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"The Estimation of Simultaneous Equation Models with Lagged
Endogenous Variables and
First Order Serially Correlated Errors," Econometrica,
May 1970, 507-516.
In this paper various methods for the estimation of simultaneous
equation models with lagged endogenous variables and first order
serially correlated errors are discussed. The methods differ in the
number of instrumental variables used. The asymptotic and small
sample properties of the various methods are compared, and the
variables which must be included as instruments to insure consistent
estimates are derived. A suggestion on how to estimate the
approximate covariance matrix of the estimators is made.
This paper discusses how the 2SLS estimator can be modified to handle
first order serial correlation of the error term. Much of the discussion
is concerned with the choice of first stage regressors when it is not
practical to use all predetermined variables as first stage regressors.
In 1968 I programmed this method into TSP under the name TSCORC, and it
has become widely used. I first used this method in my forecasting
model, 1971#5 (see in particular Chapter 2),
and it is still the main method
that I use in my macroeconometric modeling.
A good way of looking at the method is that it is a special case of the
nonlinear 2SLS estimator in Takeshi Amemiya, "The Nonlinear Two-Stage
Least Squares Estimator," Journal of Econometrics, 1974,
105-110. This is discussed in Section 6.3 in
1984#2. This framework can handle an
autoregressive structure of the error term of any order (not just first
The method is programmed into the Fair-Parke program. The order of the
autoregessive process of the error term is specified in the EQ command, and
estimation is done using the 2SLS command. For some issues regarding
the choice of first stage regressors, one should read the ALT2SLS
option of the SETUPEST command in the FP User's Guide.