The permanent income and borrowing constraints models make the neutral assumption that intergenerational altruism is not related to parental income. Deviations from this assumption change the predictions of those models for the dynamics of inequality. Consider, for example, the permanent income model. If we suppose that richer parents are less altruistic then, as shown in Figure 13, expansion paths are concave and consumption regresses to the mean across generations. If instead richer parents are more altruistic, expansions paths are convex and consumption regresses away from the mean. Which of these assumptions is correct? This Chapter writes down two models of the formation of altruism. Rather than assuming that altruism is related in one way or another to income and other variables, the models predict these relationships and therefore have implications for the dynamics of inequality. The first model maintains the assumption from previous chapters that all parents have one child, focusing on the incentives to accumulate altruism.
I also present an alternative model of the effect of economic status on intergenerational altruism. The model, due to Becker and Barro (1988), abstracts from the purposeful accumulation of altruism but allows parents to choose the number of children. I present a graphical exposition of the Becker-Barro model and show that - at least for modern economies - their model counterfactually predicts regression away from the mean of consumption. Chapter XII incorporates both the purposeful accumulation of altruism from my model and the fertility choice from the Becker-Barro model into a single model.