[Paper Review] Estimation and Applications of Quantile Regression for Binary Longitudinal Data

Mohammad Arshad Rahman, Angela Vossmeyer|RePEc: Research Papers in Economics|Sep 12, 2019

demographic modeling and climate adaptation8 citations

TL;DR

This paper proposes a novel Bayesian hierarchical quantile regression model for binary longitudinal data using a Markov chain Monte Carlo (MCMC) algorithm with blocking and normal-exponential mixture representation of the asymmetric Laplace error distribution. It enables flexible modeling of both common and individual-specific effects, revealing heterogeneous covariate impacts across quantiles—particularly showing stronger effects of children's age and wealth on female labor force participation and home ownership at lower quantiles, offering policy-relevant insights beyond mean regression.

ABSTRACT

This paper develops a framework for quantile regression in binary longitudinal data settings. A novel Markov chain Monte Carlo (MCMC) method is designed to fit the model and its computational efficiency is demonstrated in a simulation study. The proposed approach is flexible in that it can account for common and individual-specific parameters, as well as multivariate heterogeneity associated with several covariates. The methodology is applied to study female labor force participation and home ownership in the United States. The results offer new insights at the various quantiles, which are of interest to policymakers and researchers alike.

Motivation & Objective

• To address the lack of flexible quantile regression methods for binary longitudinal data, which are common in econometric panel studies.
• To overcome computational challenges in estimating quantile models with binary outcomes and individual heterogeneity in panel data.
• To develop a computationally efficient MCMC algorithm that allows for joint estimation of fixed and random effects in a quantile regression framework.
• To apply the model to two key socioeconomic outcomes—female labor force participation and home ownership—to uncover heterogeneity in covariate effects across the utility distribution.
• To provide policy-relevant insights by identifying how determinants of binary outcomes vary across different quantiles of the latent utility scale.

Proposed method

• Adopts a hierarchical Bayesian model with latent utility framework to interpret binary outcomes as manifestations of unobserved willingness or propensity.
• Uses the asymmetric Laplace (AL) distribution for error terms in quantile regression, leveraging its normal-exponential mixture representation for full Gibbs sampling.
• Employs a blocking MCMC algorithm that improves computational efficiency by updating multiple parameters jointly, avoiding tuning of Metropolis-Hastings steps.
• Incorporates both common (fixed) and individual-specific (random) effects to model multivariate heterogeneity across covariates and individuals.
• Applies conditional posterior distributions derived from the hierarchical structure to enable tractable posterior simulation and inference.
• Uses simulation studies to validate the computational efficiency and convergence properties of the proposed MCMC algorithm.

Experimental results

Research questions

• RQ1 How do the effects of covariates on female labor force participation vary across different quantiles of the latent utility distribution?
• RQ2 What is the impact of children's age and family structure on labor force participation, and how does this vary across the utility distribution?
• RQ3 How do determinants of home ownership—such as gender, marital status, wealth, and health insurance—differ across quantiles of willingness to own a home?
• RQ4 To what extent does state dependence in home ownership persist across quantiles, especially around the Great Recession?
• RQ5 How do results from quantile regression differ from those of mean regression (PBLD) in capturing heterogeneous effects in binary longitudinal outcomes?

Key findings

• The effect of being female on home ownership probability is 2.9 percentage points at the 25th quantile and 1.6 percentage points at the 75th quantile, indicating a decreasing impact at higher willingness levels.
• Being married increases the probability of home ownership by 8.7 percentage points at the 25th quantile and 5.4 percentage points at the 75th quantile, with a stronger effect at lower willingness levels.
• Health insurance increases home ownership probability by 1.59 percentage points at the 25th quantile but only 0.06 percentage points at the 75th quantile, with the latter not statistically different from zero.
• A $50,000 increase in net wealth increases the probability of home ownership by 2.03 percentage points at the 75th quantile, showing greater impact at higher willingness levels.
• Earning a bachelor’s degree or higher increases the probability of home ownership by 1.53 percentage points at the 75th quantile, indicating stronger effects for highly motivated individuals.
• The model reveals non-trivial differences in state dependence effects post-Great Recession, with results diverging significantly from mean regression, especially at lower quantiles.