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 Treb 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

Outline2

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

Motivation and research goals (I)

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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

Motivation and research goals (II)

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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…

Methods (I)5

Delta method The most frequently used, WTP est is asympt. ~ N(~

distributed Assumptions Pros:…

Cons:…

Not only Delta method but also…

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 SimulationThe distinction rests on the use of either the analytic or simulated

distribution of the parameter estimator.

Methods (III)7

Scheme (lo faccio io)

Contributions to the literature (I)

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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.

Contributions to the literature (II)

9

Scheme (lo faccio io)

Data10

… Simulated data

TPL… Airport…

Real data

Test settings 11

…

…

Performance indicators12

…

…

Results and discussion (I)13

Output

Results and discussion (II)14

…

General considerations:

Conclusion15

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

Thanks for your attention!16

Questions? Questions?

Questions?

Questions?

Questions?

WTP in a MNL framework17

…

Diciamo qualcosa sul rapporto di due coefficienti stimati con la massima verosimiglianza???