1. 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

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

3. 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

4. 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…

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

6. 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.

7. Methods (III) 7  Scheme (lo faccio io)

8. 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.

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

10. Data 10 ……  Simulated data  TPL…  Airport…  Real data

11. Test settings 11 …… ……

12. Performance indicators 12 …… ……

13. Results and discussion (I) 13  Output

14. Results and discussion (II) 14 ……  General considerations:

15. 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

16. Thanks for your attention! 16  Questions?  Questions? Questions?

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