# Working Papers del DiSIA

### Indirect estimation and econometrics exams: how to live a round life

### Giorgio Calzolari

The use of Monte Carlo methods to generate exam data sets is nowadays a well-established practice among econometrics examiners all over the world. Its advantages are well known: providing each student a different data set ensures that estimates are actually computed individually, rather than copied from someone sitting nearby. The method however has a major fault: initial "random errors", such as mistakes in downloading the assigned dataset, might generate downward bias in student evaluation. We propose a set of calibration algorithms, typical of indirect estimation methods, that solve the issue of initial "random errors" and reduce evaluation bias. Ensuring round initial estimates of the parameters for each individual data set, our calibration procedures allow the students to determine if they have started the exam correctly. When initial estimates are not round numbers, this random error in the initial stage of the exam can be corrected for immediately, thus reducing evaluation bias. The procedure offers the further advantage of rounding markers’ life by allowing them to check round numbers answers only, rather than lists of numbers with many decimal digits.

Working Papers del Dipartimento

### Uncertain Lives. Insights into the Role of Job Precariousness in Union Formation

### Daniele Vignoli, Valentina Tocchioni, Silvana Salvini

The diffusion of temporary job contracts in contemporary European societies has raised concern that these jobs, even while deemed useful for combating unemployment, may also constitute a source of insecurity and precariousness for young workers. Little is known about their possible social and demographic consequences, especially as regards family formation. We focused on this knowledge-gap by examining how job precariousness affects union formation practices in Italy. We studied both genders and combined the empirical evidence from both qualitative and quantitative research. Based on the qualitative evidence, we advanced the hypothesis that cohabitation can be linked to the growing labor market uncertainty while marriage can be linked to stability. The subsequent quantitative analysis provided strong support for this hypothesis in the general population.

Published as Demographic Research, Volume 35, Issue 1, pp. 253-282, 2016; link, published.

Working Papers del Dipartimento

### Demographic Trends in Developing Countries: Convergence or Divergence Processes?

### Maria Silvana Salvini, Giuseppe Gabrielli, Anna Paterno, Isabella Corazziari

Recent years are characterized by both a rise in life expectancy and a further fall in fertility in the developing countries (DCs). These processes coexist with large heterogeneity according to the specific living conditions of countries. The aim of our research is to analyze the trends of specific demographic parameters regarding mortality and fertility, jointly with some socio-economic characteristics of more than 100 DCs, to assess if convergence patterns in demographic behaviors prevail or if marked differences persist. As the paths of mortality and fertility in fact differ deeply over space and time, we need a specific statistical multi-way analysis technique that consider the time series dimension. Thus, we apply Dynamic Factor Analysis and Cluster Analysis of trajectories in order to evaluate at macro-level the main demographic trends of DCs in the 1995-2010 period. Results let us reconsider the processes of convergence and enlighten the heterogeneity among clusters.

Working Papers del Dipartimento

### A parametric test to discriminate between a linear regression model and a linear latent growth model

### Marco Barnabani

In longitudinal studies with subjects measured repeatedly across time, an important problem is how to select a model generating data choosing between a linear regression model and a linear latent growth model. Approaches based both on information criteria and on asymptotic hypothesis test on the variances of ”random” components are largely used but not completely satisfactory. In the paper we propose a finite sample parametric test based on the trace of the product of estimates of two variance covariance matrices, one defined when data come from a linear regression model, the other defined when data come from a linear latent growth model. The sampling distribution of the test statistic so defined depends on the model generating data. It can be a ”standard” F-distribution or a linear combination of F-distributions. In the paper a unified sampling distribution based on a generalized F-distribution is proposed. The knowledge of this distribution allows us to make inference in a classical hypothesis testing framework. The test statistic can be used by itself to discriminate between the two models and/or, duly modified, it can be used to test randomness on single components of the linear latent growth model avoinding the boundary problem of the likelihood ratio test statistic. Moreover, it can be used in conjunction with some indicators based on information criteria giving estimates of probability of accepting or rejecting the model chosen.

Working Papers del Dipartimento

### Searching secrets rationally

### Michele Boreale, Fabio Corradi

We study quantitative information flow, from the perspective of an analyst who is interested in maximizing its expected gain in the process of discovering a secret, or settling a hypothesis, represented by an unobservable X, after observing some Y related to X. In our framework, inspired by Bayesian decision theory, discovering the secret has an associated reward, while the investigation of the set of possibilities prompted by the observation has a cost. We characterize the optimal strategy for the analyst and the corresponding expected gain (payoff) in a variety of situations. We argue about the importance of advantage, defined as the increment in expected gain after the observation if the analyst acts optimally, and representing the value of the information conveyed by Y. We also argue that the proposed strategy is more effective than others, based on probability coverage. Applications to cryptographic systems and to familial DNA searching are examined.

Working Papers del Dipartimento

### Bayesian inference for causal mechanisms with application to a randomized study for postoperative pain control

### Michela Baccini, Alessandra Mattei, Fabrizia Mealli

Principal stratification and mediation analysis are two ways to conceptualize the mediating role of an intermediate variable in the causal pathways by which a treatment affects an outcome. They are often viewed as competing frameworks, and their role in dealing with issues concerning causal mechanisms has often fired up glowing discussions. However a thoughtful comparative analysis, highlighting the substantive differences between the two frameworks is still lacking. We aim at filling this gap conducting both principal stratification and mediation analysis using, as a motivating example, a prospective, randomized, double-blind study to investigate to which extent the positive overall effect of treatment on postoperative pain control is mediated by postoperative self administration of intra-venous analgesia by patients. Using the Bayesian approach for inference, we estimate both associative and dissociative principal strata effects arising in principal stratification analysis, as well as natural effects and controlled direct effects from mediation analysis. We highlight that principal stratification and mediation analysis focus on different causal estimands, answer different causal questions and involve different sets of identifying assumptions. We discuss these aspects along the results arising from our analyses.

Working Papers del Dipartimento

Ultimo aggiornamento 27 aprile 2017.