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The Official Journal of the Pan-Pacific Association of Input-Output Studies (PAPAIOS)

Table 3 Test of cointegration of bivariate model

From: Estimating the growth effects of services sector: a cointegration analysis for Pakistan

Null hypothesis

Alternative hypothesis

Trace statistics

Critical value (0.05)

Johansen cointegration test

 r = 0

r = 1

17.1302

13.1994

 r ≤ 1

r = 2

0.272

03.8410

Model

F stats

Imposing one lag length

F stats

Optimal lag length

F stats

Lag length

ARDL cointegration testa

 ln gdp = f(lser)

7.0360

6.5865

2

 ln gdp = f(lwrt)

6.2550

6.2550

1

 ln gdp = f(lfi)

7.1071

10.5041

3

 ln gdp = f(ltc)

5.7146

5.3793

2

 ln gdp = f(ledu)

4.5189

7.2515

2

 ln gdp = f(lhlt)

5.0984

5.9894

3

 ln gdp = f(lser, lcap, lopen, lcpi)

6.3286

5.5003

2

  1. aThe calculated values are compared with critical values of Pesaran et al. (2001)