Identification of structural dynamic discrete choice models

This paper presents new identification results for the class of structural dynamic discrete choice models that are built upon the framework of the structural discrete Markov decision processes proposed by Rust (1994). We demonstrate how to semiparametrically identify the deep structural parameters of interest in the case where utility function of one choice in the model is parametric but the distribution of unobserved heterogeneities is nonparametric. The proposed identification method does not rely on the availability of terminal period data and hence can be applied to infinite horizon structural dynamic models. For identification we assume availability of a continuous observed state variable that satisfies certain exclusion restrictions. If such excluded variable is accessible, we show that the structural dynamic discrete choice model is semiparametrically identified using the control function approach. This is a substantial revision of "Semiparametric identification of structural dynamic optimal stopping time models", CWP06/07.

Semiparametric identification of structural dynamic optimal stopping time models

This paper presents new identification results for the class of structural dynamic optimal stopping time models that are built upon the framework of the structural discrete Markov decision processes proposed by Rust (1994). We demonstrate how to semiparametrically identify the deep structural parameters of interest in the case where the utility function of an absorbing choice in the model is parametric but the distribution of unobserved heterogeneity is nonparametric. Our identification strategy depends on availability of a continuous observed state variable that satisfies certain exclusion restrictions. If such excluded variable is accessible, we show that the dynamic optimal stopping model is semiparametrically identified using control function approaches.Structural dynamic discrete choice models, semiparametric identification, optimal stopping

Maximum Score Estimation of Preference Parameters for a Binary Choice Model under Uncertainty

This paper develops maximum score estimation of preference parameters in the binary choice model under uncertainty in which the decision rule is affected by conditional expectations. The preference parameters are estimated in two stages: we estimate conditional expectations nonparametrically in the first stage and then the preference parameters in the second stage based on Manski (1975, 1985)'s maximum score estimator using the choice data and first stage estimates. The paper establishes consistency and derives rate of convergence of the two-stage maximum score estimator. Moreover, the paper also provides sufficient conditions under which the two-stage estimator is asymptotically equivalent in distribution to the corresponding single-stage estimator that assumes the first stage input is known. These results are of independent interest for maximum score estimation with nonparametrically generated regressors. The paper also presents some Monte Carlo simulation results for finite-sample behavior of the two-stage estimator

Have Econometric Analyses of Happiness Data Been Futile? A Simple Truth About Happiness Scales

Econometric analyses in the happiness literature typically use subjective well-being (SWB) data to compare the mean of observed or latent happiness across samples. Recent critiques show that comparing the mean of ordinal data is only valid under strong assumptions that are usually rejected by SWB data. This leads to an open question whether much of the empirical studies in the economics of happiness literature have been futile. In order to salvage some of the prior results and avoid future issues, we suggest regression analysis of SWB (and other ordinal data) should focus on the median rather than the mean. Median comparisons using parametric models such as the ordered probit and logit can be readily carried out using familiar statistical softwares like STATA. We also show a previously assumed impractical task of estimating a semiparametric median ordered-response model is also possible by using a novel constrained mixed integer optimization technique. We use GSS data to show the famous Easterlin Paradox from the happiness literature holds for the US independent of any parametric assumption

Entanglement Detection by Local Orthogonal Observables

We propose a family of entanglement witnesses and corresponding positive maps that are not completely positive based on local orthogonal observables. As applications the entanglement witness of the $3\times 3$ bound entangled state [P. Horodecki, Phys. Lett. A {\bf 232}, 333 (1997)] is explicitly constructed and a family of $d$-dimensional bound entangled states is designed so that the entanglement can be detected by permuting local orthogonal observables. Further the proposed physically not implementable positive maps can be physically realized by measuring a Hermitian correlation matrix of local orthogonal observables.Comment: 4 pages, 1 figur