Quantile

Background

Quantiles are statistical measures that divide a data set into equal-sized, consecutive segments based on a given proportion or probability distribution. They are particularly useful in economic analysis for understanding the distribution, variability, and skewness of economic variables.

Historical Context

The use of quantiles dates back to the statistics field’s early developments, with formal concepts gaining detailed treatment in the 20th century. Economists and statisticians have employed quantiles to study income distribution, wealth, consumption patterns, and many other aspects vital for economic theory and policy-making.

Definitions and Concepts

Quantiles are points taken at regular intervals from the cumulative distribution function (CDF) of a random variable. For any number \( p \) between 0 and 1, the \( p \)-th population quantile is the number \( x \) that satisfies the equation \( P(X < x) = p \). In simpler terms, the percentage \( p \) of observations fall below this value \( x \), making it the inverse of the cumulative distribution function.

In a sample of size \( N \), the \( p \)-th quantile is the observation such that approximately \( Np \) of the observations are less than this observation, and \( N(1−p) \) of the observations are larger. Notably:

• The \( 0.5 \)-th quantile is the median.
• The \( 0.25 \) and \( 0.75 \)-th quantiles are the lower and upper quartiles, respectively.
• The interquartile range (IQR), defined as the difference between the upper and lower quartiles, is used as a measure of statistical dispersion.

Major Analytical Frameworks

Quantiles are pivotal in various schools of economic thought, each applying them for different analytical purposes:

Classical Economics

Classical economics primarily employed mean and median measures for simplifying economic behavior, using quantiles minimally.

Neoclassical Economics

Quantiles are used in consumer theory to analyze variations in consumer preferences, hedonic pricing, and game theory models.

Keynesian Economics

Keynesian analysis uses quantiles to study consumption, savings behavior, and wealth distribution, often relating them to overall economic stability.

Marxian Economics

Marxist economists might use quantiles to explore disparities in capital and income distribution, providing empirical support for critique of capitalist economies.

Institutional Economics

Quantiles help map institutional impact on income distribution, assessing how rules and policies skew economic well-being.

Behavioral Economics

Behavioral economists use quantiles to understand how psychological factors influence economic choices across different population segments.

Post-Keynesian Economics

Quantiles are applied to dissect income distribution and economic inequality, critical in post-Keynesian approaches that stress heterogeneity in economic agents.

Austrian Economics

Austrian economics, with its methodological individualism, finds limited but vital use of quantile data in exploring variable time preferences and production cycles.

Development Economics

Quantiles are instrumental in analyzing income distribution, poverty rates, and economic growth dynamics across developed and developing nations.

Monetarism

Used to understand inflation’s differential impact across quantiles of income and wealth, quantiles play a less prominent but insightful role.

Comparative Analysis

Economic schools vary greatly in how they interpret and apply quantile data. For instance, neoclassical models often assume normally distributed preferences, whereas Keynesian models might focus more on skewness in economic behavior.

Case Studies

1. Income Inequality and Welfare: Quantile analysis has been used to study the effectiveness of welfare policies by examining shifts in income distribution.
2. Housing Market Analysis: Real estate studies often use quantile regression to predict housing prices studying the distribution at different points.
3. Healthcare Access: Evaluation of healthcare services quality disparities across different economic quantiles within a population.

Suggested Books for Further Studies

1. “Quantile Regression” by Roger Koenker
2. “Statistics for Business and Economics” by Paul Newbold, William L. Carlson, and Betty Thorne
3. “The Distributional Effects of Economic Policy” by Don Fullerton and Diane Lim Rogers

Related Terms with Definitions

• Percentile: Refers to the value below which a given percentage of data falls.
• Median: The middle value separating the higher half from the lower half of a data sample or population.
• Quartile: The three points that divide data into four equal parts.
• Interquartile Range (IQR): The range between the first (25th percentile) and third (75th percentile) quartiles, measuring statistical dispersion.
• Cumulative Distribution Function (CDF): A function representing the probability that a random variable takes on a value equal to or less than a specific value.