Heteroskedasticity

Abstract

One of the basic assumptions of the classical regression model

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

is that the variance of the regression disturbance ε_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.