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We develop a general equilibrium endogenous growth model of a monetary union between two countries that differ in economic dimension and level of development. By solving transitional dynamics towards the steady state, we examine the impact of fiscal shocks that may lead to excessive deficits. Results suggest that the individual and the whole impact of such deficits depend on which country they occur. In such context, we argue that the small and less developed country should be allowed to temporarily run an excessive deficit, in order to improve economic convergence within the union.