residential water demand in a Mediterranean tourist region
4.5 Econometric analysis
66 V. Statzu and E. Strazzera
idiosyncratic error iid N (0, σ ε2 ). The random- effects model is consistent and more efficient than the fixed- effect one if there is no correlation between αi and regressors.
A Breusch–Pagan test allows us to compare the validity of the pooled OLS versus the random effect estimator. The null hypothesis is that the variance of εi
is zero. If the null is not rejected, then we can presume that the pooled OLS is unbiased and consistent; if the null is rejected, the random- effects estimator should be preferred to the pooled OLS.
A Hausman test (1978) can be used to compare fixed and random effects. The Hausman test verifies exogeneity of individual effects: rejection of the null hypothesis of no systematic differences between FE and RE coefficients implies that there is correlation between regressors and unobserved individual heteroge-neity. If this is the case, RE, as well as OLS, are not consistent and should be rejected, and the fixed- effects model, or alternative models such as the instru-mental variables models, should be used instead. Unfortunately, in some cases the application of the Hausman test is not conclusive: when the matrix of the squares of the differences of the variances of the coefficients is not positive definite, the test is not reliable. Alternatively, Wooldridge (2002: 290–291) pro-poses a test to compare fixed- and random- effects models. This test consists in estimating a random- effects model where the time- demeaning variables of time- variant variables are inserted. Then a Wald test is used to see whether the time- demeaning variables are jointly not significantly different from zero; if this is the case, the random- effects model can be accepted.
Analysis of residential water demand 67
• annual income variable per tax payer (INCOME);
• demographic variables [household size (HHSIZE), proportion of people not part of the workforce (NWF )];
• housing characteristics [share of property homes (OWNERS), share of houses not renovated in the period 1991–2001 (NORENOV)];
• geographical variables [altitude of municipalities (ALT), population of towns (POP5000, POPOV15000) and the tourist impact dummy variables (TOUR1, TOUR2, TOUR3)];
• climate variable [summer evapotranspiration rate (SUMEVATRA)];
• water utilities dummies [(SIINOS, SIM, GOVOSSAI)];
• a variable that takes into account the number of hours of regular water dis-tribution (HOURS);
• year dummies (YEAR 2001, YEAR 2002, YEAR 2003, YEAR 2004, YEAR 2005).
The tourist impact variable and the summer evapotranspiration rate require some explanation. The tourist dummy variables indicate different levels of impact produced by tourists lodged in holiday homes: TOUR1 indicates towns with low impact (ratio tourists/residents less than 40 per cent), TOUR2 an intermediate impact (ratio tourists/residents between 40 per cent and 90 per cent) and TOUR3 high impact (ratio tourists/residents over 90 per cent). The summer evapotran-spiration rate indicates the environmental demand for water due to the inter-action between climate and vegetation. This variable considers the influence on indoor and outdoor consumption, since it represents the interaction between tem-perature and other climatic variables and allows one to account for the perceived climate in a region: areas with higher evapotranspiration in the summer months are characterized by higher perceived temperatures.
Average price, income, the summer evapotranspiration rate, the tourist impact and the water utilities variables are cross- sectional time series variables; the year dummies are time series variables; all other variables are cross- sectional time- invariant variables. Descriptive statistics can be found in Table 4.4.
We estimate the water demand model as an equation, linear in logarithms:
Log WATCONit( )=β0+β1log(APit)+β2log(INCOMEit)+β3log(HHSIZEi))
log( ) log( ) log( ) log( )
+
+ + + +
β4 NLFi β5 OWNERSi β6 NORENOVi β7 ALTi
ββ β β β
β8 5000 9 150001 10 2 11 3
12
( ) ( ) ( ) ( )
(
POP i + POPOV + TOUR i + TOUR i + TTOUR SUMEVATRAit HOURSit
SIMit
4 13 14
15 16
) log( ) log( )
( )
+ +
+ +
β β
β β (( ) ( ) ( )
( SIINOSit GOVOSSAIit YEAR it
YEAR it
+β +β +
β 17 18 2001
19 2002 ))+β20(YEAR2003it)+β21(YEAR2004it)+β22(YEAR2005it uit)+ when uit = αi + εit.
68 V. Statzu and E. Strazzera
The estimation results are reported in Table 4.5.
We start the analysis with the simplest model, the pooled OLS: its covariate specification was selected using standard Wald and F tests. Next, we test the OLS pooled model against the random effect estimator. Finally, we test the random- effects against the fixed- effects estimator.
The Breusch–Pagan test (test value: 327.96; p- value: 0.000) for the presence of random effects rejects the null hypothesis, which implies that the pooled OLS is inefficient and the random- effects estimator should be preferred.
In order to compare the random- effects and the fixed- effects estimators, we first used a Hausman test: however, in our application this test is not reliable since the matrix of the squares of the differences of the variances of the coeffi-cients is not positive definite. As was explained in section 4.4, we can apply an alternative test: the Wooldridge test does not reject the random- effects model, so we select this model as our preferred specification.
Further tests for heteroscedasticity and serial correlation in data (the Breusch–Pagan test for heteroscedasticity: test value: 0.00; p- value: 0.979; the
Table 4.4 Statistical description of variables
Media Std. dev. Data Measure Source
WATCON 130 49 CS–TS mc Water utilities
AP 1.06 0.96 CS–TS Euros Water utilities
INCOME 9541 2560 CS–TS Euros Ministry of Treasury
HHSIZE 2.74 0.23 CS Number ISTATa
NLF 0.57 0.05 CS Share ISTAT
OWNERS 0.85 0.07 CS Share ISTAT
NORENOV 0.75 0.06 CS Share ISTAT
ALT 264 222 CS Metres ISTAT
POP5000 0.87 0.34 CS Dummy ISTAT
POPOV15000 0.008 0.090 CS Dummy ISTAT
TOUR2 0.03 0.17 CS Dummy ISTAT
TOUR3 0.09 0.29 CS Dummy ISTAT
TOUR4 0.04 0.19 CS Dummy ISTAT
SUMEVATRA 151.13 16.17 CS–TS Mm RAS
HOURS 5880 2472 CS–TS Number Water utilities and
SIM 0.003 0.059 CS–TS Dummy RAS
SIINOS 0.003 0.059 CS–TS Dummy
GOVOSSAI 0.06 0.24 CS–TS Dummy
YEAR2001 0.17 0.37 TS Dummy
YEAR2002 0.17 0.37 TS Dummy
YEAR2003 0.17 0.37 TS Dummy
YEAR2004 0.17 0.37 TS Dummy
YEAR2005 0.17 0.37 TS Dummy
Notea ISTAT (Italian Institute of Statistics), National Census, 2001.
Table 4.5 Estimation results
OLS FIXED EFFECT RANDOM EFFECT – GLS
INTERCEPT 0.207 2.50*** 0.609
(0.35) (3.35) (1.00)
AP −0.136*** −0.139*** −0.146***
(−6.36) (−6.49) (−7.50)
INCOME 0.194*** 0.066 0.163***
(5.61) (1.61) (3.61)
HHSIZE 1.138*** 1.141***
(13.33) (8.34)
NLF −0.254*** −0.281**
(−3.15) (−2.16)
OWNERS −0.434*** −0.453***
(−4.35) (−2.81)
NORENOV 0.189** 0.154
(2.25) (1.14)
ALT −0.020*** −0.022**
(−3.53) (−2.44)
POP5000 0.075*** 0.639*
(3.28) (1.75)
POPOV15000 0.458*** 0.449***
(6.34) (3.87)
TOUR2 0.093*** 0.095**
(3.85) (2.42)
TOUR3 0.193*** 0.172***
(4.59) (2.57)
TOUR4 0.253*** 0.250***
(6.55) (4.01)
SUMEVATRA 0.157*** 0.083 0.108**
(2.75) (1.41) (1.97)
HOURS 0.032 0.052 0.045
(0.65) (1.24) (1.08)
SIM 0.705*** 0.086 0.505***
(6.35) (0.40) (3.47)
SIINOS −0.211* 0.154 −0.079
(−1.84) (0.73) (−0.54)
GOVOSSAI 0.093** −0.046 0.038
(2.24) (−0.80) (0.88)
YEAR 2001 0.668*** 0.677*** 0.669***
(28.47) (33.50) (33.87)
YEAR 2002 0.516*** 0.551*** 0.532***
(13.90) (16.23) (16.58)
YEAR 2003 0.551*** 0.574*** 0.558***
(19.88) (20.72) (22.58)
YEAR 2004 0.509*** 0.531*** 0.515***
(12.90) (13.81) (14.73)
YEAR 2005 0.465*** 0.480*** 0.470***
(10.98) (11.18) (12.36)
N 1440 1440 1440
R-squared 0.63 0.43 0.63
Notes
In parentheses: t statistics: * 10% significance level; ** 5% significance level; *** 1% significance level.
Analysis of residential water demand 69
70 V. Statzu and E. Strazzera
Wooldridge test for serial correlation of order 1: test value: 9.284; p- value:
0.026; DW = 1.62) show the absence of heteroscedasticity and a slight presence of serial correlation. Wooldridge (2002: 274) notes that serial correlation could be a problem when strong correlation is present and T is quite large. If serial correlation is low and T is short, as in our application, it may be preferable not to correct for this problem, as this would imply a cost in terms of loss of observations.
The random- effects estimates show a significant effect of price, with an elas-ticity value of −0.146. This value is somewhat lower than the value (about
−0.20) found in other studies that use average price and aggregated data (Höglund, 1999; Nauges and Thomas, 2000). Also, the income variable is signi-ficant and shows the correct positive sign. The elasticity value is +0.105, close to the values found in previous literature, apart from Mazzanti and Montini (2006), who find higher values (a range varying from +0.40 to +0.71).
The household size variable is significant, and its coefficient indicates that consumption increases a little more than proportionally following an increase in the household size.
The proportion of people not in the workforce is significant and with a negat-ive sign. In the literature, similar variables (housewnegat-ives, retired and unem-ployed people) are inserted to see whether people who spend more time at home have different levels of water consumption as compared with the rest of the population. Our result could be explained by a reduction in social life conse-quent on the reduction in working activity, as argued by Liao and Chang (2002) in a survey study of the consumption of hot water and electricity by older people in the United States. Another explanation could be that people who spend more time at home may control leaks or other water waste more efficiently.
Homeowners consume less than renters. This result is found quite often in the literature and is probably due to the fact that often the rent includes the water bill, so that renters do not receive the correct price signals in relation to Table 4.6 Test results
Test Test value p-value
Breusch–Pagan test for no heteroscedasticity in pooled
OLS 0.00 0.979
Wooldridge test for no autocorrelation in panel data 9.284 0.0026
Durbin–Watson test for serial correlation 1.62 Lower DW bound:
about 1.89 Hausman test for no endogeneity between FE and RE 23.38 0.025*
Wooldridge test for no differences between FE and RE 7.57 0.1085 Note* Matrix of coefficients is not positive definite.
Analysis of residential water demand 71 their consumption behaviour. The efficiency of the indoor and outdoor water system (pipes, taps and toilets) should influence the total consumption amount, but the variable indicating renovation is not significant in the random- effects model.
The altitude variable has a significant negative effect on water consumption.
This may be due to the characteristics of houses in different territories in Sar-dinia: houses in hilly towns generally do not have gardens, unlike valley and coastal towns. Unfortunately, lack of data on the presence and size of gardens in the municipalities prevents us from explicitly evaluating the influence of the presence of gardens on water demand. The dummy variables for population indi-cate that water consumption is not monotonic with town size, since medium- sized municipalities consume less than do either small or large towns. The climate variable is significant and with the expected sign. Where the summer evapotranspiration rate is higher, water consumption increases. High values of this variable imply that the climate is more arid (the level of precipitation is low) and the temperature is higher: this situation leads to high water consumption, probably for outdoor uses. As we said earlier, lack of data prevents us from directly measuring the influence of the presence of gardens on water consumption.
Considering the water management variables, we notice that the coefficient of the variable hours (i.e. hours in a day with regular service) is not signific-ant: this implies that water- rationing measures did not have a significant influ-ence on consumer behaviour. In fact, after a first year (2000) when the restrictions were effective in reducing consumption, users adopted defensive measures (water tanks) that offset the regulations imposed. Year dummies show that even though water- rationing measures were implemented, 2001 and 2003 are characterized by the highest average yearly consumption. Lower coefficient values are associated with 2004 and 2005, when there was a regular distribution of water; the lowest coefficient is that for 2005; we may recall that this is the year when the reform of the water supply system came into effect.
The water utilities dummies indicate that SIM customers consume more than the ESAF customers, while the opposite is the case for the SIINOS customers.
These differences can be explained by differences in the tariff systems (the number and size of blocks applied by SIINOS penalize higher consumption more than do SIM tariffs) and in the management of the billing procedures (SIM had not sent bills to customers for a long period, while SIINOS sent out its bills every six months).
Finally, the estimated coefficients give a measure of how tourism in holiday homes affects the level of water consumption for residential uses. The effect is quite relevant: towns characterized by a high tourism impact are expected to consume about 32 cubic metres per year per user more than non- tourist towns (see Table 4.7).
For a relatively small number of visitors (a ratio of tourists to residents of less than 40), tourism is estimated to induce a 10 per cent increase in the levels of consumption of water; when the ratio of tourists to residents is between 40 and
72 V. Statzu and E. Strazzera
90, we expect a rise of about 19 per cent; while higher ratios of tourists to resi-dents will increase the residential yearly water consumption by about 28 per cent per user.