# **4.2 Baseline results**

Our baseline results concerning catch-up growth in the four YL countries are summarized in Table 4, which takes height-for-age _z_ -scores (HAZ) as the primary outcome of interest.<sup>17</sup> Results for three different estimators of equation (6a) are reported. In each case, the same specification is employed and we include a set of control variables spanning a range of both fixed and time-varying characteristics. These are _inter alia_ : the child’s gender; whether children come from the majority ethno-linguist group (ELG) of the region of residence; whether they have older siblings; if the location is urban; the age and highest level of education of their mother (at time of birth); a household wealth index; household size; and household exposure to shocks.<sup>18</sup> For comparison, Appendix Table A2 reports the same results, excluding the additional control variables. These are highly similar and thus do not merit separate discussion.

Before reviewing the results in detail, the scaling of the age variable merits comment. It is well known that estimates of both the intercept and the slope-intercept covariance in latent growth models are sensitive to the point at which one sets _t_ = 0 (Biesanz et al. 2004, Stoel and Van Den Wittenboer 2003). While different choices can help address different analytical questions, Tu and Gilthorpe (2011) demonstrate that age/time must be demeaned (i.e., one must use _ti_<sup>_∗_=</sup><sup>_ti −t_ ̄) to</sup> avoid distortion of the null hypothesis of zero correlation between the slope and the intercept (see also Blance et al. 2005, Tu and Gilthorpe 2007). We apply this adjustment here, thus ensuring a clean interpretation of the estimated slope-intercept correlation coefficient under the null hypothesis that it is equal to zero. Consequently, the individual intercept terms ( _α_ 0 + _αi_ ) represent the expected outcome for the child at around 6.5 years of age.

For each country and estimator, Table 4 reports estimates for the three parameters of interest: the mean outcome in the sample (i.e., the average difference in stature relative to the reference median, _α_ 0), the mean growth velocity ( _β_ 0), and the conditional correlation between the estimated latent variables ( _ραβ_ ). In the case of the POLS estimator, the latent variables are ignored and thus not estimated. Even so, a proxy for individual-specific slopes can be derived by interacting the child’s age with the set of time-invariant controls. In turn, the correlation between these slopes and the estimated conditional mean size of each child yields a crude first-pass approximation to _ραβ_ . For the CRE estimator, the same correlation coefficient is estimated directly as a model parameter. For the FEIS estimator, implemented in Stata via the reghdfe command, the fixed effects are retrieved after estimation (see Guimarães and Portugal 2010). In turn, the correlation coefficient is calculated directly from the estimated fixed effects.<sup>19</sup>

> 17 HAZ scores are chosen as they are the _de facto_ standard in the literature (e.g., see Table 1).

> 18 All control variables are demeaned (at the country-level) to assist comparison of estimates. The variables are chosen following previous studies and in accordance with variables that are common to all countries and rounds of the YL datasets. For further discussion see Section 4.4.

> 19 To adjust for measurement error, the fixed effects are shrunk toward the sample mean of zero in accordance with the number of observations used to estimate each effect. This corresponds to an empirical Bayes procedure (see the discussion in Koedel et al. 2015), yielding a shrinkage factor of 80% in the majority of cases where the child is

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