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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.
pdf file--200bpi (601KB), pdf file--300bpi (994KB).

Abstract

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.
Comments

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 order).

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.