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The non-linear Calvo model at the zero bound: Some analytic solutions and numerical results


  • Sanjay Singh

    (Brown University)

  • Gauti Eggertsson

    (Brown University)


This paper shows closed form solutions for the non-linear Calvo model at the zero bond under the assumption that uncertainty is given by a two state Markov chain with an absorbing state. This allows us to explicitly compare the solution of the non-linear model to the better known log-linearized version. In line with the log-linear model, we confirm in the non-linear setting i) large drops in output as shocks become more persistent until bifurcation occurs, ii) large government spending multipliers that have to be above 1 and iii) the paradox of toil. These results are in contrast with some recent literature on non-linearities at the ZLB. Mostly this is because that literature assumes particular form of Rotemberg prices which leads to "implausible" large cost of price adjustment in a way we make precise. Overall the non-linear Calvo model behaves similarly as its linearized counterpart both qualitatively and quantitatively with some important caveats we document.

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  • Sanjay Singh & Gauti Eggertsson, 2015. "The non-linear Calvo model at the zero bound: Some analytic solutions and numerical results," 2015 Meeting Papers 1204, Society for Economic Dynamics.
  • Handle: RePEc:red:sed015:1204

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    References listed on IDEAS

    1. Matthew Denes & Gauti B. Eggertsson, 2009. "A Bayesian approach to estimating tax and spending multipliers," Staff Reports 403, Federal Reserve Bank of New York.
    2. Lawrence Christiano & Martin Eichenbaum & Sergio Rebelo, 2011. "When Is the Government Spending Multiplier Large?," Journal of Political Economy, University of Chicago Press, vol. 119(1), pages 78-121.
    3. Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
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    Cited by:

    1. Gauti Eggertsson & Bulat Gafarov & Saroj Bhatarai, 2014. "Time Consistency and the Duration of Government Debt: A Signalling Theory of Quantitative Easing," 2014 Meeting Papers 1292, Society for Economic Dynamics.
    2. Gauti B. Eggertsson & Kevin B. Proulx, 2016. "Bernanke’s No-Arbitrage Argument Revisited: Can Open Market Operations in Real Assets Eliminate the Liquidity Trap?," Central Banking, Analysis, and Economic Policies Book Series,in: Elías Albagli & Diego Saravia & Michael Woodford (ed.), Monetary Policy through Asset Markets: Lessons from Unconventional Measures and Implications for an Integrated World, edition 1, volume 24, chapter 3, pages 063-104 Central Bank of Chile.

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