A microfinance institution (MFI) currently operates in about 50 villages in Uganda, and wants to learn more about the impact of their microfinance loans on small business owners. Specifically, the MFI is interested in learning whether having a loan allows a business to expand their operations, increase sales, and earn more revenue. The MFI has conducted a survey of 250 business owners across the 50 villages where it operates. Some of these business owners have a microfinance loan and some don't. The results of this survey includes whether the business owner currently has a microfinance loan (LOANi) and the value of business revenues over the past month (REV ENUEi).

The MFI asks you to run the following short regression:

REV ENUEi=0+1LOANi+i

You learn that the MFI also collected educational attainment (measured as number of years education completed) (EDUi) as part of the survey. Now you are able to run the following long regression:

REV ENUEi=0+1LOANi+2EDUi+i

(c) (3 pts) Write down the auxiliary regression (use0and1as parameters). Interpret each of0and1.

1. (d)(3 pts) Plug the auxiliary into the long regression, and derive the expression showing how1and1relate. In your own words, interpret this expression.