The Kalman Filter is used to estimate a structural time-series model of cotton supply for 30 countries and 16 aggregated regions. Estimated short run supply elasticities with respect to the world price are presented for all 46 countries and regions. While they are broadly within the expected range in light of previous work, they indicate extensive cross-country and regional heterogeneity, as well as considerable parameter uncertainty in some cases. Finally, some proposals are made for incorporating both the core estimates and their sampling distributions into applied equilibrium models.