This paper estimates the size and macroeconomic effects of base erosion and profit shifting (BEPS) using a computable general equilibrium model designed for corporate taxation and multinationals. Our central estimate of the impact of BEPS on corporate tax losses for the EU amounts to €36 billion annually or 7.7% of total corporate tax revenues. The USA and Japan also appear to loose tax revenues respectively of €101 and €24 billion per year or 10.7% of corporate tax revenues in both cases. These estimates are consistent with gaps in bilateral multinationals´ activities reported by creditor and debtor countries using official statistics for the EU. Our results suggest that by increasing the cost of capital, eliminating profit shifting would slightly reduce investment and GDP. It would however raise corporate tax revenues thanks to enhanced domestic production. This in turn could reduce other taxes and increase welfare.