Simultaneous causality bias:

Question

BlackTom AI · Accepted Answer

Simultaneous causality occurs when X and Y affect each other: X → Y and Y → X. This two-way causal link makes X endogenous in the regression of Y on X, violating the OLS assumption that regressors are uncorrelated with the error term and leading to biased and inconsistent OLS estimates.

Relevant knowledge points:
- OLS consistency requires E[X·u] = 0 (no correlation between regressor and error).
- Reverse causality (Y → X) creates endogeneity: X is partly determined by Y, which depends on the error term in the structural equation for Y.
- Simultaneous equations can be written in structural form and solved to see the induced correlation.
- Bias arises because OLS attributes all X–Y covariance to the coefficient on X, not to the mutual causation.

Step-by-step reasoning with equations:
1. Structural equations: Y = βX + u (equation of interest), and X = γY + v (feedback equation).
2. Substitute Y into X: X = γ(βX + u) + v = γβX + γu + v.
3. Rearrange: X(1 − γβ) = γu + v.
4. Solve for X: X = [γ/(1 − γβ)]u + [1/(1 − γβ)]v.
5. This representation shows X contains a component proportional to u. Therefore Cov(X, u) = [γ/(1 − γβ)]Var(u) + Cov(v, u)/(1 − γβ). Unless γ = 0 and Cov(v,u)=0, Cov(X,u) ≠ 0.
6. Nonzero Cov(X,u) violates OLS exogeneity; OLS estimator is biased and inconsistent.

Why the correct choice is correct:
- The chosen option explicitly states the defining feature of simultaneous causality: a causal link from Y back to X in addition to X → Y, which is precisely the source of endogeneity and bias.

Why other options are incorrect:
- "Is also called sample selection bias": sample selection bias arises from nonrandom sampling, not from mutual causation.
- "Results in biased estimators if there is heteroskedasticity": heteroskedasticity does not bias OLS coefficients (it affects standard errors and efficiency); it is not the cause of simultaneous causality bias.
- "Happens in complicated systems of equations called block recursive systems": block recursive (recursive) systems are ordered so no simultaneity/reverse causation exists; simultaneity arises in nonrecursive systems.

Conclusion: The correct answer states that simultaneous causality arises when, besides X → Y, there is a causal link Y → X; this matches and confirms the provided answer.

Simultaneous causality bias:单项选择题

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