This paper develops a model positing a nonlinear relationship between public investment and growth. The model is then applied to a panel of African countries, using nonlinear estimating procedures. The growth-maximizing level of public investment is estimated at about 10% of GDP, based on System GMM estimation. The paper further runs simulations, obtaining the constant optimal public investment share that maximizes the sum of discounted consumption as between 8.1% and 9.6% of GDP. Compared with the observed end-of-panel mean value of no more than 7.26%, these estimates suggest that there has been significant public underinvestment in Africa.