EXAMPLESIX.RPF

EXAMPLESIX.RPF is a Getting Started example of the use of a RATS format file, and estimation by Non-Linear Least Squares.

Full Program

open data ExampleSix.rat

calendar(q) 1950:1

data(format=rats) 1950:01 2000:04 realcons realdpi

* Set up the parameter set and the non-linear formula

nonlin a b g

frml cfrml realcons = a+b*realdpi^g

* Give guess values to a, b and g using the linear regression when g=1.

linreg realcons

# constant realdpi

compute a=%beta(1),b=%beta(2),g=1.0

* Estimate the model

nlls(frml=cfrml)

Output

Linear Regression - Estimation by Least Squares

Dependent Variable REALCONS

Quarterly Data From 1950:01 To 2000:04

Usable Observations 204

Degrees of Freedom 202

Centered R^2 0.9964481

R-Bar^2 0.9964306

Uncentered R^2 0.9993226

Mean of Dependent Variable 2999.4357843

Std Error of Dependent Variable 1459.7066917

Standard Error of Estimate 87.2098267

Sum of Squared Residuals 1536321.8808

Regression F(1,202) 56669.7234

Significance Level of F 0.0000000

Log Likelihood -1199.9952

Durbin-Watson Statistic 0.0920

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. Constant -80.35474883 14.30585151 -5.61691 0.00000006

2. REALDPI 0.92168567 0.00387175 238.05403 0.00000000

Nonlinear Least Squares - Estimation by Gauss-Newton

Convergence in 65 Iterations. Final criterion was 0.0000003 <= 0.0000100

Dependent Variable REALCONS

Quarterly Data From 1950:01 To 2000:04

Usable Observations 204

Degrees of Freedom 201

Centered R^2 0.9988339

R-Bar^2 0.9988223

Uncentered R^2 0.9997776

Mean of Dependent Variable 2999.4357843

Std Error of Dependent Variable 1459.7066917

Standard Error of Estimate 50.0945979

Sum of Squared Residuals 504403.21571

Regression F(2,201) 86081.2782

Significance Level of F 0.0000000

Log Likelihood -1086.3906

Durbin-Watson Statistic 0.2960

Variable Coeff Std Error T-Stat Signif

************************************************************************************

1. A 458.79905447 22.50138682 20.38981 0.00000000

2. B 0.10085209 0.01091037 9.24369 0.00000000

3. G 1.24482749 0.01205479 103.26415 0.00000000