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.
Borjas, George. "Attenuation Bias in Measuring the Wage Impact of Immigration." Journal of Labor Economics 29.1 (January 2011): 69-113.