4.10. (A different form of measurement error.) Suppose the true relationship between social infrastructure (SI) and log income per person (y) is yi = a +

bSIi + ei . There are two components of social infrastructure, SI A and SI B

(with SIi = SI A i + SI B i ), and we only have data on one of the components, SI A.

Both SI A and SI B are uncorrelated with

e. We are considering running an OLS regression of y on a constant and SI A.

(a) Derive an expression of the form, yi = a + bSI A i + other terms.