In recent years a number of European countries have shifted their tax structure more strongly towards indirect taxes, motivated, inter alia, by the intention to foster competitiveness. Against this background, this paper develops a tractable two-country model of a monetary union, characterised by national fiscal and supranational monetary policy, with price-setting firms and endogenously determined terms of trade. The paper discusses a number of monetary and fiscal policy questions which emerge if one of the countries shifts its tax structure more strongly towards indirect taxes. Qualitatively, it is shown that the long-run effects of such a unilateral policy shift on output and consumption within and between the two countries depend sensitively on whether indirect tax revenues are used to lower direct taxes or to finance additional government expenditures. Moreover, short-run dynamics are shown to depend significantly on the speed at which fiscal adjustments take place, on the choice of the inflation index stabilised by the central bank, and on whether the tax shift is anticipated or not. Quantitatively, the calibrated model version indicates that only if the additional indirect tax revenues are used to finance a cut in direct taxes there is some, though limited scope for non-negligible spillovers between countries.