Consider the following simultaneous equations model:
Before estimating the above model, a researcher performed the test of identification using order and rank conditions, and found that equation (2) is overidentified. Then, which of the following methods is appropriate to estimate equation (2)?
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Answer: (A)
In a simultaneous equations model, applying Ordinary Least Squares (D) directly to an equation with an endogenous regressor (here, appears on the right side of equation (2), but is itself jointly determined with ) produces biased and inconsistent estimates due to simultaneity bias — (D) is inappropriate.
Indirect Least Squares (B) is a valid method, but only works for exactly identified equations — it recovers structural parameters by solving the reduced-form OLS estimates back out, which requires a unique (one-to-one) mapping that only exists under exact identification. Since equation (2) is overidentified, ILS does not apply directly here.
Weighted Least Squares (C) addresses heteroscedasticity, not simultaneity — irrelevant to this specific problem.
Two-Stage Least Squares (2SLS) (A) is the standard, appropriate estimator for both exactly identified and overidentified equations in a simultaneous system — it uses the exogenous variables as instruments in a first stage to purge the endogeneity, then estimates the structural equation in a second stage.
Therefore the answer is (A) Two-Stage Least Squares.
Students who recall that 'Indirect Least Squares is used for simultaneous equations' without the specific caveat that ILS is restricted to exactly-identified cases may pick (B) as a generically correct answer for 'simultaneous equations estimation,' missing the overidentification detail that specifically rules ILS out and points to 2SLS instead.
Consider the following simultaneous equations model: Yₜ = β₁+β₂Xₜ+β₃Xₜ₋₁+β₄Zₜ+μ₁ₜ (1) Zₜ = δ₁+δ₂Yₜ+δ₃Wₜ+μ₂ₜ (2) Before estimating the above model, a researcher performed the test of identification using order and rank conditions, and found that equation (2) is overidentified. Then, which of the following methods is appropriate to estimate equation (2)? (A) Two-Stage Least Squares (B) Indirect Least Squares (C) Weighted Least Squares (D) Ordinary Least Squares
Also written as: Consider the following simultaneous equations model: Y_t = beta_1+beta_2X_t+beta_3X_(t-1)+beta_4Z_t+mu_(1t) (1) Z_t = delta_1+delta_2Y_t+delta_3W_t+mu_(2t) (2) Before estimating the above model, a researcher performed the test of identification using order and rank conditions, and found that equation (2) is overidentified. Then, which of the following methods is appropriate to estimate equation (2)?
Endogeneity, instruments and simultaneous equations has come up 8 times in 3 exams since 2021.
This question is on Simultaneous equations: identification and estimation, part of Endogeneity, instruments and simultaneous equations in Econometrics.
When a system of equations can be estimated and by which method.
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