The literature on water demand estimations shows that the functional form for the water demand equation can affect the price elasticity estimates. This paper evaluates the impact of different functional forms in the estimation of price and income elasticities within the discrete-continuous choice (DCC) models commonly used for increasing block price (IBP) schemes. This issue, functional forms in the DCC model of demand, has not been analyzed before in the water demand literature.
The estimation of the residential water demand is of course a recurring subject in the literature. From Headley (1963) and Howe and Linaweaver (1967) to date, there has been an increasing number of studies aimed at determining water demand, analyzing the factors influencing consumption or analyzing the impact of economic variables on the water demand. These efforts had led to extensive literature reviews (Arbués, García-Valiñas, and Martinez-Espiñeira (2003) and Ferrara (2008)), and to the development of meta-analyses intended to summarized the methodological characteristics of the studies and their implications (M. Espey, Espey, and Shaw (1997), and subsequently, Dalhuisen et al. (2003)).
Despite the fact that Arbués, García-Valiñas, and Martinez-Espiñeira (2003) show that the literature presents differences regarding the functional form used for the water demand equation, to the best of our knowledge, this literature has not analyzed this fact in the DCC model. Furthermore, In the continues demand models some functional forms prevailed, but a full discussion of the reasons to choose one functional form over the others is scarce in the literature. Some studies attempt to mitigate the uncertainty about functional forms by using more several specification and comparing their implications in terms of prediction and elasticities.
In fact, Dalhuisen et al. (2003) show that the functional form can affect the price elasticity results of the water demand. Therefore, water demand studies should consider the possible variability in their results when using a specific functional form. Whereas using more than one function to estimate the water demand does not solve the problem, it does allow expanding the number of possible results and obtaining the prediction and consumption elasticities for each one of the proposed functions.
The challenge when estimating water demand under increasing block pricing schemes is both the construction of the likelihood function and the estimation of the highly complicated elasticities. First, if consumers face an increasing block price system, there can be simultaneity in the choice of price and consumption. Hewitt and Hanemann (1995) and Olmstead, Hanemann, and Stavins (2007) solve this issue by using the DCC to estimate the water demand, assuming a logarithmic demand equation and since them the literature on DCC has continuo using that functional form.
Our paper fills this gap in literature. We estimate water residential demand under the DDC model using four functional forms (linear, logarithmic, semi logarithmic and Stone Gary) and analyze the differences between the expected consumption and price elasticity of the demand. Our results show the existence of significant differences between the expected water consumption and price elasticity when using different functional forms.