Uncertainty shocks, precautionary pricing, and optimal monetary policy

doi:10.1016/j.jmacro.2021.103343

Journal of Macroeconomics

Volume 69, September 2021, 103343

https://doi.org/10.1016/j.jmacro.2021.103343 Get rights and content

Abstract

Existing studies show that, in standard New Keynesian models, uncertainty shocks manifest as cost-push shocks due to the precautionary pricing channel. We study optimal monetary policy in response to uncertainty shocks when the precautionary pricing channel is operative. We show that, in the absence of real imperfections, the optimal monetary policy fully stabilizes the output gap and inflation, implying no policy trade-offs. Our result suggests that precautionary pricing matters only insofar as expected inflation is volatile. Thus, a simple Taylor rule that places high weight on inflation leads to a stabilized output gap, thereby attaining the “divine coincidence”.

Introduction

Time-varying uncertainty has recently received considerable attention from policymakers and academics, spurring the burgeoning literature on identifying transmission mechanisms of uncertainty shocks. It has been shown that a precautionary pricing motive is an important mechanism that amplifies uncertainty shocks. This mechanism is present in New Keynesian models when sticky prices are modeled according to Calvo (1983) and monetary policy follows an empirical Taylor rule. Due to the presence of a precautionary pricing motive, uncertainty shocks behave like cost-push shocks; a rise in uncertainty causes an increase in inflation but a fall in the output gap. A classic and important question for policymakers is whether these shocks generate the well-known output–inflation trade-off that emerges in response to cost-push shocks.

This paper studies optimal monetary policy when the precautionary pricing channel is present. Our main result is that the output gap and inflation are both stabilized under optimal monetary policy, meaning that policy trade-offs do not emerge. Our finding suggests that the precautionary pricing channel is operative only in an environment in which inflation is volatile. Therefore, monetary policy that fully stabilizes inflation eliminates the inefficiencies related to the precautionary pricing channel, thus allowing policymakers to attain efficient allocation.

Our conclusion is drawn from comparing allocations under optimal monetary policy in two popular price-setting approaches. The first is Calvo (1983) pricing, under which firms face a constant probability of not being allowed to reoptimize their price in every period. The second is Rotemberg (1982) pricing, under which firms can always adjust their price upon payment of a quadratic price adjustment cost. While the precautionary saving motive is operative under both Calvo and Rotemberg pricing, precautionary pricing is only operative with Calvo pricing (Oh, 2020). Accordingly, comparing allocations under the optimal monetary policy in Calvo and Rotemberg allows us to evaluate the extent to which precautionary pricing matters for a monetary policy prescription.

Specifically, under Rotemberg pricing, uncertainty shocks act as negative demand shocks; a rise in uncertainty increases the households’ precautionary savings motive, which causes a decrease in both inflation and the output gap. In contrast, under Calvo pricing, a rise in uncertainty triggers firms’ precautionary pricing motives along with households’ precautionary saving motives. A precautionary pricing motive stems from firms’ exposure to the risk of not being able to set their desired price level in the future. Under Calvo, as long as the future expected inflation is volatile, this risk is always present. Price-resetting firms that are exposed to such risk raise prices today to hedge against an uncertain future profit stream. This causes a rise in inflation and a sharper fall in the output gap, as the resulting inflation increase further compresses aggregate demand. Therefore, because of the precautionary pricing channel, uncertainty shocks are more amplified in Calvo than in Rotemberg. We find that, under optimal monetary policy, the differences between allocations in Calvo and Rotemberg disappear. This implies that the precautionary pricing channel is not operative under optimal monetary policy. Moreover, the joint stabilization of the output gap and inflation in Rotemberg suggests that a precautionary saving motive does not pose any policy trade-off, which is consistent with the property of demand shocks in textbook New Keynesian models.

The joint stabilization of the output gap and inflation under optimal monetary policy suggests that the divine coincidence holds in the case of uncertainty shocks; inflation stabilization also brings about the output gap stabilization. Thus, a simple rule that places extremely high weight on inflation (i.e., the strict inflation targeting rule) closes the output gap. It is worth noting that the divine coincidence does not emerge in response to uncertainty shocks in all models. As discussed in Blanchard and Galí (2007), the divine coincidence emerges only in the absence of nontrivial real imperfections. We confirm their results by showing that a trade-off between the output gap and inflation arises in response to uncertainty shocks when real wage rigidities are introduced.

Our paper is related to three main streams of literature. The first focuses on the transmission of uncertainty shocks in New Keynesian models. Leduc and Liu (2016) and Basu and Bundick (2017) focus on the demand channel of uncertainty shocks due to precautionary saving behavior. Moreover, Born and Pfeifer (2014), Fernández-Villaverde et al. (2015), and Mumtaz and Theodoridis (2015) study the supply channel of uncertainty shocks engendered by precautionary pricing. We contribute to this literature by studying the implications of the demand and supply channels of uncertainty shocks in designing optimal monetary policy.

Our paper is also related to the extensive body of literature on optimal monetary policy in New Keynesian models such as Khan et al. (2003), Yun (2005), Blanchard and Galí (2007), and Faia (2008) among many others. These papers study how monetary policy should be implemented in the presence of frictions in the real and monetary sectors. All of the papers in this literature focus on first-moment shocks, whereas our interest lies in second-moment shocks.

Finally, our paper is related to the literature that compares normative results under the Calvo and Rotemberg pricing assumptions. Nisticó (2007) and Lombardo and Vestin (2008) compare the welfare implications of the Calvo and Rotemberg models. [13] compares the inflation bias. All of these papers present an environment in which monetary policy is suboptimal. In contrast, our work compares the dynamics in response to uncertainty shocks when monetary policy is optimal.

The rest of the paper is structured as follows. Section 2 gives a brief overview of the optimality conditions of a textbook New Keynesian model under the Calvo and Rotemberg pricing schemes. Section 3 describes the problem of the Ramsey optimal monetary policy. Section 4 describes the calibration and solution method. Section 5 discusses both the analytical and numerical results on optimal monetary policy in response to uncertainty shocks. In Section 6, we discuss the optimal responses in the presence of real wage rigidities. Section 7 concludes.

Section snippets

Textbook New Keynesian models

We describe the equilibrium conditions of a basic New Keynesian model under the Calvo (1983) and Rotemberg (1982) price rigidities. The model features a utility-maximizing household, perfectly competitive final good firms, monopolistically competitive intermediate good firms, and exogenous productivity subject to second-moment shocks.

The optimal labor supply and consumption of a representative household are characterized by: $\frac{χ {N_{t}}^{η}}{{C_{t}}^{- γ}} = w_{t},$ ${C_{t}}^{- γ} = β E_{t} {C_{t + 1}}^{- γ} \frac{R_{t}}{π_{t + 1}},$ where $C_{t}$ indicates consumption, $N_{t}$

Ramsey optimal monetary policy

Following [20], we assume that, in every period, the Ramsey planner honors commitments made in the very distant past, i.e., $t = - \infty$ , in choosing optimal policy. This means that the constraints that the planner faces at date $t \geq 0$ are the same as those at date $t < 0$ . This is referred to as an optimal policy from the timeless perspective (Woodford, 2003).

Calibration and solution method

The models are calibrated to a quarterly frequency. Table 1 provides a summary of the key parameters. The discount factor $β$ is calibrated to 0.99 to match a steady-state annual real interest rate of 4%. The risk-aversion parameter $γ$ is $2$ . The inverse of labor supply elasticity $η$ is set to $1$ . The labor disutility parameter $χ$ is calibrated to match the steady-state hours worked of $1 ∕ 3$ . The elasticity of substitution between differentiated intermediate goods $ϵ$ is fixed to $11$ , implying a

Results

To illustrate the presence of the precautionary pricing channel, we start by showing the impulse responses to uncertainty shocks under a simple Taylor rule: $log R_{t} - log R = ϕ_{π} log π_{t},$ where $ϕ_{π} = 1.5$ , in line with the empirical literature.

Fig. 1 shows the impulse responses to a one standard deviation increase in uncertainty when monetary policy follows Eq. (20). An increase in uncertainty induces risk-averse households to cut consumption and engage in precautionary savings. When prices are flexible, the

Optimal monetary policy with real wage rigidity

In our baseline model, the distance between the natural level of output and the efficient level output is constant and invariant to uncertainty shocks. In this scenario, a policy that fully stabilizes inflation closes the gap between the actual and natural output and so closes the gap between the actual and efficient output, i.e., the output gap. However, when the distance between the natural and efficient output is time varying, a policy that closes the gap between the actual and natural

Conclusion

Existing studies document that, when monetary policy follows an empirical Taylor rule, the precautionary pricing channel is key to the propagation of uncertainty shocks. In contrast, we have shown that the precautionary pricing channel is not operative when monetary policy is optimal, and real imperfections are absent. We have illustrated this result by comparing allocations under optimal monetary policy in the presence and absence of precautionary pricing. We have found that allocations under

CRediT authorship contribution statement

Daeha Cho: Conceptualization, Methodology, Formal analysis, Writing – original draft, Writing – review & editing. Yoonshin Han: Conceptualization, Methodology, Formal analysis, Writing – original draft, Writing – review & editing. Joonseok Oh: Conceptualization, Methodology, Formal analysis, Writing – original draft, Writing review & editing. Anna Rogantini Picco: Conceptualization, Methodology, Formal analysis, Writing – original draft, Writing – review & editing.

Acknowledgments

We are grateful to Pablo Anaya, Flora Budianto, Seonghoon Cho, Mira Kim, Evi Pappa, Mathias Trabandt, and Ulf Söderström for many insightful discussions. We particularly benefit from the detailed comments of the editor Oliver de Groot and two anonymous referees. All errors are our own.

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^☆: An earlier version of the paper was previously circulated under the title “Optimal Monetary Policy and Uncertainty Shocks”. The opinions expressed in this article are the sole responsibility of the authors and should not be interpreted as reflecting the views of the Korea Deposit Insurance Corporation or the Sveriges Riksbank.

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Uncertainty shocks, precautionary pricing, and optimal monetary policy☆

Abstract

Introduction

Section snippets

Textbook New Keynesian models

Ramsey optimal monetary policy

Calibration and solution method

Results

Optimal monetary policy with real wage rigidity

Conclusion

CRediT authorship contribution statement

Acknowledgments

J. Monetary Econ.

J. Monetary Econ.

J. Monetary Econ.

J. Monetary Econ.

J. Econom. Dynam. Control

Econom. Lett.

Econom. Lett.

Dynare: Reference Manual Version 4Dynare Working Papers 1

The pruned state-space system for non-linear DSGE models: Theory and empirical applications

Rev. Econom. Stud.

Uncertainty shocks in a model of effective demand

Econometrica

Real wage rigidities and the New Keynesian model

J. Money Credit Bank.