Multiple Regression

Background§

Multiple regression is a statistical technique that assesses the relationship between a dependent variable and several independent variables. It allows for the understanding and quantification of how multiple factors simultaneously impact the dependent variable.

Historical Context§

The concept of multiple regression has its roots in the early 20th century, evolving as a part of the broader development of regression analysis and statistical methods in economics and other social sciences.

Definitions and Concepts§

Multiple regression can be formally defined as a regression analysis with two or more explanatory variables. The multiple linear regression equation takes the form:

$$y = β_0 + β_1x_1 + β_2x_2 + … + β_Kx_K + ε$$

Here:

• $y$ is the dependent variable.
• $x_1, x_2, …, x_K$ are the independent (explanatory) variables.
• $β_0, β_1, β_2, …, β_K$ are the coefficients for each independent variable.
• $ε$ is the error term.

Major Analytical Frameworks§

Classical Economics§

In classical economics, multiple regression analysis may be employed to test and quantify theories about how various factors influence economic outcomes.

Neoclassical Economics§

Neoclassical economics often utilizes multiple regression to understand the relationships between variables such as consumption, income, and production factors.

Keynesian Economics§

Keynesian models may use multiple regression to explore relationships such as those between government spending, economic output, and inflation.

Marxian Economics§

While less common, multiple regression could be applied in Marxian analyses to examine how different aspects of capital impact labor dynamics and economic structures.

Institutional Economics§

Institutional economists may use multiple regression to study how institutions, rules, and regulations impact economic behavior and outcomes.

Behavioral Economics§

Behavioral economists employ multiple regression to analyze how psychological and cognitive factors influence economic decisions alongside more traditional economic variables.

Post-Keynesian Economics§

Post-Keynesian theorists might use multiple regression to delve into complex relationships between macroeconomic factors and economic policies.

Austrian Economics§

Austrian economists typically favor qualitative over quantitative analysis, but multiple regression might still be used to empirically test certain hypotheses or theories.

Development Economics§

Development economists use multiple regression extensively to understand how variables like education, health, infrastructure, and policy interventions influence economic development.

Monetarism§

Monetarists may use multiple regression to study the relationship between money supply, inflation, and interest rates, and how these impact economic variables.

Comparative Analysis§

Multiple regression stands out for its ability to account for the simultaneous effects of multiple variables, offering a more comprehensive analysis than simple regression methods. It is widely adopted across various economic theories to empirically validate hypotheses and theories.

Case Studies§

Several economic studies employ multiple regression to disentangle complex relationships in areas such as labor economics, financial economics, health economics, and public economics. Case studies often reveal the nuanced interdependence between multiple variables that straightforward analysis might miss.

Suggested Books for Further Studies§

1. “Introductory Econometrics: A Modern Approach” by Jeffrey M. Wooldridge
2. “Econometric Analysis” by William H. Greene
3. “The Regression Problem: Geometry & Analysis” by Dale J. Nelson

Related Terms with Definitions§

• Simple Regression: Regression analysis with a single explanatory variable.
• Independent Variable (Explanatory Variable): A variable that is believed to influence or predict the outcome of another variable.
• Dependent Variable (Response Variable): The outcome variable whose variation is being studied.
• Coefficient: A numerical value indicating the strength and direction of the relationship between variables in regression analysis.