Nonlinear and Heterogeneous Effects of a Continuous Treatment

Suppose you were a policymaker with $1k to allocate across any set of families of your choosing when their children were at any age of your choosing. To whom would you give the cash? An empirically-grounded answer to this question requires one to begin from an assumption that the effect of income is both nonlinear and heterogeneous. Once we make that assumption, the “effect of family income" is no longer as simple as a single coefficient in a regression model. Instead, the effect of family income is a high-dimensional set of parameters such that no person can digest them all.

Lundberg and Brand’s task is one of discovery: we need to look algorithmically over all subpopulations and follow a computational procedure to select the causal quantities of interest worth summarizing. Then, in a new sample we need to estimate those quantities with flexible machine learning estimators designed for nonlinear and heterogeneous eects. The first contribution of this paper is to methodology: we develop that procedure for discovery with continuous treatments. The second contribution of this paper is to child development and status attainment: our discoveries of when, for whom, and at what values income matters point toward useful modifications to theories about how material circumstances in childhood shape life outcomes.