Weighting a census as a non-probability sample: A doubly robust framework for differential undercoverage and the institutional capacity of national statistical offices (Uruguay's 2023 census)

The 2023 Uruguayan Census yielded an estimated total population of 3,444,451 at an estimated undercoverage of 10.3%. How a national statistical office corrects such differential undercoverage is inseparable from what that office is: a question of institutional capacity and data governance as much as of statistical method. Administrative records recover counts but not selection bias, leaving enumerated-microdata estimates biased. We treat enumerated households as a non-probability sample and weight them with a doubly robust estimator combining a response-propensity model (web linkage rate as contact proxy) with calibration to census demographic totals, at three million records. We then offer a framework to guide statistical offices in choosing adjustments given their registers and paradata. We argue that this choice is not merely technical but institutional: it depends on an office's capacity to integrate administrative registers, to capture and retain paradata, and to field a powered post-enumeration survey, together with the governance conditions (legal access to data, interoperability, autonomy, and public trust) that make such capacities possible. Read this way, the Uruguayan experience clarifies what a national statistical office must be able to do to correct differential undercoverage, and what it implies for offices, particularly across South America, that operate without those conditions.