**b) How would you estimate equation 2? Please describe in detail.**(Note: In the given text, there are no graphs or diagrams needing explanation. The content is primarily textual, focusing on the estimation of an equation.) ### System of Equations: Identifiability Analysis**1. Consider the following system of equations. $ Y_1 $, $ Y_2 $ and $ Y_3 $ are endogenous variables and $ X_1 $, $ X_2 $ and $ X_3 $ are exogenous variables.**\[\begin{align*}Y_1 &= \alpha_1 + \alpha_2 Y_2 + \alpha_3 Y_3 + \alpha_4 X_1 + \alpha_5 X_2 + u_1 \quad &\text{(Eq. 1)} \\Y_2 &= \beta_1 + \beta_2 Y_1 + \beta_3 Y_3 + \beta_4 X_2 + u_2 \quad &\text{(Eq. 2)} \\Y_3 &= \gamma_1 + \gamma_2 X_1 + \gamma_3 X_2 + \gamma_4 X_3 + u_3 \quad &\text{(Eq. 3)}\end{align*}\]**(a) Determine if each equation is just identified, over-identified or unidentified. Consider both rank and order conditions.****Explanation:**Analyzing each equation involves applying the *rank* and *order conditions* to determine whether the equations are **just identified**, **over-identified**, or **under-identified**.### Order Condition:- **Just Identified:** The number of excluded exogenous variables (from the specific equation) should be equal to the number of endogenous variables minus one.- **Over-identified:** The number of excluded exogenous variables is greater than the number of endogenous variables minus one.- **Under-identified (Unidentified):** The number of excluded exogenous variables is less than the number of endogenous variables minus one.### Rank Condition:To fully confirm identifiability, the rank condition must also be met, which involves matrix manipulations to ensure that the necessary parameters can be uniquely determined.### Equations Breakdown:1. **(Eq. 1):** - Endogenous Variables: $ Y_2 $, $ Y_3 $ - Exogenous Variables: $ X_1 $, $ X_2 $2. **(Eq. 2):** - Endogenous Variables: \( Y

Equation 1:Endogenous Variables: Exogenous Variables: Parameters to be Estimated: Rank…

Answered: a) Determine if each equation is just…

a) Determine if each equation is just identified, over identified or unidentified. Consider both rank and order conditions. is

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ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

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Question

**b) How would you estimate equation 2? Please describe in detail.**

(Note: In the given text, there are no graphs or diagrams needing explanation. The content is primarily textual, focusing on the estimation of an equation.)

### System of Equations: Identifiability Analysis

**1. Consider the following system of equations. $ Y_1 $, $ Y_2 $ and $ Y_3 $ are endogenous variables and $ X_1 $, $ X_2 $ and $ X_3 $ are exogenous variables.**

\[
\begin{align*}
Y_1 &= \alpha_1 + \alpha_2 Y_2 + \alpha_3 Y_3 + \alpha_4 X_1 + \alpha_5 X_2 + u_1 \quad &\text{(Eq. 1)} \\
Y_2 &= \beta_1 + \beta_2 Y_1 + \beta_3 Y_3 + \beta_4 X_2 + u_2 \quad &\text{(Eq. 2)} \\
Y_3 &= \gamma_1 + \gamma_2 X_1 + \gamma_3 X_2 + \gamma_4 X_3 + u_3 \quad &\text{(Eq. 3)}
\end{align*}
\]

**(a) Determine if each equation is just identified, over-identified or unidentified. Consider both rank and order conditions.**

**Explanation:**

Analyzing each equation involves applying the *rank* and *order conditions* to determine whether the equations are **just identified**, **over-identified**, or **under-identified**.

### Order Condition:
- **Just Identified:** The number of excluded exogenous variables (from the specific equation) should be equal to the number of endogenous variables minus one.
- **Over-identified:** The number of excluded exogenous variables is greater than the number of endogenous variables minus one.
- **Under-identified (Unidentified):** The number of excluded exogenous variables is less than the number of endogenous variables minus one.

### Rank Condition:
To fully confirm identifiability, the rank condition must also be met, which involves matrix manipulations to ensure that the necessary parameters can be uniquely determined.

### Equations Breakdown:

1. **(Eq. 1):**
- Endogenous Variables: $ Y_2 $, $ Y_3 $
- Exogenous Variables: $ X_1 $, $ X_2 $

2. **(Eq. 2):**
- Endogenous Variables: \( Y

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