SEEMINGLY UNRELATED REGRESSIONS MODEL
1. Equation systems
a. Types of equation systems
1. Seemingly unrelated equations system
2. Simultaneous equations system
3. Recursive equations system
4. Block recursive equations system
2. Introduction to SUR equations system
a. Two ways equations may be related
1. Error terms are related
2. Parameters are related
b. Example
3. Specification of the SUR model
a. Assumptions
1. Functional form is linear in parameters
2. Error term has mean zero
3. Errors are nonspherical and satisfy the following assumptions.
a. Each individual equation has constant error variance
b. Error variance may differ for different equations
c. Each individual equation has uncorrelated errors
d. Errors for different equations are contemporaneously correlated
4. Error term has a normal distribution
5. Error term in not correlated with explanatory variables
b. Variance-covariance matrix of errors
4. Estimation
a. Choice of estimator
1. Ordinary least squares (OLS) estimator
2. Generalized least squares (GLS) estimator
3. Feasible generalized least squares (FGLS) estimator
4. Iterated feasible generalized least squares (IFGLS) estimator
b. OLS estimator
1. OLS rule
2. OLS properties
c. GLS estimator
1. GLS rule
2. GLS properties
3. Shortcoming
d. FGLS estimator / Zellner’s SUR estimator
1. FGLS rule
2. Estimating the variance-covariance matrix of errors
a. Zellner’s method
3. FGLS properties
e. IFGLS estimator / Zellner’s iterated SUR (ISUR) estimator
1. IFGLS rule
2. IFGLS properties
3. Singular SUR models
f. Common properties of the SUR and ISUR estimators
a. SUR and ISUR collapse to OLS if errors not correlated
b. SUR and ISUR collapse to OLS if equations have identical data matrices
c. SUR and ISUR are more efficient than OLS if there are cross-equation restrictions
5. Specification testing
a. Breusch-Pagan test of independent errors
6. Hypothesis testing
a. Tests
1. Asymptotic t-test
2. Approximate F-test
3. Likelihood ratio test
4. Wald test
5. Lagrange multiplier test
b. Testing and/or imposing cross-equation restrictions
7. Goodness-of-fit
a. Individual R2 statistic
b. Generalized R2 statistic