Long-run water demand estimation: habits, adjustment dynamics and structural breaks

Abstract

This article examines a water demand equation for Milan for the second half of the 20th century: 1950–2001. We focus mainly on the effects of price and habits, but also account for other factors in the demand for water such as climate, income and productive activity. Allowing for trend break stationarity or nonlinear trend stationarity, we find evidence against the unit root hypothesis for many time series. Based on this result, standard cointegration analysis would not be appropriate; therefore we adopt an alternative estimation and testing procedure. We focus, in particular, on the so-called bounds testing approach, which can be applied irrespective of the level of integration of the variables and which can be a useful modelling strategy given that dynamics are important when estimating a water demand equation. The main results are that long-run price elasticity is higher than short-run elasticity, and that consumption habits are relevant. We also find that both climate, sectoral and technological modifications affect water consumption, while income is not significant. Finally, the changes to pricing schemes in the mid-1970s provoked reactions of different magnitudes among households and firms.

Notes

¹ Pesaran et al. (2001) make a nonstandard assumption that the roots of are either outside the unit circle |z| = 1 or satisfy z = 1. This enables the elements of z _t to be I(1), I(0) or cointegrated.

² Probably, the main limitation of our data is that they do not allow the decomposition of total water consumption with respect to different typologies of users (residential industrial and commercial) except for few years at the end of the period. In a micro-econometric setting with disaggregated data, water demand for a water of each typology of user is estimated in a specific way. While residential water demand is obtained by maximizing consumers’ utility, industrial water is introduced as an input of production (generally it is considered as a substitute of labour and complementary to capital; Renzetti, 1992) and it is often estimated in a cost function framework. In spite of such a limitation, we believe that our data allow us to provide interesting new information about long-run structural dynamics of total water consumption in a relevant policy scenario, which is that of a big European city. Moreover, we did some nonreported robustness checks using an alternative definition of the dependent variable relative to consumption since we add total employment to total population within the denominator. This alternative definition could be relevant for studying industrial water consumption. Nonreported results confirm our main findings.

³ In the year 2001, the most relevant part of the water bill regards the first block price rate which considers per capita consumption within 350 litres per day. The average water supplied for domestic consumption by Milan's water network is around 353 litres per day, obtained by 172.7 million m³ supplied in the year to the 1 339 933 citizens. Statistics about water consumption relative to the 50 years considered in this analysis and depicted in Fig. 1 concern total water consumption and not only residential/domestic water consumption. A recent comparative report on water consumption in Europe shows that Milan, with around 350 litres per day, presents a very high per capita domestic consumption compared to other European cities (Ambiente Italia, 2006).

⁴ Obviously there are many other variables involved in water demand, such as the demographic structure of the city. Unfortunately, yearly data on this and other variables are not available; many time series that would have provided interesting data are collected by the national census only every 10 years.

⁵ In choosing m we are faced with a tradeoff: if m is too low – i.e. the nonlinear trend is more nonlinear than the Chebishev polynomial approximation – this might reduce the power of the test. On the other hand, if m is too high it may also reduce the power of the test by estimating superfluous parameters. We conducted the test using different values for m; the results were similar and are available upon request.

⁶ Draw the model errors from normal distribution with zero mean and variance from the squared (Ordinary Least Squared (OLS)) residuals.

⁷ See Pesaran and Shin (1999) and Pesaran et al. (2001) for a more detailed discussion of the different specifications.

⁸ Note, that since price and income present some degree of collinearity (see also Martínez Espiñeira, 2007) we also estimated the model including income, but excluding price as a regressor. The results (which are not reported here) confirm that income is never significant and presents an estimated coefficient still very close to zero.

⁹ See, among others, Carver and Boland (1980), Agthe and Billings (1980), Dandy et al. (1997), Renzetti (2002), Rossi (2005), Nauges and Thomas (2000, 2003).

¹⁰ For example, in 2001, the price of the third block was, € 0.41 per m³, while in many other European cities it was € 1–2 (UNEP, 2004).