An Exact Analytical Grossing-Up Algorithm for Tax-Benefit Models

In this paper, we propose a grossing-up algorithm that allows for gross income calculation based on tax rules and observed variables in the sample. The algorithm is applicable in tax-benefit microsimulation models, which are mostly used by taxation policy makers to support government legislative processes. Typically, tax-benefit microsimulation models are based on datasets, where only the net income is known, though the data about gross income is needed to successfully simulate the impact of taxation policies on the economy. The algorithm that we propose allows for an exact reproduction of a missing variable by applying a set of taxation rules that are known to refer to the variable in question and to other variables in the dataset during the data generation process. Researchers and policy makers can adapt the proposed algorithm with respect to the rules and variables in their legislative environment, which allows for complete and exact restoration of the missing variable. The algorithm incorporates an estimation of partial analytical solutions and a trial-and-error approach to find the initial true value. Its validity was proven by a set of tax rule combinations at different levels of income that are used in contemporary tax systems. The algorithm is generally applicable, with some modifications, for data imputation on datasets derived from various tax systems around the world.