Estimation of Forward-Looking Relationships in Closed Form: An Application to the New Keynesian Phillips Curve

73 Pages Posted: 21 Jun 2011

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: May 21, 2011

Abstract

We illustrate the importance of placing model-consistent restrictions on expectations in the estimation of forward-looking Euler equations. In two-stage limited-information settings where first-stage estimates are used to proxy for expectations, parameter estimates can differ substantially, depending on whether these restrictions are imposed or not. This is shown in an application to the New Keynesian Phillips Curve (NKPC), first in a Monte Carlo exercise, and then on actual data. The closed-form (CF) estimates require by construction that expectations of inflation be model-consistent at all points in time, while the difference-equation (DE) estimates impose no model discipline on expectations.

Between those two polar extremes there is a wide range of alternative DE specifications, based on the same dynamic relationship, that explicitly impose model restrictions on expectations for a finite number of periods. In our application, these last estimates quickly converge to the CF estimates, and illustrate that the DE estimates in Cogley and Sbordone (2008) are not robust to imposing modest model requirements on expectations. In particular, our estimates show that the NKPC is not purely forward-looking, and thus that time-varying trend inflation is insufficient to explain inflation persistence.

Keywords: closed form, model-consistent expectations, New Keynesian Phillips curve, forward-looking Euler equation, time-varying trend inflation

JEL Classification: E12, E31, E52

Suggested Citation

Barnes, Michelle L. and Gumbau-Brisa, Fabia and Lie, Denny and Olivei, Giovanni, Estimation of Forward-Looking Relationships in Closed Form: An Application to the New Keynesian Phillips Curve (May 21, 2011). Available at SSRN: https://ssrn.com/abstract=1866338 or http://dx.doi.org/10.2139/ssrn.1866338

Michelle L. Barnes

Federal Reserve Bank of Boston ( email )

600 Atlantic Avenue
Boston, MA 02210
United States

Fabia Gumbau-Brisa (Contact Author)

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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