Does trade openness affect economic growth in India? Evidence from threshold cointegration with asymmetric adjustment

Figures & data

Figure 1. The trend of economic growth (GDP) and trade openness (TOP) in India over the period 1960–2018.

Table 1. Covariance and correlation matrix

		GDP	TOP
GDP	covariance	9.283
	correlation	1
TOP	covariance	0.998	0.390
	correlation	0.524*** (0.000)	1

Note: ***, **, and * shows significance at the 1 %, 5% and 10% level, respectively. p-values are reported in parenthesis.

Table 2. Descriptive statistics and unit root test of the variables

Statistics	TOP		GDP
	Level	First difference	Level	First difference
ADF with intercept	0.158 (0.967)	−5.951*** (0.000)	−1.189 (0.130)	−6.581*** (0.000)
ADF with intercept & trend	−2.653 (0.259)	−5.952*** (0.000)	−1.339 (0.199)	−6.575*** (0.000)
Decision	I (1)		I (1)
Mean	2.962		3.290
Median	2.748		3.785
Maximum	4.021		7.299
Minimum	2.0470		−7.388
Std. Dev.	0.630		3.073
Jarque-Bera	4.636		18.109
probability	0.098		0.0001
Sum Sq. Dev.	22.650		538.433
Obs.	58		58

Note: ***, **, and * shows significance at the 1 %, 5% and 10% level, respectively. For unit root tests, p-values are reported in parenthesis.

Table 3. Unit root test in the presence of two-time structural break (AO)

Variables	${\delta }_1$	${\delta }_2$	$\left(\hat{\rho }-1\right)$	First Break	Second Break
GDP	3.456***	2.227	−1.165*	1981	2001
	[2.592]	[1.496]	[−1.917]
	(0.014)	(0.145)	−5.490 (5% critical value)
TOP	0.578***	0.957***	−0.320***	1976	2001
	[8.3543]	[14.091]	[−3.157]
	(0.000)	(0.000)	5.490 (5% critical value)

Notes: Two-break test of Clemente et al. (1998), AO model. Structural breaks, year dummy variable coefficients are represented by $\delta$. ***, ** and * are significance at the 1%, 5% and 10% level, respectively. $\left(\hat{\rho }-1\right)$: $H_0:$ Unit root rejected at the 1%, 5% and 10% level. Values in [] and () represents t-statistics and p-values respectively.

Figure 2. Clemente, Montanes, and Reyes (CMR) (1998) unit roots in the presence of a one-time structural break for economic growth (GDP) and trade openness (TOP) during the period 1960–2018.

Figure 3. Clemente, Montanes, and Reyes (CMR) (1998) unit roots in the presence of a two-time structural break for economic growth (GDP) and trade openness (TOP) during the period 1960–2018.

Figure 4. The threshold value of the TAR model during the period 1960–2018.

Figure 5. The threshold value of the M-TAR model during the period 1960–2018.

Table 4. Results of Engle-Granger and threshold cointegration tests during the period 1960–2018

Item	Engle-Granger	TAR	C-TAR	MTAR	C-MTAR
Lag		3	3	3	3
Threshold		0	−1.421	0	−3.422
${{\rho }_1}^{+}$†	2.557***	−2.162***	−2.155***	−2.171***	−2.176***
	[4.609]	[−5.883]	[−5.926]	[−5.785]	[−6.522]
${{\rho }_1}^{-}$		−1.969***	−1.964***	−1.982***	−1.802***
		[−5.84]	[−5.789]	[−5.945]	[−5.064]
Diagnostics Test
AIC	4.775	256.351	256.358	256.375	254.554
BIC		268.284	268.291	268.309	266.487
${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(4\right)$	_	0.994	0.992	0.996	0.998
${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(8\right)$	_	0.882	0.885	0.907	0.811
$Q_{LB}\left(12\right)$		0.698	0.715	0.748	0.739
Hypothesis Testing
${\mathrm{H}}_0$: No Symmetric Cointegration	0.210* (0.109)	19.838	19.832	19.818	21.338
${\mathrm{H}}_0$: No APT/cointegration	___	1.553	2.547*	1.531	2.230*
${\mathrm{H}}_0$: p-value		(0.261)	(0.101)	(0.270)	(0.102)
Total obs.	58	58	58	58	58
Cointegration obs.		54	54	54	54

Notes: † For the Engle-Granger cointegration test, ${\rho }_1$ refers to $\rho$ in Equation (6)(6) $\mathrm{\Delta }{\widehat{ϵ}}_{\mathrm{t}}={\rho }_1{\mathrm{I}}_{\mathrm{t}}{\widehat{ϵ}}_{\mathrm{t}-1}+{\rho }_2\left(1-{\mathrm{I}}_{\mathrm{t}}\right){\widehat{ϵ}}_{\mathrm{t}-1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\varnothing }}_{\mathrm{i}}\mathrm{\Delta }{\widehat{ϵ}}_{\mathrm{t}-1}+{ϵ}_{\mathrm{t}}$(6) . For the Engle-Granger cointegration test, the critical values are −2.606, −1.946, and −1.613 at the 1%, 5%, and 10% level, respectively. AIC and BIC represent the Akaike information criterion and Bayesian information criterion. APT denotes asymmetric price transmission. ${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(\mathrm{p}\right)$ indicates the significance level for the Ljung-Box Q statistic; it tests serial correlation based on p autocorrelation coefficients (p = 4, 8, 12). $\varphi$ is the threshold cointegration test with the critical values from Enders and Siklos (2001). $F(H_0:{\rho }_1={\rho }_2)$ is a standard F-test to check the asymmetric price transmission between the variables of our interest. ***, **, * indicates significant at 1%, 5%, and 10% level, respectively. Numbers in brackets () and [] are p-values and t-statistics, respectively.

Table 5. Results of the asymmetric error correction model with threshold cointegration during the period 1960–2018

Parameters	GDP		TOP
	estimates	t-statistics	estimates	t-statistics
Θ	0.104*	1.973	−0.034	−0.026
α1^+	−0.011	−0.537	5.77	0.744
α2^+	−0.013	−0.764	−2.859	−0.393
α3^+	−0.002	−0.147	1.131	0.158
α4^+	−0.005	−0.757	2.112	0.298
α1^‒	−0.019	−0.815	−8.325	−0.779
α2^‒	−0.003	−0.164	−8.324	−0.765
α3^‒	−0.006	−0.44	−9.906	−0.93
α4^‒	0.004	0.393	−1.732	−0.145
β1^+	−0.096	−0.301	1.03**	2.056
β2^+	0.134	0.451	0.697*	1.676
β3^+	−0.375	−1.276	0.224	0.728
β4^+	−0.059	−0.205	0.014	0.086
β1^‒	0.776*	1.774	0.912.	1.585
β2^‒	−0.09	−0.202	0.733*	1.704
β3^‒	0.41	0.941	0.778**	2.416
β4^‒	0.266	0.544	0.123	0.451
δ ^+	0.015	0.632	−2.336***	−4.01
δ ^‒	0.022	0.759	−1.958***	−2.731
R^2	0.236	_	0.746	_
AIC	−79.107	_	259.581	_
BIC	−39.701	_	298.987	_
Q LB (4)	0.931	_	0.476	_
Q LB (8)	0.990	_	0.371	_
H01: α1^+ = α1^‒ = 0 for all lags	0.765	[0.64]	0.651	[0.73]
H02: βi^+ = βi^‒ = 0 for all lags	0.401	[0.91]	1.344*	[0.102]
H03: α2^+ = α2^‒	0.129	[0.72]	0.129	[0.71]
H04: β4^+ = β4^‒	0.568	[0.46]	0.123	[0.73]
H05: $\sum _{i=1}^4{\alpha }_i+=\sum _{i=1}^4{\alpha }_i-$	2.148	[0.15]	1.383	[0.25]
H06: $\sum _{i=1}^4{\beta }_i+=\sum _{i=1}^4{\beta }_i-$	0.127	[0.72]	1.263	[0.27]
H07: δ ^+ = δ ^‒	0.115	[0.74]	0.532	[0.47]

Numbers in brackets [] are p-values. The hypotheses, H_01, and H₀₂, evaluate the Granger causality tests, H₀₃and H₀₄ evaluate distributed asymmetric lag effect, H₀₅ and H₀₆ assess the cumulative asymmetric effect and H₀₇ evaluates the equilibrium adjustment path asymmetric effect.

***, **, * indicates significant at the 1%, 5%, 10% level, respectively.

Table 6. Results of Engle-Granger and threshold cointegration tests during the pre-reforms period 1960–1990

Item	Engle-Granger	TAR	C-TAR	MTAR	C-MTAR
Lag		3	3	3	3
Threshold		0	−2.979	0	−3.431
${{\rho }_1}^{+}$†	−1.459***	−2.329***	−2.331***	−2.428***	−2.352***
	[−4.937]	[−4.116]	[−4.509]	[−4.27]	[−4.702]
${{\rho }_1}^{-}$		−2.004***	−1.847***	−1.994***	−1.779***
		[−3.95]	[−3.555]	[−4.009]	[−3.474]
Diagnostics Test
AIC	5.	138.547	137.355	137.852	136.275
BIC		146.095	144.903	145.4	143.824
${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(4\right)$	_	0.989	0.956	0.994	0.995
${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(8\right)$	_	0.978	0.925	0.954	0.868
$Q_{LB}\left(12\right)$		0.744	0.763	0.841	0.899
Hypothesis Testing
${\mathrm{H}}_0$: No Symmetric Cointegration	0.223 [1.167]	9.268	10.195	9.803	11.072
${\mathrm{H}}_0$: No APT/Cointegration		0.746	1.766	1.336	2.732*
${\mathrm{H}}_0$: p-value		(0.397)	(0.198)	(0.261)	(0.103)
Total obs.		30	30	30	30
Cointegration obs.		26	26	26	26

Notes: † For the Engle-Granger cointegration test, ${\rho }_1$ refers to $\rho$ in Equation (6)(6) $\mathrm{\Delta }{\widehat{ϵ}}_{\mathrm{t}}={\rho }_1{\mathrm{I}}_{\mathrm{t}}{\widehat{ϵ}}_{\mathrm{t}-1}+{\rho }_2\left(1-{\mathrm{I}}_{\mathrm{t}}\right){\widehat{ϵ}}_{\mathrm{t}-1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\varnothing }}_{\mathrm{i}}\mathrm{\Delta }{\widehat{ϵ}}_{\mathrm{t}-1}+{ϵ}_{\mathrm{t}}$(6) . For the Engle-Granger cointegration test, the critical values are −2.62, −1.95, and −1.61 at the 1%, 5%, and 10% level, respectively. AIC and BIC represent the Akaike information criterion and Bayesian information criterion. APT denotes asymmetric price transmission. ${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(\mathrm{p}\right)$ indicates the significance level for the Ljung-Box Q statistic; it tests serial correlation based on p autocorrelation coefficients (p = 4, 8, 12). $\varphi$ is the threshold cointegration test with the critical values from Enders and Siklos (2001). $F(H_0:{\rho }_1={\rho }_2)$ is a standard F-test to check the asymmetric price transmission between the variables of our interest. ***, **, * indicates significant at the 1%, 5%, and 10% level. Numbers in brackets () and [] are p-values and t-statistics, respectively.

Table 7. Results of Engle-Granger and threshold cointegration tests during the post-reforms period 1991–2018

Item	Engle-Granger	TAR	C-TAR	MTAR	C-MTAR
Lag		3	3	3	3
Threshold		0	−2.048	0	0.602
${{\rho }_1}^{+}$†	−1.112***	−1.377**	−1.282**	−1.246**	−1.043
	[−4.175]	[−2.459]	[−2.286]	[−2.138]	[−1.573]
${{\rho }_1}^{-}$		−1.515**	−1.6***	−1.562***	−1.489***
		[−2.753]	[−2.91]	[−2.953]	[−2.975]
Diagnostics Test
AIC		103.727	103.269	103.25	102.783
BIC		110.795	110.338	110.318	109.851
${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(4\right)$	_	0.997	0.999	0.998	0.99
${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(8\right)$	_	0.976	0.962	0.887	0.822
$Q_{LB}\left(12\right)$		0.673	0.708	0.543	0.472
Hypothesis Testing
${\mathrm{H}}_0$: No Symmetric Cointegration	0.166 [0.912]	4.11	4.372	4.383	4.656
${\mathrm{H}}_0$: No APT/Cointegration		0.097	0.465	0.481	0.863
${\mathrm{H}}_0$: p-value		(0.759)	(0.504)	(0.496)	(0.364)
Total obs.		28	28	28	28
Cointegration obs.		24	24	24	24

Notes: † For the Engle-Granger cointegration test, ${\rho }_1$ refers to $\rho$ in Equation (6)(6) $\mathrm{\Delta }{\widehat{ϵ}}_{\mathrm{t}}={\rho }_1{\mathrm{I}}_{\mathrm{t}}{\widehat{ϵ}}_{\mathrm{t}-1}+{\rho }_2\left(1-{\mathrm{I}}_{\mathrm{t}}\right){\widehat{ϵ}}_{\mathrm{t}-1}+\sum _{\mathrm{i}=1}^{\mathrm{p}}{\mathrm{\varnothing }}_{\mathrm{i}}\mathrm{\Delta }{\widehat{ϵ}}_{\mathrm{t}-1}+{ϵ}_{\mathrm{t}}$(6) . For the Engle-Granger cointegration test, the critical value is −2.62, −1.95, and −1.61 at the 1%, 5%, and 10% level, respectively. AIC and BIC represent the Akaike information criterion and Bayesian information criterion. APT denotes asymmetric price transmission. ${\mathrm{Q}}_{\mathrm{L}\mathrm{B}}\left(\mathrm{p}\right)$ indicates the significance level for the Ljung-Box Q statistic; it tests serial correlation based on p autocorrelation coefficients (p = 4, 8, 12). $\varphi$ is the threshold cointegration test with the critical values from Enders and Siklos (2001). $F(H_0:{\rho }_1={\rho }_2)$ is a standard F-test to check the asymmetric price transmission between the variables of our interest. ***, **, * indicates significant at the 1%, 5%, and 10% level. Numbers in brackets () and [] are p-values and t-statistics, respectively.

Figure 6. The threshold value of the TAR model during the pre-reforms period 1960–1990.

Figure 7. The threshold value of the M-TAR model during the pre-reforms period 1960–1990.

Figure 8. The threshold value of the TAR model during the post-reforms period 1991–2018.

Figure 9. The threshold value of the M-TAR model during the post-reforms period 1991–2018.

Table 8. Results of the asymmetric error correction model with threshold cointegration during the pre-reforms period 1960–1990

Parameters	GDP		TOP
	Estimates	t-statistics	estimates	t-statistics
Θ	0.136*	1.263	3.58	1.333
α1^+	0.398	0.667	−21.396	−1.466
α2^+	−0.609*	−1.791	19.417	1.031
α3^+	0.304	0.4	−33.08.	−1.776
α4^+	0.24	0.33	28.737	1.614
α1^‒	−0.087	−0.105	14.252	0.704
α2^‒	0.434	0.486	−45.958*	−2.105
α3^‒	0.69	0.792	−5.571	−0.261
α4^‒	0.373	0.402	−31.301	−1.377
β1^+	−0.005	−0.105	1.787	1.563
β2^+	−0.038	−0.922	2.444**	2.451
β3^+	−0.012	−0.345	0.059	0.072
β4^+	−0.003	−0.236	−0.342	−1.111
β1^‒	−0.028	−0.535	3.559**	2.759
β2^‒	0.01	0.261	1.429	1.507
β3^‒	−0.016	−0.567	2.215**	3.203
β4^‒	0.009	0.357	0.187	0.314
δ ^+	0.008	0.155	−3.533**	−2.849
δ ^‒	0.026	0.414	−4.964**	−3.258
R^2	0.652	_	0.926	_
AIC	−34.232	_	125.646	_
BIC	−9.854	_	150.024	_
Q LB (4)	0.722	_	0.966	_
Q LB (8)	0.96	_	0.271	_
H01: α1^+ = α1^‒ = 0 for all lags	0.516	[0.81]	1.415	[0.35]
H02: βi^+ = βi^‒ = 0 for all lags	0.597	[0.76]	2.066***	[0.02]
H03: α2^+ = α2^‒	0.614	[0.46]	4.033*	[0.09]
H04: β4^+ = β4^‒	0.27	[0.62]	0.925	[0.37]
H05: $\sum _{\mathrm{i}=1}^4{\alpha }_{\mathrm{i}}+=\sum _{\mathrm{i}=1}^4{\alpha }_{\mathrm{i}}-$	0.346	[0.58]	1.932	[0.21]
H06: $\sum _{\mathrm{i}=1}^4{\beta }_{\mathrm{i}}+=\sum _{\mathrm{i}=1}^4{\beta }_{\mathrm{i}}-$	0.299**	[0.06]	5.92*	[0.05]
H07: δ ^+ = δ ^‒	0.206	[0.67]	2.205	[0.19]

Notes: Numbers in brackets [] are p-values. The hypotheses, H_01, and H₀₂ evaluate the Granger causality tests, H₀₃ and H₀₄ evaluate distributed asymmetric lag effect, H₀₅ and H₀₆ assess the cumulative asymmetric effect and H₀₇ evaluates the equilibrium adjustment path asymmetric effect. ***, **, * indicates significant at the 1%, 5%, 10% level, respectively.

Table 9. Results of the asymmetric error correction model with threshold cointegration during the post-reforms period 1991–2018

Parameters	GDP		TOP
	estimates	t-statistics	estimates	t-statistics
Θ	0.092	0.3	1.425	0.346
α1^+	−0.421	−0.242	27.889*	1.692
α2^+	1.101	0.716	−9.265	−0.448
α3^+	0.275	0.233	−19.75	−1.245
α4^+	−0.657	−0.561	−7.735	−0.491
α1^‒	1.437*	1.807	−7.009	−0.292
α2^‒	0.001	0.001	−9.644	−0.717
α3^‒	−1.513	−0.77	13.072	0.494
α4^‒	1.341	0.44	1.524	0.037
β1^+	−0.023	−0.203	0.956	0.639
β2^+	0.018	0.155	−0.82	−0.515
β3^+	−0.024	−0.418	−0.295	−0.376
β4^+	−0.029*	−1.792	0.374	0.749
β1^‒	0.025	0.21	0.075	0.046
β2^‒	−0.029	−0.281	0.495	0.359
β3^‒	0.003	0.04	0.204	0.19
β4^‒	0.006	0.075	−0.048	−0.048
δ ^+	−0.026*	1.198	−1.995*	−1.167
δ ^‒	−0.012	−0.076	−0.724	−0.328
R^2	0.661	_	0.901	_
AIC	−29.319	_	90.289	_
BIC	−6.609	_	112.999	_
Q LB (4)	0.593	_	0.391	_
Q LB (8)	0.923	_	0.427	_
H01: α1^+ = α1^‒ = 0 for all lags	0.426	[0.86]	1.691*	[0.103]
H02: βi^+ = βi^‒ = 0 for all lags	0.271	[0.94]	1.634*	[0.094]
H03: α2^+ = α2^‒	0.405	[0.56]	0	[0.99]
H04: β4^+ = β4^‒	0.224	[0.66]	0.18	[0.69]
H05: $\sum _{\mathrm{i}=1}^4{\alpha }_{\mathrm{i}}$^+ = $\sum _{\mathrm{i}=1}^4{\alpha }_{\mathrm{i}}$^‒	0.029	[0.87]	0.008	[0.93]
H06: $\sum _{\mathrm{i}=1}^4{\beta }_{\mathrm{i}}$^+ = $\sum _{\mathrm{i}=1}^4{\beta }_{\mathrm{i}}$^‒	0.103	[0.76]	0.037	[0.86]
H07: δ ^+ = δ ^‒	0.155	[0.71]	0.95	[0.38]

Notes: Numbers in brackets [] are p-values. The hypotheses, H_01, and H₀₂ evaluate the Granger causality tests, H₀₃andH₀₄ evaluate distributed asymmetric lag effect, H₀₅ and H₀₆ assess the cumulative asymmetric effect and H₀₇ evaluates the equilibrium adjustment path asymmetric effect. ***, **, * indicates significant at 1%, 5%, 10% level, respectively.

Clemente, J., Montanes, A., & Reyes, M. (1998). Testing for a unit root in variables with a double change in the mean. Economics Letters, 59(2), 175–182. https://doi.org/10.1016/S0165-1765(98)00052-4

 Web of Science ®Google Scholar

Enders, W., & Siklos, P. L. (2001). Cointegration and Threshold Adjustment. Journal of Business & Economic Statistics, 19(2), 166–176. https://doi.org/10.1198/073500101316970395

 Web of Science ®Google Scholar