An empirical approach to model estimation and evaluation based on Bayesian Maximum Likelihood is introduced to the post-Keynesian literature. To illustrate the method, it is applied to a simple neo-Kaleckian model of euro area business cycle fluctuations including endogenous fiscal and monetary policy as well as endogenous wage formation. The estimated model parameters are broadly in line with the literature. To evaluate the empirical performance, we compare its marginal likelihoods and impulse-response functions to those of a corresponding Bayesian vector autoregression model after relaxing the theory-implied cross-coefficient restrictions as well as a benchmark dynamic stochastic general equilibrium model. The results suggest that both outperform the neo-Kaleckian model. In particular, we identify misspecification problems in the fiscal and monetary policy transmission mechanisms. Future research should be directed at improving the empirical fit of models in the post-Keynesian tradition and the current paper provides useful tools for doing so.