The fertility integration of Mexican-Americans across generations: confronting the problem of the ‘third’ generation*

The manner in which ‘third generation’ Mexican-Americans are identified, predicated on self-reported ethnic identity rather than grandparental nativity, is imprecise and potentially confounded with later generations. This study examines the degree to which this imprecision accounts for the stagnation found in many past studies of integration, including fertility integration. We use data from the study Immigration and Intergenerational Mobility in Metropolitan Los Angeles (IIMMLA), which includes questions on grandparental nativity, to construct a better-defined third generation. When IIMMLA data are aggregated into the commonly measured third-plus generation, the findings show a pattern of slow intergenerational-fertility integration, similar to previous research using the Current Population Survey or other data with third-plus generation measures. However, when we consider a third generation identified by grandparental nativity, evidence emerges of a faster fertility decline, bringing the third generation's fertility more in line with the native-born population as a whole. The results suggest that conclusions about integration based on third-plus generation measures should be regarded with greater scepticism and support efforts to include in surveys questions on grandparental nativity to enable the isolation of a genuine third generation among ethnic groups with immigrant origins.     

Crown width models for woody plant species growing in urban areas of the U.S.

Urban Ecosystems - Crown widths of woody plant species growing in urban areas are of considerable importance as an overall indicator of health and also serve as an important factor for assessing...     

WHAT DO BICYCLE HELMET LAWS DO? EVIDENCE FROM CANADA

Twenty‐one states and the District of Columbia require youths to wear helmets when riding a bicycle, and there has been a push to extend such laws to adults. We provide new evidence on helmet laws by studying Canada using difference‐in‐differences models and restricted area‐identified public health survey data with information on cycling and helmet use for nearly 800,000 individuals from 1994 to 2014. We first confirm prior patterns from the United States that laws requiring youths to wear helmets significantly increased youth helmet use. We then provide the literature's first comprehensive evidence that “all‐age” bicycle helmet laws significantly increased both adult and youth helmet use by 50%–190% relative to pre‐reform levels, with larger effects for younger adults and less‐educated adults. All‐age helmet laws had modest effects at reducing cycling and increasing in‐home exercise during winter months among adults but did not meaningfully affect weight. Overall, our findings confirm that all‐age helmet laws can be effective at increasing population helmet use without significant unintended adverse health consequences. (JEL I18, I12, K32)     

Managing a Remanufacturing System with Random Yield: Properties,Observations, and Heuristics

We study a remanufacturing system that involves the ordering of a serviceable product and the remanufacturing of multiple types of returned products (cores) into the serviceable product. In addition to random demand for the serviceable product and random returned quantities of different types of cores in each time period, the remanufacturing yield of each type of core is also uncertain. By analyzing a multi‐period stochastic dynamic program, we derive several properties of the optimal ordering/remanufacturing policy. In addition to some insights, these properties can be used to reduce the search effort of the optimal policy. We also demonstrate that some existing results derived from related models no longer hold in remanufacturing systems with random yield. Recognizing the optimal ordering/remanufacturing policy is highly complex, we examine three simple heuristics that can be efficiently solved and implemented in practice. Among these three heuristics, our numerical analysis suggests that the heuristic that captures most of the yield uncertainty and future system evolvement as well as some of the properties of the optimal ordering/remanufacturing policy outperforms the other two heuristics.     

An Elementary Introduction to Maximum Likelihood Estimation for Multinomial Models: Birch's Theorem and the Delta Method

A fairly complete introduction to the large sample theory of parametric multinomial models, suitable for a second-year graduate course in categorical data analysis, can be based on Birch's theorem (1964) and the delta method (Bishop, Fienberg, and Holland 1975). I present an elementary derivation of a version of Birch's theorem using the implicit function theorem from advanced calculus, which allows the presentation to be relatively self-contained. The use of the delta method in deriving asymptotic distributions is illustrated by Rao's (1973) result on the distribution of standardized residuals, which complements the presentation in Bishop, Fienberg, and Holland. The asymptotic theory is illustrated by two examples.     

Linear Transformations of Linear Mixed-Effects Models

A number of articles have discussed the way lower order polynomial and interaction terms should be handled in linear regression models. Only if all lower order terms are included in the model will the regression model be invariant with respect to coding transformations of the variables. If lower order terms are omitted, the regression model will not be well formulated. In this paper, we extend this work to examine the implications of the ordering of variables in the linear mixed-effects model. We demonstrate how linear transformations of the variables affect the model and tests of significance of fixed effects in the model. We show how the transformations modify the random effects in the model, as well as their covariance matrix and the value of the restricted log-likelihood. We suggest a variable selection strategy for the linear mixed-effects model.     

Adjusting Cornish–Fisher expansions and confidence intervals for the effect of roundoff

Suppose we want to estimate some smooth function of two types of parameters. The first can be estimated by sample means, while the second is known exactly up to the number of decimal places recorded, that is they are subject to roundoff. We obtain the Cornish–Fisher expansions and associated nonparametric confidence intervals for such functions. These results are illustrated by a simulation study.     

Expressions for the distribution and percentiles of the sums and products of chi-squares

Linear combinations of central or non-central chi-squares occur naturally in a variety of contexts. The products of chi-squares occur when a variance has a chi-square prior and in electrical engineering. Here, we give expansions for their distribution and quantiles and also for the products of the powers of chi-squares, including ratios. These provide much more accurate approximations than those based on asymptotic normality. The larger the degrees of freedom or the larger the non-centrality parameters, the better the approximations. We give the first four terms of these expansions. These provide approximations with errors smaller by five magnitudes than those based on asymptotic normality or on Satterthwaite's approximation. His method matched the first two moments of the target and a multiple of a chi-square and is only a first-order approximation like that based on the central limit theorem. We show that it can be made second order by matching the first three moments. The appendices show how to obtain analytical expressions for the distribution of weighted sums of chi-squares.