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Estimation of forward-looking relationships in closed form: an application to the New Keynesian Phillips curve

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  • Michelle L. Barnes
  • Fabia Gumbau-Brisa
  • Denny Lie
  • Giovanni P. Olivei

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 imposes 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.

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  • Michelle L. Barnes & Fabia Gumbau-Brisa & Denny Lie & Giovanni P. Olivei, 2011. "Estimation of forward-looking relationships in closed form: an application to the New Keynesian Phillips curve," Working Papers 11-3, Federal Reserve Bank of Boston.
  • Handle: RePEc:fip:fedbwp:11-3
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    Cited by:

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    2. Laurence M. Ball, 2013. "The Case for Four Percent Inflation," Central Bank Review, Research and Monetary Policy Department, Central Bank of the Republic of Turkey, vol. 13(2), pages 17-31.
    3. Sophocles Mavroeidis & Mikkel Plagborg-Møller & James H. Stock, 2014. "Empirical Evidence on Inflation Expectations in the New Keynesian Phillips Curve," Journal of Economic Literature, American Economic Association, vol. 52(1), pages 124-188, March.
    4. Laurence M. Ball, 2014. "The Case for a Long-Run Inflation Target of Four Percent," IMF Working Papers 2014/092, International Monetary Fund.
    5. Gumbau-Brisa, Fabià & Lie, Denny, 2015. "Comments on &amp;amp;quot;Trend Inflation, Indexation, and Inflation Persistence in the New Keynesian Phillips Curve&amp;amp;quot;," Working Papers 2015-13, University of Sydney, School of Economics.
    6. Kim, Insu & Yie, Myung-Soo, 2016. "Trend inflation, firms' backward-looking behavior, and inflation gap persistence," Economic Modelling, Elsevier, vol. 58(C), pages 116-125.

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    Phillips curve; Economic forecasting;

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