accounts. If we assume that the number of procurement firms relative to the value of procurement is the same in our sample as in the whole population, we can scale up the share of procurement firms to 3.8% (0.005 / 0.13 = 0.038). However, this is probably a lower bound for the number of firms active in procurement because our procurement dataset is biased towards contracts awarded by the central government, which are bigger than the contracts awarded by other governments layers (e.g., local governments), and hence are probably more concentrated to a few firms.

To have a more credible estimate of the actual number of firms active in procurement, we make use of a recently available dataset provided by Spanish Government, _Plataforma de Contrataci ́on del Sector P ́ublico (PLACSP)_ , where all types of public agencies in Spain are required to upload their procurement activity. Although the platform includes information since 2013, compliance was only strong starting in March 2018, when introducing information on all contracts became compulsory by law.<sup>23</sup> Using information for the year 2019 (when the coverage is already high and before COVID), we measure around 75,000 firms with at least one procurement contract in the platform, which represents around 12% of the total number of active firms in the data. In our baseline calibration, we therefore set _mg_ equal to 12% and use the 3.8% as a robustness exercise.

We calibrate the level parameter _η_ 0 to ensure that the fraction of firms doing procurement equals the fraction of goods bought by the government, _mg_ , which is the equilibrium condition (e) (see section 4.9). Regarding the curvature parameter _η_ 1, we identify it by matching the selection pattern of firms into procurement observed in the data. We proceed as follows. In the data, we select firms with no procurement contracts between 1999 and 2005. Then, we classify as procurement firms those firms that obtain at least one contract in 2006. We define the “procurement premium” as the relative difference in size (measured by value added) between procurement and non-procurement firms in 2005 (only exploiting variation across firms within the same 4-digit industry). That is, we want the model to match the ex-ante difference in size between procurement and non-procurement firms. We measure this procurement premium to be 72%.

The intuition why the parameter _η_ 1 affects the selection of firms into procurement is as follows. When _η_ 1 approaches zero, the probability function _g_ ( _b_ ) exhibits strong diminishing marginal returns in _b_ : the marginal increase in probability falls quickly as firms invest more. This makes differences in _b_ across firms inconsequential for their probability of selling to the government, and hence generates very little selection, with complete randomness in allocation when _η_ 1 = 0. Conversely, when _η_ 1 approaches 1, the diminishing marginal returns are small: the marginal increase in probability falls slowly with _b_ as firms invest more. This implies that differences in _b_ translate into big differences in the probability of participating in procurement, which generates a strong selection pattern.

> 23In particular, that law (“Ley 9/2017, de 8 de noviembre, de Contratos del Sector P ́ublico”) was aimed to adopt the European Parliament directives 2014/23/UE and 2014/24/UE.

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