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    Question

    When estimating a structural equation in a

    simultaneous-equation model (e.g., a supply-demand model), why does the use of Ordinary Least Squares (OLS) on a single equation typically result in inconsistent coefficient estimates?
    A The sample size is usually too small for the OLS estimator to achieve asymptotic efficiency. Correct Answer Incorrect Answer
    B The regressors are perfectly correlated with each other (perfect multicollinearity). Correct Answer Incorrect Answer
    C The system is under identified, making it impossible to solve for the structural parameters. Correct Answer Incorrect Answer
    D The error term of the equation is correlated with one or more of the endogenous regressors on the right-hand side. Correct Answer Incorrect Answer

    Solution

    Solution: The fundamental assumption for OLS consistency is that the error term (系i) is uncorrelated with all the independent variables (regressors) in the model: Cov(X,系)=0. 路 Simultaneity Problem: In a system of simultaneous equations (like supply and demand), an endogenous variable (e.g., Q) is determined by the interaction of the system. If we estimate the demand equation (where Q is on the left and P is an endogenous regressor on the right), the price P is correlated with the error term (系) because any unobserved shock in the demand error term (e.g., a sudden increase in taste for the good) simultaneously affects the price (P). 路 Result: This correlation between the regressor (P) and the error term (系) leads to Simultaneous Equations Bias, which is a form of endogeneity. This bias does not disappear as the sample size increases, meaning the OLS estimator is inconsistent.

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