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The relationship between inflation and the output gap can be modeled simply and effectively by including an unobserved random walk component in the model. The dynamic properties match the stylized facts and the random walk component satisfies the properties normally required for core inflation. The model may be generalized to as to include a term for the expectation of next period's output, but it is shown that this is difficult to distinguish from the original specification. The model is fitted as a single equation and as part of a bivariate model that includes an equation for GDP. Fitting the bivariate model highlights some new aspects of unobserved components modeling.
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