Nowadays, causal inference methods using information from observational studies play a fundamental role in empirical research, in order to understand the effects of interventions, treatments and policies in different fields. This work aims to measure the causal effect of Artificial Intelligence (AI) and Big Data Analytics (BDA) on innovation in businesses accounting for heterogeneous causal effects within the potential outcomes framework, with a particular focus on the conditional average treatment effect (CATE). The data analyzed in the study are taken from a survey on European Small and Medium Enterprises (SMEs). Propensity score matching (PSM) is used to address possible imbalances in the sample. Afterwards, CATE is estimated using Bayesian Additive Regression Trees (BART). Our results suggested a significant and varying effect across different enterprise sizes, highlighting the importance of considering heterogeneity in causal effects for effective policy interventions.