Heteroscedasticity Problem - Econometric Modeling - Lecture Notes, Study notes of Econometrics and Mathematical Economics

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Module‐ 15: HETEROSCEDASTICITY PROBLEM

Lecture‐16: HETEROSCEDASTICITY PROBLEM

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1. MODULE OBJECTIVE

This module attempts to explore the possibilities of volatility of error variables.

The estimated model by the application of OLS, discussed earlier, is based on the assumption that error variance should be uniform over time/ cross sectional units. That is covariance between two errors variables should equal to a constant [i.e. Cov (Ui, Uj ) = 0 for i = j]. If this assumption is violated, then it is heteroskedasticity; otherwise, it is the situation of homoskedasticity (i.e. equal error variance).

In this module, we deal with the followings:

1. WHAT IS HETEROSKEDASTICITY AND HOW IS ITS NATURE?
2. WHAT ARE ITS CONSEQUENCES?
3. DOES IT REALLY A PROBLEM?
4. DETECTION CRITERIA
5. CAUSES OF HETEROSKEDASTICITY
6. REMEDIAL MEASURES

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DETECTION OF HETEROSCEDASTICITY

The detection of heteroskedasticity can be done only after the estimation process. So, first we should have estimated model and then we can have the error term. Once we get the error term, the process of detecting heteroskedasticity is feasible. The residuals in case of heteroskedasticity can be calculated by plotting them in the time sequence plot or alternatively we can plot the standardized residuals against time. Apart from these there are several quantitative tests that one can apply in order to supplement the pure qualitative approach. These are as follows:

PARK TEST GLESJER TEST SPEARMAN’S RANK CORRELATION TEST GOLDFELD QUANDT TEST BREUSCH PAGAN GODFREY TEST WHITE GENERAL TEST

Among them, Goldfeld- Quandt test and Spearman Rank Correlation is very popular. So, we briefly highlight these two tests here.

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GOLDFELD QUANDT TEST

In this method we do the following steps:  rank the observations from lowest value  Omit the central c observations and divide the rest of the observations in two halves  Find the RSS of the two sets of observations and RSS of the original model  Compute F-stat, which is as follows:

It can be further shown that the follows the F distribution and if it is significant, then there is presence of heteroskedasticity; otherwise there is no heteroskedasticity in the system.

Spearman Rank Correlation TEST

In this test, we first assign rank to error term and any of the variables and then find out the rank correlation. If the correlation coefficient is statistically significant then there is presence of heteroskedasticity; otherwise there is no heteroskedasticity in the system.

CAUSES OF HETEROSKEDASTICITY

 Error improvement model  Growth and trend factors  Misspecification of the random term  An over determined model  An under-determined model

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THE SAMPLE PROBLEMS

Increases in saving, over income, attract interest among the earnings people in the household.

The objective of the example is to find whether some factors affect saving of the society. From the literature, it is found that income and some other macroeconomic factors affect the household savings. So, the objective now is to find whether income and other macroeconomic determinants can affect the household saving. Specifically, we want to evaluate the following equation:

Household Saving =  1 +  2 * household income +  i * macroeconomic determinants (for i = 3, 4,…)

Let us target the  2 coefficients. If  2 is found to be statistically significant then, we can say that household income can affect the household savings; in the similar, way we can interpret for other macroeconomic determinants.

But for examining savings determinants, we expect there is heteroskedasticity problem; due to changes in various economic policies like monetary policy, fiscal policy, taxation policy, forex policy and so on.