# Heteroskedasticity

Reference work entry

First Online:

**DOI:**https://doi.org/10.1057/978-1-349-95189-5_1162

## Abstract

One of the basic assumptions of the classical regression modelis that the variance of the regression disturbance ε

$$ {Y}_i={\beta}_1+{\beta}_2{X}_{i2}+\cdots +{\beta}_k{X}_{iK}+{\varepsilon}_i\kern2em \left(i=1,2,\dots, n\right) $$

_{i}is constant for all observations, that is, that \( \mathrm{Var}\left({\upvarepsilon}_i\right)={\upsigma}^2 \) for all*i*. This feature of ε_{i}is known as*homoskedasticity*and its absence is called*heteroskedasticity*. The homoskedasticity assumption is quite reasonable for observations on aggregates over time, since the values are of a similar order of magnitude for all observations. It is, however, implausible with respect to observations on microeconomic units such as households or firms included in a survey, since there are likely to be substantial differences in magnitude of the observed values. For example, in the case of survey data on household income and consumption, we would expect less variation in consumption of low-income households, whose average level of consumption is low, than in consumption of high-income households, whose average level of consumption is high. Empirical evidence suggests that this expectation is in accord with actual behaviour. Heteroskedasticity also arises when the data are in the form of group averages and the groups are of unequal size.This is a preview of subscription content, log in to check access

### Bibliography

- Kmenta, J. 1986.
*Elements of econometrics*, 2nd ed. New York: Macmillan.Google Scholar - Prais, S.J., and H.S. Houthakker. 1955.
*The analysis of family budgets*. Cambridge: Cambridge University Press.Google Scholar - Stone, J.R.N. 1954.
*The measurements of consumers’ expenditure and behaviour in the United Kingdom, 1920–1938*, vol. I. Cambridge: Cambridge University Press.Google Scholar

## Copyright information

© Macmillan Publishers Ltd. 2018