Estimating the Technology of Cognitive and Noncognitive Skill Formation



one is:


θ2 = γ1θ1 + γ2I1 + (1 - γ1 - γ2) θP .

For period two it is:

θ3 = min{θ2,I2P} .

These patterns of complementarity are polar cases that represent, in extreme form, the
empirical pattern found for cognitive skill accumulation: that substitution possibilities are
greater early in life compared to later in life.

The problem of society is to choose how much to invest in child A and child B in periods
1 and 2 to maximize total aggregate skills, θ
3A + θ3B , subject to the resource constraint
I
1A + I2A + I1B + I2B ≤ M , where M is total resources available for investment. Formally, the
problem is

min γ1θ1A + γ2I1A + (1 - γ1 - γ2) θPA, I2A, θPA +
min
{γiθB + Y2I1B + (1 - Y1 - Y2) θB, IB, θp }

subject to: I1A + I2A + I1B + I2B ≤ M

(4.6)


When the resource constraint in (4.6) does not bind, which it does not if M is above a
certain threshold (determined by θ
P), optimal investments are

I1A


(Y1 + Y2) θA - YιθA
γ2


I1B


(Y1 + Y2) θB - YιθB
γ2


I2A = θPA


I2B = θPB

Notice that if child A is disadvantaged compared to B on both measures of disadvantage,
1A < θ1B and θPA < θPB), it can happen that

I1A > I1B , but I2A < I2B

if

θA - θB >   γ1   (θA - θΒ

P P   γ1 + γ2   1    1

Thus, if parental endowment differences are less negative than child endowment differences
(scaled by
γγ γ ), it is optimal to invest more in the early years for the disadvantaged and
less in the later years. Notice that since (1 - γ
1 - γ2) = γP is the productivity parameter on
θ
P in the first period technology, we can rewrite this condition as (θA — θB) > ɪ (θA — θB).
The higher the self-productivity (γ
1) and the higher the parental environment productivity,
γ
P , the more likely will this inequality be satisfied for any fixed level of disparity.

35



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