Electronic Supplementary Material from Valuation to Governance: Using Choice Experiment to Value Street Trees

This paper reports a choice experiment used to estimate the value of street trees in the city center of Lodz, Poland, and the broader context of how valuation results helped to improve governance of urban ecosystem services in this city. Based on a simplified inventory of trees, we prepared a set of hypothetical programs which put varying emphasis on the different ways to increase the numbers of trees, along with different levels of a hypothetical tax that would have to be paid by respondents to implement a given program. Our study indicated that the 351 surveyed Lodz residents were willing to pay the highest price for greening those streets where currently there are few or no trees and confirmed the general importance of planting trees. The results provided an argument in the debate on the new development strategy for the city and helped to promote the concept of ecosystem services. Electronic supplementary material The online version of this article (doi:10.1007/s13280-014-0516-9) contains supplementary material, which is available to authorized users.


Choice experiment
In a choice experiment individuals are asked to identify their preferred choice i from a given set of J alternatives. The data analysis follows a RUM under which, it is assumed that the observed choice from individual n is the one he/she expects to provide him/her with the highest utility (McFadden 1974). His/her utility function, ni U , can be decomposed into a systematic part, V ni , and a stochastic part, ni ε , i.e.: The probability P ni that individual n chooses alternative i instead of another alternative j of the choice set is: If nj ε is assumed to be an independently and identically distributed extreme value type I, this probability has a closed form expression, , where x is a vector of variables and β a vector of parameters. The above expression is often referred to as a logit choice probability function or Multinomial Logit Model (MNL).
The standard MNL has three limitations, as listed by Train (2003): (i) it exhibits a property of independence from irrelevant alternatives; (ii) MNL can represent only the systematic preference variation but not random preference variations; (iii) it cannot handle situations where the unobserved part of the utility function is correlated over time.
In addition to an MNL model, the data were analyzed with a mixed logit model, a model which relaxes the above limitations of MNL. Mixed logit probabilities can be expressed as the integrals of standard logit probabilities over a density of parameters. Following Train (2003) is the density of the random coefficients with mean b and covariance Ω.
In a standard MNL the unobserved factors that affect respondents are assumed to be independent over the repeated choices, which may be considered unrealistic as respondents usually make more than one choice. There might be some unobserved factors that are constant

Distribution assumption in MMNL
There has been discussion in the field of choice modeling about acceptability of different distributions for the cost coefficient (e.g. Hensher and Greene 2003). As pointed by Daly, Hess, and Train (2012), this discussion has generally focused on the behavioral realism of 3 allowing for positive values in the distribution of the cost coefficient, rather than the possibility of non-existence of moments for the willingness to pay (WTP) distributions. Daly et al. (2012) showed that some popular distributions used for the cost coefficient in random coefficient models, including normal, truncated normal, uniform and triangular, imply infinite moments for the distribution of WTP, even if truncated or bounded at zero. Daly et al. (2012) also presented a theorem that allows researchers to test whether the distribution of WTP has finite moments. Using this theorem, they showed that log-normal and Johnson's Sb distribution have all inverse moments in their basic specifications (i.e. with the domains between 0 and infinity for the log-normal, and 0 and 1, or any other positive number, for the Johnson Sb). Given that in the field of environmental valuation the moments of WTP distribution, especially the mean, are of crucial interest, we decided to assume log-normal distribution for the cost. This assumption guarantees that the resulting distributions of WTP are useful and meaningful.
Assuming cost to follow log-normal distribution is not often in non-market valuation, a standard practice is to assume the cost coefficient to be fixed. The three most commonly given reasons for this are: (i) the distribution of the marginal WTP for an attribute is then simply the distribution of that attribute's coefficient; (ii) in this way analysts wish to restrict the price variable to be non-positive for all individuals; (iii) analysts avoid assuming lognormal cost because it is often found to produce behaviorally implausible estimatesi.e. 'exploding' implicit prices (Daly et al. 2012;Carlsson, Frykblom, and Liljenstolpe 2003).
In order to avoid problems with 'exploding' WTP values, in this paper we follow the approach proposed by Giergiczny et al. (2012), i.e. we assumed cost to be log-normally distributed but in order to prevent dividing by very small values we add into the utility function cost/income ratio. This approach allows price sensitivities, hence WTP, to vary with income level. All other non-monetary attributes were assumed to be normally distributed.