Optimal taxation with unobservable investment in human capital

In a Ramsey model of optimal taxation, if human capital investment can be observed separately from consumption, it is optimal not to distort human or physical capital accumulation in the long run, and only labour income taxes should be used. However, in reality the government can't always distinguish between investment in human capital and pure consumption, so a tax on labour or consumption will necessarily tax human capital. We find that when investment in human capital is unobservable, the optimal policy is to tax human capital at a positive rate, even in the long run. Whether physical capital should be taxed or not depends on its degree of complementarity with human capital versus labour.