To compare the systems of child benefits and of family tax deductions, we create a model with endogenous fertility and basic income, also financed from proportional wage taxes. Pensioners are neglected but younger and older workers are distinguished: the former raise children and receive child benefits, while the latter not. Through the balance equation, current average fertility depends on past average fertility. To have a socially optimal positive child benefit, past average fertility has to be less than 1. The deduction's efficiency is presumably lower than the benefit's and may even be lower than that of pure basic income.
progressive income tax child benefits family tax deductions endogenousfertility