On the surjectivity of the mapping between utilities and choice probabilities

@inproceedings{Norets2013OnTS,
  title={On the surjectivity of the mapping between utilities and choice probabilities},
  author={Andriy Norets and Satoru Takahashi},
  year={2013}
}
This note considers a standard multinomial choice model. It is shown that if the distribution of additive utility shocks has a density, then the mapping from deterministic components of utilities to choice probabilities is surjective. In other words, any vector of choice probabilities can be obtained by selecting suitable utilities for alternatives. This result has implications for at least three areas of interest to econometricians: the Hotz and Miller (1993) estimator for structural dynamic… CONTINUE READING

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