This paper ties broadband development to regional economic growth and focuses on the optimal timing of investments. A Directional Distance Function framework is proposed for characterising the relationship between broadband investment and economic development, and a two-stage estimation procedure combining Convex Nonparametric Least Squares with Linear Programming is developed for estimating optimal investment paths. The model framework is applied to a novel dataset comprising 21 regions in the Baltic countries. The results indicate that Gross Regional Domestic Product could be increased by up to 10 per cent by adopting optimal regional investment paths. We find intercountry differences, where Latvian regions exhibit more inefficient investment strategies compared to regions subordinate to their neighbouring countries. There are also signs of over-investment in broadband in some regions.