This paper studies the interdependence between fiscal and monetary policy in a DSGE model with sticky prices and non-zero trend inflation. We characterize the fiscal and monetary policies by a rule whereby a given fraction k of the government debt must be backed by the discounted value of current and future primary surpluses. The remaining fraction of debt is backed by seigniorage revenues. When k = 1, there is no fiscal dominance, since the fiscal authority backs all debt and accommodates (independent) monetary policy, by adjusting current or future primary surpluses to satisfy the government's intertemporal budget constraint. If k = 0, all debt is backed by the monetary authority and there is complete fiscal dominance. A continuum of possibilities lies between these two polar cases. We numerically show that: 1) the degree of fiscal dominance, as measured by (1 k), is positively related to trend inflation, and 2) when prices are sticky, k has significant effects on the business cycle dynamics. The model is estimated using Bayesian techniques. Estimates of k imply a high degree of fiscal dominance in both Mexico and South Korea, but almost no fiscal dominance in Canada and the U.S. The country-specific estimates of the structural parameters are used in a second-order approximation of the equilibrium around the deterministic steady-state to evaluate the welfare costs of fiscal dominance. Results suggest significant welfare losses for countries with high degrees of fiscal dominance.