THE TOURIST DEMAND IN THE AREA OF EPIRUS THROUGH COINTEGRATION ANALYSIS

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1 THE TOURIST DEMAND IN THE AREA OF EPIRUS THROUGH COINTEGRATION ANALYSIS N. DRITSAKIS Α. GIALITAKI Assistant Professor Lecturer Department of Applied Informatics Department of Social Administration University of Macedonia Demokritos University of Thrace 156, Egnatia str. P.C , P. Tsardari str. P.C Salonica Komotini Summary The objective of this paper is to examine and predict the tourist demand in the region of Epirus through the approach of the cointegration analysis. An effort is made to investigate whether there is a long-term balance between financial factors and tourist demand at this region, and also if a shorterm relation exists, enabling us to extract the desirable prediction. Introduction In order to examine and predict the tourist demand in the region of Epirus, four countries were selected, which represent the best clients of the region s tourism and Greece s in general. These countries are: England, France, Germany and Italy. The function of tourist demand (Haiyan, Romilly and Liu 2000), (Lim and Mcaller 2000) (incoming tourists in this region in relation to the population of the country of origin) is defined as follows: R it = ARit POP it where: i = The country of origin of the tourists. t = The time period AR it = Arrivals of the tourists of the country of origin i during the time period t. POP it = Population of the country of origin i during the time period t. This function consists of four explanatory variables. The first explanatory variable refers to the real per capita income (Kim and Song 1998). To 1

2 calculate this income we have used the Gross Domestic Product of the tourists country of origin; the variable was defined as follows: Y it = GDPit POP * CPI it it where: GDP it = Gross Domestic Product of the country of origin i during the time period t. POP it = Population of the country of origin i during the time period t. CPI it = Consumer index (1990 = 100) of the country of origin i during the time period t. The second explanatory variable refers to the relative prices between the tourists country of origin and country of destination (Witt and Martin 1987) and is defined as follows: CN it = CPI EXR CPI jt ijt it where: j = The tourists destination country. CPI jt = The consumer index (1990 = 100) of the country of destination j during the time period t. EXR ijt = The exchange rate of the country of destination j in relation to the exchange rate of the country of origin i during the time period t. CPI it = The consumer index (1990 = 100) of the country of origin i during the time period t. The above mentioned formula depicts the actual cost of tourism in the country of destination. This cost is raised when domestic exchange rates increase more rapidly than the corresponding rates of the tourists country of origin. The third explanatory variable refers to the parity of exchange (Dritsakis and Athanasiadis 2000) which is defined as follows: EX = drachmas $ foreigncurrency $ i.e. the more Drachmas that correspond in one unit of foreign currency, the cheaper the tourist services will become in the country of destination, which naturally translates to a raise in tourist demand. In conclusion, the fourth explanatory variable ( INV ) refers to the investments made in the tourist sector of the country of destination. (Dritsakis and Papanastasiou 1998). In lack of precise data on the tourist sector s 2

3 investments we have used the overall investments referring to the Greek economy, a percentage of which we regard as corresponding to the tourist sector, and an other percentage as corresponding to the tourist sector of the region of Epirus. Kulendran, N. (1996) Kulendran and King (1997) has applied a similar model for the tourist flow in Australia, using the cointegration analysis on the tourist demand of this country. This paper is based on that particular study. To examine the effects of the above mentioned variables on tourist demand we have used annual data covering the time period between 1960 and 1996 developing a multivariate vector autoregressive model (VAR). More precisely, this paper has the following structure. At the first part, the methodology and technical tools used for the long-term equilibrium relationship are being presented briefly. At the second part, the shorterm relationships are being presented adopting the Hendry (Maddala 1992) method, while at the third part some estimations are being made concerning the tourist demand. The overall conclusions of this study are mentioned at the fourth part. 2. Methodology 2.1 Testing the order of integration of time series In previous econometric studies by adopting the point of view that variables are stationary, the estimation of the equations is made by traditional econometric procedures. Nevertheless, the absence of stability of time series raises some doubt as to the credibility of the statistical results, during the evaluation of the models (Granger, and Newbold 1974, Nelson and Plosser 1982, Philips 1986). Subsequently, from the start, one should check the order of integration of time series included in the model under question. The tests used for the integration of time series were held through tests for unit root D - F and the adjusted test of D - F (ADF) in the case where the disturbance term is autocorrelated (Dickey Fuller 1981), whereas, in order to determine the time lags the Akaike and Schwarz Bayesian criteria were put to use. The Dickey - Fuller tests have suggested that time series are not stationary in their levels but in their differences. Therefore, it is highly likely that a cointegration actually exists between the variables. Tables 1 and 2 present the results of these tests. On the same tables we also see the Q statistic of Ljung Box, by which the test for the existence of autocorrelation was held. The choice of the time lags was based on the Akaike and Schwarz Bayesian criteria. 3

4 Table 1 Testing for stationarity in the logarithms of the variables ENGLAND LR 2-0, , , ,591 LY 0-2, , , ,092 LCN 1-2, , , ,257 LEX 3-1, , , ,808 LINV 2-2, , , ,220 FRANCE LR 0-1, , ,4848 (3,551) 28,966 LY 2-1, , , ,869 LCN 0-1, , , ,446 LEX 1-1, , , ,664 LINV 2-2, , , ,220 GERMANY LR 1-1, , , ,651 LY 1-2, ,8687 (0,001) 1-2, ,857 LCN 2-1, , , ,871 LEX 1-1, , , ,458 LINV 2-2, , , ,220 4

5 ITALY LR 3-2, , , ,757 LY 2-1, , , ,868 LCN 1-1, , , ,528 LEX 1-0, , , ,213 LINV 2-2, , , ,220 Table 2 Testing for stationarity in first differences of the logarithms of the variables ENGLAND LR 1-6,3874 0,01741 (0,8951) 1-6,2819 0,0189 (0,891) LY 0-4,5112 1,4084 (0,235) 0-4,6795 1,5291 (0,216) LCN 0-3,8807 3,8557 (0,050) 0-3,0396 4,1862 (0,041) LEX 2-1,8643 3, ,9916 3,1875 LINV 2-3,0489 (0,087) 2,2056 (0,380) 3-4,8664 (0,069) 2,4264 (0,489) FRANCE LR 0-7,2146 2,5464 (0,111) 1-5,0657 2,7464 (0,096) LY 0-4,6370 0,7497 (0,387) 2-4,8795 0,8205 (0,663) LCN 1-5,6885 0,0186 (0,891) 1-5,5896 0,0202 (0,887) LEX 1-3,0178 2, ,7211 2,0145 LINV 2-3,0489 (0,138) 2,2056 (0,380) 3-4,8664 (0,214) 2,4264 (0,489) 5

6 GERMANY LR 0-7,7564 3,3099 (0,069) 0-7,7420 3,5936 (0,058) LY 0-5,3754 0,0021 (0,964) 0-5,3307 0,0022 (0,962) LCN 1-4,1754 5,7271 (0,057) 1-4,2392 6,2572 (0,044) LEX 0-2,9950 3, ,6107 3,1876 LINV 2-3,0489 (0,084) 2,2056 (0,380) 3-4,8664 (0,078) 2,4264 (0,489) ITALY LR 3-4,2122 3,3928 (0,183) 3-5,3280 3,7409 (0,154) LY 1-5,3727 0,5768 (0,448) 1-5,5277 0,6262 (0,429) LCN 3-3,6372 4,0677 (0,254) 3-3,5796 4,4694 (0,216) LEX 0-3,6779 1, ,6964 1,5512 LINV 2-3,0489 Comments: (0,214) 2,2056 (0,380) 3-4,8664 (0,298) 2,4264 (0,489) 1) The values in the columns with the indication p, refer to the time lag order in the relationship Χ t = α 0 + α 1 t + α 2 Χ t-1 + β i X t i + e t p i= 1 Where Χ t represents one of the time series LR, LY, LCN, LEX, LINV. The choice of time lags was based on the Akaike criteria (AIC) from the relationship AIC m = ln SSR n M + 2 n m and the Schwarz Bayesian criteria (SBC) from the relationship SBC m = ln SSR n M n + ln n m 6

7 Where m represents the number of time lags, n the sample size and SSR m the sum of the square residuals. 2) The values in round brackets on the columns with the indication ADF are the critical values at a 5% significance level by the MacKinnon (1991) tables. Their selection was based on the number of the observations and on the fact that the corresponding regression includes only a constant term or a constant term and trend at the same time. 3) The values in square brackets, on the columns with the indication Q are potential values for the Ljung - Box statistic which is calculated by the following relationship Q = n (n+2) m ) 2 pk X 2 m k = 1 n k Where ) p k represents the value of the correlation function and n the number of observations. If the Ljung Box statistic, which follows an Χ 2 distribution with m degrees of freedom, has the lowest value of the critical value of the tables, we can thus conclude that the time series under consideration is not autocorrelated. 2.2 Cointegration analysis Tables 3a and 3b present the results arising from the respective cointegration tests through the Johansen approach. The results of the grater eigenvalue (λ max ) and trace ( J t ) (Table 3b) suggest the presence of two cointegrated vectors for all the countries in question. The significance of the eigenvalues (Table 3a) depict the relation between the cointegrated vector and the part of the model which is stationary. All eigenvalues present relatively high numbers, suggesting the existence of strong relationships of cointegration. In cases where statistic tests have revealed more than one equilibrium relation, the choice of vector was based on the economic theory regarding the signs and significance of the coefficients. Below you will find the chosen vectors with normalized coefficients, in regard to the variable LR for every country individually. LR LY LCN LEX LINV ENGLAND 1,0000 4,8527-3,8293 1,1357 2,5368 FRANCE 1,0000 2,3523-0,3074 2,7005 2,4209 GERMANY 1,0000 2,4268-2,2452 1,4093 0,6454 ITALY 1,0000 3,9027-0,6201 0,6394 1,8352 All variable coefficients have the expected sign. The income coefficient ( LY ) reaches the highest values in all functions except in the case of France, where the coefficient for the currency rate variable appears to be higher than the income coefficient, indicating the importance attributed by the French to the currency rate for long-term equilibrium. 7

8 In general, the above mentioned results are similar to the results deriving from the use of traditional econometric methods. In cases where the income has a positive effect on tourist demand and the elasticity is higher than one, thus suggesting that tourism may be considered as luxury product. The variables representing the cost of tourism in Greece (LCN, LEX) are apparently very important for tourist demand, while investments in the tourist sector remain a significant determinative factor for tourist demand. Further down, an estimation is made of the short-term dynamic relation for each country of origin, by introducing the residuals of cointegrated functions on the models of the adjusted error. Table 3a Johansen maximum likelihood procedure. Eigenvalues in ascending order ENGLAND FRANCE 0,723 0,626 0,312 0,295 0,199 0,708 0,579 0,356 0,333 0,183 GERMANY ITALY 0,723 0,626 0,312 0,295 0,199 0,708 0,579 0,356 0,333 0,183 Table 3b - Cointegration test of the greater eigenvalue and trace of the stochastic table Null Hypothesis Alternative Hypothesis ENGLAND FRANCE Ηο (1) Η Ε (2) Η Ε (3) λ max (4) J t (5) λ max (4) J t (5) r=0 r=1 r>=1 44, ,547 43, ,212 r<=1 r=2 r>=2 34, , , ,0297 r<=2 r=3 r>=3 13, , , ,7164 r<=3 r=4 r>=4 12, , , ,2992 r<=4 r=5 r=5 7,7708 7,7708 7,0826 7, % Critical Values λ max : 34,40 28,27 22,04 15,87 9,16 95% Critical Values J t : 75,98 53,48 34,87 20,18 9,16 90% Critical Values λ max : 31,73 25,80 19,86 13,81 7,53 90% Critical Values J t : 71,81 49,95 31,93 17,88 7,53 8

9 Null Hypothesis Alternative Hypothesis GERMANY ITALY Ηο (1) Η Ε (2) Η Ε (3) λ max (4) J t (5) λ max (4) J t (5) r=0 r=1 r>=1 35, , , ,410 r<=1 r=2 r>=2 28, , , ,832 r<=2 r=3 r>=3 17, , , ,925 r<=3 r=4 r>=4 11, ,0954 8, ,850 r<=4 r=5 r=5 4,4096 4,4096 4,3517 4, % Critical Values λ max : 34,40 28,27 22,04 15,87 9,16 95% Critical Values J t : 75,98 53,48 34,87 20,18 9,16 90% Critical Values λ max : 31,73 25,80 19,86 13,81 7,53 90% Critical Values J t : 71,81 49,95 31,93 17,88 7,53 Comments: 1) The values on the columns (4) have been calculated by the relationship: λ max ( r ) = -T ln(1 - ) λ r+1 ) where Τ represents the sample size and ) λ i the roots (eigenvalues). 2) The values on the columns (5) have been calculated by the relationship: λ trace ( r ) = - T n ) ln( 1 ) i= r+ 1 where Τ represents the sample size and λ i ) λ i the roots (eigenvalues). 3) The critical values have been obtained by Johansen and Juselius (1990). 3. The vector autoregressive error correction model Since it has been defined that the variables of the model are cointegrated, an estimation of a VAR model with an integrated error correction mechanism should follow (EC). The negative sign of the EC coefficient on the LR variable is consistent with the hypothesis that this term is correcting the tourist demand deviations from the long-term equilibrium. The final form of the model has been estimated using the Hendry method (Maddala 1992). The initial time lag used in all variables was two periods, which were considered sufficient to include the short-term dynamic. The residual diagnostic tests include LM tests for possible presence of autocorrelation and heteroscedasticity, the Ramsey RESET test for specification, and the Bera - Jarque test for normality. Finally, in order to test the forecasting capability of the models, the second Chow test was used. In addition, the introduction of dummy variables, has produced positive results, both to the diagnostic tests and the form of the functions. 9

10 These dummy variables are related to the facts affecting the tourist demand of the specific region and Greece in general, just like the two global energy crises (D1), the political events in Greece (D2), the effusion of terrorism (D3) and the civil conflict in Yugoslavia (D4). The error correction models are presented in Table 4. All the results satisfy the statistic criteria. The explanatory capability of the models is satisfactory given that the values of the coefficient of determination (R 2 ) range between 0,60 for England and 0,88 for Germany. The residuals at the diagnostic tests appear to be consistent with the assumptions, whereas the error correction term (EC) appears statistically important, having a negative sign and confirming the existence of long-term equilibrium between tourist demand and other economic defining factors. The error correction coefficient suggests the magnitude of the function s partial adaptation after the precedent time period which lacked equilibrium. The relatively high absolute values of the coefficients display that any long-term information included in the variables play a significant part in the process of adaptation to the conditions of equilibrium. A general test of the models reveals the positive relationship between the income variation (DLY) and the tourist demand variation (DLR) for all the countries in question. Specifically in France and Italy, a time lag in the income variable was required, in order to achieve their adaptation to equilibrium. Additionally, in Italy the income variable was proven to be unimportant at a level of 5%. This is probably due to the fact that the distance between Italy and the region of Epirus is very small, and as a result, a part of the income influence is absorbed. The cost variable of the country of origin (DCN) has a negative sign and is statistically important for all the countries and in particular with one and two time lags for Italy, while the currency rates present the expected sign in all countries but are not statistically significant at a 5% level for France. Finally, the investment variable presents time lags in all the countries in question, whereas the pseudo variables used in the same models can not be characterized as statistically important at a level of 5%. A forecast for the next two years ( ) was made, based on the above mentioned results and in particular those regarding the predictive power of the models. England Table 4 Error correction models DLR1 t = -0, ,7079 DLY1 t - 2,3881DLCN1 t + 0,468DLEX1 t-1 (-1,021) (2,074) (-1,901) (2,345) + 0,82940 DLINV t-1-0,20048ec1 t + 0,123D3 (1,762) (-2,068) (1,238) R 2 = 0,607 F(6, 26) = 3,34 DW = 1,97 SC: X 2 (1) = 0,293 FF: X 2 (1) = 0,129 NORM: X 2 (2) = 7,543 HER: X 2 (1) = 1,128 PF : F( 2, 26 ) = 1,379 10

11 France DLR2 t = -0, ,4601 DLY2 t-1-1,0135dlcn2 t-1 + 0,19793DLEX2 t-1 (-0,2675) (3,237) (-2,376) (1,674) + 0,32230 DLINV t-2-0,2533ec2 t + 0,123D1 + 0,684D2 + 0,8302D3 (1,752) (1,731) (4,237) (1,123) (1,894) R 2 = 0,723 F(8, 22) = 12,75 DW = 2,16 SC: X 2 (1) = 1,697 FF: X 2 (1) = 0,038 NORM: X 2 (2) = 0,853 HER: X 2 (1) = 1,141 PF : F(2,22) = 0,0035 Germany DLR3 t = -3, ,6017 DLY3 t - 0,98670DLCN3 t-2 + 1,7064DLEX3 t-1 (-2,4928) (2,4216) (-1,7294) (2,0310) + 0,32443 DLINV t + 0,54368DLINV t-1-0,53930ec3 t + 0,123D2 + 0,3425D3 (1,6460) (2,1187) (-2,4685) (1,2786) (1,7639) R 2 = 0,880 F(8, 22) = 6,12 DW = 1,93 SC: X 2 (1) = 0,015 FF: X 2 (1) = 0,344 NORM: X 2 (2) = 1,578 HER: X 2 (1) = 0,168 PF : F(2,22 ) = 0,585 Italy DLR4 t = -4,504 +2,332DLY4 t-1-2,887dlcn4 t - 0,314DLCN4 t-1 (-2,510) (1,754) (-2,464) (-2,255) - 0,356DLCN4 t-2 + 0,907DLEX4 t-2 + 0,194DLINV t +0,235DLINV t-2 (-1,278) (2,339) (2,494) (1,986) - 0,674EC4 t + 0,481D1 (-2,435) (1,543) R 2 =0,723 F(9, 21) = 2,88 DW = 2,29 SC: X 2 (1) = 1,029 FF: X 2 (1) = 1,506 NORM: X 2 (2) = 6,360 HER: X 2 (1) = 1,560 PF : F(2,21) = 1,952 11

12 4. Tourist demand forecast The forecast using cointegration error correction models presupposes the development of a system of structural equations including the long-term and short-term relationships of the variables Witt and Witt (1992), Smeral and Witt (1996). In this structural system, which consists of three functions; The first function represents the error correction model, the second uses the tourist demand forecast, and the third constitutes a cointegrated function, with the residuals being the dependent variable. The forecasts made for the time period as well as the current values of tourist demand for the region of Epirus are presented in Table 5. The forecast values indicate a remarkable decrease of arrivals from all countries for the year The greatest decrease of arrivals was observed in the tourist arrivals from Italy with a percentage of 10,94%, while for the year 1998 there has been an increase of arrivals from all the countries in question. Table 5 Forecasts of tourist demand ENGLAND Arrivals Variation % (-6,2) (4,9) DLR1-0, , ,42314 FRANCE Arrivals Variation % (-2,33) (1,24) DLR2-0, , ,04244 GERMANY Arrivals Variation % (-4,98) (4,55) DLR3-0, , ,13148 ITALY Arrivals Variation % (-10,94) (7,32) DLR4-0, , , Conclusions This study has shown that the economic variables which determine the tourist demand from four Ε.Ε countries, present a unit root, i.e. integrated order one I(1). On this basis, the cointegration analysis and a methodology of error correction models were used to estimate both long-term and short-term relationships. The selected vectors have produced error correction coefficients, statistically important for the short-term dynamic functions, which suggests that the tourist demand at the region of Epirus and the economic factors expressing this demand are in a long-term relation. This realization constitutes a very important element for the elaboration of a support frame which could influence the decision making and planning process for tourist demand, when based on the arrivals of the tourists. 12

13 Bibliography Dickey, D.A and W. A. Fuller (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root. Econometrica 49, Dritsakis, N and J. Papanastasiou (1998). An econometric investigation of Greek tourism. Journal studies in economics and econometrics, Vol Dritsakis, N and S. Athanasiadis (2000). An econometric model of tourist demand: The case of Greece. Journal of hospitality & leisure marketing, Vol Granger, C.W.J, and P. Newbold (1974). Spurious regressions in econometrics. Journal of econometrics, 2, Haiyan, S, P. Romilly and X. Liu (2000). An empirical study of outbound tourism demand in the U.K, Applied Economics, Vol. 32, Johansen, S. and Juselius, K. (1990). Maximum Likelihood Estimation and Inference on Cointegration with Application to the Demand for Money. Oxford Bulletin of Economics and Statistics, 52, Kim, S and Song (1998). Analysis of tourism demand in South Korea: a coitegration and error correction approach, Tourism Analysis, Vol. 3, Kulendran, N (1996). Modeling quarterly tourist flows to Australia using cointegration analysis. Tourism economics, 3, Kulendran, N and M, L King (1997). Forecasting international quarterly tourist flows using error correction and time series models. International Journal of Forecasting, Vol. 13, Lim C. M. Mcaller (2000). A seasonal analysis of Asia tourist arrivals to Australia. Applied Economics, Vol. 32, MacKinnon, J.G (1991). Critical Values for Cointegration Tests. In R. F. Engle and C.W.J Granger (Eds). Long - Run Economic Relationships: Readings in Cointegration pp Oxford University Press. Maddala, G. R. (1992). Introduction to econometrics, 2 nd edition, MacMillan Press, New York. Nelson,C.R and C. Plosser (1982). Trends and random walks in macroeconomics time series: Some evidence and implications. Journal of monetary economics, Philips, P.C.B (1986). Understanding spurious regressions in econometrics,

14 Smeral, E, and S. F Witt (1996). Econometric forecasts of tourism demand to Annals of Tourism Research, Vol 23, Witt, S. F and C. A. Martin (1987). Tourism demand forecasting models: choice of an appropriate variable to represent tourists cost of living. Tourism Management, Vol Witt, S. F, and C. A Witt (1992). Modelling and Forecasting Demand in Tourism. Academic Press: London. 14