Birth Spacing Effect on Children's Attainments: Indentification Using Instrument Variables

In this study, I address the relationship between an often overlooked dimension of family structure—the spacing between children’s births—and the degree of children’s attainments such as Mathematics, Reading Cognition and Reading Comprehension. Comparing to the results of OLS estimation, 2SLS Estimation using Twin and Catholic as Instrument Variables shows less significant effects on children’s attainments. Hausman Test shows that OLS estimators are not consistent with 2SLS estimators, which means there is endogenous problem in OLS estimation. As the result in 2SLS shows the different spacing effects in different spacing groups, it is possible to use nonlinear estimation (quadratic form of birth spacing) and semi-parametric estimation to draw the curve of birth spacing effects, and find the most efficient birth spacing, golden birth spacing. These two estimations, to a large extent, match each other in the range of golden birth spacing

Iterative Decoding and Turbo Equalization: The Z-Crease Phenomenon

Iterative probabilistic inference, popularly dubbed the soft-iterative paradigm, has found great use in a wide range of communication applications, including turbo decoding and turbo equalization. The classic approach of analyzing the iterative approach inevitably use the statistical and information-theoretical tools that bear ensemble-average flavors. This paper consider the per-block error rate performance, and analyzes it using nonlinear dynamical theory. By modeling the iterative processor as a nonlinear dynamical system, we report a universal "Z-crease phenomenon:" the zig-zag or up-and-down fluctuation -- rather than the monotonic decrease -- of the per-block errors, as the number of iteration increases. Using the turbo decoder as an example, we also report several interesting motion phenomenons which were not previously reported, and which appear to correspond well with the notion of "pseudo codewords" and "stopping/trapping sets." We further propose a heuristic stopping criterion to control Z-crease and identify the best iteration. Our stopping criterion is most useful for controlling the worst-case per-block errors, and helps to significantly reduce the average-iteration numbers.Comment: 6 page