EGTESTRESIDS Procedure

@EGTESTRESIDS performs an Engle-Granger residual-based cointegration test taking as input the residuals from a preliminary regression. @EGTEST is similar, but takes as input the endogenous variables and runs the preliminary regression.

@EGTESTRESIDS(options) u start end

Parameters

u	residuals from preliminary Engle-Granger regression (static regression of one endogenous variable on the others plus deterministics)
start, end	estimation range, by default, the range of u.

Options for Selecting Lags

LAGS=number of additional lags [0]

MAXLAGS=maximum number of additional lags to consider [number of observations^.25]

You can use either of these to select either the (maximum) number of additional lags. If you don't use either option, the LAGS default of 0 will be used for METHOD=INPUT and the MAXLAGS default will be used for the others.

METHOD=[INPUT]/AIC/BIC/HQ/TTEST/GTOS

METHOD=INPUT uses the input number of LAGS only. METHOD=AIC/BIC/HQ tests the D-F regressions for everything from 0 to LAGS/MAXLAGS and chooses the minimizer for the chosen criterion. METHOD=TTEST/GTOS starts with the full set of lags and deletes lags as long as the final one has a marginal significance level less than the cutoff given by the SIGNIF option. (GTOS is short for General-TO-Specific).

SIGNIF=cutoff significance level for METHOD=TTEST or GTOS[.10]

Other Options

NVAR=number of endogenous variables in the cointegrating regression, counting the dependent variable [2]

DET=NONE/[CONSTANT]/TREND

Choose what deterministic components were included in the original regression. This changes the critical values.

[PRINT]/NOPRINT

TITLE=Title for output ["Engle-Granger Cointegration Test"]

Variables Defined

%NOBS	number of regression observations + 1 (tables are based upon this) (INTEGER)
%CDSTAT	test statistic (REAL)
%NVAR	number of variables (INTEGER)
%%AUTOP	number of lags used (INTEGER)

Example

* Pindyck & Rubinfeld, Econometric Models and Economic Forecasts, 4th edition

* Example 16.5 from page 515

open data ex165.xls

calendar(q) 1960:1

data(format=xls,org=columns) 1960:1 1995:4 gcq gydq

* We first have to check that the series involved have a unit root. This

* checks that with a variety of choices for the number of lags.

@dfunit(lags=1) gcq

@dfunit(lags=2) gcq

@dfunit(lags=4) gcq

@dfunit(lags=1) gydq

@dfunit(lags=2) gydq

@dfunit(lags=4) gydq

linreg gcq

# constant gydq

@egtest

# gcq gydq

Sample Output

The first part of the output is from a linear regression of the first endogenous variable on all the others plus the chosen deterministic variables. The second is the test statistic generated from the first-stage residuals.

Linear Regression - Estimation by Least Squares

Dependent Variable GCQ

Quarterly Data From 1960:01 To 1995:04

Usable Observations 144

Degrees of Freedom 142

Centered R^2 0.9973657

R-Bar^2 0.9973472

Uncentered R^2 0.9997470

Mean of Dependent Variable 2899.6409692

Std Error of Dependent Variable 948.3894538

Standard Error of Estimate 48.8474061

Sum of Squared Residuals 338821.81013

Regression F(1,142) 53762.6779

Significance Level of F 0.0000000

Log Likelihood -763.2931

Durbin-Watson Statistic 0.3254

Variable Coeff Std Error T-Stat Signif

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

1. GYDQ 0.93461707 0.00403082 231.86780 0.00000000

2. Constant -89.93878564 13.52077674 -6.65189 0.00000000

Engle-Granger Cointegration Test

Null is no cointegration (residual has unit root)

Regression Run From 1960:02 to 1995:04

Observations 144

Using fixed lags 0

Constant in cointegrating vector

Critical Values from MacKinnon for 2 Variables

Test Statistic -3.61347*

1%(**) -3.97470

5%(*) -3.37957

10% -3.07473