‘Statistical adequacy’ is an important prerequisite for securing reliable inference in empirical modelling. This paper argues for more emphasis on replication that specifically assesses whether the results reported in empirical studies are based on statistically adequate models, i.e., models with valid underpinning statistical assumptions that satisfy relevant diagnostic tests of misspecification. A replication plan is briefly outlined to illustrate what this would involve in practice in the context of a specific study by Acemoglu, Gallego and Robinson (Institutions, human capital, and development, Annual Review of Economics, 2014).