Deconvoluting preferences and errors: a model for binomial panel data

Fosgerau, Mogens and Nielsen, Søren Feodor (2007): Deconvoluting preferences and errors: a model for binomial panel data.

Abstract

Let U be an unobserved random variable with compact support and let e_t be unobserved i.i.d. random errors also with compact support. Observe the random variables V_t, X_t, and Y_t = 1{U +d X_t+e_t < V_t}, t <= T, where d is an unknown parameter. This type of model is relevant for many stated choice experiments. It is shown that under weak assumptions on the support of U +e_t, the distributions of U and e_t as well as the unknown parameter d can be consistently estimated using a sieved maximum likelihood estimation procedure. The model is applied to simulated data and to actual data designed for assessing the willingness-to-pay for travel time savings.

• Item Type: MPRA Paper
• Institution: Technical University of Denmark
• Language: English
• Keywords: semi-nonparametric; nonparametric; method of sieves; binomial panel; willingness-to-pay; value of time
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C23 - Panel Data Models ; Spatio-temporal Models; R - Urban, Rural, Regional, Real Estate, and Transportation Economics > R4 - Transportation Economics > R41 - Transportation: Demand, Supply, and Congestion ; Travel Time ; Safety and Accidents ; Transportation Noise; D - Microeconomics > D1 - Household Behavior and Family Economics > D12 - Consumer Economics: Empirical Analysis; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C14 - Semiparametric and Nonparametric Methods: General; Q - Agricultural and Natural Resource Economics ; Environmental and Ecological Economics > Q5 - Environmental Economics > Q51 - Valuation of Environmental Effects; C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C25 - Discrete Regression and Qualitative Choice Models ; Discrete Regressors ; Proportions ; Probabilities

References

Belluzzo, W. (2004) Semiparametric Approaches to Welfare Evaluations in Binary Response Models. Journal of Business and Economic Statistics 22(3), 322–330.

Chen, H. Z. and Randall, A. (1997) Semi-nonparametric estimation of binary response models with an application to natural resource valuation. Journal of Econometrics 76(1-2), 323–340.

Doornik, J. A. (2001) Ox: An Object-Oriented Matrix Language Timberlake Consultants Press London.

Fosgerau, M. (2006) Investigating the distribution of the value of travel time savings. Transportation Research Part B: Methodological 40(8), 688–707.

Fosgerau, M. (2007) Using nonparametrics to specify a model to measure the value of travel time. Transportation Research Part A: Policy and Practice Forthcoming.

Fosgerau, M., Hjort, K. and Lyk-Jensen, S. V. (2007) An approach to the estimation of the distribution of marginal valuations from discrete choice data. Working Paper .

Gabler, S., Laisney, F. and Lechner, M. (1993) Seminonparametric Estimation of Binary-Choice Models With an Application to Labor-Force Participation. Journal of Business and Economic Statistics 11(1), 61–80.

Gallant, A. R. and Nychka, D. W. (1987) Semi-nonparametric maximum likelihood estimation Econometrica 55(2), 363–390.

Hanemann, W. M. and Kanninen, B. (1998) The Statistical Analysis of Discrete-Response CV Data in I. J. Bateman and K. G. Willis (eds), Valuing Environmental Preferences. Theory and Practice of the Contingent Valuation Method in the US, EC and Developing Countries Oxford University Press (forthcoming).

Honoré, B. E. and Lewbel, A. (2002) Semiparametric binary choice panel data models without strictly exogenous regressors. Econometrica 70(5), 2053–2063.

Horowitz, J. and Markatou, M. (1996) Semiparametric Estimation of Regression Models for Panel Data The Review of Economic Studies 63(1), 145–168.

Lewbel, A., Linton, O. and McFadden, D. (2002) Estimating features of a distribution from binomial data. unpublished work.

Li, Q. and Racine, J. S. (2007) Nonparametric Econometrics: Theory and Practice. Princeton University Press Princeton and Oxford.

Rouwendal, J. and de Blaeijj, A. T. (2004) Inconsistent and Lexicographic Choices in Stated Preference Analysis. Tinbergen Institute Discussion Papers 04-038/3.

Rudin, W. (1986) Real and Complex Analysis. McGraw-Hill Singapore.

Sælensminde, K. (2001) Inconsistent choices in stated choice data. Use of the logit scaling approach to handle resulting variance increases. Transportation 28(3), 269–296.

Sælensminde, K. (2002) The Impact of Choice Inconsistencies in Stated Choice Studies. Environmental and Resource Economics 23(4), 403–420.

Train, K. (2003) Discrete Choice Methods with Simulation. Cambridge University Press Cambridge, MA.

van der Vaart, A. and Wellner, J. (1996) Weak convergence and empirical processes. Springer Series in Statistics 1 edn Springer.