Are children a source of happiness or not?

I think that in every model with fertility choice, children are modeled as beneficial but costly. The number of children enters positively in the utility function, and there is some cost, either monetary or in time, of raising them. Yet, it appears that quite consistently empirical studies on the happiness of people reveal that the number of children has a negative impact on happiness indicators. Then why would people have children? Social pressure, bad luck with contraception or stupidity? What if the empirics are flawed?

Leonardo Becchetti, Elena Giachin Ricca and Alessandra Pelloni find that the typical way the empirical studies are conducted is flawed. Among the controls, there is usually income. But this make it difficult to disentangle the monetary for the non-monetary impact of children. Using equivalised household income (income adjusted for the number of people in the household) allows to focus only on the impact on happiness, and children now have a positive impact. Decomposing their sample (the German Socio-Economic Panel), they find that opportunity costs do matter. Theory is saved.