2-step Gradient Boosting approach to selectivity bias correction in tax audit: an application to the VAT gap in Italy

The revenue loss from tax avoidance can undermine the effectiveness and equity of the government policies. A standard measure of its magnitude is known as the tax gap, that is defined as the difference between the total taxes theoretically collectable and the total taxes actually collected in a given period. Estimation from a micro perspective is usually tackled in the context of bottom-up approaches, where data regularly collected through fiscal audits are analyzed in order to provide inference on the general population. However, the sampling scheme of fiscal audits performed by revenue agencies is not random but characterized by a selection bias toward risky taxpayers. The current standard adopted by the Italian Revenue Agency (IRA) for overcoming this issue in the Tax audit context is the Heckman model, based on linear models for modeling both the selection and the outcome mechanisms. Here we propose the adoption of the CART-based Gradient Boosting in place of standard linear models to account for the complex patterns often arising in the relationships between covariates and outcome. Selection bias is corrected by considering a re-weighting scheme based on propensity scores, attained through the sequential application of a classifier and a regressor. In short we refer to the method as 2-step Gradient Boosting. We argue how this scheme fits the sampling mechanism of the IRA fiscal audits, and it is applied to a sample of VAT declarations from Italian individual firms in the fiscal year 2011. Results show a marked dominance of the proposed method over the currently adopted Heckman model in terms of predictive performances.