Model selection in the presence of incidental parameters

Abstract

This paper considers model selection of nonlinear panel data models in the presence of incidental parameters (i.e., large-dimensional nuisance parameters). The main interest is in selecting the model that approximates best the structure with the common parameters after concentrating out the incidental parameters. New model selection information criteria are developed that use either the Kullback-Leibler information criterion based on the profile likelihood or the Bayes factor based on the integrated likelihood with the robust prior of Arellano and Bonhomme (2009, Econometrica 77: 489-536). These model selection criteria impose heavier penalties than those of the standard information criteria such as AIC and BIC. The additional penalty, which is data-dependent, properly reflects the model complexity from the incidental parameters. As a particular example, a lag order selection criterion is examined in the context of dynamic panel models with fixed individual effects, and it is illustrated how the over/under-selection probabilities are controlled for.

Aggregate effects and measuring regional dynamics

“…We retain the estimated factor loadings for step 2. Estimate by OLS, stacking the factor loadings from step 1 in . We use the Lee and Phillips () panel data Schwarz criterion for selecting the lag order. A single lag is selected. Apply a Cholesky factorization of the reduced‐form residual variance‐covariance matrices to identify the labour demand shocks. Compute the impulse response functions to a –1% labour demand shock. Apply the bootstrap method to obtain 95% confidence intervals.…”

“…As above, we use Efron's () centred percentile bootstrap. The Lee and Phillips () Schwarz criterion selects one lag.…”

Identification and estimation in panel models with overspecified number of groups

“…Assumption A1. (a) assumes cross-sectional independence among the individuals which is standard for panel data, e.g., [20] and [24]. Assumption A1.…”

An Exponential Class of Dynamic Binary Choice Panel Data Models with Fixed Effects

“…One strand of the literature has focussed on developing modified maximum likelihood estimators that attain bias reductions when T is fixed. Examples include the papers by Arellano (2003) for static binary choice panel data models, and by Carro (2007), Bartolucci, Bellio, Salvan, and Sartori (2012), and Lee and Phillips (2015) for dynamic binary choice panel data models. This approach still requires T to be relatively large to attain significant bias reductions, as demonstrated in a number of Monte Carlo studies reported in the literature, even in the simplest case where the initial values are taken to be fixed constants.…”