Modeling measurement error via nonparametric Bayesian belief nets

Measurement error is the difference between the value provided by the respondent and the true (but unknown) value. It is sometimes defined as observation error, since it is related to the observation of the variable at the data collection stage. The problem of measurement error in financial assets is studied. The measurement error is modeled by means of non parametric Bayesian belief networks, that are graphical models expressing the dependence structure through bivariate copulas associated to the edges of the graph without introducing any distributional assumption. A new error correction procedure based on non parametric Bayesian belief networks is proposed. Measurement error modeling and microdata correction are illustrated by means of an application to the Banca d’Italia Survey on Household Income and Wealth 2008. The measurement model and its parameters have been estimated via a validation sample. The sensitivity of the conditional distribution of the true value given the observed one to different evidence configurations is analysed.