Consider the following system of equations:
​$$\begin{aligned}Y_1 &= \alpha_0 + \alpha_1 Y_2 + \alpha_3 Y_3 + \alpha_4 X_1 + \alpha_5 X_2 + U_1 \\Y_2 &= \beta_0 + \beta_1 Y_3 + \beta_2 Y_1 + \beta_3 X_2 + U_2 \\Y_3 &= \lambda_0 + \lambda_1 X_1 + \lambda_2 X_2 + \lambda_3 X_3 + U_3\end{aligned}$$​​
According to the order condition, the first equation is:

Correct option is A

Correct Option: A. Unidentified
Explanation:

• The Order Condition is a necessary condition for the identification of a structural equation.
• It compares the number of excluded exogenous variables to the number of included endogenous variables (minus one).
• If the number of excluded exogenous variables is less than the number of included endogenous variables minus one, the equation is unidentified.
  

Information Booster:

• Formula: $$K - k \ge g - 1$$​​
  
  • $$K = 3$$​: Total exogenous variables in the system ($$X_1, X_2, X_3$$​).
    
  • $$k = 2$$​: Exogenous variables in the first equation ($$X_1, X_2$$​).
    
  • $$g = 3$$​: Total endogenous variables in the first equation ($$Y_1, Y_2, Y_3$$​).
    
• Calculation:
  
  • Excluded Variables ($$K - k$$) : $$3 - 2 = 1$$​ (Only $$X_3$$​ is excluded).
    
  • RHS Endogenous Variables ($$g - 1$$​): $$3 - 1 = 2$$​ ($$Y_2\ and \ Y_3$$​ appear on the RHS).
    
• Conclusion: Since $$1 < 2$$ (Excluded < Required), the equation is Unidentified.
  

Additional Knowledge:

• Just Identified: Condition holds with equality ($$K - k = g - 1$$​).
  
• Over Identified: Excluded variables are greater than required ($$K - k > g - 1$$​).
  
• Rank Condition: While the Order Condition is necessary, the Rank Condition is both necessary and sufficient for identification. It checks if the matrix of excluded coefficients has full rank.