as a function of maternal endowments with one interesting twist. The optimal investment
ratio is non-monotonic in the mother’s cognitive skill for each level of her noncognitive skills.
At very low or very high levels of maternal cognitive skills, it is better to invest relatively
more in the second period than if the mother’s cognitive endowment is at the mean.
The optimal ratio of early-to-late investment depends on the desired outcome, the en-
dowments of children and the budget. Figure 6 plots the density of the optimal ratio of
early-to-late investment for education and crime.49 For both outcomes and for most initial
endowments, it is optimal to invest relatively more in the first stage. Crime is more intensive
in noncognitive skills than educational attainment, which depends much more strongly on
cognitive skills. Because compensation for adversity in cognitive skills is much more costly
in the second stage than in the first stage, it is efficient to invest relatively more in cognitive
traits in the first stage relative to the second stage to promote education. Because crime is
more intensive in noncognitive skills and for such skills the increase in second stage compen-
sation costs is less steep, the optimal policy for preventing crime is relatively less intensive
in first stage investment.
These simulations suggest that the timing and level of optimal interventions for dis-
advantaged children depend on the conditions of disadvantage and the nature of desired
outcomes. Targeted strategies are likely to be effective especially for different targets that
weight cognitive and noncognitive traits differently.50
4.3.1 Some Economic Intuition that Explains the Simulation Results
This subsection provides an intuition for the simulation results just discussed. Given the
(weak) complementarity implicit in technology (2.3) and (2.4), how is it possible to obtain our
result that it is optimal to invest relatively more in the early years of the most disadvantaged?
The answer hinges on the interaction between different measures of disadvantage.
Consider the following example where individuals have a single capability, θ. Suppose
that there are two children, A and B , born with initial skills θ1A and θ1B , respectively. Let θPA
and θPB denote the skills of the parents A and B , respectively. Suppose that there are two
periods for investment, which we denote by periods 1 (early) and 2 (late). For each period,
there is a different technology that produces skills. Assume that the technology for period
49The optimal policy is not identical for each h and depends on θ1,h, which varies in the population. The
education outcome is the number of years of schooling attainment. The crime outcome is whether or not the
individual has been on probation. Estimates of the coefficients of the outcome equations including those for
crime are reported in Web Appendix 10.
50Web Appendix 13 presents additional simulations of the model for an extreme egalitarian criterion that
equalizes educational attainment across all children. We reach the same qualitative conclusions about the
optimality of differentially greater investment in the early years for disadvantaged children.
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