How far from identifiability? A systematic overview of the statistical matching problem in a non parametric framework

Statistical matching consists in estimating the joint characteristics of two variables observed in two distinct and independent sample surveys, respectively. In a parametric setup, ranges of estimates for non identifiable parameters are the only estimable items, unless restrictive assumptions on the probabilistic relationship between the non jointly observed variables are imposed. These ranges correspond to the uncertainty due to the absence of joint observations on the pair of variables of interest. The aim of this paper is to analyze the uncertainty in statistical matching in a non parametric setting. A measure of uncertainty is introduced, and its properties studied: this measure studies the “intrinsic” association between the pair of variables, which is constant and equal to 1/6 whatever the form of the marginal distribution functions of the two variables when knowledge on the pair of variables is the only one available in the two samples. This measure becomes useful in the context of the reduction of uncertainty due to further knowledge than data themselves, as in the case of structural zeros. In this case the proposed measure detects how the introduction of further knowledge shrinks the intrinsic uncertainty from 1/6 to smaller values, zero being the case of no uncertainty. Sampling properties of the uncertainty measure and of the bounds of the uncertainty intervals are also proved.     

Modeling agricultural risk management policies – The implementation of the Income Stabilization Tool in Italy

This paper investigates the potential impact of the income stabilisation tool (IST), currently introduced in the European Common Agricultural Policy to reduce farmers’ income risks using Italian agriculture as case study. The paper extends the existing literature by investigating the effects of two implementation issues: level of aggregation of mutual funds (MF); definition of farmers’ contribution (i.e. premium) to MF. We use a simulation approach based on a FADN panel data set of 3421 farms over a period of 7 years to investigate effects on (i) farm-level income variability, (ii) the expected level and variability of indemnifications at the level of mutual funds and (iii) the distribution of net benefits from this policy instrument across the farm population. We find that the introduction of the IST would lead to a significant reduction of income variability in Italian agriculture. Our results support the establishment of a national mutual fund due to the high volatility of indemnification levels at more disaggregated (e.g. regional or sectoral) levels. In addition, our results propose that farmers’ contribution to mutual funds, i.e. premiums paid, should be modulated according to farm size as this reduces the inequality of the distribution of benefits of such tool within the farm population.     

The problem of being a paradigm: the emergence of neural stem cells as example for “Kuhnian” revolution in biology or misconception of the scientific community?

In a thought experiment we want to test how the emergence of adult neural stem cells could constitute an example for a scientific revolution in the sense of Thomas Kuhn. In his major work, “The structure of scientific revolutions, 3rd edn, University of Chicago Press, Chicago” (Kuhn 1996), the philosopher of science, Thomas Kuhn, states that scientific progress is not a cumulative process, but new theories appear by a rather revolutionary sequence of events. Kuhn built his theory on landmark events taken from chemistry and physics, lacking examples from biology. Beginning with Ramon y Cajal’s famous quote, “no new neurons after birth”, from the early years of the twentieth century, and Reynolds and Weiss’s conflicting finding in 1992 of adult neural stem cells giving rise to new neurons, we will test how the finding of neural stem cells in the adult brain matches with Kuhn’s theory. The pivotal problem of defining a paradigm will be our main focus, since the emergence of adult neural stem cells has been acclaimed by the scientific community as the rebuttal of Ramon y Cajal’s paradigm.     

A class of estimators for quantitative sensitive data

Randomized response methods for quantitative sensitive data are treated in an unified approach which includes the use of auxiliary information at the estimation stage. A class of estimators for the mean of a sensitive variable is proposed under a generic randomization model and the optimum estimator is obtained. Some special models are discussed in detail. To evaluate the degree of respondents’ confidentiality in models using auxiliary variables, a new measure of privacy protection is introduced. Different models are then compared both from the perspective of efficiency and privacy protection.     

Income Variance Dynamics and Heterogeneity

Recent theoretical work has shown the importance of measuring microeconomic uncertainty for models of both general and partial equilibrium under imperfect insurance. In this paper the assumption of i.i.d. income innovations used in previous empirical studies is removed and the focus of the analysis is placed on models for the conditional variance of income shocks, which is related to the measure of risk emphasized by the theory. We first discriminate amongst various models of earnings determination that separate income shocks into idiosyncratic transitory and permanent components. We allow for education‐ and time‐specific differences in the stochastic process for earnings and for measurement error. The conditional variance of the income shocks is modelled as a parsimonious ARCH process with both observable and unobserved heterogeneity. The empirical analysis is conducted on data drawn from the 1967–1992 Panel Study of Income Dynamics. We find strong evidence of sizeable ARCH effects as well as evidence of unobserved heterogeneity in the variances.     

Conditional tests in a competing risks model

Testing for equality of competing risks based on their cumulative incidence functions (CIFs) or their cause specific hazard rates (CSHRs) has been considered by many authors. The finite sample distributions of the existing test statistics are in general complicated and the use of their asymptotic distributions can lead to conservative tests. In this paper we show how to perform some of these tests using the conditional distributions of their corresponding test statistics instead (conditional on the observed data). The resulting conditional tests are initially developed for the case of k = 2 and are then extended to k > 2 by performing a sequence of two sample tests and by combining several risks into one. A simulation study to compare the powers of several tests based on their conditional and asymptotic distributions shows that using conditional tests leads to a gain in power. A real life example is also discussed to show how to implement such conditional tests.     

Reversible jump and the label switching problem in hidden Markov models

Reversible jump Markov chain Monte Carlo (RJMCMC) algorithms can be efficiently applied in Bayesian inference for hidden Markov models (HMMs), when the number of latent regimes is unknown. As for finite mixture models, when priors are invariant to the relabelling of the regimes, HMMs are unidentifiable in data fitting, because multiple ways to label the regimes can alternate during the MCMC iterations; this is the so-called label switching problem. HMMs with an unknown number of regimes are considered here and the goal of this paper is the comparison, both applied and theoretical, of five methods used for tackling label switching within a RJMCMC algorithm; they are: post-processing, partial reordering, permutation sampling, sampling from a Markov prior and rejection sampling. The five strategies we compare have been proposed mostly in the literature of finite mixture models and only two of them, i.e. rejection sampling and partial reordering, have been presented in RJMCMC algorithms for HMMs. We consider RJMCMC algorithms in which the parameters are updated by Gibbs sampling and the dimension of the model changes in split-and-merge and birth-and-death moves. Finally, an example illustrates and compares the five different methodologies.