"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"
accepted for publication at Journal of Econometrics
[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.

Working Papers

Testing Overidentifying Restrictions with a Restricted Parameter Space—New version coming soon!
[old version]

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.