Introductory Econometrics: A Modern Approach 6th Edition by Jeffrey M Wooldridge

Exercise 26

Suppose you have a sample of size n on three variables, y, x₁, and x₂, and you are primarily interested in the effect of x₁ on y. Let  be the coefficient on x₁ from the simple regression and  the coefficient on x₁ from the regression y on x₁, x₂. The standard errors reported by any regression package are

where  is the SER from the simple regression,  is the SER from the multiple regression, , and  is the R-squared from the regression of x₁ on x₂. Explain why  can be smaller or larger than .

Step 1 of 2

The standard error measures the statistical accuracy of an estimate and it is standard deviation of sampling distribution.