Spatial Disaggregation of Social Indicators: An Info-Metrics Approach

In this paper we propose a methodology to obtain social indicators at a detailed spatial scale by combining the information contained in census and sample surveys. Similarly to previous proposals, the method proposed here estimates a model at the sample level to later project it to the census scale. The main novelties of the technique presented are that (i) the small-scale mapping produced is perfectly consistent with the aggregates -regional or national- observed in the sample, and (ii) it does not require imposing strong distributional assumptions. The methodology suggested here follows the basics presented on Golan (2018) by adapting a cross-moment constrained Generalized Maximum Entropy (GME) estimator to the spatial disaggregation problem. This procedure is compared with the equivalent methodology of Tarozzi and Deaton (2009) by means of numerical experiments, providing a comparatively better performance. Additionally, the practical implementation of the methodology proposed is illustrated by estimating poverty rates for small areas for the region of Andalusia (Spain).

Entropy-Based Solutions for Ecological Inference Problems: A Composite Estimator

Information-based estimation techniques are becoming more popular in the field of Ecological Inference. Within this branch of estimation techniques, two alternative approaches can be pointed out. The first one is the Generalized Maximum Entropy (GME) approach based on a matrix adjustment problem where the only observable information is given by the margins of the target matrix. An alternative approach is based on a distributionally weighted regression (DWR) equation. These two approaches have been studied so far as completely different streams, even when there are clear connections between them. In this paper we present these connections explicitly. More specifically, we show that under certain conditions the generalized cross-entropy (GCE) solution for a matrix adjustment problem and the GME estimator of a DWR equation differ only in terms of the a priori information considered. Then, we move a step forward and propose a composite estimator that combines the two priors considered in both approaches. Finally, we present a numerical experiment and an empirical application based on Spanish data for the 2010 year.

Effect of Actual and Perceived Violence on Internal Migration: Evidence from Mexico’s Drug War

According to the Organisation for Economic Co-operation and Development (OECD), violence should be considered by examining both actual and perceived crime. However, the studies related to violence and internal migration under the Mexican drug war episode focus only on one aspect of violence (perception or actual), so their conclusions rely mostly on limited evidence. This article complements previous work by examining the effects of both perceived and actual violence on interstate migration through estimation of a gravity model along three 5-year periods spanning from 2000 to 2015. Using the methods of generalized maximum entropy (to account for endogeneity) and the Blinder–Oaxaca decomposition, the results show that actual violence (measured by homicide rates) does affect migration, but perceived violence explains a greater proportion of higher average migration after 2005. Since this proportion increased after 2010 and actual violence, the results suggest that there was some adaptation to the new levels of violence in the period 2010–2015.

Comparative Study between Generalized Maximum Entropy and Bayes Methods to Estimate the Four Parameter Weibull Growth Model

The Weibull growth model is an important model especially for describing the growth instability; therefore, in this paper, three methods, namely, generalized maximum entropy, Bayes, and maximum a posteriori, for estimating the four parameter Weibull growth model have been presented and compared. To achieve this aim, it is necessary to use a simulation technique to generate the samples and perform the required comparisons, using varying sample sizes (10, 12, 15, 20, 25, and 30) and models depending on the standard deviation (0.5). It has been shown from the computational results that the Bayes method gives the best estimates.

(Generalized) Maximum Cumulative Direct, Residual, and Paired Φ Entropy Approach

A distribution that maximizes an entropy can be found by applying two different principles. On the one hand, Jaynes (1957a,b) formulated the maximum entropy principle (MaxEnt) as the search for a distribution maximizing a given entropy under some given constraints. On the other hand, Kapur (1994) and Kesavan and Kapur (1989) introduced the generalized maximum entropy principle (GMaxEnt) as the derivation of an entropy for which a given distribution has the maximum entropy property under some given constraints. In this paper, both principles were considered for cumulative entropies. Such entropies depend either on the distribution function (direct), on the survival function (residual) or on both (paired). We incorporate cumulative direct, residual, and paired entropies in one approach called cumulative Φ entropies. Maximizing this entropy without any constraints produces an extremely U-shaped (=bipolar) distribution. Maximizing the cumulative entropy under the constraints of fixed mean and variance tries to transform a distribution in the direction of a bipolar distribution, as far as it is allowed by the constraints. A bipolar distribution represents so-called contradictory information, which is in contrast to minimum or no information. In the literature, to date, only a few maximum entropy distributions for cumulative entropies have been derived. In this paper, we extended the results to well known flexible distributions (like the generalized logistic distribution) and derived some special distributions (like the skewed logistic, the skewed Tukey λ and the extended Burr XII distribution). The generalized maximum entropy principle was applied to the generalized Tukey λ distribution and the Fechner family of skewed distributions. Finally, cumulative entropies were estimated such that the data was drawn from a maximum entropy distribution. This estimator will be applied to the daily S&P500 returns and time durations between mine explosions.