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The Scars of Supply Shocks
Luca Fornaro and Martin Wolf∗
This version: April 2021
First version: October 2020
Abstract We study the effects of supply disruptions - for instance caused by the emergence of a pandemic - in an economy with Keynesian unemployment and endogenous productivity growth. By negatively affecting investment, even purely transitory negative supply shocks generate permanent output losses. The associated negative wealth effect depresses consumers’ demand, which may even fall below the exogenous fall in supply. In this case, the optimal monetary policy response flips relative to conventional wisdom, as monetary expansions are needed to fight negative output gaps. If monetary policy is not expansionary enough a supply-demand doom loop emerges, causing a recession characterized by unemployment and weak productivity growth. Innovation policies, by fostering firms’ investment, can restore full employment and healthy growth.
JEL Codes: E22, E31, E32, E52, E62, O Keywords: supply shocks, Covid-19, hysteresis, investment, endogenous growth, monetary policy, fiscal policy, zero lower bound, Keynesian growth, stagnation traps.
∗Luca Fornaro: CREI, Universitat Pompeu Fabra, Barcelona GSE and CEPR; LFornaro@crei.cat. Martin Wolf: University of St. Gallen and CEPR; martin.wolf@unisg.ch. This paper builds on and extends our earlier work “Covid- 19 Coronavirus and Macroeconomic Policy”. We thank Cristiano Cantore, Davide Debortoli, Jordi Gali, Vaishali Garga, Gaston Navarro, Ludwig Straub and seminar/conference participants at the Bank of England, the Federal Reserve Board, the World Bank and CREI for very helpful comments. We are grateful to Selena Tezel for excellent research assistance. Luca Fornaro acknowledges financial support from the European Research Council under the European Union’s Horizon 2020 research and innovation program, Starting Grant (851896-KEYNESGROWTH) and the Spanish Ministry of Economy and Competitiveness, through the Severo Ochoa Programme for Centres of Excellence in RD (CEX2019-000915-S), and from the Generalitat de Catalunya, through CERCA and SGR Programme (2017-SGR-1393).
1 Introduction
The ongoing Covid-19 pandemic - by forcing factories to shut down and disrupting global supply chains - is causing substantial damage to the productive capacity of the economy. Moreover, many commentators and policy institutions expect the Covid-19 shock to leave deep scars, by inducing a very persistent drop in output below its pre-pandemic trend (e.g., Wolf, 2020; IMF, 2020).^1 These facts have renewed interest in the macroeconomic implications of negative supply shocks. How do supply disruptions affect aggregate demand? What are the optimal monetary and fiscal responses to negative supply shocks? These questions are at the forefront of the current debate. Much of the conventional thinking about these issues builds on the New Keynesian paradigm (Gal´ı, 2009). In the New Keynesian model, following a negative supply shock demand contracts less than supply, and so the natural interest rate rises. The optimal policy response then entails a monetary tightening, to prevent the economy from experiencing excessive demand, overheating and inflation above target. The New Keynesian framework, however, assumes that after the shock dissipates the economy quickly bounces back to its pre-shock trend, and so does not allow for the possibility that supply disruptions might have scarring effects. This paper provides a theory in which negative supply shocks may leave persistent scars on the economy, and shows that this effect might radically change the macroeconomic implications of supply disruptions relative to the traditional view. Our idea is that negative supply shocks - even if purely transitory - induce firms to reduce investment, and thus destroy the future productive capacity of the economy. The associated drop in wealth depresses consumers’ demand, which may even fall below the reduction in supply. In this case, the natural interest rate declines and the optimal monetary policy response flips relative to conventional wisdom, as monetary expansions are needed to fight insufficient demand and negative output gaps. Moreover, fiscal interventions aiming at sustaining investment may be a crucial complement to monetary policy in stabilizing aggregate demand. To formalize these insights, we provide a Keynesian growth framework with two key features. First, as in standard models of vertical innovation (Aghion and Howitt, 1992), firms invest in innovation in order to appropriate future monopoly rents. Second, as in the New Keynesian tradition, the presence of nominal rigidities implies that output may deviate from its potential level. Our theory thus combines the Keynesian insight that unemployment may arise due to weak aggregate demand, with the notion, developed by the endogenous growth literature, that sustained productivity growth is the result of investment in innovation by profit-maximizing agents. We study the response of the economy to supply disruptions, modeled as standard negative (^1) For instance, the Covid-19 pandemic has lead the International Monetary Fund to revise substantially downward its forecast for the growth rate of global real GDP per capita for the 2019-2025 period, relative to its pre-pandemic projections. In its October 2020 World Economic Outlook (IMF, 2020), the IMF writes: “The medium-term pro- jections also assume that the economies will experience scarring from the depth of the recession”. Interestingly, the IMF has recently revised upward its projections for medium run growth in the United States, in response to the fiscal expansion envisaged by the Biden’s administration (see the April 2021 World Economic Outlook). Underpinning this revision is the idea that fiscal stimulus might reverse the scarring effects triggered by the Covid-19 recession, and lead to persistent improvements in potential output.
help to rationalize the experience of the 1970s oil shocks, which were followed by high inflation, high unemployment, as well as low productivity growth (Blanchard and Gali, 2007). We finally turn to fiscal interventions aiming at boosting future potential output, such as the forthcoming Biden’s infrastructure plan. We show that these policies can complement monetary interventions as demand stabilization tools. By stimulating firms’ investment and productivity growth, in fact, these fiscal interventions also foster consumers’ demand. Through this force, a policy typically associated with the supply side of the economy can help sustain demand and employment. In fact, we show that when monetary policy does not stimulate demand enough to close the output gap, as it is the case during liquidity traps, it is optimal for the government to foster investment and future potential output, in order to bring the economy closer to full employment. This paper is related mainly to two strands of the literature. First, it is connected to a recent literature, motivated by the Covid-19 epidemic, revisiting the macroeconomic implications of supply disruptions. Guerrieri et al. (2020) study an economy with multiple consumption goods. In their model, a shock reducing the supply of some goods may induce consumers to cut spending also on those goods not directly affected by the shock. If this effect is strong enough, aggregate demand falls by more than supply. They dub supply shocks with this property Keynesian supply shocks. Baqaee and Farhi (2020) derive a similar result in an economy with production networks and multiple intermediate goods. Caballero and Simsek (2020) show that supply shocks can be Keynesian due to spillovers between asset prices and aggregate demand. In Bilbiie and Melitz (2020) supply disruptions depress demand by inducing firms’ exit, while in L’Huillier et al. (2021) Keynesian supply shocks emerge due to the presence of diagnostic expectations.^2 Our paper studies a different - and complementary - channel through which supply shocks can become Keynesian, based on the endogenous response of investment and productivity growth.^3 Second, this paper is related to the literature unifying the study of business cycles and en- dogenous growth. Some examples of this literature are Fatas (2000), Comin and Gertler (2006), Benigno and Fornaro (2018), Moran and Queralto (2018), Anzoategui et al. (2019), Bianchi et al. (2019), Queralto (2019), Garga and Singh (2020), Cozzi et al. (2021) and Vinci and Licandro (2020).^4 Among this body of work, this paper is closest to Benigno and Fornaro (2018) and Garga and Singh (2020). Our paper builds on the framework introduced by Benigno and Fornaro (2018), who study an endogenous growth model with vertical innovation and nominal wage rigidities. They show that in this Keynesian growth framework fluctuations can be driven by animal spirits, and derive the optimal monetary and fiscal policy. Garga and Singh (2020) derive, in a similar Key- nesian growth mode, the optimal monetary policy response to fundamental demand shocks. Our paper, instead, employs a Keynesian growth model to study supply shocks. To the best of our (^2) See Bilbiie (2008) for an early model in which supply shocks have Keynesian features. (^3) In our own earlier work (Fornaro and Wolf, 2020), we argued that permanent negative supply shocks can be Keynesian. In this paper, we move beyond the analysis in Fornaro and Wolf (2020) by providing a Keynesian growth model in which productivity growth is the result of firms’ investment. We show that temporary negative supply shocks can be Keynesian by triggering endogenous drops in investment and productivity growth. 4 See Cerra et al. (2020) for a recent survey of this literature.
knowledge, we are the first to show that the scars of supply shocks may change dramatically the macroeconomic implications of supply disruptions. The rest of the paper is composed of five sections. Section 2 describes the baseline model. Section 3 derives the optimal monetary policy, and shows that the natural interest rate may fall after a supply disruption. Section 4 discusses the implications of imperfect monetary stabilization and the supply-demand doom loop. Section 5 studies optimal innovation policies. Section 6 con- cludes. Appendix A provides the proofs of all propositions, while Appendix B contains additional derivations, as well as model extensions.
2 Baseline model
This section lays down our baseline Keynesian growth model. The economy has two key elements. First, the rate of productivity growth is endogenous, and it is the outcome of firms’ investment. Second, the presence of nominal wage rigidities implies that output and employment can deviate from their potential levels. In order to illustrate transparently our key results, the framework in this section is kept voluntarily simple. Throughout the paper, however, we will extend this baseline framework in several directions. Consider an infinite-horizon closed economy. Time is discrete and indexed by t ∈ { 0 , 1 , 2 , ...}. The economy is inhabited by households, firms, and by a government that sets monetary and fiscal policy. For simplicity, we focus on a perfect foresight economy.
2.1 Households
There is a continuum of measure one of identical households deriving utility from consumption of a homogeneous “final” good. The lifetime utility of the representative household is
∑^ ∞ t=
βt^ log Ct, (1)
where Ct denotes consumption and 0 < β < 1 is the subjective discount factor. Each household is endowed with L¯ units of labor and there is no disutility from working. However, due to the presence of nominal wage rigidities to be described below, a household might be able to sell only Lt < L¯ units of labor on the market. Moreover, households can trade in one-period, non-state contingent bonds Bt. Bonds are denominated in units of currency and pay the nominal interest rate it. Finally, households own all the firms and each period they receive dividends Dt from them. The problem of the representative household consists in choosing Ct and Bt+1 to maximize expected utility, subject to a no-Ponzi constraint and the budget constraint
PtCt + (^) 1 +Bt+1 i t = WtLt + Bt + Dt,
This expression implies that each monopolist charges a constant markup 1/α > 1 over its marginal cost. Equations (6) and (7) imply that the quantity produced of a generic intermediate good j is
xj,t = α 1 −^2 α^ Aj,tZtLt. (8)
Combining equations (4) and (8) gives
Yt = α 12 −αα AtZtLt, (9)
where At ≡
0 Aj,tdj^ is an index of average productivity of the intermediate inputs.^ Hence, production of the final good is increasing in the average productivity of intermediate goods, in the exogenous component of labor productivity, and in the amount of labor employed in production. The profits earned by the monopolist in sector j are given by
(Pj,t − Pt)xj,t = Pt$Aj,tZtLt,
where $ ≡ (1/α − 1)α^2 /(1−α). According to this expression, the producer of an intermediate input of higher quality earns higher profits. Moreover, profits are increasing in ZtLt due to the presence of a market size effect. Intuitively, high production of the final good is associated with high demand for intermediate inputs, leading to high profits in the intermediate sector.
2.4 Investment and productivity growth
Firms operating in the intermediate sector can invest in innovation in order to improve the quality of their products. In particular, a firm that invests Ij,t units of the final good sees its productivity evolve according to Aj,t+1 = Aj,t + χIj,t, (10)
where χ > 0 determines the productivity of investment. Innovation-based endogenous growth models typically assume that knowledge is only partly excludable. For instance, this happens if inventors cannot prevent others from drawing on their ideas to innovate. For this reason, in most endogenous growth frameworks, the social return from investing in innovation is higher than the private one.^6 A simple way to introduce this effect in the model is to assume that every period, after production takes place, there is a constant probability 1 − η that the incumbent firm dies, and is replaced by another firm that inherits its technology. This assumption encapsulates all the factors that might lead to the termination of the rents from innovation, including patent expiration and imitation by competitors. Firms producing intermediate goods choose investment in innovation to maximize their dis- (^6) See for instance Aghion and Howitt (1992).
counted stream of profits net of investment costs
∑^ ∞ t=
(βη)t PtCt^ (Pt$Aj,tZtLt^ −^ ηPtIj,t)^ ,^ (11)
subject to (10) and given the initial condition Aj, 0 > 0. Since firms are fully owned by domestic households, they discount profits using the households’ discount factor βt/(PtCt), adjusted for the survival probability η. From now on, we assume that firms are symmetric and so Aj,t = At. Moreover, in our base- line model we focus on equilibria in which investment in innovation is always positive. Optimal investment in research then requires^7
1 χ =^
βCt Ct+
$Zt+1Lt+1 + (^) χη
Intuitively, firms equalize the marginal cost from performing research 1/χ, to its marginal benefit discounted using the households’ discount factor. The marginal benefit is given by the increase in next period profits ($Zt+1Lt+1) plus the savings on future research costs 1/χ, adjusted for the firm survival probability η.
2.5 Aggregation and market clearing
Market clearing for the final good implies^8
Yt −
0
xj,tdj = Ct + It, (13)
where It ≡
0 Ij,tdj. The left-hand side of this expression is the GDP of the economy, while the right-hand side captures the fact that all the GDP has to be consumed or invested. Using equations (8) and (9) we can write GDP as
Yt −
0
xj,tdj = ΨAtZtLt, (14)
where Ψ ≡ α^2 α/(1−α)(1 − α^2 ). The assumption about labor endowment implies that Lt ≤ L¯. Since labor is supplied inelasti- cally by the households, L¯ − Lt can be interpreted as the unemployment rate. For future reference, when Lt = L¯ we say that the economy is operating at full employment, while when Lt < L¯ the (^7) See Appendix B.1 for the derivation of equation (12). (^8) The goods market clearing condition can be derived by combining the households’ budget constraint with the expression for firms’ profits
Dt = PtYt − WtLt − Pt α^1
∫ (^1) ︸ ︷︷ 0 xj,tdj︸ profits from final goods sector
∫ (^1) 0
( (^1) α −^1
) xj,tdj − Pt
∫ (^1) ︸ ︷︷ 0 Ij,tdj︸ profits from intermediate goods sector
.
We also use the equilibrium condition Bt+1 = 0, which is implied by the assumption of identical households.
in wages puts upward pressure on marginal costs and leads to a rise in prices, while a rise in productivity reduces marginal costs and prices. This expression, combined with the law of motion for wages, can be used to derive an equation for price inflation
πt ≡ (^) PPt t− 1
which implies that gross price inflation is constant and normalized to 1. This property of the baseline model is convenient, because it will allow us to focus attention on the two key variables at the heart of our analysis: employment and productivity growth. Later on, in Section 4.4, we will consider the implications of our model for inflation. Monetary policy controls the nominal rate it. For now, we leave the central bank behavior unspecified. Throughout the paper, we will consider different monetary policy regimes.
2.7 Equilibrium
Given a path for it, the equilibrium of the economy can be described by three simple equations. The first equation captures the demand side of the economy. Start with the Euler equation, which determines households’ consumption decisions. Combining households’ optimality conditions (2) and (3) gives 1 Ct^ =^ β(1 +^ it)^
Ct+1πt+^. According to this expression, demand for consumption is increasing in future consumption and decreasing in the real interest rate, (1 + it)/πt+1. To understand how productivity growth relates to demand for consumption, it is useful to combine the previous expression with At+1/At = gt+1 and πt+1 = 1 to obtain
ct = (^) βgt(1 ++1ct +1i t)^
where we have defined ct ≡ Ct/At as consumption normalized by the productivity index. This equation implies a positive relationship between productivity growth and present demand for con- sumption. The reason is that faster productivity growth is associated with higher future wealth. This wealth effect leads households to increase their demand for current consumption in response to a rise in productivity growth. The second key relationship in our model is the growth equation, which is obtained by combining equation (2) with the optimality condition for investment in research (12)
gt+1 = β (^) cct t+ (χ$Zt+1Lt+1 + η). (20)
This equation implies a positive relationship between growth and future market size. Intuitively, a rise in Zt+1Lt+1 is associated with higher future monopoly profits. In turn, higher profits induce entrepreneurs to invest more in research, leading to a positive impact on the growth rate of the
economy. This is the classic market size effect emphasized by the endogenous growth literature.^10 At the same time, growth depends inversely on the growth rate of normalized consumption ct+1/ct. This is a cost of funds effect: when today’s consumption is low, relative to future consumption, firms pay out dividends to households rather than invest. Both the market size effect and the cost of funds effect will play an important role in mediating the impact of supply shocks on investment and growth. The third equation combines the goods market clearing condition (13), the GDP equation (14) and the fact that It/At = (gt+1 − 1)/χ
ΨZtLt = ct + gt+1 χ^ − 1. (21)
Keeping output constant, this equation implies a negative relationship between productivity- adjusted consumption and growth, because to generate faster growth the economy has to devote a larger fraction of output to investment, reducing the resources available for consumption. We are now ready to define an equilibrium as a set of sequences {gt+1, Lt, ct}+ t=0∞ satisfying the three equations (19), (20) and (21), as well as Lt ≤ L¯, gt+1 > 1 and ct > 0 for all t ≥ 0, given paths for monetary policy {it}+ t=0∞ and the supply shock {Zt}+ t=0∞.
2.8 The balanced growth path
Before studying the implications of the model, let us spend a few words on the balanced growth path - or steady state - of the economy. A steady state is characterized by constant values for gt+1, Lt, ct, it and Zt that satisfy equations (19)-(21). For most of the paper, we will be studying economies that fluctuate around a full employment steady state. From now on, we will denote the value of a variable in this steady state with an upper bar, and we normalize steady state productivity to Z¯ = 1. We now make some assumptions to ensure that a full employment steady state exists.
Proposition 1 Suppose that the parameters satisfy
β(χ$ L¯ + η) > 1 , (22)
and that monetary policy is such that
1 + ¯i = χ$ L¯ + η. (23)
Then there exists a unique full employment steady state. Moreover, this steady state is characterized by ¯g > 1. (^10) To be clear, what matters for our results is that productivity growth is increasing in employment relative to potential. This means that our key results would also apply to a setting in which scale effects related to population size were not present. For instance, in the spirit of Young (1998) and Howitt (1999), these scale effects could be removed by assuming that the number of intermediate inputs is proportional to population size.
More precisely, assume that firms’ investment has no impact on productivity growth (χ = 0), and that Zt follows the process log Zt = ρ log Zt− 1 , (24)
where 0 ≤ ρ < 1 determines the persistence of the exogenous component of productivity. Now suppose that the economy is hit by a previously unexpected negative supply shock, which corresponds to the initial condition Z 0 < 1. The path of the interest rate that implements the allocation under the optimal policy is then given by^12
1 + it = Z βZt+ t
= Z
ρt(ρ−1) 0 β.^ (25)
Since Z 0 < 1, this expression implies that the policy rate increases in response to a temporary supply disruption. In absence of a monetary policy tightening, in fact, the negative supply shock would trigger excess demand for consumption. This result forms part of the conventional wisdom on the optimal conduct of monetary policy. As we will see, however, this conventional wisdom might fail once the impact of supply shocks on investment and productivity growth is taken into account.
3.2 Back to the Keynesian growth framework
We now present our first, and perhaps most striking, result: in an economy in which productivity growth is driven by firms’ investment, a negative supply shock might trigger a demand shortage that is larger than the supply disruption itself. When this happens, the natural rate declines in response to the shock. The optimal monetary policy response therefore consists in cutting the policy rate.
Proposition 3 Assume that Zt is governed by the process (24), and that Z 0 < 1. If ρ > 0 , the path of interest rates that implements the allocation under optimal policy is characterized by it < ¯i for all t ≥ 0. If ρ = 0, optimal policy implies it = ¯i for all t ≥ 0.
To understand Proposition 3, let us start by studying the behavior of investment and produc- tivity growth. By equation (20), under the optimal monetary policy productivity growth evolves according to gt+1 = β (^) cct t+
χ$Zt+1 L¯ + η
There are two channels through which the supply shock reduces growth. First, a transitory drop in Zt leads to a drop in ct/ct+1. This corresponds to an increase in the rate at which households discount future profits, reducing firms’ incentives to invest. Moreover, if the shock is persistent, the fall in Zt+1 lowers the profits that firms appropriate by investing in innovation. Both effects point toward a negative impact of supply disruptions on investment and productivity growth. (^12) To derive this expression, notice that if χ = 0 then gt+1 = 1 and ct = ΨZtLt for every t.
What are the implications for aggregate demand? The fall in investment constitutes a drag on demand in itself. Quantitatively, this effect is stronger the higher the share of investment in GDP. Now imagine that, following standard practice in the endogenous growth literature, we interpret firms’ investment in innovation as their expenditure in R&D. Given that spending in R&D represents a small fraction of GDP, in this case the direct impact of fluctuations in investment on innovation on aggregate demand will be small. There is, however, a second channel through which a fall in investment depresses aggregate demand. Lower investment drives down productivity growth and so agents’ future income. This negative wealth effect causes a drop in consumption demand. This second effect, on its own, might be strong enough to reverse the response of the natural rate to a supply shock, relative to the case in which productivity growth is exogenous. To see this point most clearly, consider the limit case where the investment share of GDP goes to zero, so that ct ≈ ΨZt L¯. From (19), the natural interest rate then evolves according to
1 + it = gt+1 βcct+ t
= gt+1Z
ρt(ρ−1) 0 β.^ (27)
This expression shows how the endogenous drop in gt+1 puts downward pressure on the natural rate. As we show in Proposition 3, as long as the supply disturbance has some persistence (ρ > 0), this effect is strong enough to induce a drop in the natural rate after a negative supply shock. To further illustrate this point, we resort to a simple numerical simulation.^13 We choose the length of a period to correspond to one year. We set χ, β and α by targeting three moments of the full employment steady state. χ is set to 1.95 so that steady state productivity growth is equal to 2%, while we choose β = 0.995 so that the real interest rate in steady state is equal to 2.5%. We set the labor share in gross output to 1 − α = 0.86, to match a ratio of spending in investment on innovation to GDP of 2%, close to the GDP share of business spending in R&D observed in the United States. This calibration choice implies a small direct impact of investment fluctuations on aggregate demand. To set the firm survival probability we follow Benigno and Fornaro (2018) and set η = 0.9. Finally, the shock is parametrized so that on impact GDP drops by 3% under the optimal monetary policy, and its persistence is set to ρ = 0.75. Figure 1 illustrates how the economy responds to a supply disruption when monetary policy is conducted optimally. Under the exogenous growth counterfactual optimal policy would prescribe a monetary tightening. But once the endogenous response of productivity growth is taken into account the optimal policy entails a fall in the interest rate. Moreover, the figure highlights another interesting aspect of the optimal policy. While the optimal monetary policy involves closing the output gap, it does not steer output back to its pre-shock trend. Therefore, a permanent drop in the level of output - i.e. the scars of supply shocks - reflects an efficient response of the economy. (^13) To be clear, our objective is not to provide a careful quantitative evaluation of the framework or to replicate any particular historical event. In fact, both of these tasks would require a much richer model. Rather, our aim is to show how the model behaves for some reasonable parameter values.
4 Imperfect stabilization and the supply-demand doom loop
We have seen that under the optimal policy the central bank lowers the policy rate and stimulates aggregate demand in response to supply disruptions. But what happens if monetary policy does not impart enough stimulus to the economy? We now show that, as a result, supply shocks can give rise to recessions characterized by lack of demand, and that the impact of these shocks on output and productivity growth is amplified by a supply-demand doom loop. One could consider several deviations of monetary policy from its optimal stance. To keep the analysis simple, we start by assuming that monetary policy follows the simple rule
1 + it = (1 + ¯i)
( L
t L^ ¯
)φ
. (28)
Under this rule the central bank seeks to stabilize output around its potential level, by cutting the interest rate in response to falls in employment. In addition to condition (23), we assume that
φ > χ$^
L¯
χ$ L¯ + η ,^ (29)
which implies that the steady state under the rule (28) is locally determinate.^15 While focusing on this particular deviation from the optimal policy is analytically convenient, much of the results extend to other cases as well. For instance, monetary policy might end up being constrained by the zero lower bound when trying to pursue the optimal policy. As we discuss later on, the key results obtained under rule (28) also hold when monetary policy is constrained by the zero lower bound.
4.1 An insightful case: a permanent supply disruption
While our focus is on temporary supply disruptions, it is useful to first study a case in which Zt drops permanently to a lower level. The advantage is that, by focusing on a permanent shock, we can illustrate the key forces at the heart of the model using a simple graphical analysis. Figure 2 shows how L and g are determined in steady state. The (GG) schedule corresponds to the growth equation (20) evaluated in steady state, given by
g = β(χ$ZL + η). (GG)
The (GG) schedule implies a positive relationship between g and L. Intuitively, an increase in employment - and so in market size - is associated with a rise in the return from investing in innovation. Naturally, firms respond by increasing investment and productivity growth accelerates. The (AD) curve, instead, summarizes the aggregate demand side of the model. It is obtained (^15) See Appendix B.3 for a proof.
(a) The L − g diagram. (b) A permanent supply disruption. Figure 2: The L − g diagram and permanent supply disruptions.
by combining equations (19) and (28), evaluated in steady state
g = β(1 + ¯i)
( L
L^ ¯
)φ
. (AD)
This equation implies a positive relationship between g and L. To understand the intuition behind this equation, consider what happens after a rise in productivity growth. Due to the associated positive wealth effect, households respond by increasing their demand for borrowing and consump- tion. Higher consumption, in turn, puts upward pressure on employment. The central bank reacts to the rise in employment by increasing the interest rate, which cools down households’ demand for borrowing and restores equilibrium on the credit market. A steady state equilibrium corresponds to an intersection of the (AD) and (GG) curves. Under our assumption about φ, there is only one intersection between the two curves satisfying L ≤ L¯, meaning that the steady state exists and is unique. The steady state shown in the left panel of Figure 2 corresponds to the full employment steady state. Now imagine that we start from the full employment steady state, and a previously unexpected permanent fall in Z occurs. As shown in the right panel of Figure 2, the decline in Z induces a downward shift of the GG curve. As already explained, the exogenous fall in labor productivity depresses firms’ profits and their incentives to invest. Firms react by reducing investment and so, holding constant L, productivity growth g drops. The fall in productivity growth, through its negative wealth effect, translates into lower aggregate demand. The central bank reacts by cutting the policy rate, but not by enough to prevent unemployment from arising. The result is a drop in employment below its efficient level (L < L¯). Therefore, the negative supply shock gives rise to a drop in aggregate demand and involuntary unemployment.^16 (^16) This effect is well known from the literature on news shocks (e.g., Lorenzoni, 2009).
Figure 3: Imperfect monetary stabilization.
the case of temporary shocks, an intertemporal supply-demand doom loop emerges. Figure 3 shows the response of the economy to a negative supply shock, both when monetary policy is conducted optimally and when monetary policy follows the rule (28). We set the response of the policy rate to the output gap to the illustrative value of φ = 0.2. The other model parameters are kept as in Section 3. As shown by the top right panel, under the simple rule on impact GDP falls by an additional 2.5% compared to optimal policy, so that the recession has a substantial component due to weak aggregate demand. Moreover, since weak aggregate demand drags down the endogenous component of productivity growth, the hysteresis effect is also larger under the interest rate rule compared to the optimal policy (lower left panel). Interestingly, the shock has a bigger impact on the economy under rule (28), in spite of the fact that on impact the policy rate in that case falls more compared to the optimal policy benchmark. This is due to agents’ forward looking behavior, coupled with the fact that in the long run monetary policy is more expansionary under the optimal policy compared to rule (28). Summing up, there are two lessons to be learned from this analysis. First, a negative shock which originates from the supply side of the economy can give rise to a slump characterized by lack of demand. Second, lack of demand feeds back into lower investment dragging down productivity growth, which further depresses consumers’ demand. This supply-demand doom loop may greatly amplify the direct impact of negative supply shocks on employment and output growth.
4.3 Supply disruptions and liquidity traps
Another instance of imperfect monetary stabilization occurs when the central bank becomes con- strained by the zero lower bound and the economy enters a liquidity trap. This might happen following a negative supply shock since, as we saw in Section 3, the optimal monetary policy re- sponse to supply disruptions might consist in lowering the policy rate. We give a full treatment of this case in Appendix B.4, here we just outline some key insights, and in particular we show that supply disruptions can give rise to stagnation traps. Imagine that monetary policy is run optimally, but that the policy rate cannot fall below zero (it ≥ 0). The solution to the optimal policy problem can be simply represented as
it(Lt − L¯) = 0. (32)
The economy thus operates at potential (Lt = L¯) whenever the zero lower bound does not bind. But when it = 0 the economy might experience unemployment due to weak aggregate demand (Lt ≤ L¯). Of course, this happens when the natural interest rate becomes negative, and the zero lower bound prevents monetary policy from providing enough stimulus to attain full employment. A large enough negative supply shock, due to its negative impact on consumers’ demand, can therefore make the zero lower bound bind and plunge the economy into a liquidity trap. Moreover, when the lower bound binds the supply-demand doom loop becomes particularly severe, since monetary policy stops responding to changes in employment and aggregate demand altogether.18, Even though monetary policy is conducted optimally, the economy then experiences a recession characterized by weak aggregate demand, involuntary unemployment and low productivity growth, in short a stagnation trap. Indeed, as observed by Benigno and Fornaro (2018), these are typical features of the liquidity trap episodes that have characterized several advanced economies in recent times. This property of the model is also in line with the empirical evidence provided by Wieland (2019), who shows that negative supply shocks hitting Japan during its liquidity trap - such as the 2011 earthquake and oil price hikes - led to contractions in output.
4.4 Implications for inflation
Inflation is commonly used as a key input in constructing output gap measures. Inflation above the central bank target, in fact, is seen as a sign of overheating, while inflation undershooting its target is normally associated with slack and insufficient demand. We now show that a supply disruption, contrary to this logic, might generate both inflation above target and unemployment (^18) In fact, in our simple model, when the zero lower bound binds investment goes all the way to zero. This strong response of investment is due to our assumption of linear investment technology. In presence of diminishing returns to investment on innovation, investment would remain positive even when the zero lower bound binds. 19 As shown by Benigno and Fornaro (2018), when the zero lower bound binds the supply-demand doom loop can be so strong as to generate fluctuations purely driven by animal spirits. In this paper we abstract from this source of multiplicity, by assuming that agents never coordinate their expectations on the stagnation traps steady state described by Benigno and Fornaro (2018). As shown in Benigno and Fornaro (2018), this is the case if an appropriately designed system of strong countercyclical subsidies to investment is in place.
