Chapter 3 : Violation of Classical Assumptions of Regression Model
The simplest econometric model is the ordinary least square model (OLS). This model
minimizes the sum of squared errors (deviation between actual values and estimated values of
the dependent variable). The classical linear regression model (CLRM) is built upon some
important assumptions.
By relaxing these assumptions of CLRM, we are confronted with some econometric problems.
Major econometric problems arises when we relax these assumptions of CLRM are;
1. Hetroscedasticity
2. Autocorrelation and
3. Multicollinearity
Hetroscedasticity
The classical linear regression model is that the disturbances ui appearing in the population
regression function are homoscedastic; that is, they all have the same variance or equal spread.
Symbolically ;
E ( Ui2) = σ2
The violation of this homoscedastic property is known as hetroscedasticity. That is, when the
conditional variance of the Y population varies with X, this situation is known appropriately
as Hetroscedasticity or unequal spread or variance. Symbolically it can be represented as
E ( Ui2) = σi2
Eg: when analysing family spending pattern, we find that there is greater variation in
expenditure on certain commodity group among high income families than low ones due to
greater discretion allowed by higher income.
Causes / Reasons for Hetroscedasticity
Various reasons for the origin of Hetroscedasticity are;
1. In an error learning model, as people learn, their error of behaviour become smaller
over time.Eg: As income grows, people have more discretionary income & hence more
scope for choice about the disposition of their income.
2. Hetroscedasticity is more likely to exist when data set have large number of
observation.
, 3. As data collecting techniques increases, variance is likely to decrease.
4. It can also arise as a result of the presence of collinear relationship among variable.
5. If there is skewness in the distribution of one or more regressors included in the model,
there is chances of hetroscedasticity.
6. Use of Incorrect data transformation.
7. Use of Incorrect functional form.
Consequences of Heteroscedasticity
Under CLRM, these OLS estimators are BLUE. Now with the presence of Heteroscedasticity,
the consequences are
1. OLS estimators are still linear
2. OLS estimators are still unbiased
3. But they no longer have minimum variance. That is, they are no longer efficient. In short,
OLS estimators are no longer BLUE in small as well as in large samples.
4. The bias arises from the fact that the conventional estimator of true o² is no longer and
unbiased estimator of oi²
5. As a result the usual confidence intervals and hypothesis tests based on t and F distributions
are unreliable. If conventional testing procedures are employed there is a possibility of drawing
wrong conclusions.
In short, in the presence of Hetroscedasticity OLS estimators are no longer BLUE. So we rely
on other methods like Generalized Least Square (GLS) for estimation. Similarly, ordinary
testing of hypothesis is not reliable raising the possibility of drawing wrong conclusions.
Therefore it is essential to detect and solve the problem of Heteroscedasticity before estimation.
Detection measures of Hetroscedasticity ( Methods to identify the presence of
hetroscedasticity)
It is noted that there are no hard and fast rules for detecting Heteroscedasticity and we have
only a few rules of thumb. But this situation is inevitable because oi² can be known only if we
have the entire Y population corresponding to the chosen X's. But such data is a rare case in
most economic investigations. Therefore in most cases, involving economic investigations
Heteroscedasticity may be a matter of intuition,
Let us examine some of the informal and formal methods of detecting Heteroscedasticity.
Informal Methods
1. Nature of Problem: -
Very often nature of the problem under consideration suggests whether Heteroscedasticity is
likely to be encountered. Based on the past studies, one can analyse the nature of
hetroscedasticity in the surveys. Now one generally assumes that in slllmilar surveys one can
expect unequal variances among the disturbances.
2. Graphical Method:
The simplest econometric model is the ordinary least square model (OLS). This model
minimizes the sum of squared errors (deviation between actual values and estimated values of
the dependent variable). The classical linear regression model (CLRM) is built upon some
important assumptions.
By relaxing these assumptions of CLRM, we are confronted with some econometric problems.
Major econometric problems arises when we relax these assumptions of CLRM are;
1. Hetroscedasticity
2. Autocorrelation and
3. Multicollinearity
Hetroscedasticity
The classical linear regression model is that the disturbances ui appearing in the population
regression function are homoscedastic; that is, they all have the same variance or equal spread.
Symbolically ;
E ( Ui2) = σ2
The violation of this homoscedastic property is known as hetroscedasticity. That is, when the
conditional variance of the Y population varies with X, this situation is known appropriately
as Hetroscedasticity or unequal spread or variance. Symbolically it can be represented as
E ( Ui2) = σi2
Eg: when analysing family spending pattern, we find that there is greater variation in
expenditure on certain commodity group among high income families than low ones due to
greater discretion allowed by higher income.
Causes / Reasons for Hetroscedasticity
Various reasons for the origin of Hetroscedasticity are;
1. In an error learning model, as people learn, their error of behaviour become smaller
over time.Eg: As income grows, people have more discretionary income & hence more
scope for choice about the disposition of their income.
2. Hetroscedasticity is more likely to exist when data set have large number of
observation.
, 3. As data collecting techniques increases, variance is likely to decrease.
4. It can also arise as a result of the presence of collinear relationship among variable.
5. If there is skewness in the distribution of one or more regressors included in the model,
there is chances of hetroscedasticity.
6. Use of Incorrect data transformation.
7. Use of Incorrect functional form.
Consequences of Heteroscedasticity
Under CLRM, these OLS estimators are BLUE. Now with the presence of Heteroscedasticity,
the consequences are
1. OLS estimators are still linear
2. OLS estimators are still unbiased
3. But they no longer have minimum variance. That is, they are no longer efficient. In short,
OLS estimators are no longer BLUE in small as well as in large samples.
4. The bias arises from the fact that the conventional estimator of true o² is no longer and
unbiased estimator of oi²
5. As a result the usual confidence intervals and hypothesis tests based on t and F distributions
are unreliable. If conventional testing procedures are employed there is a possibility of drawing
wrong conclusions.
In short, in the presence of Hetroscedasticity OLS estimators are no longer BLUE. So we rely
on other methods like Generalized Least Square (GLS) for estimation. Similarly, ordinary
testing of hypothesis is not reliable raising the possibility of drawing wrong conclusions.
Therefore it is essential to detect and solve the problem of Heteroscedasticity before estimation.
Detection measures of Hetroscedasticity ( Methods to identify the presence of
hetroscedasticity)
It is noted that there are no hard and fast rules for detecting Heteroscedasticity and we have
only a few rules of thumb. But this situation is inevitable because oi² can be known only if we
have the entire Y population corresponding to the chosen X's. But such data is a rare case in
most economic investigations. Therefore in most cases, involving economic investigations
Heteroscedasticity may be a matter of intuition,
Let us examine some of the informal and formal methods of detecting Heteroscedasticity.
Informal Methods
1. Nature of Problem: -
Very often nature of the problem under consideration suggests whether Heteroscedasticity is
likely to be encountered. Based on the past studies, one can analyse the nature of
hetroscedasticity in the surveys. Now one generally assumes that in slllmilar surveys one can
expect unequal variances among the disturbances.
2. Graphical Method:
