Consider the two models, log w_i = beta_0 + beta_1 Black_i + beta_2 Asian_i + X_

Question

Consider the two models, log w_i = beta_0 + beta_1 Black_i + beta_2 Asian_i + X_i + u_i; log w_i = alpha_0 + alpha_1 White_i + alpha_2 Asian_i + X_i delta + u_i; a) Write the relationship between the beta's, gamma's, alpha's and delta's. I.e., if one knows the "true value" of (beta, gamma), how can one derive the "true values of (alpha, delta)? b) Write the relationship between the beta's, gamma's, alpha's, and delta's. I.e., if one knows the value of (beta, gamma), how can one derive the values of (alpha, delta)? c) Construct a model to measure how the return to getting a high school diploma and getting a college degree varies over sex and race. Divorce rates vary across time and across states. List ten variables that you think might affect divorce rates. For each one, discuss how you think it would affect divorce rates and what would happen if you could not get data on that variable. Go to the Social Science data center and get data on divorce rates and at least five of the variables you included Run an OLS regression using your data and report the results.

Explanation / Answer

a) If color is coded as binary (White = 1 and Black = 0), then Beta = 1 - Alpha

c) Let gender and race be 2 binary variables (Male = 1, Female = 0), Race (Asian = 1, Non-Asian = 0)

    Futher use 2 more dummy variables for high school diploma and college degree (1= Has Degree, 0 = No)

    log w = b0 + b1*highschool + b2*college + b3*gender + b4*race + e where

    b1-b4 are dummies as decribed as above.

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