@REGCRITS is a post-processor for an estimation instruction which computes and (optionally) displays various information criteria. It has no parameters, as it just picks the information off from the accessible variables.

 

This should be used immediately after any estimation instruction which computes a log likelihood such as LINREG, NLLS, BOXJENK, GARCH, ESTIMATE or MAXIMIZE. However, it can't be applied if you estimated LINREG or NLLS with the INSTRUMENTS option, since instrumental variables/GMM isn't likelihood-based. This uses the value of %LOGL defined by the preceding estimation instruction, and (by default), uses the values of %NOBS for the number of observations and %NFREE for the number of free parameters. Note that %NFREE counts things like the regression variance. The IC's for regression equations usually don't include that (counting only the regressors), because it doesn't matter in comparing two regression equations. It does matter in comparing (say) a regression equation to a GARCH model as the GARCH model explicitly includes parameters for estimating the variance, while the regression concentrates the variance out, but still actually estimates it.

 

It computes the (standardized forms of the) Akaike Information Criterion, Schwarz Bayesian Criterion, Hannan-Quinn, and FPE. See Information Criteria for details. Their values will look fairly similar. Of course, the key to their use is the comparison across models of a particular criterion. Although these use standardized forms of the criteria and so don't have a strong sensitivity of the number of observations used, it's still considered to be correct procedure to make sure that the competing estimates are done with the same data range.

 

@REGCRITS( options )    (no parameters)

Options

T=number of observations [%NOBS]

K=number of freely estimated parameters [%NFREE]

 

[PRINT]/NOPRINT

TITLE="title for report"  ["Information Criteria"]

Variables Defined

Example

*

* Verbeek, A Guide to Modern Econometrics, 4th edition

* Illustration 8.8 from pp 311-314

*

open data inflation_extended.txt

calendar(q) 1951:2

data(format=prn,org=columns) 1951:2 2010:04 infl_sa_new

set infl = infl_sa_new

*

* While the data actually start in 1951Q2, all the analysis is set to

* start at 1960Q1.

*

graph(footer="Figure 8.7 Quarterly inflation in the United States, 1960-2010")

# infl 1960:1 *

*

@dfunit(lags=2) infl 1960:1 *

@dfunit(lags=4) infl 1960:1 *

*

* Do KPSS test with up to 12 lags in Newey-West window

*

@kpss(lmax=12) infl 1960:1 *

*

* Do the sample autocorrelations and partial autocorrelations of the

* series.

*

@bjident infl 1960:1 *

*

* In order for the information criteria to be comparable, the estimates

* need to be done over a common range. That's possible here because we

* are fixing the start at 1960:1 even though we have data for many

* years earlier than that.

*

boxjenk(const,ar=3) infl 1960:1 *

@regcrits(title="AR(3) model")

boxjenk(const,ar=4) infl 1960:1 *

@regcrits(title="AR(4) model")

boxjenk(const,ar=3,ma=1) infl 1960:1 *

@regcrits(title="ARMA(3,1) model")

boxjenk(const,ar=6) infl 1960:1 *

@regcrits(title="AR(6) model")

boxjenk(const,ar=||1,2,3,6||) infl 1960:1 *

@regcrits(title="AR(6) with lags 4,5 omitted")

 

Sample Output

This is the output from the first of the Box-Jenkins instructions from above, followed by the output from the @REGCRITS that follows it. We've also included the @REGCRITS output from a larger AR(6) model. Since you want to minimize the chosen criterion, all the criteria favor of the smaller AR(3), though it's a close call if you're using AIC or FPE.

 

Box-Jenkins - Estimation by LS Gauss-Newton

Convergence in     3 Iterations. Final criterion was  0.0000000 <=  0.0000100

Dependent Variable INFL

Quarterly Data From 1960:01 To 2010:04

Usable Observations                       204

Degrees of Freedom                        200

Centered R^2                        0.4947772

R-Bar^2                             0.4871989

Uncentered R^2                      0.7930760

Mean of Dependent Variable       3.9528686302

Std Error of Dependent Variable  3.3003435126

Standard Error of Estimate       2.3633803711

Sum of Squared Residuals         1117.1133557

Regression F(3,200)                   65.2883

Significance Level of F             0.0000000

Log Likelihood                      -462.9026

Durbin-Watson Statistic                1.9651

Q(36-3)                               47.3534

Significance Level of Q             0.0504660

 

    Variable                        Coeff      Std Error      T-Stat      Signif

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

1.  CONSTANT                     3.9892902356 0.9175027739      4.34799  0.00002187

2.  AR{1}                        0.2919680365 0.0678154845      4.30533  0.00002610

3.  AR{2}                        0.2273418840 0.0689302756      3.29814  0.00115192

4.  AR{3}                        0.3003124483 0.0688887684      4.35938  0.00002085

 

AR(3) model

AIC          4.587

SBC          4.669

Hannan-Quinn 4.620

(log) FPE    4.587

 

AR(6) model

AIC          4.588

SBC          4.718

Hannan-Quinn 4.640

(log) FPE    4.588

 

Copyright © 2025 Thomas A. Doan