On distinguishing the direct causal effect of an intervention from its efficiency-enhancing effects

Copyright © 2023 The Authors. This paper proposes an innovative methodology for handling endogeneity issues in the evaluation of policy performance. By estimating a regression discontinuity design with a four-component stochastic frontier panel data model, we estimate the causal impact of a policy intervention on the outcome variable, whenever the treatment status depends on an exogenous threshold. We distinguish between (i) the direct effect of the intervention, (ii) the efficiency-enhancing effect, or (iii) their combination. Moreover, we distinguish between persistent (time-invariant) and transient (time-varying) inefficiency components while accounting for unobserved heterogeneity, which is important for policy implications. We showcase the practical usefulness of the proposed approach by estimating the effect of providing additional resources on schools that exceed an exogenously set share of disadvantaged students in secondary schools in Flanders, Belgium. We also demonstrate the trade-off between balance of the covariates in the treated and control group and statistical power. Thus, despite insignificant effects in a balanced but smaller sample close to the discontinuity, the results become significant in the unbalanced sample with more statistical power. In both samples, we observe that the policy had an effect on the outcome mostly through the efficiency-enhancing channel. To this extent, we show that the model specification including both direct and indirect effects outperforms the other two specifications and it offers a more exhaustive perspective from a policy view point.Research Foundation – Flanders, FWO (Postdoctoral Fellowship 12U0219N)

Higher-order corrections to the relativistic perihelion advance and the mass of binary pulsars

We study the general relativistic orbital equation and using a straightforward perturbation method and a mathematical device first introduced by d'Alembert, we work out approximate expressions of a bound planetary orbit in the form of trigonometrical polynomials and the first three terms of the power series development of the perihelion advance. The results are applied to a more precise determination of the total mass of the double pulsar J0737-3039.Comment: 8 pages. Accepted for publication in "Astrophysics & Space Science

Entropy of the Universe

After a discussion on several limiting cases where General Relativity turns into less sophisticated theories, we find that in the correct thermodynamical and cosmological weak field limit of Einstein's field equations the entropy of the Universe is R^(3/2) -- dependent, where R stands for the radius of the causally related Universe. Thus, entropy grows in the Universe, contrary to Standard Cosmology prediction.Comment: To be published by International Journal of Theoretical Physic

Ion trap simulations of quantum fields in an expanding universe

We propose an experiment in which the phonon excitation of ion(s) in a trap, with a trap frequency exponentially modulated at rate kappa, exhibits a thermal spectrum with an Unruh temperature given by k(B)T=h kappa. We discuss the similarities of this experiment to the response of detectors in a de Sitter universe and the usual Unruh effect for uniformly accelerated detectors. We demonstrate a new Unruh effect for detectors that respond to antinormally ordered moments using the ion's first blue sideband transition

Time and Dirac Observables in Friedmann Cosmologies

A cosmological time variable is emerged from the Hamiltonian formulation of Friedmann model to measure the evolution of dynamical observables in the theory. A set of observables has been identified for the theory on the null hypersurfaces that its evolution is with respect to the volume clock introduced by the cosmological time variable.Comment: 11 page

Hamiltonians for Reduced Gravity

A generalised canonical formulation of gravity is devised for foliations of spacetime with codimension $n\ge1$. The new formalism retains n-dimensional covariance and is especially suited to 2+2 decompositions of spacetime. It is also possible to use the generalised formalism to obtain boundary contributions to the 3+1 Hamiltonian.Comment: 18 pages, revtex, 3 postscript figures include

Axiomatizing relativistic dynamics without conservation postulates

A part of relativistic dynamics (or mechanics) is axiomatized by simple and purely geometrical axioms formulated within first-order logic. A geometrical proof of the formula connecting relativistic and rest masses of bodies is presented, leading up to a geometric explanation of Einstein's famous $E=mc^2$. The connection of our geometrical axioms and the usual axioms on the conservation of mass, momentum and four-momentum is also investigated.Comment: 21 pages, 7 figure

The horizon-entropy increase law for causal and quasi-local horizons and conformal field redefinitions

We explicitly prove the horizon-entropy increase law for both causal and quasi-locally defined horizons in scalar-tensor and $f(R)$ gravity theories. Contrary to causal event horizons, future outer trapping horizons are not conformally invariant and we provide a modification of trapping horizons to complete the proof, using the idea of generalised entropy. This modification means they are no longer foliated by marginally outer trapped surfaces but fixes the location of the horizon under a conformal transformation. We also discuss the behaviour of horizons in "veiled" general relativity and show, using this new definition, how to locate cosmological horizons in flat Minkowski space with varying units, which is physically identified with a spatially flat FLRW spacetime.Comment: 23 page

Twin Paradox and the logical foundation of relativity theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization SpecRel of special relativity from the literature. SpecRel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in SpecRel. As it turns out, this is practically equivalent to asking whether SpecRel is strong enough to "handle" (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to SpecRel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of SpecRel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that the Twin Paradox becomes provable in AccRel, but it is not provable without IND.Comment: 24 pages, 6 figure

On Special Re-quantization of a Black Hole

Quantized expressions for the gravitational energy and momentum are derived from a linearized theory of teleparallel gravity. The derivation relies on a second-quantization procedure that constructs annihilation and creation operators for the graviton. The resulting gravitational field is a collection of gravitons, each of which has precise energy and momentum. On the basis of the weak-field approximation of Schwarzschild's solution, a new form for the quantization of the mass of a black hole is derived.Comment: 4 page