Before revision:  However, economists lack a robust method for estimating the tax gap through a bottom-up approach  based on fiscal audits. This is difficult because the declared tax base is available on the whole population but the income reported to the tax authorities is generally available only on a small, non-random sample of audited units. This induces a selection bias which invalidates standard statistical methods. Here, we use machine learning based on a 2-steps Gradient Boosting model,  to correct for the selection bias without requiring any strong assumption on the distribution.
After revision:  However, economists lack a robust method for estimating the tax gap through a bottom-up approach based on a 2-steps Gradient Boosting model, to correct for the selection bias without requiring any strong assumption on the distribution.