Based on a multi-county trade model developed by Furusawa and Konishi (2007), we analyze how the economic incentive to sign a bilateral free trade agreement (FTA) is affected by pre-existing FTAs of potential FTA partners. On the one hand, a country's own pre-existing FTAs strengthen her incentive to sign a new FTA because the decrease in her domestic firms' home-market profits resulting from increased competition will be smaller compared with the case without such pre-existing FTAs: pre-existing FTA members' firms will share the loss in profits from her home market. On the other hand, her potential FTA partner's pre-existing FTAs weaken her incentive to sign a new FTA because such pre-existing FTA members' preferential market access to her partner's market will erode her domestic firm's potential profit gains from preferential access to that market. These third-country (not directly involved in signing a new bilateral FTA) effects are named as a “loss-sharing effect” for the former effect and a “concession-erosion effect” for the latter one, by Chen and Josh (2010).

In contrast to Chen and Joshi (2010) who analyze the third-country effects based on a three-country model and attempt to empirically test simply the implication of such effects on FTA formation, our analysis based on a n-country model enables us to develop a theory-based empirical model and a calibration exercise to test our model using undirected dyadic data of 355,320 observations with 17,766 country-pair of 189 countries from 1993 to 2012. More specifically, our theory-based empirical model generates two distinctive variables to measure the third-country effects of a country's pre-existing FTAs, one for a loss-sharing effect and the other one for a concession-erosion effect. Having such distinctive variables is important in testing the model because we need to distinguish a loss-sharing effect of pre-existing FTAs of a country on her incentive to sign a new FTA from a concession erosion effect of the same pre-existing FTAs on her partner's incentive to sign a FTA with her: note that a country's pre-existing FTAs affects her incentive and her potential FTA partner's incentive to sign a new bilateral FTA in the opposite direction, which in turn necessitates such distinction.

Using the spatial econometric analysis often employed in the empirical studies of FTA formation, our analysis provides an evidence for the existence of these third-country effects on countries' incentive to sign a bilateral FTA. It also provides an empirical evidence for supporting our model's prediction on how other economic factors affect FTA formation: a new bilateral FTA is more likely to be signed, the more similar the two countries' tariff levels are, and the more similar the two countries' industrialization levels are, the factors emphasized by Furusawa and Konish (2007) in the context of identifying the conditions for a pairwise stable global FTA network. We also conduct a calibration exercise that finds a substitutability parameter for product varieties and each country's FTA signing threshold to fit the data the best, generating a predictive success rate of 93.4% for not-signing FTA cases and a predictive success rate of 72% for signing FTA cases.