Consider the following simple regression model y = β₀ + β₁x₁ + u. Suppose Corr(x,u) 0, Corr(z,x) 0, and Corr(z,u)

Question

Consider the following simple regression model y = β₀ + β₁x₁ + u. Suppose Corr(x,u) > 0, Corr(z,x) > 0, and Corr(z,u) < 0. Then, the OLS estimator has a(n) _____. A)downward bias B)asymptotic bias C)upward bias D)substantial bias

Quizplus · Accepted Answer

The OLS estimator in this case has an upward bias. This is because the presence of a positive correlation between x and u means that OLS tends to overestimate the coefficient β₁. The presence of a positive correlation between z and x reinforces this upward bias, while the negative correlation between z and u has no direct impact on the bias. However, it may have indirect effects if it leads to omitted variable bias or measurement error.

​Consider the Following Simple Regression Model Y = β0

Consider the Following Simple Regression Model Y = β₀