Question

What is the difference between proxy variable (also called a control variable) and instrumental variable?explain how they handle endogeneity.What criteria do they have to satisfy to be good choices?

Answer 1

Proxy variable is a variable that has correlation with variable of interest and can be easily measurable. The proxy variable is used in a place of a variable of interest that cannot be easily quantifiable. For example consumer price index (CPI) can be used to measure consumers' tastes and preferences.

Instrumental variable is a regression method to correct the endogeneity problem of other variables involved in regression analysis. The finding of endogenous variables that are strongly correlated with error term in an regression function is done by a third variable known as Instrumental variable. The wages and productivity of employees depends on skills of employees, that cannot be easily measurable. Therefore, both wages and productivity can be endogenous variables that are strongly correlated with each other but cannot be determined due to non-quantifiable variable employee skills. In that case, a proxy variable such as performance scores can be used to measure employee skills and eliminate endogeneity issue in the regression analysis of wages and productivity of employees.

Both proxy and instrumental variables are used to minimize the error terms in correlation estimates of two or more endogenous variables. Consider two dependent variables household income and education and one independent variable health of people. Here health of people is difficult to measure therefore, a third variable such as Health expenditure of people can be used to assess the health condition of people. In many economic analysis, linking a non-quantifiable variable with a proxy or instrumental variable is a good way to remove errors in correlation estimates.