Collinearity

Background

Collinearity is a statistical phenomenon in regression analysis where one predictor variable in a model can be linearly predicted from the others with a substantial degree of accuracy. This occurrence leads to potential issues in the estimation of regression coefficients.

Historical Context

The recognition of collinearity traces back to the early development of regression analysis in statistics. As regression models became more complex, the need to understand the relationships between explanatory variables became evident. Collinearity and its more severe form, multicollinearity, were formally identified as key issues that could distort the analytical validity of regression models.

Definitions and Concepts

Collinearity: Collinearity often implies that two forecasted variables show a linear relationship. While simple collinearity refers to correlations among pairs of variables, multicollinearity extends this concept to encompass multiple variables and their interrelationships.

Multicollinearity: When collinearity involves more than two variables, it is termed as multicollinearity. It can make it difficult to ascertain the individual effect of a predictor variable in a regression model.

Major Analytical Frameworks

Classical Economics

In Classical Economics, collinearity might affect the simplicity of models taught by early economists. The idea is to keep independent variables sufficiently distinct.

Neoclassical Economics

Neoclassical models often employ multiple predictors, raising concerns of collinearity which economists aim to minimize through various statistical techniques.

Keynesian Economics

Keynesian models, dealing with multiple macroeconomic indicators, must often account for collinearity to maintain the precision of aggregate regression output.

Marxian Economics

Marxian economic analyses might account for collinearity in understanding the relationships between various economic variables, although it is not a primary focus.

Institutional Economics

In Institutional Economics, collinearity could arise when examining the role of various institutions and their interdependence would need to address for empirical model accuracy.

Behavioral Economics

Behavioral Economics, involving diverse predictors of human behavior, deals with collinearity to ensure that the impact of individual psychological factors is clear.

Post-Keynesian Economics

These models body’s addressing complex interrelationships within economic dynamics might face collinearity issues thus should adopt multicollinearity management strategies.

Austrian Economics

While many Austrian models aim for simplicity which reduces the risk of collinearity, it is crucial if multiple economic influencers are considered simultaneously.

Development Economics

Development economists are often analyzing data with numerous influencing factors where collinearity can complicate determining the influence of each variable on growth.

Monetarism

Monetarism that uses variables such as money supply, interest rates might experience multicollinearity which requires careful model specification to avoid misestimations.

Comparative Analysis

Collinearity must be managed across different economic theories and models, with each framework potentially employing distinct strategies to address it depending on the complexity of variable interrelationships inherent to their specific analyses.

Case Studies

Case studies often handle collinearity by using variance inflation factors (VIFs) to detect and mitigate it. For instance:

• Economic Growth Models: Examine how including multiple growth predictors might introduce collinearity.
• Macroeconomic Policy Analysis: Consider policies aimed at inflation that might be multicollinear with employment rates.

Suggested Books for Further Studies

• “Regression Analysis by Example” by Samprit Chatterjee and Ali S. Hadi
• “Applied Regression Analysis” by Norman R. Draper and Harry Smith
• “Principles of Econometrics” by R. Carter Hill, William E. Griffiths, and Guay C. Lim

Related Terms with Definitions

• Multicollinearity: The state of very high intercorrelations among the independent variables in a multiple regression model, often leading to unreliable statistical inferences.
• Variance Inflation Factor (VIF): A measure that quantifies the extent of multicollinearity in a set of multiple regression variables.
• Regression Coefficient: The value that represents the relationship between an independent variable and the dependent variable in regression analysis.