3.1. Households

A representative household maximizes lifetime utility:

(1) \begin{equation}\max_{\left\{ c_{t}\right\} ,\left\{ h_{t}\right\} ,\left\{ i_{t}\right\} ,\left\{ k_{t}\right\} ,\left\{ B_{t}\right\} }E_{0}\sum_{t=0}^{\infty}\beta^{t}\left[\frac{c_{t}^{1-\sigma}}{1-\sigma}-\frac{h_{t}^{1+\nu}}{1+\nu}\right]\end{equation}

subject to the budget constraint:

(2) \begin{equation}P_{t}c_{t}+P_{t}i_{t}+B_{t}+T_{t}=W_{t}^{h}h_{t}(1+\tau_{t})+R_{t}^{k}k_{t-1}+R_{t-1}B_{t-1}+Div_{t}\end{equation}

and the capital accumulation rule with investment adjustment costs:

(3) \begin{equation}k_{t}=(1-\delta)k_{t-1}+\left(1-S\left(\frac{i_{t}}{i_{t-1}}\right)\right)i_{t}.\end{equation}

Above, $P_{t}$ , $W_{t}^{h}$ , $R_{t,}^{k}$ and $R_{t}$ are, respectively, the price of final goods, the wage received by the household, the capital rental rate, and the interest rate on bonds. Further, $c_{t}$ denotes consumption, $B_{t}$ bond holdings, $k_{t}$ capital, $i_{t}$ investments, $Div_{t}$ dividends paid by imperfectly competitive intermediate goods producers, $T_{t}$ lump-sum taxes levied by the government, $\tau_{t}$ is a labor market subsidy rate chosen by the government and $S(\!\cdot\!)$ —a quadratic investment adjustment cost function (with $\left(S(\!\cdot\!)\right)^{'}>0$ and $\left(S(\!\cdot\!)\right)^{''}>0$ ). We assume a standard quadratic cost function $S\left(\frac{i_{t}}{i_{t-1}}\right)=\frac{\kappa}{2}\left(\frac{i_{t}}{i_{t-1}}-1\right)^{2}$ . Finally, $\beta$ denotes the discount rate, $\delta$ the capital depreciation rate, $\sigma$ the inverse of the intertemporal rate of substitution, and $\nu$ is the inverse of the Frisch elasticity of labor supply.

3.2. Producers

Final goods $y_{t}$ used for consumption and investment purposes are assembled by perfectly competitive producers who buy goods $y_{t}(i)$ at price $P_{t}(i)$ and maximize profits:

(4) \begin{equation}P_{t}y_{t}-\int P_{t}(i)y_{t}(i)di\end{equation}

subject to the technological constraint:

(5) \begin{equation}y_{t}=\left(\int y_{t}(i)^{\frac{1}{\mu^{p}}}di\right)^{\mu^{p}},\end{equation}

where $\mu^{p}$ is the steady-state markup. The solution results in the demand function for intermediate goods:

(6) \begin{equation}y_{t}(i)=\left(\frac{P_{t}\left(i\right)}{P_{t}}\right)^{\frac{-\mu^{p}}{\mu^{p}-1}}y_{t}.\end{equation}

Intermediate goods producers combine labor and capital to produce differentiated goods according to technology:

(7) \begin{equation}y_{t}(i)=k_{t-1}^{\alpha}(i)\left(a_{t}n_{t}(i)\right)^{1-\alpha},\end{equation}

where $a_{t}$ is TFP process and $n_{t}(i)$ is the effective number of hours employed by producer i as defined below. They minimize production costs:

(8) \begin{equation}\min_{k_{t-1}\left(i\right),n_{t}\left(i\right)}\left[r_{t}^{k}k_{t-1}\left(i\right)+w_{t}n_{t}\left(i\right)\right].\end{equation}

Next, they solve a pricing problem, maximizing the discounted stream of profits subject to the demand function for their goods. We assume a standard Calvo pricing scheme, with probability $\theta$ of receiving a signal to change the price:

(9) \begin{equation}\max_{P_{t}^{new}\left(i\right),\left\{ y_{t+j}\left(i\right)\right\} _{j=0}^{\infty}}E_{t}\sum_{j=0}^{\infty}\left(\beta\theta\right)^{j}\Lambda_{t+j}\left(\frac{P_{t}^{new}\left(i\right)}{P_{t+j}}-mc_{t+j}\right)y_{t+j}(i).\end{equation}

Here $P_{t}^{new}\left(i\right)$ is the price set by the optimizing firm, $mc_{t}$ is the real, marginal cost of production and $\Lambda_{t}$ is the marginal utility of consumption of the representative household.

3.3. Skill accumulation and lockdown

Like in Chang et al. (Reference Chang, Gomes and Schorfheide2002), workers own skills $x_{t}$ which increase the effective hours used by producers. However, at the same time they can be forced by the lockdown (i.e. administrative supply-side measures) to set a part $l_{t}$ of the workforce idle:

(10) \begin{equation}n_{t}(i)=x_{t}(1-l_{t})h_{t}(i).\end{equation}

The way we introduce the lockdown is thus in the spirit of Guerrieri et al. (Reference Guerrieri, Lorenzoni, Straub and Werning2020) and Baqaee and Farhi (Reference Baqaee and Farhi2021). Our approach is also in line with findings of Brinca et al. (Reference Brinca, Duarte and e Castro2020) that 2/3 of labor force adjustment in the US stemmed from supply shocks. We compare our way of introducing the lockdown with using a TFP shock (an alternative method popular in the literature to model lockdown/COVID pandemic) in Appendix C.

Agents accumulate skills $x_{t}$ when they work:

(11) \begin{equation}\frac{x_{t}}{x}=\left(\frac{x_{t-1}}{x}\right)^{\phi}\left(\frac{(1-l_{t-1})h_{t-1}}{h}\right)^{\mu}.\end{equation}

Since the labor market is competitive, the real wage received by households is as follows:

(12) \begin{equation}w_{t}^{H}=x_{t}(1-l_{t})w_{t}.\end{equation}

3.4. Imperfect information

Agentsdo not posses full information about the persistence of the lockdown. Instead, we assume that they receive a noisy signal about its duration. To be precise, we assume that lockdown $l_{t}$ consists of two components—a temporary one $l_{t}^{T}$ and a persistent one $l_{t}^{P}$ :

(13) \begin{equation}l_{t}=l_{t}^{T}+l_{t}^{P}\end{equation}

(14) \begin{equation}l_{t}^{T}=\varepsilon_{t}^{T}\end{equation}

(15) \begin{equation}l_{t}^{P}=\rho_{Z}l_{t-1}^{P}+\varepsilon_{t}^{P},\end{equation}

where $0<\rho_{Z}<1$ is an autoreggresion coefficient while $\varepsilon_{t}^{P}$ and $\varepsilon_{t}^{T}$ denote persistent and temporary i.i.d. lockdown shocks, respectively. Agents observe only $l_{t}$ , not either of its elements. Moreover, they receive a noisy signal:

(16) \begin{equation}s_{t}=l_{t}^{P}+\varepsilon_{t}^{N}\end{equation}

about its persistent part, where $\varepsilon_{t}^{N}$ is an i.i.d. noise shock (a false information about the lockdown being persistent). Introducing a noisy signal allows to study the role of lockdown information precision. To infer whether the lockdown is persistent or temporary agents solve a Kalman filtering problem (see Appendix A).

3.5. Policymakers

The central bank stabilizes output and inflation by means of a standard Taylor rule

(17) \begin{equation}\frac{R_{t}}{R}=\left(\frac{R_{t-1}}{R}\right)^{\gamma_{R}}\left[\left(\frac{\pi_{t}}{\pi}\right)^{\gamma_{\pi}}\left(\frac{y_{t}}{y}\right)^{\gamma_{y}}\right]^{1-\gamma_{R}}.\end{equation}

The government runs a balanced budget. Every period it collects lump-sum taxes $T_{t}$ and finances the labor market subsidy $\tau_{t}W_{t}^{h}h_{t}$ . The subsidy rate $\tau_{t}$ is set so as to reimburse the fraction $\gamma\in<0,1>$ of wage income foregone due to the lockdown implying that:

(18) \begin{equation}W_{t}^{h}h_{t}(1+\tau_{t})=W_{t}x_{t}h_{t}\left(1-l_{t}\right)+\gamma W_{t}x_{t}h_{t}l_{t}.\end{equation}

This yields the following:

(19) \begin{equation}\tau_{t}=\frac{\gamma l_{t}}{1-l_{t}}.\end{equation}

Note that if $\gamma=0$ there is no subsidy, while if $\gamma=1$ the government fully compensates households the impact of lockdown on wages.

3.6. Market clearing

The model is closed by standard market clearing conditions. In particular, the goods market clears according to:

(20) \begin{equation}c_{t}+i_{t}+S\left(\frac{i_{t}}{i_{t-1}}\right)i_{t}=y_{t}.\end{equation}

3.7. Calibration

We calibrate the model to the US economy and present parameter values in Table 1. Since the new Keynesian core of the model is standard, we follow the existing literature in its calibration. In particular, we set the discount rate to $\beta=0.995$ to match a 2% real interest rate on annual basis. In line with standard practice, the depreciation rate $\delta$ is calibrated to 2.5% and the capital share $\alpha=0.33$ . Parameters of the monetary policy rule follow Taylor (Reference Taylor1993). The Calvo parameter of price stickiness sis set to $\theta=0.8$ , somewhat higher than suggested by estimates (e.g. Smets and Wouters (Reference Smets and Wouters2007)) for the US. However, to keep the model concise we consider only one nominal friction (wages are not sticky), as a consequence price stickiness needs to be set at a higher level for the model to match for example the empirical evidence on the transmission of monetary policy shocks.

Table 1.

Calibrated parameters

Now we move to parameters related to the less standard parts of the model. As for the skill accumulation mechanism, we closely follow the estimation presented in Chang et al. (Reference Chang, Gomes and Schorfheide2002). Accordingly, we set $\phi=0.8$ and $\mu=0.11$ , being the means of the posterior distributions in this study.

It is less obvious how to calibrate the information friction. Values of four parameters need to be set: persistent shock autoregression $\rho$ and the standard deviations of $\varepsilon_{t}^{P}$ , $\varepsilon_{t}^{T}$ and $\varepsilon_{t}^{N}$ .^{Footnote 3} We set $\rho=0.9$ to give the persistent lockdown a half-life of approximately one year. This is supposed to reflect the (relatively consistent) publicly available information in Spring/Summer 2020 that it should take between one and two years to develop and introduce a vaccine against COVID-19. The standard deviations of the lockdown shocks are chosen such that they cause a 5% drop in GDP on impact, roughly half of the cumulative decline of US GDP in the first halfof 2020.

Finally, let us concentrate on the volatility of noise. In the literature from which we draw (Blanchard et al. (Reference Blanchard, L’Huillier and Lorenzoni2013)) this is estimated from the US data. However, information there is noisy with respect to technology, something that one can claim was always present in the data. Our case is different, information about the lockdown is fairly recent and unique; hence, estimation on historical US data series would completely miss the point. Instead, we propose an alternative procedure.

First, we note that the noise about the persistent lockdown by definition causes false expectations about the future lockdown. Using Google searches in a number of countries for flights in April and in the Summer as instruments for mobility in period t and $t+1,$ we calculate the degree of lockdown in both periods. To this end, we compare the number of flight searches in 2020 with those in normal times (i.e. 2016–2019). The results seem to be consistent with other measures of mobility, such as those presented by Worldometers.info and data on travel restrictions presented by United Nations World Tourism Organization. In contrast to the latter two sources, our approach allows to calculate the lockdown expected in April for Summer 2020 by comparing searches about flights in Summer conducted in April 2020 with their counterparts from Aprils in previous years. Having the instrument for lockdown and expectations about it, we compute the standard deviation of the noise shock in a simplified signal extraction problem (see Appendix B for more details and formal description). This approach yields the standard deviation of the noise shock of approximately 13%. Given the stylized calibration process, we later conduct an extensive robustness check with respect to this parameter.

4.1. Temporary and persistent lockdown

We start with simulating fundamental lockdown shocks that lower GDP by around 5% on impact. As described in Section 3, our model features two types of such shocks, a temporary and a persistent one. Figure 2 shows the reaction of GDP, consumption, investments, effective labor hours used by firms, skills, and inflation to both shocks. Not surprisingly, in a qualitative sense they work similarly. The reduction of effective labor hours drags GDP down. As income falls, so do consumption and investments. Since households work less, they loose skills. As a result, the skill accumulation mechanism aggravates the initial response widening the wedge between supplied and effective labor even further. Importantly, as the economy faces a supply shock, inflation increases. The main difference between the temporary and persistent lockdowns is quantitative. In the latter case, the scale of output fall is larger following not only an immediate drop in effective labor supply but also agents’ reaction to the expected prolonged slowdown.

Figure 2.

Impulse responses to fundamental lockdown shocks. Note: values are expressed in percentage deviations from the steady state, with the exception of inflation expressed in percentage points. The time unit is one quarter.

4.2. Noise about persistent lockdown

Let us now move to our second point of interest—what happens when agents receive a signal that a persistent lockdown started? In what follows we will assume that the signal was false, no lockdown occurs in reality. Hence, impulse responses in this subsection present reactions to pure noise, not contaminated by any physical lockdown, whether temporary or persistent.

Having received the signal agents expect an economic contraction. In response, households lower consumption and investments (Figure 3). As a consequence, output declines and firms lower labor demand. The drop in labor hours translates into skill deterioration that makes the downturn last longer. Thus, the responses of macroeconomic aggregates to the noise shock resemble their counterparts in the case of fundamental shocks. Interestingly, this also holds for inflation as firms expect marginal costs to increase. Hence, in contrast to technology noise shocks studied in the earlier literature (e.g. Blanchard et al. (Reference Blanchard, L’Huillier and Lorenzoni2013), Hürtgen (Reference Hürtgen2014)), the lockdown noise shock is inflationary. Importantly, the response to the noise shock is economically significant. One standard deviation of noise shock lowers GDP on impact by more than half of the response to fundamental shocks.

Figure 3.

Impulse responses to the noise about lockdown. Note: values are expressed in percentage deviations from the steady state, with the exception of inflation presented in percentage points. The time unit is one quarter.

It should be kept in mind that we assumed a relatively fast way of learning which, so far, seems to corresponds well with uncertainty about lockdown persistence that is rather a short-term phenomenon. However, historically some forms of imperfect information have affected macroeconomic dynamics for many years (see e.g. Suda (Reference Suda2018)). Under some negative circumstances (e.g. repeated emergence of vaccine-resistant mutations), the COVID-related uncertainty can also exert an impact on the economy that lasts much longer than our simulations suggest.

4.3. Noise and information precision

We are now ready to discuss our main point of interest—the role of information precision. In this section, we look how it affects the impact of the noise shock. The next section shows how information precision affects the transmission of fundamental lockdown shocks.

Figure 4 shows how the impact of the noise shock on GDP on impact depends on the noise volatility. Interestingly, the resulting curve is U-shaped. If the noise volatility is very small, it has little impact on macroeconomic variables since agents can tell apart persistent and temporary lockdown shocks. However, if it is very large, the signal about persistent lockdown becomes so noisy that agents attach little probability that it may convey information about fundamental lockdown. As a result, the impact of the noise shock decreases above a certain parameter value—in our case it is around 0.2, somewhat exceeding our calibration (0.135). An interesting and potentially important consequence of the U-shaped relationship can be observed when information is initially very noisy, that is we are in the right end of the figure. In this case, improving its precision only slightly may actually deepen the fall in GDP and hence be undesirable. Under such circumstances, only a radical improvement of information precision (i.e. moving to the left end of the figure) helps reduce the impact of noise on the economy. In terms of robustness check, it should be noted that, except for the case of a very precise signal, the noise has a significant impact on GDP which may be even stronger than under our baseline calibration.

Figure 4.

Initial GDP impulse response to the noise about lockdown conditional on signal precision. Note: The figure presents the reaction on impact of GDP to a noise shock for various levels of standard deviation of noise shocks.

To complete the picture, we also investigate how the GDP response to the noise shock depends on the volatility of lockdown shocks. Figure 5 presents the initial (first period) GDP reaction to the noise shock as a function of volatilities of two shocks: persistent and temporary lockdown keeping constant the baseline noise volatility. Fundamental shock volatilities matter as they impact the noise to signal ratio in the filtering problem. Indeed, when either persistent or temporary volatility is zero, noise does not influence agents’ decisions. In this case, they can easily infer about fundamental shocks; thus, they ignore noise. By the same token, noise shocks are of little importance when the variance of one fundamental shock is unproportionally small compared to the other. Only when both variances are substantial, do agents find it difficult to distinguish between the two fundamental shocks. In this case, noisy signals strongly shape their expectations about the future downturn caused by the lockdown.

Figure 5.

Initial GDP impulse responses to the noise shock conditional on $\sigma^{T}$ and $\sigma^{P}$ . Note: The figure presents the reaction on impact of GDP to a noise shock for various volatilities of fundamental lockdown shocks.

4.4. Lockdown shocks and information precision

So far we have seen how the impact of the noise shock depends on the signal precision. Let us now move to our final problem—whether and how information precision affects the responses to fundamental lockdown shocks. To address this point, Figure 6 shows reaction functions of GDP to persistent and temporary lockdown shocks for three levels of information precision—perfect information (agents perfectly observe both components of lockdown, i.e. $\sigma^{N}=0$ ), baseline calibration ( $\sigma^{N}=0$ .135), and no signal (the signal about the persistent lockdown is uninformative $\sigma^{N}\rightarrow\infty$ ). Under the baseline calibration, impulse responses are the same as on Figure 2. Assuming perfect information agents observe persistent and temporary lockdowns separately and hence do not confuse them. As a result, they do not react as strongly to the temporary shock (which under imperfect information they confuse with the persistent one) and react more strongly to the persistent lockdown. At the opposite extreme, when agents do not receive meaningful signal about the persistent lockdown they are highly confused and strongly overreact to the temporary shock, while underreacting to the persistent lockdown. Reactions are corrected over time, as new information allows agents to better distinguish the shocks.

Figure 6.

GDP response to lockdown shocks conditional on signal precision. Note: The figure presents impulse responses to one standard deviation shocks. The time unit is one quarter.

Importantly, these differences are not only intuitive in a qualitative sense but also significant from the quantitative perspective. To focus attention, the GDP reaction on impact to a persistent shock is almost twice as strong under perfect information than in the no-signal case. As a mirror reflection, a temporary shock affects output in the first quarter twice as strong when no signal is provided than under perfect information.

4.5. Policy implications

So far we argued that noisy information can affect the impact of the lockdown on the economy or can itself be a source of economic fluctuations. We believe that these findings call for formulating policy conclusions. This is especially important in the context of the ongoing COVID-19 pandemic and the pressing question how public authorities should design and communicate the lockdown policy. Before addressing this question, we would like to stress that, since we do not explicitly account for the pandemic in our setup, a lockdown obviously deteriorates welfare and it is pointless to optimize policy with respect to it. Only if lockdown explicitly saved lives in the model, it could be an optimal policy.

Hence, in formulating policy conclusions we will assume that policymakers have reasons, that originate beyond our model, to introduce a lockdown. In particular, we assume that they intend to achieve a given economic slowdown (and a related fall in social interactions) that perfectly reflects the fundamental impact of the lockdown. Any further (positive or negative) macroeconomic effects related in particular to miscommunication are assumed undesired.

Noisy communication has two unwelcome effects: (i) a false (noisy) signal about a lockdown can be interpreted as a true one and cause an unwelcome contraction and (ii) a true signal can be wrongly interpreted as being false and hence weaken the effects of the lockdown that authorities wish to introduce. What are the consequences for information policy? Under the assumption formulated above, precise information is clearly in the interest of public authorities. While this conclusion may not come by surprise, our model offers further important insights.

First, a quantitative one. Both the impact of noise shocks and the way the presence of noise modifies fundamental impulse responses can be quantitatively important. To recall but one effect, as Section 4.4 documents, the initial reaction of the economy to a lockdown shock can be even twice as strong under perfect than under imperfect information. This means that information policy can indeed make a substantial difference to how the economy (and as a result the epidemic) reacts to lockdown policy.

Second, as the reaction of output to noise shocks is U-shaped in noise volatility (see Section 4.3), optimal policy conclusions are more nuanced than just a simple call for more precision. If information is very noisy, then only a radical improvement will decrease the role of noise shocks. Half-measures may in contrast prove counterproductive.

Having said this, one should remember that noisy information about the pandemic and the lockdown does not only stem from the authorities. Both the public and the private sectors face uncertainty concerning the evolution of the pandemic. Consequently, there is plenty of information concerning the future course of the pandemic and lockdowns in the public domain, some being true, some false. The public sector may have an information advantage about the lockdown policy and likely pandemic evolution. It also has the means to communicate with the public and possibly to override the cacophony and correct fake news. Our study calls for action is these areas.

5.1. Noise and the structure of the economy

In this section, we analyze what (and to what extent) determines the impact of noise by manipulating standard parameters in the macroeconomic setup (Figure 7).

Figure 7.

Impulse responses to the noise about lockdown depending on selected parameters. Note: GDP expressed in percentage deviations from the steady state, inflation in percentage points. The time unit is one quarter. The size of the shock is one standard deviation.

We begin with a parameter that has been shown to play an important role in the literature on noisy technology—the response to inflation in the Taylor rule. Chahrour and Jurado (Reference Chahrour and Jurado2018) show that low values of this parameter strengthen the impact of noise about productivity on output. In our model, this parameter is important as well (see first row of Figure 7). However, in contrast, in the case of lockdown noise it is a strong monetary policy response that strengthens the reaction. This happens due to the inflationary impact of noise shocks. The central bank reacts to higher inflation by raising interest rates and hence lowers output. Consequently, a weaker response to inflation ( $\gamma_{\pi}=1.25$ ) weakens the reaction of output.

Hysteresis effects seem to be of little importance for our results (second row of Figure 7). In principle, this parameter determines how strongly changes in labor supply affect workers skills. If we switch off the parameter that governs it, such impact is absent. Nevertheless, GDP and inflation reactions to the noise shock change only slightly as compared to the baseline. Similarly, we do not observe much of the impact after doubling the parameter value to reflect that the COVID-19 shock might have led to much stronger deterioration of skills than in the past.

Next, we consider the parameter that determines how the government subsidy to households responds to the lockdown.^{Footnote 4} In the baseline, such subsidy is absent. Here, we allow for either full or 50% reimbursement of the wage income loss ( $\gamma=1$ or $\gamma=0.5$ ). As the third row of Figure 7 indicates, the subsidy attenuates the impact of the noise shock as it narrows down the wedge between the wage effectively paid by firms and received by households. However, even eliminating this wedge completely does not make the impact of the noise shock disappear. This suggests that the more important wedge is the one between households labor supply and labor effectively utilized by firms. To put it differently, in our case it is more important that workers cannot work than that they do not receive the full salary.

Finally, we look at the role of price stickiness. Besides our baseline, value we consider more sticky ( $\theta=0.95$ ) and less sticky prices ( $\theta=0.5$ ). Both increasing and decreasing price stickiness lowers the impact of noise on output and inflation. Thus, interestingly and in contrast to the previously discussed parameters the reaction seems to be non-monotonic. We look further into this issue in the next section.

5.2. Is noise a demand or a supply shock?

As the non-monotonic relation between price stickiness and response to the noise shock calls for more in-depth analysis, the left column of Figure 8 presents the on-impact reaction of output and inflation to the noise shock as a function of $\theta$ . Two interesting features emerge. First, as expected, the response of GDP and inflation is non-monotonic and reaches a minimum (maximum for inflation) at $\theta=0.7$ . Second, the impact on inflation is not only non-monotonic but also changes the sign. For low values of $\theta$ inflation declines (and hence, given the negative GDP reaction, noise behaves like a demand shock), while under higher price stickiness inflation increases (looks like a supply shock). These features seem puzzling, especially that fundamental shocks behave more predictably. In the remaining columns, we plot for comparison reactions on impact to a persistent lockdown and a time preference shock.^{Footnote 5} Clearly, bothfunctions are monotonic and both shocks have a well-defined supply (lockdown) or demand (preference) nature for allvalues of $\theta$ .

Figure 8.

Responses of GDP to selected shocks depending on price stickiness. Note: GDP expressed in percentage deviations from the steady state, inflation in percentage points.

Let us first explain the changing demand/supply nature of the noise shock. In order to understand it better, it is useful to consider its demand and supply effects. As for the former, it affects households’ spending as they feel poorer and reduce consumption. If prices are allowed to adjust freely (low $\theta$ ), this leads, as expected, to lower inflation. However, when prices are sticky, supply effects dominate. After receiving a noisy signal, intermediate good producers initially expect a persistent lockdown. Thus, they foresee costs to increase and hence, those who are allowed to adjust prices, raise them. This explains why under sticky prices the reaction of inflation is reversed and supply-side effects dominate.

Let us now explain why the reactions are non-monotonic in $\theta$ ? When prices are very sticky and $\theta$ approaches unity, the impact of the shock on inflation becomes low again. This is not surprising. But why does the impact on GDP become low as well? We see a role for monetary policy in the explanation. Since due to price stickiness inflation hardly changes, the monetary policy trade-off between inflation and output stabilization vanishes and the central bank can set nominal interest rates to counteract the output drop. As a consequence, the reaction of output becomes small as well.