Three Essays on Internal Migration and Nutrition in Tanzania

ing from the case when the variance of childhood height approaches infinity, β approaches zero if the covariance between adult height and childhood height approaches zero. In other words, β approaches zero when childhood height is not a good predictor of adult height. Such an outcome is possible if short and stunted children catch-up others – or if the growth of the taller children in the sample stagnates. As such, β is only picking up movements within the HAZ distribution over time but researchers cannot tell whether this is due to improvements in HAZ or not. Second, as the β coefficient focuses on the changes within the distribution it fails to capture a widespread catch-up growth in the population. Such uniform movement of the distribution (as for example in Figure 5.3 presented later) only affects the estimated constant (α), not the β coefficient. This is a particular concern if the population under scrutiny is largely malnourished. Another important caveat is introduced by regression-to-the-mean (even in the absence of measurement error). Finding that β<1 may imply convergence (reduction in the dispersion of the height distribution over time) or simply reflect a natural variation in growth rates (height distribution remains intact). Quah (1993) demonstrates this algebraically using the Cauchy-Schwarz inequality: