White's Test

Background

White’s test is a statistical test named after Halbert White, used in regression analysis to detect heteroscedasticity. Heteroscedasticity refers to the circumstance in which the variance of errors differs across observations. When this condition is present, it signifies that the variability of variables is different rather than being constant, violating one of the key assumptions of the ordinary least squares (OLS) regression method.

Historical Context

Halbert White introduced this test in 1980 as an approach to ensure the accuracy and consistency of regression analysis. Before the advent of White’s test, methods to detect heteroscedasticity were less versatile and not as comprehensive in capturing the nuances of heteroscedasticity in complex models.

Definitions and Concepts

• Homoscedasticity: The situation in which the variance of residuals or errors is the same across all levels of the independent variables. White’s test aims to test the null hypothesis of homoscedasticity.
• Heteroscedasticity: The condition where the variance of residuals or errors varies across the levels of the independent variables.
• Ordinary Least Squares (OLS) Estimator: A method for estimating the parameters in a linear regression model, assuming homoscedasticity to make unbiased and consistent estimates.
• Covariance Matrix: In an OLS regression context, it refers to the matrix that contains the variances and covariances associated with the regression model’s parameter estimates.

Major Analytical Frameworks

Classical Economics

Classical economics, emphasizing broad principles of market efficiency and inherent economic order, does not specifically delve into empirical tests like White’s test.

Neoclassical Economics

White’s test fits within the broader framework of Neoclassical Economics, which relies heavily on statistical methods to test hypotheses and ensure that model assumptions hold because they directly impact economic inference and policy recommendations.

Keynesian Economics

Keynesian economics, focusing on fiscal and monetary policies’ implications, often employs regression analyses to test various economic theories. White’s test ensures the reliability of these analyses by testing for heteroscedasticity.

Marxian Economics

While Marxian Economics may not directly engage in OLS regression, White’s test is crucial for quantitative studies that might explore economic disparities and structures through regression models.

Institutional Economics

This approach emphasizes the role of institutions; regression models can provide insights into institutional performance. Thus, ensuring homoscedasticity via White’s test can improve the robustness of such models.

Behavioral Economics

Since this field integrates psychological insights into economic models, the accuracy of regression analysis plays a crucial role. White’s test becomes valuable in verifying the consistency of these models’ error terms.

Post-Keynesian Economics

Focused on real-world applicability and empirical relevance, post-Keynesian approaches require robust statistical methods, with White’s test serving as a critical instrument for ensuring correct variance assumptions in regressions.

Austrian Economics

Though less focused on empirical analysis and more on logical deductive methods, any quantitative model within Austrian Economics would benefit from White’s test to ensure reliability.

Development Economics

Regression models are key in developing economies for policy formulation and effectiveness measurement. White’s test helps to preserve the accuracy of such models, addressing heteroscedasticity which is common in real-world data prevalent in development studies.

Monetarism

Monetarists rely on empirical evidence to bolster theories on managing and predicting economic cycles. White’s test aids in verifying the reliability of these empirical models.

Comparative Analysis

White’s test stands as one of the universal tools in the econometric toolkit, providing a safeguard for empirical models used across many different economic theories against the variance instability of residuals.

Case Studies

Studies range from microeconomic models dealing with individual behavior to large macroeconomic models assessing national policies. For instance, using the test on household income data ensures that variance consistency assumptions are rightly verified for policy implications pertaining to income distribution.

Suggested Books for Further Studies

1. “Econometric Analysis” by William H. Greene.
2. “Introductory Econometrics: A Modern Approach” by Jeffrey M. Wooldridge.
3. “Principles of Econometrics” by R. Carter Hill, William E Griffiths, and Guay C. Lim.

Related Terms with Definitions

• Homoscedasticity: Equal variances of error terms among all levels of an independent variable in regression analysis.
• Heteroscedasticity: Variances of error terms differ among different levels of an independent variable in regression analysis.
• Ordinary Least Squares (OLS): A method for estimating the parameters in a linear regression, meant to minimize the sum of