Indirect effects of an aid program: how do liquidity injections affect non-eligibles' consumption?

Aid programs in developing countries are likely to affect both the treated and the non-treated households living in the targeted areas. Studies that focus on the treatment effecton the treated may fail to capture important spillover effects. We exploit the unique designof an aid program's experimental trial to identify its indirect effect on consumption for non-eligible households living in treated areas. We find that this effect is positive, and that itoccurs through changes in the insurance and credit markets: non-eligible households receivemore transfers, and borrow more when hit by a negative idiosyncratic shock, because of theprogram liquidity injection; thus they can reduce their precautionary savings. We also testfor general equilibrium effects in the local labor and goods markets; we find no significantchanges in labor income and prices, while there is a reduction in earnings from sales ofagricultural products, which are now consumed rather than sold. We show that this classof aid programs has important positive externalities; thus their overall effect is larger thanthe effect on the treated. Our results confirm that a key identifying assumption - that thetreatment has no effect on the non-treated - is likely to be violated in similar policy designs. Aid programs in developing countries are likely to affect both the treated and the non-treated households living in the targeted areas. Studies that focus on the treatment effecton the treated may fail to capture important spillover effects. We exploit the unique designof an aid program's experimental trial to identify its indirect effect on consumption for non-eligible households living in treated areas. We find that this effect is positive, and that itoccurs through changes in the insurance and credit markets: non-eligible households receivemore transfers, and borrow more when hit by a negative idiosyncratic shock, because of theprogram liquidity injection; thus they can reduce their precautionary savings. We also testfor general equilibrium effects in the local labor and goods markets; we find no significantchanges in labor income and prices, while there is a reduction in earnings from sales ofagricultural products, which are now consumed rather than sold. We show that this classof aid programs has important positive externalities; thus their overall effect is larger thanthe effect on the treated. Our results confirm that a key identifying assumption - that thetreatment has no effect on the non-treated - is likely to be violated in similar policy designs

A New Approach to Equations with Memory

In this work, we present a novel approach to the mathematical analysis of equations with memory based on the notion of a state, namely, the initial configuration of the system which can be unambiguously determined by the knowledge of the future dynamics. As a model, we discuss the abstract version of an equation arising from linear viscoelasticity. It is worth mentioning that our approach goes back to the heuristic derivation of the state framework, devised by L.Deseri, M.Fabrizio and M.J.Golden in "The concept of minimal state in viscoelasticity: new free energies and applications to PDEs", Arch. Ration. Mech. Anal., vol. 181 (2006) pp.43-96. Starting from their physical motivations, we develop a suitable functional formulation which, as far as we know, is completely new.Comment: 39 pages, no figur

Application of the inhomogeneous Lippmann-Schwinger equation to inverse scattering problems

In this paper we present a hybrid approach to numerically solve two-dimensional electromagnetic inverse scattering problems, whereby the unknown scatterer is hosted by a possibly inhomogeneous background. The approach is `hybrid' in that it merges a qualitative and a quantitative method to optimize the way of exploiting the a priori information on the background within the inversion procedure, thus improving the quality of the reconstruction and reducing the data amount necessary for a satisfactory result. In the qualitative step, this a priori knowledge is utilized to implement the linear sampling method in its near-field formulation for an inhomogeneous background, in order to identify the region where the scatterer is located. On the other hand, the same a priori information is also encoded in the quantitative step by extending and applying the contrast source inversion method to what we call the `inhomogeneous Lippmann-Schwinger equation': the latter is a generalization of the classical Lippmann-Schwinger equation to the case of an inhomogeneous background, and in our paper is deduced from the differential formulation of the direct scattering problem to provide the reconstruction algorithm with an appropriate theoretical basis. Then, the point values of the refractive index are computed only in the region identified by the linear sampling method at the previous step. The effectiveness of this hybrid approach is supported by numerical simulations presented at the end of the paper.Comment: accepted in SIAM Journal on Applied Mathematic

Ground-state factorization and quantum phase transition in dimerized spin chains

We study the occurrence of ground-state factorization in dimerized $XY$ spin chains in a transverse field. Together with the usual ferromagnetic and antiferromagnetic regimes, a third case emerges, with no analogous in translationally-invariant systems, consisting of an antiferromagnetic Ne\'{e}l-type ground state where pairs of spins represent the unitary cell. Then, we calculate the exact solution of the model and show that the factorizing field represent an accidental degeneracy point of the Hamiltonian. Finally, we extend the study of the existence of ground-state factorization to a more general class of models

Village economies and the structure of extended family networks

This paper documents how the structure of extended family networks in rural Mexico relates to the poverty and inequality of the village of residence. Using the Hispanic naming convention, we construct within-village extended family networks in 504 poor rural villages. Family networks are larger (both in the number of members and as a share of the village population) and out-migration is lower the poorer and the less unequal the village of residence. Our results are consistent with the extended family being a source of informal insurance to its members

Family networks and school enrolment: evidence from a randomized social experiment

We present evidence on whether and how a household’s behavior is influenced by the presence and characteristics of its extended family. Using data from the PROGRESA program in Mexico, we exploit information on the paternal and maternal surnames of heads and spouses in conjunction with the Spanish naming convention to identify the inter and intra generational family links of each household to others in the same village. We then exploit the randomized research design of the PROGRESA evaluation data to identify whether the treatment effects of PROGRESA transfers on secondary school enrolment vary according to the characteristics of extended family. We find PROGRESA only raises secondary enrolment among households that are embedded in a family network. Eligible but isolated households do not respond. The mechanism through which the extended family influences household schooling choices is the redistribution of resources within the family network from eligibles that receive de facto unconditional cash transfers from PROGRESA, towards eligibles on the margin of enrolling children into secondary school

Quantum correlation dynamics in photosynthetic processes assisted by molecular vibrations

During the long course of evolution, nature has learnt how to exploit quantum effects. In fact, recent experiments reveal the existence of quantum processes whose coherence extends over unexpectedly long time and space ranges. In particular, photosynthetic processes in light-harvesting complexes display a typical oscillatory dynamics ascribed to quantum coherence. Here, we consider the simple model where a dimer made of two chromophores is strongly coupled with a quasi-resonant vibrational mode. We observe the occurrence of wide oscillations of genuine quantum correlations, between electronic excitations and the environment, represented by vibrational bosonic modes. Such a quantum dynamics has been unveiled through the calculation of the negativity of entanglement and the discord, indicators widely used in quantum information for quantifying the resources needed to realize quantum technologies. We also discuss the possibility of approximating additional weakly-coupled off-resonant vibrational modes, simulating the disturbances induced by the rest of the environment, by a single vibrational mode. Within this approximation, one can show that the off-resonant bath behaves like a classical source of noise

Quantum synchronization as a local signature of super- and subradiance

We study the relationship between the collective phenomena of super and subradiance and spontaneous synchronization of quantum systems. To this aim we revisit the case of two detuned qubits interacting through a pure dissipative bosonic environment, which contains the minimal ingredients for our analysis. By using the Liouville formalism, we are able to find analytically the ultimate connection between these phenomena. We find that dynamical synchronization is due to the presence of long standing coherence between the ground state of the system and the subradiant state. We finally show that, under pure dissipation, the emergence of spontaneous synchronization and of subradiant emission occur on the same time scale. This reciprocity is broken in the presence of dephasing noise.Comment: 12 pages, 6 figure

Maximally discordant mixed states of two qubits

We study the relative strength of classical and quantum correlations, as measured by discord, for two-qubit states. Quantum correlations appear only in the presence of classical correlations, while the reverse is not always true. We identify the family of states that maximize the discord for a given value of the classical correlations and show that the largest attainable discord for mixed states is greater than for pure states. The difference between discord and entanglement is emphasized by the remarkable fact that these states do not maximize entanglement and are, in some cases, even separable. Finally, by random generation of density matrices uniformly distributed over the whole Hilbert space, we quantify the frequency of the appearance of quantum and classical correlations for different ranks

A semi-Lagrangian scheme for the game pp-Laplacian via pp-averaging

We present and analyze an approximation scheme for the two-dimensional game $p$-Laplacian in the framework of viscosity solutions. The approximation is based on a semi-Lagrangian scheme which exploits the idea of $p$-averages. We study the properties of the scheme and prove that it converges, in particular cases, to the viscosity solution of the game $p$-Laplacian. We also present a numerical implementation of the scheme for different values of $p$; the numerical tests show that the scheme is accurate.Comment: 34 pages, 3 figures. To appear on Applied Numerical Mathematic