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

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

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.

Suggested Citation

  • Barnes, Michelle L. & Gumbau-Brisa, Fabià & Lie, Denny & Olivei, Giovanni P., 2011. "Estimation of Forward-Looking Relationships in Closed Form: An Application to the New Keynesian Phillips Curve," Working Papers 2011-05, University of Sydney, School of Economics.
  • Handle: RePEc:syd:wpaper:2123/7708
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    Cited by:

    1. Lie, Denny & Yadav, Anirudh S., 2015. "Time-Varying Trend Inflation and the New Keynesian Phillips Curve in Australia," Working Papers 2015-14, University of Sydney, School of Economics.
    2. 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.
    3. 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.
    4. Laurence M. Ball, 2014. "The Case for a Long-Run Inflation Target of Four Percent," IMF Working Papers 14/92, International Monetary Fund.
    5. Gumbau-Brisa, Fabià & Lie, Denny, 2015. "Comments on "Trend Inflation, Indexation, and Inflation Persistence in the New Keynesian Phillips Curve"," Working Papers 2015-13, University of Sydney, School of Economics.
    6. repec:bla:ecorec:v:93:y:2017:i:300:p:42-66 is not listed on IDEAS
    7. repec:jhu:papers:607 is not listed on IDEAS

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    Keywords

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

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