Dottorato in SCUOLA DI SCIENZE STATISTICHE

Titolo della tesi: Bias correction of survey-data on household wealth components

Recent initiatives integrate household surveys with supervisory and national accounts aggregates to produce timely, reliable distributional statistics on household income and wealth. This thesis develops a framework that aligns Italian survey microdata with supervisory targets for deposits, bonds, listed shares, and investment fund shares, with the objective of delivering Distributional Wealth Accounts that are reconciled at both the aggregate and distributional levels. Three building blocks precede the main calibration. First, we develop methods to estimate instrument-specific target distributions from aggregates, motivate Pareto-lognormal splice margins over simpler lognormal forms, provide parameter-recovery procedures, and introduce a tail test to discriminate between the two. Second, we reconcile Banking Supervisory Reports (BSR) with the Household Finance and Consumption Survey (HFCS) by mapping deposit accounts to households and disentangling securities accounts reported as range sums, thereby placing administrative targets on a household footing. Third, we formalise a benchmark univariate calibration - already used operationally for deposits - that iteratively matches class totals with regularisation to limit class changes; we extend this benchmark to all four instruments as a reference. Building on these elements, we introduce a distribution-aware univariate calibration with a composite L2 loss that balances a Cramér-von Mises shape term on the empirical CDF and a relative cumulative-amount term, while keeping survey weights fixed. The method attains the benchmark’s aggregate alignment and produces smoother, more credible within-class adjustments, substantially reducing boundary piling. We then extend the composite-loss calibration to the multivariate case to account explicitly for cross-instrument dependence. The multivariate layer maps adjusted values through parametric probability-integral transforms to Gaussian scores and aligns regime-specific correlations across instruments, while preserving the marginal fit; the composite loss retains the Cramér-von Mises and relative-amount terms and adds a dependence penalty on the Gaussian-score scale. Applications show that the univariate implementation closes aggregate gaps to supervisory totals and reduces distributional divergence from target margins, and that the multivariate calibration maintains those gains while improving cross-instrument coherence and correcting the top tail more accurately. On the marginals and in terms of coverage, the multivariate procedure performs on a par with the univariate distribution-aware calibration, while concentration indicators decrease as tail alignment improves. End-to-end indicators remain stable after proportional allocation, indicating that distributional improvements survive the full DWA pipeline. The framework is modular and auditable, conditional on HFCS-BSR harmonisation and splice-based margins, and it provides a production-ready, distribution-aware alternative to current practice without altering survey weights.