# Research

#### Working Papers

These papers are all being updated. Updated versions will come out soon.

**Should we use IV to estimate dynamic linear probability models with fixed effects?** (link here)

I give a set of pros and cons of this procedure and conclude that this procedure should be treated with caution, especially in fixed-T settings. Even if we ignore the possibility that average marginal effects may not be point-identified, directly applying IV/GMM estimators to this dynamic LPM identifies incorrectly-weighted average marginal effects, which may differ from the true average marginal effect, under large-n, fixed-T or large-n, large-T asymptotics. I also show that there exist certain DGPs that can push the large-n, fixed-T limits of these IV estimators outside the identified set for the true average marginal effect. The only good news is that nonparametrically testing the point null of zero first-order state dependence is possible with default routines. Unfortunately, this nonparametric test can have low power. In relation to this, I demonstrate through an empirical example that the resulting IV/GMM estimates of the average treatment effect of fertility on female labor force participation are outside the nonparametric bounds under monotonicity.

**Simultaneous equations for discrete outcomes: Coherence and completeness using panel data** (link here)

Modeling jointly determined discrete outcomes via simultaneous equations require the so-called coherency condition to guarantee the existence of a unique reduced form. These conditions effectively convert a model where the endogenous variables are jointly determined into a model that is triangular or recursive. In the spirit of a suggestion by Lewbel (2007), I propose using panel data to decide how the coherency condition will hold without restricting error supports or imposing triangularity for all observations.

**Estimation and inference in dynamic nonlinear fixed effects panel data models by projection** (link here)

I develop a bias reduction method for the estimators of structural parameters of a panel data model (whether linear or nonlinear) using a projection argument. A corrected score is calculated by projecting the score vector for the structural parameters onto the orthogonal complement of a space characterized by incidental parameter fluctuations.

**The role of sparsity in panel data models** (link here)

Sparsity of the fixed effects means that some fixed effects have absolute value of zero while others are bounded and other are large. The proposed estimator attempts to detect the large values of the fixed effects so that they can be removed in the second step. I tune the regularization parameter to encourage sparsity and allow for contemporaneously exogenous regressors. As a second step, I remove the large non-zero fixed effects so that pooled OLS may be applied.

#### Work in progress

**An adjusted profile score for estimating dynamic panel data models with fixed and time effects** (with Geert Dhaene)

We study an adjusted likelihood obtained from bias-correcting the profile score derived from a linear dynamic panel data model with both individual-specific and time fixed effects.

**Large-n, large-T properties of an IV estimator based on the Ahn-Schmidt moment conditions** (with Markus Fritsch and Joachim Schnurbus) -- Paper forthcoming

We examine how Ahn-Schmidt moment conditions alone can be used to identify the AR(1) parameter under persistent and unit root cases.

**Computational aspects of a GMM estimator based on the Ahn-Schmidt moment conditions** (with Markus Fritsch and Joachim Schnurbus)

We provide R code to help researchers in implementing the Ahn-Schmidt moment conditions along with the usual Arellano-Bond moment conditions.

**The linear probability model and its discontents** (link here)

An older version of "On IV estimation of the dynamic linear probability model with fixed effects" with more drama.