Monetary Policy, Incomplete Information, and the Zero Lower Bound


In the context of a stylized New Keynesian model, we explore the interaction between imperfect knowledge about the state of the economy and the zero lower bound. We show that optimal policy under discretion near the zero lower bound responds to signals about an increase in the equilibrium real interest rate by less than it would when far from the zero lower bound. In addition, we show that Taylor-type rules that either include a time-varying intercept that moves with perceived changes in the equilibrium real rate or respond aggressively to deviations of inflation and output from their target levels perform similarly to optimal discretionary policy. Our analysis of first-difference rules highlights that rules with interest rate smoothing terms carry forward current and past misperceptions about the state of the economy and can lead to suboptimal performance.

This is a preview of subscription content, log in to check access.

Figure 1
Figure 2
Figure 3
Figure 4
Figure 5
Figure 6
Figure 7
Figure 8
Figure 9
Figure 10


  1. 1.

    In the context of the New Keynesian model that we use, the equilibrium real rate corresponds to the rate of interest associated with the efficient economy that is undistorted by nominal or real rigidities.

  2. 2.

    Ben Bernanke’s Blog, “Why are interest rates so low?” March 30, 2015,

  3. 3.

    See, for example, Laubach and Williams (2015) and Pescatori and Turunen (2015).

  4. 4.

    From a practical viewpoint, the forward guidance put in place by the Federal Reserve was not necessarily designed to approximate this sort of optimal commitment strategy. During the course of the March 2016 post-FOMC press conference, Chair Yellen indicated that “I want to make clear that our inflation objective is 2 percent, and we are projecting a move back to 2 percent. And we are not trying to engineer an overshoot of inflation, not to compensate for past undershoots, so 2 percent is our objective. But it is a symmetric objective, and we certainly don’t seek to overshoot our objective.”

  5. 5.

    The relationship of these shocks with the specification of preferences and technology is described in “Appendix”. Both shocks follow first-order autoregressive processes.

  6. 6.

    As shown in “Appendix,” the nonstochastic efficient level of output is constant, that is \(y_{t}^{e}=0\).

  7. 7.

    Adam and Billi (2007) and Nakov (2008) also offer discussions of the effect of the effective zero lower bound on optimal monetary policy under discretion.

  8. 8.

    See Coibion, Gorodnichenko, and Wieland (2012) and the references therein, for a discussion of how the optimal steady-state inflation is affected by the presence of the zero lower bound.

  9. 9.

    For the simulations, the innovations (including the noisy ones) for the efficient real rate and marginal cost shocks are simulated according to their exogenous stochastic distributions, while initial values for the marginal cost shocks are set to zero.

  10. 10.

    When we increase the volatility of the underlying shocks, we keep the same signal-to-noise ratio as in the previous exercises.

  11. 11.

    All of the numbers in Table 1 are expressed in percent.

  12. 12.

    The welfare loss is relatively flat for relatively high values of these coefficients.

  13. 13.

    These results are similar to those reported in Boehm and House (2014), who study optimal policy rules in a standard NK model with mis-measurement of inflation and the output gap but do not impose the zero lower bound constraint. Such large optimal responses in both our setup and theirs may reflect that the uncertainty about economic relationships is larger in reality than the information frictions considered here as well as in their work.

  14. 14.

    If the central bank objective function contained the variability of the interest rate, as in Woodford (2003b), interest rate smoothing in Taylor rules may have an additional beneficial role.


  1. Adam, K. and R. M. Billi, 2007, “Discretionary Monetary Policy and the Zero Lower Bound on Nominal Interest Rates,” Journal of Monetary Economics, Vol. 54, No. 3, pp. 728–752.

    Article  Google Scholar 

  2. Aoki, K., 2003, “On the Optimal Monetary Policy Response to Noisy Indicators,” Journal of Monetary Economics, Vol. 50, No. 3, pp. 501–523.

    Article  Google Scholar 

  3. Blanchard, O. and J. Gal, 2007, “Real Wage Rigidities and the New Keynesian Model,” Journal of Money, Credit and Banking, Vol. 39, No. s1, pp. 35–65.

  4. Boehm, C. E. and C. L. House, 2014, “Optimal Taylor Rules in New Keynesian Models,” Technical Report.

  5. Christiano, L. J. and J. D. M. Fisher, 2000, “Algorithms for Solving Dynamic Models with Occasionally Binding Constraints,” Journal of Economic Dynamics and Control, Vol. 24, No. 8, pp. 1179–1232.

    Article  Google Scholar 

  6. Clarida, R., J. Galí, and M. Gertler, 1999, “The Science of Monetary Policy: Evidence and Some Theorj,” Journal of Economic Literature, Vol. 37, pp. 1661–1707.

    Article  Google Scholar 

  7. Coenen, G. and V. Wieland, 2003, “The Zero-Interest-Rate Bound and the Role of the Exchange Rate for Monetary Policy in Japan,” Journal of Monetary Economics, Vol. 50, No. 5, pp. 1071–1101.

    Article  Google Scholar 

  8. Coibion, O., Y. Gorodnichenko, and J. Wieland, 2012, “The Optimal Inflation Rate in New Keynesian Models: Should Central Banks Raise their Inflation Targets in Light of the Zero Lower Bound?” The Review of Economic Studies, Vol. 74, No. 4, pp. 1371–1406.

  9. Eggertsson, G. B. and M. Woodford, 2003, “Zero Bound on Interest Rates and Optimal Monetary Policy,” Brookings Papers on Economic Activity, Vol. 2003, No. 1, pp. 139–233.

    Article  Google Scholar 

  10. Evans, C., J. Fisher, S. Krane, and F. Gourio, 2013, “Risk Management for Monetary Policy Near the Zero Lower Bound,” Brookings Papers on Economic Activity, Vol. 46, No. 1, pp. 141–219.

  11. Galí, J., 2008, “Monetary Policy, Inflation and the Business Cycle: An Introduction to the New Keynesian Framework” (Princeton University Press, Princeton).

  12. Gust, C. J., D. López-Salido, and M. E. Smith, 2012, “The Empirical Implications of the Interest-Rate Lower Bound,” Finance and Economics Discussion Series Working Paper, No. 83.

  13. Hamilton, J. D., E. S. Harris, J. Hatzius, and K. D. West, 2015, “The Equilibrium Real Funds Rate: Past, Present and Future,” National Bureau of Economic Research Working Paper, No. 21476.

  14. Johannsen, B. K. and E. Mertens, 2016, “A Time Series Model of Interest Rates With the Effective Lower Bound,” Finance and Economics Discussion Series Working Paper, No. 33.  

  15. Kiley, M. T., 2015, "What Can the Data Tell Us About the Equilibrium Real Interest Rate?" Finance and Economics Discussion Series Working Paper, No. 77.

  16. Laubach, T. and J. C. Williams, 2015, “Measuring the Natural Rate of Interest Redux,” Hutchins Center on Fiscal and Monetary Policy at Brookings Working Paper.

  17. Levin, A. T., J. D. López-Salido, E. Nelson, T. Yun, 2010, “Limitations on the Effectiveness of Forward Guidance at the Zero Lower Bound,” International Journal of Central Banking, Vol. 6, No. 1, pp. 143–189.

  18. Nakov, A., 2008, “Optimal and Simple Monetary Policy Rules with Zero Floor on the Nominal Interest Rate,” International Journal of Central Banking, Vol. 4, No. 2, pp. 73–127.

    Google Scholar 

  19. Orphanides, A. and J. C. Williams, 2012, “Robust Monetary Policy Rules with Unknown Natural Rates,” Brookings Papers on Economic Activity, No. 2, pp. 63–145.

  20. Pescatori, A. and Mr J. Turunen, 2015, “Lower for Longer: Neutral Rates in the United States,” IMF Working Paper 15/135, Washington, DC.

  21. Reifschneider, D. and J. C. Williams, 2000, “Three Lessons for Monetary Policy in a Low-Inflation Era,” Journal of Money, Credit and Banking, Vol. 34, No. 4, pp. 936–966.

  22. Rotemberg, J. and M. Woodford, 1997, “An Optimization-Based Econometric Framework for the Evaluation of Monetary Policy,” NBER Macroeconomics Annual, Vol. 12, pp. 297–361.

    Article  Google Scholar 

  23. Svensson, L. E. O. and M. Woodford, 2003, “Indicator Variables for Optimal Policy,” Journal of Monetary Economics, Vol. 50, No. 3, pp. 691–720.

    Article  Google Scholar 

  24. ——, 2004, “Indicator Variables for Optimal Policy Under Asymmetric Information,” Journal of Economic Dynamics and Control, Vol. 28, No. 4, pp. 661–690.

    Article  Google Scholar 

  25. Taylor, J. B., 1993, “Discretion Versus Policy Rules in Practice,” in Carnegie-Rochester Conference Series on Public Policy, Vol. 39, pp. 195–214.

    Article  Google Scholar 

  26. ——, 1999, “ A Historical Analysis of Monetary Policy Rules,” in Monetary Policy Rules, pp. 319–348.

  27. Woodford, W., 2003a, “Interest Rate and Prices” (Princeton University Press, Princeton).

  28. ——, 2003b, “Optimal Interest-Rate Smoothing,” The Review of Economic Studies, Vol. 70, No. 4, pp. 861–886.

    Article  Google Scholar 

Download references

Author information



Corresponding author

Correspondence to Benjamin K. Johannsen.

Additional information

*Christopher J. Gust is Assistant Director at the Board of Governors of the Federal Reserve System. His work focuses on monetary policy and macroeconomics. He received his Ph.D. in Economics from Northwestern University. Benajmin K. Johannsen is Senior Economist at the Board of Governors of the Federal Reserve System. His research relates to monetary economics and macroeconomics.  He holds a Ph.D. in Economics from Northwestern University. He is the corresponding author and his email address is: J. David López-Salido is Associate Director at the Board of Governors of the Federal Reserve System. His research relates an array of topics in macroeconomics and monetary economics. He received his Ph.D. in Economics from the CEMFI. Prepared for the IMF Sixteenth Jacques Polak Annual Research Conference—November 5–6, 2015. We thank François Gourio, Andy Levin, and two anonymous referees for comments; all remaining errors are our own. We also thank Kathryn Holston for outstanding research assistance. The views expressed in this paper are solely those of the authors and do not necessarily reflect the views of the Board of Governors of the Federal Reserve System, the Reserve Banks, or any of their staffs.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Electronic supplementary material 1 (zip 1496 kb)



A Detailed Description of the Model

The economy consists of a representative household, a continuum of monopolistically competitive firms producing differentiated intermediate goods, perfectly competitive final goods firms, and a central bank that is responsible for monetary policy.


There is a representative household that values streams of consumption \(C_{t}\) and hours worked \(H_{t}\) according to preferences given by the utility function

$$E_{t}\sum _{\ell =0}^{\infty }\delta _{t+\ell -1}\left( \log \left[ C_{t+\ell }\right] -H_{t+\ell }\right)$$

where \(E_{t}\) represents the mathematical expectation conditional on all exogenous shocks and endogenous prices and quantities up to time t. The household maximizes expected utility flows subject to a sequence of budget constraints,


where household nominal expenditures on consumption at date t are given by \(P_{t}C_{t}\), where \(P_{t}\) denotes the aggregate price level for consumption goods, \(B_{t}\) are risk-less nominal bonds sold at the price \(R_{t}^{-1}\) in period \(t-1\), and \(R_{t}=(1+i_{t})\) denotes the gross nominal return on these bonds. A household receives income from any bonds carried over from last period in addition to its labor income, \(W_{t}H_{t}\). A household also pays lump-sum taxes and receives dividends from intermediate goods firms, the sum of which is denoted by \(T_{t}\).

To capture exogenous changes in the household’s desire to save, we allow for stochastic time discounting. The rate of time discounting at time t is given by \(\delta _{t}=\beta ^{t}\left( \prod \nolimits _{s=0}^{t}1+\eta _{t+s}\right) ^{-1},\) where \(0<\beta <1\). Hence, \({\frac{\delta _{t+1}}{\delta _{t}}}={\frac{\beta }{1+\eta _{t}}}\), and \(\eta _{t}\) is the shock to the rate of time discounting and follows an AR(1) process in logs, such that

$$\log (1+\eta _{t})=\rho _{\eta }\log (1+\eta _{t-1})+\varepsilon _{\eta, t}$$

where \(\rho _{\eta }\) denotes the persistence of the shock and \(\sigma _{\eta }\) denotes the standard deviation of the innovations, \(\varepsilon _{\eta, t}\). A decrease in \(\eta _{t}\) represents an exogenous factor that induces a temporary rise in a household’s propensity to save, and reduces current household demand for goods.

The first-order necessary conditions for optimality from the household’s problem can be written as follows

$$1={\frac{\beta }{1+\eta _{t}}}R_{t}E_{t}\left\{ {\frac{C_{t}}{C_{t+1}}}\Pi _{t+1}^{-1}\right\},$$

where \(w_{t}\equiv {\frac{W_{t}}{P_{t}}}\) denotes the real wage, and \(\Pi _{t+1}\equiv {\frac{P_{t+1}}{P_{t}}}\) is the inflation rate between t and \(t+1\). The linear specification for labor services in Eq. (12) along with a competitive labor market implies that there is a perfectly elastic supply of labor available to the economy’s firms.


There is a continuum of monopolistically competitive firms producing differentiated intermediate goods. The latter are used as inputs by perfectly competitive firms that produce a single final good, \(Y_{t}\), using a constant returns to scale production technology, \(Y_{t}=\left( \int _{0}^{1}Y_{t}(j)^{\frac{\epsilon -1}{\epsilon }}\ dj\right) ^{\frac{\epsilon }{\epsilon -1}}\), where \(Y_{t}(j)\) is the quantity of intermediate good j used as an input, and \(\epsilon >1\) is the elasticity of substitution. Profit maximization and perfect competition yield the set of demand schedules, \(Y_{t}(j)=\left( {\frac{P_{t}(j)}{P_{t}}}\right) ^{-\epsilon }Y_{t}\) and aggregate price index, \(P_{t}=\left( \int _{0}^{1}P_{t}(j)^{1-\epsilon }\ dj\right) ^{\frac{1}{1-\epsilon }}\).

The production function for intermediate good j is given by


Since intermediate goods are imperfect substitutes, the intermediate goods-producing firms sell their output in a monopolistically competitive market. During period t, the firm sets its nominal price \(P_{t}(j)\), subject to the requirement that it satisfies the demand of the representative final goods producer at that price.

A fraction \(1-\theta\) of firms are able to change their price optimally in any given period. The remaining firms change their price at a rate consistent with the target level of inflation, which is determined exogenously. Firms that change their price solve the following problem

$$\max _{\tilde{P}_{t}}E_{t}\sum _{\ell =0}^{\infty }\theta ^{\ell }{\frac{\delta _{t-1+\ell }}{\delta _{t-1}C_{t+\ell }}}Y_{t+\ell }\left\{ \left( {\frac{\tilde{P}_{t}{\bar{\Pi }}^{\ell }}{P_{t+\ell }}}\right) ^{1-\epsilon }-\left( {\frac{\tilde{P}_{t}{\bar{\Pi }}^{\ell }}{P_{t+\ell }}}\right) ^{-\epsilon }(1-\tau _{t})w_{t+\ell }\right\},$$

where \({\frac{\delta _{t-1+\ell }}{\delta _{t-1}C_{t+\ell }}}\) measures the marginal value—in time t utility terms—to the representative household of an additional unit of real profits received in the form of dividends during period \(t+\ell\), \(w_{t+\ell }\) is the firm’s real marginal cost at time \(t+\ell\), and \(\tau _{t}\) is an employment subsidy that is financed out of lump-sum taxes paid by the household. We assume that

$$1-\tau _{t}={\frac{\epsilon -1}{\epsilon }}(1+\mu _{t})$$


$$\log (1+\mu _{t})=\rho _{\mu }\log (1+\mu _{t-1})+\epsilon _{\mu, t}$$

where \(\epsilon _{\mu, t}\sim N(0,\sigma _{\mu }^{2})\) and can be interpreted as an innovation in the price-over-wage markup. The first-order condition for this problem is

$$E_{t}\sum _{\ell =0}^{\infty }\theta ^{\ell }{\frac{\delta _{t-1+\ell }}{\delta _{t-1}C_{t+\ell }}}Y_{t+\ell }\left( {\frac{{\bar{\Pi }}^{\ell }}{P_{t+\ell }}}\right) ^{-\epsilon }\left\{ {\frac{\tilde{P}_{t}{\bar{\Pi }}^{\ell }}{P_{t+\ell }}}-{\frac{\epsilon }{\epsilon -1}}(1-\tau _{t})w_{t+\ell }\right\} =0,$$

Define \(\tilde{p}_{t}\equiv \tilde{P}_{t}/P_{t}\) and \(\Pi _{t,t+\ell }\equiv {\frac{P_{t+\ell }}{P_{t}}}\). Then the first-order condition becomes

$$\tilde{p}_{t}= {\frac{E_{t}\sum _{\ell =0}^{\infty }\theta ^{\ell }{\frac{\delta _{t-1+\ell }}{\delta _{t-1}C_{t+\ell }}}Y_{t+\ell }\left( {\frac{\Pi _{t,t+\ell }}{{\bar{\Pi }}^{\ell }}}\right) ^{\epsilon }{\frac{\epsilon }{\epsilon -1}}(1-\tau _{t})w_{t+\ell }}{E_{t}\sum _{\ell =0}^{\infty }\theta ^{\ell }{\frac{\delta _{t-1+\ell }}{\delta _{t-1}C_{t+\ell }}}Y_{t+\ell }\left( {\frac{\Pi _{t,t+\ell }}{{\bar{\Pi }}^{\ell }}}\right) ^{\epsilon -1}}}\equiv {\frac{K_{t}}{F_{t}}}$$
$$K_{t}= {\frac{\epsilon }{\epsilon -1}}(1-\tau _{t})w_{t}+{\frac{\beta }{1+\eta _{t}}}\theta E_{t}\left( {\frac{\Pi _{t+1}}{{\bar{\Pi }}}}\right) ^{\epsilon }K_{t+1}$$
$$F_{t}= {\frac{Y_{t}}{C_{t}}}+{\frac{\beta }{1+\eta _{t}}}\theta E_{t}\left( {\frac{\Pi _{t+1}}{{\bar{\Pi }}}}\right) ^{\epsilon -1}F_{t+1}$$

Price Dispersion and Market Clearing

Prices evolve so that

$$P_{t}^{1-\epsilon }=\theta {\bar{\Pi }}^{1-\epsilon }P_{t-1}^{1-\epsilon }+(1-\theta )\tilde{P}_{t}^{1-\epsilon }$$

meaning that

$$\tilde{p}_{t}=\left[ {\frac{1-\theta {\bar{\Pi }}^{1-\epsilon }\Pi _{t}^{\epsilon -1}}{1-\theta }}\right] ^{\frac{1}{1-\epsilon }}$$

From demand curves,

$$Y_{t}=p_{t}^{*}H_{t} \quad {\text{where}}\quad p_{t}^{*}\equiv \left( {\frac{P_{t}^{*}}{P_{t}}}\right) ^{\epsilon }\quad {\text{and}}\quad P_{t}^{*}\equiv \left[ \int _{0}^{1}P_{t}(j)^{-\epsilon }dj\right] ^{-\frac{1}{\epsilon }}$$

which means that

$$\left(p_{t}^{*}\right)^{-1}=(1-\theta )\tilde{p}_{t}^{-\epsilon }+\theta {\bar{\Pi }}^{-\epsilon }\Pi _{t}^{\epsilon }\left(p_{t-1}^{*}\right)^{-1}$$

The aggregate resource constraint can be written as


Finally, bonds are in zero net supply so bond market clearing implies \(B_{t}=0\).


The log-linearization of Eqs. (25) and (27) implies that, to first order, \(p_{t}^{*}\approx 1\). Equations (21), (22), (23), and (25) become

$$\pi _{t}={\frac{(1-\theta )(1-\beta \theta )}{\theta }}\left[ y_{t}+\mu _{t}\right] +\beta E_{t}\left\{ \pi _{t+1}\right\}$$

where \(x_{t}\equiv \log (X_{t}/X)\) where X denotes the steady-state value of \(X_{t}\). The intertemporal Euler equation is

$$y_{t}=E_{t}\left\{ y_{t+1}\right\} -E_{t}\left\{ i_{t}-\pi _{t+1}-\eta _{t}\right\}$$

where, in a slight abuse of notation, we have used \(i_{t}\equiv \log (R_{t}/R)\).

Natural and Efficient Levels

The natural rate of output and the real interest rate are defined as the levels in an associated economy without price rigidities. The flexible price equilibrium is characterized by the following two equations

$$\begin{aligned}&&1={\frac{\beta R_{t}^{n}}{\eta _{t}}}E_{t}\left\{ {\frac{Y_{t}^{n}}{Y_{t+1}^{n}}}\right\} \\ &&(1-\tau _{t})Y_{t}^{n}={\frac{\epsilon -1}{\epsilon }} \end{aligned}$$

where \(R_{t}^{n}\) is the real natural rate of interest.

We assume that, in the nonstochastic steady state, the employment subsidy is set such that it offsets the monopoly distortion. A log-linearized approximation around the natural equilibrium steady state yields

$$\begin{aligned} r_{t}^{n}&=\eta _{t}-E_{t}\{\mu _{t+1}-\mu _{t}\}\\ y_{t}^{n}&=-\mu _{t} \end{aligned}$$

A decrease in the desired to save (an increase in \(\eta _{t}\)) and expected decrease in marginal costs cause the natural rate of interest to rise. The efficient equilibrium corresponds to that of flexible prices and no exogenous variation in marginal costs. The efficient allocations can be described as follows

$$\begin{aligned} 1&= {\frac{\beta R_{t}^{e}}{\eta _{t}}}E_{t}\left\{ {\frac{Y_{t}^{e}}{Y_{t+1}^{e}}}\right\} \\ Y_{t}^{e}&= 1 \end{aligned}$$

where \(R_{t}^{e}\) is the efficient real interest rate. The log-linear approximation around the efficient nonstochastic steady state implies that

$$r_{t}^{e}=\eta _{t}$$

and the efficient level of output is constant.

Solution Method

To solve the nonlinear model, under optimal discretionary policy, we use a projection method similar to Gust, López-Salido, and Smith (2012) and Lawrence and Fisher (2000). The solution algorithm involves parameterizing the unknown functions \(E_{t}x_{t+1}=f^{x}\left( \xi _{t},s_{t},\xi _{t-1}\right)\), \(E_{t}\pi _{t+1}=f^{\pi }\left( \xi _{t},s_{t},\xi _{t-1}\right),\) where \(E_{t}\) denotes rational expectations based on private-sector information. Then we can write the central bank’s first-order condition, using (1), (2), and (10), as

$$i_{t}-{\frac{\phi _{t}}{\lambda +\kappa ^{2}}}=E\left[ \left( E_{t}x_{t+1}+E_{t}\pi _{t+1}+r_{t}^{e}\right) +\left( \beta E_{t}\pi _{t+1}+\kappa \mu _{t}\right) {\frac{\kappa }{\lambda +\kappa ^{2}}}\Big |\left\{ s_{t},\xi _{t-1},\xi _{t-2}, \ldots \right\} \right]$$

We parameterize a function \(f^{r}\left( s_{t},\xi _{t-1}\right)\), defined so that

$$i_{t}-{\frac{\phi _{t}}{\lambda +\kappa ^{2}}}=f^{r}\left( s_{t},\xi _{t-1}\right) +E\left\{r_{t}^{e}+\left( {\frac{\kappa ^{2}}{\lambda +\kappa ^{2}}}\right) \mu _{t}|\left\{ s_{t},\xi _{t-1}\right\} \right\}$$

To solve for the optimal policy we use the fact that \(\phi _{t}=0\) when \(i_{t}\) is greater than or equal to the lower bound constraint. Notice that this is essentially an application of the approach used in Lawrence and Fisher (2000); however, in our model we also include unknown time t expectations of private agents in the parameterized expectations of the central bank.

To be consistent with the information structure, the function \(f^{r}\) does not take \(\xi _{t}\) as an argument. This ensures that the solution imposes that the monetary authority is unable to use information encoded in the private-sector decisions in the current period. To solve for the unknown parameters of these functions, we conjecture a guess and iterate until the parameters satisfy the private-sector equilibrium conditions and the central bank’s first-order condition at a finite number of points. Note that the above expression can be used to determine the short-term interest rate and the Lagrange multiplier \(\phi _{t}\) as follows. If the right-hand side is positive (\(f^{r}\left( s_{t},\xi _{t-1}\right) +E\left\{r_{t}^{e}+\left( {\frac{\kappa ^{2}}{\lambda +\kappa ^{2}}}\right) \mu _{t}|\left\{ s_{t},\xi _{t-1}\right\} \right\}>0\)) then \(i_{t}=f^{r}\left( s_{t},\xi _{t-1}\right) +E\left\{r_{t}^{e}+\left( {\frac{\kappa ^{2}}{\lambda +\kappa ^{2}}}\right) \mu _{t}|\left\{ s_{t},\xi _{t-1}\right\} \right\}\); otherwise \(i_{t}=0\) and \(\phi _{t}=-\left[f^{r}\left( s_{t},\xi _{t-1}\right) +E\left\{r_{t}^{e}+\left( {\frac{\kappa ^{2}}{\lambda +\kappa ^{2}}}\right) \mu _{t}|\left\{ s_{t},\xi _{t-1}\right\} \right\}\right]\).

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Gust, C., Johannsen, B.K. & López-Salido, J.D. Monetary Policy, Incomplete Information, and the Zero Lower Bound. IMF Econ Rev 65, 37–70 (2017).

Download citation


  • E32
  • E52