**Econometric Modeling**

Typically, economic models are fitted using least-squares regression or maximum-likelihood estimation methods. Regression estimation methods relate one or more right-hand side (independent) variables to each left-hand side (dependent) variable.

If right-hand side variables are unavailable or unknown, then a time series method may be more appropriate. Simple time series methods fit the time series to its own past values. More complex time series methods can relate several time series to each other and also include right-hand side variables.

Some questions are still more complex, requiring combinations of regression and time series methods. These combinations include time series cross-sectional methods and transfer functions. Time series cross-sectional models are often designed to compare the behavior of several cross-sectional groups across time. Transfer functions enable you to incorporate the variability of the right-hand side variables into the forecasts of the dependent variable for more realistic forecasts. To fit a transfer function, you fit a time series model to the right-hand side variables in addition to fitting a regression model to the dependent variable.

After estimating your model, you may want to test and validate it with individual and joint parameter hypothesis tests.
Tests of the residuals may also assist in assessing the acceptability of your model. Additionally, some statistical tests
are designed for use with certain types of data and do not provide useful information with other types. For example, the
Durbin-Watson *d* statistic, used to test for correlation between time series residuals, does not provide useful
information with cross-sectional data.

You can also use goodness-of-fit statistics to evaluate competing models. As you explore models, you may learn more about the relationship among the variables, and that knowledge may assist you in fine-tuning the model.

You can use SAS/ETS software to estimate

- OLS regression models
- models with and without dummy variables
- models that are corrected for autocorrelation
- models that are corrected for heteroscedasticity
- regression models with lagged variables
- systems of linear equations
- nonlinear models
- systems of ordinary differential equations
- time series cross-sectional models

*ODS Diagnostic plots for a non-linear model estimated with PROC MODEL*

You can choose from a long list of available tests to judge any model at any point. This list includes

- heteroscedasticity tests
- autocorrelation tests
- normality tests
- unit root stationarity tests
- white noise tests
- linear hypotheses tests
- hypothesis tests for nonlinear parameter estimates
- Hausman's test
- Chow test
- fixed and random effects tests

**Simulation**

Simulation is an integral part of developing accurate models that capture the behavior of historical data. The first step in simulation is finding a suitable model of how the endogenous (dependent) variable changes as a function of one or more exogenous (independent) variables, where suitability is determined by one or more goodness-of-fit criteria. Once an appropriate model is found, it is used to simulate, or predict, values of the endogenous variable for specific values of the exogenous variables. By changing the values of the exogenous variables, you gain insight into how alternative situations affect the endogenous variable.

Simulation is important for *what-if* and *goal-seeking* analyses. What-if analysis involves simulating endogenous
variable values for different sets of exogenous variable values. Goal-seeking analysis involves determining the value of an
exogenous variable, given a desired value of the endogenous variable.

**Forecasting**

When you are satisfied that the model is realistic and reliable, it can be used to forecast the future. To forecast, you must generate values for the exogenous variables in the model that reflect your expectations about what is likely to occur. Forecasts are the expected values of the endogenous (dependent) variable determined by evaluating the model at new values of exogenous (independent) variables.

Forecasting can involve generating a point estimate and confidence limits for the most likely scenario of the future, or it can involve comparing forecasts generated by different expectations of the future.

The following procedures are used for econometrics and systems modeling: