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Analysis of tourism trends in Spain
Pergamon
Annals of Tourism Research, Vol. 23, No. 4, pp. 739-754, 1996 CopyrIght 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0160-7383/96 $15.00+0.00
SOlSO-7383(96)00019-9
ANALYSIS OF TOURISM TRENDS IN SPAIN
University
Pilar Gonzailez Paz Moral of the Basque Country, Spain
Abstract: This paper studies the evolution of the international tourism demand for Spain in order to forecast its trends. The analysis is carried out within the framework of structural time series models that are formulated in terms of unobserved components stochastically specified. A measure of the underlying rate of growth of the international demand is derived in order to evaluate whether the sector is in a period of expansion or recession. The empirical results show that the worst period of the crisis suffered at the end of the 80s by the industry is over now and the future prospects are optimistic in the short run. Keywords: international tourism demand, trend, seasonality, underlying rate of growth, Kalman filter. Copyright 0 1996 Elsevier Science Ltd R&urn& Analyse des tendances du tourisme en Espagne. Cet article examine I’tvolution de la demande internationale pour le tourisme en Espagne afin de prtvoir ses tendances. L’analyse est realiste dans le cadre des modeles de series temporelles structurelles qui sent formulees en tant que fonctions de composantes non observees et choisis au hasard. On fait une tvaluation du taux de croissance sous-jacent de la demande internationale pour determiner si le secteur est en expansion ou en recession. Les r&hats empiriques montrent que la plus mauvaise periode de crise, que I’industrie a soufferte a la fin des anntes 80, a fini et que les perspectives d’avenir sent encourageantes a court terme. Mots-cl&: demande de tourisme internationale, tendance, saisonalite, taux sous-jacent de croissance, filtre de Kalman. Copyright 0 1996 Elsevier Science Ltd.
INTRODUCTION The tourism sector is one of the most important industries in the world as far as employment and expenditures are concerned. Its spectacular development started in the 50s due to increases in the standard of living and in leisure time after the Second World War. The importance of tourism for the local economies depends on the country, but it is a key sector in the economic development strategy of many developing countries. In 1990, Spain was the fourth country as regards tourism earnings, following the United States, France, and Italy. Therefore, this sector is very important to the Spanish economy According to the Spanish Institute of Tourist Studies sources, tourism represented 8.09% of the GDP and 11.2% of the employment in 1990. Furthermore, the amount of foreign currency generated by tourism contributed to reducing the commercial deficit of the balance of Pilar Gonztiez, Ph.D. in economics, is currently a lecturer in the Department of Econometrics and Statistics (University of the Basque Country, 48015 Bilbao, Spain. Email [email protected]). Her articles have appeared in Journal of Forecasting, International Journal oj Forecasting, and Reuista Espniiola de Economia. Paz Moral is completing her Ph.D. in economics at the same university. Her research interests are in the areas of time series analysis and applied econometrics. She has published in the International Journal of Forecasting. 739
740
TOURISM TRENDS IN SPAIN
payments by 73.3% in 1992. However, the evolution of tourism in Spain has been irregular during the last 30 years. It grew very quickly during the 60s due to an attractive offer based on warm and sunny beaches, and low prices. The international demand, in particular, was one of the main factors in this spectacular growth which has been crucial for the development of some Spanish regions. After the irregular behavior of the sector during the 7Os, the industry as a whole has known an expansion period during the 8Os, although it has suffered from quantitative and qualitative changes on both the demand and the supply sides. In this sense, there has been an important increase in the domestic demand, while international tourism began to decrease in the late 80s. The purpose of this paper is to study quantitatively the evolution of international tourism demand within the framework of time series analysis. The objectives are focused, first, on the analysis of the recession suffered by the sector and the strength of its recovery and, second, on forecasting the prospectives for the tourism industry in Spain in the short run. Univariate time series models are very simple since the information set consists only of the past values of the series considered and it is impossible to perform any causal analysis. Nevertheless, there are two good reasons for choosing to model a univariate time series: to provide a description of the series and to forecast future observations. The extraction of the main elements of the series may help to identify important aspects of its evolution. The estimation of the trend allows one to analyze more clearly the long-term movements of the series that can be hidden in the raw data due to their greater variability. The analysis of the seasonal behavior may also be of interest in a series like tourism demand in Spain which is very much affected by climatic cycles. On the other hand, although prediction from a univariate model is naive in the sense that it is just an extrapolation of past movements, it is often quite effective and it provides a yardstick against which the performance of more elaborate models may be assessed. This study of international tourism demand will be carried out within the framework of structural time series models. The main characteristic of these models is that they are formulated in terms of unobservable components which have a direct interpretation as trend, are of interest in themselves to the seasonality, etc., and that economists. Once the unknown parameters of the model are estimated, it is quite easy to compute the components of interest of the series, and to forecast future values for both the series and its components. The first problem met in the analysis of the international tourism sector is the election of a reliable indicator of the external demand. According to standard definitions, tourism can be said to include all the goods and services that any tourist consumes while traveling. Since tourism demand is a conglomerate of goods and services, the variable is not directly observable and a proxy has to be used. International tourism demand is generally measured in terms of tourist expenditures or the numbers of visits from a given country to a foreign destination. This paper will focus on the specification and estimation of a time series model for the tourist expenditures variable which is, in principle, the most appropriate indicator of the amount of tourist services consumed in a country. The analysis of its evolution over the
GONZALEZ
AND MORAL
741
last 16 years (1979-1994) is p er f ormed by means of the estimated seasonal and trend components. Special attention is given to the derivation of a smoothed measure of the growth rate of the trend that enables distinction between periods of expansion and recession of the sector. However, it has to be taken into account that total tourist expenditures measures a global quantity. It can be expressed as the product of three factors: the number of tourists, average length of stay, and average expenditure per diem. Since one cannot readily obtain information about the length of stay or the expenditure per diem, the number of tourists data will be analyzed later in this paper to complement the study of the international tourism demand as a whole. ANALYSIS
OF TOURISM
IN SPAIN
A good indicator for the real demand for tourism services could be obtained by carrying out surveys to draw information about tourist expenditures in accommodation, transport, food, entertainments, etc., as it is done in some countries such as the United States, Canada, the United Kingdom, and elsewhere. But there is no such information available in Spain and a proxy has to be used. The data chosen to measure the tourist expenditures variable has been the Tourism and Travel Receipts series taken from the balance of payments statistics. This variable includes all the banking operations related to buying foreign currency bought by non-resident travelers (unless they explicitly declare another use) and other operations difficult to classify statistically, The analysis of this series is important for the institutions and governments because the expenditure in foreign currency is a major item of the balance of payments, representing in 1990, for example, 18.6% of revenue in the current account balance and 49.1% in the services balance. The i%ui.sm and Travel Receipts series is published by the Bank of Spain Economic Statistics in current pesetas. In order to work in real terms, the data should be deflated by a measure of the tourists’ cost of living. One problem with the models for the international tourism demand is that the appropriate variable to measure tourism price is by no means clear (Martin and Witt 1987). Theoretically, the variable should consist of an exchange rate adjusted price of the “basket” of goods and services bought by tourists. Although some attempts have been made to incorporate in tourism demand models a specific tourists’ cost of living variable (Witt 1980), the Consumer Price Index (CPI) is the proxy used, in general, on the grounds of lack of more suitable data (Kwack 197‘2; Summary 1987; Uysal and Crompton 1984). The Spanish Bureau of Tourist Studies compiles a monthly unpublished Tourist Price Index (TPI), starting from 1971. This index is compiled from the same disaggregated price indexes from which the CPI is prepared, but with a system of weights that are taken from the input-output tables for tourism produced by the Secretaria General de Turismo. The TPI index has been used as a deflator for nominal tourist expenditures (Espasa and Cancel0 1993; Espasa, Gomez-Churruca and JareAo 1990). But this indicator is not free of problems. Since the same information is used as for the CPI, prices for goods and services, such as hotels and transport
TOURISM TRENDS IN SPAIN
742
(weighted by 53.81 and 22.59%, respectively), are biased upwards. The prices for these entries are taken from brochures and refer to the prices applied in cases of individual demand, while a large number of tourists come with “tour operators” who negotiate much lower prices. Furthermore, the TPI looks like a step function because the aforementioned brochures are usually revised only once a year, so the seasonal pattern of tourism prices is ignored. In this paper, the indicator chosen to measure the real tourist expenditures has been the monthly Tourism and TravelReceipts series deflated by the CPI (base 1985= 100). Model Spe@ation Views on time series modeling are based on the idea that the time series analyst should seek to identify the main observable features of the phenomena under study and incorporate in her/his model an explicit allowance for each of these main features. Visual inspection of graphs of time series usually reveals trends, seasonals, and cycles as important observable features of the data, and it seems desirable to model these characteristics explicitly. This may be achieved by formulating a model that decomposes the observed series into a set of elements of interest, that is: Observed
series
= f(trend,
seasonal,
cycle,
irregular),
where trends, seasonals, and cycles capture the “permanent” components of the series, while the irregular component represents the transitory variations not explained by the others. The models built in terms of unobserved components with a direct interpretation are called structural time series models (Engle 1978). The evolution of the monthly series of “Real Tourist Expenditures” from January 1979 to July 1994 shows a time structure which is typical of many socioeconomic variables. The most prominent characteristics of this series consist of an upward trend that represents the long-term movements in the series and a seasonal pattern that repeats itself more or less every year. The starting point for the construction of a structural model follows the representation:
where TE, is the Real Tourist Expenditures, and p,, ‘yl, and et are the trend, seasonal, and irregular components, respectively. The series TE, is measured in logarithms in order to homogenize the differences in variability observed in the raw data. Each component of the series can be modeled in several ways. A very simple specification for the trend component consists of a global deterministic linear trend, l-4 = CL + where these
Pt,
/..Land p denote the level and the slope, respectively. models are of very limited application. It does
However, not seem
GONZALEZ AND MORAL
743
reasonable to assume that the trend is deterministic since it implies that the series is constrained to move for ever around a deterministic function of time. Some authors (such as Espasa et al 1990) include ad hoc breaks in the trend as a response to solve these difftculties. This modeling allows for changes in the structure of the trend, but the points of break are chosen arbitrarily. The idea herein is that the specification should be flexible enough to allow the component to respond to general changes in the direction of the series. This could be done by setting up the model in terms of stochastic components. Espasa and Cancel0 (1993) include a stochastic trend implicitly in the model by taking first differences to the dependent variable, while others (such as Martin and Witt i988), use a lagged endogenous variable as a proxy for a habit persistence variable. The stochastic formulation proposed for the trend component is a flexible one since it allows the level p( and the slope /3, to evolve slowly over time (Harvey 1983):
where qt and 5, are normally independent white noise processes with zero mean and variances u,,’ and uc2, respectively. The seasonal component x is usually constructed in terms of deterministic dummy variables or sine-cosine waves. Take a seasonal pattern of length s and regard it as the sum of oscillations at the seasonal frequencies, A, = 27tj/s, j = 1, 2 ,..., s/2: s/2 3/l = _I&> j=l
(4)
xt = LYJcos hjt
+ /3, sin h,t,
j
= I,2 ,*.*, “.
2
This specification implies that the seasonal factors are constrained to be constant in time, that is yr = yt.,, while it seems that, in practice, there are certain facts that are smoothing the seasonal behavior: the increase in length of winter holidays or second holidays, weekends, the posibility of taking vacation out of the “high” season period. Therefore, by specifying the seasonal component stochastically, it can reflect the changes observed in the seasonal pattern of tourism demand during the sample period: s/2
Yt
=
c
Y.I”
j=l
TOURISM TRENDS IN SPAIN
744
where y;! is an artificial term that appears by construction, and oJl and 0;; are normal errors with zero mean and equal variance a,,,‘. Seasonahty changes slowly by means of a mechanism that guarantees that the sum of the seasonal factors over any consecutive s time periods has an expected value of zero and a variance that remains constant over time. The smaller the variance, the more stable the component. It would be more flexible to assume that the variance of each component r,, can be different. But little is lost in terms of goodness-of-fit by assuming that they are all equal, and the number of parameters to estimate is reduced enormously. The model specified by relations (I), (3), and (5) is known in the literature (Harvey and Todd 1983) as the basic structural model (BSM). The error terms q,, &, and w, are independent of each other and of the irregular component E,, assumed to be a normal white noise with zero mean and variance uE2. This model can be interpreted as a generalization of the classical linear regression model. to It can be observed that if crEE:! = ai’ = a,’ = 0, the BSM collapses variables given by a standard regression model (1) with explanatory a linear deterministic time trend (2) and a seasonal component built in terms of deterministic sine-cosine waves (4). Empirical Results The BSM was estimated with monthly data from January 1979 to December 1991, while available data from January 1992 to July 1994 have been kept to check the forecasting performance of the model. The unknown parameters of the model are given by the variances of the unobserved components TV,,p,, and yt and of the irregular term 4. From the technical point of view, it is interesting to note that all aspects of these models (parameter estimation, diagnostic checking, and forecasting) can be handled by putting them into state space form and using the Kalman filter (Harvey and Peters 1990). The results of the estimation of the parameters of the model with the STAMP package are the following: a;
= 0.00,
a5* = 0.83 x 1o-“,
a: = 0.11
(0.41 x 10-y
x
10-4,
(0.43 x IO-‘)
(7: = 0.40
x
1o-‘,
(0.66 x IO-‘)
where the figures in parentheses under the parameter estimates are asymptotic standard errors calculated in the frequency domain. The diagnostics are based on the innovations, or one-step-ahead prediction errors. If the model is well-specified, these innovations should be white noise: r(1)
= -0.03,
Q( 15) = 32.62,
H(47)
=
1.67,
N = 5.86,
where r( 1) is the first-order autocorrelation of the innovations; Q(P) is the Box-Ljung statistic, based on the first P autocorrelations; H is a heteroscedasticity test; and N is the Jarque and Bera statistic for testing normality which follows asymptotically a x2 distribution with 2 degrees of freedom under the null. It can be observed that
GONZALEZ AND MORAL
745
the diagnostics results are quite satisfactory. The parameter estimates are statistically significant and there is no statistical evidence of autocorrelation, heteroscedasticity, or non-normatility in the innovations. The following measures of goodness-of-fit have been computed: cr2 = 0.0082,
R:, = 0.82,
R2, = 0.25,
where a2 is the estimated one-step-ahead prediction error variance. The conventional coeffkient of determination, R2, is not very useful as a measure of goodness-of-fit when analyzing univariate time series that exhibit strong upward or downward trends and/or seasonal cycles. New coefficients of determination have been proposed in the literature (Harvey 1990): R& substituting the observations by their first differences, and, if the series presents seasonal behavior, Rg, substituting the observations by the first differences of the series around the seasonal means. The results show that the estimated BSM is able to explain 25% more of the variation of the real tourist expenditures variable than a very simple model that includes a lagged endogenous variable (as a proxy for a stochastic trend) and a deterministic seasonal component. The goodness-of-fit of the model in the post-sample period, January 1992-July 1994, was tested using the post-sample predictive test, E(I), based on the onestep-ahead prediction errors (Box and Tiao 1976), that approximately follows an F-distribution with (I, T-s-l) degrees of freedom. For the data in question, the value of the statistic was 0.74, which is clearly not significant. As far as the predictive power of the model is concerned, this result implies that the structure of the model is stable for the out of sample period. Once the parameters of the model have been estimated within the sample period, optimal predictions of future observations, together with their conditional mean squared errors, can be computed by applying the Kalman filter. The forecast function for the BSM model extrapolates into the future a local linear trend with a local seasonal pattern superimposed upon it:
TE,(l)
= mT + lb, + c.,.(l),
1 =
1, 2,...,
(6)
where 1 is the forecast horizon, mT and 6, are the estimates of the level and slope of the trend component at the end of the sample, given by 11.64 (in logarithms) and 0.83% respectively, and cT are the estimated seasonal factors: January=-0.10 May=O.OO September=0.27
February=-0.33 June = 0.02 October=O.22
March=-0.32 July=O.37 November=-0.18
April =-0. 11 August =0.48 December=-0.32.
The forecasting performance of the BSM is compared with two of the more commonly-used models in the time series analysis literature: the regression model (RM) and the ARIMA model. Predictions from January 1992 to July 1994 are computed for the deterministic
746
TOURISM TRENDS IN SPAIN
yOgI;Ve;)by
expressions (I), (2) and (4), and for the ARIMA(0, 1, which is the appropriate model for the TE, series. In orde’r tb astess the accuracy of the predictions for the three competing models, the root mean squared prediction errors (RMSEs) have been calculated with the following results: RMSE,,s,,=0.0081, RMSE,,,=0.0269, and RMSE~,,,~,=0.0155. It can be observed that the BSM model compares favorably with both the ARIMA and the deterministic RM. On the other hand, it should be noted that the models with stochastic trend and seasonal components, BSM and ARIMA, perform better than the deterministic model. In particular, it can be checked that the latter seems to generate far too optimistic predictions. This may be due to the fact that, although the forecast function for the standard regression model with deterministic components has the same structure given by equation (6), the trend and seasonal components that project are global in the following sense: the values for the level and the slope of the trend, m and b, respectively, and the seasonal factors c(l) are estimated globally giving the same weight to all the sample observations. However, in a structural time series model, the trend and seasonality are both local since they have been estimated as a weighted average of the observations, giving more weight to the more recent observations. Therefore, they are able to capture better the behavior of the series at the end of the sample. The extent to which past observations are discounted depends on the relative values of the variances of the components.
Evolution of the Components of the Series A descriptive analysis of the evolution of the international tourism demand may be provided in terms of trends and seasonalities, components that capture the “permanent” characteristics of the series. One may wish to examine the trend in order to identify the main movements which have taken place in the series and that may be hidden in the seasonal cycles and transitory shocks. The seasonal behavior of the series may also be of interest, and for some purposes it may be desirable to extract the seasonal component to produce a seasonally-adjusted series. The estimation of these unobserved components at all points throughout the sample is known in the literature as signal extraction. Traditionally, signal extraction has been carried out without recourse to a statistical model, via ad hoc procedures such as moving averages, etc. The advantage of working with an explicit statistical model, such as the structural time series models, is that all the underlying assumptions are clear and it is possible to adapt signal extraction to the particular characteristics of the series and to test the adequacy of the model to the available sample. Hence it is likely to yield a better description of the series and its components. The objectives here are to estimate the “permanent” components of the real expenditures variable and to forecast the trend and underlying growth in order to evaluate the future prospects of the international tourism demand. Since the BSM is formulated directly in terms of the unobserved components, once the
GONZALEZ AND MORAL
747
unknown parameters are estimated with data from January 1979 to July 1994, the extraction of the components is rendered trivial in practice by using smoothing algorithms based on the Kalman filter. The evolution of the seasonal component is very interesting for a series like TE,, which is very much affected by climatic cycles. Tourism in Spain exhibits a strong seasonal behavior that negatively affects its profit margin, since several touristic installations are forced to close during the low season. The fact that the development of the industry was based on the weather conditions, the so-called “sun and sea” market, has contributed to the concentration of tourism in the summer, mainly in August. Nevertheless, some considerations should be given to the evolution of the distribution of the seasonal factors throughout the year, since arrival frequency is becoming more homogeneous. The results show a reduction in the amplitude of the seasonal cycle, during the period 1979-94, due mainly to a lesser concentration of tourism in August (from 0.51 in 1980 to 0.46 in 1993) and to an increase in the winter seasonal factors (from -0.38 in 1979 to -0.33 in 1992 in February). The worst figures in winter are obtained in December, February, and March, while January presents much better results and can be considered a very promising month from a tourism point of view. Since the expenditures data are global, it cannot be said with certainty if this behavior is due to an increase in the number of tourists, the average length of stay, or the average expenditure per diem. It is interesting to note that the Easter holiday period does not seem to be of any particular importance as far as tourism performance is concerned. The analysis of the underlying evolution of the series can be performed by means of the extraction of the long-term signal. The trend component can be defined as the long-term movement once the cyclical and irregular components have been removed from the series. The estimated parameters of the model for tourist expenditures show that the trend of the series is quite stable with a fixed level and a slope that changes slowly over the sample period. The evolution of the trend estimated with information up to July 1994 (Figure 1) shows a sector growing during the beginning of the 80s and able to react firmly to the short stagnation periods, such as in 1985. Nevertheless, the situation changes dramatically from 1988 onwards, when a downward trend can be observed. The good results of 1991 mark the beginning of the recovery of the sector. The trend forecasts computed from August 1994 to July 1995 show good perspectives as far as the long-term evolution of tourism demand is concerned. Figure 1 also includes the trend computed with a shorter sample, from January 1979 to December 1991, and the corresponding forecasts from January 1992 to July 1994. The perspectives for the industry measured in terms of the trend forecasts computed in December 1991 turn out to be too optimistic when compared to the estimated trend based on actual observations. It should be noted that the sharp slope of the trend forecast in December 1991 cannot be found in the actual data during the year of 1992 and it is only recovered by the end of 1993. This is an interesting result if one
748
TOURISM TRENDS IN SPAIN
Figure
1. Trend
Component
takes into account that three international events took place simultaneously in Spain during 1992 that were expected to increase international arrivals: the Olympic Games in Barcelona, the World Exposition in Seville, and the appointment of Madrid as the European Culture Capital. It does not seem to have been the case. Furthermore, in relation to this topic, Figure 1 shows that the actual expenditures numbers did not exceed the forecasts as could have been expected. As a matter of fact, the actual figures were even worse than the forecasts, especially in summertime. This can be due to the fact that the expectations generated by these events resulted in an increase in prices for tourism services such as accommodation, restaurants, etc., that could have dissuaded the regular international tourist from visiting Spain in 1992. Since the behavior of the long-term component is so smooth, it will be of interest to analyze the evolution of the growth rates of the series that allow distinctions between periods of expansion and recession. The evolution of the growth rate of a monthly series could be measured by the series of monthly increments. Although this series contains all the information about the structure of growth of the series, it is not very useful as an indicator because it oscillates too much. On the other hand, when working with monthly or quarterly seasonal series, the analysis of growth is usually done by means of the annual rates due to institutional reasons and because, in this way, the movements related to the seasonal component are extracted. Since the variables are measured in logarithms, the annual rate of growth from monthly data may be approximated by the seasonal difference, G, = TE,Substituting
TE,_,, = A,2TE1.
TEt by the BSM model G, = S&)/L
+ S,&)E,
one
gets:
+ Am, + A,+,,
(7)
GONZ.kLEZ AND MORAL
where order
L is the lag operator 12, defined as:
and
749
S,,(L) is the sum lag operator
of
S,,(L) = 1 + L + L2 +...+ L”. The analysis of the growth of an economic time series is supposed to be able to extract the main aspects of an economic phenomenon, but the behavior of the series of annual rates, A,*TE(, is very irregular. One can propose a smoother measure of the growth of the series called underlying growth and defined (Fernandez-Macho 1990) as:
Formula (8) is one of the terms of the decomposition performed in equation (7); therefore, the underlying growth indicator /3,’ is a sensible one and it can be taken as a smoothed version of the raw annual growth rates. This measure also presents the advantage of being related to the long-term component of the series since, as the model is written in logs, the slope p, can be interpreted as the monthly growth rate of the trend. Both rates, the annual difference A,2TE1 and the underlying growth, &*, are not centered with respect to the monthly increments, that is, the maxima and minima of the cyclical oscillations of the series do not take place at the same time. It is necessary to center these rates, or to assign their value to the center of the interval. This fact implies that for computing the value of the underlying growth rate at moment t, it is necessary to use data up to moment t+5. Therefore, for the last periods of the sample, since there is not enough real data available, one will need to use predictions. The underlying growth of tourist expenditures estimated with the whole available sample from January 1979 to July 1994, is shown in Figure 2 (see the line denoted Ju194). Since the underlying growth series has to be centered, Figure 2 shows the estimated p,’ series
4.4
\
JUI bd 80
I81
Figure
I 82 I 83 I 84 I 25 I 86
2. Profiles
I 87
I 28 I89
of Tourism
I 00 I 91
Demand
-
JUlol
I 02 I 03
I 04 Cd
Growth
750
TOURISM TRENDS IN SPAIN
from July 1979 to January 1994 along with the forecasts from February 1994 to January 1995. It can be observed that after the great expansion experienced by the industry at the beginning of the 8Os, the growth of the sector is quite stable, but for the recession of 1984-85 that probably reflected the high increase in the cost of living in Spain in those years prior to joining the EEC. The first signs of crisis appeared very early, in 1986, with a high drop in the growth rates that are even negative from 1988 onwards. At the end of the 8Os, the recession seemed to touch bottom and the growth rates started increasing, but they were not positive again until 1991. The high growth rates at the beginning of the 90s experience a short period of recession during 1992, from which they recover in 1993. It would be interesting to complete the analysis of the industry evolution during the later years by studying several growth rate profiles computed with different sample sizes. The live lines displayed in Figure 2 represent the profiles estimated with samples all beginning in January 1979 and ending in October 1989, December 1990, December 1991, December 1992, and July 1994, respectively, along with the correspondent forecasts. Comparison of the growth projections computed at different points of time allows one to evaluate what the perspectives for the tourism sector were at each moment and how they have evolved in time. It can be seen that the expectations derived with data up to October 1989 were too pesimistic. There is no sign of recovery in the sector until December 1990. As a matter of fact, the results obtained that year allow one to forecast a moderate increment in the rates in the short term. The good results of the sector during the year 1991 lead to very optimistic forecasts for the growth rates that have to be revised downwards due to the recession in 1992. This result can be observed by comparing the lines Dec91 and Dec92 (Figure 2). The forecasts of the underlying growth profile computed with the whole sample, up to July 1994, suggest that the perspectives of tourism are quite optimistic, probably due to the quick recovery of the sector in 1993 onwards. A Time Series Model for the Number of Tourists The standard definition of an international tourist is “a person usually resident in another country who visits the destination country for a stay of 1 to 365 nights for any purpose other than following an occupation remunerated from within the destination country” (Baron 1984). International tourism demand in terms of number of arrivals may be measured by two indicators published monthly by the Spanish Bureau of Statistics: frontier entries and overnight stays in officially approved accommodations. Since it seems that the series of overnight stays can be underestimated, the “number of arrivals at Spanish borders” has been chosen as the indicator for the number of tourist visits, although it does not give any information about either the length of the stay or the quantity of the demand. In order to adjust the data to the definition of international tourist, only 45% of the French arrivals and 10% of the
GONZALEZ AND MORAL
751
Portuguese are considered as tourists, following the methodology provided by the Spanish Bureau of Tourist Studies. The evolution of the number of tourists series from January 1979 to June 1994 presents an upward trend and a strong seasonal behavior. The Easter holidays effect cannot be captured by the seasonal component due to its mobility so it has to be modeled separately. Furthermore, the strength and length of the Easter effect could be different depending on the month it takes place (e.g., March or April). In order to be able to pick up this effect, the model includes a dummy variable, EASTER, that takes the value one in the Easter month and zero otherwise. If the Easter period is split into March and April, the dummy variable takes the value 0.5 in each month. The time series model for the number of tourists is: NT, = p, + 3/1+ ~EASTER,+E,,
(9)
where NT, is the number of tourist series (in logarithms), the trend pu,is given by equations (3), the seasonal component 3/tby equations (5) and the irregular term follows an AR(l) process:
The results of the estimation able sample are the following: u2CL= 0.00,
a;
= 0.29 x lo-“, (0.15 x 10-i)
A = 0.16, (0.02)
of the model with the whole avail-
a2 = 0.12
x
10-4,
(0.32 x 10-y
a:=
0.12
x
10-2,
(0.25 X 10-3)
p = 0.44. (0.13)
It is interesting to note that the Easter effect is significant with an estimated coefficient of 0.16. Since one is dealing with a dummy variable, and the model is specified in logs, this result means that at Easter the number of tourists increase by 17%. The diagnostics are satisfactory in general. The large departure from normality (N=35.34) suggests the possibility of outliers. Looking at the residuals, two positive outliers were found, with normalized values 4.49 (July 1980) and 2.75 (August 1980). It has to be taken into account that at the beginning of the 80s the industry started to recover from the crisis of the 70s so quickly that it could not be captured immediately by the model. Concerning the analysis of the estimated “permanent” components of the series, although the results are very similar to those of the tourist expenditures variable, it can be interesting to point out some relevant differences in the behavior of both series. As far as the seasonal component is concerned, it makes even more evident the concentration of tourist arrivals in summer, although the amplitude of the seasonal cycle decreases by the end of the sample: from 0.98 in July and 0.94 in August of 1980 to 0.73 in July and 0.83 in August of 1983. It should also be noted that the evolution of the
152
TOURISM TRENDS IN SPAIN
seasonal component for the month of October is increasing steadily along the sample, becoming positive from 1988 onwards. All these facts can be interpreted as signs of homogenization of the seasonal behavior throughout the year. The best winter results can be found in December in contrast to the tourist expenditures series. The estimated seasonal factor for January, -0.46 in 1994, shows that the size of the seasonal factor of expenditures in this month must be due to longer periods of stay and/or bigger expenditures per diem, but not to a change in the seasonal behavior of the number of tourist visits. With regard to the long-term evolution of this series, the estimated parameters of the trend component show that it is quite stable. From the analysis of the underlying rate of growth, it may be concluded that the number of tourists was very sensitive to the economic crisis of 1982, not recovering the high growth rates until the end of 1984. The growth rate series started to decline in 1987 but at a slower rate than the series of expenditures and it only shows negative values for a short period at the end of the 8Os, 1989, starting the recovery in 1990 with high positive growth rates in 1991. After a period of stagnation in 1992, the growth rates of the tourist visits recovered quickly in 1993. This behavior may be a reflection of the fidelity that characterizes the international tourism that comes to Spain according to the results of the surveys that show that an important percentage of tourists repeat their visit for several years. CONCLUSIONS The BSM has proved to be a powerful tool to analyze the evolution of international tourism demand in Spain. This model is directly formulated in terms of unobserved components, such as trends and seasonalities, that are specified stochastically. Therefore, it is very easy to compute the components of interest at every point throughout the sample; and since they are locally estimated it is possible to observe how they evolve over time capturing the changes in the behavior of the series. In this sense, a global analysis of the raw expenditures data will indicate an increasing long-term behavior of the series, while the estimated local trend and underlying growth allow one to identify clearly the crisis suffered by the sector (with negative growth rates) at the end of the 80s and the rapid recovery of the growth rates after the good results of 1991. On the other hand, it has been observed that, although the international tourism demand is still highly concentrated in summer, the distribution of the seasonal factors throughout the year is becoming more homogeneous. Factors such as the increase in the length of “second holidays”, the possibility of vacations out of the high season period, and the increase in the standard of living in developed countries that allows retired people to spend part of the year in warm countries are extremely positive because they mean a more efficient use of the Spanish tourism resources. Two indicators have been used as proxies for external tourism demand: real tourist expenditures and number of tourists. Since
GONZALEZ
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tourist expenditures is a global indicator that includes number of tourists, average length of stay, and average expenditure per diem, the separate study of the number of tourists variable allows for more precision when interpreting the results. Furthermore, the estimation of trends, seasonalities, and underlying growth yield results that are somewhat different for the two series, making the analysis of both indicators complementary. The Easter vacation effect, for example, is not noticeable in the expenditures variable. However, this does not mean that it does not exist; there is a significant increase in the number of tourists, but it is not reflected in expenditures because the period of stay is too short. The same reasoning can be applied to Christmas results. Visual inspection of the underlying growth graphs of both indicators reveals some interesting points. It can be observed that the industry is recovering at the beginning of the 8Os, but the response of the two indicators to the economic crisis in 1982 is quite different; while the growth rates of expenditures remain stable, there is a clear recession in the number of visits. In relation to the serious crisis suffered by the industry at the end of the 8Os, it is detected in the expenditures series whose growth rates start declining at the beginning of 1986, while the number of tourists still shows positive increments. It should also be noted that the recession period in the number of visits is shorter and less profound than in the expenditures indicator. It may be concluded that the last crisis of international tourism demand did not start due to a reduction in visits but was due to shorter periods of stay and/or a reduction in the expenditures per diem. The industry starts its recovery in 1990, reaching positive growth rates in 1991. This period of expansion exhibits a sudden halt in 1992 that is reflected more seriously in the expenditure series, whose growth rates decline, than in the number of tourists variable, which remains quite stable. It is clear that all the important events (such as the Olympic Games and the World Exposition) were not able to improve the long-term behavior of external tourism demand. It has to be taken into account, on the one hand, that prices increased in this period due to the expectation of an increase in the number of visits while, on the other hand, most of the Spanish international tourism comes from Europe which was suffering an economic crisis in 1992. The evolution of tourism during 1993-94 is very promising, the growth rates are quite important and the perspectives are optimistic in the short run. It should be mentioned that the recovery of the industry during the first part of the 90s may have been favorably influenced by the political instability suffered by some countries of the Mediterranean area that have been direct competitors of Spain, such as Yugoslavia, Egypt, and Turkey. This possibility implies that one should evaluate the recent results with some care. On the other hand, it seems reasonable for the tourism authorities to continue implementing the political and economic measures taken at the end of the 80s to solve the critical situation of the tourism industry and designed to diversify the supply in order to attract a new type of tourist to Spain. 0 0
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REFERENCES Baron, R. R. V. 1984 Tourism Terminology and Standard Definitions. Tourist Review 39( 1):2%4. Box, G., and G. Tiao 1976 Comparison of Forecast and Actuality. Applied Statistics 25:195-200. Engle, R. 1978 Estimating Structural Models of Seasonality. liz Seasonal Analysis of Economic Time Series, A. Zellner, ed., pp. 281-308. Washington DC: National Bureau of Research Economics. Espasa, A., and J. T. Cancel0 1993 Metodos cuantitativos para el analisis de la coyuntura economica. Madrid: Alianza Economia. Espasa, A., R. Gbmez-Churruca, and J. Jarefio 1990 Un analisis de 10s ingresos por turismo en la economia espafiola. Working Paper No. 90.02. Madrid: Banco de EspaAa. Fern&es-Macho, F. J. 1993 Underlying Trends and Growth in Economic Variables. Estadistica Espat’ioia 126:73-98. Harvey, A. C. 1983 The Formulation of Structural Time Series Models in Discrete and Continuous Time. Ouestioo 7:563-575. 1990 Forecasting, St&ctural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press. Harvey, A. C., and S. Peters 1990 Estimation Procedures for Structural Time Series Models. Journal of Forecasting 9:89-108. Harvey, A. C., and P. Todd 1983 Forecasting Economic Time Series with Structural and Box-Jenkins Models. Iournal of Business and Economic Statistics 1:299-315. KwaTk, S. Y. 1972 Effects of Income and Prices on Travel Spending Abroad, 1960 III-1967 IV. International Economic Review 13:245-256. Martin, C., and S. F. Witt 1987 Tourism Demand Forecasting Models: Choice of Appropriate Variable to Represent Tourists’ Cost of Living. Tourism Management 8:233-246. 1988 Substitute Prices in Models of Tourism Demand. Annals of Tourism Research 15:255-268. Summary, R. 1987 Estimation of Tourism Demand by Multivariate Regression Analysis: Evidence from Kenya. Tourism Management 8:3 17-322. Uysal, M., and J. Crompton 1984 Determinants of Demand for International Tourist Flows to Turkev. Tourism Management 5:288-297. Witt, S. 1980 An Abstract Mode-Abstract (Destination) Node Model of Foreign Holiday Demand. Applied Economics 12:163-180. Submitted 10 November 1993 Resubmitted 12 December 1994 Accepted 12 May 1995 Refereed anonymously Coordinating Editor: Rebecca Summary
Annals of Tourism Research, Vol. 23, No. 4, pp. 739-754, 1996 CopyrIght 0 1996 Elsevier Science Ltd Printed in Great Britain. All rights reserved 0160-7383/96 $15.00+0.00
SOlSO-7383(96)00019-9
ANALYSIS OF TOURISM TRENDS IN SPAIN
University
Pilar Gonzailez Paz Moral of the Basque Country, Spain
Abstract: This paper studies the evolution of the international tourism demand for Spain in order to forecast its trends. The analysis is carried out within the framework of structural time series models that are formulated in terms of unobserved components stochastically specified. A measure of the underlying rate of growth of the international demand is derived in order to evaluate whether the sector is in a period of expansion or recession. The empirical results show that the worst period of the crisis suffered at the end of the 80s by the industry is over now and the future prospects are optimistic in the short run. Keywords: international tourism demand, trend, seasonality, underlying rate of growth, Kalman filter. Copyright 0 1996 Elsevier Science Ltd R&urn& Analyse des tendances du tourisme en Espagne. Cet article examine I’tvolution de la demande internationale pour le tourisme en Espagne afin de prtvoir ses tendances. L’analyse est realiste dans le cadre des modeles de series temporelles structurelles qui sent formulees en tant que fonctions de composantes non observees et choisis au hasard. On fait une tvaluation du taux de croissance sous-jacent de la demande internationale pour determiner si le secteur est en expansion ou en recession. Les r&hats empiriques montrent que la plus mauvaise periode de crise, que I’industrie a soufferte a la fin des anntes 80, a fini et que les perspectives d’avenir sent encourageantes a court terme. Mots-cl&: demande de tourisme internationale, tendance, saisonalite, taux sous-jacent de croissance, filtre de Kalman. Copyright 0 1996 Elsevier Science Ltd.
INTRODUCTION The tourism sector is one of the most important industries in the world as far as employment and expenditures are concerned. Its spectacular development started in the 50s due to increases in the standard of living and in leisure time after the Second World War. The importance of tourism for the local economies depends on the country, but it is a key sector in the economic development strategy of many developing countries. In 1990, Spain was the fourth country as regards tourism earnings, following the United States, France, and Italy. Therefore, this sector is very important to the Spanish economy According to the Spanish Institute of Tourist Studies sources, tourism represented 8.09% of the GDP and 11.2% of the employment in 1990. Furthermore, the amount of foreign currency generated by tourism contributed to reducing the commercial deficit of the balance of Pilar Gonztiez, Ph.D. in economics, is currently a lecturer in the Department of Econometrics and Statistics (University of the Basque Country, 48015 Bilbao, Spain. Email [email protected]). Her articles have appeared in Journal of Forecasting, International Journal oj Forecasting, and Reuista Espniiola de Economia. Paz Moral is completing her Ph.D. in economics at the same university. Her research interests are in the areas of time series analysis and applied econometrics. She has published in the International Journal of Forecasting. 739
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TOURISM TRENDS IN SPAIN
payments by 73.3% in 1992. However, the evolution of tourism in Spain has been irregular during the last 30 years. It grew very quickly during the 60s due to an attractive offer based on warm and sunny beaches, and low prices. The international demand, in particular, was one of the main factors in this spectacular growth which has been crucial for the development of some Spanish regions. After the irregular behavior of the sector during the 7Os, the industry as a whole has known an expansion period during the 8Os, although it has suffered from quantitative and qualitative changes on both the demand and the supply sides. In this sense, there has been an important increase in the domestic demand, while international tourism began to decrease in the late 80s. The purpose of this paper is to study quantitatively the evolution of international tourism demand within the framework of time series analysis. The objectives are focused, first, on the analysis of the recession suffered by the sector and the strength of its recovery and, second, on forecasting the prospectives for the tourism industry in Spain in the short run. Univariate time series models are very simple since the information set consists only of the past values of the series considered and it is impossible to perform any causal analysis. Nevertheless, there are two good reasons for choosing to model a univariate time series: to provide a description of the series and to forecast future observations. The extraction of the main elements of the series may help to identify important aspects of its evolution. The estimation of the trend allows one to analyze more clearly the long-term movements of the series that can be hidden in the raw data due to their greater variability. The analysis of the seasonal behavior may also be of interest in a series like tourism demand in Spain which is very much affected by climatic cycles. On the other hand, although prediction from a univariate model is naive in the sense that it is just an extrapolation of past movements, it is often quite effective and it provides a yardstick against which the performance of more elaborate models may be assessed. This study of international tourism demand will be carried out within the framework of structural time series models. The main characteristic of these models is that they are formulated in terms of unobservable components which have a direct interpretation as trend, are of interest in themselves to the seasonality, etc., and that economists. Once the unknown parameters of the model are estimated, it is quite easy to compute the components of interest of the series, and to forecast future values for both the series and its components. The first problem met in the analysis of the international tourism sector is the election of a reliable indicator of the external demand. According to standard definitions, tourism can be said to include all the goods and services that any tourist consumes while traveling. Since tourism demand is a conglomerate of goods and services, the variable is not directly observable and a proxy has to be used. International tourism demand is generally measured in terms of tourist expenditures or the numbers of visits from a given country to a foreign destination. This paper will focus on the specification and estimation of a time series model for the tourist expenditures variable which is, in principle, the most appropriate indicator of the amount of tourist services consumed in a country. The analysis of its evolution over the
GONZALEZ
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last 16 years (1979-1994) is p er f ormed by means of the estimated seasonal and trend components. Special attention is given to the derivation of a smoothed measure of the growth rate of the trend that enables distinction between periods of expansion and recession of the sector. However, it has to be taken into account that total tourist expenditures measures a global quantity. It can be expressed as the product of three factors: the number of tourists, average length of stay, and average expenditure per diem. Since one cannot readily obtain information about the length of stay or the expenditure per diem, the number of tourists data will be analyzed later in this paper to complement the study of the international tourism demand as a whole. ANALYSIS
OF TOURISM
IN SPAIN
A good indicator for the real demand for tourism services could be obtained by carrying out surveys to draw information about tourist expenditures in accommodation, transport, food, entertainments, etc., as it is done in some countries such as the United States, Canada, the United Kingdom, and elsewhere. But there is no such information available in Spain and a proxy has to be used. The data chosen to measure the tourist expenditures variable has been the Tourism and Travel Receipts series taken from the balance of payments statistics. This variable includes all the banking operations related to buying foreign currency bought by non-resident travelers (unless they explicitly declare another use) and other operations difficult to classify statistically, The analysis of this series is important for the institutions and governments because the expenditure in foreign currency is a major item of the balance of payments, representing in 1990, for example, 18.6% of revenue in the current account balance and 49.1% in the services balance. The i%ui.sm and Travel Receipts series is published by the Bank of Spain Economic Statistics in current pesetas. In order to work in real terms, the data should be deflated by a measure of the tourists’ cost of living. One problem with the models for the international tourism demand is that the appropriate variable to measure tourism price is by no means clear (Martin and Witt 1987). Theoretically, the variable should consist of an exchange rate adjusted price of the “basket” of goods and services bought by tourists. Although some attempts have been made to incorporate in tourism demand models a specific tourists’ cost of living variable (Witt 1980), the Consumer Price Index (CPI) is the proxy used, in general, on the grounds of lack of more suitable data (Kwack 197‘2; Summary 1987; Uysal and Crompton 1984). The Spanish Bureau of Tourist Studies compiles a monthly unpublished Tourist Price Index (TPI), starting from 1971. This index is compiled from the same disaggregated price indexes from which the CPI is prepared, but with a system of weights that are taken from the input-output tables for tourism produced by the Secretaria General de Turismo. The TPI index has been used as a deflator for nominal tourist expenditures (Espasa and Cancel0 1993; Espasa, Gomez-Churruca and JareAo 1990). But this indicator is not free of problems. Since the same information is used as for the CPI, prices for goods and services, such as hotels and transport
TOURISM TRENDS IN SPAIN
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(weighted by 53.81 and 22.59%, respectively), are biased upwards. The prices for these entries are taken from brochures and refer to the prices applied in cases of individual demand, while a large number of tourists come with “tour operators” who negotiate much lower prices. Furthermore, the TPI looks like a step function because the aforementioned brochures are usually revised only once a year, so the seasonal pattern of tourism prices is ignored. In this paper, the indicator chosen to measure the real tourist expenditures has been the monthly Tourism and TravelReceipts series deflated by the CPI (base 1985= 100). Model Spe@ation Views on time series modeling are based on the idea that the time series analyst should seek to identify the main observable features of the phenomena under study and incorporate in her/his model an explicit allowance for each of these main features. Visual inspection of graphs of time series usually reveals trends, seasonals, and cycles as important observable features of the data, and it seems desirable to model these characteristics explicitly. This may be achieved by formulating a model that decomposes the observed series into a set of elements of interest, that is: Observed
series
= f(trend,
seasonal,
cycle,
irregular),
where trends, seasonals, and cycles capture the “permanent” components of the series, while the irregular component represents the transitory variations not explained by the others. The models built in terms of unobserved components with a direct interpretation are called structural time series models (Engle 1978). The evolution of the monthly series of “Real Tourist Expenditures” from January 1979 to July 1994 shows a time structure which is typical of many socioeconomic variables. The most prominent characteristics of this series consist of an upward trend that represents the long-term movements in the series and a seasonal pattern that repeats itself more or less every year. The starting point for the construction of a structural model follows the representation:
where TE, is the Real Tourist Expenditures, and p,, ‘yl, and et are the trend, seasonal, and irregular components, respectively. The series TE, is measured in logarithms in order to homogenize the differences in variability observed in the raw data. Each component of the series can be modeled in several ways. A very simple specification for the trend component consists of a global deterministic linear trend, l-4 = CL + where these
Pt,
/..Land p denote the level and the slope, respectively. models are of very limited application. It does
However, not seem
GONZALEZ AND MORAL
743
reasonable to assume that the trend is deterministic since it implies that the series is constrained to move for ever around a deterministic function of time. Some authors (such as Espasa et al 1990) include ad hoc breaks in the trend as a response to solve these difftculties. This modeling allows for changes in the structure of the trend, but the points of break are chosen arbitrarily. The idea herein is that the specification should be flexible enough to allow the component to respond to general changes in the direction of the series. This could be done by setting up the model in terms of stochastic components. Espasa and Cancel0 (1993) include a stochastic trend implicitly in the model by taking first differences to the dependent variable, while others (such as Martin and Witt i988), use a lagged endogenous variable as a proxy for a habit persistence variable. The stochastic formulation proposed for the trend component is a flexible one since it allows the level p( and the slope /3, to evolve slowly over time (Harvey 1983):
where qt and 5, are normally independent white noise processes with zero mean and variances u,,’ and uc2, respectively. The seasonal component x is usually constructed in terms of deterministic dummy variables or sine-cosine waves. Take a seasonal pattern of length s and regard it as the sum of oscillations at the seasonal frequencies, A, = 27tj/s, j = 1, 2 ,..., s/2: s/2 3/l = _I&> j=l
(4)
xt = LYJcos hjt
+ /3, sin h,t,
j
= I,2 ,*.*, “.
2
This specification implies that the seasonal factors are constrained to be constant in time, that is yr = yt.,, while it seems that, in practice, there are certain facts that are smoothing the seasonal behavior: the increase in length of winter holidays or second holidays, weekends, the posibility of taking vacation out of the “high” season period. Therefore, by specifying the seasonal component stochastically, it can reflect the changes observed in the seasonal pattern of tourism demand during the sample period: s/2
Yt
=
c
Y.I”
j=l
TOURISM TRENDS IN SPAIN
744
where y;! is an artificial term that appears by construction, and oJl and 0;; are normal errors with zero mean and equal variance a,,,‘. Seasonahty changes slowly by means of a mechanism that guarantees that the sum of the seasonal factors over any consecutive s time periods has an expected value of zero and a variance that remains constant over time. The smaller the variance, the more stable the component. It would be more flexible to assume that the variance of each component r,, can be different. But little is lost in terms of goodness-of-fit by assuming that they are all equal, and the number of parameters to estimate is reduced enormously. The model specified by relations (I), (3), and (5) is known in the literature (Harvey and Todd 1983) as the basic structural model (BSM). The error terms q,, &, and w, are independent of each other and of the irregular component E,, assumed to be a normal white noise with zero mean and variance uE2. This model can be interpreted as a generalization of the classical linear regression model. to It can be observed that if crEE:! = ai’ = a,’ = 0, the BSM collapses variables given by a standard regression model (1) with explanatory a linear deterministic time trend (2) and a seasonal component built in terms of deterministic sine-cosine waves (4). Empirical Results The BSM was estimated with monthly data from January 1979 to December 1991, while available data from January 1992 to July 1994 have been kept to check the forecasting performance of the model. The unknown parameters of the model are given by the variances of the unobserved components TV,,p,, and yt and of the irregular term 4. From the technical point of view, it is interesting to note that all aspects of these models (parameter estimation, diagnostic checking, and forecasting) can be handled by putting them into state space form and using the Kalman filter (Harvey and Peters 1990). The results of the estimation of the parameters of the model with the STAMP package are the following: a;
= 0.00,
a5* = 0.83 x 1o-“,
a: = 0.11
(0.41 x 10-y
x
10-4,
(0.43 x IO-‘)
(7: = 0.40
x
1o-‘,
(0.66 x IO-‘)
where the figures in parentheses under the parameter estimates are asymptotic standard errors calculated in the frequency domain. The diagnostics are based on the innovations, or one-step-ahead prediction errors. If the model is well-specified, these innovations should be white noise: r(1)
= -0.03,
Q( 15) = 32.62,
H(47)
=
1.67,
N = 5.86,
where r( 1) is the first-order autocorrelation of the innovations; Q(P) is the Box-Ljung statistic, based on the first P autocorrelations; H is a heteroscedasticity test; and N is the Jarque and Bera statistic for testing normality which follows asymptotically a x2 distribution with 2 degrees of freedom under the null. It can be observed that
GONZALEZ AND MORAL
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the diagnostics results are quite satisfactory. The parameter estimates are statistically significant and there is no statistical evidence of autocorrelation, heteroscedasticity, or non-normatility in the innovations. The following measures of goodness-of-fit have been computed: cr2 = 0.0082,
R:, = 0.82,
R2, = 0.25,
where a2 is the estimated one-step-ahead prediction error variance. The conventional coeffkient of determination, R2, is not very useful as a measure of goodness-of-fit when analyzing univariate time series that exhibit strong upward or downward trends and/or seasonal cycles. New coefficients of determination have been proposed in the literature (Harvey 1990): R& substituting the observations by their first differences, and, if the series presents seasonal behavior, Rg, substituting the observations by the first differences of the series around the seasonal means. The results show that the estimated BSM is able to explain 25% more of the variation of the real tourist expenditures variable than a very simple model that includes a lagged endogenous variable (as a proxy for a stochastic trend) and a deterministic seasonal component. The goodness-of-fit of the model in the post-sample period, January 1992-July 1994, was tested using the post-sample predictive test, E(I), based on the onestep-ahead prediction errors (Box and Tiao 1976), that approximately follows an F-distribution with (I, T-s-l) degrees of freedom. For the data in question, the value of the statistic was 0.74, which is clearly not significant. As far as the predictive power of the model is concerned, this result implies that the structure of the model is stable for the out of sample period. Once the parameters of the model have been estimated within the sample period, optimal predictions of future observations, together with their conditional mean squared errors, can be computed by applying the Kalman filter. The forecast function for the BSM model extrapolates into the future a local linear trend with a local seasonal pattern superimposed upon it:
TE,(l)
= mT + lb, + c.,.(l),
1 =
1, 2,...,
(6)
where 1 is the forecast horizon, mT and 6, are the estimates of the level and slope of the trend component at the end of the sample, given by 11.64 (in logarithms) and 0.83% respectively, and cT are the estimated seasonal factors: January=-0.10 May=O.OO September=0.27
February=-0.33 June = 0.02 October=O.22
March=-0.32 July=O.37 November=-0.18
April =-0. 11 August =0.48 December=-0.32.
The forecasting performance of the BSM is compared with two of the more commonly-used models in the time series analysis literature: the regression model (RM) and the ARIMA model. Predictions from January 1992 to July 1994 are computed for the deterministic
746
TOURISM TRENDS IN SPAIN
yOgI;Ve;)by
expressions (I), (2) and (4), and for the ARIMA(0, 1, which is the appropriate model for the TE, series. In orde’r tb astess the accuracy of the predictions for the three competing models, the root mean squared prediction errors (RMSEs) have been calculated with the following results: RMSE,,s,,=0.0081, RMSE,,,=0.0269, and RMSE~,,,~,=0.0155. It can be observed that the BSM model compares favorably with both the ARIMA and the deterministic RM. On the other hand, it should be noted that the models with stochastic trend and seasonal components, BSM and ARIMA, perform better than the deterministic model. In particular, it can be checked that the latter seems to generate far too optimistic predictions. This may be due to the fact that, although the forecast function for the standard regression model with deterministic components has the same structure given by equation (6), the trend and seasonal components that project are global in the following sense: the values for the level and the slope of the trend, m and b, respectively, and the seasonal factors c(l) are estimated globally giving the same weight to all the sample observations. However, in a structural time series model, the trend and seasonality are both local since they have been estimated as a weighted average of the observations, giving more weight to the more recent observations. Therefore, they are able to capture better the behavior of the series at the end of the sample. The extent to which past observations are discounted depends on the relative values of the variances of the components.
Evolution of the Components of the Series A descriptive analysis of the evolution of the international tourism demand may be provided in terms of trends and seasonalities, components that capture the “permanent” characteristics of the series. One may wish to examine the trend in order to identify the main movements which have taken place in the series and that may be hidden in the seasonal cycles and transitory shocks. The seasonal behavior of the series may also be of interest, and for some purposes it may be desirable to extract the seasonal component to produce a seasonally-adjusted series. The estimation of these unobserved components at all points throughout the sample is known in the literature as signal extraction. Traditionally, signal extraction has been carried out without recourse to a statistical model, via ad hoc procedures such as moving averages, etc. The advantage of working with an explicit statistical model, such as the structural time series models, is that all the underlying assumptions are clear and it is possible to adapt signal extraction to the particular characteristics of the series and to test the adequacy of the model to the available sample. Hence it is likely to yield a better description of the series and its components. The objectives here are to estimate the “permanent” components of the real expenditures variable and to forecast the trend and underlying growth in order to evaluate the future prospects of the international tourism demand. Since the BSM is formulated directly in terms of the unobserved components, once the
GONZALEZ AND MORAL
747
unknown parameters are estimated with data from January 1979 to July 1994, the extraction of the components is rendered trivial in practice by using smoothing algorithms based on the Kalman filter. The evolution of the seasonal component is very interesting for a series like TE,, which is very much affected by climatic cycles. Tourism in Spain exhibits a strong seasonal behavior that negatively affects its profit margin, since several touristic installations are forced to close during the low season. The fact that the development of the industry was based on the weather conditions, the so-called “sun and sea” market, has contributed to the concentration of tourism in the summer, mainly in August. Nevertheless, some considerations should be given to the evolution of the distribution of the seasonal factors throughout the year, since arrival frequency is becoming more homogeneous. The results show a reduction in the amplitude of the seasonal cycle, during the period 1979-94, due mainly to a lesser concentration of tourism in August (from 0.51 in 1980 to 0.46 in 1993) and to an increase in the winter seasonal factors (from -0.38 in 1979 to -0.33 in 1992 in February). The worst figures in winter are obtained in December, February, and March, while January presents much better results and can be considered a very promising month from a tourism point of view. Since the expenditures data are global, it cannot be said with certainty if this behavior is due to an increase in the number of tourists, the average length of stay, or the average expenditure per diem. It is interesting to note that the Easter holiday period does not seem to be of any particular importance as far as tourism performance is concerned. The analysis of the underlying evolution of the series can be performed by means of the extraction of the long-term signal. The trend component can be defined as the long-term movement once the cyclical and irregular components have been removed from the series. The estimated parameters of the model for tourist expenditures show that the trend of the series is quite stable with a fixed level and a slope that changes slowly over the sample period. The evolution of the trend estimated with information up to July 1994 (Figure 1) shows a sector growing during the beginning of the 80s and able to react firmly to the short stagnation periods, such as in 1985. Nevertheless, the situation changes dramatically from 1988 onwards, when a downward trend can be observed. The good results of 1991 mark the beginning of the recovery of the sector. The trend forecasts computed from August 1994 to July 1995 show good perspectives as far as the long-term evolution of tourism demand is concerned. Figure 1 also includes the trend computed with a shorter sample, from January 1979 to December 1991, and the corresponding forecasts from January 1992 to July 1994. The perspectives for the industry measured in terms of the trend forecasts computed in December 1991 turn out to be too optimistic when compared to the estimated trend based on actual observations. It should be noted that the sharp slope of the trend forecast in December 1991 cannot be found in the actual data during the year of 1992 and it is only recovered by the end of 1993. This is an interesting result if one
748
TOURISM TRENDS IN SPAIN
Figure
1. Trend
Component
takes into account that three international events took place simultaneously in Spain during 1992 that were expected to increase international arrivals: the Olympic Games in Barcelona, the World Exposition in Seville, and the appointment of Madrid as the European Culture Capital. It does not seem to have been the case. Furthermore, in relation to this topic, Figure 1 shows that the actual expenditures numbers did not exceed the forecasts as could have been expected. As a matter of fact, the actual figures were even worse than the forecasts, especially in summertime. This can be due to the fact that the expectations generated by these events resulted in an increase in prices for tourism services such as accommodation, restaurants, etc., that could have dissuaded the regular international tourist from visiting Spain in 1992. Since the behavior of the long-term component is so smooth, it will be of interest to analyze the evolution of the growth rates of the series that allow distinctions between periods of expansion and recession. The evolution of the growth rate of a monthly series could be measured by the series of monthly increments. Although this series contains all the information about the structure of growth of the series, it is not very useful as an indicator because it oscillates too much. On the other hand, when working with monthly or quarterly seasonal series, the analysis of growth is usually done by means of the annual rates due to institutional reasons and because, in this way, the movements related to the seasonal component are extracted. Since the variables are measured in logarithms, the annual rate of growth from monthly data may be approximated by the seasonal difference, G, = TE,Substituting
TE,_,, = A,2TE1.
TEt by the BSM model G, = S&)/L
+ S,&)E,
one
gets:
+ Am, + A,+,,
(7)
GONZ.kLEZ AND MORAL
where order
L is the lag operator 12, defined as:
and
749
S,,(L) is the sum lag operator
of
S,,(L) = 1 + L + L2 +...+ L”. The analysis of the growth of an economic time series is supposed to be able to extract the main aspects of an economic phenomenon, but the behavior of the series of annual rates, A,*TE(, is very irregular. One can propose a smoother measure of the growth of the series called underlying growth and defined (Fernandez-Macho 1990) as:
Formula (8) is one of the terms of the decomposition performed in equation (7); therefore, the underlying growth indicator /3,’ is a sensible one and it can be taken as a smoothed version of the raw annual growth rates. This measure also presents the advantage of being related to the long-term component of the series since, as the model is written in logs, the slope p, can be interpreted as the monthly growth rate of the trend. Both rates, the annual difference A,2TE1 and the underlying growth, &*, are not centered with respect to the monthly increments, that is, the maxima and minima of the cyclical oscillations of the series do not take place at the same time. It is necessary to center these rates, or to assign their value to the center of the interval. This fact implies that for computing the value of the underlying growth rate at moment t, it is necessary to use data up to moment t+5. Therefore, for the last periods of the sample, since there is not enough real data available, one will need to use predictions. The underlying growth of tourist expenditures estimated with the whole available sample from January 1979 to July 1994, is shown in Figure 2 (see the line denoted Ju194). Since the underlying growth series has to be centered, Figure 2 shows the estimated p,’ series
4.4
\
JUI bd 80
I81
Figure
I 82 I 83 I 84 I 25 I 86
2. Profiles
I 87
I 28 I89
of Tourism
I 00 I 91
Demand
-
JUlol
I 02 I 03
I 04 Cd
Growth
750
TOURISM TRENDS IN SPAIN
from July 1979 to January 1994 along with the forecasts from February 1994 to January 1995. It can be observed that after the great expansion experienced by the industry at the beginning of the 8Os, the growth of the sector is quite stable, but for the recession of 1984-85 that probably reflected the high increase in the cost of living in Spain in those years prior to joining the EEC. The first signs of crisis appeared very early, in 1986, with a high drop in the growth rates that are even negative from 1988 onwards. At the end of the 8Os, the recession seemed to touch bottom and the growth rates started increasing, but they were not positive again until 1991. The high growth rates at the beginning of the 90s experience a short period of recession during 1992, from which they recover in 1993. It would be interesting to complete the analysis of the industry evolution during the later years by studying several growth rate profiles computed with different sample sizes. The live lines displayed in Figure 2 represent the profiles estimated with samples all beginning in January 1979 and ending in October 1989, December 1990, December 1991, December 1992, and July 1994, respectively, along with the correspondent forecasts. Comparison of the growth projections computed at different points of time allows one to evaluate what the perspectives for the tourism sector were at each moment and how they have evolved in time. It can be seen that the expectations derived with data up to October 1989 were too pesimistic. There is no sign of recovery in the sector until December 1990. As a matter of fact, the results obtained that year allow one to forecast a moderate increment in the rates in the short term. The good results of the sector during the year 1991 lead to very optimistic forecasts for the growth rates that have to be revised downwards due to the recession in 1992. This result can be observed by comparing the lines Dec91 and Dec92 (Figure 2). The forecasts of the underlying growth profile computed with the whole sample, up to July 1994, suggest that the perspectives of tourism are quite optimistic, probably due to the quick recovery of the sector in 1993 onwards. A Time Series Model for the Number of Tourists The standard definition of an international tourist is “a person usually resident in another country who visits the destination country for a stay of 1 to 365 nights for any purpose other than following an occupation remunerated from within the destination country” (Baron 1984). International tourism demand in terms of number of arrivals may be measured by two indicators published monthly by the Spanish Bureau of Statistics: frontier entries and overnight stays in officially approved accommodations. Since it seems that the series of overnight stays can be underestimated, the “number of arrivals at Spanish borders” has been chosen as the indicator for the number of tourist visits, although it does not give any information about either the length of the stay or the quantity of the demand. In order to adjust the data to the definition of international tourist, only 45% of the French arrivals and 10% of the
GONZALEZ AND MORAL
751
Portuguese are considered as tourists, following the methodology provided by the Spanish Bureau of Tourist Studies. The evolution of the number of tourists series from January 1979 to June 1994 presents an upward trend and a strong seasonal behavior. The Easter holidays effect cannot be captured by the seasonal component due to its mobility so it has to be modeled separately. Furthermore, the strength and length of the Easter effect could be different depending on the month it takes place (e.g., March or April). In order to be able to pick up this effect, the model includes a dummy variable, EASTER, that takes the value one in the Easter month and zero otherwise. If the Easter period is split into March and April, the dummy variable takes the value 0.5 in each month. The time series model for the number of tourists is: NT, = p, + 3/1+ ~EASTER,+E,,
(9)
where NT, is the number of tourist series (in logarithms), the trend pu,is given by equations (3), the seasonal component 3/tby equations (5) and the irregular term follows an AR(l) process:
The results of the estimation able sample are the following: u2CL= 0.00,
a;
= 0.29 x lo-“, (0.15 x 10-i)
A = 0.16, (0.02)
of the model with the whole avail-
a2 = 0.12
x
10-4,
(0.32 x 10-y
a:=
0.12
x
10-2,
(0.25 X 10-3)
p = 0.44. (0.13)
It is interesting to note that the Easter effect is significant with an estimated coefficient of 0.16. Since one is dealing with a dummy variable, and the model is specified in logs, this result means that at Easter the number of tourists increase by 17%. The diagnostics are satisfactory in general. The large departure from normality (N=35.34) suggests the possibility of outliers. Looking at the residuals, two positive outliers were found, with normalized values 4.49 (July 1980) and 2.75 (August 1980). It has to be taken into account that at the beginning of the 80s the industry started to recover from the crisis of the 70s so quickly that it could not be captured immediately by the model. Concerning the analysis of the estimated “permanent” components of the series, although the results are very similar to those of the tourist expenditures variable, it can be interesting to point out some relevant differences in the behavior of both series. As far as the seasonal component is concerned, it makes even more evident the concentration of tourist arrivals in summer, although the amplitude of the seasonal cycle decreases by the end of the sample: from 0.98 in July and 0.94 in August of 1980 to 0.73 in July and 0.83 in August of 1983. It should also be noted that the evolution of the
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TOURISM TRENDS IN SPAIN
seasonal component for the month of October is increasing steadily along the sample, becoming positive from 1988 onwards. All these facts can be interpreted as signs of homogenization of the seasonal behavior throughout the year. The best winter results can be found in December in contrast to the tourist expenditures series. The estimated seasonal factor for January, -0.46 in 1994, shows that the size of the seasonal factor of expenditures in this month must be due to longer periods of stay and/or bigger expenditures per diem, but not to a change in the seasonal behavior of the number of tourist visits. With regard to the long-term evolution of this series, the estimated parameters of the trend component show that it is quite stable. From the analysis of the underlying rate of growth, it may be concluded that the number of tourists was very sensitive to the economic crisis of 1982, not recovering the high growth rates until the end of 1984. The growth rate series started to decline in 1987 but at a slower rate than the series of expenditures and it only shows negative values for a short period at the end of the 8Os, 1989, starting the recovery in 1990 with high positive growth rates in 1991. After a period of stagnation in 1992, the growth rates of the tourist visits recovered quickly in 1993. This behavior may be a reflection of the fidelity that characterizes the international tourism that comes to Spain according to the results of the surveys that show that an important percentage of tourists repeat their visit for several years. CONCLUSIONS The BSM has proved to be a powerful tool to analyze the evolution of international tourism demand in Spain. This model is directly formulated in terms of unobserved components, such as trends and seasonalities, that are specified stochastically. Therefore, it is very easy to compute the components of interest at every point throughout the sample; and since they are locally estimated it is possible to observe how they evolve over time capturing the changes in the behavior of the series. In this sense, a global analysis of the raw expenditures data will indicate an increasing long-term behavior of the series, while the estimated local trend and underlying growth allow one to identify clearly the crisis suffered by the sector (with negative growth rates) at the end of the 80s and the rapid recovery of the growth rates after the good results of 1991. On the other hand, it has been observed that, although the international tourism demand is still highly concentrated in summer, the distribution of the seasonal factors throughout the year is becoming more homogeneous. Factors such as the increase in the length of “second holidays”, the possibility of vacations out of the high season period, and the increase in the standard of living in developed countries that allows retired people to spend part of the year in warm countries are extremely positive because they mean a more efficient use of the Spanish tourism resources. Two indicators have been used as proxies for external tourism demand: real tourist expenditures and number of tourists. Since
GONZALEZ
AND MORAL
753
tourist expenditures is a global indicator that includes number of tourists, average length of stay, and average expenditure per diem, the separate study of the number of tourists variable allows for more precision when interpreting the results. Furthermore, the estimation of trends, seasonalities, and underlying growth yield results that are somewhat different for the two series, making the analysis of both indicators complementary. The Easter vacation effect, for example, is not noticeable in the expenditures variable. However, this does not mean that it does not exist; there is a significant increase in the number of tourists, but it is not reflected in expenditures because the period of stay is too short. The same reasoning can be applied to Christmas results. Visual inspection of the underlying growth graphs of both indicators reveals some interesting points. It can be observed that the industry is recovering at the beginning of the 8Os, but the response of the two indicators to the economic crisis in 1982 is quite different; while the growth rates of expenditures remain stable, there is a clear recession in the number of visits. In relation to the serious crisis suffered by the industry at the end of the 8Os, it is detected in the expenditures series whose growth rates start declining at the beginning of 1986, while the number of tourists still shows positive increments. It should also be noted that the recession period in the number of visits is shorter and less profound than in the expenditures indicator. It may be concluded that the last crisis of international tourism demand did not start due to a reduction in visits but was due to shorter periods of stay and/or a reduction in the expenditures per diem. The industry starts its recovery in 1990, reaching positive growth rates in 1991. This period of expansion exhibits a sudden halt in 1992 that is reflected more seriously in the expenditure series, whose growth rates decline, than in the number of tourists variable, which remains quite stable. It is clear that all the important events (such as the Olympic Games and the World Exposition) were not able to improve the long-term behavior of external tourism demand. It has to be taken into account, on the one hand, that prices increased in this period due to the expectation of an increase in the number of visits while, on the other hand, most of the Spanish international tourism comes from Europe which was suffering an economic crisis in 1992. The evolution of tourism during 1993-94 is very promising, the growth rates are quite important and the perspectives are optimistic in the short run. It should be mentioned that the recovery of the industry during the first part of the 90s may have been favorably influenced by the political instability suffered by some countries of the Mediterranean area that have been direct competitors of Spain, such as Yugoslavia, Egypt, and Turkey. This possibility implies that one should evaluate the recent results with some care. On the other hand, it seems reasonable for the tourism authorities to continue implementing the political and economic measures taken at the end of the 80s to solve the critical situation of the tourism industry and designed to diversify the supply in order to attract a new type of tourist to Spain. 0 0
754
TOURISM
TRENDS
IN SPAIN
REFERENCES Baron, R. R. V. 1984 Tourism Terminology and Standard Definitions. Tourist Review 39( 1):2%4. Box, G., and G. Tiao 1976 Comparison of Forecast and Actuality. Applied Statistics 25:195-200. Engle, R. 1978 Estimating Structural Models of Seasonality. liz Seasonal Analysis of Economic Time Series, A. Zellner, ed., pp. 281-308. Washington DC: National Bureau of Research Economics. Espasa, A., and J. T. Cancel0 1993 Metodos cuantitativos para el analisis de la coyuntura economica. Madrid: Alianza Economia. Espasa, A., R. Gbmez-Churruca, and J. Jarefio 1990 Un analisis de 10s ingresos por turismo en la economia espafiola. Working Paper No. 90.02. Madrid: Banco de EspaAa. Fern&es-Macho, F. J. 1993 Underlying Trends and Growth in Economic Variables. Estadistica Espat’ioia 126:73-98. Harvey, A. C. 1983 The Formulation of Structural Time Series Models in Discrete and Continuous Time. Ouestioo 7:563-575. 1990 Forecasting, St&ctural Time Series Models and the Kalman Filter. Cambridge: Cambridge University Press. Harvey, A. C., and S. Peters 1990 Estimation Procedures for Structural Time Series Models. Journal of Forecasting 9:89-108. Harvey, A. C., and P. Todd 1983 Forecasting Economic Time Series with Structural and Box-Jenkins Models. Iournal of Business and Economic Statistics 1:299-315. KwaTk, S. Y. 1972 Effects of Income and Prices on Travel Spending Abroad, 1960 III-1967 IV. International Economic Review 13:245-256. Martin, C., and S. F. Witt 1987 Tourism Demand Forecasting Models: Choice of Appropriate Variable to Represent Tourists’ Cost of Living. Tourism Management 8:233-246. 1988 Substitute Prices in Models of Tourism Demand. Annals of Tourism Research 15:255-268. Summary, R. 1987 Estimation of Tourism Demand by Multivariate Regression Analysis: Evidence from Kenya. Tourism Management 8:3 17-322. Uysal, M., and J. Crompton 1984 Determinants of Demand for International Tourist Flows to Turkev. Tourism Management 5:288-297. Witt, S. 1980 An Abstract Mode-Abstract (Destination) Node Model of Foreign Holiday Demand. Applied Economics 12:163-180. Submitted 10 November 1993 Resubmitted 12 December 1994 Accepted 12 May 1995 Refereed anonymously Coordinating Editor: Rebecca Summary