Using Eviews to construct an ARDL Bound Test

1. These criteria are suggested for author to select the optimum lag in the ARDL modeling, namely

1. Akaike Information Criterion 2. Schwarz Bayesian Criterion 3. General to specific model

For Example: Our regression model RPCC = f(RGDPC, UN, WAGE, TAX, LL)

(See the file poverty and fd) and the selected optimum lag length is (1, 1, 0, 0, 0, 0)

ARDL Model Equation (1):

itr

i

tit

q

i

tit

p

i

t UNRGDPCRPCCconstRPCC0

,3

0

,2

1

,1

ttit

v

i

tit

u

i

tit

s

i

t DUMLLTAXWAGE

,70

,6

0

,5

0

,4

where

RPCC = real Consumption Per capita

Const = constant

RGDPC = real GDP Per capita

UN = unemployment

WAGE = Wages

TAX = Individual Tax

LL = Liquid Liability

DUM = 1 for crisis and 0 for otherwise; the crisis is refer to the Malaysian

oil crisis at 1973, 1974, 1980 and 1981; commodities crisis at 1985 to 1986;

and 1997/98 for Asian financial Crisis.

p, q, r, s, u, v = optimum lag length uses in model

t = residual

Such based on the AIC or SBC criteria, the selected lag length for this model (p, q,

r, s, u, v) is (1, 1, 0, 0, 0, 0). This can use Microfit or Rats programming code to

obtain the optimum lag base on such listed criteria.

2. After selected lag length, using Eviews to estimate the Long-run OLS. The Eviews output is showed as following:

Dependent Variable: RPCC

Method: Least Squares

Date: 06/28/09 Time: 21:23

Sample (adjusted): 1971 2004

Included observations: 34 after adjustments Variable Coefficient Std. Error t-Statistic Prob. C 1.380580 1.142938 1.207922 0.2384

RPCC(-1) 0.688508 0.175616 3.920539 0.0006

RGDPC 0.981537 0.179936 5.454926 0.0000

RGDPC(-1) -0.866497 0.237380 -3.650252 0.0012

UN 0.010227 0.036818 0.277762 0.7835

WAGE -0.019567 0.047700 -0.410202 0.6852

TAX 0.071253 0.047672 1.494647 0.1475

LL -0.095664 0.036619 -2.612439 0.0150

DUM 0.015761 0.016593 0.949891 0.3513 R-squared 0.992724 Mean dependent var 7.949910

Adjusted R-squared 0.990396 S.D. dependent var 0.307982

S.E. of regression 0.030182 Akaike info criterion -3.941225

Sum squared resid 0.022774 Schwarz criterion -3.537189

Log likelihood 76.00083 Hannan-Quinn criter. -3.803437

F-statistic 426.3952 Durbin-Watson stat 1.789455

Prob(F-statistic) 0.000000

3. After the estimate ARDL model, we have using the Wald Test to compute the long run elasticities and it standard error.

According to Pesaran et al. (2001) the Long run elasticities should compute as

follow:

p

i

t

q

i

t

RGDPCforesElasticiti

,1

,2

1

__

= Sum of the independent coefficients (RGDPC)

1 Sum of the dependent coefficients

The coefficient for the

variables in the Eviews

output is shows as:

c(1)

c(2)

c(3)

c(4)

c(5)

c(6)

c(7)

c(8)

c(9)

4. Go to View Coefficient Test Wald Test

Eviews Output:

Wald Test:

Equation: Untitled Test Statistic Value df Probability F-statistic 0.507750 (1, 25) 0.4827

Chi-square 0.507750 1 0.4761

Null Hypothesis Summary: Normalized Restriction (= 0) Value Std. Err. (C(3) + C(4)) / (1 - C(2)) 0.369318 0.518293

Delta method computed using analytic derivatives.

For others variables elasticities are showed as: constant (4.4322), RGDPC (0.36932), UN

(0.032831), WAGE (-0.062815), TAX (0.22875), LL (-0.30712), DUM (0.050599).

Type in the code:

(c(3)+c(4))/(1-c(2))=0

In the Wald Test

windows

The value of elasticities

is shows as 0.369318.

The standard error is

0.518293. However, the

t-statistic need compute

by the user, where t-stat

= coefficient / std. Err.

The probability 0.4827

also represent as p-

value for the computed

elasticities.

5. After computed the all long-run elasticities, we need proceed into short-run Error correction Model.

a. Firstly, compute the values of Error Correction Term (ECT). Based on the knowledge the ECT is represent as a long-run steady point for the model or

more statistically the ECT is a residual from long-run cointegration model.

Long-run Cointegration Model (Equation 2):

tp

i

t

s

i

t

tp

i

t

r

i

t

tp

i

t

q

i

t

p

i

t

t WAGEUNRGDPCconst

RPCC

1

,1

0

,4

1

,1

0

,3

1

,1

0

,2

,1 1111

tp

i

t

tp

i

t

v

i

t

tp

i

t

u

i

t

ECTDUMLLTAX

1

,1

7

1

,1

0

,6

1

,1

0

,5

111

(2)

After some mathematical adjustment, the Error correction term equation is shows

as:

tp

i

t

s

i

t

tp

i

t

r

i

t

tp

i

t

q

i

t

t WAGEUNRGDPCRPCCECT

1

,1

0

,4

1

,1

0

,3

1

,1

0

,2

111

tp

i

t

v

i

t

tp

i

t

u

i

t

LLTAX

1

,1

0

,6

1

,1

0

,5

11

(3)

Therefore, based on the previous example model and using the calculated

elasticities, the Long-run Cointegrated Model is shows as following:

RPCC = 4.4322 + 0.36932 RGDPC + 0.032831 UN 0.062815 WAGE +

0.22875 TAX 0.30712 LL + 0.050599 DUM

Hence, the ECT equation shows as:

ECT = RPCC 0.36932*RGDPC 0.032831*UN + 0.062815*WAGE

0.22875*TAX + 0.30712*LL

So, generate this ECT equation in the Eviews before the Short-run dynamic model.

b. Type in the ECT equation on the upper blank box of Eviews and then Enter.

6. After generated the ECT series, now we have go to Quick Estimate Equation

choose the method TSLS.

Type in this equation on the top

blank box:

ECT = RPCC 0.36932*RGDPC

0.032831*UN + 0.062815*WAGE

0.22875*TAX + 0.30712*LL

Furthermore, press the Enter and

the ECT will shows in the workfile

windows.

7. Now the Eviews shows you two boxes, one is for Equation specification and other

one is for instrument list.

a. The Equation Specification is refer to the Short-run dynamic model, which is:

itq

i

tit

p

i

ttt RGDPCRPCCECTconstRPCC1

0

,2

1

1

,11

itu

i

tit

s

i

tit

r

i

t TAXWAGEUN1

0

,5

1

0

,4

1

0

,3

ttit

v

i

t DUMLL

,71

0

,6

For our Example:

The Equation Specification code is follows:

D(RPCC) C ECT(-1) D(RGDPC) D(UN) D(WAGE)

D(TAX) D(LL) DUM

b. The instrument list refers to the endogenous for ECT models. For our Example,

the Eviews code to represent the exogenous variables for our ECT model is:

C RPCC(-1) RGDPC RGDPC(-1) UN WAGE TAX

LL

Type in this equation on the

Equation Specification box:

D(RPCC) C ECT(-1)

D(RGDPC) D(UN) D(WAGE)

D(TAX) D(LL) DUM

Furthermore, type in the

instrument list:

C RPCC(-1) RGDPC

RGDPC(-1) UN WAGE TAX

LL

After that click Options and tick that Heteroskedasticity consistent coefficient

covariance and Newey-West and then click ok.

8. After that you should get the Short-run dynamic results as follows:

Dependent Variable: D(RPCC)

Method: Two-Stage Least Squares

Date: 06/29/09 Time: 10:19

Sample (adjusted): 1971 2004

Included observations: 34 after adjustments

Newey-West HAC Standard Errors & Covariance (lag truncation=3)

Instrument list: C RPCC(-1) RGDPC RGDPC(-1) UN WAGE TAX LL Variable Coefficient Std. Error t-Statistic Prob. C 1.380587 1.160771 1.189371 0.2450

ECT(-1) -0.311494 0.259603 -1.199883 0.2410

D(RGDPC) 0.981566 0.410089 2.393546 0.0242

D(UN) 0.010237 0.146174 0.070031 0.9447

D(WAGE) -0.019561 0.058823 -0.332532 0.7422

D(TAX) 0.071255 0.046388 1.536072 0.1366

D(LL) -0.095667 0.049627 -1.927704 0.0649

DUM 0.015762 0.018952 0.831679 0.4132 R-squared 0.768700 Mean dependent var 0.031574

Adjusted R-squared 0.706427 S.D. dependent var 0.054622

S.E. of regression 0.029595 Sum squared resid 0.022773

F-statistic 12.34394 Durbin-Watson stat 1.789467

Prob(F-statistic) 0.000001 Second-Stage SSR 0.022774

Click on Options and

tick the box of

Heteroskedasticity

consistent coefficient

covariance and Newey-

West.

And then click ok.

As compared to the Microfit Output:

Error Correction Representation for the Selected ARDL Model

ARDL(1,1,0,0,0,0) selected based on Schwarz Bayesian Criterion

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

Dependent variable is dRPCC

34 observations used for estimation from 1971 to 2004

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

Regressor Coefficient Standard Error T-Ratio[Prob]

dRGDPC .98154 .17994 5.4549[.000]

dUN .010227 .036818 .27776[.783]

dWAGE -.019567 .047700 -.41020[.685]

dTAX .071253 .047672 1.4946[.147]

dLL -.095664 .036619 -2.6124[.015]

dINPT 1.3806 1.1429 1.2079[.238]

dDUM .015761 .016593 .94989[.351]

ecm(-1) -.31149 .17562 -1.7737[.088]

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

List of additional temporary variables created:

dRPCC = RPCC-RPCC(-1)

dRGDPC = RGDPC-RGDPC(-1)

dUN = UN-UN(-1)

dWAGE = WAGE-WAGE(-1)

dTAX = TAX-TAX(-1)

dLL = LL-LL(-1)

dINPT = INPT-INPT(-1)

dDUM = DUM-DUM(-1)

ecm = RPCC -.36932*RGDPC -.032831*UN + .062815*WAGE -.22875*TAX + .30

712*LL -4.4322*INPT -.050599*DUM

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

R-Squared .76870 R-Bar-Squared .69468

S.E. of Regression .030182 F-stat. F( 7, 26) 11.8689[.000]

Mean of Dependent Variable .031574 S.D. of Dependent Variable .054622

Residual Sum of Squares .022774 Equation Log-likelihood 76.0008

Akaike Info. Criterion 67.0008 Schwarz Bayesian Criterion 60.1322

DW-statistic 1.7895

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

R-Squared and R-Bar-Squared measures refer to the dependent variable

dRPCC and in cases where the error correction model is highly

restricted, these measures could become negative.