The paper Stature and Status: Height, Ability, and Labor Market Outcomes (Journal of Political Economy [2008]: 499532)

The paper €œStature and Status: Height, Ability, and Labor Market Outcomes€ (Journal of Political Economy [2008]: 499€“532) describes a study of the association between height and cognitive ability. The paper states: €œWe first regress individual test scores on growth between ages 11 and 16 and then on growth between ages 16 and 33. We estimate separate models for boys and girls.€ Cognitive ability at age 11 was measured by three different tests€”verbal language, nonverbal language, and math. Six different simple linear regression models were used to describe the relationships between height gain from age 11 to 16 and each of the three test scores and between height gain from age 16 to 33 and each of the three test scores. The following table gives the slopes for each of the six regression models for boys.

a. In this study, height gain (the x variable) was measured in inches and the test scores were reported as percentage correct. The paper states that boys who grew more from age 11 to 16 had, on average, higher cognitive test scores at age 11, with each extra inch of height gain being associated with an increase in test scores of between 2 and 3 percentage points. Explain how the reported slopes are consistent with this statement.
b. The paper also states that boys who had a late growth spurt (after age 16) had lower test scores at age 11, with each extra inch of height gain being associated with a decrease in test scores of between 3.1 and 3.8 percentage points. Explain how the reported slopes are consistent with this statement.
c. The authors of the paper conclude that boys who grow early (age 11 to 16) have higher cognitive scores at age 11 than boys who grow late (age 16 to 33). Consider two boys who were the same height at age 11 and who both had total height gains of 5inches. If one boy had his 5-inch height gain before age 16 and the other boy had his 5-inch height gain after age 16, what would you estimate the difference in their age 11 math scores to have been? Is this consistent with the authors€™ conclusion?

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Slope of estimated regression line Height gain from Verbal language Height gain from Nonverbal language Height gain from Math Score Height gain from Verbal language Height gain from Nonverbal language3.8 Height gain from Math Score 2.0 age 11-16 age 11-16 age 11-16 age 16-33 age 16-33 age 16-33 2.3 score