1. MULTIVARIATE REGRESSION MODELS
CHAPTER 21
MULTIVARIATE
REGRESSION MODELS
Damodar Gujarati
Econometrics by Example, second edition

2. MULTIVARIATE REGRESSION MODELS (MRMs)
MRM may be the appropriate method of estimation in situations where dependent variables are correlated.
Damodar Gujarati
Econometrics by Example, second edition

3. ADVANTAGES OF JOINT ESTIMATION
1. A better understanding of the topic under study.
2. Nominal and true levels of Type I error (probability of falsely rejecting the null hypothesis) may be different.
3. Separate estimation of each regression will neglect the correlation in error terms.
MRM methodology considers this correlation in estimating the between-equation covariances.
4. OLS regressions will neither produce multivariate results nor will they allow us to test coefficients across equations.
5. Taking into account intercorrelations across equations, we may be able to obtain more efficient estimates of the parameters.
Damodar Gujarati
Econometrics by Example, second edition

4. MRM ASSUMPTIONS
1. Each regression in the system is linear in the parameters.
2. The error variance in each regression is homoscedastic.
3. The error terms in each regression are uncorrelated.
4. However, the error terms in the two (or more) regressions may be correlated. This is called contemporaneous correlation:
5. The dependent variables in the system follow a multivariate normal distribution – that is, they are jointly normally distributed.
Damodar Gujarati
Econometrics by Example, second edition

5. Seemingly Unrelated Regression Equations (SURE):
SURE MODELS
Seemingly Unrelated Regression Equations (SURE):
In MRMs, the regressands are different, but the regressors are the same.
In SURE, the regressands are the same, but the regressors may be different.
If the regressors are the same, then there is no difference between the coefficients in OLS and SURE (only the standard errors).
Damodar Gujarati
Econometrics by Example, second edition

6. INDIVIDUAL VS. JOINT ESTIMATION
The SURE method may not be appropriate in all situations.
First, the number of equations in the system must be smaller than the number of observations per equation.
Second, if the error terms in the system of equations are uncorrelated, OLS may be more efficient than SURE.
Third, OLS and SURE will give identical estimates if the same regressors appear in each equation.
Damodar Gujarati
Econometrics by Example, second edition