Background
The Glejser test, introduced by Herbert Glejser, is used in econometrics to test for heteroscedasticity, a problem that occurs when the variance of errors in a regression model is not constant. Understanding whether the error variance changes with the level of independent variables is important for accurate statistical inference.
Historical Context
Heteroscedasticity has been a concern for econometricians because it violates classic regression assumptions, e.g., ordinary least squares (OLS) estimates may be inefficient, and standard errors may be biased, leading to invalid hypothesis tests. Although multiple tests exist to detect heteroscedasticity, the Glejser test gained traction due to its response to the specific case where the size of random error increases proportionally with changes in one or more exogenous variables.
Definitions and Concepts
The Glejser test examines the relationship between the absolute values of OLS residuals and one or more exogenous variables. Heteroscedasticity in the data is identified if these residual values consistently increase with the levels of the exogenous variables.
- Null Hypothesis (H0): The variance of errors is constant (homoscedasticity).
- Alternative Hypothesis (H1): The variance of errors varies (heteroscedasticity).
In mathematical terms, the test involves fitting a regression model of the form:
\[ |u_i| = \alpha + \beta \times Z_i + \epsilon \]
where \( |u_i| \) are the absolute OLS residuals from the main regression, and \( Z_i \) is one of the exogenous variables. If \( \beta \) is statistically significant, this suggests the presence of heteroscedasticity.
Major Analytical Frameworks
Classical Economics
Deals typically with general equilibrium models assuming homoscedastic error terms, unaffected by the findings of the Glejser test directly.
Neoclassical Economics
Assumes rational expectations and usually deals with homoscedastic assumptions in models, but methods to address heteroscedasticity, such as the Glejser test, are used to ensure robustness of econometric analysis.
Keynesian Economics
Glejser’s method can verify the assumptions of simpler models commonly used in Keynesian analysis where income and output equations are applied.
Marxian Economics
Empirical analyses in Marxian economics, which often concern inequality studies, may employ heteroscedasticity tests like the Glejser test to validate model assumptions.
Institutional Economics
The proper specification and validation of heteroscedasticity within models in institutional economics can help in understanding the variability within institutional impacts.
Behavioral Economics
Behavioral economists might use the Glejser test to check the rigour of their models when studying variability in human decision-making under different levels of stress or other exogenous factors.
Post-Keynesian Economics
These economists, who focus on explaining economic scenarios without classical assumptions of equilibriums, can incorporate the Glejser test to check variances in their regression models against real-world observables.
Austrian Economics
Austrian economics, emphasizing qualitative data, may however benefit during empirical econometrics by using robust heteroscedasticity checks where large sample data exist.
Development Economics
In analyzing cross-sectional or panel data in developing economies where high variability is common, the Glejser test provides an important check on data reliability.
Monetarism
Empirical verification of models in monetarism requires adjusted variance checks; hence Glejser tests could verify homoscedasticity in the monetary aggregates data models.
Comparative Analysis
Compared to other heteroscedasticity tests like the Breusch-Pagan test or White test, the Glejser test is simpler and particularly suited when the pattern of heteroscedasticity corresponds to one or more of the independent variables exerting systematic influence on error variance.
Case Studies
- Application in financial economics examining volatility and risk factors affecting residuals.
- Use in labor economics to check the dispersion of wage residuals relative to explanatory variables like education or experience.
Suggested Books for Further Studies
- “Econometric Analysis” by William H. Greene
- “Introductory Econometrics: A Modern Approach” by Jeffrey M. Wooldridge
- “A Guide to Econometrics” by Peter Kennedy
Related Terms with Definitions
- Homoscedasticity: Condition in a regression analysis where the variance of errors is constant.
- Heteroscedasticity: Condition where the variance of errors differs across observations.
- Residual: The difference between the observed value and the estimated value of the quantity of interest.