Question

Mark as true or false and briefly explain the reason

8. Classical measurement error in the dependent variable implies that the OLS estimator of the slope coefficient will be downward biased.
9. One solution to the issue of omitted variable bias is to use the method of two-stage least squares with an instrumental variable that satisfies the instrument relevance condition and the exclusion restriction.
10. Say you want to estimate the effect of schooling on wages using the method of two-stage least squares. Then the instrument exogeneity condition implies that the correlation between the instrumental variable and schooling should be zero.

Answer 1

8) False,

A classical measurement error will not cause any unbiasedness, yet it might cause increase in standard error in the estimated term.

yi* = yi + ti , where ti gives the unbiased error in yi.

if we do ordinary least sqaure on yi without considering ti.

that yi = α + βxi + ui

both α and β estimates will be unbiased because consider the ti , so that to above equation we add this ti disturbance term

then yi+ti=α + βxi + ui+ti

this can be written as yi*=α + βxi + ui* where ui*=ui+ti, thus this error term only increased not creating any biasedness problem for both estimates of α and β.

9)True,

The omitted variable problem create a problem of unbiasedness when only the omitted variable and the dependent variable are correlated as well it have a relation with indepedent variable and there is thus correlation between endogenous variable and error term within the omitted variable problematic model.

As a result two possible solutions is to use proxy variable or instrumental variable. Using instrumental variable which is exogenous and have correlation with endogenous variable we can use a Two SLS method further.

10) False,

In this problem, it is clear that schooling is independent variable and wages is dependent variable.

We use two stage least square method( 2-SLS) in the situation of simultaneous equation problem , here the problem is correlation between endogenous or independent variable and the error term.

The simple regression model is

y=β0+β1x+u, consider there is a probelm that x (schooling) and u(error term) have correlation such that we have to use an instrumental variable Z such that there is correlation between Z and S but not correlation between Z and U.

So yes Z and yes should have correaltion this is called instrument relevance conditon.

The instrument exogenity condition imply there is no relation between Z(instrument variable) and U(error term) such that Z won't have direct impact on Y.