Hidden group patterns in democracy developments: Bayesian inference for grouped heterogeneity

Abstract

We propose a nonparametric Bayesian approach to estimate time-varying grouped patterns of heterogeneity in linear panel data models. Unlike the classical approach in Bonhomme and Manresa (Econometrica, 2015(Econometrica, , 83, 1147(Econometrica, -1184, our approach can accommodate selection of the optimal number of groups and model estimation jointly, and also be readily extended to quantify uncertainties in the estimated group structure. Our proposed approach performs well in Monte Carlo simulations. Using our approach, we successfully replicate the estimated relationship between income and democracy in Bonhomme and Manresa and the group characteristics when we use the same number of groups. Furthermore, we find that the optimal number of groups could depend on model specifications on heteroskedasticity and discuss ways to choose models in practice. KEYWORDSbayesian inference, dirichlet process prior, panel data JEL CLASSIFICATIONF50, C11, C14

Forecasting with Bayesian Grouped Random Effects in Panel Data

“…Many methods have been suggested to estimate the optimal number a posteriori from the data such as BIC (Keribin 2000, Bonhomme andManresa 2015), marginal likelihoods (Frühwirth-Schnatter, 2004), or the integrated classification likelihood (Biernacki, Celeux, and Govaert, 2000). Bayesian approaches sometimes pursue a similar strategy, often adding the DIC to the list of model choice criteria, e.g., Celeux, Forbes, Robert, and Titterington (2006) and Kim and Wang (2019). If both N and T are large enough, the information criterion could select the true group structure.…”

“…In general, it is determined throughout the whole sampling period, which makes our model attractive in comparison with existing panel data models. We follow the Bayesian approach proposed by Kim and Wang (2019), who is considered as the Bayesian version of Bonhomme and Manresa (2015). In particular, we don't truncate the number of components at a predetermined level but leave the largest possible number unrestricted, and directly estimate the optimal partition under the assumption that group membership remains constant over time.…”

“…Armed with a proper Bayesian approach, we step further and examine whether such a grouped Bayesian estimator helps us make predictions for short panel data. Bonhomme and Manresa (2015) and its Bayesian counterpart Kim and Wang (2019) aim at estimating This Version: August 28, 2020 the heterogeneous coefficients and understanding the finite-sample properties of the grouped estimator. None of them explore the potential merit of the grouped estimator in terms of forecasting.…”

“…The contributions of this paper are fourfold. First, closely following Kim and Wang (2019) and Liu (2020), we develop a posterior sampling algorithm that addresses the nonparametric estimation of latent grouped effects and proposes Bayesian Grouped Random Effects (BGRE) estimator. Instead of using the Finite Mixture model, which needs to specify the number of groups a priori, we use Dirichlet Process (DP) prior, in particular the stick-breaking prior, that allows for infinite potential groups and direct estimation of the number of groups along with parameters of interest.…”

“…Our paper relates to several branches of the literature. Our work is closely related to Bonhomme and Manresa (2015), Bonhomme, Lamadon, and Manresa (2019) and Kim and Wang (2019). All of these three papers aim to estimate the unobserved heterogeneity in a linear dynamic panel data model and develop statistical inference methods.…”