Abstract
Concerns about unobserved heterogeneity—either in preference or attribute space—have led environmental economists to turn increasingly to discrete choice models that incorporate random parameters and alternative specific constants. We use four recreation data sets and several empirical specifications to show that although these modeling innovations often lead to substantial improvements in overall model fit, they also generate poor in-sample predictions relative to observed choices. Given the apparent tradeoff between fit and prediction, we then propose and empirically investigate a series of ‘second-best’ strategies that attempt to correct for the poor prediction we observe.
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Notes
Only differences in utility enter into the logit model precluding estimation of the full set of ASCs. The normalized ASC is captured by a constant in the second stage of estimation.
See Berry et al. (2004b) for a discussion of the asymptotic properties of this approach.
The authors collected information on day trips to 62 beaches from New Jersey to Maryland, but our analysis focuses on the 44 beaches that at least one respondent reported visiting.
For compactness we do not report parameter estimates and standard errors for the different data sets and specifications, although these are available upon request. We note only that the parameters have intuitive signs that are consistent with published literature using these same data and are generally statistically significant.
As is common in the recreation literature, we do not allow for correlation in the random parameters across attributes. As a sensitivity, we also considered truncated normal and triangular distributions for mixing distributions. These results were not qualitatively different, so we do not report them here.
We do not include any demographic interactions in this model because preliminary testing suggested that they did not improve model fit.
For random coefficient specifications, 200 Halton draws are used to estimate E(Tin) separately for each trip.
The one where the random parameter model outperforms the latent class model in terms of percentage absolute prediction error is the Alberta trip-allocation model without ASCs. In all other cases, the latent class model predicts better in-sample than the random coefficient model, and in some cases by a large margin.
In particular, it is well known that the standard formula for the compensating variation (CVi) for the loss of site j (assuming fixed parameters) simplifies to \( CV_{i} = \tfrac{ - 1}{\beta }\ln (1 - \Pr_{i} (j|\beta )) \), where β is the travel cost coefficient. The formula implies a positive correlation between the predicted number of trips to the lost site and the welfare loss, ceteris paribus. Thus models that predict more trips to the lost site will also predict larger losses assuming the travel cost coefficient is relatively stable across alternative models. More generally with welfare scenarios involving changes in site attributes, the implications of poor prediction are unclear. In these cases, welfare measures not only depend critically on baseline predictions but also the estimated attribute parameters. Depending on how these parameters and baseline predictions change across model specifications, the welfare measures could either increase or decrease.
To avoid excessive notation we ignore the panel nature of most recreation data sets (i.e., the possibility that a given individual makes several discrete choices) although the results presented here generalize to the panel data case.
Because latent class models can be interpreted as random parameter with discrete mixing distributions, this result also holds for latent class models.
We chose to use a nonpanel specification to aid in identification of random parameters as this specification effectively treats each choice occasion as a new individual giving us 5279 individuals in the “true” specification.
A key challenge is choosing the weight to put on the additive penalty function. Too large of a weight will prevent the maximum likelihood routine from taking any steps away from the starting values, while too small a weight will not result in a model with good in sample predictions. Our experience is that choosing the optimal weight requires several iterations where the researcher must balance both of these concerns, and the final weight chosen might imply less than exacct in sample predictions.
Another limitation with including ASCs arises with policies involving the introduction of new sites where estimates of the new site’s ASC. This problem is akin to the well-known problem of out-of-sample forecasting from fixed effects models. Berry et al. (2004) develop strategies for dealing with this problem within the discrete choice framework.
References
Adamowicz W, Swait J, Boxall P, Louviere J, Williams M (1997) Perceptions vs. objective measures of environmental quality in combined revealed and stated preference models of environmental valuation. J Environ Econ Manag 32:65–84
Bayer P, Timmins C (2007) Estimating equilibrium models of sorting across locations. Econ J 117:353–374
Bayer P, Keohane N, Timmins C (2009) Migration and hedonic valuation: the case of air quality. J Environ Econ Manag 58(1):1–14
Ben-Akiva M, Lerman S (1985) Discrete choice analysis. MIT Press, Cambridge
Berry S (1994) Estimating discrete-choice models of product differentiation. RAND J Econ 25(2):242–262
Berry S, Levinsohn J, Pakes A (1995) Automobile prices in equilibrium. Econometrica 63:841–890
Berry S, Levinsohn J, Pakes A (2004a) Differentiated products demand systems from a combination of micro and macro data: the new car market. J Polit Econ 112:68–105
Berry S, Linton O, Pakes A (2004b) Limit theorems for estimating the parameters of differentiated product demand systems. Rev Econ Stud 3(1):613–654
Bujosa A, Riera A, Hicks RL, McConnell KE (2015) Densities rather than shares: improving the measurement of congestion in recreation demand models. Environ Resour Econ 61(2):127–140
Dempster A, Laird N, Rubin D (1977) Maximum likelihood from incomplete data via the EM algorithm. J Roy Stat Soc B 39(1):1–38
Gourieroux C, Monfort A, Trognon A (1984) Pseudo-maximum likelihood methods: application to Poisson models. Econometrica 52:701–720
Haener M, Boxall P, Adamowicz W (2001) Modeling recreation site choice: do hypothetical choices reflect actual behavior? Am J Agr Econ 83:629–642
Hynes S, Hanley N, Scarpa R (2008) Effects on welfare measures of alternative means of accounting for preference heterogeneity in recreation demand models. Am J Agr Econ 90(4):1011–1027
Klaiber HA, Phaneuf DJ (2010) Valuing open space in a residential sorting model of the Twin Cities. J Environ Econ Manag 60(2):57–77
McFadden D, Train K (2000) Mixed MNL of discrete response. J Appl Econom 15:447–470
Moeltner K, von Haefen R (2011) Microeconometric strategies for dealing with unobservables and endogenous variables in recreation demand models. Ann Rev Res Econ 3:375–396
Murdock J (2006) Handling unobserved site characteristics in random utility models of recreation demand. J Environ Econ Manag 51:1–25
Parsons G, Massey DM, Tomasi T (1999) Familiar and favorite sites in a random utility model of beach recreation. Mar Resour Econ 14:299–315
Shonkwiler JS, Englin J (2005) Welfare losses due to livestock grazing on public lands: a count data systemwide treatment. Am J Agr Econ 87:302–313
Thiene M, Scarpa R, Train K (2008) Utility in willingness to pay space: a tool to address confounding random scale effects in destination choice to the Alps. Am J Agr Econ 90(4):994–1100
Timmins C, Murdock J (2007) A revealed preference approach to the measurement of congestion in travel cost models. J Environ Econ Manag 53:230–249
Tra C (2010) A discrete choice equilibrium approach to valuing large environmental changes. J Public Econ 94:183–196
Train K (2009) Discrete choice methods with simulation, 2nd edn. Cambridge University Press, Cambridge
Train K, Winston G (2007) Vehicle choice behavior and the declining market share of U.S. automakers. Int Econ Rev 48(4):1469–1496
von Haefen R (2003) Incorporating observed choice into the construction of welfare measures from random utility models. J Environ Econ Manag 45(2):145–165
von Haefen R, Phaneuf D (2008) Identifying demand parameters in the presence of unobservables: a combined revealed and stated preference approach. J Environ Econ Manag 56(1):19–32
White H (1980) A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity. Econometrica 48(4):817–838
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Klaiber, H.A., von Haefen, R.H. Do Random Coefficients and Alternative Specific Constants Improve Policy Analysis? An Empirical Investigation of Model Fit and Prediction. Environ Resource Econ 73, 75–91 (2019). https://doi.org/10.1007/s10640-018-0250-z
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DOI: https://doi.org/10.1007/s10640-018-0250-z
Keywords
- Discrete choice
- Recreation demand
- Revealed preference
- Stated preference
- Alternative specific constants
- Random parameters