# Abstract

This paper uses a dynamic framework of a small open economy to study the volatility effects of partially anticipated monetary policy shocks in which the public has imperfect information about the size and/or the timing of the future expansionary policy intervention. Our two main results are as follows: (i) Partially anticipated monetary policy shocks may be stabilizing, i. e. lead to a lower volatility than a fully anticipated monetary policy shock of the same form. (ii) However, we typically obtain a trade off in volatilities such that a simultaneous stabilization of inflation and output is not possible. If the public underestimates (overestimates) the size of the shock, output (inflation) may be stabilized. Our results imply that the central bank may have an incentive to withhold information from the public about the true central bank’s intention.

## 1 Introduction

This paper studies the volatility effects of monetary policy disturbances, which are not fully anticipated by the public. So far, the literature has only considered two extreme cases of anticipation. Either the public has perfect information and fully anticipates the shock process or the public is completely uninformed and does not anticipate the shock process at all. This paper introduces an intermediate scenario of partial anticipation, which covers both extreme scenarios as special cases. Under partial anticipation, the public has partially correct and partially incorrect expectations about the exact evolution (i. e. about size and timing) of the monetary shock process. To the best of our knowledge, we are the first to study this kind of partially anticipated shocks.
^{[1]}

The importance of anticipated shocks in general (like pre-announced future monetary policy interventions), also known as news shocks, for business cycle fluctuations is confirmed by several empirical studies. Most prominently, Schmitt-Grohé and Uribe (2012) find in an estimated real business cycle model that about 50 percent of economic fluctuations can be attributed to fully (or possibly partially) anticipated disturbances.
^{[2]}Milani and Treadwell (2012) focus on anticipated monetary policy. They find that anticipated monetary policy shocks have a larger impact on output fluctuations than unanticipated monetary policy shocks.
^{[3]} They conclude that the central bank’s communication can be an effective monetary policy tool.
^{[4]}

Central banks may not be able or not willing to communicate the exact timing and/or size of a (future) monetary intervention in advance so that the public needs to form expectations about it. For example, in July 2012 at the Global Investment Conference in London, the President of the European Central Bank, Mario Draghi, signalized further purchases of government bonds by stating that “the ECB is ready to do whatever it takes to preserve the euro” to bring down risk premiums on government bonds. However, Draghi is mute about the exact threshold of risk premiums at which the ECB is planning to intervene. This limited information strategy leaves room for public misperceptions such that the monetary intervention may only be partially anticipated.
^{[5]}

The main aim of this paper is twofold: First, we aim to study the (de)stabilizing effects of partially anticipated monetary disturbances on inflation and output fluctuations, where we define stabilization as follows: Partial anticipation (de)stabilizes a particular variable if the variable’s volatility under partial anticipation is (larger) smaller than under fully correct anticipation of the same shock process. Second, we aim to derive the optimal central bank’s communication strategy. Is it possible to obtain a lower central bank loss by either directly deceiving the public or withholding information about the true monetary policy intentions?

To this end, we consider several partial anticipation scenarios, in which the public initially has incorrect expectations about the size and/or the timing of the monetary disturbances. With interest rates at the zero lower bound, central banks are forced to use unconventional policy instruments to stimulate the economy. In line with this change in policy, we model monetary policy interventions as (temporary) increases in the money growth rate. To discuss the limited information strategy of the ECB during the European sovereign debt crisis, we consider increases in the money growth rate not only in isolation but also as response to increasing risk premiums on government bonds, where the public may have incorrect expectations about the start of the monetary intervention.
^{[6]}

As model framework, we use a continuous-time Dornbusch-type
^{[7]} model of a small open economy. This framework has been used in several papers to study the dynamic impacts of (fully) anticipated shocks. Early studies include Turnovsky (1986a, 1986b). More recent studies include Clausen and Wohltmann (2005), who study anticipated and unanticipated monetary and fiscal policy in an asymmetric monetary union and Clausen and Wohltmann (2013), who study anticipated oil price shocks in a similar model of a small open monetary union. Recently, the continuous-time formulation also has gained some attention in the New Keynesian literature. Posch et al. (2011) formulate and solve the New Keynesian model in continuous time.

Our two main results are as follows: (i) Partially anticipated monetary policy shocks may stabilize inflation and output fluctuations, i. e. lead to a lower volatility than a fully anticipated monetary policy shock of the same form. (ii) However, we typically obtain a trade off in volatilities such that a simultaneous stabilization of output and inflation is not possible. If the public underestimates (overestimates) the size of the shock, output (inflation) may be stabilized.

Our results are in line with the literature: The existence of a trade off in volatilities of inflation and output is well known and already described in Taylor (1979) and revisited in Taylor (1994). He finds the trade off in volatilities – in contrast to the trade off in levels – to be stable in the long run for the U.S. economy. Further related to this paper is the literature on news shocks which studies the potential destabilizing effects of completely anticipated shocks. Fève et al. (2009) show in a purely forward-looking discrete-time framework with rational expectations that anticipated shocks destabilize the economy, i. e. lead to a higher volatility than non-anticipated shocks of the same size. The volatility increases with increasing length of anticipation. This result does not hold unambiguously for the hybrid case with backward-looking elements as it is shown by Winkler and Wohltmann (2011).
^{[8]} They find the same trade off in volatilities of inflation and output in the estimated Euro area model of Smets and Wouters (2003). With increasing anticipation horizon, output volatility increases, but inflation volatility decreases. Our paper may help to explain why this trade off in volatilities occurs and why anticipated shocks may lead to a (de)stabilization of the economy.

For the aforementioned results of this paper, we implicitly assume a stable relation between base and broad money such that the central bank can perfectly control the money stock. However, since the outburst of the financial crisis in 2008, such a stable relation in the Euro area is questionable as e. g. De Grauwe and Ji (2013) demonstrate. We, therefore, also study partially anticipated changes in the monetary base that have no effect on the money stock. We find that changes in the monetary base may still have real effects on the economy and may impose cyclical adjustment movements even if the relation between base and broad money is non-existent. This requires, however, that the public indeed believes in a stable relation.

The remainder of the paper is organized as follows: Section 2 describes the model frame-work. Section 3 introduces our (partial) anticipation scenarios and studies the responses to a temporary increase in the money growth rate. Section 4 introduces our volatility measure and discusses the (de)stabilizing effects of partially anticipated changes in the monetary growth rate for different degrees of expectation biases. Section 5 introduces two communication strategies in which the central bank either deceives the public or withhold information from the public to obtain a lower central bank loss. As a digression, Section 6 discusses the responses to partially anticipated increases in the monetary base in the presence of an unstable relation between base and broad money. Section 7 discusses six modifications including a simultaneous increase in the risk premium on government bonds and in the money growth rate. The last section concludes.

## 2 Model framework

As model framework we use a dynamic continuous-time Dornbusch-type model for a small open economy. The economy is described by the following set of log-linearized equations:

All variables, except for the (nominal and real) interest rate and the inflation rate, are in logarithm. The notation is as follows: *i**, *y**, *p**) are denoted by a superscript star. A dot above a variable *E* is the expectations operator. We assume rational expectations. In a deterministic framework this implies ^{[9]} Further details will be provided in the subsequent sections.

Equation [1] is a standard IS equation, determining the short-run development of output. The first term in brackets stands for real private absorption depending on real income and the real interest rate. The second term in brackets stands for the trade balance depending on domestic and foreign income and the terms of trade. The terms of trade are defined in eq. [2]. Equation [3] represents the money market equilibrium and is a traditional LM curve. Equation [4] is the uncovered interest rate parity (UIP), and eq. [5] represents a Phillips-type inflation equation. Equation [6] specifies the augmentation term in the Phillips curve, which we set equal to the expected long-term rate of inflation. According to montaristic theory, we assume that inflation is solely determined by the money growth rate in the long run.
^{[10]} In the short to medium run, inflation might temporarily deviate from its long-term rate. However, inflation is, as we will see in the subsequent sections, rather tied to the money growth rate.
^{[11]} For completeness, the last equation describes the long-run relation between output and the terms of trade. Since changes in the money growth rate do not alter the steady state of output and the terms of trade, we can neglect this equation until Section 7, where we also consider changes in the risk premium on government bonds.
^{[12]}

The model can be reduced to a two-dimensional system of ordinary differential equations with the terms of trade ^{[13]}

Parameter | Value | Definition |

a_{1} | 0.7 | Income elasticity of private consumption |

a_{2} | 0.3 | Real interest rate (semi-)elasticity of private absorption |

b_{1} | 0.2 | Income elasticity of the trade balance |

b_{3} | 0.1 | Terms of trade elasticity of the trade balance |

l_{1} | 1.0 | Income elasticity of money demand |

l_{2} | 4.0 | Interest rate (semi-)elasticity of money demand |

0.2 | Slope of the Phillips curve |

In the subsequent simulations, we use the calibration given in Table 1.
^{[14]} We focus on deviations from the initial steady state. Therefore, we do not need to specify *a*_{0}, *b*_{0}, and *b*_{2}. For the remaining parameters, we broadly follow the textbook calibration given in Galí (2008) and Walsh (2010) and the estimates from Moons et al. (2007), who estimate a stylized open-economy New Keynesian model for the euro area.

The income elasticity and the interest rate semi-elasticity of the money demand are set to *l*_{1} reported in Walsh (2010) suggest values greater than unity, whereas Ball (2001) finds a value of 0.5. Estimates of *l*_{2} reported in Walsh (2010) range from 1 to 10, which is in line with the estimate of 5 found by Ball (2001).
^{[15]} The income elasticity of private consumption is set to ^{[16]} The income elasticity of the trade balance is set to 0.2.
^{[17]} Then, the net effect of the real interest rate and of the terms of trade on goods demand is given by ^{[18]} The slope of the Phillips curve is set to ^{[19]} In Section 7, we investigate how our results change for different parameter values for *b*_{3}.

## 3 Anticipation scenarios and responses to a monetary shock

This section introduces our anticipation scenarios and discusses the responses to a temporary increase in the money growth rate in the above model framework.

The realized but not necessarily correctly anticipated shock process is the same across all anticipation scenarios. The evolution of the shock process is described in Table 2. The increase in the money growth is implemented at a constant rate *c* over the implementation period

In the long run, a temporary increase in the money growth rate does not alter the steady state of the real variables.
^{[20]} The steady state of the nominal money stock changes according to

which implies a change in the steady-state values of the price level and the nominal exchange rate of equal size, i. e. *c* is the magnitude, *T* is the start, and *t*_{1} is the end or exit of the shock process.

We consider five anticipation scenarios: one full anticipation scenario in which the public correctly anticipates the full monetary policy intervention (denoted as FA), three partial anticipation regimes in which the public has partially correct and partially incorrect expectations (denoted as PA), and one non-anticipation scenario in which the policy intervention completely comes as a surprise (denoted as NA). Table 3 summarizes the complete set of anticipation scenarios.
^{[21]} In the three scenarios of partially correctly anticipated shocks, the public forms incorrect expectations either about the magnitude *c* (scenario PA-MAG), about the starting point *T* (scenario PA-START), or about the exit point *t*_{1} (scenario PA-EXIT) of the increase in the money growth rate. Note that in all three partial anticipation scenarios, the public has incorrect expectations about the size of the shock.

FA | NA | PA-MAG | PA-START | PA-EXIT | ||

Magnitude | E(c) | c | 0 | c | c | |

Start | E(T) | T | – | T | T | |

Exit | E(t_{1}) | t_{1} | – | t_{1} | t_{1} | |

Length | – | |||||

Size | – | |||||

Breakpoint | t* | – | T | T | min[E(T),T] | min[E(t_{1}), t_{1}] |

Since we aim to study only temporary and not permanent anticipation errors, we have to define how the public switches to correct expectations. For simplicity, we assume that the switch from partially incorrect to fully correct expectations occurs at once at some particular breakpoint *t*.
^{[22]} Hence, the public has correct expectations for *T*) and the magnitude (*c*), but has incorrect expectations about the end (*t*_{1}) of the shock process. Since *T*. If the public expects an earlier end of the shock process, i. e.

In the following, we subsequently study the responses to the above temporary increase in the money growth rate under the partial anticipation scenarios PA-MAG, PA-START, and PA-EXIT in comparison to the full anticipation scenario FA.

### 3.1 Scenario PA-MAG and NA

Figure 1 depicts the responses to a temporary increase in the money growth rate under the full anticipation scenario FA and the partial anticipation scenario PA-MAG, where the public either underestimates

### Figure 1:

To start with, the adjustment process in the anticipation scenario FA can be described as follows: In *T*. Simultaneously, the real money stock continuously declines, which is equivalent to a continuous upward adjustment of prices. The devaluation of the home currency leads via the UIP to a rise in the nominal interest rate. The inflation response on impact and during the anticipation phase is relatively small such that the real interest rate rises. Despite the contractionary real interest rate effect, output unambiguously stays above its steady state value on impact and during the anticipation phase. This immediately follows from the inverse Phillips curve

which determines output by the change in the real money stock.

In *T*, but continuously decreases over the implementation phase.

After the implementation phase

Note that the impact and anticipation reaction of inflation is relatively small compared to the inflation reaction during the implementation phase. This is mainly due to our assumption that long-term inflation expectations are exclusively driven by changes in the money growth rate.

In the following, we denote this FA scenario as benchmark scenario and compare the responses of the remaining three anticipation scenarios to this benchmark scenario. Since we only change the nature of anticipation and leave the realized shock process unchanged, differences to the full anticipation case mainly occur on impact and during the anticipation period. After the occurrence of the shock, differences to the benchmark scenario are less visual.

In the anticipation scenario PA-MAG, the public has incorrect expectations about the magnitude *c*, but is correct about the start and the end of the shock process. In case the public underestimates the magnitude ^{[23]} The decline in the real money stock is, however, steeper than in the benchmark scenario, converging towards the FA solution path. The terms of trade are, on the other hand, allowed to react discontinuously to this new information. To compensate for the sluggishness of the real money stock, the terms of trade undershoot its benchmark value.
^{[24]} Likewise, output and inflation overshoot and the real interest rate undershoots their benchmark values. During the implementation phase, the real money stock, output, inflation and the nominal interest rate stay above, and the terms of trade and the real interest rate stay below the benchmark responses.

If the public overestimates the magnitude (and the size) of the shock

Scenario NA, where the public does not anticipate the increase in the money growth at all, is equivalent to the special case *T*, all variables remain constant. In

### 3.2 Scenario PA-START and PA-EXIT

Figure 2 depicts the responses for scenario PA-START. For reference purposes, we again include the benchmark scenario FA, where the public has fully correct expectations. In scenario PA-START, the public has incorrect expectations about the start of implementation. The end *t*_{1} and the magnitude *c* of the shock process are, on the other hand, correctly anticipated. This implies that the public overestimates (underestimates) the size of the shock ^{[25]}

### Figure 2:

Consequently, if the public expects a later start of the monetary policy shock

If the public expects an earlier start of the shock process *t**. This time, however, the switch to correct expectations already occurs during the anticipation phase in

As a last scenario, Figure 3 shows the responses under scenario PA-EXIT. In this scenario, the public has incorrect expectations about the end of the monetary intervention. The start and the magnitude of the shock process are, on the other hand, correctly anticipated. This implies that the public overestimates (underestimates) the size of the shock *c*(*t*_{1} − *T*) if it expects a later (an earlier) end of the monetary intervention implying a stronger (smaller) reaction on impact and during the anticipation phase.

### Figure 3:

The main difference to the other two partial anticipation scenarios is that the switch to correct expectations now occurs during the implementation phase and not during the anticipation phase. Since the start and the magnitude are correctly anticipated, the public expectations about the shock process and the true shock process do not deviate from one another until

## 4 Measuring the (de)stabilization effects

In order to study the (de)stabilizing effects of partially anticipated monetary policy interventions, we use a relative volatility measure, which relates the volatility under partial anticipation to the volatility under full anticipation. The relative volatility for

where *x* from its initial steady state *D* given the expectation assumptions of scenario S and FA, respectively:
^{[26]}

*E*(

*c*) ranging from –1 to 6 in scenario PA-MAG, for

*E*(

*T*) ranging from 0.5 to 3.5 in scenario PA-START, and for

*E*(

*t*1) ranging from 2.5 to 7 in scenario PA-EXIT. With correct expectations

### Figure 4:

Let us first have a look at the overall relative volatility over the whole adjustment process. In scenario PA-MAG and PA-START, we have a trade off between output and inflation stabilization. If the public underestimates the size of the shock

Next, we consider the relative volatility during the three subperiods. Two points are common in all three scenarios: First, the trade off in volatilities that we obtain based on the overall adjustment process in scenarios PA-MAG and PA-START is not present if we consider the three phases in isolation. In all three subperiods, output and inflation are both either stabilized or destabilized. Second, during the anticipation and return phase, the relative volatility in output and inflation is even identical.
^{[27]} Differences in the relative volatility only occur during the implementation phase. This follows from the structure of the Phillips curve [5], where the expected future inflation is pinned down by the money growth rate. During the anticipation and return phase, the money growth rate is at its steady state level such that changes in the inflation rate are proportional to changes in output.
^{[28]} During the implementation phase

During the anticipation phase

During the implementation phase

This trade off between stabilizing the system during the anticipation (and return) phase and during the implementation phase is not present in scenario PA-EXIT. The main reason is that in this scenario the switch to correct expectations occurs much later during the implementation phase. If the public underestimates the shock size ^{[29]}

During the return phase

The question arises, why do we face in scenario PA-MAG and PA-START a trade off between inflation and output over the whole adjustment process, but not in any of the three subperiods separately. This trade off in overall volatilities results from the combination of the following two arguments: First, as described above, output and inflation can not be stabilized in all three subperiods simultaneously. A smaller (stronger) reaction during the anticipation phase causes the system to respond more strongly (less strongly) during the implementation phase. Second, inflation strongly responds to realizations in the money growth rate during the implementation phase, whereas the anticipation effect on inflation is relatively small. The difference between anticipation and implementation reaction is less pronounced for output. Under fully correct expectations, the volatility share of the anticipation phase contributing to overall volatility only amounts to 0.2 percent for inflation and to almost 12 percent for output.
^{[30]} Therefore, we find that the anticipation effect is dominant for output, whereas the opposite implementation effect is dominant for inflation.

## 5 Two communication strategies

In the last section, we have shown that the volatility in inflation and output under partial information can be reduced below the volatility under full anticipation, although not necessarily simultaneously. This section discusses the policy implication of partially anticipated monetary shocks. We introduce two communication strategies and show how these strategies may improve the central bank loss compared to the FA scenario. The first communication strategy presumes that the central bank has a sufficiently strong influence on private expectations and is, thereby, able to control the expectations

In the second communication strategy, the central bank does not create, but is confronted with biased expectations about its future monetary intervention. The central bank now controls the breakpoint, at which the central bank is revealing the true evolution of the monetary shock and the public switches to fully correct expectations. We denote this breakpoint as

The central bank aims to stabilize inflation and output. In particular, we assume that the central bank’s loss function is given by

During the simulation, we set ^{[31]} To compare the loss between partially and fully anticipated increases in the money growth rate, we compute the relative loss, which is the ratio of the loss under partial anticipation and under full anticipation.

We start with the deception strategy. Figure 5 shows the relative loss for different values of

### Figure 5:

In all three partial anticipation scenarios, it is possible to improve the central bank loss in comparison to scenario FA. The lowest loss is obtained in scenario PA-EXIT if the public expects an earlier end (lower size) of the shock process, i. e.

Next, we discuss the withholding strategy. Until now, we have assumed that the public switches to fully correct expectations in the very last possible moment in *t**, i. e. when the public realizes for the first time that the expected evolution of the shock process deviates from the true one. We now discuss how the central bank loss and the volatility in inflation and output change if the switch to correct expectations occurs earlier than assumed so far ^{[32]} In the top three plots of Figure 6, the central bank is confronted with a public that initially underestimates the shock size (either by

### Figure 6:

If the central bank reveals the true shock process during the anticipation phase

Under the loss function [12], the best communication strategy is as follows: If the public overestimates the size of the shock (lower three plots), the FA scenario produces the best outcome, i. e. the best central bank’s policy is to inform the public as soon as possible about the true evolution. If, on the other hand, the public underestimates the size of the shock (upper three plots), the best central bank’s policy is to inform the public as late as possible. Note that this communication strategy typically stabilizes output, but destabilizes inflation (unless ^{[33]}

This section has shown that the central bank may have the incentive to improve the central bank loss by either actively deceiving private expectations (deception strategy) or by withholding information about the true evolution of the shock process (withholding strategy). However, this section should not be understood as a policy advice since both strategies may involve drawbacks that have not been mentioned so far, including the following: First, both strategies, particularly the deception strategy, may involve reputational costs by reducing the central bank’s credibility in future periods. Second, the central bank has to be able to correctly monitor the expectations bias. Withholding information about the true shock process may, therefore, lead to a higher central bank loss if the public is biased in the opposite direction.

## 6 Unstable money multiplier

Until now, we have assumed that the central bank can perfectly control the money growth rate, which requires a stable relation between the (adjusted) monetary base and broad money. This stable relation implies that the asset purchases from central banks – without neutralization – lead to increases in the money stock. Since the financial crisis in 2008, we do not observe such a stable relation between base and broad money in the euro zone.
^{[34]} Therefore, we consider in this section the case

Central bank interventions (e. g. asset purchases) that lead to an expansion of the monetary base then have no effect on the economy if the public correctly anticipates this unstable relation. Figure 7 shows two scenarios in which expansions in the monetary base have real effects even without a stable money multiplier. In both scenarios, we presume that the public initially believes in a stable money supply multiplier and expects in

### Figure 7:

In the following, we discuss the two scenarios in more detail. On impact and during the anticipation phase, the two scenarios produce the same responses as under a stable money multiplier since the initial expectations on the increase in the money growth rate are the same. In *T* to fully correct expectations and correctly expects no change in the money growth rate (i. e. *T* and converge from below to the old steady state.

In the second scenario (multiple expectations adjustment), the public believes in *T* still in a stable money multiplier and sequentially expects a later start of the increase in the money stock. Note that we assume that the public also sequentially updates its expectations on the end of the increase in the money growth rate *t*_{1} such that the expectations on the size of the shock remain the same. In *T*_{1}, no change in the money stock occurred and the public expects a start in *T, T*_{1}*, T*_{2}, …), the system jumps on a higher trajectory in the phase plane, which corresponds with an immediate output contraction. During two contractions, output gradually increases in anticipation of the expansionary increase in the money stock. Only after several expectations adjustments (in

To sum up, this section has shown that changes in the monetary base may have real effects on the economy and may impose cyclical adjustment movements even if a stable relation between the monetary base and a broader money aggregate is non-existent. This requires, however, that the public indeed believes in a stable relation between base and broad money and expects a future increase in the money growth rate.

## 7 Modifications

In this section, we apply six modifications. First, we change our parameter calibration. Second, we modify the length of anticipation relative to the length of the implementation phase. Third, we consider a further partial anticipation scenario PA-ST/EX which is an intermediate scenario of PA-START and PA-EXIT. Fourth, we change the mechanism with which the private expectations switch to correct expectations. Fifth, we modify the augmentation term in the Phillips curve. Finally, we consider a simultaneous increase in the risk premium *s* and in the money growth rate

**1. Parameter calibration**: To check the robustness of our volatility results, we simulate our model for different parameter calibrations for scenario PA-MAG, where the public has incorrect expectations about the magnitude *c* of the increase in the money growth rate. We consider the following alternative parameter specifications: We use ^{[35]} Figures C.1 and C.2 show the relative volatility of output and inflation. Figures C.3 and C.4 show the corresponding responses to a fully anticipated increase in the money growth rate. Table C.1 gives the volatility share of the three subperiods on overall inflation and output volatility in the full anticipation scenario.

The volatility results for the alternative parameter specifications are as follows: First, we do not find any qualitative change in the relative volatility during the three subperiods. During the anticipation phase, the differences are so small that they are not visual. Second, for all parameter specifications, we find that an isolated stabilization of output and inflation is possible while a simultaneous stabilization is not possible. Indeed, we obtain the same trade off in overall volatility as in the baseline calibration. This trade off vanishes only when the anticipation effect of output is sufficiently small, i. e. the volatility share of the anticipation phase has to be at least below 1.3 percent.
^{[36]} Third, the anticipation effect of inflation remains very small for all parameter sets under consideration. Therefore, we obtain no qualitative change in the overall inflation volatility.

**2. Anticipation length**: In this modification, we change the length of the anticipation phase relative to the length of the implementation phase in scenario PA-MAG. Until now, we have assumed that the anticipation and implementation period are of similar length, where we set the anticipation length to

**3. Scenario PA-ST/EX**: In this modification, we consider the partial anticipation scenarios PA-ST/EX, which is a combination of scenarios PA-START and PA-EXIT. So far, in each of the three partial anticipation scenarios, the public has implicitly incorrect expectations about the size of the shock. In scenario PA-ST/EX, the public has incorrect expectations about the start and the end of the monetary shock, but is correct about the length and the size. That is, the expectations bias on the start and the end of the shock has to be the same.
^{[37]} Figure C.9 depicts the responses to a temporary increase in the money growth rate, and Figure C.10 shows the relative volatility in this scenario. Both, the responses and the relative volatility are very similar to scenario PA-START. Consequently, not only the expected size of the shock, but also the expected timing of the shock matters.

**4. Sequential correction of expectations**: So far, we have assumed that the switch to correct expectations occurs immediately at one particular point in time *t**. We now assume that the public sequentially adapts its expectations over time in several steps. With each step the public gains more information about the true evolution of the shock process. For simplicity, we assume that the information gain is equally distributed over time. Figure C.11 shows the response of the three anticipation scenarios (PA-MAG with

The more frequent the public adjusts its expectations, the smaller is the discontinuous adjustment in the non-predetermined variables for

For all three scenarios, we compute the relative volatility using continuous expectations adjustments instead of the single adjustment frequency of Section 3. Figure C.12 summarizes our results. We find no notable differences to the relative volatility analysis from Section 4. In Section 5, we have seen that our volatility results crucially depend whether the switch to correct expectations occurs during the anticipation or during the implementation phase. However, this modification has shown that the pace with which the switch occurs is somewhat irrelevant.

**5. Inflation expectations based on consumer price index**: Until now, we have assumed that the augmentation term in the Phillips curve is given by the trend rate of inflation *p _{c}* for scenario PA-MAG, PA-START, and PA-EXIT. The augmentation term then reads as

where

We do not observe a qualitative change in the relative volatility during the three subperiods. Furthermore, an isolated reduction in the overall volatility of output and inflation is possible. Again, a simultaneous stabilization of output and inflation is not possible, even in scenario PA-EXIT. However, this trade off in volatilities is reversed compared to our baseline model: If the public underestimates (overestimates) the size of the shock, output (inflation) may be destabilized, i. e. not stabilized as in our baseline model.

The reason for this reversed trade off in volatilities is as follows: First, inflation responds now much more strongly during the anticipation phase than in our baseline model. Inflation expectations in the Phillips curve are not anchored anymore to the exogenous money growth, which does not change until *T*. Instead, inflation expectations that are based on CPI inflation already change during the anticipation phase. The last row of Table C.1 shows that more than 50 percent of overall inflation volatility is accumulated during the anticipation phase in case

Second, the volatility share of the anticipation phase also increases for output, i. e. output reacts more strongly during the anticipation phase. However, the relative output volatility during the implementation phase is now much more sensitive to anticipation errors than in our baseline model. Therefore, the implementation effect is now dominant for output and overall output volatility may only be stabilized if it is stabilized during the implementation phase.

**6. Risk premium shock**: In the sixth and last modification, we apply our volatility analysis to the recent developments during the European sovereign debt crisis, where several (southern) European countries are suffering from increasing risk premiums on government bonds. To oppose these risk premiums, the President of the ECB, Mario Draghi, signalized in July 2012 further purchases of government bonds at the Global Investment Conference in London. He is, however, mute about the exact threshold

To this end, we consider a simultaneous increase in the risk premium and in the money growth rate. The true, but not necessarily correctly anticipated evolution of the increase in the risk premium and in the money growth rate is summarized in Table C.2: In *c*. Without neutralization and stable money supply multiplier, this is equivalent to a temporary increase in the money growth rate and a permanent increase in the money stock. We assume that this monetary intervention leads quasi-endogenously to a gradual decline in the risk premium until it reaches its initial level in

In *T* of the monetary intervention and, therefore, on the start of the decline in the risk premium. Contrarily to an isolated monetary shock in scenario PA-START, the public overestimates (underestimates) the size of the risk premium shock and the monetary intervention if the public expects a later (an earlier) monetary intervention. Table C.3 summarizes the expectation biases under partial anticipation.

The responses under full and partial anticipation are shown in Figure C.17. Figure C.18 and C.19 summarize our volatility results: If the public expects an earlier intervention of the central bank to bring down the risk premiums on government bonds, the volatility in output and inflation may be reduced. Under flexible inflation targeting, the best central bank’s communication policy then is to withhold information about the true shock process as long as possible. If, on the other hand, the public expects a later monetary intervention, output is and inflation may be destabilized. Under flexible inflation targeting, the fully correct anticipation scenario then typically gives the lowest central bank loss. Hence, the best policy is to inform the public as soon as possible about the true intentions of the central bank.
^{[38]}

## 8 Conclusion

In this paper, we use a continuous-time Dornbusch-type model of a small open economy to study the (de)stabilizing effects of fully anticipated, fully non-anticipated, and partially anticipated increases in the money growth rate. Under partial anticipation, the public has either imperfect information about the magnitude, the start, and/or the end of the future monetary policy intervention, and, therefore, has implicitly imperfect information about the size of the shock.

Our main results are as follows: (i) Partially anticipated monetary policy shocks may stabilize inflation and output fluctuations, i. e. lead to a lower volatility than a fully anticipated monetary policy shock of the same form. (ii) However, we typically obtain a trade off in volatilities of output and inflation over the whole adjustment process such that a simultaneous stabilization of output and inflation is not possible. If the public underestimates (overestimates) the size of the shock, output (inflation) may be stabilized. (iii) This trade off in volatilities does typically not exist during the three subperiods (anticipation phase, implementation phase, and return phase) separately. If the public underestimates (overestimates) the size of the shock, both output and inflation are stabilized (destabilized) during the anticipation phase and are destabilized (stabilized) during the implementation phase. (iv) The volatility gain/loss from partial anticipation is (much) larger for output than for inflation. Under flexible inflation targeting, the best central bank’s communication strategy, therefore, is typically to stabilize output fluctuations. If the public underestimates the size of the shock, the central bank then has an incentive to withhold information from the public about the true central bank’s future policy intentions.

The aforementioned results can be explained as follows: First, during the anticipation phase the economy is driven by expectations. If the public overestimates (underestimates) the shock size, both output and inflation respond more strongly (less strongly) than under fully correct expectations. Under price stickiness, the economy is not able to jump on the solution path of fully correct expectations. To compensate for this price stickiness, the system (including output and inflation) overreacts when the true shock process is revealed and typically leads to smaller (larger) reaction of output and inflation during the implementation phase. This leads to the opposite volatility pattern during the anticipation and the implementation phase as described in result (iii). Second, we find that the anticipation response of inflation is relatively small compared to the anticipation response of output. Therefore, the volatility share of the anticipation contributing to overall volatility is smaller for inflation than for output. In combination with result (iii), this gives rise to an overall trade off in output and inflation volatility.

We find two exceptions in which results (ii) and (iii) do not or only partially hold: First, when the public underestimates the shock for a sufficiently long time (i. e. the expectations are biased also during the implementation of the shock), overall output and inflation may be stabilized in all three subperiods simultaneously. Therefore, a simultaneous stabilization of output and inflation over the whole adjustment process is possible and the overall trade off in volatilities vanishes. Second, if the anticipation effect of inflation (output) is sufficiently large (small), result (ii) may be reversed. That is, inflation (output) may be stabilized if the public underestimates (overestimates) the shock.

We further study partially anticipated monetary interventions in the presence of an unstable money multiplier. We find that changes in the monetary base may have real effects on the economy and may impose cyclical adjustment movements even if the relation between the monetary base and a broader money aggregate is non-existent. This requires, however, that the public indeed believes in a stable relation between base and broad money and expects a future increase in the money growth rate.

# Acknowledgments

We thank Peter Winker and three anonymous referees for valuable comments and suggestions.

### References

Ball, L. (2001), Another Look at The Long-Run Money Demand. Journal of Monetary Economics 47 (1): 31–44. Search in Google Scholar

Barsky, B., E. Sims (2011), News Shocks and Business Cycles. Journal of Monetary Economics 58 (3): 273–289. Search in Google Scholar

Beaudry, P., B. Lucke (2010), Letting Different Views about Business Cycles Compete. NBER Macroeconomics Annual 24: 413–455. Search in Google Scholar

Beaudry, P., F. Portier (2004), An Exploration into Pigou’s Theory of Cycles. Journal of Monetary Economics 51 (6): 1183–1216. Search in Google Scholar

Beaudry, P., F. Portier (2006), Stock Prices, News, and Economic Fluctuations. American Economic Review 96 (4): 1293–1307. Search in Google Scholar

Blinder, A.S., M. Ehrmann, M. Fratzscher, J. De Haan, D. -J. Jansen (2008), Central Bank Communication and Monetary Policy: A Survey of Theory and Evidence. Journal of Economic Literature 46 (4): 910–945. Search in Google Scholar

Clausen, V., H.-W. Wohltmann (2005), Monetary and Fiscal Policy Dynamics in an Asymmetric Monetary Union. Journal of International Money and Finance 24 (1): 139–167. Search in Google Scholar

Clausen, V., H.-W. Wohltmann (2013), Oil Price Dynamics and Monetary Policy in a Heterogeneous Monetary Union. Journal of Economics and Statistics 233 (2): 159–187. Search in Google Scholar

De Grauwe, P., Y. Ji (2013), Fiscal Implications of the ECB’s Bond Buying Program. Open Economies Review 24 (5): 843–852. Search in Google Scholar

Dornbusch, R. (1976), Expectations and Exchange Rate Dynamics. Journal of Political Economy 84: 1161–1176. Search in Google Scholar

Fève, P., J. Matheron, J. -G. Sahuc (2009), On the Dynamics Implications of News Shocks. Economics Letters 102 (2): 96–98. Search in Google Scholar

Fischer, S. (1979), Anticipations and the Nonneutrality of Money. Journal of Political Economy 87 (2): 225–252. Search in Google Scholar

Friedman, M. (1977), Nobel Lecture: Inflation and Unemployment. Journal of Political Economy 85 (3): 451–472. Search in Google Scholar

Fujiwara, I., Y. Hirose, M. Shintani (2011), Can News be A Major Source of Aggregate Fluctuations? A Bayesian DSGE Approach. Journal of Money, Credit and Banking 43 (1): 1–29. Search in Google Scholar

Galí, J. (2008), Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework. Princeton, Princeton University Press. Search in Google Scholar

Khan, H., J. Tsoukalas (2012), The Quantitative Importance of News Shocks in Estimated DSGE Models. Journal of Money, Credit and Banking 44 (8): 1535–1561. Search in Google Scholar

Leeper, E.M., T.B. Walker, S.-C.S. Yang (2008), Fiscal Foresight and Information Flows. Econometrica 81 (3): 1115–1145. Search in Google Scholar

Mertens, K., M.O. Ravn (2010), Measuring the Impact of Fiscal Policy in the Face of Anticipation: A Structural VAR Approach. Economic Journal 120 (544): 393–413. Search in Google Scholar

Milani, F., J. Treadwell (2012), The Effects of Monetary Policy “News” and “Surprises”. Journal of Money, Credit and Banking 44 (8): 1667–1692. Search in Google Scholar

Moons, C., H. Garretsen, B. van Aarle, J. Fornero (2007), Monetary Policy in the New-Keynesian Model: An Application to the Euro Area. Journal of Policy Modelling 29 (6): 879–902. Search in Google Scholar

Pigou, A. (1927), Industrial Fluctuations. London, Macmillian. Search in Google Scholar

Posch, O., J.F. Rubio-Ramírez, J. Fernández-Villaverde (2011), Solving the new Keynesian model in continuous time. 2011 Meeting Paper 829, Society for Economic Dynamics. Search in Google Scholar

Offick, S., H.-W. Wohltmann (2013), News Shock, Nonfundamentalness and Volatility. Economics Letters 119 (1): 17–19. Search in Google Scholar

Schmitt-Grohé, S., M. Uribe (2012), What’s News in Business Cycles. Econometrica 80 (6): 2733–2764. Search in Google Scholar

Smets, F., R. Wouters (2003), An Estimated Dynamics Stochastic General Equilibrium Model for the Euro Area. Journal of the European Association 1 (5): 1123–1175. Search in Google Scholar

Smets, F., R. Wouters (2007), Shocks and Frictions in U.S. Business Cycles: A Bayesian DSGE Approach. American Economic Review 97 (3): 586–606. Search in Google Scholar

Svensson, L.E.O. (1999), Inflation Targeting as Monetary Policy Rule. Journal of Monetary Economics 43 (3): 607–654. Search in Google Scholar

Taylor, J.B. (1979), Estimation and Control of a Macroeconomic Model with Rational Expectations. Econometrica 47 (5): 1267–1286. Search in Google Scholar

Taylor, J.B. (1994), The Inflation-Output Variability Trade-off Revisited. In Goals, Guidelines, and Constraints Faceing Monetary Policymakers, Federal Reserve Bank of Boston Conference Series 38. Search in Google Scholar

Turnovsky, S.J. (1977), Structural Expectations and the Effectiveness of Government Policy in a Short-Run Macroeconomic Model. American Economic Review 67 (5): 851–866. Search in Google Scholar

Turnovsky, S.J. (1986a), Short-Term and Long-Term Interest Rates in a Monetary Model of a Small Open Economy. Journal of International Economics 20 (3–4): 291–311. Search in Google Scholar

Turnovsky, S.J. (1986b), Monetary and Fiscal Policy Under Perfect Foresight: A Symmetric Two-Country Analysis. Economica 53 (210): 139–157. Search in Google Scholar

Walsh, C.E. (2010), Monetary Theory and Policy. Cambridge, MIT Press (third edition). Search in Google Scholar

Winkler, R.C., H.-W. Wohltmann (2011), On the (De)stabilizing Effects of News Shocks. Economics Letters 114(3): 256–258. Search in Google Scholar

**Received:**2014-5-7

**Revised:**2014-11-26

**Accepted:**2015-3-11

**Published Online:**2016-7-2

**Published in Print:**2016-2-1

©2016 by De Gruyter Mouton