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.