Exploratory data analysis for counts using the empirical probability generating function 1

We present a graphical method based on the empirical probability generating function for preliminary statistical analysis of distributions for counts. The method is especially useful in fitting a Poisson model, or for identifying alternative models as well as possible outlying observations from general discrete distributions.     

New Mothers’ Labour Force Participation in Italy: The Role of Job Characteristics

Abstract. In this paper we use newly available individual‐level data from the Longitudinal Survey of Italian Households to investigate the factors associated with female labour force participation after the birth of the first child. We focus on the role of pre‐marital job characteristics and find that new mothers who worked without a contract are less likely to participate, while those who worked in the public sector or in a large private firm have a higher probability of being in the labour force after childbearing. We suggest that these effects could be at least partly attributed to differences in the level of job protection and employment stability enjoyed by workers. This implies that in Italy women with highly protected and stable jobs might find it easier to combine career and family, whereas those who are less sheltered by the legislation might be more likely to be inactive after becoming mothers.     

Risks of Paralytic Disease Due to Wild or Vaccine-Derived Poliovirus After Eradication

After the global eradication of wild polioviruses, the risk of paralytic poliomyelitis from polioviruses will still exist and require active management. Possible reintroductions of poliovirus that can spread rapidly in unprotected populations present challenges to policymakers. For example, at least one outbreak will likely occur due to circulation of a neurovirulent vaccine-derived poliovirus after discontinuation of oral poliovirus vaccine and also could possibly result from the escape of poliovirus from a laboratory or vaccine production facility or from an intentional act. In addition, continued vaccination with oral poliovirus vaccines would result in the continued occurrence of vaccine-associated paralytic poliomyelitis. The likelihood and impacts of reintroductions in the form of poliomyelitis outbreaks depend on the policy decisions and on the size and characteristics of the vulnerable population, which change over time. A plan for managing these risks must begin with an attempt to characterize and quantify them as a function of time. This article attempts to comprehensively characterize the risks, synthesize the existing data available for modeling them, and present quantitative risk estimates that can provide a starting point for informing policy decisions.     

Average and Quantile Effects in Nonseparable Panel Models

Nonseparable panel models are important in a variety of economic settings, including discrete choice. This paper gives identification and estimation results for nonseparable models under time‐homogeneity conditions that are like “time is randomly assigned” or “time is an instrument.” Partial‐identification results for average and quantile effects are given for discrete regressors, under static or dynamic conditions, in fully nonparametric and in semiparametric models, with time effects. It is shown that the usual, linear, fixed‐effects estimator is not a consistent estimator of the identified average effect, and a consistent estimator is given. A simple estimator of identified quantile treatment effects is given, providing a solution to the important problem of estimating quantile treatment effects from panel data. Bounds for overall effects in static and dynamic models are given. The dynamic bounds provide a partial‐identification solution to the important problem of estimating the effect of state dependence in the presence of unobserved heterogeneity. The impact of T, the number of time periods, is shown by deriving shrinkage rates for the identified set as T grows. We also consider semiparametric, discrete‐choice models and find that semiparametric panel bounds can be much tighter than nonparametric bounds. Computationally convenient methods for semiparametric models are presented. We propose a novel inference method that applies in panel data and other settings and show that it produces uniformly valid confidence regions in large samples. We give empirical illustrations.     

Local Identification of Nonparametric and Semiparametric Models

In parametric, nonlinear structural models, a classical sufficient condition for local identification, like Fisher (1966) and Rothenberg (1971), is that the vector of moment conditions is differentiable at the true parameter with full rank derivative matrix. We derive an analogous result for the nonparametric, nonlinear structural models, establishing conditions under which an infinite dimensional analog of the full rank condition is sufficient for local identification. Importantly, we show that additional conditions are often needed in nonlinear, nonparametric models to avoid nonlinearities overwhelming linear effects. We give restrictions on a neighborhood of the true value that are sufficient for local identification. We apply these results to obtain new, primitive identification conditions in several important models, including nonseparable quantile instrumental variable (IV) models and semiparametric consumption‐based asset pricing models.     

QUALITATIVE VARIABLE DISCRIMINANT ANALYSIS AND ITS USE IN PRODUCT VERSION SELECTION

The purpose of this article is to illustrate the use of multiple discriminant analysis in those cases in which all discriminating variables are qualitative. The authors will show that an appropriate qualitative variable discriminant analysis model is a reformulation of the Bayesian decision theoretic model. Rules for the use of multiple discriminant analysis also are suggested for the cases in which some variables are qualitative and some are measurable on at least an interval scale. The qualitative variable discriminant analysis model is illustrated as an appropriate device for selecting a product version that will minimize a manufacturer's risk of product introduction.