Frequency and time in recreational demand

ABSTRACT

In the standard single-site travel cost model, it is assumed that time spent on-site is exogenous. This assumption results in a willingness to pay (WTP) for time on-site of zero, which may be less realistic for many urban parks that are frequently visited by local residents. We develop a single-site travel cost model where a visitor simultaneously chooses the number of visits and how much time to spend on-site. In this model, the WTP estimate includes the price of the trip and the price of time spent on-site. Next, we develop a two-part hurdle model with non-zero correlation between the number of trips and time spent on-site. We use data gathered in an urban park in Iceland to estimate the model. The estimated WTP values are more than twice as high as the estimates of the standard single-site model.

KEYWORDS:

• Count data
• endogenous time on-site
• hurdle model
• travel cost model
• urban parks
• willingness to pay

JEL:

• Codes: C51
• Q26
• Q51

Acknowledgement

This paper is based on a survey conducted for the project: ‘Heiðmörk – the economic value of ecosystem services’, funded by the Icelandic Research Council, City of Reykjavík, the municipality of Garðabær, Reykjavík Energy and the University of Iceland.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Notes

1 There are few empirical applications of the single-site travel cost model to urban parks. Exceptions include Lockwood and Tracy’s (1995) application of a zonal travel cost model to data on recreational use of Centennial Park in Sydney and Martinez-Cruz and Sainz-Santamaria’s (2017) application of a latent class count data model to recreational use of two parks in Mexico City. However, these studies did not explore the effects of endogenous time spent on-site. Another issue related to urban parks is the limited variation in travel costs of the users. We also note that empirical estimation of welfare estimates is complicated when urban parks, such as Central Park, are tourist attractions. Not only is it difficult to allot travel cost for a multipurpose trip, but there are at least two latent demand functions behind the recreational demand, one for locals and another for out of town visitors. The locals’ demand curve is likely to be relatively flat in travel cost while the visitors’ demand curve will be much steeper and more in line with what is seen for national parks. However, these problems are beyond the scope of this article.

2 The importance of time costs in welfare calculations are discussed in Goolsbee and Klenow (2006). They pointed out that for some goods, such as the Internet or watching television, the main cost is not buying the product but the opportunity cost of time spent using them. They also showed that the endogeneity of time is crucial for welfare estimates related to such goods.

3 Hellström (2006) used the number of nights spent at the location as a time unit, and assumed a discrete data generating process of time spent on-site. Our focus is on urban parks where time on-site is measured in hours and minutes, and we assume that time spent on-site is continuous.

4 Due to computational challenges, few studies have applied hurdle models that account for non-zero correlation between stages in count data literature. Two examples of such studies are Winkelmann (2004) and Min and Agresti (2005).

5 As mentioned in Martinez-Cruz and Sainz-Santamaria (2017), it is usually difficult to find close substitutes to urban ecosystems or urban parks. This is also the case for the Reykjavik area with no other urban parks, and substitute sites are not a part of the model. However, it is straightforward to extend the model to account for substitute sites.

6 Constant time on-site on each trip for one individual is a simplification, however, it is consistent with our data. This consistency may suggest that most individuals have a quite habitual pattern in their visits to the park. 

7 Total travel cost per trip can be defined as: $p_n=p_c+p_{\tau }\tau$, where $p_c$ is all out of-pocket costs incurred by a trip, $\tau$ is travel time and $p_{\tau }$ is the price per unit (hour) of travel time.

8 For complete derivations of Equation (3), the dual optimization problem, and associated identities, we refer the reader to the online supplementary material.

9 For a general overview of the Riemann-Stieltjes integral see, for example, Widder (1989). See the online supplementary material for a complete derivation of the WTP estimates.

10 The number of trips and time spent on-site are complements in the sense that one cannot consume the recreational good without taking a trip. However, the visitor is likely to make a trade-off between the number of visits and time spent on-site.

11 We assume that the decision-making process for the number of trips is continuous even though observed trips are discrete.

12 This can occur for two reasons. First, for users who live near the area, the cost of travel is negligible. For example, the transportation costs are negligible for many local users of Central Park in New York, where a large share of Manhattan's residents live within a mile radius from the park. Second, the opportunity cost of total time on-site may be high. For the opportunity cost of total time on-site to be able to dwarf the price of the trip, the price of time on-site must be relatively high since the daily time on-site is bounded by the individual's available time. A relatively high price of time on-site is plausible in affluent metropolitan areas where individuals often need to work long hours to keep up with their employers’ demands.

13 This conclusion does not change even if the opportunity cost of time spent on-site, $t{p}_t$, is added to the travel cost variable in the standard single-site model.

14 For more details on the econometric model, see the online supplementary material.

15 Note that we do not need to assume a truncated distribution for trips since the data includes zeroes for those who did not take a trip in the previous calendar month.

16 We refer readers to McKean, Johnson, and Taylor (2003) for a method of adjusting overdispersion and endogenous stratification simultaneously.

17 However, given an income variable that is independent of the prices, it is straightforward to include income in the empirical specification. Furthermore, the direct effect of income on WTP is limited to part (c) of Equation (10), which again is scaled by the income share spent on travel to recreational site. The effects of not using income as a separate variable in the empirical estimation are therefore likely to be small. A discussion about the theoretical issues related to how the opportunity cost of time should be estimated is beyond the scope of this paper. We refer readers to McKean, Johnson, and Walsh (1995), McKean, Johnson, and Taylor (2003), Amoako-Tuffour and Martinez-Espineira (2012), and references therein for developments in estimating the opportunity cost of time.

18 A 1/3 of the hourly wage rate is widely accepted as a lower bound of the opportunity cost of time (Parsons 2003; Hagerty and Moeltner 2005; Voltaire et al. 2016).

19 The marginal cost of driving was assumed to be the price of petrol. Following Victoria Transport Policy Institute (2015), the average fuel consumption was assumed 51/100km for motorcycles, 9.51/100km for mid-sized sedans, and 13.51/100 for SUVs. The cost of petrol was based on monthly prices of petrol from June of 2008 to September of 2009. The price of petrol, 95 Octane, on January 1^st 2008 was 139.5 ISK/l. Monthly changes in the price were obtained from Statistics Iceland (2015). The marginal cost of other travel modes than driving, i.e., walking, running, cycling, or horseback riding was assumed to be zero.

20 Although the self-reported percentage of a multipurpose trip is an imperfect measure, it is better to use this measure than dropping observations that report a multipurpose trip, which would lead to a bias in the WTP measure. It can also be argued that this measure is no more flawed than the acceped way to measure the opportunity cost of travel time. We refer readers to Martínez-Espineira and Amoako-Tuffour (2009) for a discussion on how to handle the issue of multipurpose trips.

21 See the online supplementary material for the derivation of the WTP estimates based on the empirical specifications of n and t.

22 Otherwise there does not exist a closed form for the WTP for access given by Equation (19).

23 The half-price elasticity shows the percentages change in the quantity demanded for the variable for a unit change in its price.

24 See the online supplementary material for proofs of homogeneity and a proof of the no symmetry condition between n and t.

25 The average exchange rate for the year 2015 was ISK 130 = US$ 1.