Quick estimation of tourist nights spent in Italy

ISTAT currently disseminates monthly provisional data on arrivals and nights spent in the Italian tourist establishments after 90 days from the end of the reference month, according to the EU Directive on Tourism Statistics. The aim of the paper is to compare some quick estimation methods able to improve timeliness and quality of provisional estimates. According to a super-population model, on the basis of available quick responses of provinces which tourist data are available within 45 days, some predictors are proposed in addition to that actually used. An empirical application has been carried out, using true monthly data on nights spent in Italy in 2002 and comparing predictors derived from balanced sampling theory and regression methods.     

A spatial analysis of health and pharmaceutical firm survival

The presence of knowledge spillovers and shared human capital is at the heart of the Marhall–Arrow–Romer externalities hypothesis. Most of the earlier empirical contributions on knowledge externalities; however, considered data aggregated at a regional level so that conclusions are based on the arbitrary definition of jurisdictional spatial units: this is the essence of the so-called modifiable areal unit problem. A second limitation of these studies is constituted by the fact that, somewhat surprisingly, while concentrating on the effects of agglomeration on firm creation and growth, the literature has, conversely, largely ignored its effects on firm survival. The present paper aims at contributing to the existing literature by answering to some of the open methodological questions reconciling the literature of Cox proportional hazards model with that on point pattern and thus capturing the true nature of spatial information. We also present some empirical results based on Italian firm demography data collected and managed by the Italian National Institute of Statistics (ISTAT).     

Alleviating linear ecological bias and optimal design with subsample data

Summary.  We illustrate that combining ecological data with subsample data in situations in which a linear model is appropriate provides two main benefits. First, by including the individual level subsample data, the biases that are associated with linear ecological inference can be eliminated. Second, available ecological data can be used to design optimal subsampling schemes that maximize information about parameters. We present an application of this methodology to the classic problem of estimating the effect of a college degree on wages, showing that small, optimally chosen subsamples can be combined with ecological data to generate precise estimates relative to a simple random subsample.     

Statistical regularity of firm size distribution: the Pareto IV and truncated Yule for Italian SCI manufacturing

In this paper we model the firm size distribution (FSD) of Italian manufacturing firms of SCI, the GDP survey of ISTAT, by a continuous and a discrete distribution: the Pareto IV distribution on total assets and the Yule distribution on Number of Employees. The Pareto IV distribution is characterized by four parameters and shows a better fit than both the Lognormal and Pareto I, which are the distributions more frequently applied to model firm size. The Pareto IV is inconsistent with Gibrat’s Law according to which the different segments of an Industry are characterized by proportionate growth and the distribution of size is Lognormal. A truncation of the Yule distribution has been necessary because the dataset is characterized by firms with at least 20 employees. The truncated Yule distribution shows a good fit for medium–large firms (firms with more than 50 employees). The partition of the dataset in innovative and non-innovative firms – both of which are well described by the Pareto IV – reveals a beneficial effect of scale on innovation. Finally, the good fit of both distributions holds not only for the composite industry, but for the single sectors too. The present work is part of a more general research project: “Industry evolution: innovation, profitability and firm’s growth”, conducted within the Department of Economic and Social Sciences of the Università Cattolica del Sacro Cuore (UCSC), Piacenza, coordinated by Professor Maurizio Baussola in cooperation with ISTAT (Italian Statistical Office, regional office for Lombardy). Part of this research was done when Lisa Crosato was a visiting research student at the LSE Statistics Department, during her Ph.D program in “Quantitative Models for Policy Analysis” at the UCSC of Piacenza.     

The new strategy for the concise presentation of sampling errors in the Italian Structural Business Statistics Survey

Reporting sampling errors of survey estimates is a problem that is commonly addressed when compiling a survey report. Because of the vast number of study variables or population characteristics and of interest domains in a survey, it is almost impossible to calculate and to publish the standard errors for each statistic. A way of overcoming such problem would be to estimate indirectly the sampling errors by using generalized variance functions, which define a statistical relationship between the sampling errors and the corresponding estimates. One of the problems with this approach is that the model specification has to be consistent with a roughly constant design effect. If the design effects vary greatly across estimates, as in the case of the Business Surveys, the prediction model is not correctly specified and the least-square estimation is biased. In this paper, we show an extension of the generalized variance functions, which address the above problems, which could be used in contexts similar to those encountered in Business Surveys. The proposed method has been applied to the Italian Structural Business Statistics Survey case.     

The Italian Labour Force Survey to estimate fertility

The own-children method (OCM) applied to the Italian Labour Force Survey (ILFS) is an alternative way to give information on fertility for the years before the survey. By deriving children information and the population at risk on the basis of parents’ characteristics, a large-scale dataset for fertility analysis in Italy becomes available, also to reconstruct event histories. The quality assessment provided by comparing the total fertility rate (TFR) calculated on ILFS with the official regional and national TFRs by ISTAT gives us usable outcomes.     

De gustibus non est disputandum? A new approach to the estimation of equivalence scales

We argue that when the household composition changes, consumption patterns vary not only because of the cost effect that equivalence scales try to measure, but also because of a “taste” or “style” effect. This effect can be identified and measured, under a few assumptions, with the use of a new methodology, calledDM ² (Decomposition Model of the effects of Demographic Metamorphosis), that can be viewed as a generalisation of Ray's (1983) price-scaling approach to the construction of equivalent scales. An empirical application to data drawn from the Istat 1995 Italian Household Budget Survey suggests that the proposed method improves our understanding of households' consumption patterns and the reliability of the equivalence scales that we derive. We gratefully acknowledge helpful comments from Giorgio Calzolari, Franco Polverini, Ugo Trivellato and an anonymous referee, but retain full responsibility for all errors, and for the processing of Istat (Italian Institute of Statistics) microdata on Household Budgets. Financial support for this research was provided by the italian MURST (Research project on “Equivalence scales” directed by Prof. Guido Ferrari, University of Firenze, Ref. No. 9913105354; and Research project on “Low fertility in Italy: between economic constraints and value changes”, directed by Prof. Massimo Livi Bacci, University of Firenze, Ref. No. MM13107238). Preliminary findings on this research topic have been presented in a few seminars and conferences: cf., e.g., De Santis and Maltagliati (2000 and 2001).     

Non-parametric tests for several sample location problem based on subsample extrema

In this paper non-parametric tests for homogeneity of several populations against locationtype alternatives are proposed. For this all possible subsamples of fixed size are drawn from each sample and their maxima and minima are computed One class of tests is obtained using these subsample minima whereas other class of tests involves use of sub sample maxima. Tests belonging t o these two classes have been compared with many of the presently available tests in terms of their Pitman asymptotic relative efficiency . Some of the members of these proposed classes of tests prove to robust in terms of efficiency.     

A note on sequential ML estimates and their asymptotic covariances

A marginal and sequential maximum likelihood estimation method is described which can be used instead of full information maximum likelihood estimation if the latter method is unfeasible. It is shown that the sequential procedure yields strongly consistent and asymptotically normal estimates under relatively general regularity conditions. It is shown that the covariance matrix of the sequential ML estimator does not coincide with the inverse of the Fisher information matrix. Hence, the corrected covariance matrix is derived. The application of the sequential procedure to the multivariate probit model with dichotomous, ordered categorical, single-sided censored and double-sided censored endogenous variables is included. This research was partially supported by a dissertation grant of theStudienstiftung des Deutschen Volkes. Comments and suggestions on earlier drafts by Gerhard Arminger, Giorgio Calzolari, Bernd Kortzen and an anonymous referee are gratefully acknowledged.     

Estimating numbers of infectious units from serial dilution assays

Summary.  The paper concerns the design and analysis of serial dilution assays to estimate the infectivity of a sample of tissue when it is assumed that the sample contains a finite number of indivisible infectious units such that a subsample will be infectious if it contains one or more of these units. The aim of the study is to estimate the number of infectious units in the original sample. The standard approach to the analysis of data from such a study is based on the assumption of independence of aliquots both at the same dilution level and at different dilution levels, so that the numbers of infectious units in the aliquots follow independent Poisson distributions. An alternative approach is based on calculation of the expected value of the total number of samples tested that are not infectious. We derive the likelihood for the data on the basis of the discrete number of infectious units, enabling calculation of the maximum likelihood estimate and likelihood-based confidence intervals. We use the exact probabilities that are obtained to compare the maximum likelihood estimate with those given by the other methods in terms of bias and standard error and to compare the coverage of the confidence intervals. We show that the methods have very similar properties and conclude that for practical use the method that is based on the Poisson assumption is to be recommended, since it can be implemented by using standard statistical software. Finally we consider the design of serial dilution assays, concluding that it is important that neither the dilution factor nor the number of samples that remain untested should be too large.     

Efficient estimation of regression parameters from multistage studies with validation of outcome and covariates

Often the variables in a regression model are difficult or expensive to obtain so auxiliary variables are collected in a preliminary step of a study and the model variables are measured at later stages on only a subsample of the study participants called the validation sample. We consider a study in which at the first stage some variables, throughout called auxiliaries, are collected; at the second stage the true outcome is measured on a subsample of the first-stage sample, and at the third stage the true covariates are collected on a subset of the second-stage sample. In order to increase efficiency, the probabilities of selection into the second and third-stage samples are allowed to depend on the data observed at the previous stages. In this paper we describe a class of inverse-probability-of-selection-weighted semiparametric estimators for the parameters of the model for the conditional mean of the outcomes given the covariates. We assume that a subject's probability of being sampled at subsequent stages is bounded away from zero and depends only on the subject's data collected at the previous sampling stages. We show that the asymptotic variance of the optimal estimator in our class is equal to the semiparametric variance bound for the model. Since the optimal estimator depends on unknown population parameters it is not available for data analysis. We therefore propose an adaptive estimation procedure for locally efficient inferences. A simulation study is carried out to study the finite sample properties of the proposed estimators.     

Unemployment duration and the length of entitlement periods for unemployment benefits: do the IAB employment subsample and the German Socio-Economic Panel yield the same results?*

Summary: We compare information on the length of unemployment spells contained in the IAB employment subsample (IABS) and in the German Socio-Economic Panel (GSOEP). Due to the lack of information on registered unemployment in the IABS, we use two proxies of unemployment in the IABS as introduced by Fitzenberger/Wilke (2004). The first proxy comprises all periods of nonemployment after an employment spell which contain at least one period with unemployment compensation transfers. The second proxy includes all episodes between two employment spells during which an individual continuously received unemployment benefits. Estimation of standard duration models indicates that conclusions drawn from the IABS and the GSOEP differ in many cases. While the GSOEP suggests that the hazard rate has a maximum at about 12 months of unemployment, the IABS results suggest that this maximum is at about 20 months. Contrary to our GSOEP results and contrary to many results based on the GSOEP found in the literature, we find a statistically significant association between longer maximum entitlement periods of unemployment benefits (‘Arbeitslosengeld’) and longer unemployment durations for men in the IABS. The results for women do not show such clear patterns. The large sample size of the IABS also allows to trace out statistically significant effects of characteristics such as regional and industry indicators, which is generally not possible in the relatively small GSOEP. * Acknowledgements: We would like to thank the editors of this special issue, Joachim M?ller and Bernd Fitzenberger, two anonymous referees, the participants of the ‘Statistische Woche 2004’ in Frankfurt (in particular Reinhard Hujer, Olaf Hübler and Gerd Ronning), seminar participants at the ZEW Mannheim (especially Fran?ois Laisney and Alexander Spermann) and Jennifer Hunt for their many helpful comments and suggestions. All remaining errors are our own. Financial support of the Deutsche Forschungsgemeinschaft (DFG) through the research project ‘Microeconometric modelling of unemployment durations under consideration of the macroeconomic situation’ is gratefully acknowledged. The data used in this paper were made available by the Institute for Employment Research (IAB) at the Federal Labour Office of Germany, Nürnberg, and the German Socio Economic Panel Study (GSOEP) at the German Institute for Economic Research (DIW), Berlin.     

On the quality of reinterview data with application to the Current Population Survey

"The [U.S.] Current Population Survey (CPS) reinterview sample consists of two subsamples: (a) a sample of CPS households is reinterviewed and the discrepancies between the reinterview responses and the original interview responses are reconciled for the purpose of obtaining more accurate responses..., and (b) a sample of CPS households, nonoverlapping with sample (a), is reinterviewed 'independently' of the original interview for the purpose of estimating simple response variance (SRV). In this article a model and estimation procedure are proposed for obtaining estimates of SRV from subsample (a) as well as the customary estimates of SRV from subsample (b).... Data from the CPS reinterview program for both subsamples (a) and (b) are analyzed both (1) to illustrate the methodology and (2) to check the validity of the CPS reinterview data. Our results indicate that data from subsample (a) are not consistent with the data from subsample (b) and provide convincing evidence that errors in subsample (a) are the source of the inconsistency."     

Modeling multiple‐response categorical data from complex surveys

Although “choose all that apply” questions are common in modern surveys, methods for analyzing associations among responses to such questions have only recently been developed. These methods are generally valid only for simple random sampling, but these types of questions often appear in surveys conducted under more complex sampling plans. The purpose of this article is to provide statistical analysis methods that can be applied to “choose all that apply” questions in complex survey sampling situations. Loglinear models are developed to incorporate the multiple responses inherent in these types of questions. Statistics to compare models and to measure association are proposed and their asymptotic distributions are derived. Monte Carlo simulations show that tests based on adjusted Pearson statistics generally hold their correct size when comparing models. These simulations also show that confidence intervals for odds ratios estimated from loglinear models have good coverage properties, while being shorter than those constructed using empirical estimates. Furthermore, the methods are shown to be applicable to more general problems of modeling associations between elements of two or more binary vectors. The proposed analysis methods are applied to data from the National Health and Nutrition Examination Survey. The Canadian Journal of Statistics © 2009 Statistical Society of Canada     

Efficiency of split questionnaire surveys

We consider a general design that allows information for different patterns, or sets, of data items to be collected from different sample units, which we call a Split Questionnaire Design (SQD). While SQDs have been historically used to accommodate constraints on respondent burden, this paper shows they can also be an efficient design option. The efficiency of a design can be measured by the cost required to meet constraints on the accuracy of estimates. Moreover, this paper shows how an SQD provides considerable flexibility when exploring the balance between the design's efficiency and the burden it places on respondents. The targets of interest to the design are analytic parameters, such as regression coefficients. Empirical results show that SQDs are worthwhile considering.     

Estimating crop yield via Gaussian quadrature

The present study proposes a method to estimate the yield of a crop. The proposed Gaussian quadrature (GQ) method makes it possible to estimate the crop yield from a smaller subsample. Identification of plots and corresponding weights to be assigned to the yield of plots comprising a subsample is done with the help of information about the full sample on certain auxiliary variables relating to biometrical characteristics of the plant. Computational experience reveals that the proposed method leads to about 78% reduction in sample size with absolute percentage error of 2.7%. Performance of the proposed method has been compared with that of random sampling on the basis of the values of average absolute percentage error and standard deviation of yield estimates obtained from 40 samples of comparable size. Interestingly, average absolute percentage error as well as standard deviation is considerably smaller for the GQ estimates than for the random sample estimates. The proposed method is quite general and can be applied for other crops as well-provided information on auxiliary variables relating to yield contributing biometrical characteristics is available.     

Preliminary Data Errors and Their Impact on the Forecast Error of Simultaneous-Equations Models

Econometric models, especially when designed for forecasting purposes, tend to use updated economic series, the last figures(s) of which embed first-published or preliminary data errors. This article identifies and assesses the contribution of errors in preliminary data to the forecast error and to the forecast error variance of linear dynamic simultaneous equation models. The effect of preliminary data errors is shown to be pervasive, although not necessarily weighty. The suggested decomposition of the forecast error is applied to a small macroeconometric model of the Italian economy.     

ON OPTIMIZING MULTI-LEVEL DESIGNS: POWER UNDER BUDGET CONSTRAINTS

This paper derives a procedure for efficiently allocating the number of units in multi‐level designs given prespecified power levels. The derivation of the procedure is based on a constrained optimization problem that maximizes a general form of a ratio of expected mean squares subject to a budget constraint. The procedure makes use of variance component estimates to optimize designs during the budget formulating stages. The method provides more general closed form solutions than other currently available formulae. As such, the proposed procedure allows for the determination of the optimal numbers of units for studies that involve more complex designs. A method is also described for optimizing designs when variance component estimates are not available. Case studies are provided to demonstrate the method.     

On bootstrap confidence limits for possibly skew distributed statistics

Statistics for which confidence limits or tests are calculated by bootstrap techniques frequently have asymmetric distributions. Approaches based only on boot-strapped variance are inadequatein such cases. In a Mte. Carlo study with a markedly skew X²-distributed statistic an approach by Edgeworth expansions using bootstrapped estimates of variance and skewness of the statistic's distribution performed well with respect to size and power and is proposed for variaus applications.     

Split Questionnaire Designs: collecting only the data that you need through MCAR and MAR designs

We call a sample design that allows for different patterns, or sets, of data items to be collected from different sample units a Split Questionnaire Design (SQD). SQDs can be thought of as incorporating missing data into survey design. This paper examines the situation where data that are not collected by an SQD can be treated as Missing Completely At Random or Missing At Random, targets are regression coefficients in a generalised linear model fitted to binary variables, and targets are estimated using Maximum Likelihood. A key finding is that it can be easy to measure the relative contribution of a respondent to the accuracy of estimated model parameters before collecting all the respondent's model covariates. We show empirically and theoretically that we could achieve a significant reduction in respondent burden with a negligible impact on the accuracy of estimates by not collecting model covariates from respondents who we identify as contributing little to the accuracy of estimates. We discuss the general implications for SQDs.