Closed-Form Estimates of the New Keynesian Phillips Curve with Time-Varying Trend Inflation

49 Pages Posted: 18 Dec 2009

See all articles by Michelle L. Barnes

Michelle L. Barnes

Federal Reserve Bank of Boston

Fabia Gumbau-Brisa

Credit Suisse AG

Denny Lie

The University of Sydney - School of Economics

Giovanni Olivei

Federal Reserve Bank of Boston

Date Written: December 12, 2009

Abstract

We compare estimates of the New Keynesian Phillips Curve (NKPC) when the curve is specified in two different ways. In the standard difference equation (DE) form, current inflation is a function of past inflation, expected future inflation, and real marginal costs. The alternative closed form (CF) specification explicitly solves the DE form to express inflation as a function of past inflation and a present-discounted value of current and expected future marginal costs. The CF specification places model-consistent constraints on expected future inflation that are not imposed in the DE form. In a Monte Carlo exercise, we show that estimating the CF version of the NKPC gives estimates that are much more efficient than the estimates obtained from the DE specification. We then compare DE and CF estimates of the NKPC with time-varying trend inflation on actual data. The data and estimation methodology are the same as in Cogley and Sbordone (2008). We show that DE and CF estimates differ substantially and have very different implications for inflation dynamics. As in Cogley and Sbordone, it is possible to estimate DE specifications of the NKPC where lagged inflation plays no role once trend inflation is taken into account. The CF estimates of the NKPC, however, typically imply as large a role for lagged inflation as for expected future inflation. These estimates thus suggest that trend inflation is not in itself sufficient to explain the persistent dynamics of inflation.

JEL Classification: E12, E31, E52

Suggested Citation

Barnes, Michelle L. and Gumbau-Brisa, Fabia and Lie, Denny and Olivei, Giovanni, Closed-Form Estimates of the New Keynesian Phillips Curve with Time-Varying Trend Inflation (December 12, 2009). FRB of Boston Working Paper No. 09-15. Available at SSRN: https://ssrn.com/abstract=1523943 or http://dx.doi.org/10.2139/ssrn.1523943

Michelle L. Barnes (Contact Author)

Federal Reserve Bank of Boston ( email )

600 Atlantic Avenue
Boston, MA 02210
United States

Fabia Gumbau-Brisa

Credit Suisse AG ( email )

New York City
United States

Denny Lie

The University of Sydney - School of Economics ( email )

Rm 370 Merewether (H04)
Sydney, NSW 2006 2008
Australia

Giovanni Olivei

Federal Reserve Bank of Boston ( email )

600 Atlantic Avenue
Boston, MA 02210
United States

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