Nonlinear Panel Data Models with Robust Correlated Random Effects

with Daniel J. Henderson and Andros Kourtellos | Link to paper | Working Paper

While linear panel data models with correlated random effects maintain consistency even under misspecification of the individual effect, this robustness property fails in nonlinear settings. We address this limitation by replacing the traditional parametric specification of individual effects with a nonparametric function, thereby preserving consistency of the structural parameters even when the relationship between individual effects and covariates is unknown. Our estimator employs a profile least squares style approach, obtaining the finite-dimensional parameters through optimization of the profiled objective function. The estimator achieves parametric rates of convergence for the structural parameters while accommodating nonparametric estimation of the nuisance function. Monte Carlo simulations confirm the theoretical results, showing consistency while existing methods are biased and inconsistent when the individual effect specification is misspecified. We illustrate the practical relevance of our approach via a study of the public capital productivity puzzle whereby we show proper modeling of the production function and individual effects leads to positive and significant returns to public capital.

Nonparametric Correlated Random-Effects Models

with Daniel J. Henderson and Alexandra Soberon | Seven Decades of Econometrics and Beyond

This chapter develops methods for estimation and inference in nonparametric panel data models with correlated random-effects. Using the Mundlak specification to control for unobserved heterogeneity, this nonparametric estimation procedure can identify both the nonparametric function and a finite-dimensional parameter associated with (potentially) observed time-invariant regressors. We develop the necessary asymptotic theory for our proposed estimator. To assess the validity of our method in practice, we propose a consistent specification test for whether the model controls for the correlation between the unobserved individual effects and the regressors. Monte Carlo simulations support the asymptotic developments. We illustrate the practical utility of our approach via an empirical application.

Contests with ambiguous prizes

with Cary Deck, Aidan Hathaway, Tigran Melkonyan, and Sam Redinger | Working Paper

This paper examines behavior in contests where the prize value is ambiguous. We develop a theoretical model of bidding in a Tullock contest with an ambiguous prize where contestants account for the ambiguity attitude of their rival. Ambiguity affects optimal behavior via two countervailing channels - a direct effect arising from contestants’ ambiguity about the value of the prize and an indirect effect corresponding to the effect of ambiguity on the opponent’s behavior. Using a controlled laboratory experiment, we elicit individual risk and ambiguity attitudes and compare predicted and observed behavior in contests with an ambiguous prize, a risky prize and certain prizes. A comparison between contests with ambiguous and risky prizes, shows that participants invest significantly less under ambiguity. Additionally, we decompose the effect of changing from a certain prize to an ambiguous prize into two components - the first is the effect of introducing risk and the second is the effect of introducing ambiguity. Empirically, we find that both effects are significant, but work in opposite directions.