You would like to study the relationship between unemployment rate and minimum wage. You have the following model:

yi = 0 + 1xi + ui

Where yi is the unemployment rate of county i and xi is the minimum wage of county i. You would like to add another variable, ci , that measures the industry composition of county i, however, you don't have access to that variable so you decide to do the analysis without it.

1. What assumption is needed here to claim the OLS estimator is still unbiased?

2. Explain why the above assumption is implausible and derive the bias term of the OLS estimator.

3. If county with higher ci (more high tech industry) also has lower unemployment rate and higher minimum wage, what would you expect the sign of the bias term to be?

4. You realize you have access to a variable zi that could be used as instrumental variable. What assumption zi has to satisfy to be a valid instrument?

5. Derive the 2SLS estimator using zi as the instrument variable.