# **2 Ex post quantification of the trade impact of different types of PTAs**

In this section, we estimate the trade impact of the 3 clusters of PTAs identified with the “kmean++” algorithm in a gravity framework in order to recover the partial effect on trade of PTAs associated with the different clusters. Specifically, we estimate the following structural gravity model, using PPML with panel data:<sup>3</sup> Where _Xij,t_ includes both intra-national and international manufacturing trade flows on 5-year intervals from 1982 to 2017.<sup>4</sup> Intra-national sales are needed as the correct benchmark for trade integration is the domestic economy (Yotov 2012). Otherwise the estimated coefficients would suffer from a missing variable bias. The data on inter- and intra-national trade come from, respectively, the CEPII BACI database and TradeProd combined with UNIDO INDSTAT2 2019.<sup>5</sup> Following standard practice, we fill in intra-national flows using linear interpolation between non-missing data and extrapolate remaining missing values using the evolution of country total exports as in Baier et al. (2019). In each year only countries with non-missing intra-national trade flows enter the estimation sample.

Our main variable of interest, _PTAij,t_ , is split across cluster groups: _PTA_<sup>_z_</sup> _ij,t_<sup>=1,</sup><sup>_PTAz_</sup> _ij,t_<sup>=2and</sup><sup>_PTAz_</sup> _ij,t_<sup>=3.The</sup> dummy _INTL BRDRij_ takes the value of one in case of an international trade flow. We interact this dummy with decades indexed by T (leaving the period after 2010 as reference). Exporter-time and importer-time fixed effects control for time-varying Multilateral Resistance Terms, while bilateral fixed effects control for timeinvariant unobserved characteristics of the country pair potentially leading to self-selection into PTAs (Baier & Bergstrand 2007). As an additional control, we also include the variable _TransitoryPTAsij,t_ , to control for agreements that are no longer in force.

The results presented in Table 5 provide the elasticity of bilateral trade to the different types of PTAS (as grouped by the clustering). This elasticity is here estimated within sample. As discussed in the Introduction, it will be introduced in a second step as a parameter in the estibration procedure.

> The first three columns exploit the raw UNIDO data we rely on. There are 99,000 observations for only 114 countries for which we observe internal flows. In order to expand internal flows coverage, in column 4 we rely

> 3 _Xij,t_ is in levels in columns 1 to 7 of Table 5, and in shares of absorption at destination – namely <u>�</u> _Xi_<sup>_X_</sup> _ij,_<sup>_ij,t_</sup> _t_<sup>–incolumn8.See</sup> discussion below.

> 4We tested the robustness of our findings over the period 1980-2015: the estimation results are not affected, see Table A2 in the Appendix.

> 5BACI is used to retrieve information on international trade flows from 1990 up to 2017 Gaulier & Zignago (2010), TradeProd provides data on both inter-national and intra-national trade from 1980 up to 2006 de Sousa, Mayer & Zignago (2012), whereas UNIDO INDSTAT2 2019 combined with BACI is used to derive domestic sales from 2007 to 2017. For the overlapping years we find a very high correlation (close to 99%) between TradeProd and the other sources for both inter-national and intra-national trade flows. When multiple sources are available for a given year we take the geometric average of the corresponding flows.

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