A note on the empirical implementation of the lens condition

"Deardorff [Journal of International Economics 36 (1994) 167-175] offers an intuitively appealing test for factor price equality (FPE). He demonstrates that FPE is impossible if the set (i.e., lens) of points defined by regional factor abundance vectors does not lie within the set of points defined by goods' input intensities. This note demonstrates that empirical implementation of the lens condition is problematic if the "true" number of either goods or regions is unknown. We show that satisfaction of the lens condition is more likely when goods are relatively disaggregate compared to regions"--National Bureau of Economic Research web site.