policy interventions based on descriptive features of growth trajectories. Put differently, while these regressions are of descriptive interest, they are unlikely to yield precise causal estimates.

# **5 Conclusion**

The aim of this study was to revisit how catch-up growth in children is defined and measured. Our motivation was that existing definitions tend to focus on specific dimensions of catch-up – namely either between-group or within-group convergence, but not both. We argued that existing studies also tend to focus on specific outcomes (e.g., HAZ) and that conventional dynamic panel estimates of catch-up are prone to bias. In contrast, we suggested that a latent growth framework is an attractive alternative. It avoids many of the technical problems with dynamic panel approaches and provides a unified setting in which to test for both between- and within-group catch-up. We outlined how the latent growth framework can be estimated in practice, proposing that a fixed-effects and individual slopes (FEIS) estimator imposes minimal assumptions relative to alternatives such as a correlated random effects (mixed effects) model. In addition, we showed how composite hypotheses regarding catch-up can be tested by combining probability values from the regression estimates.

In our application of this approach, we compared the performance of various latent growth estimators using four rounds of the Young Lives data collected in (sentinel sites) in Ethiopia, India, Peru and Vietnam. All of the samples come from relatively disadvantaged populations and, as expected, on average the sampled children display lower height and body mass than those from a healthy international reference population. On the basis of externally-standardized HAZ scores, our latent growth estimates revealed there has been statistically significant catch-up growth in Peru and Vietnam, but that the speed of catch-up has been slow. All countries other than Vietnam were also found to display some degree of within-group catch-up, but again this appears to have proceeded at a relatively moderate pace. Together, and as depicted in Figure 1, these results confirm the importance of conceptually and practically distinguishing between within- and between-group catch-up. Indeed, while the (predicted) distribution of HAZ scores for the sample in India is narrowing, the overall trend for the sample is declining. Only in Peru do we find evidence for both forms of catch-up simultaneously.

In terms of technical insights, we found that the FEIS estimator outperforms existing alternatives. Estimates based on a POLS or CRE estimator were found to be inconsistent (biased) and showed poorer goodness-of-fit. At the same time, conclusions about catch-up were found to be highly sensitive to the outcome metric chosen, especially in the case of height outcomes. As found elsewhere, evidence on catch-up based on HAZ scores tends to be more optimistic than evidence based on absolute or relative height differences. We argued that while there is unlikely to be a single ‘best’ metric, the choice of outcome metric is far from trivial and needs to be justified in relation to substantive research questions. Moreover, checking whether findings about catch-up 32