Although economic theory predicts an inverse relation between
relative wages and immigration-induced supply shifts, it has been
difficult to document such effects. The weak evidence may be partly
due to sampling error in a commonly used measure of the supply
shift, the immigrant share of the workforce. After controlling for
permanent factors that determine wages in specific labor markets,
little variation remains in the immigrant share. We find significant
sampling error in this measure of supply shifts in Canadian and
U.S. census data. Correcting for the resulting attenuation bias can
substantially increase existing estimates of the wage impact of immigration.