Distribution-free estimation with interval-censored contingent valuation data: Troubles with Turnbull?

Brett Day

Research output: Contribution to journalArticlepeer-review

7 Citations (Scopus)


Contingent valuation (CV) surveys frequently employ elicitation procedures that return interval-censored data on respondents’ willingness to pay (WTP). Almost without exception, CV practitioners have applied Turnbull’s self-consistent algorithm to such data in order to obtain nonparametric maximum likelihood (NPML) estimates of the WTP distribution. This paper documents two failings of Turnbull’s algorithm; (1) that it may not converge to NPML estimates and (2) that it may be very slow to converge. With regards to (1) we propose starting and stopping criteria for the algorithm that guarantee convergence to the NPML estimates. With regards to (2) we present a variety of alternative estimators and demonstrate, through Monte Carlo simulations, their performance advantages over Turnbull’s algorithm.
Original languageEnglish
Pages (from-to)777-795
Number of pages19
JournalEnvironmental and Resource Economics
Issue number4
Early online date13 Jan 2007
Publication statusPublished - Aug 2007


  • Interval-censored data
  • Turnbull’s self-consistent algorithm
  • Nonparametric maximum likelihood
  • Contingent valuation

Cite this