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We develop a semi-structural new-Keynesian open-economy model, with separate food and non-food inflation dynamics, for forecasting and monetary policy analysis in low-income countries and apply it to Kenya. We use the model to run several policy-relevant exercises. First, we filter international and Kenyan data (on output, inflation and its components, exchange rates and interest rates) to recover a model-based decomposition of most variables into trends (or potential values) and temporary movements (or gaps)—including for the international and domestic relative price of food. Second, we use the filtration exercise to recover the sequence of domestic and foreign macroeconomic shocks that a...