Analysis of the economic impact of water management policy on residential prices: Modifying choice set formation in a discrete house choice analysis

Abstract

This paper extends discrete residential choice models by incorporating choice set formation. Most discrete residential choice models make relatively arbitrary assumptions about the choice set – the set of houses to be considered by the purchaser. In this paper we explore several formulations of endogenous choice sets in which the decision maker's selection of a choice set is based on certain attributes and the final selection is made from this reduced choice set. The proposed approach is empirically applied to a housing transaction dataset and welfare measures are generated for non-marginal changes associated with a water management policy. A comparison of models across different temporal windows to define an individual's choice set shows that model parameters are sensitive to the assumptions used to define the choice sets. The models that approximate choice set formation improve the efficiency of estimation and influence estimated welfare measures suggesting the importance of choice set formation in the context of discrete housing choice models.

Introduction

Most empirical studies have employed hedonic property analysis to investigate the economic value of environmental attributes associated with property values. Even though the value of changes in environmental attributes can be evaluated by marginal implicit prices obtained from a first-stage and quasi-experimental hedonic property analysis, this value would be valid only for marginal changes in attributes (Grafton et al., 2004). As well, it will be a good approximation of welfare change only if the assumption regarding a localized impact of change in environmental attributes is met.

For validating non-marginal changes in attributes as well as identifying more precise welfare measures, two different methodologies using revealed preference data (market data) can be considered; a two-stage hedonic approach and a discrete residential choice model. The two-stage hedonic method can be used to recover an inverse demand function but this approach is challenging to apply since it must deal with issues such as data availability and econometric-related issues (Phaneuf and Requate, 2017, Bockstael and McConnell, 2007).

The discrete residential choice model, initially developed by McFadden (1978),¹ can also be used to value changes in housing attributes. The main distinction between the hedonic model and the discrete choice model are the different approaches used to uncover preference parameters (Bockstael and McConnell, 2007). While the hedonic approach depends on the precise gradient of the estimated hedonic function since it requires marginal implicit prices of attributes in order to incorporate them into a second-stage hedonic model, the discrete choice model does not require this step since preference parameters can be directly recovered from the utility function identified from parameter estimates. This advantage has appeal for the application of a discrete choice model in the environmental valuation literature.

In this study we develop discrete residential choice models based on random utility theory to investigate non-marginal changes in major environmental attributes (water resources) in a local area. Prior use of discrete choice models to examine residential choice in the context of environmental amenities include Palmquist and Israngkura (1999) and Banzhaf and Smith (2007). We extend this literature by examining the issue of the choice set, which approximates home buyers' consideration set in their housing purchase behavior. While choice set formation has been addressed in other literatures such as transportation mode choice and recreational site choice, it has not been well-researched in the residential choice literature. Examples include Manski, 1977, Swait and Ben-Akiva, 1987a, Swait and Ben-Akiva, 1987b, Horowitz and Louviere, 1995, Ben-Akiva and Boccara, 1995, Peters et al., 1995, Haab and Hicks, 1997, Cascetta and Papola, 2001, Martinez et al., 2009, and Truong (2013). In these studies the motivation for examining choice set formation relates to the decision makers' costs of acquiring information. While they might want to be fully informed about all choice alternatives, they typically do not have time or energy to characterize their full choice set and therefore use rules of thumb or heuristics to pare down the number of alternatives. In residential choice cases, however, while buying a house is an important decision and thus home buyers could expend considerable effort on discovering complete choice alternatives, they don't necessarily need to when defining their consideration set. For example, they could provide a realtor with a list of priority residential attributes; then the realtor will find a set of houses which meet their requirements. So, even for such an important decision, home buyers may not necessarily be willing to incur the costs of developing a fully informed choice set.²

Therefore, in the context of residential choice analysis, the choice set issue will be important because an analyst must make assumptions about the size and extent of the set of choices from which a home buyer will make a purchase. As discussed by Banzhaf and Smith (2007), the model parameter estimates of attributes will be affected by the assumptions regarding the choice set and thus the assessment of welfare measures associated with environmental attributes will vary depending on these assumptions.

Our approach to construct sets of choice alternatives is different from previous studies in terms of relaxing some of the assumptions to be made. First, unlike previous studies that assumed all households face the same number of alternatives, we allow for the number of choice alternatives to vary among each household depending on the temporal windows used to define the choice set. We think this better represents the purchasing environment faced by prospective buyers. Second, given the choice sets defined by spatial and temporal extent, we relax the assumption that decision makers equally consider all alternatives in their choice set. That is, while some alternatives in the choice set are available to the decision maker, the degree of their consideration could differ based on particular attributes of those alternatives. To allow for varying degrees of availability of properties, we take into consideration some important housing attributes (e.g. house prices and perceived need for renovation) that home buyers could consider for their final purchase decision.

Our application involves housing in the Town of Chestermere and nearby Glenmore reservoir in Calgary, Alberta from 2000 to 2010. Our particular focus involves the use of a discrete residential choice model to assess the economic value of increases in the supply of aquatic ecosystem services provided by a major local water body - Chestermere Lake used for irrigation water storage.³ We focus on investigating welfare measures associated with the implementation of the 2005 Water Management Agreement signed by the Town and the Western Irrigation District⁴ who is in charge of managing/operating Chestermere Lake to control water level and quality in the lake for irrigators. In the next section, we provide background information in more detail regarding the water management policy in the study area.

We compare various choice models defined using different choice sets. For the comparisons of models defined by different temporal windows, we apply statistical tests discussed by Ben-Akiva and Lerman (1985) and examine consistency with theory to determine the models of interest. Given the choice sets defined with different temporal dimensions, we estimated models with/without the choice set formation using one sample of choice sets that we chose as a preferred model and compare welfare measures associated with a hypothetical situation involving no implementation of the water management agreement to examine the impact of choice set considerations on welfare measures.

Section 2 provides background on the study area. The relevant literature is reviewed in section 3. We also discuss two different approaches to define the unit of choice in residential choice modelling settings as well as their advantages, disadvantages, and the appropriate context for their application. The forth section outlines our empirical model specifications including our strategy used to define choice sets. The data employed in this study are described in section 5, while section 6 presents the empirical results and welfare measures. Section 7 concludes the analysis.