Figure 2:

This figure shows how we use the IRT model to relocate and rescale maternal subjective probability reports (shown in the vertical axis) to error-ridden measures of the expectation of the natural log of human capital at age two years (shown in the horizontal axis) for two scenarios of investments (“high” vs. “low”) when human capital at birth is “high.” When the investment is “low,” the mother reports that there is a 25% chance that the child will learn how to speak a partial sentence with three words or more by age 24 months. When the investment is “high,” the mother reports that the probability is 75% by age 24 months. These probabilities correspond to 2.75 = ln 16 and 3.076 = ln 22, respectively. According to the IRT model, 25% of the 16-month-old children and 75% of the 22-month-old children speak a partial sentence with three words or more.