Estimation of Nonparametric Functions in Simultaneous Equations Models, with an Application to Consumer Demand

We present a method for consistently estimating nonparametric functions and distributions in simultaneous equations models. This method is used to identify and estimate a random utility model of consumer demand. Our identification conditions for this particular model extend the results of Houthakker (1950), Uzawa (1971) and Mas-Colell (1977), where a deterministic utility function is uniquely recovered from its deterministic demand function.

Nonparametric Identification and Estimation of Nonadditive Hedonic Models

This paper studies the identification and estimation of preferences and technologies in equilibrium hedonic models. In it, we identify nonparametric structural relationships with nonadditive heterogeneity. We determine what features of hedonic models can be identified from equilibrium observations in a single market under weak assumptions about the available information. We then consider use of additional information about structural functions and heterogeneity distributions. Separability conditions facilitate identification of consumer marginal utility and firm marginal product functions. We also consider how identification is facilitated using multimarket data.hedonic models, hedonic equilibrium, nonadditive models, identification, non-parametric estimation

Simulation and Estimation of Nonaddative Hedonic Models

Making use of restrictions imposed by equilibrium, theoretical progress has been made on the nonparametric and semiparametric estimation and identification of scalar additive hedonic models (Ekeland, Heckman, and Nesheim, 2002) and scalar nonadditive hedonic models (Heckman, Matzkin, and Nesheim, 2002). However, little is known about the practical aspects of estimating such models or of the characteristics of equilibrium in such models. This paper presents computational and analytical results that fill some of these gaps. We simulate and estimate examples of equilibrium in the additive hedonic models and provide evidence on the performance of several estimation techniques. We also simulate examples of equilibria in nonadditive models and provide evidence on the performance of the nonadditive estimation techniques developed in Heckman, Matzkin, and Nesheim (2002).

Classical statistical distributions can violate Bell-type inequalities

We investigate two-particle phase-space distributions in classical mechanics characterized by a well-defined value of the total angular momentum. We construct phase-space averages of observables related to the projection of the particles' angular momenta along axes with different orientations. It is shown that for certain observables, the correlation function violates Bell's inequality. The key to the violation resides in choosing observables impeding the realization of the counterfactual event that plays a prominent role in the derivation of the inequalities. This situation can have statistical (detection related) or dynamical (interaction related) underpinnings, but non-locality does not play any role.Comment: v3: Extended version. To be published in J. Phys.

Effect of a moving mirror on the free fall of a quantum particle in a homogeneous gravitational field

We investigate the effect of time-dependent boundary conditions on the dynamics of a quantum bouncer -- a particle falling in a homogeneous gravitational field on a moving mirror. We examine more particularly the way a moving mirror modifies the properties of the entire wavefunction of a falling particle. We find that some effects, such as the fact that a quantum particle hitting a moving mirror may bounce significantly higher than when the mirror is fixed, are in line with classical intuition. Other effects, such as the change in relative phases or in the current density in spatial regions arbitrarily far from the mirror are specifically quantum. We further discuss how the effects produced by a moving mirror could be observed in link with current experiments, in particular with cold neutrons

From observer-dependent facts to frame-dependent measurement records in Wigner friend scenarios

The description of Wigner-friend scenarios -- in which external agents describe a closed laboratory containing a friend making a measurement -- remains problematic due to the ambiguous nature of quantum measurements. One option is to endorse assumptions leading to observer-dependent facts, given that the friend's measurement outcome is not defined from the point of view of the external observers. We introduce in this work a model showing that these assumptions can also lead to measurement records that depend on the inertial reference frame in which the agents make their observations. Our model is based on an entangled pair shared by the friend and a distant agent performing space-like separated measurements. An external observer at rest relative to the closed laboratory and observers in a moving frame do not agree on the observed records, which are not Lorentz transforms of one another

Contribution of forbidden orbits in the photoabsorption spectra of atoms and molecules in a magnetic field

In a previous work [Phys. Rev. A \textbf{66}, 0134XX (2002)] we noted a partial disagreement between quantum R-matrix and semiclassical calculations of photoabsorption spectra of molecules in a magnetic field. We show this disagreement is due to a non-vanishing contribution of processes which are forbidden according to the usual semiclassical formalism. Formulas to include these processes are obtained by using a refined stationary phase approximation. The resulting higher order in $\hbar$ contributions also account for previously unexplained ``recurrences without closed-orbits''. Quantum and semiclassical photoabsorption spectra for Rydberg atoms and molecules in a magnetic field are calculated and compared to assess the validity of the first-order forbidden orbit contributions.Comment: 12 pages, 6 figure

Making sense of relativistic Wigner friend scenarios

Wigner-friend scenarios -- in which external agents describe a closed laboratory containing a friend making a measurement -- highlight the difficulties inherent to quantum theory when accounting for measurements. Recently, several works have investigated Wigner-friend scenarios with relativistic constraints, systematically resulting in a contradiction between observations made in different inertial reference frames. We examine in this paper the reasons for and the implications of these contradictions. Having in mind the well-known tensions between quantum theory and relativity, we will put a particular emphasis on the role of the relativistic constraints in these scenarios

Observing trajectories with weak measurements in quantum systems in the semiclassical regime

We propose a scheme allowing to observe the evolution of a quantum system in the semiclassical regime along the paths generated by the propagator. The scheme relies on performing consecutive weak measurements of the position. We show how weak trajectories" can be extracted from the pointers of a series of measurement devices having weakly interacted with the system. The properties of these "weak trajectories" are investigated and illustrated in the case of a time-dependent model system.Comment: v2: Several minor corrections were made. Added Appendix (that will appear as Suppl. Material). To be published in Phys Rev Let

Observation of diffractive orbits in the spectrum of excited NO in a magnetic field

We investigate the experimental spectra of excited NO molecules in the diamagnetic regime and develop a quantitative semiclassical framework to account for the results. We show the dynamics can be interpreted in terms of classical orbits provided that in addition to the geometric orbits, diffractive effects are appropriately taken into account. We also show how individual orbits can be extracted from the experimental signal and use this procedure to reveal the first experimental manifestation of inelastic diffractive orbits.Comment: 4 fig