Endogeneity, causality, and instrumental variables

  1. Write the structural model: \(y_1=\beta_1 y_2 + \beta_2 x_1+u\) where \(y_2\) is endogenous and \(x_1\)is exogenous
  2. First LS: \(y_2=\gamma_1 z_1+\gamma_2 z_2+e\)
  3. Calculate \(\hat{y_2}\)
  4. Second LS: \(y_1=\beta_1 \hat{y}_2 + \beta_2 x_1+u\)