What are the basic conditions for obtaining a consistent estimate of the average partial effect over all PTAs, ϕˆ?. To answer this and identify the different sources of bias we first note the following property of gravity models. The bilateral market access between any xm pair has no direct effect on exports from the rest of the world to m (or any other countries) if we condition on Xx and Mm. This suggests we can estimate ϕˆ as an average treatment effect under the standard condition that the treatment, PTA membership, satisfies the conditional independence assumption. That is, conditional on (i) the relevant additive determinants of the exporter and importer characteristics and (ii) the determinants of bilateral access, the PTA treatment is “random” so we can obtain Tˆ as the conditional average difference in ln T between pairs of countries in a PTA and those outside.

While the conditional independence cannot be directly tested, we can examine how the results change as we move toward meeting it in terms of the econometric and economic model. To do so let us write the true value of the (log) XxMm, and ϕxm each as a (different) function of some vector of observable variables, summarized by Zi=ZxZmZxm, and an error term for each {ϵx, ϵm, ϵxm}. Using this we write log exports in its conditional expectation form, where uxm is a random error

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