We take these two functional relationships to get equations linking arrivals ( _A_ ) and departures ( _D_ ) in a region solely to its average temperature ( _T_ ), in Celsius degrees: where _KA_ and _KD_ are country-specific constants, accounting for all other factors different from temperature. We calibrate these parameters on the basis of regional data on yearly arrivals, departures and average temperature.

We can see that both relationships are non-linear. The maximum number of arrivals is obtained at the optimal average temperature of 13.9°C. The minimum number of departures is obtained at 18.6°C. For increases in temperature below the 13.9°C threshold, arrivals increase and departures decrease, therefore a country gets a beneficial net inflow of foreign currency. The opposite is found for increases in temperature above the 18.6°C threshold. For variations between 13.9°C and 18.6°C, effects are ambiguous, not only because arrivals and departures push to different directions, but also because the average expenditure level of an incoming tourist may be different from the expenditure level of an outgoing tourist<sup>2</sup> .

We estimated changes in arrivals and departures for 1, 2, 3, 4 and 5 °C increases in average temperature from its baseline level, for all 140 countries and regions. Variations in arrivals multiplied by per capita expenditure minus variations in departures multiplied by per capita expenditure give a first estimate of changes in net foreign currency inflow.

Of course, changes can be be both positive and negative. Furthermore, summing up all changes does not typically gives a zero result. However, as it will be made clearer in Sub-section 6.3, if foreign currency flows are interpreted as international income transfers, we would actually need to impose that all variations sum up to one.

To this end, we scaled up or down all our estimates, by subtracting the average net inflow if positive, or adding it if it turns out to be negative. One possible interpretation of this ex-post rescaling is in terms of relative competitiveness, since flows are not only affected by local conditions, but also by conditions in competing destinations.

# _6.2 Results overview_

Our rescaled estimates of changes in net foreign currency inflows, relative to the 2011 GDP level, are displayed in Table A8 of the Appendix. These variations follows a rather non-linear path. Limited increases of temperature are beneficial but higher levels are detrimental in China, the Republic of Korea, Italy and Turkey. Vice versa, initial negative impacts turn positive at +5°C in Mongolia, Estonia, Lithuania, Slovak Republic, Slovenia, Bulgaria, Belarus, Romania and Kazakhstan.

Benefits are concentrated in a few countries. For example, at +3°C only 26 countries get an increase in tourism revenue, whereas as many as 97 countries experience a relative loss. Benefitted countries include North European and North American countries, Japan and the Russian Federation, which are all rich nations: tourism impacts have adverse distributional consequences.

Furthermore, the dispersion of income flows gets larger as temperature rises. The standard deviation of the distribution of net revenue inflows increases progressively from about 1.48 billions US$ at +1°C up to around 5.36 billions US$ at +5°C.

> 2 We estimated per capita expenditure data on the basis of IMF data on tourism revenue (IMF, 2014).

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