Modelling of nonlinear asymmetric effects of changes in tourism on economic growth in an autonomous small-island economy

Garrod, Brian; Almeida, António; Machado, Luiz

doi:10.2478/ejthr-2023-0013

Figures & Tables

GDP (constant prices; 103€) and Arrivals 1976–2019

Cumulative effects of tourism receipts on GDP

Asymmetry tests (‘Levels’ model)

Exog. var. (Level)	Long-run effect [+]			Long-run effect [−]
	coef.	F-stat	p>F	coef.	F-stat	p>F
Guestsd	0.001	8.698	0.004	−0.007	60.43	0.000
	Long-run asymmetry			Short-run asymmetry
	F-stat	p>F		F-stat	p>F
	31.96	0.000		5.257	0.023

Unit root tests with structural breaks test (Clemente et al_, 1998)

Variable	GDPramd
	du1	du2	(rho-1)	Const	Breaks	Conclusion
Coefficient	1848.71	1477.313	−0.08559	1344.68	66,106	I(1)
t-statistic	19.260	15.442	−2.855	-
p-value	0.000	0.000	−5.490		5% critical value
Variable	lnGDPramd
	du1	du2	(rho-1)	Const	Breaks	Conclusion
Coefficient	0.88582	0.57510	−0.17024	6.95088	50,91	I(*)
t-statistic	26.425	18.898	−3.673
p-value	0.000	0.000	−5.490		5% critical value
Variable	dlnGDPramd
	du1	du2	(rho-1)	Const	Breaks	Conclusion
Coefficient	0.00026	−0.01267	−0.18663	0.01408	44,140	I(0)
t-statistic	0.072	−3.210	−2.925
p-value	0.943	0.002	−5.490		5% critical value
Variable	Guests
	du1	du2	(rho-1)	Const	Breaks	Conclusion
Coefficient	329392.43145	478287.07218	−0.03461	3.71*105	62,102	I(1)
t-statistic	10.006	14.903	−1.508
p-value	0.000	0.000	−5.490		5% critical value
Variable	lnArrivalsd
	du1	du2	(rho-1)	Const	Breaks	Conclusion
Coefficient	0.62720	0.52407	−0.06774	12.81938	62,102	I(1)
t-statistic	16.182	13.871	−1.985
p-value	0.000	0.090	−5.490		5% critical value
Variable	dlnArrivalsd
	du1	du2	(rho-1)	Const	Breaks	Conclusion
Coefficient	−0.03432	0.03460	−0.32932	0.01114	131,135	I(0)
t-statistic	−3.815	3.714	−3.156
p-value	0.000	0.000	−5,490		5% critical value

Unit root tests with structural breaks (Bai & Perron; 1998, 2002)

	GDPramd			Lngdpram
Break Test	F-statistic	Break dates		F-statistic	Break dates
0 vs. 1	521,5253	2012Q2	1987Q4	412.4835	1987Q4	1987Q3
1 vs. 2	39.08879	1987Q4	2003Q4	356.4038	1997Q4	1996Q3
2 vs. 3*	65.76110	2003Q4	2011Q4	34.70772	2004Q1	2004Q1

Traditional unit root tests

ADF test
	Test statistic	1%	5%	10%	p-value	Conclusion
GDPram	−1.025	−3.486	−2.885	−2.575	0,7939	Unit root
lnGDPram	−4.490	−3.486	−2.885	−2.575	0.0002	No unit root
ΔlnGDP	−4.321	−3.486	−2.885	−2.575	0.0006	No unit root
Guests	−2.451	−3.486	−2.885	−2.575	0.9990	Unit root
lnGuests	−0.951	−3.486	−2.885	−2.575	0.7708	Unit root
ΔlnGDP	−3.923	−3.486	−2.885	−2.575	.00019	No unit root

Unit root tests with structural breaks (Zivot &Andrew, 1992)

8		Critical Values			Conclusion	Break
Variable	t	1%	5%	10%
lnGDPramd	−3.992	−5.34	−4.80	−4.58	I(1)	1987Q2
GDPramd	−4.596	−5.34	−4.80	−4.58		2009Q4
Arrivals	−4.066	−5.34	−4.80	−4.58	I(0)	2012Q2
lnArrivalsd	−5.175	−5.34	−4.80	−4.58		2008Q2

NARDL model

Model in logs	coeff.	t-sta	prob.	Model in levels	coeff.	t-sta	prob.
Constant				Constant
lnGdpt-1	−0.0617946	−4.39	0.000	Gdpt-1	−0.0826226	−6.19	0.000
lnGt-1⁺	0.0668194	2.11	0.037	TRt-1⁺	0.0001177	2.81	0.006
lnGt-1⁻	0.0631038	1.21	0.229	TRt-1⁻	0.0005806	5.48	0.000
LndGDP	0.7167527	11.29	0.000	dgdp	0.6413531	11.68	0.000
dlnGt+	0.2763233	1.48	0.141	dGt+	0.0009089	2.17	0.032
dlnGt-1+	−0.2286913	−0.97	0.333	dGt-1+	−0.0007912	−1.50	0.136
dlnGt-2+	−0.0507689	−0.22	0.824	dGt-2+	−0.0000488	−0.10	0.924
dlnGt-3+	−0.0143055	−0.06	0.952	dGt-3+	−0.0000943	−0.18	0.855
dlnGt-4+	0.3506473	1.50	0.137	dGt-4+	0.0013204	2.54	0.012
dlnGt-5+	−0.3761953	−2.04	0.044	dGt-5+	−0.0012687	−3.09	0.002
dlnGt-	0.3489861	0.98	0.330	dGt-	0.0006949	0.97	0.332
dlnGt-1-	−0.2399715	−0.55	0.582	dGt-1-	−0.000539	−0.60	0.550
dlnGt-2-	−0.0110366	−0.03	0.978	dGt-2-	−0.0002911	−0.33	0.743
dlnGt-3-	−0.0146184	−0.04	0.972	dGt-3-	−0.0005999	−0.67	0.503
dlnGt-4-	0.3083835	0.74	0.461	dGt-4-	−0.0017387	-1.94	0.054
dlnGt-5-	−0.1674042	−0.50	0.617	dGt-5-	0.0006251	0.87	0.383
time	−0.0000262	−0.05	0.960	time	1.805742	3.70	0.000
lneuropegdppcd	0.0207644	2.00	0.048	europegdppcd	0.0020522	1.87	0.063
program94	−0.0041191	−0.44	0.659	program94	4.479043	3.73	0.000
program00	−0.013331	−1.27	0.208	program00	5.729251	3.17	0.002
program07	−0.0267423	−2.24	0.027	program07	4.053956	1.82	0.071
program14	−0.0404413	−2.20	0.030	program14	3.086442	0.98	0.328
lnInflation	−0.0010019	−0.46	0.644	Inflation	−0.7801926	−1.88	0.062
_cons	0.2386126	2.11	0.037	_cons	5.635482	4.12	0.000
long-run asymmetric effects				long-run asymmetric effects
lnTR+	1.081	0.026		lnTR+	0.001	0.004
lnTR−	−1.021	0.201		lnTR−	−0.007	0.000
statistics and diagnostics				statistics and diagnostics
R2	0.7312			R2	0.7721
adj R2	0.6775			adj R2	0.7354
χ² sc	55.2	0.0554		χ² sc	52.18	0.0940
χ² nor	39.77	0.0000		χ² nor	1.287	0.2567
χ² het	0.5535	0.6468		χ² het	2.319	0.0781
χ² FF	38.15	0.0000		χ² FF	190.2	0.0000
tBDM	−43.942			tBDM	−6.1897
FPSS	65.278			FPSS	13.6448
WLR	0.003045	0.957		WLR	31.96	0.000
WSR	0.4803	0.490		WSR	5.257	0.023

ARDL output and tests

D.	Model in logs				Model in levels
gdpram1976d	Coef.	Std. err.	t	P>t	Coef.	Std. err.	T	P>t
ADJ
gdpram1976d
L1.	−0.0594771	0.0122647	−4.85	0.000	−0.0330029	0.0091816	−3.59	0.000
LR
arrivalsd
L1.	0.8091705	0.2351952	3.44	0.001	0.0040375	−.0010514	3.84	0.000
SR
gdpram1976d	0.6974089	0.0561645	12.42	0.000	0.6984926	.0549762	12.71	0.000
LD.
arrivalsd
D1.	0.207203	0.0908929	2.28	0.024	0.0007792	0.0002723	2.86	0.005
LD.	−0.1308579	0.0931934	−1.40	0.163	−0.0005403	0.0002726	−1.98	0.049
time	−0.0001365	0.0002144	−0.64	0.526	−0.3488995	0.4398681	−0.79	0.429
lnexchangerate	0.0160653	0.0084455	1.90	0.059	6.499078	4.891799	1.33	0.186
lneuropegdppcd	0.0242059	0.0080123	3.02	0.003	0.0015652	0.0010925	1.43	0.154
program07	−0.0115173	0.0065889	−1.75	0.083	−2.428 026	1.282889	−1.89	0.060
program14	−0.0191729	0.0098561	−1.95	0.054	−5.055188	0.197285	−2.56	0.011
lninflation	−0.0020383	0.001732	−1.18	0.241	−0.6519132	0.3604449	−1.81	0.072
Goodness of fit
_cons	−0.3830505	0.1785376	−2.15	0.034	−1.630177	1.90022	−0.86	0.393
R2	0.7153				0.7134
adj R2	0.6914				0.6936
F-bounds test
F	12,208				8,211
t	−4,849				−3,594
Model diagnostics
B.–G. LM test for autocorrelation	χ=0.005; p=0.9576				χ=1.376; p=0.2409
Durbin’s test for autocorrelation	χ=0.003; p=0.9595				χ=1.281; p=0.2577
B.–P./C.–W. test for heteroskedasticity	χ=38.09; p=0.0000				χ=3.53; p=0.0602
White’s test	chi(44)=68.94; p=0.5472				chi(44)=111.12; p=0.0034
C. & T. decomposition of IM-test
Heteroskedasticity	chi(2)= 68.94; p=0.5472				chi(2); 111.12; p=0,0043
Skewness	chi(2)=15.32; p=0.1681				chi(2)=36.79; p=0.000
Kurtosis	chi(2)=1.34; p=0.2462				chi(2)=1.34; p=0.2462
Total	chi(2)=85.86; p=0.4006				chi(2)=9.62; p=0.0019
Skewness and kurtosis tests for normality	chi(2)=73.25; p=0.0000				chi(2)=26.84; p=0.0000
Skewness	p=0.000				p=18.03
Kurtosis	p=0.000				p=0.000
Cumulative sum test for parameter stability					t=0.4793 ((1%)1.6276;(5%)1.3581;(10%)1.2238)
estimated break	199Q4 (p=261.2984; p=0.000)				2012Q2 (p=1043.050; p=0.000)

Granger causality test

Equation	Excluded	chi²	df	Prob > chi²
dlnGDP	dlnTR	11.785	2	0.005
dlnPIB	ALL	11.785	2	0.005
dlnTR	dlnGDP	2.0885	2	0.572
dlnTR	ALL	2.0885	2	0.574

Modelling of nonlinear asymmetric effects of changes in tourism on economic growth in an autonomous small-island economy

Figures & Tables

Figure 1:

Figure 2:

Asymmetry tests (‘Levels’ model)

Unit root tests with structural breaks test (Clemente et al_, 1998)

Unit root tests with structural breaks (Bai & Perron; 1998, 2002)

Traditional unit root tests

Unit root tests with structural breaks (Zivot &Andrew, 1992)

NARDL model

ARDL output and tests

Granger causality test

Paradigm

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