catch-up hypotheses (Table 2), focussing on conventional HAZ scores; Section 4.3 considers the sensitivity of these results across alternative metrics of height as well as BMI; and Section 4.4 explores specific time-invariant child characteristics associated with child size and growth velocity.

# **4.1 Data**

We use the four latest public-use rounds of the YL data and focus exclusively on the youngest cohort, who were approximately one year old in the first round and around 12 years old in the fourth round.<sup>14</sup> Table 3 summarizes the analytical dataset we use hereafter. We have removed children who have missing data for their age (1,116 observations removed), or who were under 6 months old in the first round (165 observations removed). Also, due to the longitudinal nature of the intended analysis, we excluded children observed in fewer than three of the four rounds (452 observations removed). This yields a final dataset containing 30,515 observations on 7,681 children.<sup>15</sup> As Part (a) of the table shows, each round contains data on almost 2,000 children in all four countries. The table also indicates that the sample is well balanced by gender, and there are only small differences in the ages of sampled children (given as the age in months divided by 12) across countries in each collection round.

The descriptive statistics in Table 3(a) report averages across rounds for a range of growth outcomes. Child height (in cm) and weight are measured directly, from which the BMI (body mass index) is derived.<sup>16</sup> Notably, average heights are broadly comparable across the countries, but mean BMIs differ – e.g., contrast Peru (17.6) and India (14.7). All remaining outcomes are expressed in relation to expectations for a child of the same age and gender in a healthy external reference population. For this, we use the latest WHO child growth standards and follow Vidmar et al. (2004; 2013) to estimate relevant healthy population medians and standard deviations.

Denoting the observed outcome (i.e., height, BMI) for child _i_ at age _t_ as _yit_ , and the corresponding median expected outcome estimated from the reference distribution as _θ_<sup> ̄</sup> _t_ , we construct the following indicators: (i) standardized differences, ( _yit − θ_<sup> ̄</sup> _t_ ) _/_ ~~�~~ Var( _θt_ ), which yield conventional _z_ -scores

> 14 To enhance replication, we use the merged or constructed YL datasets, available at: https://www.younglives. org.uk/content/young-lives-rounds-1-4-constructed-files . The older cohorts are excluded since academic analysis of growth recovery (faltering) has typically focussed on the growth trajectories of younger children (e.g., Leroy et al. 2014, Victora et al. 2010). Furthermore, children from the older cohorts attain puberty during the data collection period, which is associated with a rapid spurt in growth. As such, the simplifying assumption of a linear (individual) growth trajectory, which is necessary given we have a maximum of four observations per child, is problematic for older cohorts. For the younger cohort, a small share (less than one-third) of girls have reached menarche by the fourth round (for further discussion see Schott et al. 2017).

> 15 Given the structure of the model, children observed in just three rounds can be retained in straightforward fashion.

> 16 We follow Crookston et al. (2013), among others, and adjust the raw heights and BMIs collected in the first round to account for differences in ages at the time of observation. As Victora et al. (2010) note, HAZ patterns in disadvantaged communities tend to decline sharply from birth until around 20 months, after which a more gradual pattern of change is found. This correction therefore addresses any non-linearities in the relation between outcomes and child age in the first round, and strengthens the general assumption of a linear trend in outcomes as applied in our regression estimates. However, this does not meaningfully alter our results.

13