Suppose that you have panel data from an experiment with T = 2 periods (so t = 1,2). Consider the panel data regression model with fixed individual and time effects

Suppose that you have panel data from an experiment with T = 2 periods (so t = 1,2). Consider the panel data regression model with fixed individual and time effects and individual characteristics W, that do not change over time, such as gender. Let the treatment be binary, so that X it = 1 for t = 2 for the individuals in the treatment group and let X u = 0 otherwise. Consider the population regression model
Y it , = i + ß 1 X it + ß 2 (D t × W i ) + ß o D 1 + v it ,
Where i are individual fixed effects, D, is the binary variable that equals 1 if t = 2 and equals 0 if t = 1, D t × W i is the product of D, and W,, and the ‘s and ‘s are unknown coefficients. Let Y i = Y i2 – Y i1. Derive Equation (13.6) (in the case of a single W regressor, so r = 1) from this population regression model.

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