Discussion Paper No.325
Estimating the Effect ofMeteorological and Economic Factors on
Tourism Demand Seasonality in Japan
Kazuhiko NAKAHIRA
Associate Professor
Faculty of Economics
Meikai University

Masahiro YABUTA
Professor
Faculty of Economics
Chuo University

December 2019

INSTITUTE OF ECONOMIC RESEARCH
Chuo University
Tokyo, Japan

Estimating the Effect of Meteorological and Economic Factors
on Tourism Demand Seasonality in Japan(Preliminary Working Draft: Please do not cite or quote without permission of the authors.)

Kazuhiko NAKAHIRA
Associate Professor, Faculty of Economics,
Meikai University
E-mail: nakahira@meikai.ac.jp
Masahiro YABUTA
Professor, Faculty of Economics, Chuo University
E-mail: yabuta@tamacc.chuo-u.ac.jp
ABSTRACTThe tourism seasonality expressed by fluctuated number of visitors to a destination is affected by various
factors. Focusing on this aspect, this paper examines the tourism seasonality of western region in Japan
including Kyoto, Osaka, Hiroshima, Fukuoka, and Okinawa (or city of Naha in Okinawa prefecture) withthe data that possibly be the meteorological fundamentals and the economic factors. Concretely, theempirical investigation based on the panel data analysis by applying the so-called “two-way fixed effects
model” is implemented.
The empirical examination derives the results as follows. The estimation result of model 1 implies thatthe sightseeing place with small amount of rain might obtain comparatively a large tourism demand. The
average air temperature and the level of vitalization of regional economy do not work as the factors to get
the tourism demand. The estimation result based on the model 2 might describe that the tourism destination
with comfortable temperature is able to attract a large tourism demand, and the one with ample sunshine
also has a chance to obtain a large number of tourists. From a different aspect, meteorological factors might
have a certain impact on tourism demand but the economic variables that possibly be the seasonal factors
are not the critical determinants of tourism demand in Japan’s western region.
Key words: Tourism, Tourism demand, Seasonality, Panel regression
JEL Classification Code: C33, L83, O18, R58, Z38

1

1. Introduction
The aim of this study is to investigate how meteorological (or climatic) and economic factors affecttourism demand fluctuations and seasonality in western Japan’s typical tourism destinations. Seasonal
tourism fluctuation can be a serious problem since this topic is critical in that it destabilizes the employment,
tourism businesses, and the regional economy. In addition, various strategies and evaluations on tourism
management should be individually determined because some causes of tourism seasonality, which are
related to natural- and socio-economic factors, do not correspond with one another. In this respect, a policy
to mitigate seasonal fluctuation is required for stable and profitable management (Lee et al. (2008)). In thispaper, we analyze the factors that cause seasonal changes in tourism, focusing on climate and economic
factors. Policies that mitigate seasonal variations in tourism depend on what causes seasonal variations.
What causes the seasonal variation in tourism? The primary factor of seasonal variation is based on thegeographical environment and the climatic condition. Regarding this matter, Cuccia and Rizzo (2011)
analyze seasonality as one of the main phenomena having an effect on tourism and insist that it depends
on the features of both tourism demand and tourism destinations from the aspect of location and services
supplied. On the other hand, Kulendran and Dwyer (2010, 2012) focus on economic factors in addition tosome meteorological elements when they examine the influence of seasonal fluctuations on tourism. Oneof the essential literatures for studying seasonal variations in tourism is Baum and Lundtorp (2001). They
give a comprehensive analysis of the seasonal variation in tourism in terms of tourism facility
managements. Butler (2001) overviews the cause and effect of seasonal variations on tourism by pointing
out the practical difficulties of mitigation of variations. To carry on the spirits of these studies, our research
focuses on meteorological and economic factors to examine the tourism demand in western region ofJapan.
In this research, panel data analysis is conducted to analyze the tourism demand fluctuation with thebalanced panel data set. Technically, it is hard to make an exhaustive investigation of seasonality on
tourism demand by a simple panel data estimation. In this respect, we apply the so-called “two-way fixed
effects model” that reflects the individual effects and the period (time) effects on panel data regression.
The implication of our result can be used to investigate the efficient operation of tourism facilities andinfrastructures as the regional economic policy at the micro- and macro-levels.
The remainder of this paper is organized as follows. In Section 2, panel unit root test and panel regression
analysis by applying two-way fixed effects model are implemented. Finally, Section 3 summarizes ourresearch.
2. Panel Regression Analysis
2.1 The Data
This section describes the data set used in our empirical panel data analysis for the influence ofmeteorological and economic variables on tourism in Japanese western region. In our panel data set, each2variable includes 12 units (monthly series), and each unit has 120 months of data (from January 2000 to
December 2017), and 5 cross-sections are included – the cities of Kyoto, Osaka, Hiroshima, Fukuoka, andNaha (in the Okinawa prefecture). Our dataset is composed of the following variables.1
V: approximate total number of overnight guests (accommodation facilities with 10 or more employees);
prefectural data (Kyoto, Osaka, Hiroshima, Fukuoka, Okinawa), monthly, final figures (Transition
Table in Table 4-2, result of the survey “Overnight Travel Statistics,” (second preliminary estimate)January to December 2017, final report, the Japan Tourism Agency, Ministry of Land, Infrastructure,
Transport, and Tourism ).
R: amounts of rainfall (mm) at observation sites (in the cities of Kyoto, Osaka, Hiroshima, Fukuoka, andNaha (in the Okinawa prefecture)), monthly, issued by the Japan Meteorological Agency.
T: average air temperature (°C) at observation sites (in the cities of Kyoto, Osaka, Hiroshima, Fukuoka,
and Naha (in the Okinawa prefecture)), monthly, issued by the Japan Meteorological Agency.
S: total sunshine duration (hours) at observation sites (in the cities of Kyoto, Osaka, Hiroshima, Fukuoka,
and Naha (in the Okinawa prefecture)), monthly, issued by the Japan Meteorological Agency.
P: consumer price index, prefectural data (Kyoto, Osaka, Hiroshima, Fukuoka, and Okinawa), monthly,
original index, all items, base year = 2015, issued by the Ministry of Internal Affairs andCommunications.
I: indices of industrial production, prefectural data (Kyoto, Osaka, Hiroshima, Fukuoka, and Okinawa),
monthly, original index, manufacturing (Item Number: 2A00000000) (Kyoto and Osaka), mining andmanufacturing (Item Number: 2000000000) (Hiroshima, Fukuoka, and Okinawa), base year = 2010,
issued by each prefectural government office and the Ministry of Economy, Trade, and Industry.
“V” is the proxy variable for tourism demand and “I” is the proxy variable for the level of vitalization of
the regional economy. In addition, our empirical analysis focuses on western region in Japan, namely, on
the cities of Kyoto, Osaka, Hiroshima, Fukuoka, and Naha (in the Okinawa prefecture). The
meteorological variables, R, T, and S were observed at the observation sites of the Japan Meteorological
Agency in each area or city. Therefore, they represent a city-level or town-level data set. By contrast, theeconomic variables, V, P, and I reflect the prefectural-level data that were observed by several local
governmental offices. In this study, the prefectural-level items are regarded as proxy variables for city- or
town-level data for the empirical research based on the regional tourism.

1

The data on “approximate total number of overnight guests” can be retrieved from the website of the Japan Tourism
Agency,MinistryofLand,
Infrastructure,
Transport,
andTourism(http://www.mlit.zgo.jp/kankocho/siryou/toukei/shukuhakutoukei.html). The “amounts of rainfall,” “average airtemperature,” and “total sunshine duration” were obtained from the Japan Meteorological Agency’s website(https://www.data.jma.go.jp/gmd/risk/obsdl/index.php#). The “consumer price index” is available from the “e-stat”
website (https://www.e-stat.go.jp/dbview?sid=0003143513). The data on “Indices of Industrial Production(prefectural data)” can be retrieved from the website of the Ministry of Economy, Trade, and Industry(http://www.meti.go.jp/statistics/tyo/iip/chiiki/index.html).

3

In our study, logarithmic transformation (natural logarithm) is performed on all the variables listed above,
and a first difference of “P” (𝑙𝑛𝑃𝑡 − 𝑙𝑛𝑃𝑡−1 ) is taken in order to have the inflation rate (monthly change).
2.2. Panel Unit Root Test
In this section, we conduct the seasonal unit root test considering the chance that seasonal pattern of thevariables may change permanently due to some shocks.2 We apply the panel unit root test proposed by Im,
Pesaran, and Shin (2003). The specification of this test3 is as follows:∆𝛾𝑖,𝑡 = α𝑖 + 𝜌𝑖 𝛾𝑖,𝑡−1 + ∑n𝑘=1 ∅𝑘 ∆𝛾𝑖,𝑡−𝑘 + 𝛿𝑖 𝑡 + 𝜃𝑡 + 𝑢𝑖,𝑡 ,(1)(i = 1, .... , N and t = 1, .... , T)
where 𝛾: variable to be tested, α: intercept of unit element of panel, 𝑖: unit element of panel, 𝑡: timeelement of panel, 𝜌: coefficient to be tested for unit root, 𝜃: intercept of time element of panel, 𝑢: residual.
Im, Pesaran, and Shin's (2003) test needs separate Augmented Dickey-Fuller (ADF) unit root tests for
the N cross-section units, and their final test statistic is the average of each statistic across groups byfollowing a normal distribution. The null hypothesis is that all units are non-stationary, and the alternative
hypothesis is that a fraction of the series in the panel is to be stationary. In our study, if the test result showsa non-stationary pattern, first order or the eventual order of differencing of the variable and panel
cointegration analysis should be considered.
The result of the Im, Pesaran, and Shin's (2003) test is described in Table 1. The test statistics in thistable show the rejections of the null hypothesis4 at conventional level of significance, and the clear signsof being I(0) for all variables. Therefore, we need not consider the differencing of the variables and panel
cointegration test.
2.3. Estimation by the Two-way Fixed Effects Model
With the characteristics of the variables known, our research proceeds to examine whether themeteorological and economic fundamentals are the determinants of tourism demand for the Japanese
western region by panel regression analysis.
The standard linear regression for panel data analysis can be written as′
y𝑖𝑡 = 𝛽0 + 𝑥𝑖𝑡
𝛽 + 𝜀𝑖𝑡 ,(2)

where 𝑥𝑖𝑡 is a K-dimensional vector of independent variables. An i is for the individual (i = 1, .... , N) anda t is for the time period (t = 1, .... , T). The constant term 𝛽0 and the slope coefficient 𝛽 are identical for
all individuals and for time periods. The error term 𝜀𝑖𝑡 changes over individuals and time, and it captures
all unobservable elements that affect the dependent variable.

2

See Hylleberg, Engle, Granger, and Yoo (1990) for details.
The explanation of the model of Im, Pesaran, and Shin (2003) in this section is partially based on Asteriou (2015).
4
Rejection of null hypothesis for Im, Pesaran, and Shin's (2003) test means that some series are stationary or
converging to their means over time.
3

4

Table 1: Im, Pesaran and Shin Test (Exogenous variables: Individual effects, individual linear trends)
Variable (level)
test statistic
p-value
optimal lag for intermediate tests
ln V-2.22322
0.0131
0 to 12ln R-8.33159
0.00000 to 36
ln T-3.33811
0.00040 to 0ln S-17.7075
0.00000 to 1ln P – ln P(-1)-13.7518
0.0000
1 to 12ln I-4.301280.00000 to 11
Notes: Optimal lag length for intermediate ADF test is determined based on the modified AIC criterion.
P-values are computed by assuming asymptotic normality.
The random effects model is described by equation (2) and the assumption:
𝜀𝑖𝑡 = 𝛼𝑖 + 𝑢𝑖𝑡 ,(3)

where 𝑢𝑖𝑡 is presumed to be homoscedastic and uncorrelated over time. The 𝛼𝑖 is time invariant andhomoscedastic across individuals. This model also assume that the observable regressors in 𝑥𝑖𝑡 are notcorrelated with the unobservable elements in both 𝛼𝑖 and 𝑢𝑖𝑡 : in short, 𝐸{𝑥𝑖𝑡 𝜀𝑖𝑡 } = 0.
The fixed effects model includes individual-specific constant terms. Thus, the fixed effects model is
described by′y𝑖𝑡 = 𝛼𝑖 + 𝑥𝑖𝑡
𝛽 + 𝑢𝑖𝑡 ,(4)

where 𝛼𝑖 are fixed unknown constants that are estimated along with 𝛽, and 𝑢𝑖𝑡 is usually assumed to bei.i.d. over individuals and time. The individual intercepts 𝛼𝑖 are often expressed as fixed (individual)
effects and grasp all unobservable time-invariant differences across individuals. Further, 𝐸{𝑥𝑖𝑡 𝜀𝑖𝑡 } ≠ 0 is
assumed.
In our empirical research, the following two types of specification are applied ("𝑙𝑛" means the natural
logarithm):<Model 1>
𝑙𝑛𝑉𝑡 = 𝛼0 + 𝛼1 𝑙𝑛𝑅𝑡 + 𝛼2 𝑙𝑛𝑇𝑡 + 𝛼3 (𝑙𝑛𝑃𝑡 − 𝑙𝑛𝑃𝑡−1 ) + 𝛼4 𝑙𝑛𝐼𝑡 + 𝑒𝑡 ,(5)<Model 2>
𝑙𝑛𝑉𝑡 = 𝛼0 + 𝛼1 𝑙𝑛𝑇𝑡 + 𝛼2 𝑙𝑛𝑆𝑡 + 𝛼3 (𝑙𝑛𝑃𝑡 − 𝑙𝑛𝑃𝑡−1 ) + 𝛼4 𝑙𝑛𝐼𝑡 + 𝑒𝑡 .

(6)First, we should detect which is better for us to choose the fixed effects model or the random effects
model. The random effects model can be consistently estimated by both the fixed effects and the random
effects estimators. The random effects estimator would be preferred if we are sure that the individual
specific effect is certainly an unrelated effect, in short, the individual specific effect is random, and it isuncorrelated with the explanatory variables for all past, current, and future periods of the same person. The
Wu-Hausman test5 is constructed to find violation of the assumption for the random effects model that theindependent variables are orthogonal to the unit (individual) effects. If no correlation is found between the5

The explanation of the Wu-Hausman test in this section is mainly based on Greene (2017) and Verbeek (2018).

5

independent variables and the unit effects, then 𝛽̂𝐹𝐸 , estimates of 𝛽 in the fixed effects model, would beclose to 𝛽̂𝑅𝐸 , estimates of 𝛽 in the random effects model. The test statistic H describes the difference
between these two estimates:−1
𝐻 = (𝛽̂𝑅𝐸 − 𝛽̂𝐹𝐸 )′[𝑉𝑎𝑟(𝛽̂𝐹𝐸 ) − 𝑉𝑎𝑟(𝛽̂𝑅𝐸 )] (𝛽̂𝑅𝐸 − 𝛽̂𝐹𝐸 ),with the condition under the null hypothesis:
𝑉𝑎𝑟(𝛽̂𝐹𝐸 − 𝛽̂𝑅𝐸 ) = 𝑉𝑎𝑟(𝛽̂𝐹𝐸 ) − 𝑉𝑎𝑟(𝛽̂𝑅𝐸 ).

(7)
(8)

H follows chi-square distribution with degrees of freedom that equal to the number of regressors under thenull hypothesis of orthogonality. Rejection of null hypothesis6 implies that the two models are different
enough, and we do not prefer the random effects model.
The results of the Wu-Hausman tests for our two models (model 1 and model 2) are indicated in Table
2-1 and Table 2-2. The test statistics show the rejection of null hypotheses at 1% level of significance.
Considering these results, we prefer the fixed effects model for our two kinds of estimation. However, theWu-Hausman test has some weak points. For example, it is only valid under i.i.d. of error term and cannot
include time (period) fixed effects. Accordingly, we focus on the latter problem. In other words, we
implement the redundant fixed effects tests to detect the existence of both cross-section and period fixed
effects. Table 3-1 depicts the result of the test for model 1 and Table 3-2 shows the result for model 2,
respectively. The test statistics reveal that the null hypotheses with regard to the individual fixed effects
and the period fixed effects are rejected. In addition, the joint null hypotheses are also rejected. These
results imply that there exist the individual effects7 and the period (time) effects in the context of the fixed
effects model. Therefore, we have to choose the so-called “two-way fixed effects model,” rather than theusual one-way fixed effect model for our estimation. The two-way fixed effects model is described by the
specification:
Y𝑖𝑡 = α + 𝛽𝑥𝑖𝑡 + 𝛾𝑖 + 𝜇𝑡 + 𝜀𝑖𝑡 ,𝜀𝑖𝑡 ~𝑁(0, 𝜎 2 ),

(9)

(10)

where 𝛾𝑖 is for the individual fixed effects, and 𝜇𝑡 stands for the period fixed effects.
The results of the estimations for model 1 and model 2 by following the “two-way fixed effects model”
using our balanced panel data set are displayed in Table 4-1 and Table 4-2. Considering the result of model
1, only two variables (except constant term) are significantly estimated and the other variables are
insignificant among the explanatory variables that reflect meteorological and economic conditions ofwestern region of Japan. The rainfall as the meteorological factor is significant at 1% level of significancewith a negative sign. On the other hand, the inflation rate as an economic element is barely significant at
10% level with a positive sign. If we enlarge on these points, we have the following implications. In the

6

Precisely speaking, rejection of null hypothesis should not directly be the evidence for the comparative advantage ofthe fixed effects model. For the lower power with respect to the severe pretest bias of the Wu-Hausman test, see
Guggenberger (2010).
7
Because of the existence of individual fixed effects, pooled estimation is inappropriate for us.

6

Table 2-1: Wu-Hausman Test for model 1
chi-sq. statistic chi-sq. d.f. p-value
1833.479672
40.0000
Table 2-2: Wu-Hausman Test 2 for model 2
chi-sq. statistic chi-sq. d.f. p-value
1909.522834
40.0000
Table 3-1: Redundant Fixed Effects Tests (cross-section and period fixed effects) for model 1
F / χ2
Statisticd.f.
p-valuecross-section F
2159.367481(4,468)0.0000cross-section χ21766.056572
40.0000period F
19.645116(118,468)
0.0000period χ21061.443252
118
0.0000cross-section / period F
90.453778(122,468)
0.00002
cross-section / period χ
1905.146109
1220.0000
Table 3-2: Redundant Fixed Effects Tests (cross-section and period fixed effects) for model 2
F / χ2
Statisticd.f.
p-valuecross-section F
2176.697085(4,468)0.00002
cross-section χ
1770.569053
40.0000period F
19.453353(118,468)
0.0000period χ21056.591122
118
0.0000cross-section / period F
92.627406(122,468)
0.0000cross-section / period χ21918.706703
1220.0000season that the sightseeing area has small amount of rain, the area might obtain comparatively a large
tourism demand. The average air temperature and the level of vitalization of regional economy do notwork at all in the case of model 1.
With respect to the model 2, two variables (except constant term) are significant. The average airtemperature is significantly estimated at 5%, while the total sunshine duration is significant at 1%. These
two have positive sighs. This result might describe that the tourism destination with comfortabletemperature is able to attract a large tourism demand, and the one with ample sunshine has a chance toobtain a large number of tourists. From a different aspect, meteorological factors might have certain
impacts on tourism demand while the economic variables that possibly be the seasonal factors are not the
crucial determinants of tourism demand in Japan’s western region.
On the whole, the result of model 1 shows that the rainfall as the meteorological factor is significant at
1% level of significance with a negative sign and the inflation rate as an economic element is barely
significant at 10% with a positive sign. This result implies that the sightseeing place with small amount ofrain might obtain comparatively a large tourism demand. The average air temperature and the level ofvitalization of regional economy do not work as the factors to get tourism demand. The estimation result

7

Table 4-1: Panel Regression Analysis (with cross-section and period fixed effects) for model 1
effects specification: cross-section fixed and period fixed effects (two-way model)
variablecoefficientstd. error
t-statistic
p-valueconst.
13.93036
0.254616
54.71121
0.0000ln R-0.029911
0.008241-3.629442
0.0003ln T
0.012778
0.028989
0.440781
0.6596ln P － ln P(-1)
4.659875
2.504988
1.860238
0.0635ln I
0.011936
0.060871
0.196082
0.8446R-squared
0.962168Log likelihood
611.0713
Adj. R-squared
0.951983
F-statistic
94.46456
S.E. of regression
0.097695
Prob (F-statistic)
0.000000
Sum squared resid.
4.466760
Notes: Dependent Variable: visitors. Method: Panel Least Squares. Sample: 2000: M1(January) – 2017: M12 (December). Periods included: 119. Cross-sections included: 5.
Total panel (balanced) observations: 595.
Table 4-2: Panel Regression Analysis (with cross-section and period fixed effects) for model 2
effects specification: cross-section fixed and period fixed effects (two-way model)
variablecoefficientstd. error
t-statistic
p-valueconst.
13.01391
0.293187
44.38777
0.0000ln T
0.060386
0.030563
1.975757
0.0488ln S
0.128705
0.025045
5.138918
0.0000ln P － ln P(-1)
3.519560
2.464457
1.428128
0.1539ln I
0.011319
0.060051
0.188491
0.8506R-squared
0.963181
Log likelihood619.1441
Adj. R-squared
0.953268
F-statistic
97.16516
S.E. of regression
0.096379
Prob (F-statistic)
0.000000
Sum squared resid.
4.347182
Notes: Dependent Variable: visitors. Method: Panel Least Squares. Sample: 2000: M1(January) – 2017: M12 (December). Periods included: 119. Cross-sections included: 5.
Total panel (balanced) observations: 595.
based on the model 2 might describe that the tourism destination with comfortable temperature is able toattract a large tourism demand, and the one with ample sunshine has a chance to obtain a large number oftourists. From a different perspective, in Japan’s western region, meteorological factors might have certain
impacts on tourism demand but the economic variables that possibly be the seasonal factors are not thecritical determinants of tourism demand.
3. Concluding Remarks
The tourism seasonality expressed by fluctuated number of visitors to a destination is affected by various
factors. Focusing on this aspect, this paper examines the tourism seasonality of western region in Japan
including Kyoto, Osaka, Hiroshima, Fukuoka, and Okinawa (or city of Naha in Okinawa prefecture) with8

the data that possibly be the meteorological fundamentals and the economic factors. Concretely, theempirical investigation based on the panel data analysis by applying the so-called “two-way fixed effects
model” is implemented.
The empirical examination by the panel data analysis based on “two-way fixed effects model” derived
the results as follows. The estimation result of model 1 (with rainfall, temperature, inflation rate, and levelof vitalization of the regional economy, as the explanatory variables) shows that the rainfall as themeteorological factor is significant at 1% level of significance with a negative sign and the inflation rate
as an economic element is barely significant at 10% with a positive sign. This result implies that thesightseeing place with small amount of rain might obtain comparatively a large tourism demand. The
average air temperature and the level of vitalization of regional economy do not work as the factors to get
the tourism demand. The estimation result based on the model 2 (with temperature, sunshine duration,
inflation rate, and level of vitalization of the regional economy, as the explanatory variables) might
describe that the tourism destination with comfortable temperature is able to attract a large tourism demand,and the one with ample sunshine has a chance to obtain a large number of tourists. From a different aspect,
meteorological factors might have certain impacts on tourism demand but the economic variables thatpossibly be the seasonal factors are not the critical determinants of tourism demand in Japan’s westernregion.
The implication of our result might be applied to the efficient operation of tourism facilities andinfrastructures as the regional economic policy at the micro- and macro-levels. However, a naturalextension and further investigation of our research are required since the empirical analysis in this paper
has some unclear results.
Acknowledgment
This research was supported by the Ministry of Education's Scientific Research Fund (Grant-in-Aid for
Scientific Research (C), No.17K02127, 2017/4-2020/39.
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