Suppose that you have panel data with two periods (t = 1, 2). Let the treatment

Question

Suppose that you have panel data with two periods (t = 1, 2). Let the treatment be binary, so that X_it = 1 for t = 2 or the individuals in the treatment group and let X_it = 0 otherwise. Note that at t = 1, no one is it in the treatment. Consider the regression model Y_it = alpha_i + beta_1 X_it + beta_0 D_t + v_it where alpha_i are individual fixed effects, D_t is the binary variable that equals 1 if t = 2 and 0 otherwise. (a) Explain why it is important to include D_t. What problems might occur if it is left out? (b) Explain why it is important to include alpha_i (c) Explain in detail how to estimate beta_1 and beta_0. Be specific about the assumptions you are making.

Explanation / Answer

Ans 1)

In regression model, a dummy variable with value 0 will cause its coefficient to disappear from the equation. Conversly, the value of 1 causes the coefficient to function as supplemental intercept, because identity property of multiplication of 1.

In logistic regression models, encoding all of the independent variable as dummy variables allows easy interpretation and calculation of the odds ration and increase the stability and significance of coefficients.

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