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ESTIMATING CONFIDENCE INTERVALS FOR WILLINGNESS TO PAY MEASURES: COMPARISONS AND EXTENSIONS 1 Gatta V. a, Marcucci E. a, Scaccia L. b a DIPES/CREI, University of Roma Tre b DIEF, University of Macerata XV Conference of the Italian Association of Transport Economics and Logistics "Transport, Spatial Organization and Sustainable Economic Development” - Venice - September 18-20, 2013

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Outline 2 Motivation and research goals Methods Contributions to literature Data Test settings Performance indicators Results and discussion Conclusions and future research

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Motivation and research goals (I) 3 WTP calculation is a core issue in transportation economics WTP measures are estimates with a given (not known) probability distribution βx/βc ► point estimate is not enough ► confidence interval (CI) need to be calculated Different methods to construct CI can be adopted Motivation Compare alternative CI estimation methods (already used in the literature and newly proposed) in the case of MNL specification Provide motivated suggestions concerning which method to use given different context scenarios. Research goals

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Motivation and research goals (II) 4 The derivation of reliable WTP measures is relevant for: project evaluation regulatory policies price and income elasticities in demand systems travel demand time reliability mode/path choice service quality evaluation etc…

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Methods (I) 5 Delta method The most frequently used, WTP est is asympt. ~ N( ~ distributed Assumptions Pros:… Cons:… Not only Delta method but also…

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Methods (II) 6 Pivotal (in which CI is constructed in the usual way, using a pivotal function, except that the quantiles of known distributions, e.g. Normal, Student's-t, are replaced by their bootstrap estimates). Non-pivotal (which all originate from the percentile method as successively more complex analytical corrections for this). Test-inversion (which exploits the duality between confidence intervals and tests). Approach Family Approximation versus Simulation The distinction rests on the use of either the analytic or simulated distribution of the parameter estimator.

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Methods (III) 7 Scheme (lo faccio io)

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Contributions to the literature (I) 8 The paper contributes in three different ways to the extant literature: provides a comprehensive illustration and systematic comparison for the methods used in choice modeling literature; proposes, borrowing from different research contexts, additional methods; introduces new performance indicators for evaluating the methods considered.

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Contributions to the literature (II) 9 Scheme (lo faccio io)

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Data 10 …… Simulated data TPL… Airport… Real data

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Test settings 11 …… ……

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Performance indicators 12 …… ……

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Results and discussion (I) 13 Output

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Results and discussion (II) 14 …… General considerations:

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Conclusion 15 Different methods to compute CI for WTP measures were compared All the scenarios considered revealed a certain degree of skewness in the distribution of WTP estimates. Delta method and bootstrap normal-theory method produce, by construction Final remarks …… Future research

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Thanks for your attention! 16 Questions? Questions? Questions?

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WTP in a MNL framework 17 …… Diciamo qualcosa sul rapporto di due coefficienti stimati con la massima verosimiglianza???

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