be smaller than the number of possible technologies _Nf_ .<sup>5</sup> We define the relative rank of a technology as _r_ ˆ _f_ = _Rrff−−_ 11<sup>.Notethat</sup><sup>_r_ˆ</sup><sup>_f∈_[0</sup><sup>_,_1].Thetechnologysophisticationofbusiness</sup> function _f_ in firm _j_ is a monotonic increasing function of the relative rank of _the most widely used technology_ of firm _j_ in function _f_ (ˆ _rf,j_ ). For example, our baseline sophistication measure is Since our baseline sophistication measure is linear, it displays constant increments in sophistication as we move up in the rank. For example, a firm that uses ERP for production planning, the frontier technology has a score of 5, while one that uses specialized planning software would have an index of 4. A priori, the sophistication measures could also be concave or convex in the rank, reflecting diminishing or increasing marginal increments in sophistication as the rank increases. In Cirera et al. (2020), we show how this simple index is robust to alternative cardinalizations.<sup>6</sup> but we use the index only in the descriptive statistics section, moving to adoption of specific advanced technologies in the empirical section.

# **2.2 Sample**

We use an original sample of about 1,500 establishments from Brazil. The data includes information from formal establishments in agriculture, manufacturing, and services with at least five employees. Table 1 contains detailed information for our sample, disaggregated at narrowly defined industries. For instance, in manufacturing, a large share of establishments are in food processing and wearing apparel, whereas in the services sectors, most establishments are in wholesale and retail. Data were collected face-to-face in 2019 for the state of Cear ́a. For the states of S ̃ao Paulo and Paran ́a, interviews were carried during 2022.

In addition to detailed information on the technology used for each business function, the FAT survey also includes information on several firms’ characteristics, which we use to control for other covariates likely to explain differences in technology adoption. For example, other than firms’ size, region, and sector, the database includes information on managers’ and workers’ education, the use of formal incentives and performance indicators, and in-

> 5In a small number of business functions, the technologies covered are used in various subgroups of tasks. For example, in the body pressing and welding functions of the automotive sector, the survey differentiates between technologies used for pressing skin panels, pressing structural components and welding the main body. In cases like this, we construct ranks of technologies for each subgroup of tasks within the business function, and then aggregate the resulting indices by taking simple averages across the task groups.

> 6The non-uniqueness of latent cardinal variables associated with an ordinal rank such as _r_ ˆ _f_ is common in many economic applications such as measures of institutional quality, quality of education, well-being, trust, social norms, and sophistication of management practices, to name a few. However, it is critical to demonstrate that these indices and results are robust to alternative plausible cardinalizations of the ordinal rankings they measure.

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