Author Template for Journal Articles s6

SUPPLEMENTARY MATERIAL S1

GRAVITY EQUATION VERSUS DEMAND EQUATION FOR TOURISM DEMAND MODELLING

On of the most popular adaptations of the consumer theory for tourism consumption is described in Morley (1992) where it is assumed that the individual utility derives from the visits to different destinations as well as from the consumption of a vector of other goods. Analytically, the utility function can be represented as:

/ (1)

where is the utility that an individual from the origin i visiting a destination J during period t; are the number of visits by an individual from origin i to destination J during t; Qit is a vector of consumption of other goods; and and are vectors of site qualities referred to the origin and destination, respectively. The constraint attached to the choices of a particular destination can be expressed as follows:

/ (2)

where is the cost of visiting destination J for an individual from origin i during t; is the price vector of the consumption goods; and Mit is the personal income of the individual.

The constrained maximization of the utility can be solved to find optimum levels of consumption of the other goods and the number of trips between any specific origin to any specific destination. Analytically, the problem can be written as:

subj. to
, / (3)

The solution of the problem could be found though the maximization of the Lagrangian equation () that could be written as:

/ (4)

where is the Langrange multiplier. The first order conditions of this problem give the following set of equations:

/ (5)

The solution of this set of equations gives the optimum levels of consumption of the other goods (Q*) and number of trips between any specific origin to any specific destination (N*):

/ (6)

Once the individual demands have been determined, the aggregated demand can be obtained through the consideration of all the residents of a particular origin I visiting a particular destination J. Then:

/ (7)

Despite the problems related to the aggregation of individual demands (Morley 1995), in line with previous assumptions about the determination of the number of trips for an individual, the number of trips between origin country I to destination country J during time t can be written as:

/ (8)

It is important to highlight how expression (8) is equivalent to the formula used by Song, Witt & Li (2009, p.2) when representing the aggregated demand function for tourism but also to the gravity model used recently for analyzing tourism flows (Eilat & Einav, 2004; Gil, Llorca & Martínez, 2006 and 2007; Fourie & Santana, 2013; Neumayer, 2010; Vietze, 2012). Frequently, but not always, the key point for using different terminologies (‘Demand model’ versus ‘gravity model’) comes from the way in which this expression is explored. Then, when the interest of researchers and planners has been centred on forecasting accurately tourism demand, the variability of site qualities () becomes irrelevant and studies center their interest income and price variables using the terminology of demand equation.

In the context of climate change and tourism, the objective focuses on the effect of climate and tourism flows and consequently the spatial dimension represented by I and/or J has been recovered through the vectors and while price of other goods ( ) has became irrelevant. However, because tourism flows have been explored using aggregated tourist data for destinations and/or for departure countries (Maddison, 2001; Lise and Tol, 2002; Hamilton et al., 2005, 2007a and 2007b, Bigano et al. 2006b) bilateral determinants (like distance between countries) has not been considered and the terminology has remained as “tourism demand model”.

The terminology of “gravity equation” has recovered recently when structural factor has focused the research and distance between countries has been introduced as determining factor. Thus, for instance, Eilat & Einav (2004) analyzed the effect of destination risks, common border and common language in determining tourism flows between a set of countries. Gil, Llorca & Martínez (2006; 2007) investigated the role of embassies and sharing a common currency on tourism flows, respectively. Fourie & Santana (2013) estimated the effect of cultural affinity and ethic reunion. Neumayer (2010) analyzed the impact of visa restrictions on international tourism flows. While Vietze (2012) studied the impact of the religion affiliation to U.S. tourist arrivals. All these studies refer to the gravity equation when they present the methodology.

In any case, the main point is that both gravity and aggregated demand equations can be derived from the same theoretical background. The main differences come from the use of bilateral flows instead of aggregated flows to a destination (or from an origin), a circumstance that determines the possibility for using distance as price factor.

References

Bigano, A., Hamilton, J., Tol, R. (2006) The impact of climate holiday destination choice. Climatic Change, 76, 389–406.

Eilat, Y., Einav, L. (2004). The determinants of international tourism: a three dimensional panel data analysis. Applied Economics, 36, 1315-1328.

Fourie, J., Santana, M. (2013). Cultural affinity and ethnic reunion. Tourism Management, 36, 411-420.

Gil-Pareja, S., Llorca R., Martínez J.A. (2006). The impact of embassies and consulates on tourism. Tourism Management, 28, 355-360.

Gil-Pareja, S., Llorca R., Martínez J.A. (2007). The effect of EMU on tourism Review of International Economics, 15, 302-312.

Hamilton, J. Maddison, D., Tol, R.S.J. (2005a). The effects on climate change on international tourism. Climate Research 29: 245-254.

Hamilton, J., Maddison, D., Tol, R.S.J. (2005b). Climate change and international tourism: A simulation study. Global Environmental Change 15: 253-266.

Hamilton, J., Tol, R.S.J., (2007). The impact of climate change on tourism in Germany, the UK and Ireland: A simulation study. Regional Environmental Change 7: 161-172.

Lise, W., Tol, R.S.J., (2002). Impact of climate on tourism demand. Climatic Change 55: 429-449.

Maddison, D., (2001). In search of warmer climates? The impact of climate change on flows of British tourist. Climatic Change 49: 193-208.

Morley, C.L. (1992). A microeconomic theory of international tourism demand. Annals of Tourism Research, 19, 250-267.

Morley, C.L. (1995). Tourism demand: characteristics, segmentation and aggregation. Tourism Economics, 1, 315-328.

Neumayer, E. (2010). Visa Restrictions and Bilateral Travel. The Professional Geographer 62(2), 171-181.

Song, H., Witt, S.F., Li, G. (2009). The Advanced Econometrics of Tourism Demand. New York: Routledge.

Vietze, C. (2012). Cultural effects on inbound tourism into the USA: a gravity approach. Tourism Economics, 18, 121-138.

SUPPLEMENTARY MATERIAL S2

Table S2. Distributional effect of climate change on international tourism arrivals.

Country / Real 2007 weigth / 2080 Climate Change (Only Climate variables) / 2080 Climate Change (Climate variables +GDPpc growth)
A2 / B1 / B2 / A2 / B1 / B2
Albania / 0,128 / 0,113 / 0,130 / 0,127 / 0,048 / 0,128 / 0,093
Algeria / 0,198 / 0,029 / 0,078 / 0,061 / 0,045 / 0,178 / 0,115
Andorra / 0,249 / 0,333 / 0,332 / 0,338 / 0,054 / 0,188 / 0,132
Angola / 0,022 / 0,007 / 0,013 / 0,011 / 0,021 / 0,023 / 0,027
Antigua and Barbuda / 0,030 / 0,006 / 0,014 / 0,010 / 0,001 / 0,032 / 0,014
Argentina / 0,519 / 0,473 / 0,625 / 0,527 / 0,558 / 1,147 / 0,736
Armenia / 0,058 / 0,115 / 0,095 / 0,103 / 0,015 / 0,059 / 0,032
Australia / 0,642 / 0,171 / 0,341 / 0,288 / 0,110 / 0,194 / 0,167
Austria / 2,362 / 2,697 / 2,816 / 2,819 / 1,685 / 1,319 / 1,546
Azerbaijan / 0,083 / 0,066 / 0,077 / 0,074 / 0,022 / 0,185 / 0,103
Bahamas, The / 0,174 / 0,032 / 0,075 / 0,057 / 0,166 / 0,199 / 0,220
Bahrain / 0,561 / 0,095 / 0,217 / 0,166 / 0,051 / 0,141 / 0,100
Bangladesh / 0,033 / 0,016 / 0,023 / 0,021 / 0,005 / 0,022 / 0,015
Barbados / 0,065 / 0,014 / 0,031 / 0,024 / 0,171 / 0,498 / 0,229
Belarus / 0,012 / 0,012 / 0,015 / 0,015 / 0,001 / 0,006 / 0,003
Belgium / N.A. / N.A. / N.A. / N.A. / N.A. / N.A. / N.A.
Belize / 0,029 / 0,009 / 0,017 / 0,014 / 0,005 / 0,015 / 0,009
Benin / 0,021 / 0,012 / 0,016 / 0,015 / 0,009 / 0,018 / 0,021
Bermuda / 0,035 / 0,008 / 0,017 / 0,014 / 0,010 / 0,024 / 0,017
Bhutan / 0,002 / 0,005 / 0,004 / 0,004 / N.A. / N.A. / N.A.
Bolivia / 0,065 / 0,029 / 0,045 / 0,041 / 0,181 / 0,174 / 0,220
Bosnia and Herzegovina / 0,035 / 0,034 / 0,038 / 0,037 / 0,013 / 0,063 / 0,041
Botswana / 0,197 / 0,051 / 0,113 / 0,098 / 0,039 / 0,116 / 0,074
Brazil / 0,571 / 0,153 / 0,317 / 0,262 / 0,169 / 0,473 / 0,360
Brunei Darussalam / 0,020 / 0,028 / 0,010 / 0,015 / 0,007 / 0,037 / 0,020
Bulgaria / 0,586 / 0,558 / 0,600 / 0,626 / 0,699 / 0,682 / 0,772
Burkina Faso / 0,033 / 0,005 / 0,017 / 0,011 / 0,022 / 0,092 / 0,051
Cambodia / 0,213 / 0,089 / 0,151 / 0,133 / 0,124 / 0,239 / 0,208
Cameroon / 0,030 / 0,010 / 0,017 / 0,015 / 0,005 / 0,032 / 0,018
Canada / 2,039 / 10,155 / 5,567 / 6,477 / 6,956 / 2,469 / 3,323
Cape Verde / 0,030 / 0,010 / 0,016 / 0,013 / 0,009 / 0,021 / 0,017
Central African Republic / 0,002 / 0,000 / 0,001 / 0,001 / N.A. / N.A. / N.A.
Chad / 0,003 / 0,000 / 0,001 / 0,001 / N.A. / N.A. / N.A.
Chile / 0,285 / 0,424 / 0,407 / 0,427 / 0,404 / 0,585 / 0,473
China / 6,222 / 14,843 / 11,767 / 12,818 / 24,206 / 20,670 / 20,259
Colombia / 0,240 / 0,138 / 0,197 / 0,185 / 0,090 / 0,149 / 0,115
Comoros / 0,002 / 0,001 / 0,001 / 0,001 / N.A. / N.A. / N.A.
Congo / 0,006 / 0,002 / 0,003 / 0,003 / N.A. / N.A. / N.A.
Costa Rica / 0,225 / 0,091 / 0,142 / 0,127 / 0,215 / 0,303 / 0,301
Cote d'Ivoire / N.A. / N.A. / N.A. / N.A. / N.A. / N.A. / N.A.
Croatia / 0,973 / 0,754 / 0,910 / 0,874 / 0,551 / 0,570 / 0,703
Cuba / 0,241 / 0,064 / 0,123 / 0,102 / 0,169 / 0,248 / 0,263
Cyprus / 0,275 / 0,145 / 0,207 / 0,190 / 0,098 / 0,132 / 0,111
Czech Republic / 1,065 / 1,032 / 1,174 / 1,146 / 0,747 / 0,699 / 0,886
Denmark / 1,056 / 0,982 / 1,122 / 1,099 / 0,513 / 0,432 / 0,481
Dominica / 0,009 / 0,003 / 0,005 / 0,004 / 0,001 / 0,002 / 0,002
Dominican Republic / 0,453 / 0,153 / 0,261 / 0,223 / 0,189 / 0,461 / 0,306
Ecuador / 0,107 / 0,081 / 0,100 / 0,097 / 0,039 / 0,107 / 0,076
Egypt, Arab Rep. / 1,206 / 0,392 / 0,694 / 0,604 / 0,522 / 1,647 / 0,806
El Salvador / 0,152 / 0,071 / 0,112 / 0,104 / 0,040 / 0,053 / 0,049
Eritrea / 0,009 / 0,002 / 0,004 / 0,003 / 0,003 / 0,004 / 0,005
Estonia / 0,216 / 0,199 / 0,236 / 0,227 / 0,238 / 0,622 / 0,609
Ethiopia / 0,035 / 0,013 / 0,024 / 0,021 / 0,004 / 0,117 / 0,045
Fiji / 0,061 / 0,034 / 0,047 / 0,043 / 0,025 / 0,094 / 0,049
Finland / 0,400 / 0,544 / 0,563 / 0,592 / 0,320 / 0,247 / 0,287
France / 9,193 / 6,719 / 8,332 / 7,884 / 4,040 / 3,903 / 4,031
Gambia, The / 0,016 / 0,003 / 0,006 / 0,005 / 0,001 / 0,013 / 0,006
Georgia / 0,120 / 0,198 / 0,172 / 0,182 / 0,134 / 0,203 / 0,162
Germany / 2,777 / 2,570 / 2,988 / 2,911 / 1,522 / 1,319 / 1,476
Ghana / 0,067 / 0,013 / 0,031 / 0,026 / 0,029 / 0,058 / 0,062
Greece / 1,838 / 1,073 / 1,444 / 1,344 / 0,831 / 0,970 / 0,897
Grenada / 0,015 / 0,001 / 0,007 / 0,005 / 0,001 / 0,008 / 0,004
Guatemala / 0,185 / 0,099 / 0,152 / 0,137 / 0,020 / 0,044 / 0,036
Guinea / 0,003 / 0,001 / 0,002 / 0,002 / N.A. / N.A. / N.A.
Guinea-Bissau / 0,003 / 0,001 / 0,001 / 0,001 / N.A. / N.A. / N.A.
Guyana / 0,015 / 0,004 / 0,008 / 0,006 / 0,001 / 0,002 / 0,001
Haiti / 0,044 / 0,012 / 0,022 / 0,019 / 0,730 / 0,497 / 0,578
Honduras / 0,094 / 0,048 / 0,074 / 0,069 / 0,063 / 0,172 / 0,104
Hong Kong / 1,951 / 0,696 / 1,136 / 1,001 / 0,545 / 0,951 / 0,949
Hungary / 0,982 / 0,807 / 0,949 / 0,914 / 0,698 / 0,695 / 0,859
Iceland / 0,120 / 0,211 / 0,195 / 0,208 / 0,341 / 0,314 / 0,421
India / 0,578 / 0,204 / 0,331 / 0,298 / 0,370 / 1,429 / 0,716
Indonesia / 0,626 / 0,306 / 0,460 / 0,421 / 0,513 / 1,152 / 0,970
Iran, Islamic Rep. / 0,252 / 0,091 / 0,159 / 0,138 / 0,118 / 0,259 / 0,191
Iraq / 0,098 / 0,031 / 0,053 / 0,043 / 0,081 / 0,382 / 0,170
Ireland / 0,947 / 0,687 / 0,873 / 0,835 / 0,272 / 0,300 / 0,285
Israel / 0,235 / 0,118 / 0,172 / 0,160 / 0,102 / 0,258 / 0,169
Italy / 4,964 / 2,751 / 3,812 / 3,483 / 1,964 / 1,926 / 2,154
Jamaica / 0,193 / 0,038 / 0,087 / 0,068 / 0,106 / 0,390 / 0,250
Japan / 0,949 / 0,896 / 1,016 / 0,998 / 0,597 / 0,529 / 0,503
Jordan / 0,390 / 0,273 / 0,367 / 0,349 / 0,316 / 0,546 / 0,410
Kazakhstan / 0,441 / 0,574 / 0,580 / 0,580 / 0,817 / 0,927 / 0,947
Kenya / 0,192 / 0,067 / 0,113 / 0,099 / 0,125 / 0,133 / 0,159
Kiribati / 0,001 / 0,000 / 0,000 / 0,000 / N.A. / N.A. / N.A.
Korea, Rep. / 0,733 / 0,456 / 0,585 / 0,552 / 0,150 / 0,141 / 0,105
Kuwait / 0,033 / 0,008 / 0,016 / 0,013 / 0,011 / 0,033 / 0,022
Kyrgyz Republic / 0,188 / 0,766 / 0,447 / 0,515 / 0,184 / 0,194 / 0,218
Lao PDR / 0,130 / 0,073 / 0,102 / 0,094 / 0,115 / 0,163 / 0,147
Latvia / 0,188 / 0,188 / 0,214 / 0,215 / 0,108 / 0,313 / 0,199
Lebanon / 0,116 / 0,109 / 0,125 / 0,124 / 0,116 / 0,184 / 0,161