Question
In the following two-equation system check the identification status of both the equations.
Y1 = α1+α2 Y2 + β1Z2 + u1
Y2 = β2 + β3Y1 + β4Z1 + β5Z2 + u2
Answer :
Word Count : 640
To determine the identification status of each equation in a simultaneous equations system, we apply the order and rank conditions. Identification refers to whether we can uniquely estimate the structural parameters of each equation from the observed data. We are given a two-equation system: 1. $Y_1 = \alpha_1 + \alpha_2 Y_2 + \beta_1 Z_2 + u_1$ 2. $Y_2 = \beta_2 + \beta_3 Y_1 + \beta_4 Z_1 + \beta_5 Z_2 + u_2$ Here, $Y_1$ and $Y_2$ are endogenous variables, and $Z_1, Z_2$ are exogenous variables. The goal is to check the identification status of each equation. --- ### Step 1: Count the endogenous and exogenous variables * Endogenous variables ($G$) = 2 → $Y_1, Y_2$ * Exogenous variables = 2 → $Z_1, Z_2$ --- ### Step 2: Apply the ___ __________ _________ _____ _______ __________ _________ _______.
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To determine the identification status of each equation in a simultaneous equations system, we apply the order and rank conditions. Identification refers to whether we can uniquely estimate the structural parameters of each equation from the observed data. We are given a two-equation system: 1. $Y_1 = \alpha_1 + \alpha_2 Y_2 + \beta_1 Z_2 + u_1$ 2. $Y_2 = \beta_2 + \beta_3 Y_1 + \beta_4 Z_1 + \beta_5 Z_2 + u_2$ Here, $Y_1$ and $Y_2$ are endogenous variables, and $Z_1, Z_2$ are exogenous variables. The goal is to check the identification status of each equation. --- ### Step 1: Count the endogenous and exogenous variables * Endogenous variables ($G$) = 2 → $Y_1, Y_2$ * Exogenous variables = 2 → $Z_1, Z_2$ --- ### Step 2: Apply the ___ __________ _________ _____ _______ __________ _________ _______.
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