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1、Environmental Economics, Volume 3, Issue 2, 2012 57 Artti Juutinen (Finland), Rauli Svento (Finland), Yohei Mitani (Norway), Erkki Mntymaa (Finland), Yasushi Shojie (Japan), Pirkko Siikamki (Finland) Modeling observed and unobserved heterogeneity in choice experiments Abstract Fast progress has rece

2、ntly been made in heterogeneity modeling in the choice experiment models. Especially scale hetero- geneity has been given new explicit role and interpretation. This paper estimates scale heterogeneity extended stated prefe- rence models with special emphasis on including both observed and unobserved

3、 heterogeneity. The results show that the scale heterogeneity augmented models are not generally enough to consider both preference and scale heterogeneity. Instead the preference heterogeneity needs to be explicitly modeled also in the Generalized Multinomial Logit model. Keywords: choice experimen

4、ts, stated preferences, scale heterogeneity, observed heterogeneity, unobserved hetero- geneity. JEL Classification: C25, Q51, Q57. Introduction Heterogeneity modeling in choice experiment set- tings has proceeded fast recently. Especially the role of scale heterogeneity modeling has reached new lev

5、els. Papers by Fiebig et al. (2010) and Greene and Hensher (2010) have shown how scale heterogeneity can be modeled and how different versions of multi- nomial logit models can be derived from their models as special cases. In this paper we use the Generalized Mixed Logit (GMXL) model and investigat

6、e the role of scale heterogeneity by modeling the respondent heterogeneity explicitly in this GMXL model. We include both observed and unobserved heterogeneity in the model. Our data is a stated preference data related to the managerial development of the Oulanka National Park in Finland (see Juutin

7、en et al., 2011). The research concerning the roles played by prefe- rence and scale heterogeneity in stated preference models is still in its beginnings. Some robust results can, however, already be stated. The differences between the studied commodities show clearly in earlier results, the more co

8、mplicated the choice situ- ation is (e.g. the particular commodity is unfamiliar It seems to be the case that the Generalized Mixed Logit model (GMXL) turns out to capture the data generating processes in a more accurate manner than the usual random parameter versions of the conditional logit model.

9、 More research, especially empirical evi- dence, is still needed in clarifying and identifying the roles of preference related and scale related heteroge- neities in the generalized logit model setting. Our hy- pothesis is that it is too bold an assumption to assume that both of these can be capture

10、d by a single scale factor in the model (see also Hess et al., 2009). The paper is organized as follows. Section 1 presents the specification and estimation details of the gene- ralized multinomial logit model. Section 2 explains our choice experiment setting and section 3 gives the results. The fin

11、al section concludes. 1. Heterogeneity in stated preferences The usual starting point in choice experiment (CE) modeling is the conditional logit model (CLM) of McFadden (1974) which assumes that the error terms have a heteroscedastic extreme value (HEV) distribution U x ,i 1, , N; j 1, , J , for re

12、spondents) the stronger the role scale hetero- geneity seems to play, see e.g. Fiebig et al. (2010). We have only one commodity in our study so that ij ij ij Prob( yi j | xi1 ,. , xi J ) e xij , j x (1) we do not open this comparison but since our case is related to environmental valuation we can ex

13、pect the scale heterogeneity to have a role in our data. Valuation of environmental commodities, especially F ij exp expij , e ij j1 in the context of national park management, can be expected to be a heterogeneity creating and hetero- geneity sensitive task. Artti Juutinen, Rauli Svento, Yohei Mita

14、ni, Erkki Mntymaad, Yasushi Shojie, Pirkko Siikamki, 2012. We thank William H. Greene, David A. Hensher and John M. Rose for helpful comments. We also thank participants at the Finnish Economic Association XXXIII Annual Meeting in Oulu 3.-4.2.2011 and at the 18th Annual Conference of the European As

15、sociation of Environmental and Resource Economists in Rome 29 June-2 July 2011. where Uij denotes utility of individual i from alterna- tive (or commodity) j, xij is a vector of the attributes related to alternative j, is a vector of parameters to be estimated and denotes the Gumbel distributed erro

16、r terms. The basic approach to model unobserved hetero- geneity of preferences is by using random parameter versions of the conditional logit model by Train (2009) also named mixed logit (MIXL). Then the Environmental Economics, Volume 3, Issue 2, 2012 58 model has the following form: Environmental

17、Economics, Volume 3, Issue 2, 2012 59 x U x , ij i ij ij Prob( yi j | xi1,. , xi J ) i vi , ei xij J , ei xij j 1 (2) tor can be estimated in the (GMXL) Generalized Mixed Logit Model. When this scaling is applied to the MIXL model without preference heterogeneity explaining covariates, the scaling f

18、actor is multip- lied out and an assumption is made that the scaling factor can have a weighted influence on unobserved heterogeneity. The model with the scale factor can where the individual specific parameter vector i is be expressed in the following form: identified with being the vector of popul

19、ation U v 1 v ) x , (4) means of the random parameters and vi is a vector of random variables which capture the individual un- observed heterogeneity with mean zero and standard deviation of one. The standard deviation of individ- ual specific parameters around the population mean are captured by th

20、e nonzero elements of the lower triangular Cholesky matrix . MIXL has been very popular recently based on the fast progress with simulation based solutions. The normal distribution is frequently used for random parameters while the willingness to pay is naturally positive and thus it is usually assu

21、med log normally distributed. Louviere et al. (2008) have, however, ij i i i i ij ij where is the weighing factor to be estimated. When approaches zero the model approaches a model where the scale heterogeneity affects both the population means and individual means of the pa- rameters. When approach

22、es one the model ap- proaches a model where the scale heterogeneity affects only the population means. The goal of this paper is to include observed cova- riates in both the random parameters and in the scale factor as explanatory variables. The scale factor to be estimated has the following form: c

23、riticized the use of normal distributions in MIXL models. Based on the distributions of utility weights i exp( + hi + wi ), (5) obtained from individual level estimations they have found that distributions do not appear to be normal. Observed preference heterogeneity can be added to the MIXL model w

24、ith heterogeneity explaining covariates in the equation of individual specific parameters in the where h is a vector of scale explaining covariates for respondent i and wi N(0,1) is a vector of random variables, and and are the corresponding parame- ters. In estimations we use the assumption that th

25、e scale variance heterogeneity is normally distributed so that, neglecting the observed heterogeneity, model (2). Then the model has the form: Ei exp(2 2). Since i enters the model as a U x , product some normalization is needed in order to iden- ij i ij ij Prob( yi j | xi1 ,. , xi J ) ei xij , j x

26、tify them both. The natural normalization is to set the mean of i equal to one so that is the mean vector of utility weights. To accomplish this we set equal to e i ij j1 2 2 . The model naturally has to be estimated using F ij exp expij , i zi vi , (3) simulation draws for the random variables v an

27、d w. 2. The choice experiment 2.1. Study area. Our choice experiment relates to 1 where zi is a set of variables which are preference hete- rogeneity explaining cofactors for person i and is the corresponding parameter vector to be estimated. In writing model (1) it has implicitly been assumed that

28、the error terms have been scaled to have unit variance so that a common scaling factor has been used. When this scale factor is made explicit the utility can be written as: Oulanka National Park in Finland . The park is located in north-eastern Finland (6622N, 2917E), adjacent to the Russian border

29、and close to the Arctic Circle. The park was established in 1956 to protect unique riparian ecosystems with rich flora and fauna. There were two major expansions to the park in 1982 and 1989, so that currently Oulanka NP covers approx- imately 28 000 hectares (Gilligan et al., 2005). It is managed b

30、y the Natural Heritage Services of Mets- hallitus, whose public administration duties include the Uij ij ij , i 1, , N ; j 1, , J . management of protected areas (Heinonen, 2007). Finnish national parks are managed within the Parlia- This scaling can of course be made on individual mentary legislati

31、on, the Ministry of the Environments basis, i.e. the scaling factor would then be i for i = 1, N. Recently Fiebig et al. (2010) and Greene and Hensher (2010) have shown how the scale fac- 1 Juutinen et al. (2011) have studied visitor valuations related to this park and thus we do not open those in t

32、his paper. Environmental Economics, Volume 3, Issue 2, 2012 58 guidelines and Metshallitus own principles and man- agement and land use plans for each park. Following the IUCN protected area management categories, Ou- lanka NP is a category II national park (Dudley, 2008; IUCN and UNEP, 2003). Follo

33、wing the growth of nature-based tourism, na- tional parks have become important tourist attrac- tions worldwide. In Finland Oulanka NP is one of the most popular national parks. The average annual number of visits tripled since 1992 from 60 000 to 185 500 visits in 2007 (Metshallitus, 2008). The num

34、ber of visitors to the park has increased to the point that the park manager, Metshallitus, now re- quires information for fulfilling the needs of the visi- tors and protecting the nature of the park. There are clear tradeoffs between development of the services and facilities and protection of the

35、biodiversity of the park. Therefore, Oulanka NP is a highly suitable case for a choice experiment exercise. 2.2. Survey design. The process started in coopera- tion with Metshallitus by preparing a questionnaire for a small scale pilot study conducted as an onsite visitor survey during five days in

36、October 2007. Based on the pilot study, the final questionnaire was developed and tested using focus groups (the ques- tionnaire is available on request from the authors). The questionnaire of the final survey consisted of four parts. The first part contained questions related to visitors environmen

37、tal attitudes and their desire for outdoor recreation. This part was an introduction to the survey, including questions related to the im- portance of nature and the environment for visitors, activity to spend time in nature, and respondents attitude to nature protection in Finland. The second and t

38、he most important part of the questionnaire con- tained the choice experiment. It gave information about Oulanka NP and choice sets related to man- agement alternatives of the park. It included descrip- tions of the attributes of the choice experiment, i.e. biodiversity, expected number of visitors,

39、 entrance fee, size and number of resting places, and informa- tion boards, as well as the levels of the attributes as shown in Table 1. The third part of the survey asked facts about this visit to the park, especially places where respondents visited as well as motives and activities during the vis

40、it in the park. The final part included questions regarding respondents socio- economic status, including year of birth, education, and employment. Table 1. Attributes and their levels with variable names used in the analysis Attributes Levels Variable name Biodiversity: number of endangered species

41、 of plants and animals in the park 1. Decreases: populations decrease so that 15 species extinct in the park. 2. Stays at the present state: number of endangered species 150*. 3. Increases: a 10 % increase in populations of endangered species. Biodiv Biodiv Biodiv + Expected number of visitors: on a

42、verage on the most visited places 1. Decreases: a visitor encounters 10 people during a 1 km walk. 2. Increases as anticipated: a visitor encounters 40 people during a 1 km walk*. 3. Increases a lot: a visitor encounters 70 people during a 1 km walk. NumVisitors - NumVisitors NumVisitors + Entrance

43、fee: for adult visitors only 1. No entrance fee*. 2. Entrance fee 2/ person/ visit. 3. Entrance fee 5/ person/ visit. 4. Entrance fee 10/ person/ visit. 5. Entrance fee 20/ person/ visit. Payment Size and number of resting places on the most visited places 1. Stays at the present state: a resting pl

44、ace after every 2 km*. 2. Expansion of present resting places: 2 new camp fire places on the most crowded ones. 3. Construction of new resting places: a resting place after every 1 km. RestPlace RestPlace + RestPlace + Information boards by the side of hiking routes in English 1. Stays at the presen

45、t state: no information boards*. 2. Few more boards: a board after every 3 km. 3. Far more boards: a board after every 1 km. InfoBoard InfoBoard + InfoBoard + Note: *The attribute level describes the basic alternative. The number of attributes and levels gave rise to 405 possible profiles (3*3*5*3*3

46、 = 405). To develop the profiles presented to respondents in the questionnaire, we applied an orthogonal main effect design (by SPSS orthogonal design procedure), which is fre- quently used in empirical studies although effective designs are coming more popular (Louviere et al., 2000). This procedur

47、e reduced the number of profiles to a level of 25 alternatives. This number was consi- dered too large a task for a respondent to complete (Louviere et al., 2000). To reach a more manageable level of alternatives, we generated three random numbers for each alternative. Then using one set of random n

48、umbers at a time we sorted the alternatives in a descending order and signed the alternatives to 12 choice sets in this order. The total number of choice sets is 36 as the procedure was repeated three times. Each choice set included two signed alterna- tives and a status quo alternative in which the levels of attributes refers to present situation except the expected number of visitors which was assumed to increase as anticipated (the basic alternative in Table 1). Thus 24 alter