Question

When estimating a multivariate model using OLS.

Discuss possible problems, such as multicollinearity, heteroscedasticity and simultaneous equation bias.

Answer 1

Ordinary least square or OLS is a type of linear least squares method for estimating the unknown parameters in a linear regression model. Now while estimating multivariate model , sometimes assumptions of ols get violated and so problems such as multicollinearity, heteroscedasticity ans simultaneous equation bias etc arises. Which has been discussed below.

Multicollinearity: Multicollinearity or inter correlation exists when atleast some of the predictor variables are correlated among themselves and a linear relationship or dependency is present between the predictors .

When correlation among regressors is low or no correlation at all, then OLS has information to estimate. But when this correlation is high , OLS has very little information to estimate the model.

Causes of multicollinearity:

i)Statisticsl model specification like adding polynomial terms or trained indicators may cause multicollinearity.

ii)Too many variables present as covariance can cause multi collinearity.

iii) There can be some errors in the data collection method used, which can lead to multicollinearity.

Heteroscedasticity: Heteroscedasticity is present when the error term differs across values of an independent variable. The problem of it is that here, we cannot estimate the model parameters by ols method.

We, know that , by definition of ols, it gives equal weights to all observation . But when heteroscedasticity is present , the observation with longer disturbances will have more weight than the other observation. The coefficient from OLS regression, where heteroscedasticity is present are therefore inefficient .

Simultaneous equation bias: When an OLS regression is used to estimate an individual equation that is actually part of a simultaneous system of equations, then this bias occurs. It is very common in social science applications because almost all variables are determined by complex interactions with each other. This can be resolved by using two stage least squares (2sls)