Graphical Markov models: overview

We describe how graphical Markov models started to emerge in the last 40 years, based on three essential concepts that had been developed independently more than a century ago. Sequences of joint or single regressions and their regression graphs are singled out as being best suited for analyzing longitudinal data and for tracing developmental pathways. Interpretations are illustrated using two sets of data and some of the more recent, important results for sequences of regressions are summarized.Comment: 22 pages, 9 figure

Graphical Markov models, unifying results and their interpretation

Graphical Markov models combine conditional independence constraints with graphical representations of stepwise data generating processes.The models started to be formulated about 40 years ago and vigorous development is ongoing. Longitudinal observational studies as well as intervention studies are best modeled via a subclass called regression graph models and, especially traceable regressions. Regression graphs include two types of undirected graph and directed acyclic graphs in ordered sequences of joint responses. Response components may correspond to discrete or continuous random variables and may depend exclusively on variables which have been generated earlier. These aspects are essential when causal hypothesis are the motivation for the planning of empirical studies. To turn the graphs into useful tools for tracing developmental pathways and for predicting structure in alternative models, the generated distributions have to mimic some properties of joint Gaussian distributions. Here, relevant results concerning these aspects are spelled out and illustrated by examples. With regression graph models, it becomes feasible, for the first time, to derive structural effects of (1) ignoring some of the variables, of (2) selecting subpopulations via fixed levels of some other variables or of (3) changing the order in which the variables might get generated. Thus, the most important future applications of these models will aim at the best possible integration of knowledge from related studies.Comment: 34 Pages, 11 figures, 1 tabl

Poverty alleviation and child labor

Does child labor decrease as household income rises? This question has important implications for the design of policy on child labor. This paper focuses on a program of unconditional cash transfers in Ecuador. It argues that the effect of a small increase in household income on child labor should be concentrated among children most vulnerable to transitioning from schooling to work. The paper finds support for this hypothesis. Cash transfers have small effects on child time allocation at peak school attendance ages and among children already out of school at baseline, but have large impacts at ages and in groups most likely to leave school and start work. Additional income is associated with a decline in paid work that takes place away from the child's home. Declines in work for pay are associated with increases in school enrollment, especially for girls. Increases in schooling are matched by an increase in education expenditures that appears to absorb most of the cash transfer. However, total household expenditures do not increase with the transfer and appear to fall in households most impacted by the transfer because of the decline in child labor.Street Children,Youth and Governance,Gender and Law,Labor Policies,Primary Education

Concepts and a case study for a flexible class of graphical Markov models

With graphical Markov models, one can investigate complex dependences, summarize some results of statistical analyses with graphs and use these graphs to understand implications of well-fitting models. The models have a rich history and form an area that has been intensively studied and developed in recent years. We give a brief review of the main concepts and describe in more detail a flexible subclass of models, called traceable regressions. These are sequences of joint response regressions for which regression graphs permit one to trace and thereby understand pathways of dependence. We use these methods to reanalyze and interpret data from a prospective study of child development, now known as the Mannheim Study of Children at Risk. The two related primary features concern cognitive and motor development, at the age of 4.5 and 8 years of a child. Deficits in these features form a sequence of joint responses. Several possible risks are assessed at birth of the child and when the child reached age 3 months and 2 years.Comment: 21 pages, 7 figures, 7 tables; invited, refereed chapter in a boo

Consumption

Macroeconomic research on consumption has been influenced profoundly by rational expectations. First, rational expectations together with the hypothesis of constant expected real interest rates implies that consumption should evolve as a random walk. Much of the research of the past decade has been devoted to testing the random walk hypothesis and to explaining its failure. Three branches of the literature have developed. The first relies on the durability of consumption to explain deviations from the random walk property. The second invokes liquidity constraints which block consumers from the credit market transactions needed to make consumption follow a random walk when income fluctuates up and down. The third branch dispenses with the assumption that expected real interest rates are constant. It attempts to explain deviations from the random walk in terms of intertemporal substitution.

Intergenerational Persistence of Earnings: The Role of Early and College Education

Recent empirical studies show that the intergenerational persistence of economic status in the U.S. is much higher than previously thought. We develop a quantitative theory of inequality and intergenerational transmission of human capital where parents invest in early and college education of their children subject to borrowing constraints. Children differ exogenously in innate abilities, which can be correlated with their parent s innate ability. An important feature of the environment is that the quality of early education determines the probability of college completion. We calibrate a stationary equilibrium of this economy to relevant statistics in aggregate U.S. data, and use it to investigate the sources of inequality and persistence in earnings. In our benchmark model, about half of the intergenerational persistence and one fourth of the inequality in earnings are accounted for by endogenous investments in education. We find that early investments in education account for most of the endogenous persistence in earnings, while college education generates most of the endogenous inequality in earnings. Our theory is suited to study the effect of educational policies on the persistence of inequality. We show that public resources devoted to early education have the largest impact on earnings mobility. Moreover, non-progressive college subsidies generate more intergenerational persistence of earnings.Human Capital, Education, Intergenerational Mobility, Ability.

Estimating time-varying sex-age-specific o/e rates of marital status transitions in family household projection or simulation

This article presents a procedure for estimating time-varying sex-age-specific occurrence/exposure (o/e) rates of marital status transitions to ensure that the projected life course propensities of marriage/union formation and dissolution are achieved consistently in the one-sex family status life table model. Procedures for estimating time-varying sex-age-specific marital status transition o/e rates that are consistent with the two-sex constraints and projected summary measures of marriage/union formation and dissolution in the future years in the two-sex family household projection model is proposed. The procedures proposed in this article are practically useful and can be applied in both macro and micro models for family household projections or simulations that need time-varying sex-age-specific o/e rates of marital status transitions.family, household, marriage, projections, simulation

Bootstrap and the physical values of πN\pi N resonance parameters

This is the 6th paper in the series developing the formalism to manage the effective scattering theory of strong interactions. Relying on the theoretical scheme suggested in our previous publications we concentrate here on the practical aspect and apply our technique to the elastic pion-nucleon scattering amplitude. We test numerically the pion-nucleon spectrum sum rules that follow from the tree level bootstrap constraints. We show how these constraints can be used to estimate the tensor and vector $NN\rho$ coupling constants. At last, we demonstrate that the tree-level low energy expansion coefficients computed in the framework of our approach show nice agreement with known experimental data. These results allow us to claim that the extended perturbation scheme is quite reasonable from the computational point of view.Comment: 41 pages, 7 figure