The morphological complexity of languages differs widely and changes over time. Pathways of change are often driven by the interplay of multiple competing factors, and are hard to disentangle. We here focus on a paradigmatic scenario of language change: the reduction of morphological complexity from Latin towards the Romance languages. To establish a causal explanation for this phenomenon, we employ three lines of evidence: 1) analyses of parallel corpora to measure the complexity of words in actual language production, 2) applications of NLP tools to further tease apart the contribution of inflectional morphology to word complexity, and 3) experimental data from artificial language learning, which illustrate the learning pressures at play when morphology simplifies. These three lines of evidence converge to show that pressures associated with imperfect language learning are good candidates to causally explain the reduction in morphological complexity in the Latin-to-Romance scenario. More generally, we argue that combining corpus, computational and experimental evidence is the way forward in historical linguistics and linguistic typology.