Modelling the sectoral allocation of labour in open economy models

Indivisible labour is not the only type of non-convexity affecting labour supply decisions. Another type of non-convexity arises in economies with sectors whenever individuals can work in only one sector at a time. I introduce this restriction into an open economy model with a tradeable and a non-tradeable sector, and I use lotteries to convexify the consumption possibilities set. This approach implies that the aggregate elasticity of labour supply becomes infinite. I compare the performance of the model with an analogous model in which the labour supply elasticity is finite. I find that there is a disconnect between the response of wages to monetary shocks and the open economy variables. The labour supply elasticity plays a more important role in the transmission of technology and government expenditure shocks to the real exchange rate and the terms of trade.