# **4. Econometric Approach and Results**

To analyze the impacts of countries’ IPA membership on international patenting activity, we implement a structural gravity model of bilateral flows of patent applications analogous to the widely used structural gravity of bilateral trade.<sup>12</sup> We specify an estimating equation given by Patentsijt = exp[β0Intraijt + β1Extra1ijt + β2Extra2ijt + β3Extra3ijt + β4ANYIPRijt + β5ANYINVijt + γit + δjt + ηij + εijt] (1) where Patentsijt is the count of the total number of patent applications originating from source country i filed at the national patent office of destination country j in year t. Intraijt is an indicator variable equaling one when both _i_ and _j_ share mutual membership in one of the three types of IPAs as defined above (legally enforceable IPAs, US, EU, and EFTA-associated IPAs, and BTRIPS/TRIPS-Plus agreements), and zero otherwise. Coefficient β1, therefore, captures the average effect of accession to an IPA on within-agreement patenting between agreement member countries.

Following are three indicator variables identifying the membership status and income group of countries _i_ and _j_ . For the latter purpose we use the World Bank’s designation of countries as either high-income (HI) or not high-income (NHI), where the latter group includes all countries in our sample designated low-income (LI), lower-middle-income (LMI) or uppermiddle-income (UMI).<sup>13</sup> Specifically, Extra1ijt takes the value of one when both countries are HI nations but only one of them is a member of an IPA, and zero otherwise. Next, Extra2ijt captures cases where the destination is NHI and part of an IPA but the source country is outside the IPA but can be any income level. Finally, Extra3ijt refers to observations in which the origin is a NHI country inside and IPA but the origin is any country outside the IPA. Thus, β1

> 12 The gravity model has been widely employed to analyze many types of bilateral flows, including trade, investment, migration, and knowledge and innovation, among others. Recently, a small but growing literature has adapted the gravity equation to assess various determinants of bilateral patenting. See, for example, Picci (2010), Scherngell and Hu (2011) on bilateral patenting in international and intranational settings, or Montobbio and Sterzi (2013) for related work on a gravity model of international patent collaborations. Most closely related to our analysis is that of Coleman (2022), who conceptualizes a theoretical basis for a gravity equation of international patenting for the purpose of measuring the impacts on patenting of countries’ accession to international IP conventions, such as the Patent Cooperation Treaty (PCT) or the WTO TRIPS Agreement.

> 13 For purposes of identification in the gravity model, it is necessary to include this income-based breakdown to estimate impacts on both directional flows with non-members. See Beverelli et al. (2018) for discussion of this point in the trade-gravity context. We also estimate our specifications accounting for heterogeneity in countries’ R&D intensity (national rates of R&D spending over GDP) to divide countries into high-R&D and non-high-R&D categories. This approach yielded no qualitative differences from the baseline results. Because the R&D data are less complete than data for our other variables, we report the results only for the income-based regressions.

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