose boundary points may
depend on sample moments in an irregular manner. Due to this feature,
simulation errors can affect the performance of inference in non-standard ways.
In particular, a (first-order) bias due to the simulation errors may remain in
the estimated boundary of the confidence set. We demonstrate, through Monte
Carlo experiments, that simulation errors can significantly reduce the coverage
probabilities of confidence sets in small samples. The size distortion is
particularly severe when the number of inequality restrictions is large. These
results highlight the danger of ignoring the sampling variations due to the
simulation errors in moment inequality models. Similar issues arise when using
predicted variables in moment inequalities models. We propose a method for
properly correcting for these variations based on regularizing the intersection
of moments in parameter space, and we show that our proposed method performs
well theoretically and in practice
Estimating Misspecified Moment Inequality Models
Abstract This paper studies partially identified structures defined by a finite number of moment inequalities. When the moment function is misspecified, it becomes difficult to interpret the conventional identified set. Even more seriously, this can be an empty set. We define a pseudo-true identified set whose elements can be interpreted as the least-squares projections of the moment functions that are observationally equivalent to the true moment function. We then construct a set estimator for the pseudo-true identified set and establish its O p (n β1/2 ) rate of convergence
Moment inequalities in the context of simulated and predicted variables
No CWP26/18, CeMMAP working papers from Centre for Microdata Methods and Practice, Institute for Fiscal StudiesThis paper explores the effects of simulated moments on the performance of inference methods based on moment inequalities. Commonly used confidence sets for parameters are level sets of criterion functions whose boundary points may depend on sample moments in an irregular manner. Due to this feature, simulation errors can affect the performance of inference in non-standard ways. In particular, a (first-order) bias due to the simulation errors may remain in the estimated boundary of the confidence set. We demonstrate, through Monte Carlo experiments, that simulation errors can significantly reduce the coverage probabilities of confidence sets in small samples. The size distortion is particularly severe when the number of inequality restrictions is large. These results highlight the danger of ignoring the sampling variations due to the simulation errors in moment inequality models. Similar issues arise when using predicted variables in moment inequalities models. We propose a method for properly correcting for these variations based on regularizing the intersection of moments in parameter space, and we show that our proposed method performs well theoretically and in practice.First author draf
Nonparametric identification of the distribution of random coefficients in binary response static games of complete information
This paper studies binary response static games of complete information allowing complex heterogeneity through a random coefficients specification. The main result of the paper establishes nonparametric point identification of the joint density of all random coefficients except those on interaction effects. Under additional independence assumptions, we identify the joint density of the interaction coefficients. Moreover, we prove that in the presence of covariates that are common to both players, the player-specific coefficient densities are identified, while the joint density of all random coefficients is not point-identified. However, we do provide bounds on counterfactual probabilities that involve this joint density