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

Brian Garrod
Brian Garrod
, 
António Almeida
António Almeida
 e 
Luiz Machado
Luiz Machado
   | 31 gen 2024
European Journal of Tourism, Hospitality and Recreation's Cover Image
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Article Category: Research Article
Pubblicato online: 31 gen 2024
Pagine: 154 - 172
Ricevuto: 21 lug 2023
Accettato: 03 ott 2023
DOI: https://doi.org/10.2478/ejthr-2023-0013
Parole chiave
© 2023 Brian Garrod et al., published by Sciendo
This work is licensed under the Creative Commons Attribution 4.0 International License.

Figure 1:

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

Figure 2:

Cumulative effects of tourism receipts on GDP
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
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