Inflation and marginal cost: on the importance of their covariance

Abstract

Many researchers have found that estimating the New Keynesian Phillips Curve (NKPC) using the output gap to proxy for real marginal cost tends to produce a counter-intuitive coefficient sign in the model, whereas using the labour income share produces the expected coefficient sign. This article investigates the potential cause of this puzzle: What causes these differing signs for the coefficient for real marginal cost? We find that this coefficient sign crucially depends on the covariance between inflation and marginal cost. Moreover, this covariance in turn critically depends on the cyclicality of the marginal cost proxy that is used.

Notes

¹This can be done because in the standard sticky price framework without variable capital, such as in Rotemberg and Woodford (1997), there is an approximately proportionate relationship between marginal cost and output.

²This finding is robust across a wide range of possible instruments sets, measures of inflation and GDP detrending procedures, as can be seen in Gali and Gertler (1999), Gali et al. (2005) and Rudd and Whelan (2007).

³We use conventional GMM, although strictly speaking this can be problematic if weak instruments are found. Qualitatively, similar results for λ are found under either technique – see Mazumder (2010).

⁴The SPF data we use start in 1968:04; hence so does our NKPC estimation when using survey data on expected inflation.

⁵This exercise works in exactly the same way if we use survey expectations of inflation instead of actual future inflation, that is,