**Abstract 2012**

**The Breaking-Down of Marriage in Italy: Trends and Trendsetters**

**Giuseppe Gabrielli, Daniele Vignoli**

During the last decades, since the mid-1970s, marriage has lost much of its centrality in Southern European Countries, such as Italy and Spain. However, the general incidence of consensual unions and marital disruption is still low compared to general European standards. Some scholars argue that the long tradition of a rigid familistic system in such countries will lay the phenomenon at very low levels. But our results reject a static picture of the Italian context and, despite persisting geographical differences, they confirm a rising breaking-down of marriage. Overall, our work places Italy at a crucial stage, in which the trends indicate a strong increase in divorce and consensual unions, and the new behaviours are no longer confined to certain trendsetters. Spain and Italy seem to be moving together in the European context.

Published as *Population Review*, Volume 52, Issue 1, pp. 87-109, 2013, forthcoming.

**Realized Volatility and Change of Regimes**

**Giampiero Gallo, Edoardo Otranto**

Persistence and occasional abrupt changes in the average level characterize the dynamics of high frequency based measures of volatility. Since the beginning of the 2000s, this pattern can be attributed to the dot com bubble, the quiet period of expansion of credit between 2003 and 2006 and then the harsh times after the burst of the subprime mortgage crisis. We conjecture that the inadequacy of many econometric volatility models (a very high level of estimated persistence, serially correlated residuals) can be solved with an adequate representation of such a pattern. We insert a Markovian dynamics in a Multiplicative Error Model to represent the conditional expectation of the realized volatility, allowing us to address the issues of a slow moving average level of volatility and of a different dynamics across regime. We apply the model to realized volatility of the S&P500 index and we gauge the usefulness of such an approach by a more interpretable persistence, better residual properties, and an increased goodness of fit.

**Volatility Swings in the US Financial Markets**

**Giampiero Gallo, Edoardo Otranto**

Empirical evidence shows that the dynamics of high frequency–based measures of volatility exhibit persistence and occasional abrupt changes in the average level. By looking at volatility measures for major indices, we notice similar patterns (including jumps at about the same time), with stronger similarities, the higher the degree of company capitalization represented in the indices. We adopt the recent Markov Switching Asymmetric Multiplicative Error Model to model the dynamics of the conditional expectation of realized volatility. This allows us to address the issues of a slow moving average level of volatility and of different dynamics across regimes. An extension sees a more flexible model combining the characteristics of Markov Switching and smooth transition dynamics.

Published as *in Grigoletto M., Lisi F., Petrone S. (eds.) Complex Models and Computational Methods in Statistics*, Springer, pp. -, 2013, ISBN 978-88-470-28.

wp2012_04 (Statistics, Econometrics)

**Using secondary outcomes and covariates to sharpen inference in randomized experiments with noncompliance**

**Fabrizia Mealli, Barbara Pacini**

Restrictions implied by the randomization of treatment assignment on the joint distribution of a primary outcome and an auxiliary variable are used to tighten nonparametric bounds for intention-to-treat effects on the primary outcome for some latent subpopulations, without requiring the exclusion restriction assumption of the assignment. The auxiliary variable can be a secondary outcome or a covariate, while the subpopulations are defined by the values of the potential treatment status under each value of the assignment. The derived bounds can be used to detect violations of the exclusion restriction and the magnitude of these violations in instrumental variables settings. It is shown that the reduced width of the bounds depends on the the strength of the association of the auxiliary variable with the primary outcome and the compliance status. We also show how the setup we consider offers new identifying assumptions of intention-to-treat effects without the exclusion restriction. The use of the bounds is illustrated in two real data examples of a social job training experiment and a medical randomized encouragement study.

wp2012_05 (Statistics, Statistics for experimental and technological research )

**Small area estimation for semicontinuos skewed georeferenced data**

**Emanuela Dreassi, Alessandra Petrucci, Emilia Rocco**

Semicontinuous random variables combine continuous distributions with point masses at one or more locations. A particular type of semicontinuous variable has been considered in this paper: a mixture of zeros and highly skewed continuously distributed positive values. This kind of variable occurs in economic surveys of individuals or establishments (e.g. specific types of income or expenditures), as well as in agricultural, epidemiological and environmental surveys. Frequently, this type of variable describes phenomena that have a spatial distribution and reliable small area estimates of their means or totals could be required. As in other small area estimation (SAE) problems, the small sample sizes (in at least some of the sampled areas) and/or the existence of non sampled areas need to use model based estimation methods. However, commonly used small area estimation methods, which assume that a linear mixed model can be used to characterize the regression relationship between the response variable and at least one auxiliary variable, are not suitable for this kind of data. In this paper we propose the use of a two-part random effects SAE model that accounts for excess of zero but also for skewness of the distribution of non zero responses. This is carried out by specifying, in the first part, a logistic regression model for the probability of a non zero occurrence and, in the second part, a gamma regression model for the mean of the non zero values. The model includes a correlation structure on the area random effects that appears in the two parts and incorporates a bivariate smooth function of the geographical coordinates of the units in order to consider the spatial structure in the data within each small area. A hierarchical Bayesian approach is suggested to fit the model, produce the small area estimates of interest, and evaluate their precision. An application to real agricultural survey data from the Italian Statistical Institute demonstrates the satisfactory performance of the method.

wp2012_06 (Statistics, Medical Statistics)

**Disease Mapping via Negative Binomial M-quantile regression**

**Ray Chambers, Emanuela Dreassi, Nicola Salvati**

A new approach to ecological regression on disease mapping is introduced: a semi-parametric method based on M-quantile models. We define a Negative Binomial M-quantile model as an alternative to Empirical Bayes or fully Bayesian approaches to disease mapping. The proposed method is easily made robust against outlying data values for covariates. Robust ecological regression on disease mapping is desirable since covariates at area level usually present measure-type error. Differences between M-quantile and usual random effects models are discussed and the alternative approaches are compared using the Scottish Lip cancer example and a simulation experiment. The example shows that the Negative Binomial M-quantile model confirms results obtained by other methods, but it seems to have less shrinkage effect than the Empirical Bayes method, so reducing the problem of oversmoothing. The simulation experiment suggests that the new model presents smaller root mean square error. The Negative Binomial M-quantile is also extended to accounting for spatial structure between areas following a Geographically Weighted Regression strategy.

wp2012_07 (Statistics, Demography)

**How education affects fertility in the presence of time-varying frailty component**

**Anna Gottard, Alessandra Mattei, Daniele Vignoli**

We investigate the association between fertility and women’s education in Italy, using data from the 2003 Household Multipurpose Survey Family and Social Subjects. We adopt a Bayesian event history approach to estimation and study the association between fertility and women’s education in the presence of a time-varying unobserved component. It is shown that the usually made assumption of time-constant unobserved heterogeneity can lead to misleading results.

**Compatibility results for conditional distributions**

**Patrizia Berti, Emanuela Dreassi, Pietro Rigo**

In various frameworks, to assess the joint distribution of a k-dimensional random vector X=(X1,...,Xk), one selects some putative conditional distributions Q1,...,Qk. Each Qi is regarded as a possible (or putative) conditional distribution for Xi given (X1,...,Xi-1,Xi+1,...,Xk). The Qi are compatible if there is a joint distribution P for X with conditionals Q1,...,Qk. Three types of compatibility results are given in this paper. First, the Xi are assumed to take values in compact subsets of R. Second, the Qi are supposed to have densities with respect to reference measures. Third, a stronger form of compatibility is investigated. Indeed, the law P with conditionals Q1,...,Qk is requested to be exchangeable.

wp2012_09 (Econometrics, Economic Statistics)

**Tests for serial dependence in static, non-Gaussian factor models**

**Gabriele Fiorentini, Enrique Sentana**

We derive simple algebraic expressions for score tests of serial correlation in the levels and squares of common and idiosyncratic factors in static factor models with (semi) parametrically specified elliptical distributions even though one must generally compute the likelihood by simulation. We also robustify our Gaussian tests against non-normality. The orthogonality conditions resemble the orthogonality conditions of models with observed factors but the weighting matrices reflect their unobservability. Our Monte Carlo exercises assess the finite sample reliability and power of our proposed tests, and compare them to other existing procedures. Finally, we apply our methods to monthly US stock returns.

**Sequential estimation of shape parameters in multivariate dynamic models**

**Dante Amengual, Gabriele Fiorentini, Enrique Sentana**

Sequential maximum likelihood and GMM estimators of distributional parameters obtained from the standardised innovations of multivariate conditionally heteroskedastic dynamic regression models evaluated at Gaussian PML estimators preserve the consistency of mean and variance parameters while allowing for realistic distributions. We assess the efficiency of those estimators, and obtain moment conditions leading to sequential estimators as efficient as their joint maximum likelihood counterparts. We also obtain standard errors for the quantiles required in VaR and CoVaR calculations, and analyse the effects on these measures of distributional misspecification. Finally, we illustrate the small sample performance of these procedures through Monte Carlo simulations.

wp2012_11 (Statistics, Econometrics)

**DMM - A Fortran program for dynamic mixture models**

**Gabriele Fiorentini, Christophe Planas, Alessandro Rossi**

DMM is a Fortran program for Bayesian analysis of dynamic mixture models which produces posterior samples of the unobserved state vector, of the discrete latent variables, and of model parameters together with the marginal likelihood of the data set. Besides computational efficiency, DMM has several attractive features: the endogenous series can be univariate or multivariate, stationary or non-stationary, with some possibly missing observations, and they may be linked to some exogenous variables. We describe the methodology implemented and we show how to use the program with some examples.

Ultimo aggiornamento 10 aprile 2013.