The MODEL procedure provides parameter estimation, simulation, and forecasting of dynamic nonlinear simultaneous equation models. The MODEL procedure includes the following features:

• nonlinear regression analysis for systems of simultaneous equations, including weighted nonlinear regression

• full range of parameter estimation methods including the following:

  • nonlinear ordinary least squares (OLS)

  • nonlinear seemingly unrelated regression (SUR)

  • nonlinear two-stage least squares (2SLS)

  • nonlinear three-stage least squares (3SLS)

  • iterated SUR

  • iterated 3SLS

  • generalized method of moments (GMM)

  • nonlinear full-information maximum likelihood (FIML)

  • simulated method of moments (SMM)

• supports dynamic multi-equation nonlinear models of any size or complexity

• uses the full power of the SAS programming language for model definition, including left-hand-side expressions

• hypothesis tests of nonlinear functions of the parameter estimates

• linear and nonlinear restrictions of the parameter estimates

• bounds imposed on the parameter estimates

• computation of estimates and standard errors of nonlinear functions of the parameter estimates

• estimation and simulation of ordinary differential equations (ODE’s)

• vector autoregressive error processes and polynomial lag distributions easily specified for the nonlinear equations

• variance modeling (ARCH, GARCH, and others)

• computation of goal-seeking solutions of nonlinear systems to find input values needed to produce target outputs

• dynamic, static, or n-period-ahead-forecast simulation modes

• simultaneous solution or single equation solution modes

• Monte Carlo simulation using parameter estimate covariance and across-equation residuals covariance matrices or user-specified random functions

• a variety of diagnostic statistics including the following

  • model R-square statistics

  • general Durbin-Watson statistics and exact p-values

  • asymptotic standard errors and t tests

  • first-stage R-square statistics

  • covariance estimates

  • collinearity diagnostics

  • simulation goodness-of-fit statistics

  • Theil inequality coefficient decompositions

  • Theil relative change forecast error measures

  • heteroscedasticity tests

  • Godfrey test for serial correlation

  • Hausman specification test

  • Chow tests

• block structure and dependency structure analysis for the nonlinear system

• listing and cross-reference of fitted model

• automatic calculation of needed derivatives by using exact analytic formula

• efficient sparse matrix methods used for model solution; choice of other solution methods

Model definition, parameter estimation, simulation, and forecasting can be performed interactively in a single SAS session or models can also be stored in files and reused and combined in later runs.