Estimation and Interpretation of Econometric Models ...

Estimation and Interpretation of Econometric Models Using EViews: Further Explanatory Notes on 6 Econodata samples – 6th June 2016 Instructor: Dr. Stephen Aro-Gordon Faculty of Management and Social Sciences Email: [email protected]

First, let’s recall statistical decision rules: i. ii.

If Tc > Tt: Reject Ho If Tc < Tt: Do not reject Ho

The p-value is the probability that the test statistic (z*, t*, x*, F*) will be exceeded, and thus, p is called the observed level of significance, in contrast to the -value which is a priori-level of significance. The default value of 2014):

= 0.05, and the relationship between P and

i.

If p

ii.

If p < , reject Ho

is as stated below (Kothari & Garg,

, do not reject Ho

The Data ECONODATA set 1-6 as subjects of these learning notes, have earlier been presented to workshop participants (in Davangere and Bangalore) in Excel spread sheet format. The estimations, interpretations, and comments herein are supplementary materials and purely for academic, classroom discussion only. The time series analysed are as follows: i. ii. iii. iv. v. vi.

Econodata-1 DGR & GDP growth of Nigeria, 1981-2014 Econodata-2 Agriculture & GDP of Nigeria, 1981-2013 Econodata-3 Global crude oil price per barrel & GDP growth of Nigeria, 1981-2014 Econodata-4 Infosys daily stock-market prices (INFOS) and NSE Nifty 50 daily prices (NIFTY), Sept-Nov. 2015 Econodata-5 Agriculture & GDP of India, 1981-2013 Econodata-6 Real GDP of India (IGDP) and World GDP (WGDP) growth rates [actual and estimates] at constant prices - 1970 - 2018

Estimation and Interpretation of Econometric Models Using EViews by Stephen Aro-Gordon, Ph.D.

1

RE: ECONODATA 1 – DGR & GDP Growth in Nigeria Kindly visit http://sdmimd.ac.in/pdfs/Sovereign_debt.pdf for the instructor’s full analysis, estimation and interpretation of Econodata-1. The article contains useful references for further consultation by the interested student.

RE: ECONODATA 2 – Agriculture & GDP of Nigeria

Fig 2.1 Graph of Nigerian Agriculture (AGDP) and GDP (NGDP) – 1981 - 2013 12,000

10,000

8,000

6,000

4,000

2,000

0 82

84

86

88

90

92

94

96

NGDP

98

00

02

04

06

08

10

12

AGDP

Key Interpretation: Both series evidently non-stationary: Unit Root Test should be conducted.


2

UNIT ROOT TEST – ECONODATA-2 Null Hypothesis: AGDP has a unit root Exogenous: Constant Lag Length: 7 (Automatic - based on SIC, maxlag=8)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level

t-Statistic

Prob.*

4.050413 -3.724070 -2.986225 -2.632604

1.0000

*MacKinnon (1996) one-sided p-values.

Null Hypothesis: D(AGDP,2) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=1)


t-Statistic

Prob.*

-9.926494 -3.670170 -2.963972 -2.621007

0.0000

KEY INTERPRETATION: AGDP series transformed to stationary (p=0.00) at 2

nd

difference.

Null Hypothesis: NGDP has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=1)


t-Statistic

Prob.*

5.099229 -3.661661 -2.960411 -2.619160

1.0000



3

Null Hypothesis: D(NGDP,2) has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=1)


t-Statistic

Prob.*

-6.685108 -3.679322 -2.967767 -2.622989

0.0000

*MacKinnon (1996) one-sided p-values. KEY INTERPRETATION: NGDP series transformed to stationary (p=0.00) at 2

nd

difference

COINTEGRATION TEST- ECONODATA-2 Date: 06/06/16 Time: 09:08 Sample (adjusted): 1983 2013 Included observations: 31 after adjustments Trend assumption: Linear deterministic trend Series: NGDP AGDP Lags interval (in first differences): 1 to 1 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s)

Eigenvalue

Trace Statistic

0.05 Critical Value

Prob.**

None * At most 1 *

0.840065 0.505097

78.62772 21.80518

15.49471 3.841466

0.0000 0.0000

Trace test indicates 2 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized No. of CE(s)

Eigenvalue

Max-Eigen Statistic

0.05 Critical Value

Prob.**

None * At most 1 *

0.840065 0.505097

56.82254 21.80518

14.26460 3.841466

0.0000 0.0000

Max-eigenvalue test indicates 2 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Interpretation: P < 0.05 infers rejection of Ho, meaning there is a short-run relationship in the series. Moreover, Tc >Tt reinforces the interpretation. Estimation and Interpretation of Econometric Models Using EViews by Stephen Aro-Gordon, Ph.D.

4

VECTOR ERROR CORRECTION ESTIMATES - ECONODATA-2 Vector Error Correction Estimates Date: 06/06/16 Time: 09:22 Sample (adjusted): 1984 2013 Included observations: 30 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq:

CointEq1

NGDP(-1)

1.000000

AGDP(-1)

-2.918859 (0.02591) [-112.645]

C

-59.69781

Error Correction:

D(NGDP)

D(AGDP)

CointEq1

-3.185677 (0.60505) [-5.26511]

0.549678 (0.24656) [ 2.22936]

D(NGDP(-1))

1.787958 (0.46983) [ 3.80555]

-0.380134 (0.19146) [-1.98546]

D(NGDP(-2))

1.394995 (0.30885) [ 4.51676]

0.022315 (0.12586) [ 0.17730]

D(AGDP(-1))

-5.072348 (1.11946) [-4.53107]

1.374113 (0.45619) [ 3.01217]

D(AGDP(-2))

0.624483 (0.99204) [ 0.62950]

0.573687 (0.40426) [ 1.41910]

C

-78.37686 (54.4785) [-1.43867]

33.43760 (22.2004) [ 1.50617]

0.899060 0.878031 898335.8 193.4701 42.75294 -197.1747 13.54498 13.82522 383.1907 553.9728

0.870683 0.843742 149179.1 78.84032 32.31809 -170.2437 11.74958 12.02982 148.3097 199.4468

R-squared Adj. R-squared Sum sq. resids S.E. equation F-statistic Log likelihood Akaike AIC Schwarz SC Mean dependent S.D. dependent

Determinant resid covariance (dof adj.)

1.26E+08


5

Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion

80371681 -358.1689 24.81126 25.46515

Interpretation: The highlighted t-statistics >1.96 suggests presence long-run relationship after 1 lag, meaning there is a long-run relationship between the series. The strength of relationship is buttressed by 2 adjusted R of 84-88%.

GRANGER CAUSALITY TEST: ECONODATA-2 Pairwise Granger Causality Tests Date: 06/06/16 Time: 09:35 Sample: 1981 2013 Lags: 2 Null Hypothesis: AGDP does not Granger Cause NGDP NGDP does not Granger Cause AGDP

Obs

F-Statistic

Prob.

31

7.09016 17.0145

0.0035 2.E-05

Key Interpretation: P=0.0035 < 0.05 (i.e. reject Ho) infers bi-directional causality, meaning agriculture granger causes GDP and (with p = 2.E-05) vice versa. And this result aligns fairly well with the theory and actual experience of many developing economies of Africa.


6

RE: ECONODATA-3: On Global crude oil price (GCOP) per barrel and Nigeria GDP growth rate (NGDP), 1981 - 2014 Fig 3 – Behaviour GCOP and NGDP, 1981-2014 120 100 80 60 40 20 0 -20 1985

1990

1995

2000

GCOP

2005

2010

NGDP

Key Interpretation: GCOP appears to be non-stationary, but NGDP can be observed to be relatively stationary: Unit Root Test should be conducted for better assurance.

UNIT ROOT TEST: ECONODATA-3 Null Hypothesis: GCOP has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=8)


t-Statistic

Prob.*

-0.202489 -3.646342 -2.954021 -2.615817

0.9286



7

Null Hypothesis: D(GCOP) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=8)


t-Statistic

Prob.*

-6.081743 -3.653730 -2.957110 -2.617434

0.0000


st

KEY INTERPRETATION: GCOP series transformed to stationary (p=0.00) at 1 difference

Null Hypothesis: NGDP has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=8)


t-Statistic

Prob.*

-4.689981 -3.646342 -2.954021 -2.615817

0.0006


KEY INTERPRETATION: As earlier deciphered from the graph analysis above, NGDP is stationary (P=0) at level, so no need for data transformation.


8

COINTEGRATION TEST: ECONODATA-3 Date: 06/06/16 Time: 10:20 Sample (adjusted): 1983 2014 Included observations: 32 after adjustments Trend assumption: Linear deterministic trend Series: GCOP NGDP Lags interval (in first differences): 1 to 1 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s)

Eigenvalue

Trace Statistic

0.05 Critical Value

Prob.**

None * At most 1

0.401482 0.001202

16.46403 0.038490

15.49471 3.841466

0.0356 0.8444

Trace test indicates 1 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Interpretation: P = 0.0356 < 0.05 infers rejection of Ho, meaning there is at least one short-run relationship in the series.

VECTOR ERROR CORRECTION- ECONODATA-3 Vector Error Correction Estimates Date: 06/06/16 Time: 10:23 Sample (adjusted): 1984 2014 Included observations: 31 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq:

CointEq1

GCOP(-1)

1.000000

NGDP(-1)

-311.6258 (75.3884) [-4.13360]

C

1345.556

Error Correction:

D(GCOP)

D(NGDP)

CointEq1

-0.003700 (0.00144) [-2.57637]

0.002531 (0.00099) [ 2.54862]

D(GCOP(-1))

-0.357054 (0.19364)

0.087850 (0.13391)


9

[-1.84389]

[ 0.65602]

D(GCOP(-2))

-0.406491 (0.19292) [-2.10701]

0.032219 (0.13342) [ 0.24149]

D(NGDP(-1))

-0.714033 (0.37248) [-1.91696]

-0.047546 (0.25759) [-0.18458]

D(NGDP(-2))

-0.234910 (0.27349) [-0.85895]

-0.103390 (0.18913) [-0.54667]

C

4.446192 (2.17433) [ 2.04485]

0.169516 (1.50366) [ 0.11274]

0.263269 0.115923 3053.713 11.05208 1.786737 -115.1341 7.815100 8.092646 2.239677 11.75436

0.434110 0.320932 1460.411 7.643065 3.835639 -103.7006 7.077460 7.355006 0.383226 9.274936


Determinant resid covariance (dof adj.) Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion

6771.833 4404.158 -218.0239 14.96928 15.61689

Key Interpretation: The highlighted t-statistics < 1.96 suggests weak long-run relationship after 2 lags, meaning there is limited long-run relationship between the series (i.e. accept Ho). The inference of 2 weakness of the relationship is buttressed by adjusted R of 11-32%, i.e. less than 0.50 thresholds.


10

GRANGER CAUSALITY TEST- ECONODATA-3 Pairwise Granger Causality Tests Date: 06/06/16 Time: 10:37 Sample: 1981 2014 Lags: 2 Null Hypothesis: NGDP does not Granger Cause GCOP GCOP does not Granger Cause NGDP

Obs

F-Statistic

Prob.

32

2.02585 0.39105

0.1514 0.6801

Key Interpretation: Non-causality is bidirectional: P=0.1514 > 0.05 infers NGDP does not Granger Cause GCOP and also (with P=0.6801 > 0.05), GCOP does not Granger Cause NGDP. And this result aligns fairly well with the theory and actual experience of the Nigerian economy. Regardless of her OPEC membership, her economy is yet too small to have any significant impact on GCOP; moreover, there are many other variables (exchange rate, inflation, etc.) that impact the Nigerian economy beyond the GCOP.

RE: ECONODATA 4: Infosys daily stock-market prices (INFOS) and NSE Nifty 50 daily prices (NIFTY), Sept-Nov. 2015 9,000 8,000 7,000 6,000 5,000 4,000 3,000 2,000 1,000 0 M9

M10

M11

2015 INFOS

NIFTY

Key Interpretation: On the face of it, both financial series appear stationary. All the same, we will proceed to conduct a Unit Root Test.


11

UNIT ROOT TEST- ECONODATA-4 Null Hypothesis: NIFTY has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=10)


t-Statistic

Prob.*

-1.625357 -3.548208 -2.912631 -2.594027

0.4634

t-Statistic

Prob.*

-7.913124 -3.550396 -2.913549 -2.594521

0.0000


Null Hypothesis: D(NIFTY) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=10)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level *MacKinnon (1996) one-sided p-values.

KEY INTERPRETATION: Nifty series transformed to stationary (p=0.00) at 1st difference

Null Hypothesis: INFOS has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=10)


t-Statistic

Prob.*

-1.888506 -3.548208 -2.912631 -2.594027

0.3354



12

Null Hypothesis: D(INFOS) has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=10)


t-Statistic

Prob.*

-6.899273 -3.550396 -2.913549 -2.594521

0.0000


KEY INTERPRETATION: Similarly, Infosys series transformed to stationary (p=0.00) at 1st difference.

COINTEGRATION TEST: ECONODATA-4 Date: 06/06/16 Time: 11:07 Sample (adjusted): 9/03/2015 11/30/2015 Included observations: 57 after adjustments Trend assumption: Linear deterministic trend Series: INFOS NIFTY Lags interval (in first differences): 1 to 1 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s)

Eigenvalue

Trace Statistic

0.05 Critical Value

Prob.**

None At most 1

0.112344 0.057682

10.17927 3.386537

15.49471 3.841466

0.2672 0.0657

Trace test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Key Interpretation: For both p-values, p > 0.05 (accept Ho), meaning there is no relationship between the two series.


13

VECTOR ERROR CORRECTION MODEL: ECONODATA-4 Vector Error Correction Estimates Date: 06/06/16 Time: 11:13 Sample (adjusted): 9/04/2015 11/30/2015 Included observations: 56 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq:

CointEq1

INFOS(-1)

1.000000

NIFTY(-1)

-0.146951 (0.06587) [-2.23085]

C

61.45889

Error Correction:

D(INFOS)

D(NIFTY)

CointEq1

-0.182352 (0.09161) [-1.99061]

-0.126885 (0.37835) [-0.33536]

D(INFOS(-1))

0.250039 (0.16774) [ 1.49061]

-0.106098 (0.69282) [-0.15314]

D(INFOS(-2))

-0.096872 (0.17018) [-0.56925]

-0.236137 (0.70286) [-0.33596]

D(NIFTY(-1))

-0.058982 (0.04099) [-1.43900]

-0.024429 (0.16929) [-0.14430]

D(NIFTY(-2))

-0.021464 (0.04098) [-0.52378]

-0.086799 (0.16926) [-0.51283]

C

0.158823 (2.35936) [ 0.06732]

2.046342 (9.74468) [ 0.21000]

0.133922 0.047314 15361.43 17.52793 1.546303 -236.6599 8.666426 8.883428 -0.204464 17.95791

0.022540 -0.075206 262046.5 72.39427 0.230601 -316.0865 11.50309 11.72009 2.004464 69.81656


Determinant resid covariance (dof adj.)

1087891.


14

Determinant resid covariance Log likelihood Akaike information criterion Schwarz criterion

867259.9 -541.7677 19.84885 20.35519

Key Interpretation: The highlighted t-statistics < 1.96 suggests weak long-run relationship after 2 lags, meaning there is very limited long-run relationship between the series (i.e. accept Ho). The inference of 2 weakness of the relationship is buttressed by adjusted R of -7%/5%, i.e. far less than required minimum of 0.50 to demonstrate significant relationship.

CAUSALITY TEST: ECONODATA-4 Pairwise Granger Causality Tests Date: 06/06/16 Time: 12:08 Sample: 9/01/2015 11/30/2015 Lags: 2 Null Hypothesis: NIFTY does not Granger Cause INFOS INFOS does not Granger Cause NIFTY

Obs

F-Statistic

Prob.

57

1.35656 0.19680

0.2665 0.8220

Key Interpretation: Non-causality is bidirectional: P=0.2665 > 0.05 infers NIFTY does not Granger Cause INFOSYS and also (with P=0.8220 > 0.05), INFOSYS does not Granger Cause NIFTY. And this result synchronises with the financial (risk-return) theory innovation/tech firms in emerging markets like India (read Brealey et al, 2014): they have comparatively lower market risk.


15

RE: ECONODATA-5 India: 'Agriculture' sector's GDP (AgricGDP) and national GDP (IGDP), 1981 - 2013 (Rupees crore) Fig 5: AGDP & India GDP 12,000,000

10,000,000

8,000,000

6,000,000

4,000,000

2,000,000

0 82

84

86

88

90

92

94

96

98

AGRICGDP

00

02

04

06

08

10

12

IGDP

Key Interpretation: Like Nigeria’s (Econodata-2), both series are evidently non-stationary: Unit Root Test should be conducted.

UNIT ROOT TEST: ECONODATA-5 Null Hypothesis: AGRICGDP has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=8)


t-Statistic

Prob.*

11.29171 -3.653730 -2.957110 -2.617434

1.0000



16

Null Hypothesis: D(AGRICGDP,2) has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=8)


t-Statistic

Prob.*

-5.953755 -3.679322 -2.967767 -2.622989

0.0000


KEY INTERPRETATION: Again, akin to Nigeria’s India AGDP series transformed to stationary (p=0.00) nd at 2 difference.

Null Hypothesis: IGDP has a unit root Exogenous: Constant Lag Length: 3 (Automatic - based on SIC, maxlag=8)


t-Statistic

Prob.*

1.726239 -3.679322 -2.967767 -2.622989

0.9994

t-Statistic

Prob.*

-5.874250 -3.679322 -2.967767 -2.622989

0.0000


Null Hypothesis: D(IGDP,2) has a unit root Exogenous: Constant Lag Length: 1 (Automatic - based on SIC, maxlag=1)

Augmented Dickey-Fuller test statistic Test critical values: 1% level 5% level 10% level *MacKinnon (1996) one-sided p-values.

KEY INTERPRETATION: IGDP series transformed to stationary (p=0.00) at 2

nd


difference

17

COINTEGRATION TEST: ECONODATA-5

Date: 06/06/16 Time: 12:59 Sample (adjusted): 1983 2013 Included observations: 31 after adjustments Trend assumption: Linear deterministic trend Series: IGDP AGRICGDP Lags interval (in first differences): 1 to 1 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s)

Eigenvalue

Trace Statistic

0.05 Critical Value

Prob.**

None At most 1

0.326010 0.057407

14.06350 1.832751

15.49471 3.841466

0.0812 0.1758

Trace test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegration Rank Test (Maximum Eigenvalue) Hypothesized No. of CE(s)

Eigenvalue

Max-Eigen Statistic

0.05 Critical Value

Prob.**

None At most 1

0.326010 0.057407

12.23075 1.832751

14.26460 3.841466

0.1023 0.1758

Max-eigenvalue test indicates no cointegration at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values Unrestricted Cointegrating Coefficients (normalized by b'*S11*b=I): IGDP -4.19E-06 3.82E-06

AGRICGDP 1.46E-05 -2.70E-05

Unrestricted Adjustment Coefficients (alpha): D(IGDP) D(AGRICGDP)

-60699.90 -12634.91

1 Cointegrating Equation(s):

2957.319 4442.868

Log likelihood

-740.6961

Normalized cointegrating coefficients (standard error in parentheses) IGDP AGRICGDP 1.000000 -3.482424 (0.66955) Adjustment coefficients (standard error in parentheses) D(IGDP) 0.254374 Estimation and Interpretation of Econometric Models Using EViews by Stephen Aro-Gordon, Ph.D.

18

D(AGRICGDP)

(0.07109) 0.052949 (0.02094)

Key Interpretation: All the highlighted p-values are > 0.05, hence acceptance of Ho inferred, meaning significant absence of short-run relationship between the series. Tc < Tt (check) reinforces the interpretation.

VECTOR ERROR CORRECTION ESTIMATES: ECONODATA-5 Vector Error Correction Estimates Date: 06/06/16 Time: 13:04 Sample (adjusted): 1984 2013 Included observations: 30 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq:

CointEq1

IGDP(-1)

1.000000

AGRICGDP(-1)

-3.011491 (0.36282) [-8.30028]

C

-1156272.

Error Correction:

D(IGDP)

D(AGRICGDP)

CointEq1

0.527573 (0.08790) [ 6.00188]

0.128539 (0.02869) [ 4.48103]

D(IGDP(-1))

-0.436528 (0.37116) [-1.17613]

-0.195579 (0.12112) [-1.61474]

D(IGDP(-2))

-1.555287 (0.38774) [-4.01111]

-0.451914 (0.12653) [-3.57146]

D(AGRICGDP(-1))

2.924820 (1.22235) [ 2.39279]

0.665862 (0.39889) [ 1.66927]

D(AGRICGDP(-2))

2.878947 (1.20328) [ 2.39259]

1.229409 (0.39267) [ 3.13089]

C

676842.6 (109383.) [ 6.18782]

163446.6 (35695.5) [ 4.57891]


19


0.971870 0.966010 1.31E+11 73921.38 165.8362 -375.5437 25.43625 25.71649 370868.4 400951.4


0.900511 0.879784 1.40E+10 24123.12 43.44665 -341.9488 23.19659 23.47682 61204.00 69574.97 1.33E+18 8.51E+17 -704.4187 47.89458 48.54847

Interpretation: The highlighted t-statistics >1.96 suggests presence of long-run relationship after 2 lags, meaning there is a long-run relationship between the two series. The strength of relationship is buttressed 2 by adjusted R of 88-97%.

GRANGER CAUSALITY TEST: ECONODATA-5 Pairwise Granger Causality Tests Date: 06/06/16 Time: 13:09 Sample: 1981 2013 Lags: 2 Null Hypothesis: AGRICGDP does not Granger Cause IGDP IGDP does not Granger Cause AGRICGDP

Obs

F-Statistic

Prob.

31

1.70873 4.61624

0.2008 0.0192

Key Interpretation: Unlike Nigeria, causality here is unidirectional, not bidirectional. P=0.2008 > 0.05 (i.e. do not reject Ho) meaning broadly that, in India, agriculture does not granger cause GDP. But with p = 0.0192 < 0.05, IGDP Granger causes AGDP. And this result aligns fairly well with India’s actual experience over the years as a better-diversified (e.g. better industrialised, IT-driven) economy than Nigeria.


20

RE: ECONODATA-6: India real GDP (IGDP) and world GDP (WGDP) growth rates [actual and projections] at constant prices - 1970 – 2018

Fig.6: India GDP (IGDP) and Global GDP (WGDP) growth rates: 1970 – 2018 12 10 8 6 4 2 0 -2 1970

1975

1980

1985

1990

1995

W GDP

2000

2005

2010

2015

IGDP

Key Interpretation: From the graph, both series appear to be stationary. All the same, Unit Root Test should be conducted for quality assurances. Note: As we already know, IGDP lies above WGDP almost throughout the series including during 2007-2008 global financial crisis and projections to 2018. And the way the lines gyrate together throughout the period makes us to suspect very strong positive relationship between the two series.


21

UNIT ROOT TEST: ECONODATA-6

Null Hypothesis: WGDP has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=10)


t-Statistic

Prob.*

-5.223972 -3.574446 -2.923780 -2.599925

0.0001


KEY INTERPRETATION: As earlier deciphered from the graph analysis above, WGDP is stationary (P=0) at level, so no need for data transformation.

Null Hypothesis: IGDP has a unit root Exogenous: Constant Lag Length: 0 (Automatic - based on SIC, maxlag=10)


t-Statistic

Prob.*

-5.958068 -3.574446 -2.923780 -2.599925

0.0000


KEY INTERPRETATION: Similarly, as earlier observed from the graph analysis above, IGDP is equally stationary (P=0) at level, so no need for data transformation. In effect, both WGDP and IGDP are stationary at level.


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COINTEGRATION TEST: ECONODATA-6 Date: 06/06/16 Time: 15:07 Sample (adjusted): 1972 2018 Included observations: 47 after adjustments Trend assumption: Linear deterministic trend Series: WGDP IGDP Lags interval (in first differences): 1 to 1 Unrestricted Cointegration Rank Test (Trace) Hypothesized No. of CE(s)

Eigenvalue

Trace Statistic

0.05 Critical Value

Prob.**

None * At most 1 *

0.407135 0.280850

40.06626 15.49519

15.49471 3.841466

0.0000 0.0001

Trace test indicates 2 cointegrating eqn(s) at the 0.05 level * denotes rejection of the hypothesis at the 0.05 level **MacKinnon-Haug-Michelis (1999) p-values

Key Interpretation: The highlighted p-values are < 0.05, hence rejection of Ho inferred, meaning there is significant presence of short-run relationship between the two series. Tc > Tt (check) reinforces our deduction.

VECTOR ERROR CORRECTION ESTIMATES: ECONODATA-6 Vector Error Correction Estimates Date: 06/06/16 Time: 15:13 Sample (adjusted): 1973 2018 Included observations: 46 after adjustments Standard errors in ( ) & t-statistics in [ ] Cointegrating Eq:

CointEq1

WGDP(-1)

1.000000

IGDP(-1)

-3.420957 (0.70956) [-4.82125]

C

17.76170

Error Correction:

D(WGDP)

D(IGDP)

CointEq1

0.016479 (0.04926) [ 0.33450]

0.339469 (0.07475) [ 4.54132]

D(WGDP(-1))

-0.336586 (0.15720)

-0.284820 (0.23853)


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[-2.14113]

[-1.19408]

D(WGDP(-2))

-0.365388 (0.14381) [-2.54084]

-0.181744 (0.21820) [-0.83292]

D(IGDP(-1))

0.131498 (0.14097) [ 0.93284]

0.280184 (0.21389) [ 1.30993]

D(IGDP(-2))

-0.062068 (0.10876) [-0.57068]

0.215086 (0.16503) [ 1.30334]

C

-0.051126 (0.21632) [-0.23634]

0.028019 (0.32823) [ 0.08536]

0.285283 0.195944 85.86575 1.465143 3.193247 -79.62648 3.722890 3.961409 -0.033043 1.633943

0.469480 0.403165 197.6888 2.223110 7.079554 -98.80638 4.556799 4.795318 0.055435 2.877624



9.280026 7.017033 -175.3542 8.232790 8.789333

Interpretation: The highlighted t-statistics 0.05 infers IGDP (India) does not Granger Cause WGDP and also (with P=0.9599 > 0.05), WGDP does not Granger Cause IGDP. Based on what you know about the India economy and recent global economic developments, can you fault these results? Discuss.

…End of the class notes…


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