In the empirical exercises on earning and height in Chapters 4 and 5, you estimated a relatively large and statistically significant effect of a worker’s height on his or her earnings. One explanation for this result is omitted variable bias: Height is correlated with an omitted factor that affects earnings. For example, Case and Paxson (2008) suggest that cognitive ability (or intelligence) is the omitted factor. The mechanism they describe is straightforward: Poor nutrition and other harmful environmental factors in utero and in early childhood have, on average, deleterious effects on both cognitive and physical development. Cognitive ability affects earnings later in life and thus is an omitted variable in the regression. Suppose that the mechanism described above is correct. Explain how this leads to omitted variable bias in the OLS regression of Earnings on Height. Does the bias lead the estimated slope to be too large or too small? [Hint: Review Equation (6.1)] Omitted Variable Bias in Regressionwith a Single Regressor6.1 Omitted Variable BiasOmitted variable bias is the bias in the OLS estimator that arises when the regres-sor, X, is correlated with an omitted variable. For omitted variable bias to occur,conditions must be true:two1. X is correlated with the omitted variable.2. The omitted variable is a determinant of the dependent variable, Y.=185Because uiand X; are correlated, the conditional mean of u; given X; is nonzero.This correlation therefore violates the first least squares assumption, and the con-sequence is serious: The OLS estimator is biased. This bias does not vanish evenin very large samples, and the OLS estimator is inconsistent.KEY CONCEPT6.1A Formula for Omitted Variable BiasThe discussion of the previous section about omitted variable bias can be sum-marized mathematically by a formula for this bias. Let the correlation between X;and u; be corr(X¡, u¡) Pxu. Suppose that the second and third least squaresassumptions hold, but the first does not because pxu is nonzero. Then the OLSestimator has the limit (derived in Appendix 6.1)OuB₁ B₁ + PXux(6.1)That is, as the sample size increases, B₁ is close to B₁ + pxu(ou/ox) with increas-ingly high probability.The formula in Equation (6.1) summarizes several of the ideas discussedabove about omitted variable bias:1. Omitted variable bias is a problem whether the sample size is large or small.Because ₁ does not converge in probability to the true value B₁, B₁ is biasedand inconsistent; that is, ₁ is not a consistent estimator of B₁ when there isomitted variable bias. The term pxu(ou/ox) in Equation (6.1) is the bias inthat persists even in large samples.

Omitted variable bias occurs when a relevant variable is left out of a regression model. If the…

Answered: n the empirical exercises on earning…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

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In the empirical exercises on earning and height in Chapters 4 and 5, you estimated a relatively large and statistically significant effect of a worker’s height on his or her earnings. One explanation for this result is omitted variable bias: Height is correlated with an omitted factor that affects earnings. For example, Case and Paxson (2008) suggest that cognitive ability (or intelligence) is the omitted factor. The mechanism they describe is straightforward: Poor nutrition and other harmful environmental factors in utero and in early childhood have, on average, deleterious effects on both cognitive and physical development. Cognitive ability affects earnings later in life and thus is an omitted variable in the regression.

Suppose that the mechanism described above is correct. Explain how this leads to omitted variable bias in the OLS regression of Earnings on Height. Does the bias lead the estimated slope to be too large or too small? [Hint: Review Equation (6.1)]