The Phillips curve seems to have flattened over time. In this article, we use a simple New Keynesian model to analyze potential pitfalls in the estimation of the slope of the structural Phillips curve. Changes in the conduct of monetary policy or in the relative importance of supply and demand shocks may bias simple estimations of the slope of the Phillips curve. Recent proposals have favored estimations using regional or city data in an effort to overcome these issues. We use a simple model of a monetary union with a continuum of economies and find that some of the drawbacks of the aggregate model are still present in a cross-section of many regions in a monetary union. The relative importance of the demand and supply shocks largely determines the empirical relation between unemployment and inflation in both the aggregate and the cross-section of regions. Our analysis shows potential pitfalls in estimating the slope of the Phillips curve, even if using regional data.