A simple alternative to the fixed effects model is called the differencing model, in which all the variables and the error term are expressed as differences. For a panel data set with two time periods, the estimating equation would be:

ΔY_i = β₀ + β₁ΔX_i + Δε_i

Where:

ΔY_i = Y_2i – Y_1i, ΔX_i = X_2i – X_1i, and Δε_i = ε_2i – ε_1i.

a. Using the data in Exercise 5, estimate a differencing model for the price of salon haircuts.

b. Now compare your answer in part a to your answer for part c of Exercise 5. What do you notice? What does this tell you about the relationship between the differencing model and the fixed effects model when there are exactly two time periods?

c. Think about the error term in the differencing model. Which of the Classical Assumptions does Δε_i seem likely to violate? How might you deal with this problem?