The difference between a SUR model and a simultaneous equations model (SEM) is:
In a SUR model no lagged variables can enter as regressors, but they can in an SEM
In a SUR model the regressors in every equation must be strictly "predetermined"
None, if the errors are normally distributed
None, if the same regressors appear in every equation
If we have a SUR model in which identical regressors appear in every equation, then:
The OLS and GLS estimates of the parameters will be identical, but they will differ from the feasible GLS estimates
The OLS and feasible GLS estimates of the parameters will be identical, but they will differ from the GLS estimates because the covariance matrix for the errors will usually be unknown
The OLS, GLS and feasible GLS estimates of the parameters will be identical
None of the above
An "allocation model" is:
A SUR model in which the same dependent variable appears in every equation, but the regressors are different across equations
A SUR model in which the sum of the dependent variables across the equations equals one of the regressors, at every point in the sample
A SUR model in which the intercept coefficient is restricted to be the saem in every equation
A SUR model in which the sum of the dependent variables across the equations is some linear combination of the regressors, at every point in the sample
When estimating an SEM we must first check that every equation is "identified" because:
Otherwise, the FIML estimator will not be asymptotically efficient
Otherwise, no consistent estimator exists for the parameters in the model, and any estimates that we obtain will be meaningless
Otherwise, any estimates that we obtain for the parameters will be biased
Otherwise, the 2SLS estimator will no longer be a valid I.V. estimator
When estimating an SEM, one advantage of using a "system" estimator (such as FIML), as opposed to a "single equation" estimator (such as 2SLS), is:
If the model is properly specfied, a "system" estimator will be asymptotically more efficient than a "single equation" estimator
If the model is properly specfied, a "system" estimator will be consistent, whereas a "single equation" estimator may be inconsistent
We will be able to convert the estimates of the structural form parameters into consistent estimates of the restricted reduced form parameters more easily
If the model is properly specfied, a "system" estimator have smaller MSE in finite samples than a "single equation" estimator
A VAR model is effectively a special type of SUR model in which:
The explanatory variables in each equation are just lagged values of the dependent variable in that equations
The explanatory variables in each equation are either lagged values or future values of the dependent variables in all or some of the equations of the system
The explanatory variables in each equation are lagged values of the dependent variables in all or some of the equations in the system, except perhaps for some simple exogenous variables such as the intercept, a time-trend, etc.
The explanatory variables in each equation are values of the dependent variables in only the other equaitons of the system
The special form of a VAR model makes it particularly suitable for:
Forecasting future values of the dependent variables
Simulating the effects of "policy shocks"
Learning about the structural parameters in the economy
Both A and B
When we have a SUR model with (at least some) different regressors in the different equations:
The feasible GLS estimator, applied to the system as a whole, will generally be more efficient (asymptotically) than the OLS estimator applied equation-by-equation
The feasible GLS estimator, applied to the system as a whole, will generally be less biased (asymptotically) than the OLS estimator applied equation-by-equation
The feasible GLS estimator, applied to the system as a whole, will generally be more efficient in finite samples than the OLS estimator applied equation-by-equation
Full MLE will result in the smallest possible bias for the parameter estimates in finite samples
If we have a structural SEM, but all of the regressors in every equation are "predetermined", then:
The model is just a VAR model
We could get consistent estimates of the parameters by using OLS on each equation
The model is just a SUR model
Both B and C
When estimating a SUR model, an "unbalanced" sample is one where:
There are more regressors in some of the equations than in others
We have a full sample of observations for some of the variables in the system, but not for all of the variables
Some of the variables are measured in units that are much greater (or much smaller) than the units of measurement for the majority of the variables in the model
The number of equations is differnt from the number of dependent variables