Merchandise exports and economic growth: multivariate time series analysis for the United Arab Emirates

Figures & data

Table 1. Descriptive statistics of the series for the period 1975–2012

Statistics	LY	LK	LHC	LX	LIMP
Mean	25.61	23.93	14.62	24.90	24.58
Median	25.52	23.78	14.58	24.73	24.68
Maximum	26.36	24.88	16.03	26.11	26.06
Minimum	24.56	22.99	13.23	23.86	22.95
Std. Dev.	0.48	0.53	0.78	0.69	0.88
Jarque-Bera	1.15	2.61	1.04	2.42	1.80
(Probability)	0.56	0.27	0.59	0.30	0.41
Observations	38	38	38	38	38

Source: Authors’ calculation

Figure 1. Patterns of the logarithms of the series over the period 1975–2012

Source: Gross domestic product and exports are taken from the WDI-World Bank, gross fixed capital formation and imports are taken from IFS-IMF (years 1999–2000 are taken from UAE National Bureau of Statistics and years 2010–2012 are taken from the WDI-World Bank). Population is obtained from the UAE National Bureau of Statistics.

Table 2. ADF, PP and SL test results at logarithmic level

	ADF	PP	SL
LY	−2.94^(a) [1]	−2.86^(a) {3}	−2.57^(a) [3]	1986 (17.44)
LK	2.62^(c) [0]	2.44^(c) {1}	−0.80^(b) [0]	2001 (3.16)
LHC	−2.44^(a) [1]	6.22^(c) {2}	−0.52^(b) [1]	2008 (19.45)
LX	2.35^(c) [0]	2.98^(c) {7}	−0.45^(b) [0]	1986 (−2.89)
LIMP	−2.77^(a) [1]	3.77^(c) {3}	0.08^(b) [1]	2001 (18.50)

*, **, ***Denote the rejection of the null hypothesis of a unit root at 10%, 5% and 1%, respectively. Numbers in [] corresponding to ADF and SL test statistics are the optimal lags, chosen based on the Schwarz information criterion (SIC). Bandwidth in {} (Newey-West automatic) uses the Bartlett kernel estimation method. Critical values for SL test are tabulated in Lanne, Lütkepohl, and Saikkonen (2002). The maximum lag length for the ADF test is found by rounding up P_max = [12* (T/100)^¼] = [12* (38/100) ^¼]≅ 9 (Schwert, 1989). For the ADF and PP tests, all the time series are tested for the unit root including intercept and trend (a), intercept only (b), and no constant or trend (c). The letters in parentheses indicate the selected model following Dolado, Jenkinson, and Sosvilla-Rivero (1990). The years in the table refer to the structural breaks. Numbers in () correspond to the t-statistics of the structural break coefficients.

Table 3. ADF, PP and SL test results at first difference

	ADF		PP	SL
DLY	−4.43^(b)*** [0]	−4.41^(b)*** {1}		−5.27^(b) *** [0]	1986 (−1.31)
DLK	−4.66^(c)*** [0]	−4.66^(c)*** {0}		−5.36^(b) *** [0]	2001 (2.08)
DLHC	−3.55^(b)** [0]	−3.58^(b)** {1}		−3.62^(b) *** [0]	2008 (2.10)
DLX	−4.66^(c)***[0]	−4.63^(c)*** {5}		−4.85^(b) ***[0]	1986 (−2.08)
DLIMP	−4.11^(b)***[0]	−4.09^(b)*** {3}		−4.49^(b) *** [0]	2001 (1.94)

*, **, ***Denote the rejection of the null hypothesis of a unit root at 10%, 5% and 1%, respectively. Numbers in [] corresponding to ADF and SL test statistics are the optimal lags, chosen based on the Schwarz information criterion (SIC). Bandwidth in {} (Newey-West automatic) uses the Bartlett kernel estimation method. Critical values for SL test are tabulated in Lanne et al. (2002). The maximum lag length for the ADF test is found by rounding up P_max = [12* (T/100)^¼] = [12* (38/100) ^¼]≅ 9 (Schwert, 1989). For the ADF and PP tests, all the time series are tested for the unit root including intercept and trend (a), intercept only (b), and no constant or trend (c). The letters in brackets indicate the selected model following Dolado et al. (1990). The years in the table refer to the structural breaks. Numbers in () correspond to the t-statistics of the structural break coefficients.

Table 4. Johansen’s cointegration test results

Hypothesized Number of Cointegrating Equations	Adjusted Trace Statistic	Critical Value
		1%	5%
r = 0	76.14**	84.45	76.07
r ≤ 1	47.93	60.16	53.12
r ≤ 2	23.93	41.07	34.91
r ≤ 3	10.19	24.60	19.96

Critical values are taken from Osterwald-Lenum (1992).

The model includes a restricted constant (model selection following Pantula, 1989)

*, ** and ***Indicate rejection at 10%, 5% and 1%, respectively

Table 5. DOLS estimation results (Equation 8)(8) $\begin{array}{rl}& L{Y}_t=c+\alpha L{K}_t+\beta LH{C}_t+\gamma L{X}_t+\delta LIM{P}_t+{\sum }_{i=-k}^{i=k}{\phi }_1\mathrm{\Delta }L{K}_{t+i}\\ & +{\sum }_{i=-k}^{i=k}{\phi }_2\mathrm{\Delta }LH{C}_{t+i}+{\sum }_{i=-k}^{i=k}{\phi }_3\mathrm{\Delta }L{X}_{t+i}+{\sum }_{i=-k}^{i=k}{\phi }_4\mathrm{\Delta }LIM{P}_{t+i}+{\epsilon }_{1\mathrm{t}}\end{array}$(8)

Dependent Variable	α	β	γ	δ
LYt	0.329***	− 0.063	0.395***	0.111
	(5.54)	(−0.955)	(7.471)	(1.452)

BG χ²(1) = 0.31, BG χ²(2) = 0.11, JB test = 0.82, $\mathrm{W}-\mathrm{h}\mathrm{e}\mathrm{t}{\chi }^2${12} = 0.82, ARCH(1) = 0.65, ARCH(2) = 0.92, ARCH(3) = 0.16. *, ** and *** indicate rejection at 10%, 5% and 1% respectively (t-statistics in parentheses).

Table 6. DOLS estimation results (Equation 9)(9) $\begin{array}{rl}& L{X}_t=c+\alpha L{K}_t+\beta LH{C}_t+\gamma L{Y}_t+\delta LIM{P}_t+{\sum }_{i=-k}^{i=k}{\phi }_1\mathrm{\Delta }L{K}_{t+i}\\ & +{\sum }_{i=-k}^{i=k}{\phi }_2\mathrm{\Delta }LH{C}_{t+i}+{\sum }_{i=-k}^{i=k}{\phi }_3\mathrm{\Delta }L{Y}_{t+i}+{\sum }_{i=-k}^{i=k}{\phi }_4\mathrm{\Delta }LIM{P}_{t+i}+{\epsilon }_{1\mathrm{t}}\end{array}$(9)

Dependent Variable	α	β	γ	δ
LXt	0.193**	0.048	0.465**	0.350***
	(2.56)	(0.63)	(2.59)	(3.83)

BG χ²(1) = 0.85, BG χ²(2) = 0.98, JB test = 0.21, $\mathrm{W}-\mathrm{h}\mathrm{e}\mathrm{t}{\chi }^2${11} = 0.99, ARCH(1) = 0.28, ARCH(2) = 0.63, ARCH(3) = 0.69. *, ** and ***Indicate rejection at 10%, 5% and 1%, respectively (t-statistics in parentheses).

Table 7. Short-run Granger causality test

	Source of Causality
	ΔLYt	ΔLKt	ΔLHCt	ΔLXt	ΔLIMPt	ALL
Dependent Variable	χ^2 (1)	χ^2 (1)	χ^2 (1)	χ^2 (1)	χ^2 (1)	χ^2 (4)
ΔLYt	-	3.126*	0.020	14.208***	3.427*	17.441***
ΔLKt	1.740	-	0.537	0.115	0.003	7.385
ΔLHCt	0.200	3.187*	-	0.026	0.517	4.378
ΔLXt	2.052	0.538	0.008	-	0.489	3.752
ΔLIMPt	0.053	0.641	1.182	1.132	-	6.953

*, ** and ***Indicate significance at 10%, 5% and 1%, respectively (df in parentheses). Diagnostic tests for the VECM model show that serial correlation is not present, while the residuals are multivariate normal and homoscedastic. In addition, the stability of the VECM is confirmed based on calculations of the inverse roots of the characteristic AR polynomial.

Figure 2. Plots of CUSUM and CUSUMQ for the estimated ECMs for economic growth and merchandise exports

Table 8. Causality based on the Toda-Yamamoto procedure

	Source of causality
	LY	LK	LHC	LX	LIMP	ALL
Dependent Variable	χ^2 (1)	χ^2 (1)	χ^2 (1)	χ^2 (1)	χ^2 (1)	χ^2 (4)
LYt	-	6.541**	0.650	2.480	0.122	14.879***
LKt	0.366	-	0.071	0.261	0.152	4.196
LHCt	0.016	2.475	-	0.114	0.032	3.935
LXt	0.136	4.359**	0.014	-	0.539	12.468**
LIMPt	0.042	0.938	0.227	1.857	-	5.529

*, ** and ***Indicate significance at 10%, 5% and 1%, respectively. The diagnostic tests for the select VAR(p) model prior to the application of the Toda-Yamamoto procedure show that serial correlation is not present, while the residuals are multivariate normal and homoscedastic.

Table A1. Johansen’s cointegration test with one structural break (year: 1986)

Hypothesized Number ofCointegrating Equations	Adjusted Trace Statistic	Critical Value
		1%	5%
r = 0	113.10***	93.24	86.07
r ≤ 1	52.83	67.99	61.75
r ≤ 2	30.23	46.78	41.45
r ≤ 3	13.70	29.50	25.02

Critical values are taken from Johansen, Mosconi, and Nielsen (2000). The model includes a restricted constant (model selection following Pantula, 1989). ***Indicates rejection at the 1% significance level.

Table A2. Johansen’s cointegration test with two structural breaks (years: 1986, 2001)

Hypothesized Number ofCointegrating Equations	Adjusted Trace Statistic	Critical Value
		1%	5%
r = 0	130.54***	106.19	98.49
r ≤ 1	69.57	79.00	72.22
r ≤ 2	44.15	55.70	49.86
r ≤ 3	23.63	36.17	31.24

Critical values are taken from Johansen et al. (2000). The model includes a restricted constant (model selection following Pantula, 1989). ***Indicates rejection at the 1% significance level.

Lanne, M., Lütkepohl, H., & Saikkonen, P. (2002). Comparison of unit root tests for time series with level shifts. Journal of Time Series Analysis, 23(6), 667–685.

 Web of Science ®Google Scholar

Schwert, G. W. (1989). Test for unit roots: A Monte Carlo investigation. Journal of Business and Economic Statistics, 7(2), 147–159.

 Web of Science ®Google Scholar

Dolado, J., Jenkinson, T., & Sosvilla-Rivero, S. (1990). Cointegration and unit roots. Journal of Economic Surveys, 4(3), 249–273.

 Google Scholar

Osterwald-Lenum, M. (1992). A note with quantiles of the asymptotic distribution of the maximum likelihood cointegration rank test statistics. Oxford Bulletin of Economics and Statistics, 54(3), 461–472.

 Web of Science ®Google Scholar

Pantula, S. G. (1989). Testing for unit roots in time series data. Econometric Theory, 5(2), 256–271.

 Web of Science ®Google Scholar

Johansen, S., Mosconi, R., & Nielsen, B. (2000). Cointegration analysis in the presence of structural breaks in the deterministic trend. Econometrics Journal, 3, 216–249.

 Google Scholar