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Stochastic Choice: Rational or Erroneous?

Dong, Xueqi and Liu, Shuo Li (2019): Stochastic Choice: Rational or Erroneous?

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Likelihood functions have been the central pieces of statistical inference. For discrete choice data, conventional likelihood functions are specified by random utility(RU) models, such as logit and tremble, which generate choice stochasticity through an ”error”, or, equivalently, random preference.For risky discrete choice, this paper explores an alternative method to construct the likelihood function: Rational Expectation Stochastic Choice (RESC). In line with Machina (1985), the subject optimally and deterministically chooses a stochastic choice function among all possible stochastic choice functions; the choice stochasticity canbe explained by risk aversion and the relaxation of the reduction of compound lottery. The model maximizes a simple two-layer expectation that disentangles risk and randomization, in the similar spirit of Klibanoff et al. (2005) where ambiguity and risk are disentangled. The model is applied to an experiment, where we do not commit to a particular stochastic choice function but let the data speak. In RESC, well-developed decision analysis methods to measure risk attitude toward objective probability can also be ap-plied to measure the attitude toward the implied choice probability. Stochastic choicefunctions are structurally estimated to estimate the stochastic choice functions, anduse standard discrimination test to compare the goodness of fit of RESC and differentRUs. The RUs are Expected Utility+logit and other leading contenders for describing decision under risk. The results suggest the statistical superiority of RESC over ”error” rules. With weakly fewer parameters, RESC outperforms different benchmarkRU models for 30%−89% of subjects. RU models outperform RESC for 0%−2% of subjects. Similar statistical superiority is replicated in a second set of experimental data.

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