In contrast to the rapid digitalization of several industries, agriculture suffers from low adoption of climate-smart farming tools. Even though AI-driven digital agriculture 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 and time consuming. 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. This way, we can increase farmers' trust via enhancing the transparency of the digital agriculture market, and in turn accelerate the adoption of technologies that aim to increase productivity and secure a sustainable and resilient agriculture against a changing climate. As a case study, we perform an empirical evaluation of a recommendation system for optimal cotton sowing, which was used by a farmers' cooperative during the growing season of 2021. We leverage agricultural knowledge to develop the causal graph of the farm system, we use the back-door criterion to identify the impact of recommendations on the yield and subsequently we estimate it using several methods on observational data. The results showed that a field sown according to our recommendations enjoyed a significant increase in yield 12% to 17%.