Nurfatima Jandarova

Aldo Rustichini

Center of Excellence in Tax Systems Research, Tampere University

Department of Economics, University of Minnesota

March 22, 2024

Focus on all three characteristics

Robustness to functional specification

Polygenic score

UKHLS

+ metadac

\(\Pi\) is the set of functions \(\pi: \mathbb{R}_+ \rightarrow [0, 1]\) that are strictly increasing, concave, continuous at 0, \(\pi(0) = 0\), \(\lim_{x \rightarrow \infty} \pi(x) = 1\).

For a given discounted college premium \(\Delta \left(W, \delta\right)\) and cost adjustment \(\Gamma(z)\)

\[ x^\star = \text{arg}\max_x \left\{\pi(x) \Delta\left(W, \delta\right) - \frac{c(x)}{\Gamma(z)}\right\} \]

Hence, \(x^\star = f^{-1}(\Delta(W, \delta)\Gamma(z))\) where \(f(x) = \frac{\pi^\prime(x)}{c^\prime(x)}\).

Characterize \(P: \mathbb{R}_+ \rightarrow [0, 1]\) such that for some \(\pi: \mathbb{R}_+ \rightarrow [0, 1]\)

\[ P(A) = \pi\left(H\left(A; \pi\right)\right) \]