From Data to Causes III: Bayesian Priors for General Cross-Lagged Panel Models (GCLM)

This article describes some potential uses of Bayesian estimation for time-series and panel data models by incorporating information from prior probabilities (i.e., priors) in addition to observed data. Drawing on econometrics and other literatures we illustrate the use of informative shrinkage or small variance priors (including so-called Minnesota priors) while extending prior work on the general cross-lagged panel model (GCLM). Using a panel dataset of national income and subjective well-being (SWB) we describe three key benefits of these priors. First, they shrink parameter estimates toward zero or toward each other for time-varying parameters, which lends additional support for an income -> SWB effect that is not supported with maximum likelihood (ML). This is useful because, second, these priors increase model parsimony and the stability of estimates (keeping them within more reasonable bounds) and thus improve out-of-sample predictions and interpretability, which means estimated effect should also be more trustworthy than under ML. Third, these priors allow estimating otherwise under-identified models under ML, allowing higher-order lagged effects and time-varying parameters that are otherwise impossible to estimate using observed data alone. In conclusion we note some of the responsibilities that come with the use of priors which, departing from typical commentaries on their scientific applications, we describe as involving reflection on how best to apply modeling tools to address matters of worldly concern.

Automated summary

This article discusses the potential uses of Bayesian estimation in time-series and panel data models by incorporating prior probabilities in addition to observed data. By using informative shrinkage or small variance priors, the article highlights the benefits of increased model parsimony, stability of estimates, and improved out-of-sample predictions and interpretability. The use of priors also allows for estimating otherwise under-identified models and higher-order lagged effects in a more trustworthy manner than under maximum likelihood estimation.