Empirical questions such as whether the Phillips curve or the Okun’s law is stable can often be framed as a model comparison—e.g., comparing a vector autoregression (VAR) in which the coefficients in one equation are constant versus one that has time-varying parameters. We develop Bayesian model comparison methods to compare a class of time-varying parameter VARs we call hybrid TVP-VARs—VARs with time-varying parameters in some equations but constant coefficients in others. Using US data, we find evidence that the VAR coefficients in some, but not all, equations are time varying. Our finding highlights the empirical relevance of these hybrid TVP-VARs.