for the HAD metric. As already argued, this finding may reflect the arithmetic properties of the HAD measure, by which initial differences grow in absolute magnitude over time. The HAR metric corrects for this problem, but remains unaffected by changes in the distribution of the reference population. These results reported in Table 5 for the height ratio are generally less pessimistic than those based on absolute differences. Nonetheless, the HAR estimates continue to provide no evidence of within-group catch-up, and between-group catch-up only obtains for the Peruvian sample.

We also investigate catch-up growth based on various measures of BMI. These are shown in Table 6, which also only uses the FEIS estimator and summarizes results for various transformations. Here, the findings appear less sensitive to the particular metric chosen. There is no evidence of between-group catch-up for the continuous variables (BAZ, BAD, BAR); and evidence of withingroup convergence is limited to Ethiopia (BAZ and BAR metrics) and Peru (BAZ only). The greater consistency of findings in this case may well reflect the properties of BMI. Since both height and weight are growing in a healthy reference population, changes in (median) BMI are expected to be fairly stable between ages one and 12. Also, the distribution of body mass shows rather less variation (changes in variance) across different age groups compared to the distribution of heights. Thus, for the BMI measure changes in dispersion are likely to play a smaller role, in turn explaining the broad similarity of findings across the continuous transformations.

The same analysis can be applied to binary indicators, in which case the outcome is a dummy variable and the specification becomes a linear probability model. Corresponding results are shown in the bottom portions of Tables 5 and 6), where the binary indicators take a value of one if a child is within a healthy group (this construction ensures the hypothesis tests can be applied in the same way as before). Three points stand out. First, consistent with the HAZ results, there is clear evidence of both between- and within-group catch-up from stunting (however defined) in the Peruvian sample. Second, all other countries show some sign of a reduction in the prevalence of stunting – i.e., there is some between-group catch-up. But this depends on the specific metric chosen. In Ethiopia, there is a reduction in both the prevalence of stunting (HAZ < -2) and severe stunting (HAZ < -3). In India, we only see a fall in severe stunting; and in Vietnam we observe a reduction in stunting, but not severe stunting. Indeed, all countries other than Vietnam show evidence of between- and within-group catch-up from severe stunting. However, this may well reflect the lower prevalence of severe stunting in Vietnam to begin with (see Table 3). Third, there is limited evidence of catch-up from wasting. Indeed, none of the countries provides evidence of either between- or within-group catch-up from very low BMI. Children from the Peru sample show some increase in the share of children with a healthy BMI. However, this is likely to be driven by a fall in those with a very high initial BMI (obese).

As a final exercise, Table 7 pulls together the results from the various hypothesis tests examined above (for the FEIS estimator). Similar to Table 2, it counts the number of test results corresponding to each combination of within and between catch-up. Part (a) of the table refers to the five height 21