Two-Stage Least Squares

Background

Two-Stage Least Squares (2SLS), also known as instrumental variable (IV) estimation, is an econometric technique used to address the issue of endogeneity in linear regression models. Endogeneity occurs when an explanatory variable is correlated with the error term, potentially leading to biased and inconsistent parameter estimates.

Historical Context

The development of 2SLS traces back to the early 20th century and was significantly advanced by econometricians such as Henri Theil in the late 1950s. The method gained prominence with the rising complexity of econometric models, where endogenous explanatory variables often posed challenges to ordinary least squares (OLS) estimation.

Definitions and Concepts

Two-Stage Least Squares involves two primary stages:

1. First Stage: The endogenous explanatory variables are regressed on instrumental variables using OLS. Instrumental variables are selected to be correlated with the endogenous explanatory variables but uncorrelated with the error term.

2. Second Stage: The original regression is estimated using OLS, substituting the endogenous explanatory variables with their fitted values obtained from the first stage.

Under suitable conditions, the 2SLS (or IV) estimator is considered consistent and efficient.

Major Analytical Frameworks

Classical Economics

Classical economists primarily focused on macroeconomic relationships and did not delve deeply into the specific methods like 2SLS. However, the notion of endogeneity and the need for consistent estimation resonate with classical principles of unbiased scientific inquiry.

Neoclassical Economics

Neoclassical economists, with their emphasis on microeconomic modeling and efficiency, have contributed to the development and refinement of econometric techniques, including 2SLS, to achieve consistent parameter estimation.

Keynesian Economics

Keynesian models, often dealing with aggregate economic variables and potential endogeneities, benefited from the introduction of 2SLS to better estimate relationships involving endogenous macroeconomic variables.

Marxian Economics

Marxian economics, although primarily historical and critical in nature, may utilize advanced econometric techniques like 2SLS to empirically test hypotheses related to capitalist dynamics and endogenous relationships in economic systems.

Institutional Economics

Institutional economists, focusing on the role of institutions and historical context in economic analysis, might use 2SLS to account for endogeneity when analyzing institutional impacts on economic development.

Behavioral Economics

Behavioral economists, studying how psychological factors affect economic decisions, might employ 2SLS to identify causality in the presence of endogeneity, for instance, between behavioral biases and economic outcomes.

Post-Keynesian Economics

Post-Keynesian economists, looking to address deficiencies of standard Keynesian models, often encounter endogeneity issues. The application of 2SLS assists in model specification and the identification of endogenous interactions.

Austrian Economics

Austrian economists emphasize methodological individualism and often critique econometric methods. However, when empirical analysis is needed, techniques like 2SLS can address issues of endogeneity within their complex individual-based models.

Development Economics

Development economists frequently deal with endogeneity in variables like foreign aid, investment, and institutional quality. The 2SLS method assists in deriving consistent estimations in such contexts.

Monetarism

Monetarists, who emphasize the role of money supply in the economy, may utilize 2SLS to overcome endogeneity in models analyzing the causal relationships between monetary variables and economic performance.

Comparative Analysis

The 2SLS method is a significant improvement over OLS in the context of endogeneity. Compared to single-equation models, 2SLS provides more reliable estimates by isolating the endogenous variables and dealing with potential biases.

Case Studies

1. Analyzing the effect of education on income where the education variable might be endogenous. By using instruments such as parental education, one can employ 2SLS for a more consistent estimation.
2. Investigating the impact of foreign aid on economic growth, addressing endogeneity issues by using historical or geopolitical instruments in the first stage to derive consistent results.

Suggested Books for Further Studies

• “Econometric Analysis” by William H. Greene
• “Introduction to Econometrics” by James H. Stock and Mark W. Watson
• “Econometric Methods” by Jack Johnston and John DiNardo

Related Terms with Definitions

• Ordinary Least Squares (OLS): A regression technique that estimates the relationship between dependent and independent variables by minimizing the sum of squared residuals.
• Endogeneity: A situation in economic modeling where an explanatory variable is correlated with the error term.
• Instrumental Variables (IV): Variables used in regression analysis to deal with endogeneity by being correlated with endogenous explanatory variables and uncorrelated with the error term.
• **Hausman