This approach gives consistent estimates of the CHB index if the gravity equation is correctly specified, i.e. if the country-specific fixed effects are consistent estimates of their theoretical counterparts. Fally (2015) shows that this automatically holds true when the Poisson pseudo-maximum-likelihood (PPML) estimator proposed by Silva and Tenreyro (2006) is employed and income and expenditure are consistent with bilateral trade flows (i.e., _Yi,t_<sup>_k,s_= �</sup> _j_<sup>_X_</sup> _ij,t_<sup>_k,s_;</sup><sup>_E_</sup> _j,t_<sup>_k,s_= �</sup> _i_<sup>_X_</sup> _ij,t_<sup>_k,s_).The peculiar properties of the estimator implies that</sup> the actual income and expenditure values equal the predicted ones, which should normally be used as both are endogenous in the general equilibrium gravity model. We thus employ the PPML estimator, which has the added advantages of controlling for heteroskedasticity in the data and statistically dealing with zero trade flows. The gravity equation in eq (6) is estimated separately for each market _s_ and sector _k_ , although covariances of the estimated coefficients are taken into account when testing significance of the difference in across public and private gravity.

To bring this empirical artillery to the data, we need information on bilateral trade that involves the public sector as a buyer, on a large enough sample of countries. Other studies that investigate trade barriers in government procurement employ data from inter-country input-output tables (Riker, 2013; Messerlin and Mirodout, 2012) as these can split public expenditures from national accounts across type of goods and services purchased and country of origin. We thus follow this route and employ data from the TiVA initiative of the OECD. Similarly to other ICIO database (e.g., Timmer, 2012), the TiVA database harmonizes national IO tables and combines them with information from national accounts and bilateral trade statistics in goods and services to obtain an international input-output table (see OECD, 2013b for details). The estimation procedure allocates output from each country and sector to intermediate usage (by all sectors) or final demand across countries. While far from perfect and inevitably rife with measurement errors (especially compared with official trade statistics), this type of data is the only one that enables international comparison of public expenditures across countries and sectors.<sup>20</sup> Data on procurement contracts that has been used in related work (Herz and Varela-Irimia (2020); Fronk (2014); see also footonote 5) are limited to one or to a group of countries (U.S. or the EU) and

> 20An alternative approach that relies only on official trade statistics is used by Rickard and Kono (2014) (and adopted also by Gourdon and Messent (2019)). It indirectly identifies the effect of trade barriers on cross-border government procurement by allowing the effect of bilateral factors on trade as recorded by official statistics to vary with the size of the government procurement sector by country. An important limitation of this approach in our setting is that it departs from a structural gravity model: total government purchases, that enter overall expenditure in the gravity equation, are allowed to influence the direct effect of trade costs.

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