In contrast to the rapid digitalization of several industries, agriculture suffers from low adoption of smart farming tools. While AI-driven digital agriculture tools can offer high-performing predictive functionalities, they lack tangible quantitative evidence on their benefits to the farmers. Field experiments can derive such evidence, but are often costly, time consuming and hence limited in scope and scale of application. To this end, we propose an observational causal inference framework for the empirical evaluation of the impact of digital tools on target farm performance indicators (e.g., yield in this case). This way, we can increase farmers' trust via enhancing the transparency of the digital agriculture market and accelerate the adoption of technologies that aim to secure farmer income resilience and global agricultural sustainability. As a case study, we designed and implemented a recommendation system for the optimal sowing time of cotton based on numerical weather predictions, which was used by a farmers' cooperative during the growing season of 2021. We then leverage agricultural knowledge, collected yield data, and environmental information to develop a causal graph of the farm system. Using the back-door criterion, we identify the impact of sowing recommendations on the yield and subsequently estimate it using linear regression, matching, inverse propensity score weighting and meta-learners. The results reveal that a field sown according to our recommendations exhibited a statistically significant yield increase that ranged from 12% to 17%, depending on the method. The effect estimates were robust, as indicated by the agreement among the estimation methods and four successful refutation tests. We argue that this approach can be implemented for decision support systems of other fields, extending their evaluation beyond a performance assessment of internal functionalities.