One of the major assumptions of a classical linear regression model is that the disturbances occurring in the model should be homogeneous in nature. If this assumption is not fulfilled, then the researcher can say that heteroscedasticity is in the model.
Let us illustrate one example in order to describe heteroscedasticity. Let us consider an income saving model where the income of a person is the independent variable, and the savings made by the person is a dependent variable for heteroscedasticity. So, if the income of a person increases, then the savings will also simultaneously increase.
However, if heteroscedasticity is present in the data, then the graph for the savings of the person will remain constant when the income of the person will increase. This also states the major difference between heteroscedasticity and homoscedasticity. Heteroscedasticity results from the presence of outlier, which is nothing but an observation that is either small or large with respect to the other observations present in the sample.
Heteroscedasticity can occur if an important variable is omitted from the model. Suppose in the income saving model that one deletes the variable based on the income of the person. In this case, the researcher would not be able to interpret anything from the model. Heteroscedasticity can also occur due to the symmetrical or the assymeterical patterns of the regressors included in the model. Heteroscedasticity also arises due to incorrect data transformation, incorrect functional form (for example: comparing a linear model with a log linear model), etc.
It should be noted by the researcher that heteroscedasticity is more common in the case of cross sectional data than in time series data. If the researcher performs an ordinary least squares (OLS) method by taking heteroscedasticity into account, then the researcher will not be able to establish the confidence intervals and the tests of hypotheses. It is because of heteroscedasticity that the variance obtained will be less than the variance of the best linear unbiased estimator (BLUE). And due to this, the results obtained through the significant tests will be inaccurate due to heteroscedasticity.
A researcher can detect the presence of heteroscedasticity in the data because there are certain informal methods that illustrate the presence of heteroscedasticity.
Quite often, the nature of the case suggests that heteroscedasticity is likely to be involved. For example, in cross sectional data analysis, suppose a small, medium and large sized firm are sampled together. In this case, heteroscedasticity is usually expected.
There is a graphical method that can help the researcher to detect heteroscedasticity. If the researcher performs some regression analysis by assuming that there is no heteroscedasticity, then the estimated residuals will exhibit certain patterns that will indicate the presence of heteroscedasticity in the data.
There are, however, some informal tests to detect the presence of heteroscedasticity.
A formal test called Spearman’s rank correlation test is used by the researcher to detect the presence of heteroscedasticity.
This test can be used in the following way:
Suppose the researcher assumes a simple linear model (say) Yi = β0 + β1Xi + ui to detect heteroscedasticity. Then the researcher fits the model to the data by obtaining the absolute value of the residual and then ranking them in ascending or descending order to detect heteroscedasticity. After this, the researcher computes the spearman’s rank correlation for heteroscedasticity. Then, moving on to the heteroscedasticity detection process, the population rank correlation coefficient is assumed at 0, and the size of the sample is assumed to be greater than 8. A significance test is carried out to detect the heteroscedasticity. If the computed value of t is more than the tabulated value, then the researcher assumes that heteroscedasticity is present in the data. Otherwise heteroscedasticity is not present in the data.
