The global slack hypothesis is central to the discussion of the trade-offs that monetary policy faces in an increasingly more integrated world. The workhorse New Open Economy Macro (NOEM) model of Martínez-García and Wynne (2010), which fleshes out this hypothesis, shows how expected future local inflation and global slack affect current local inflation. In this paper, I propose the use of the orthogonalization method of Aoki (1981) and Fukuda (1993) on the workhorse NOEM model to further decompose local inflation into a global component and an inflation differential component. I find that the log-linearized rational expectations model of Martínez-García and Wynne (2010) can be solved with two separate subsystems to describe each of these two components of inflation. I estimate the full NOEM model with Bayesian techniques using data for the U.S. and an aggregate of its 38 largest trading partners from 1980Q1 until 2011Q4. The Bayesian estimation recognizes the parameter uncertainty surrounding the model and calls on the data (inflation and output) to discipline the parameterization. My findings show that the strength of the international spillovers through trade—even in the absence of common shocks—is reflected in the response of global inflation and is incorporated into local inflation dynamics. Furthermore, I find that key features of the economy can have different impacts on global and local inflation—in particular, I show that the parameters that determine the import share and the price-elasticity of trade matter in explaining the inflation differential component but not the global component of inflation.