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Family expenditure on hotels and holidays
Annals ofTourism Research, Vol. 19, pp. 691-699, Printed in the USA. All rights reserved.
1992 Copyright
0160-7383/92 $5.00 + .OO 0 1992 Pergamon Press Ltd.
FAMILY EXPENDITURE ON HOTELS AND HOLIDAYS
Staffordshire
Brian Davies JeanMangan University, UK
Abstract: This study uses the United Kingdom Family Expenditure Survey data to investigate the effect of incomes on hotel and holiday expenditures. The results confirm the general understanding in tourism studies that such expenditure is income elastic. Additionally, the study suggests that the elasticity varies considerably between income groups, with very high income elasticities for low income groups and lower, but still elastic, responsiveness by high income groups. This suggests that spending on hotels and holidays is a long way from saturation point, and people with low incomes may increase their consumption considerably as income levels rise. However, firm estimation of the relationships requires a more detailed investigation. Keywords: tourism demand, cross sectional, income elasticities, hotel expenditure. Resume: Les dtpenses pour les nuits d’h&el et les vacances. La prCsente etude s’appuie sur les donnCes d’une enquCte sur les dCpenses de mtnages au Royaume Uni pour examiner l’influence des revenus sur les dtpenses pour les vacances et les nuits d’hbtel. Les r&ultats confirment que ces dtpenses sont tlastiques par rapport aux revenus. En plus, on sugggre que I’tlasticitC varie considCrablement entre les cattgories de revenus: les Clasticitts-revenus sont trts 6levCes pour les categories de revenus bas; les rbactions sont plus faibles, mais toutefois tlastiques, pour les categories de revenus tlevCs. On peut en conclure que les dCpenses pour les nuits d’hbtel et les vacances sont loin d’&tre B saturation. 11 faudrait pourtant faire une enquete plus d&taillCe. Mats-cl&: tourisme (demande), tlasticitt-revenu, dtpenses, enqu&te.
INTRODUCTION Demand forecasting is an area of tourism studies that has received considerable attention. A recent article in this journal (Pyo, Uysal and McLellan 1991) develops a linear expenditure model for tourism demand. This follows the tradition exemplified by the classic study, “The Analysis of Consumer Demand in the U.K., 1900-1970” (Deaton 1974). However, most studies have been concerned with individual Brian Davies and Jean Mangan are Senior Lecturers in Economic History and Economics, respectively (Division of Economics, Staffordshire University, Stoke-onTrent, ST4 2DF, UK). Both are interested in the application of economic concepts in tourism studies. The former teaches tourism and has published in the area. The latter is involved in business forecasting teaching and consultancy.
692
FAMILY
EXPENDITURE
ON HOLIDAYS
commodities rather than systems. In this context, the applicability of forecasting techniques is discussed, for example, in the survey article by Witt and Martin (1987). Th ere is a wealth of research work on practical applications of such techniquesfor instance, the study by Guerts (1982) of the Hawaiian tourism market. The greater emphasis in the literature has been on time series and econometric methods using time series data. Some of these studies have included a crosssectional element, considering different countries of origin and destination, different modes of transportation and input-output analysis (cf. Witt 1980). At the microeconomic level, Gravity and Trip models, such as Morgan’s (1986) model of visits to U.S. National Parks, have been used to define the demand curve for a particular attraction based on the impact of travel costs, distance, and time costs as constraints. However, little use has been made in tourism studies of econometric methods in investigating cross-sectional family expenditure data. The aims of this paper are to redress the balance and to indicate how cross-sectional studies can be used to estimate income elasticities for different income groups. Such detailed knowledge may prove a useful input into the tourism forecasting and planning process. The basis of the approach is the seminal work by Engel (1857). This suggests a relationship between a particular category of expenditure and income levels, both at the individual family and aggregate levels. The estimation of such relationships enables a consideration of the responsiveness of such expenditure to income changes. This is not to deny that the use of time series data is important, but there are some limits that circumscribe its usefulness. Time series data is highly aggregated and of a macroeconomic nature. Homogeneity over time periods is assumed so that the existing pattern holds into the future. Cross-sectional data also has its limitations, but it does, at least, provide a different dimension by using observations at an instant of time, and allows investigation into different categories of spenders. As Klein puts it: In such samples [time series] we estimate fundamental parameters on the basis of time variation, from period to period, of economic quantities for an individual economic unit or an aggregate of units and for an individual good or an aggregate of goods. We could equally as well base our estimates on a different type of variation, arising from internamely, spatial, instead of time, variation individual differences at a given point of time (1962:53). The estimates in this study use the spending on tourism by household categories as defined by, and using the data in, the Family ExpenFamily Expenditure Survey diture Survey. The United Kingdom (FES) is a continuous survey undertaken by the Office of Population, Censuses and Surveys on behalf of the Department of Employment. It is based on a representative sample of households, with around 7,000 cooperating in the survey in any one year. Information is gathered on household characteristics, expenditure, and income, based on detailed record keeping by the sample families. The original purpose of the survey was to provide the weights for the UK Retail Price Index. The survey has been extended over the years and now provides a
DAVIES AND MANGAN
693
multipurpose database for various UK government departments. The results in aggregate groupings are published in an annual report. This approach may help identify how tourism expenditures are affected by income, allowing quantitative estimates to be made of the income/expenditure relationship at different levels. Such information is a useful input in the development of management strategies. If, for instance, a small change of income at the bottom end of the scale brings a large proportionate change in tourist expenditure, this has implications for the total amount and type of holiday that may be needed, given such a change. DEVELOPMENT
OF THE
MODEL
The model used in this paper is based on Engel’s (1857) that expenditure is a function of income. Thus,
curve, such
H = f(Y) where
H= Y=
expenditure on the product by households (in this investigation: hotel and holiday expenditure) Household income
Given that the data is from a particular point in time, the other factors that standardly affect demand are constant (i.e., the price of the goods, the price of other goods and tastes). An Engel curve over the whole range of income is taken to be sigmoid in shape. Curvature is assumed because expenditure steeply rises at first as income rises, but the rate of increase declines as saturation is approached. The purchase behavior for an individual household may show discontinuities as certain critical points in terms of income levels are reached. At the aggregate level continuity is assumed. In estimating an Engel curve, the best fit to the data is required and needs to reflect any curvature. However, the data from a particular point in time may not cover the whole income range considered in the model and thus only parts of the curve will be estimated. The semi-logarithmic function is used to estimate necessities with curvature reflecting the approach to saturation, while the double logarithmic form is used for luxuries. Hotel and holiday expenditures would be expected to fall in the luxury category. The use of the double logarithmic functional form applies where there is no tendency at current income levels for the elasticity to decline. A priori, it would be expected that the expenditure on hotels and holidays is income elastic. The initial presumption of this study is that the double logarithmic form would apply. This form gives constant income elasticities for every income level. The initial investigation of cross-sectional data considered here uses the published Family Expenditure Survey of 1988. This gives hotel and holiday expenses by 16 income groupings. The use of grouped data improves the measure of goodness of fit, as individual variations are averaged. The original model needed to be adjusted before estimation in the light of the data used. Total expenditure rather than income
FAMILY
694
EXPENDITURE
ON HOLIDAYS
was used as an explanatory variable, as only income groupings were available. If the elasticity between income and expenditure is constant, this is not a major drawback.
H=AE) where
E = total expenditure
(2)
by households
The plot of the relationship is given in Figure 1. To quantify this relationship, regression analysis was used. As Figure 1 does not portray obvious nonlinearity, thus, in estimating the relationship, both the double logarithmic form considered above and a linear form were estimated to compare the goodness of fit. Therefore, the equations were: log H = cl + cp (log E>
(3)
H = 6, + 6, (E)
(4)
and
In the Family Expenditure Survey, there are a different number of respondents in each income category and this gives rise to the technical problem of heteroscedasticity. It is a requirement for ordinary least squares estimation to be efficient that the variance in each category is equal. This data does not meet this requirement. The variances are not f perweek
6
0
50
150
0
250 TOTAL
350 EXPENDITURE
Figure 1. Total and Holiday Expenditure
450
550
DAVIES
695
AND MANGAN
equal because variance is reduced by using grouped data by different amounts according to the size of the sample in each category. This averaging problem can be corrected by weighting the categories by the square root of the sample size, a procedures used in obtaining the the coefficients in the results presented here. Thus, for estimating equations above, the following forms were used: filog
H
(1ogE)
= &cl
+
ficp
= J;Eb,
+
fib&??)
(5)
and J;iH
(6)
Results and Interpretations
The results show a good fit for both formulations. Total expenditure is highly significant, and around 90% of the variation in the data is explained by the regression. The estimated relationships are: for equation
(3)
and for equation
1ogH (4)
H
= =
-9.89 - 5.01
+ 2.17 (log&J + 0.059
(E)
Details of the statistical results are given in Table 1. The elasticities of tourist expenditure vary according to which model is taken. The figures are given in Table 2. The results confirm the a priori assumption that spending on holidays and hotels is income elastic. However, there are considerable differences between the equations. The double logarithmic form gives a constant elasticity across all income groups. A 1% increase in total expenditure leads to over a 2 % increase in hotel and holiday expenditure. The linear formulation suggests elasticities that are highly income elastic at low incomes and are only moderately income elastic at high incomes. For those on low incomes, an increase in total expenditure of 1% leads to over a 6% increase in hotel and holiday expenditure. The figure for those on high income is close to a 1.5 % increase, still income elastic but of a much lower magnitude. For decreases in income the changes in hotel and holiday expenditure are correspondingly negative. Which of these formulations is correct is important for the tourist market, given future changes in the general level and distribution of Table 1. Statistical Results of Original Model Cons
J;;H J;; log (H)
- 5.02 (-4.13)” -9.89 (- 8.82)”
m
&logE
+ 0.059 (11.97)”
The figures in parenthesis are t-statistics “Significant at .Oi level of probability.
+2.17 (10.06)
R2
F
0.9
143.5
0.88
110.2
696
FAMILY
Table
EXPENDITURE
2. Elasticities
ON HOLIDAYS
from the Original
Model
Elasticities Expenditure E204.4 f102.2 f306.6
Level
(mid-point)
Equation 3 (double log)
Equation 4 (linear)
2.2 2.2 2.2
1.7 6.0 1.4
income. In the double logarithmic form, the general level of income is important, but the distribution is not. On the other hand, in the linear form, the distribution is important with considerable potential for growth at the lower end of the market. However, it should be noted that elasticities relate to proportionate changes and that the absolute increase in tourist expenditures may still be higher further up the income scale as income increases. Further Development of the Model In estimating regression relationships all relevant variables should be included. Household composition is usually held to be the second most important determinant of consumption for many categories of goods. If household composition is important to holiday and hotel expenditure and is left out of the regression (i.e., relegated to the error term), then the estimates of income elasticity may be biased. The effect of number of children (N) on hotel and holiday expenditure is not clear. Also, the effect of children on expenditure may depend on income level and, thus, a cross product term (EN) is included. The published data does allow for an initial investigation including this factor, but because of difficulties in comparison between different types of household, the empirical work was restricted to families consisting of two adults and 0, 1, 2, and 3 children. Thus, the model was extended to the formulation: H = f (23, N, EN)
(7)
Again, the investigation used the double logarithmic and linear functional forms in estimation, using ordinary least squares with the correction for heteroscedasticity. Equation (7) could not be estimated in logs with the inclusion of N, because of the presence of families without children. When only expenditure on hotels and holidays (H) and total expenditure (E) were logged, the results proved to be poor. The number of children, as such, appeared to be insignificant and the percentage of the variation in the data explained by the regression equation was only 50%. The full results are given in Table 3. The estimates of the linear form proved more promising. The total expenditure variable was highly significant and showed a strong positive relationship to holiday expenditure. The inclusion of either the
DAVIES
Table
3. Statistical
Cons.
GE
Results
J;;L~~E
of Amended
Model
&EN
J;;H
- 10.44 (-3.01)”
+0.008 (6.35)b
-0.0068 (-0.69)
J;;H
- 10.28 (-3.96)b
+0.08 (8.0)b
- 0.006 (-2.0)
J;;H
-8.99 (- 3.32)b
+ 0.078 (7.81)b
&log(H)
-11.7 (- 1.68)
+2.5 (1.95)
-13.39
+2.81 (2.84)”
&log(H)
697
AND MANGAN
&N +0.202 (0.074)
- 1.58 (-1.83)
(-2.5) J;; log (H) - 14.63 (- 2.55)”
+3.02 (2.82)
+0.001
- 0.79 (0.77)
(0.4)
-0.4 (- 1.2) -0.0012 (-0.98)
R~
F
0.81
22.9
0.83
37.2
0.82
35.5
0.4
4.29
0.44
6.8
0.42
6.34
Note: The figures in parenthesis are t-statistics. “Significant at .05 level of probability. bSignificant at .Ol level of probability.
number of children or the cross product term between children and expenditure improved the fit. Eighty-two percent of the variation in the data was explained. However, there appeared to be problems of multicollinearity between N and EN. Dropping either led to income being significant (at the 95% confidence level) and children nearly significant (significant at the 90% confidence level). In either case, increases in the number of children meant a reduction in expenditure on holidays and hotels. The estimated equation with the cross product term (cf. Table 3) is:
H = -10.28
+ 0.0834
E - 0.0061
EN
(8)
This form of equation does not give constant elasticities. The estimated expenditure elasticities at various points are given in Table 4. Hotel and holiday expenditure is income elastic for all income groups. The
Table
4. Elasticities
Expenditure E251.1 f170 E376.6
Level
(mid-point)
of the Amended
Model
Elasticity Equation 8 (linear) 2.1 4.1 1.5
Note: The elasticities presented are for households without children. The effect of EN alters the elasticities slightly for families with children. For instance, the elasticity at the midpoint for a family with three children is 2.6.
698
FAMILY EXPENDITURE
ON HOLIDAYS
estimates suggest that an increase in total expenditure of 1% for lower income groups leads to over 4 % increase in hotel and holiday expenditure. For upper income groups, the corresponding increase is only 1.5 76. For decreases in total expenditure the reverse would apply. The calculated elasticities are very similar to the results reported in the previous section, even given the different aggregation and the small sample sizes. What is important is that both calculations show a very high responsiveness by low income families. Low income families spend very little on hotels and holidays, but may be prepared to increase such expenditure rapidly with small income gains. At low level of incomes, it could be expected that the additional financial burden of children would reduce expenditure in this area. The results suggest that, even at medium and high levels of income, the number of children in a family reduce the expenditure on hotels and holidays. CONCLUSIONS The study confirms the general understanding in tourism studies that tourist expenditures are a long way from saturation point. From the investigation, using the simple model, the estimates for the double logarithmic and linear forms both show a good fit, but the implications for the tourism industry differ. The double log form gives a constant expenditure elasticity, while the linear formulation has elasticities that are very high at low income levels, and lower but still elastic at high income levels. The results of the extended model further suggest that the linear formulation is more appropriate. This implies that at the lower end of the income scale, a small difference in income has a large impact on hotel and holiday expenditures. Increases in real incomes may well continue to bring rapid growth to the hotel and holiday market. This growth may be more pronounced for low income groups. In general, these findings may be interpreted positively by the industry. However, in times of cyclical decline, the magnitude of the estimates suggest that the decline in the industry will be far greater than any decline in income. Expenditure by low income households will particularly suffer. From the extended model, it is not clear that the number of children is of importance in determining hotel and holiday expenditure. To the extent that it is important, the effect appears to be negative. Therefore, holiday and hotel businesses may need to think more about the nature of the products they provide. The family holiday is of some importance, but families appear to restrict the market in the short term. An aging population may well have a positive effect, a baby boom a negative one. The results considered here are only an initial investigation using published aggregate data. The results on the expenditure elasticities and household composition suggest that a more detailed study is warranted using a larger sample size. Family Expenditure Survey data is available as an anonymized data tape for academic research. Using this gives access to a larger sample size. Such an investigation is necessary to be able to clarify the functional form and to identify behavioral
DAVIES
AND MANGAN
699
characteristics that may influence differing spending patterns. Further work can also be undertaken comparing results over different years, given the need to generalize to developments over time for forecasting purposes. 0 0 REFERENCES Deaton, Angus S. 1974 The Analysis of Consumer Demand in the United Kingdom, 1900-1970. Econometrica 42:341-367. Engel, Ernst 1857 Die Produktions und Consumptionsverhaltnisse des Consumptionsverhaltnisse des Konigreichs Sachsen. Zeitschrift des Statistischen Bureaus des Koniglich Sachsischen Ministerium des Innern 22. Guerts, Michael 1982 Forecasting the Hawaiian Tourist Market. Journal of Travel Research 2 1: 1821. Klein, Lawrence 1962 An Introduction to Econometrics. London: Prentice Hall. Morgan, James N. 1986 The Impact of Travel Costs on Visits to U.S. National Parks. Journal of Travel Research 25:23-28. Pyo, Sung Soo, Muzaffer Uysal, and Robert McLellan 1991 A Linear Expenditure Model for Tourism Demand. Annals of Tourism Research 18:443-454. Witt, Stephen 1980 An Abstract Node: Abstract (Destination) Node Model of Foreign Holiday Demand. Applied Economics 12 : 163- 180. Witt, Stephen, and Christine Martin 1987 Econometric Models for Forecasting International Tourism Demand. Journal of Travel Research 26:23-30. Submitted 10 January 1991 Revised paper submitted 22 February 1991 Second revised paper submitted 17 June 1991 Final version submitted 12 December 199 1 Refereed anonymously Coordinating Editor: Turgut Var
1992 Copyright
0160-7383/92 $5.00 + .OO 0 1992 Pergamon Press Ltd.
FAMILY EXPENDITURE ON HOTELS AND HOLIDAYS
Staffordshire
Brian Davies JeanMangan University, UK
Abstract: This study uses the United Kingdom Family Expenditure Survey data to investigate the effect of incomes on hotel and holiday expenditures. The results confirm the general understanding in tourism studies that such expenditure is income elastic. Additionally, the study suggests that the elasticity varies considerably between income groups, with very high income elasticities for low income groups and lower, but still elastic, responsiveness by high income groups. This suggests that spending on hotels and holidays is a long way from saturation point, and people with low incomes may increase their consumption considerably as income levels rise. However, firm estimation of the relationships requires a more detailed investigation. Keywords: tourism demand, cross sectional, income elasticities, hotel expenditure. Resume: Les dtpenses pour les nuits d’h&el et les vacances. La prCsente etude s’appuie sur les donnCes d’une enquCte sur les dCpenses de mtnages au Royaume Uni pour examiner l’influence des revenus sur les dtpenses pour les vacances et les nuits d’hbtel. Les r&ultats confirment que ces dtpenses sont tlastiques par rapport aux revenus. En plus, on sugggre que I’tlasticitC varie considCrablement entre les cattgories de revenus: les Clasticitts-revenus sont trts 6levCes pour les categories de revenus bas; les rbactions sont plus faibles, mais toutefois tlastiques, pour les categories de revenus tlevCs. On peut en conclure que les dCpenses pour les nuits d’hbtel et les vacances sont loin d’&tre B saturation. 11 faudrait pourtant faire une enquete plus d&taillCe. Mats-cl&: tourisme (demande), tlasticitt-revenu, dtpenses, enqu&te.
INTRODUCTION Demand forecasting is an area of tourism studies that has received considerable attention. A recent article in this journal (Pyo, Uysal and McLellan 1991) develops a linear expenditure model for tourism demand. This follows the tradition exemplified by the classic study, “The Analysis of Consumer Demand in the U.K., 1900-1970” (Deaton 1974). However, most studies have been concerned with individual Brian Davies and Jean Mangan are Senior Lecturers in Economic History and Economics, respectively (Division of Economics, Staffordshire University, Stoke-onTrent, ST4 2DF, UK). Both are interested in the application of economic concepts in tourism studies. The former teaches tourism and has published in the area. The latter is involved in business forecasting teaching and consultancy.
692
FAMILY
EXPENDITURE
ON HOLIDAYS
commodities rather than systems. In this context, the applicability of forecasting techniques is discussed, for example, in the survey article by Witt and Martin (1987). Th ere is a wealth of research work on practical applications of such techniquesfor instance, the study by Guerts (1982) of the Hawaiian tourism market. The greater emphasis in the literature has been on time series and econometric methods using time series data. Some of these studies have included a crosssectional element, considering different countries of origin and destination, different modes of transportation and input-output analysis (cf. Witt 1980). At the microeconomic level, Gravity and Trip models, such as Morgan’s (1986) model of visits to U.S. National Parks, have been used to define the demand curve for a particular attraction based on the impact of travel costs, distance, and time costs as constraints. However, little use has been made in tourism studies of econometric methods in investigating cross-sectional family expenditure data. The aims of this paper are to redress the balance and to indicate how cross-sectional studies can be used to estimate income elasticities for different income groups. Such detailed knowledge may prove a useful input into the tourism forecasting and planning process. The basis of the approach is the seminal work by Engel (1857). This suggests a relationship between a particular category of expenditure and income levels, both at the individual family and aggregate levels. The estimation of such relationships enables a consideration of the responsiveness of such expenditure to income changes. This is not to deny that the use of time series data is important, but there are some limits that circumscribe its usefulness. Time series data is highly aggregated and of a macroeconomic nature. Homogeneity over time periods is assumed so that the existing pattern holds into the future. Cross-sectional data also has its limitations, but it does, at least, provide a different dimension by using observations at an instant of time, and allows investigation into different categories of spenders. As Klein puts it: In such samples [time series] we estimate fundamental parameters on the basis of time variation, from period to period, of economic quantities for an individual economic unit or an aggregate of units and for an individual good or an aggregate of goods. We could equally as well base our estimates on a different type of variation, arising from internamely, spatial, instead of time, variation individual differences at a given point of time (1962:53). The estimates in this study use the spending on tourism by household categories as defined by, and using the data in, the Family ExpenFamily Expenditure Survey diture Survey. The United Kingdom (FES) is a continuous survey undertaken by the Office of Population, Censuses and Surveys on behalf of the Department of Employment. It is based on a representative sample of households, with around 7,000 cooperating in the survey in any one year. Information is gathered on household characteristics, expenditure, and income, based on detailed record keeping by the sample families. The original purpose of the survey was to provide the weights for the UK Retail Price Index. The survey has been extended over the years and now provides a
DAVIES AND MANGAN
693
multipurpose database for various UK government departments. The results in aggregate groupings are published in an annual report. This approach may help identify how tourism expenditures are affected by income, allowing quantitative estimates to be made of the income/expenditure relationship at different levels. Such information is a useful input in the development of management strategies. If, for instance, a small change of income at the bottom end of the scale brings a large proportionate change in tourist expenditure, this has implications for the total amount and type of holiday that may be needed, given such a change. DEVELOPMENT
OF THE
MODEL
The model used in this paper is based on Engel’s (1857) that expenditure is a function of income. Thus,
curve, such
H = f(Y) where
H= Y=
expenditure on the product by households (in this investigation: hotel and holiday expenditure) Household income
Given that the data is from a particular point in time, the other factors that standardly affect demand are constant (i.e., the price of the goods, the price of other goods and tastes). An Engel curve over the whole range of income is taken to be sigmoid in shape. Curvature is assumed because expenditure steeply rises at first as income rises, but the rate of increase declines as saturation is approached. The purchase behavior for an individual household may show discontinuities as certain critical points in terms of income levels are reached. At the aggregate level continuity is assumed. In estimating an Engel curve, the best fit to the data is required and needs to reflect any curvature. However, the data from a particular point in time may not cover the whole income range considered in the model and thus only parts of the curve will be estimated. The semi-logarithmic function is used to estimate necessities with curvature reflecting the approach to saturation, while the double logarithmic form is used for luxuries. Hotel and holiday expenditures would be expected to fall in the luxury category. The use of the double logarithmic functional form applies where there is no tendency at current income levels for the elasticity to decline. A priori, it would be expected that the expenditure on hotels and holidays is income elastic. The initial presumption of this study is that the double logarithmic form would apply. This form gives constant income elasticities for every income level. The initial investigation of cross-sectional data considered here uses the published Family Expenditure Survey of 1988. This gives hotel and holiday expenses by 16 income groupings. The use of grouped data improves the measure of goodness of fit, as individual variations are averaged. The original model needed to be adjusted before estimation in the light of the data used. Total expenditure rather than income
FAMILY
694
EXPENDITURE
ON HOLIDAYS
was used as an explanatory variable, as only income groupings were available. If the elasticity between income and expenditure is constant, this is not a major drawback.
H=AE) where
E = total expenditure
(2)
by households
The plot of the relationship is given in Figure 1. To quantify this relationship, regression analysis was used. As Figure 1 does not portray obvious nonlinearity, thus, in estimating the relationship, both the double logarithmic form considered above and a linear form were estimated to compare the goodness of fit. Therefore, the equations were: log H = cl + cp (log E>
(3)
H = 6, + 6, (E)
(4)
and
In the Family Expenditure Survey, there are a different number of respondents in each income category and this gives rise to the technical problem of heteroscedasticity. It is a requirement for ordinary least squares estimation to be efficient that the variance in each category is equal. This data does not meet this requirement. The variances are not f perweek
6
0
50
150
0
250 TOTAL
350 EXPENDITURE
Figure 1. Total and Holiday Expenditure
450
550
DAVIES
695
AND MANGAN
equal because variance is reduced by using grouped data by different amounts according to the size of the sample in each category. This averaging problem can be corrected by weighting the categories by the square root of the sample size, a procedures used in obtaining the the coefficients in the results presented here. Thus, for estimating equations above, the following forms were used: filog
H
(1ogE)
= &cl
+
ficp
= J;Eb,
+
fib&??)
(5)
and J;iH
(6)
Results and Interpretations
The results show a good fit for both formulations. Total expenditure is highly significant, and around 90% of the variation in the data is explained by the regression. The estimated relationships are: for equation
(3)
and for equation
1ogH (4)
H
= =
-9.89 - 5.01
+ 2.17 (log&J + 0.059
(E)
Details of the statistical results are given in Table 1. The elasticities of tourist expenditure vary according to which model is taken. The figures are given in Table 2. The results confirm the a priori assumption that spending on holidays and hotels is income elastic. However, there are considerable differences between the equations. The double logarithmic form gives a constant elasticity across all income groups. A 1% increase in total expenditure leads to over a 2 % increase in hotel and holiday expenditure. The linear formulation suggests elasticities that are highly income elastic at low incomes and are only moderately income elastic at high incomes. For those on low incomes, an increase in total expenditure of 1% leads to over a 6% increase in hotel and holiday expenditure. The figure for those on high income is close to a 1.5 % increase, still income elastic but of a much lower magnitude. For decreases in income the changes in hotel and holiday expenditure are correspondingly negative. Which of these formulations is correct is important for the tourist market, given future changes in the general level and distribution of Table 1. Statistical Results of Original Model Cons
J;;H J;; log (H)
- 5.02 (-4.13)” -9.89 (- 8.82)”
m
&logE
+ 0.059 (11.97)”
The figures in parenthesis are t-statistics “Significant at .Oi level of probability.
+2.17 (10.06)
R2
F
0.9
143.5
0.88
110.2
696
FAMILY
Table
EXPENDITURE
2. Elasticities
ON HOLIDAYS
from the Original
Model
Elasticities Expenditure E204.4 f102.2 f306.6
Level
(mid-point)
Equation 3 (double log)
Equation 4 (linear)
2.2 2.2 2.2
1.7 6.0 1.4
income. In the double logarithmic form, the general level of income is important, but the distribution is not. On the other hand, in the linear form, the distribution is important with considerable potential for growth at the lower end of the market. However, it should be noted that elasticities relate to proportionate changes and that the absolute increase in tourist expenditures may still be higher further up the income scale as income increases. Further Development of the Model In estimating regression relationships all relevant variables should be included. Household composition is usually held to be the second most important determinant of consumption for many categories of goods. If household composition is important to holiday and hotel expenditure and is left out of the regression (i.e., relegated to the error term), then the estimates of income elasticity may be biased. The effect of number of children (N) on hotel and holiday expenditure is not clear. Also, the effect of children on expenditure may depend on income level and, thus, a cross product term (EN) is included. The published data does allow for an initial investigation including this factor, but because of difficulties in comparison between different types of household, the empirical work was restricted to families consisting of two adults and 0, 1, 2, and 3 children. Thus, the model was extended to the formulation: H = f (23, N, EN)
(7)
Again, the investigation used the double logarithmic and linear functional forms in estimation, using ordinary least squares with the correction for heteroscedasticity. Equation (7) could not be estimated in logs with the inclusion of N, because of the presence of families without children. When only expenditure on hotels and holidays (H) and total expenditure (E) were logged, the results proved to be poor. The number of children, as such, appeared to be insignificant and the percentage of the variation in the data explained by the regression equation was only 50%. The full results are given in Table 3. The estimates of the linear form proved more promising. The total expenditure variable was highly significant and showed a strong positive relationship to holiday expenditure. The inclusion of either the
DAVIES
Table
3. Statistical
Cons.
GE
Results
J;;L~~E
of Amended
Model
&EN
J;;H
- 10.44 (-3.01)”
+0.008 (6.35)b
-0.0068 (-0.69)
J;;H
- 10.28 (-3.96)b
+0.08 (8.0)b
- 0.006 (-2.0)
J;;H
-8.99 (- 3.32)b
+ 0.078 (7.81)b
&log(H)
-11.7 (- 1.68)
+2.5 (1.95)
-13.39
+2.81 (2.84)”
&log(H)
697
AND MANGAN
&N +0.202 (0.074)
- 1.58 (-1.83)
(-2.5) J;; log (H) - 14.63 (- 2.55)”
+3.02 (2.82)
+0.001
- 0.79 (0.77)
(0.4)
-0.4 (- 1.2) -0.0012 (-0.98)
R~
F
0.81
22.9
0.83
37.2
0.82
35.5
0.4
4.29
0.44
6.8
0.42
6.34
Note: The figures in parenthesis are t-statistics. “Significant at .05 level of probability. bSignificant at .Ol level of probability.
number of children or the cross product term between children and expenditure improved the fit. Eighty-two percent of the variation in the data was explained. However, there appeared to be problems of multicollinearity between N and EN. Dropping either led to income being significant (at the 95% confidence level) and children nearly significant (significant at the 90% confidence level). In either case, increases in the number of children meant a reduction in expenditure on holidays and hotels. The estimated equation with the cross product term (cf. Table 3) is:
H = -10.28
+ 0.0834
E - 0.0061
EN
(8)
This form of equation does not give constant elasticities. The estimated expenditure elasticities at various points are given in Table 4. Hotel and holiday expenditure is income elastic for all income groups. The
Table
4. Elasticities
Expenditure E251.1 f170 E376.6
Level
(mid-point)
of the Amended
Model
Elasticity Equation 8 (linear) 2.1 4.1 1.5
Note: The elasticities presented are for households without children. The effect of EN alters the elasticities slightly for families with children. For instance, the elasticity at the midpoint for a family with three children is 2.6.
698
FAMILY EXPENDITURE
ON HOLIDAYS
estimates suggest that an increase in total expenditure of 1% for lower income groups leads to over 4 % increase in hotel and holiday expenditure. For upper income groups, the corresponding increase is only 1.5 76. For decreases in total expenditure the reverse would apply. The calculated elasticities are very similar to the results reported in the previous section, even given the different aggregation and the small sample sizes. What is important is that both calculations show a very high responsiveness by low income families. Low income families spend very little on hotels and holidays, but may be prepared to increase such expenditure rapidly with small income gains. At low level of incomes, it could be expected that the additional financial burden of children would reduce expenditure in this area. The results suggest that, even at medium and high levels of income, the number of children in a family reduce the expenditure on hotels and holidays. CONCLUSIONS The study confirms the general understanding in tourism studies that tourist expenditures are a long way from saturation point. From the investigation, using the simple model, the estimates for the double logarithmic and linear forms both show a good fit, but the implications for the tourism industry differ. The double log form gives a constant expenditure elasticity, while the linear formulation has elasticities that are very high at low income levels, and lower but still elastic at high income levels. The results of the extended model further suggest that the linear formulation is more appropriate. This implies that at the lower end of the income scale, a small difference in income has a large impact on hotel and holiday expenditures. Increases in real incomes may well continue to bring rapid growth to the hotel and holiday market. This growth may be more pronounced for low income groups. In general, these findings may be interpreted positively by the industry. However, in times of cyclical decline, the magnitude of the estimates suggest that the decline in the industry will be far greater than any decline in income. Expenditure by low income households will particularly suffer. From the extended model, it is not clear that the number of children is of importance in determining hotel and holiday expenditure. To the extent that it is important, the effect appears to be negative. Therefore, holiday and hotel businesses may need to think more about the nature of the products they provide. The family holiday is of some importance, but families appear to restrict the market in the short term. An aging population may well have a positive effect, a baby boom a negative one. The results considered here are only an initial investigation using published aggregate data. The results on the expenditure elasticities and household composition suggest that a more detailed study is warranted using a larger sample size. Family Expenditure Survey data is available as an anonymized data tape for academic research. Using this gives access to a larger sample size. Such an investigation is necessary to be able to clarify the functional form and to identify behavioral
DAVIES
AND MANGAN
699
characteristics that may influence differing spending patterns. Further work can also be undertaken comparing results over different years, given the need to generalize to developments over time for forecasting purposes. 0 0 REFERENCES Deaton, Angus S. 1974 The Analysis of Consumer Demand in the United Kingdom, 1900-1970. Econometrica 42:341-367. Engel, Ernst 1857 Die Produktions und Consumptionsverhaltnisse des Consumptionsverhaltnisse des Konigreichs Sachsen. Zeitschrift des Statistischen Bureaus des Koniglich Sachsischen Ministerium des Innern 22. Guerts, Michael 1982 Forecasting the Hawaiian Tourist Market. Journal of Travel Research 2 1: 1821. Klein, Lawrence 1962 An Introduction to Econometrics. London: Prentice Hall. Morgan, James N. 1986 The Impact of Travel Costs on Visits to U.S. National Parks. Journal of Travel Research 25:23-28. Pyo, Sung Soo, Muzaffer Uysal, and Robert McLellan 1991 A Linear Expenditure Model for Tourism Demand. Annals of Tourism Research 18:443-454. Witt, Stephen 1980 An Abstract Node: Abstract (Destination) Node Model of Foreign Holiday Demand. Applied Economics 12 : 163- 180. Witt, Stephen, and Christine Martin 1987 Econometric Models for Forecasting International Tourism Demand. Journal of Travel Research 26:23-30. Submitted 10 January 1991 Revised paper submitted 22 February 1991 Second revised paper submitted 17 June 1991 Final version submitted 12 December 199 1 Refereed anonymously Coordinating Editor: Turgut Var