Indirect Least Squares

Background

Indirect Least Squares (ILS) is a statistical technique primarily used within the field of econometrics to derive the structural parameters of a specific equation contained within a simultaneous equations model. This technique allows economists and statisticians to disentangle and estimate relationships among multiple endogenous variables when they jointly determine each other.

Historical Context

The method has roots going back to the evolution of econometric methods in the mid-20th century, as advancements in computational techniques necessitated more sophisticated tools for dealing with the intricacies of simultaneous interactions amongst economic variables. It extends the principles of ordinary least squares (OLS), tailored specifically for the challenges posed by multiple equations influencing each other.

Definitions and Concepts

Indirect Least Squares (ILS) involves the following key steps and concepts:

• Simultaneous Equations Model: A statistical model where multiple interdependent equations describe the causal relationships among endogenous variables.
• Reduced Form: The simplified set of equations expressing endogenous variables solely in terms of exogenous variables and error terms.
• Ordinary Least Squares (OLS): A method to estimate minimal squared differences between observed and predicted values in a regression model.
• Structural Parameters: Parameters that represent the theoretically established causal relationships between endogenous variables.

Major Analytical Frameworks

Classical Economics

Although primarily associated with the neoclassical school, classical economics paved the way for more formalized approaches to interactions and dynamics in economies.

Neoclassical Economics

In this paradigm, ILS allows us to estimate optimal parameter values for predicting economic behaviors more accurately when dealing with complex interdependencies.

Keynesian Economics

ILS is instrumental when modeling Keynesian systems characterized by multiple interacting aggregate demand and supply relationships.

Marxian Economics

Though less traditionally grounded in quantitative econometrics, structural modeling through techniques like ILS can quantify complex interrelated labor, capital, and production relationships.

Institutional Economics

Analyzing institutional behaviors often requires ILS due to various entities influencing each other in multiple dimensions concurrently.

Behavioral Economics

ILS could adjust for psychological and cognitive factors in models where multiple behavioral influences act simultaneously.

Post-Keynesian Economics

This school benefits from this method to understand dynamics where traditional macroeconomic relations coexist with financial and historical time processes.

Austrian Economics

Though skeptical of empirical analysis, Austrians’ models of spontaneous order and intertemporal subjectivity find indirect links within ILS akin frameworks.

Development Economics

ILS helps in capturing and reducing complexities in developmental variables interacting with each other in evolving economies.

Monetarism

ILS methodologies prove vital in fitting models where monetary policies and key economic indicators heavily interact dynamically.

Comparative Analysis

Comparing ILS with other methods such as Two-Stage Least Squares (2SLS) highlights its unique approach to solving complex econometric systems under certain identification conditions. While both approaches solve for structural parameters, ILS leverages the reduced form directly for estimation.

Case Studies

Case studies using ILS include econometric models of market equilibrium, where demand and supply constantly adjust influencing each other, and fiscal multipliers in macroeconomic planning.

Suggested Books for Further Studies

1. “Econometrics” by Fumio Hayashi
2. “Introduction to the Theory and Practice of Econometrics” by Judge, Griffiths, Hill, Lütkepohl, and Lee
3. “Econometric Analysis” by William H. Greene

Related Terms with Definitions

• Simultaneous Equations Model: A set of equations in which the endogenous variables are subject to simultaneous determination.
• Reduced Form: Representation of a model where each endogenous variable is expressed purely in terms of exogenous variables and errors.
• Ordinary Least Squares (OLS): A method for estimating linear regression models by minimizing the sum of squared residuals.
• Two-Stage Least Squares (2SLS): Another method for dealing with endogeneity in simultaneous equation models, using instrumental variables.

This entry on Indirect Least Squares provides a concise yet comprehensive exposé touching upon definitions, frameworks, comparative insight, and historical underpinnings, aimed at scholars, students, and professionals in economics and econometrics.