Convergence Hypotheses are Ill-Posed:Non-stationarity of Cross-Country Income Distribution D

The recent literature on “convergence� of cross-country per capita incomes has been dominated by two competing hypotheses: “global convergence� and “club-convergence�. This debate has recently relied on the study of limiting distributions of estimated income distribution dynamics. Utilizing new measures of “stochastic stability�, we establish two stylized facts that question the fruitfulness of the literature’s focus on asymptotic income distributions. The first stylized fact is non-stationarity of transition dynamics, in the sense of changing transition kernels, which renders all “convergence� hypotheses that make long-term predictions on income distribution, based on relatively short time series, less meaningful. The second stylized fact is the periodic emergence, disappearance, and re-emergence of a “stochastically stable� middle-income group. We show that the probability of escaping a low-income poverty-trap depends on the existence of such a stable middle income group. While this does not answer the perennial questions about long-term effects of globalization on the cross-country income distribution, it does shed some light on the types of environments that are conducive to narrowing/global income distribution; convergence clubs; transition kernel; stochastic stability

When Does an Ensemble of Matrices with Randomly Scaled Rows Lose Rank?

We consider the problem of determining rank loss conditions for a concatenation of full-rank matrices, such that each row of the composing matrices is scaled by a random coefficient. This problem has applications in wireless interference management and recommendation systems. We determine necessary and sufficient conditions for the design of each matrix, such that the random ensemble will almost surely lose rank by a certain amount. The result is proved by converting the problem to determining rank loss conditions for the union of some specific matroids, and then using tools from matroid and graph theories to derive the necessary and sufficient conditions. As an application, we discuss how this result can be applied to the problem of topological interference management, and characterize the linear symmetric degrees of freedom for a class of network topologies.Comment: submitted to IEEE Transactions on Information Theory; shorter version to appear at IEEE International Symposium on Information Theory (ISIT 2015

Interest and the Paradox of Contemporary Islamic Law and Finance

In Sections 1 and 2, the article shall provide a brief introduction to various notions of Islamic law as they exist today, as well as the common-law nature of Islamic jurisprudence to establish the possibility of finding a compromise that renders minor modifications of the existing juristic positions coherent. In Sections 3 and 4, the article will provide translations of the entire Azhar Islamic Research Institute (IRI) fatwa, and large excerpts from the Council of the Islamic Jurisprudence Academy\u27s (IJA) rebuttal together with discussions of the juristic backgrounds of each opinion. In Section 5, the author will discuss the ideological roots of contemporary Islamic finance, which continue to shape Muslim views, both for jurists and lay people, regarding interest and permissible profit. In Section 6, the author will provide a brief survey of the most prominent Islamic financial instruments, illustrating the incoherence of juristic views that denounce “interest” and yet maintain that Islamic finance is “interest-free.” Lastly, the author will conclude by proposing a possible compromise between the two extreme views espoused by the IRI fatwa and the IJA rebuttal, which would allow for a coherent juristic and financial nexus in Islamic finance

The Deterministic Capacity of Relay Networks with Relay Private Messages

We study the capacity region of a deterministic 4-node network, where 3 nodes can only communicate via the fourth one. However, the fourth node is not merely a relay since it can exchange private messages with all other nodes. This situation resembles the case where a base station relays messages between users and delivers messages between the backbone system and the users. We assume an asymmetric scenario where the channel between any two nodes is not reciprocal. First, an upper bound on the capacity region is obtained based on the notion of single sided genie. Subsequently, we construct an achievable scheme that achieves this upper bound using a superposition of broadcasting node 4 messages and an achievable "detour" scheme for a reduced 3-user relay network.Comment: 3 figures, accepted at ITW 201

A Consistent Test of Stationary Ergodicity

A formal statistical test of stationary-ergodicity is developed for known Markovian processes on R^d. This makes it applicable to testing models and algorithms, as well as estimated time series processes ignoring the estimation error. The analysis is conducted by examining the asymptotic properties of the Markov operator on density space generated by the transition in the state space. The test is developed under the null of stationary-ergodicity, and it is shown to be consistent against the alternative of nonstationary-ergodicity. The test can be easily performed using any of a number of standard statistical and mathematical computer packages