Omitted Variable Bias

Background§

Omitted Variable Bias (OVB) pertains to the domain of econometrics and statistical analysis, precisely in the context of linear regression models. It occurs when a relevant variable that influences both the dependent and included explanatory variables is left out from the model. This omission leads to a biased and inconsistent estimation of the model parameters.

Historical Context§

The concept of OVB has been pivotal in econometric studies dating back to the mid-20th century, as linear regression models became a fundamental tool in econometric analysis. Researchers recognized that failing to account for important variables could distort the conclusions drawn from econometric models, leading to fallacious interpretations and policy recommendations.

Definitions and Concepts§

Omitted Variable Bias: A bias of the ordinary least squares estimator of coefficients in a linear regression, arising from the omission of a relevant variable that is correlated with at least one of the included explanatory variables.

For example, consider the regression model:

$$y_i = \beta_0 + \beta_1 x_{1i} + u_i$$

If there exists another relevant variable $x_{2i}$ such that,

$$y_i = \beta_0 + \beta_1 x_{1i} + \beta_2 x_{2i} + u_i$$

but $x_{2i}$ is omitted, the estimated coefficient $\hat{\beta_1}$ will be biased if $x_{1i}$ and $x_{2i}$ are correlated.

Major Analytical Frameworks§

Classical Economics§

Classical economists did not extensively delve into the nuances of econometrics as modern practitioners do. However, they laid the groundwork for economic modeling that eventually necessitated accurate and unbiased parameter estimation.

Neoclassical Economics§

Neoclassical economists commonly use regression analysis to identify and predict economic relationships. The applicability of unbiased, consistent models is crucial to their analysis.

Keynesian Economics§

Efficiency in estimation processes enhances Keynesian macroeconomic models, particularly when explaining the relationships between aggregate demand, investment, and consumption.

Marxian Economics§

Though less prevalent in regression-based econometrics, recognizing bias in variable omission is critical in empirically validating Marxian models where inequality and other multifaceted variables are crucial.

Institutional Economics§

Institutional economists focus on various non-market variables. Their accurate estimation models often necessitate including significant factors to avoid OVB.

Behavioral Economics§

Behavioral approaches demand thoughtful consideration of numerous psychological and subjective variables. Ignoring these can introduce substantial biases.

Post-Keynesian Economics§

Important to Post-Keynesian analyses are interactions between multiple influencing factors. Models missing relevant variables can produce misleading results.

Austrian Economics§

While Austrian economists are typically skeptical of heavy reliance on econometrics, when applied, ensuring full variable inclusion is crucial.

Development Economics§

Analysts must control for numerous socioeconomic indicators. OVB in development metrics can vastly skew policy recommendations.

Monetarism§

Central to Monetarist views are precise econometric estimates regarding money supply and its macroeconomic effects, which are sensitive to omitted predictors.

Comparative Analysis§

In modern econometric practice, the prominence of machine learning and advanced computational techniques places a higher emphasis on the inclusion of relevant variables or the application of data-driven methodologies to mitigate OVB.

Case Studies§

Historical examples where OVB significantly impacted economic policy or academic conclusions can illuminate its practical implications.

Suggested Books for Further Studies§

• “Econometric Analysis” by William H. Greene
• “Basic Econometrics” by Damodar N. Gujarati and Dawn C. Porter
• “A Guide to Econometrics” by Peter Kennedy
• “Mostly Harmless Econometrics” by Joshua D. Angrist and Jörn-Steffen Pischke

Related Terms with Definitions§

• Endogeneity: Situations where explanatory variables correlate with the error term.
• Multicollinearity: A phenomenon where explanatory variables in a model are highly correlated.
• Heteroskedasticity: Instances where the variability of errors differs across values of independent variables.