15 15 with varying degrees of protectionism in government procurement.<sup>7</sup> As in the cross-country regression, we control for other importer-specific variables that are likely to correlate with both protectionism in government procurement and trade openness: dummies for membership in the WTO, WTO GPA, EU, and GDP (in logs), GDP per capita (in logs) and the average index of quality of institutions (fixed over time). These controls collected in the term are thus interacted with the internal trade dummy. Finally, we control also for the influence of time-varying determinants of bilateral imports that come from entry into trade ii,tt VV agreements: WTO membership and PTAs. Because of our interest in indicators that code national laws in government procurement, we include dummies for membership of both the importer and the exporter in the WTO, WTO GPA, PTAs without provisions on government procurement, PTAs with provisions in government procurement (except the EU) and the EU. The data on WTO and EU memberships come from the CEPII Gravity Database, whereas information on WTO GPA membership comes from the WTO website. Data on PTAs membership and provisions on government procurement are sourced from the Deep Trade Agreements Database (Mattoo, Rocha, and Ruta 2020).

Following the literature, the gravity models are estimated with the Poisson estimator (hence the exponential function in the gravity equation), which permits to include zero trade flows (around 30 percent of our sample) and accommodates heteroskedasticity in trade data (Silva and Tenreyro 2006). Following Egger and Tarlea (2015), we cluster the standard errors by importer, exporter and undirected country pair (the _ij_ and _ji_ pairs belong to the same cluster).

Unlike the literature that deals with estimation of trade effects of trade agreements (Baier and Bergstrand 2007; Piermartini and Yotov 2016), our empirical specification lacks bilateral fixed effects, because our variables of interest –indicators of protectionism in government procurement laws – are time-invariant (their interaction with the internal trade dummy would be absorbed by the country-pair fixed effects). This limitation of our empirical setting prevents us from credibly identifying causal effects. Besides adding an exhaustive set of control variables as explained above, we try to lessen potential omitted variable bias by further controlling for interactions between year dummies and the internal trade dummy in additional specifications. As Bergstrand, Larch, and Yotov (2015) argue, controlling for trends in the border effect can net out important variation, which in our case might well correlate with the interaction between internal trade and protectionism in government procurement laws.

Table 2 reports the results of the gravity estimations on the yearly sample, using the composite indicator for protectionism in government procurement laws – equal to one if the laws lack a national treatment provision (“discrimination”), they provide preferential

> 7 Mulabdic and Rotunno (2022) employ a similar empirical specification to estimate the impact on bilateral government procurement of provisions in PTAs that are likely to be multilateral (that apply equally to members and non-members).

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