Recall that assuming a freely traded, CRS-produced outside good when writing a trade model is non-trivial [Davis (AER, 1998)]:
In the present paper, I show that what previously was regarded as an assumption of convenience – transport costs only for the differentiated goods – matters a great deal. In a focal case in which differentiated and homogeneous goods have identical transport costs, the home-market effect disappears.
In a recently posted paper (pdf), Svetlana Demidova and Andrés Rodriguez-Clare remind us that a curious result lurking in the heterogeneous firms literature – that unilateral trade liberalization decreases a country’s welfare – hinges on exactly that assumption.
It is interesting to compare this result to that in Demidova (2008) for the setting with CES preferences and Melitz and Ottaviano (2008) for the setting with linear demand, where lowering trade barriers for foreign firms reduces welfare at Home. The reason for this result is that such liberalization in country 1 makes country 2 a better export base, which results in the additional entry of firms there. This entry intensifies competition, which results in less entry and lower welfare in country 1. Our model shows that this result no longer holds when there is no outside good pinning down the wage in both countries.
Chaney (AER, 2008) also assumes a freely traded homogeneous good, so I presume that the same conclusion applies in his environment.
The Demidova & Rodriguez-Clare paper introduces a small open economy version of Melitz (2003), which lets them analyze asymmetric trade policies with endogenous wages very nicely in a (relatively) simple setting. Check it out.