Joint Conditional Maximum Likelihood Estimation of Beta Regression for Panel Data with Higher-Order Autoregressive Errors
Abstract
Existing panel beta regression estimators do not accommodate higher-order autoregressive dependence within a joint likelihood framework. We develop such an estimator: a joint conditional maximum-likelihood beta-AR(k) model extended from a single time series to panel data, and extend it to panel inference through two new covariance estimators - a generalization of Beck-Katz panel-corrected standard errors (PCSE) and a Driscoll-Kraay-style alternative (DK) - to account for the cross-panel dependence the extension introduces. The estimator is evaluated by Monte Carlo simulation spanning AR(1)-AR(3) error structures, three panel sizes, and five series lengths, under both independent panels and genuine cross-panel dependence, against an uncorrected baseline. PCSE generally exhibited superior Type I error control and coverage relative to DK, at a power cost that was modest and partly illusory given DK's own miscalibration. Under genuine cross-panel dependence, the uncorrected estimator's Type I error was severe and did not diminish with additional data, while both corrections resolved it, with PCSE again preferred. An illustrative multi-site disease management example is provided, along with a Stata implementation (xtbetark).
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BibTeX
@misc{linden2026joint,
title = {{Joint Conditional Maximum Likelihood Estimation of Beta Regression for Panel Data with Higher-Order Autoregressive Errors}},
author = {Ariel Linden},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.26226},
eprint = {2609.26226},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.26226},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Joint Conditional Maximum Likelihood Estimation of Beta Regression for Panel Data with Higher-Order Autoregressive Errors
AU - Ariel Linden
PY - 2026
DA - 2026/09/01
PB - arXiv
DO - 10.48550/arxiv.2609.26226
UR - https://arxiv.org/abs/2609.26226
AB - Existing panel beta regression estimators do not accommodate higher-order autoregressive dependence within a joint likelihood framework. We develop such an estimator: a joint conditional maximum-likelihood beta-AR(k) model extended from a single time series to panel data, and extend it to panel inference through two new covariance estimators - a generalization of Beck-Katz panel-corrected standard errors (PCSE) and a Driscoll-Kraay-style alternative (DK) - to account for the cross-panel dependence the extension introduces. The estimator is evaluated by Monte Carlo simulation spanning AR(1)-AR(3) error structures, three panel sizes, and five series lengths, under both independent panels and genuine cross-panel dependence, against an uncorrected baseline. PCSE generally exhibited superior Type I error control and coverage relative to DK, at a power cost that was modest and partly illusory given DK's own miscalibration. Under genuine cross-panel dependence, the uncorrected estimator's Type I error was severe and did not diminish with additional data, while both corrections resolved it, with PCSE again preferred. An illustrative multi-site disease management example is provided, along with a Stata implementation (xtbetark).
ER -