We build a semi-endogenous growth model for developing countries with non-rivalrous public factors, imported capital goods, and an export demand function. The model exhibits the three-way interaction between public and private investment and trade shown recently in the empirical literature. A parameter for government-investment inefficiency has transitional growth effects distorting between public investment and private capital, consumption, and exports, the latter biasing the terms of trade. Our analysis of a vector error-correction model (VECM) for Trinidad &Tobago shows that additional expenditure for public investment increases output less than taxes decrease per capita consumption and therefore is sub-optimal there. Both temporary and permanent shocks on public investment have level effects supporting semi-endogenous growth modeling and demonstrate that the VECM effects are in line with the logic of the theoretical model; terms of trade are endogenous.