Modelling Fertility: A Semi-Parametric Approach

This article presents a categorical model of fertility based on the statistical theory of the Generalised Linear Model (GLM). Focussing on the individual probability of giving birth to a child, we derive distributions which can be embedded in a GLM framework. A major advance of that methodology is the knowledge of the distribution of the random variable, which leads to a Maximum Likelihood estimation procedure. The approach takes into account the smooth shapes of parameter development over the age of the mother as well as over time. The estimation of this semi-parametric approach is done using the Local-Likelihood-method. The presented method provides stable results of the fertility, especially for smaller populations. This is illustrated by using a data set which consists of less than 100,000 inhabitants. Dieser Aufsatz stellt ein kategorielles Modell der Geburtenhäufigkeit auf Basis der statistischen Theorie des Verallgemeinerten Linearen Modells (VLM) vor. Ausgehend von individuellen Gebär-Wahrscheinlichkeiten leiten wir Verteilungen ab, welche in einen VLM-Rahmen eingebettet werden können. Ein besonderer Vorteil dieser Methode ist das Wissen um die Verteilung der Zufallsvariablen, welches ein Maximum-Likelihood Schätzverfahren ermöglicht. Der Ansatz berücksichtigt den gleichmäßigen Verlauf der Parameter-Entwicklung über das Alter der Mutter und über die Zeit. Die Schätzung dieses semi-parametrischen Ansatzes erfolgt mit Hilfe der Local-Likelihood-Methode. Die vorgestellte Methode liefert solide Ergebnisse zur Geburtenhäufigkeit, insbesondere bei kleineren Bevölkerungszahlen. Dies wird anhand eines Datensatzes mit weniger als 100.000 Einwohnern gezeigt.Geburtenentwicklung ; Semiparametrische Schätzung ; Verallgemeinertes lineares Modell; ;

The mortality of the Italian population: Smoothing techniques on the Lee--Carter model

Several approaches have been developed for forecasting mortality using the stochastic model. In particular, the Lee-Carter model has become widely used and there have been various extensions and modifications proposed to attain a broader interpretation and to capture the main features of the dynamics of the mortality intensity. Hyndman-Ullah show a particular version of the Lee-Carter methodology, the so-called Functional Demographic Model, which is one of the most accurate approaches as regards some mortality data, particularly for longer forecast horizons where the benefit of a damped trend forecast is greater. The paper objective is properly to single out the most suitable model between the basic Lee-Carter and the Functional Demographic Model to the Italian mortality data. A comparative assessment is made and the empirical results are presented using a range of graphical analyses.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS394 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Estimating Equivalence Scales for Tax and Benefits Systems

When comparing, say, the welfare derived from income by a family that is comprised of two adults and three children to that of a single adult, it is necessary to take into consideration the relative needs of the respective households. The most common means by which applied studies in economics currently relate the needs of heterogeneous income units is through the use of equivalence scales. Despite a considerable research effort, however, almost every aspect of equivalence scale specification remains controversial. What characteristics should equivalence scales take into account? Should the scales apply an additive or multiplicative adjustment to income? Is the assumption of base independence valid?1 How should a reference unit be selected? Is it reasonable to assume that there is no inequality within an income unit? What criteria are most sensible for selecting a functional form? And, arguably most important, do the cardinal relations implied by equivalence scales permit income units to be compared in terms of underlying welfare? All of these questions remain largely unresolved. This paper is concerned with estimating the relativities that are implicit in tax and benefits policy. Using observed tax and benefits payments to estimate equivalence scales may mitigate some of the criticisms to which alternative scale specification criteria have been subject. For example, most econometric estimates of equivalence scales used for distributional analysis are based on consumer demand behaviour. Pollak and Wales (1979, p. 216) have notably criticised this methodology on the basis that “the equivalence scales required for welfare comparisons are logically distinct from those which arise in demand analysis”. The central difficulty is that demand analysis fails to provide a basis for making cardinal comparisons of welfare between households, and so equivalence scales that are estimated from expenditure data necessarily depend upon exogenously imposed value judgements. In contrast, part of the intuitive appeal of equivalence scales based on a country’s transfer system is the perception that such relativities embody a social consensus; that the tax and benefits system, being an observable instrument of government, can be used to infer the value judgements made by government when acting in its role as administrative agent for society. Comparison of the relativities that underlie taxation with equivalence scales based on the costs borne by heterogeneous income units could also provide a useful means for evaluating the adequacy of associated provisions made by transfer systems. Alternatively, the equivalence scales implicit in transfer systems could be used to compare the provisions made through time and/or between countries. Such equivalence scales could also play a role in the tax design process itself. In view of the fact that the redistributive systems of many countries are comprised of numerous different tax and benefit schemes, it is difficult to ensure that the overall system does in fact achieve the desired redistribution. Information about implicit scales — which may on reflection be found to differ from the values held by policy makers — can be useful in suggesting that certain features of the tax system need adjusting.

Tracing the income-fertility nexus: Nonparametric Estimates for a Panel of Countries

We apply the a nonparametric method of kernel regression on a dataset for 109 countries to estimate the income fertility nexus in demo-economic transition. The results suggest the existence of a critical level of per capita income above which fertility decreases exponentially with rising income. For income levels below fertility stays on a high level and its relation to income is of minor significance. The critical income threshold changes over time and is lower for more recent periods, which gives evidence of major structural shifts in the relationship under investigation.

Spatial profiles in the analysis of event histories: an application to first sexual intercourse in Italy

-

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

High Resolution Spectrometry of Leaf and Canopy Chemistry for Biochemical Cycling

High-resolution laboratory spectrophotometer and Airborne Imaging Spectrometer (AIS) data were used to analyze forest leaf and canopy chemistry. Fundamental stretching frequencies of organic bonds in the visible, near infrared and short-wave infrared are indicative of concentrations and total content of nitrogen, phosphorous, starch and sugar. Laboratory spectrophotometer measurements showed very strong negative correlations with nitrogen (measured using wet chemistry) in the visible wavelengths. Strong correlations with green wet canopy weight in the atmospheric water absorption windows were observed in the AIS data. A fairly strong negative correlation between the AIS data at 1500 nm and total nitrogen and nitrogen concentration was evident. This relationship corresponds very closely to protein absorption features near 1500 nm

Global estimation of child mortality using a Bayesian B-spline Bias-reduction model

Estimates of the under-five mortality rate (U5MR) are used to track progress in reducing child mortality and to evaluate countries' performance related to Millennium Development Goal 4. However, for the great majority of developing countries without well-functioning vital registration systems, estimating the U5MR is challenging due to limited data availability and data quality issues. We describe a Bayesian penalized B-spline regression model for assessing levels and trends in the U5MR for all countries in the world, whereby biases in data series are estimated through the inclusion of a multilevel model to improve upon the limitations of current methods. B-spline smoothing parameters are also estimated through a multilevel model. Improved spline extrapolations are obtained through logarithmic pooling of the posterior predictive distribution of country-specific changes in spline coefficients with observed changes on the global level. The proposed model is able to flexibly capture changes in U5MR over time, gives point estimates and credible intervals reflecting potential biases in data series and performs reasonably well in out-of-sample validation exercises. It has been accepted by the United Nations Inter-agency Group for Child Mortality Estimation to generate estimates for all member countries.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS768 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

Endogenous Population and Environmental Quality

This paper provides with empirical and theoretical studies of the relationship between population, economic growth and environmental quality. Using a simple endogenous growth model we obtain results close to empirical findings. We show existence of a sustainable balanced growth path (BGP) equilibrium in which perpetual economic growth goes in parallel with environmental quality preservation. At the BGP equilibrium, when all exogenous factors are controlled, a negative relationship between fertility rate and economic growth (termed neo-Malthusian relationship) and a negative relationship between population growth rate and environmental quality emerge.Environmental quality; Endogenous population; Endogenous growth; Deforestation