the scope of the current paper, being cognizant of the potential impact of using the unit context model on small area estimates is important.

First, the bias that has been reported in the literature is relative to an assumed gold-standard unit (household) level model and the availability of up-to-date household-level census microdata. It is our view that if recent census data are available, the census-EBP method should be preferred. We argue, however, that in the absence of recent census data, the use of geospatial covariates may constitute a valid alternative for providing up-to-date small area estimates until data from the next census becomes available. Second, we have observed that the extent of bias in the unit context model depends on the method used to account for sample weights. In this paper, weights are incorporated following Guadarrama et al. (2018). This weighting procedure was implemented in a way that adjusts the estimates of the regression coefficients and random effects to account for sample weights but does not account for weights when estimating the variance components.<sup>6</sup> As shown below, this can cause significant differences in small area estimates which are larger for models with lower predictive power, which is typically the case with unit context models. In Section 4 we explore both weighted and unweighted versions of the unit context model to assess how this impacts the estimates. Third, noting that aggregation is unavoidable due to the way geospatial data are processed, it is worth mentioning that the geographic level at which geospatial covariates are processed and linked to survey data (grid size) impacts the estimation. Because of this and because geospatial covariates can only act as proxies for the kind of variables typically used to model income (or consumption), it is reasonable to assume that the unit context model may show lower levels of predictive power and higher uncertainty than the unit (household) level model. However, because the estimators of interest are aggregations of individual-level predictions, it is not obvious that the lower predictive power and higher uncertainty will substantially reduce the quality of the small area estimates obtained by using the unit context model. Finally, as is the case with any modelbased method, model building, variable selection and residual diagnostics are critical. The data analyst can try to mitigate the impact of aggregation by processing the geospatial data at as a fine spatial level as possible to maximize the effective sample size. However, this may increase the risk of observing outliers in the geospatial data. The use of transformations may help make the data more consistent with the assumptions that the functional form is linear, and the error terms are distributed normally. As always, the use of model-diagnostics is crucial.

In addition, Corral et al. (2021) report concerns with the estimated measures of uncertainty under a unit context model. From our perspective, if the model assumptions are satisfied, a parametric bootstrap MSE estimator will provide a valid estimator of the uncertainty under the assumed model. Since the true data generating process is unknown, we cannot know a-priori the extent to which the model assumptions are violated, regardless of the type of model assumed. In Section 4, we present results from Burkina Faso comparing coverage rates derived from the parametric bootstrap under the unit context model, treating census-based estimates as truth, with those from other estimators. For sampled areas, coverage rates under the unit context model for sampled areas are slightly below those from direct estimates and slightly above those obtained from an area-level model, indicating that the estimated measures of uncertainty obtained through the parametric bootstrap are reasonable in this case.

In summary, we prefer to avoid making definitive statements about whether the unit context model works well or poorly. We instead posit that in the absence of a recent census, a unit context model with geospatial data may be considered as an alternative to the use of outdated

> 6 “For the pseudo-EB estimator, we used the weighted estimator given in You and Rao (2002) and the REML estimators of 2 and 2 .”  (Guadarrama et al, 2018, p.8) ββ̂ vv εε σσ� σσ�