This article describes some potential uses of Bayesian estimation for time-series and panel data models by incorporating information from prior probabilities in addition to observed data. Drawing on econometrics and other literatures we illustrate the use of informative “shrinkage” or “small variance” priors while extending prior work on the general cross-lagged panel model. Using a panel dataset of national income and subjective well-being 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. This is useful because, second, these priors increase model parsimony and the stability of estimates 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. (shrink)