Question

Discuss the following two statements:

(1) If we have an unobserved variable in an equation and we are interested in the sign of its coefficient, we should always use a proxy, since the estimated coefficient of the proxy will give us the correct sign.

(2) In regressions of income (or wage) on schooling where schooling is measured with error, omitting variables that measure ability will overestimate the effect of schooling on income.

Answer 1

(1)

This statement is studied under the "Errors in Variables" scope. The unobserved variable may lead to Errors in the included independent variables. Reliability of such variables to explain the effect on the dependent variable reduces. That's why the use of Instrument Variable is suggest. However, following two conditions by the instrumental variable must be satisfied:

- Instrument Relevance: the instrument variable must be related to the independent variable

- Instrument Exogeniety: the instrument variable must not be related with the error term

If the variable obeys these two conditions, then the variable can be taken up as a proxy variable for the independent variable. It is believed that the "errors in variables" problem in the independent variable will be eliminated and the estimated coefficient of the proxy variable will give correct sign.

(2)

This situation leads to Measurement Errors in the model. Omitted variables like ability can affect on schooling with their indirect impact through error term. It leads to Omitted Variable Bias. Such biased would overestimate the effect of schooling on income and leads to higher standard errors and variances.