Quantile Regression

Background

Quantile regression is a statistical technique employed in econometrics to estimate the quantiles (e.g., median, quartiles) of the conditional distribution of a dependent variable as functions of independent variables. Unlike ordinary least squares regression, which focuses on estimating the mean of the dependent variable given specific values of explanatory variables, quantile regression examines the conditional median or other quantiles of the response variable.

Historical Context

Quantile regression was first introduced by Roger Koenker and Gilbert Bassett in 1978. It extended the idea of regression to the estimation of various quantiles, thereby providing a more comprehensive view of the relationship between variables. This method is particularly useful for understanding the impact of explanatory variables on different points in the distribution of the dependent variable, which can be more informative than mean regression in cases with heteroscedasticity, skewed distributions, or outliers.

Definitions and Concepts

Quantiles: Points in a distribution that divide the data into equal-sized intervals. For example, the quartiles split the data into four quarters.
Conditional Distribution: The distribution of the dependent variable conditional upon certain values of the explanatory variables.
Dependent Variable: The outcome or variable being predicted or explained.
Explanatory Variables: The variables that are assumed to influence or predict the dependent variable.

Major Analytical Frameworks

Classical Economics

Classical economics focuses on long-term supply-side determinants of income. While quantile regression is not a traditional tool in classical economics, it can enrich classical analysis by providing insights on the distribution of outcomes.

Neoclassical Economics

Quantile regression aligns well with neoclassical models that analyze how differing levels of productivity, as driven by capital and labor inputs, impact economic outcomes. This method offers more detailed distributional insights than mean regression alone.

Keynesian Economics

In Keynesian economics, the focus is on aggregate demand and state intervention. Quantile regression could enhance understanding of how fiscal policies impact different segments of the economy—e.g., how changes in spending affect economic output across the distribution of income.

Marxian Economics

Marxian economics, with its emphasis on income distribution and labor dynamics, can benefit from quantile regression by better understanding wage distributions and the economic conditions of different social classes.

Institutional Economics

Quantile regression can help analyze the effect of institutional changes on various points in the distribution of economic outcomes, rather than just focusing on average effects.

Behavioral Economics

Understanding economic behavior often requires delving into how variables affect different parts of the distribution, not just central tendencies. Quantile regression can reveal how cognitive biases and heuristics play roles at various quantiles of the distribution.

Post-Keynesian Economics

This school focuses on income distribution, inequality, and uncertainty, making quantile regression particularly suitable for its analyses, offering more granular insights into income and consumption patterns.

Austrian Economics

Austrian economics can use quantile regression to study how individual decision-making impacts various points on the economic distribution spectrum, complementing the focus on marginal utility and individual actions.

Development Economics

Quantile regression is instrumental in evaluating policies in developing countries, providing insights into the distribution of income, education, and health outcomes across different quantiles rather than just average impacts.

Monetarism

Quantile regression can be used to analyze the distributional impacts of monetary policy, how changes in money supply affect different parts of the economic distribution, and whether monetary effects differ across sectors.

Comparative Analysis

Quantile regression is distinct from other regression methods that focus solely on the mean effect. It provides a richer, more nuanced understanding of the influence of explanatory variables across different points in the distribution of the dependent variable.

Case Studies

Income Distribution: Quantile regression can be used to assess how educational attainment affects income across various quantiles, not just the mean, offering insights on inequality.
Health Economics: It can analyze how different socio-economic factors impact various health outcomes, revealing how these factors may affect extreme outcomes differently.
Labor Market: Understanding the impact of training programs on wage levels at different quantiles can provide insight into their effect across the wage distribution.

Suggested Books for Further Studies

“Quantile Regression” by Roger Koenker (2005)
“Quantile Regression Analysis” by Lingxin Hao and Daniel Q. Naiman (2007)
“Quantitative Techniques for Competition and Antitrust Analysis” by Peter Davis and Eliana Garcés (2009), which includes applications of quantile regression in competition economics.

Regression Analysis: A set of statistical processes for estimating the relationships among variables.
**Heteroscedastic