Transforming Wealth: Using the Inverse Hyperbolic Sine (IHS) and Splines to Predict Youth’s Math Achievement
Abstract: Wealth is increasingly included alongside income for predicting youth’s educational outcomes. However, the natural log and categorical transformations may not always be appropriate for adjusting for skewness given wealth’s unique properties. We introduce an alternative transformation—the inverse hyperbolic sine (IHS)—for simultaneously dealing with skewness and accounting for wealth’s unique properties. We also explore non-linearity and accumulation thresholds by combining IHS transformed wealth with splines. We predict youth's math achievement with two data sources: (1) U.S. households from the Panel Study of Income Dynamics and (2) Ghanaian households from the YouthSave Ghana Experiment. IHS transformed wealth relates to youth’s math achievement similarly when compared to categorical and natural log transformations. In both U.S. and Ghanaian households, we find evidence of non-linearity between wealth and youth’s math achievement. We also find evidence for wealth accumulation thresholds that relate to youth’s math achievement. In an aggregate sample of U.S. households, accumulating zero and negative net worth is significantly related to decreases in youth’s math achievement whereas accumulating moderate values of positive net worth is significantly related to increases in youth’s math achievement. Among black and low-to-moderate income U.S. households, holding net worth sufficient to remain above the poverty line for three months is significantly related to youth’s improved math achievement. In Ghanaian households, accumulating assets between the 25th and 50th percentiles is related to a significant increase in youth’s math achievement.