"Subvector inference when the true parameter vector may be near or at the boundary" Journal of Econometrics, December 2018, 207(2), pp. 285-306
[abstract|paper|supplementary material]

Extremum estimators are not
asymptotically normally distributed when the estimator satisfies the
restrictions on the parameter space—such as the
non-negativity of a variance parameter—and the true parameter
vector is near or at the boundary. This possible
lack of asymptotic normality makes it difficult to construct tests for
testing subvector hypotheses that control asymptotic size in a uniform
sense and have good local asymptotic power irrespective of whether the
true parameter vector is at, near, or far from the boundary. We propose
a novel estimator that is asymptotically normally distributed even when
the true parameter vector is near or at the boundary and the objective
function is not defined outside the parameter space. The proposed
estimator allows the implementation of a new test based on the
Conditional Likelihood Ratio statistic that is easy-to-implement,
controls asymptotic size, and has good local asymptotic power
properties. Furthermore, we show that the test enjoys certain
asymptotic optimality properties when the parameter of interest is
scalar. In an application of the random coefficients logit model
(Berry, Levinsohn, and Pakes, 1995) to the European car market, we find
that, for most parameters, the new test leads to tighter confidence
intervals than the two-sided t-test commonly used in practice.

"On asymptotic size distortions in the random
coefficients logit model" Journal of Econometrics, October 2019, 212(2), pp. 413-432
[abstract|paper]

We show that, in the random coefficients logit model, standard
inference procedures can suffer from asymptotic size distortions. The
problem arises due to boundary issues and is aggravated by the standard
parameterization of the model, in terms of standard deviations. For
example, in case of a single random coefficient, the asymptotic size of
the nominal 95% confidence interval obtained by inverting the two-sided
t-test for the standard deviation equals 83.65%. In seeming
contradiction, we also show that standard error estimates for the
estimator of the standard deviation can be unreasonably large. This
problem is alleviated if the model is reparameterized in terms of
variances. Furthermore, a numerical evaluation of a conjectured lower
bound suggests that the asymptotic size of the nominal 95% confidence
interval obtained by inverting the two-sided t-test for variances
(means) is within 0.5 percentage points of the nominal level as long as
there are no more than five (four) random coefficients and as long as
an optimal weighting matrix is employed.

"Testing overidentifying restrictions with a restricted parameter space" Economics Letters, December 2019, 185, 108743
[abstract|paper|supplementary material]

We show that the standard test for testing overidentifying restrictions, which compares
the J-statistic (Hansen, 1982) to χ2 critical values, does not control asymptotic size
when the true parameter vector is allowed to lie on the boundary of the (optimization)
parameter space. We also propose a modified J-statistic that, under the null hypothesis,
is asymptotically χ2 distributed, such that the resulting test does control asymptotic size.

Work
in Progress

Detailed Decomposition of Differences in Distribution: A Causal Interpretation
(with
Blaise Melly)

Measurement Error and Omitted Variable Bias in Nonlinear Models
(with
Blaise Melly)

Measuring sex-selective abortion: How many women abort?
(with
Aditi Dimri and Véronique Gille)

Computer
Programs

This
Matlab
code estimates the Random
Coefficients Logit Model with respect to variances rather than standard
deviations, as suggested in "On asymptotic size distortions in the random coefficients logit model."
It also implements the
estimator proposed in "Subvector inference when the true parameter vector may be near or at the boundary" and the
modified J-statistic proposed in "Testing overidentifying restrictions with a restricted parameter space."
It is a modified version of the
code that can be found on Professor Dubé's website
and uses the MPEC formulation of the estimation problem.