Question:
Consider a simple pooled regression model: yit = β0 + β1xit + vit where vit = μi + ∈it and Cov(xit, μi) ≠ 0. Here, μi captures the unknown individual specific effects and it is the idiosyncratic error uncorrelated with both xit and μi. If the parameters of this model are estimated using the ordinary least squares (OLS) method, then the estimated slope coefficient will be
Consider a simple pooled regression model: yit = β0 + β1xit + vit where vit = μi + ∈it and Cov(xit, μi) ≠ 0. Here, μi captures the unknown individual specific effects and it is the idiosyncratic error uncorrelated with both xit and μi. If the parameters of this model are estimated using the ordinary least squares (OLS) method, then the estimated slope coefficient will be
Updated On: Aug 21, 2025
- biased
- inconsistent
- unbiased but consistent
- unbiased but efficient
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The Correct Option is A, B
Solution and Explanation
In the given pooled regression model, the equation is: yit = β0 + β1xit + vit, where vit = μi + ∈it. The variable μi represents individual-specific effects, and ∈it is the idiosyncratic error. A crucial detail provided is Cov(xit, μi) ≠ 0, indicating that xit is correlated with μi.
When estimating parameters using OLS, a key assumption is that the regressors are uncorrelated with the error term. However, Cov(xit, μi) ≠ 0 violates this assumption, meaning the regressor xit is correlated with the composite error term vit.
Due to this correlation, the OLS estimator will not consistently estimate the true parameter values. This leads to:
- Bias: The estimated coefficients will be systematically off from the true population parameters because the omitted individual-specific effects μi correlate with xit.
- Inconsistency: As the sample size increases, an inconsistent estimator will not converge to the true parameter values, reflecting the persistent bias in the presence of correlated regressors and error terms.
In conclusion, under these circumstances, the OLS estimated slope coefficient is both biased and inconsistent.
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