generally, see Head and Mayer (2014). A remaining problem is to include all relevant control variables to capture differential evolutions in the economic environment of treatment and control observations. This problem can be overcome by generalizing the approach to include a third dimension.

One can estimate equation (2) using a difference-in-differences analysis at the country level by comparing export growth for countries that do or do not benefit from liberalized market access. Alternatively, if only a subset of products benefit from the trade liberalization, one can compare export growth for treated and control products only for eligible countries. If not all countries in the sample are treated and not all products in treated countries benefit from the trade liberalization, we can estimate the following specification: ′ i i i i i . (5) ii ii ii ccii ccii ii The subscript _i_ is replaced by the country-product subscript yy = ββXX II + ZZ γγ+ γγ + γγ + γγ _ip,_ + εεand all possible doubleinteraction fixed effects are included as controls. In principle, we can still include control variables _Z,_ but in practice it is hard to obtain any variables that vary at the country-productyear level. The key indicator variable i captures whether product _p_ from country _i_ benefits from improved market access in the post-treatment period. If this set of products is the same II in each treated country, it can be written as , but it is not necessary. ii ii There are two ways to understand the intuition behind the identification of the coefficient II ∗II of interest in specification (5). Abstracting from the control variables and assuming the market access improvement is equally large for each treated country-product observation, the parameter captures: ββ i ~~�~~ i ~~�~~ . (6) ii cci ii cci It is a triple difference, i.e. a double difference in export growth rates. The difference in �Δyy −Δyy −�Δyy −Δyy export growth between a treated country _i_ and a control country _c_ for a non-treated product _d_ , is subtracted from the same difference in growth rates for a treated product _p._ Hence, if there are beneficial circumstances i in country _i_ that raise its exports across the board, it will also raise exports for non-treated products and the calculation will control for that. An example would be a country only becoming eligible for preferential market access under AGOA after ZZ it exits a civil war, which could coincide with an overall recovery of its economy. Similarly, if there are product-specific circumstances i that raise imports of product _p_ from everywhere, the calculation also controls for that as export growth for that product from non-treated countries will be elevated as well. An example here would be the EU granting more ZZ generous market access for textile products exactly at a time when the emergence of fast cci Δyy fashion firms is raising demand for apparel products overall.

An alternative way to understand the logic of the triple-difference specification is to see what the included fixed effects in equation (5) implicitly accomplish. The country-product interaction fixed effect has the effect of taking a within-difference of the dependent variable, such that only the growth over time in exports within each country-product category can contribute to the identification. To the extent that this within-growth rate is correlated with the country-products combinations being treated, it will raise the estimate of . However, not the full correlation contributes, only the correlation that remains after projecting the within ββ 16