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Efects ofCovid19 onEuro area GDP andinfation: demand vs. supply disturbances

RobertKollmann1,2,3 Accepted: 6 August 2021 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021 Abstract This paper analyzes the macroeconomic efects of the Covid-19 epidemic on Euro Area (EA) GDP and infation, using a stylized New Keynesian model. Covid is interpreted as a combination of aggregate demand and aggregate supply disturbances. Ofsetting aggregate demand and supply changes are shown to account for the stability of EA infation, in the face of Covid. The evidence presented here indicates that Covid-induced aggregate demand and supply shifts were persistent. An aggregate supply contraction is identifed as the dominant force driving the sharp fall of EA GDP in 2020. Keywords Covid Real activity Infation Aggregate demand Aggregate supply JEL codes E31 E32 E43 E52 E65 1 Introduction The global Covid-19 health crisis that erupted in early 2020 has triggered a sharp contraction in worldwide real activity. This paper studies the response of Euro Area (EA) GDP and infation to the Covid crisis. The Covid epidemic is a very large and truly unexpected and exogenous disturbance. This distinguishes Covid from standard macro shocks in "normal" times. Due to its huge size, the Covid shock is likely to have dominated other macroeconomic disturbances in 2020-2021. Thus it is plausible that macroeconomic developments, in 2020-2021, were mainly caused by Covid. Covid thus provides a unique laboratory for analyzing the determination of * Robert Kollmann r..n@yahoo.com 1 Solvay Brussels School ofEconomics andManagement, Universit Libre de Bruxelles, SBSEM, CP114, ULB, 50 Av. Roosevelt, Brussels1050, Belgium 2 Centre forEconomic Policy Research (CEPR), London, UK 3 ERUDITE, Universit Paris-Est Crteil (UPEC), Crteil, France International Economics and Economic Policy (2021) 18:475-492 / Published online: 28 September 2021 R.Kollmann 1 3 real activity and prices in the face of a large exogenous disturbance. Understanding the transmission of exogenous disturbances is, e.g., important for designing efective policy responses. A vast (and growing) literature has analyzed the economic repercussions of Covid.1 Early studies on the macroeconomic efects of Covid include Eichenbaum etal. (2020) who incorporated an epidemiological model into a Real Business Cycle framework; and Guerrieri etal. (2020) and Pfeifer etal. (2020) who considered New-Keynesian models. The contribution of the present paper is to provide simple analytics of the macroeconomic transmission of Covid, using a stylized New Keynesian model. An important feature of the analysis here is that it compares the adjustment to the Covid shock in a liquidity trap, i.e. a situation in which the zero lower bound (ZLB) constraint for the nominal interest rate binds, to adjustment when the ZLB constraint does not bind. The framework is used to assess the relative role of aggregate demand (AD) and aggregate supply (AS) shifts, during Covid. The use of a liquidity trap model is motivated by the fact that Covid hit the EA (and other advanced economies) in a situation of persistently ultra-low interest rates. With monetary policy interest rates at the zero lower bound (ZLB), the central bank cannot stimulate real activity by lowering the policy interest rate.2 AS shifts are modeled as total factor productivity (TFP) shocks, while AD shifts are modeled as shocks to the household subjective discount rate. As documented below, Covid induced a reduction of EA GDP of about 7.8% in 2020, but Covid only had a negligible efect on infation. The model suggests that the macroeconomic situation under Covid must be interpreted as the outcome of joint AD and AS shocks, whose ofsetting efects stabilized infation. The muted response of infation indicates that Covid did not afect the output gap, so that the Covid-induced contraction of GDP corresponds to the contraction that would have obtained in a fex-price economy. The model suggests that Covid amounted to a 7.8% drop in EA TFP during 2020; this AS disturbance was accompanied by a fall in the subjective rate of time preference, that stabilized the natural real interest rate. The size of the concomitant model-inferred AD and AS shocks that reproduce the actual GDP contraction of 2020, at an unchanged infation rate, is invariant to the persistence of these shocks, and to other model parameters. However, the model-inferred relative contribution of AD vs. AS shocks to the GDP contraction, in a liquidity trap, is sensitive to the assumed shock persistence. When the Covid-induced AD and AS shifts are assumed very transient, the liquidity trap model attributes the Covid GDP contraction to a fall in AD (low household demand). However, the (predicted) slow recovery of EA output in 2021 indicates that the adverse AD and AS shifts induced by Covid are persistent (annual 1 The IDEAS/RePec database lists approx. 20,000 economic research papers related to Covid [August 2021]. 2 Liquidity traps have also been considered in a small number of other macroeconomic studies of Covid, however, the focus of those studies is diferent. For example, Fornaro and Wolf (2020) use an endogenous growth model of a liquidity trap to highlight possible adverse long-term efect on productivity ('scarring'); Pfeifer etal. (2020) and Clemens and Roeger (2021) use rich quantitative models with a ZLB to analyze fscal policy responses to Covid. 476 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... autocorrelation: 0.6). Under realistic shock persistence, the liquidity trap model attributes the Covid output contraction in 2020 to the negative efect of Covid on AS. However, AS and AD shifts mattered equally for the observed stability of infation. In a liquidity trap, persistent negative AS shifts lower infation, while persistent adverse AD shifts raise infation. If Covid had solely afected AS, the EA would thus have experienced a sharp fall in infation and a contraction in GDP that would have been deeper than the actual contraction, according to the liquidity trap model; that model suggests that the contraction in AD had a stabilizing efect on EA GDP during the Covid crisis. Interestingly, a model version that abstracts from the ZLB constraint (and assumes that the central bank sets the policy rate according to a Taylor rule) produces the same estimates of the Covid-induced AD and AS shifts, as the liquidity trap model. In that no-liquidity-trap model version, the Covid output contraction is unambiguously interpreted as an AS shift (irrespective of shock persistence). However, a model version without ZLB constraint predicts that if Covid had solely afected AS, the EA would have experienced a sharp rise in infation and a contraction in GDP that would have been smaller than the actual contraction. Section2 presents empirical evidence on the EA macroeconomy during Covid. Section 3 presents the model. Section 4 interprets the EA macroeconomy during Covid through the lens of the model. Section5 concludes. 2 The EA macroeconomy underCovid Table 1 reports predicted and realized annual EA macro variables for the years 2019-2021, as published by the European Commission (EC) in its November 2019 and May 2021 Economic Forecasts (European Commission 2019, 2021).3 Cols. (1)-(3) are predictions for 2019-2021 taken from the EC November 2019 forecast.4 Col. (4) shows predictions for 2021 from the May 2021 Forecast. Cols. (5), (6) show actual (realized) variables for 2019 and 2020, respectively (as reported in the May 2021 Forecast). Cols. (7), (8) show pre-Covid forecast errors, i.e. the diference between actual variables in 2019 and 2020 and the corresponding EC predictions made in Nov. 2019. Finally, Col. (9) shows forecast revisions, between Nov. 2019 and May 2021, for 2021 variables. The forecast errors for 2019 variables (Col. (7)) are very small, but the forecast errors for 2020 variables (Col. (8)) are substantial, and so are the forecast revisions for 2021 variables (Col. (9)). I interpret the forecast errors for 2020 variables, and the forecast revisions for 2021 variables, as (largely) refecting the efect of Covid. Due to its large size and unexpected nature, the Covid shock is likely to have swamped the efect of other unexpected disturbances in 2020 (as argued above). 3 The EC Economic Forecast is published twice a year (spring and autumn). 4 Statistics for 2019 shown in Col. (1) are predictions, as these statistics were published before the end of 2019. 477 R.Kollmann 1 3 In November 2019 the European Commission predicted EA GDP (Y) and private consumption (C) growth rates (year-on-year, y-o-y) and infation () for 2020 of 1.2%, 1.2% and 1.5%, respectively (see Col. (2), Table1). Actual 2020 growth rates/infation were6.6%,8.0% and 1.5%, respectively (Col. (6)). Thus the realized growth rates of EA GDP and consumption in 2020 were 7.8 and 9.2 percentage points (ppt) below predicted values (Col. (8)). By contrast, realized EA infation in 2020 equaled predicted infation. Between the November 2019 and May 2021 forecasts, we note a +3.1% revision of y-o-y predicted GDP growth for 2021 (Col. (9)). That forecast revision amounts to a 4.7% revision in the predicted level of 2021 GDP.5 Thus, Covid is predicted to have a persistent negative efect on the level of future GDP. By contrast, we notice only a very small revision in predicted 2021 infation:0.3% (Col. (9)). These are the key empirical observations that the theoretical model below will address. In summary: Covid triggered a sharp contraction of GDP that is predicted to be persistent; by contrast, Covid did not change infation in 2020, and its efect on predicted 2021 infation is very muted. Table 1 also reports predicted and actual growth rates of EA government consumption (G), investment (I), employment (L) and of labor productivity 5 The level of 2021 GDP predicted in the May 2021 EC forecast falls short by 4.7 ppt of the GDP level that would have obtained if the 2020 and 2021 growth rates predicted in Nov. 2010 had actually materialized: (6.6%+4.3%) (1.2%+1.2%)= 4.7%. Table 1 Euro Area macroeconomic performance, 2019-2021 (predicted and actual) Forecast Forecast error Forecast revision Forecast 11/2019 05/2021 Actual 2019 2020 2021 2021 2019 2020 2019 2020 2021 (1) (2) (3) (4) (5) (6) (7) (8) (9) Y 1.1 1.2 1.2 4.3 1.3 -6.6 0.2 -7.8 3.1 C 1.1 1.2 1.2 2.7 1.3 -8.0 0.2 -9.2 1.5 G 1.6 1.5 1.3 3.8 1.8 1.3 0.2 -0.2 2.5 I 4.3 2.0 1.9 6.7 5.7 -8.2 1.4 -10.2 4.8 NX/Y 2.9 2.8 2.7 3.4 3.0 3.4 -0.1 0.6 0.7 L 1.1 0.5 0.5 0.0 1.2 -1.6 0.1 -2.1 -0.5 Y/L 0.0 0.7 0.7 4.3 0.1 -5.0 0.1 -5.7 3.6 1.5 1.5 1.5 1.2 1.7 1.5 0.2 0.0 -0.3 Notes: Forecasted and realized year-on-year growth rates of 2019-2021 Euro Area (EA) real GDP (Y), private consumption (C), government consumption (G), investment (I), employment (L) and labor productivity (Y/L) are shown as well as the forecasted and realized GDP defator () and next exports/GDP ratio (NX/Y). (Net exports pertain to merchandise trade.) Growth rates are in percent (%); infation and the NX/Y ratio are in percentage points (ppt). Cols. (1)-(3) are predictions for 2019-2021 taken from the European Commission's (EC) Economic Forecast November 2019. (Statistics for 2019 shown in Col. (1) are predictions, as these statistics were published before the end of 2019.) Col. (4) shows predictions for 2021 taken from the EC May 2021 Economic Forecast. Cols. (5),(6) show actual (realized) variables for 2019 and 2020, respectively (as reported in the EC May 2021 Economic Forecast). Cols. (7),(8) show the diference between actual variables in 2019 and 2020 and the corresponding EC predictions made in Nov. 2019. [Col.(7) = Col.(5)-Col.(1); Col.(8) = Col.(6)-Col.(2)] Col. (9) shows forecast revisions, between Nov. 2019 and May 2021 EC forecasts, for 2021 variables. [Col.(9) = Col.(4)-Col.(3)]. Source: European Commission (2019, 2020) 478 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... (Y/L) in 2020 and 2021; also shown is the actual and predicted (merchandise) trade balance/GDP ratio (NX/Y). Covid only had a very small efect on EA government consumption in 2020 (0.2%), it depressed 2020 investment by 10.2%, and it led to a slight trade balance improvement,+0.6 ppt (see Col. (8)). Thus, Covid had a combined efect on EA government consumption and the trade balance that is negligible compared to the large GDP contraction. The theoretical model discussed below will abstract from government consumption and foreign trade (a closed economy will be considered). The Covid-induced contraction of investment in 2020 was roughly of the same proportion as the change in private consumption (-9.2%); as the EA consumption/GDP ratio (about 55%) is much higher than the investment/GDP ratio (20%), the collapse in EA private consumption accounts for the bulk of the fall in EA GDP, in 2020. For analytical tractability, the theoretical model will abstract from physical capital and investment. 3 Model economy A standard New Keynesian model is considered (e.g., Kollmann 2001a,b, 2002, 2004, 2005, 2008). The model assumes a closed economy with: a representative household; a central bank; monopolistic competitors that produce a continuum of intermediate goods indexed by s[0,1] using labor; competitive frms that bundle intermediates into a homogeneous fnal good. The household consumes the fnal good, supplies labor and owns all frms. The central bank sets the short-term nominal interest rate. Intermediate goods prices are sticky; all other prices and the wage rate are fexible. The labor market is competitive. 3.1 The representative household The intertemporal preferences of the representative household are described by E0 t=0 t t{ln(Ct) 1 1+1 (Lt) 1+1} where Ct and Lt are fnal consumption and aggregate hours worked at date t. 0 << 1is the household's steady state subjective discount factor and > 0is the Frisch labor supply elasticity. t > 0is a stationary exogenous preference shock that alters the household's rate of time preference. The household equates the marginal rate of substitution between leisure and consumption to the real wage rate, which implies. There is a market for a one-period riskless nominal bond (in zero net supply). The nominal interest rate on that bond is rt between periods t and t + 1. The gross nominal rate is denoted Rt 1 + rt. The household's Euler equation for this bond is: (1C (1) t)(WtPt)=(Lt) 1. Rt Et(t+1t)(CtCt+1)t+1 = 1, (2) 479 R.Kollmann 1 3 where t+1 Pt+1Pt is the gross infation rate between t and t + 1. If t follows a stationary AR(1) process, as assumed below, then a positive shock to the date t preference shifter t lowers the expected subjective discount factor Ett+1t between dates t and t+1, and thus the shock raises the household's subjective discount rate. In what follows, I will hence refer to the preference shock t as a (subjective) discount rate shock. A rise in t can be interpreted as a positive aggregate demand shock as, for a given real interest rate, it boosts desired current consumption (by inducing the household to substitute future consumption by current consumption). 3.2 Firms The fnal good is produced using the technology Yt { 1 0 (yt(s))(1)ds}(1) , with >1, where Yt is date t fnal output. yt(s) is the quantity of the type-s intermediate good. Let pt(s) be the nominal price of that intermediate. Cost minimization in fnal good production implies yt(s)=(pt(s)Pt) Yt , where Pt { 1 s=0 pt(s) 1ds}1(1) is a price index for intermediate goods. Perfect competition implies that the fnal good price is Pt (its marginal cost). The technology for producing intermediate good s is yt(s) = tLt(s), where Lt(s) is the labor input at date t, while t > 0 is an exogenous stochastic productivity parameter (identical for all intermediate good producers). t is an aggregate supply shock. Intermediate good producers face quadratic price adjustment costs. The real proft, in units of fnal output, of the frm that produces intermediate good s is: where Wt is the nominal wage rate. The last term in this equation is the real price adjustment cost, where is the steady state gross infation rate. At date t, the frm sets pt(s) to maximizes the present value of profts Et =0 t,t+t+ (s), where t,t+ is the household's intertemporal marginal rate of substitution in consumption between periods t and t + . All intermediate good frms face identical decision problems, and they produce identical quantities and set identical prices: pt(s) = Pt s [0, 1]. 3.3 Monetary policy The central bank sets the nominal interest rate rt , subject to the zero lower bound (ZLB) constraint rt 0, i.e.Rt 1. t(s) (pt(s) Wtt)yt(s)Pt 1 2 ([pt(s) pt1(s)]Pt1) 2, > 0, 480 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... 3.4 Market clearing Markets for intermediates clear as intermediate goods producers meet all demand at posted prices. Labor market clearing requires Lt = 1 s=0 Lt(s)ds. Final good market clearing requires Ct = Yt, where Yt = tLt is GDP. 3.5 Solving themodel I linearize all model equations around a deterministic steady state. Let xt (xt x)x denote the relative deviation of a variable xt from its steady state value x 0 (variables without time subscript denote steady state values). Using the market clearing condition Ct = Yt, the linearised Euler Eq.(2) can be written as: Linearizing the frst-order condition of the intermediate good frms' decision problem gives a standard 'forward-looking' Phillips equation: where mct = (Wtt)Pt is real marginal cost (defated by the fnal good price) in the intermediate good sector (e.g., Kollmann 2002). w > 0 is a coefcient that is a decreasing function of the price adjustment cost parameter . Using the nominal wage implied by the labor supply Eq.(1), and the conditions Ct = Yt and Yt = tLt , one can express real marginal costs as mct = (Ytt) 1+1, which implies In a fex-price economy (w = ), real marginal cost would be constant. Thus, (5) implies Y Flex t = t, where Y Flex t denotes GDP under fexible prices. Defne the output gap zt as the deviation of GDP from its fex-price level: Using this defnition, the Phillips curve (4) can be expressed as: while the Euler Eq.(3) can be written as Rnat t is the risk-free gross real interest rate between dates t and t+1 (expressed in deviation from the steady state gross rate) that would obtain under fexible prices. I refer to Rnat t as the natural real interest rate. R (3) t = Et{t+1 + Y t+1 Y t + t t+1}. (4) t = w mc t + Ett+1, mc t = (5) 1+ (Y t t). z (6) t Y t Y Flex t . (7) t = zt + Ett+1, with w 1+ , (8) Rt = Et{t+1 +zt+1 zt} + Rnat t , with Rnat t Et{[Y Flex t+1 Y Flex t ][t+1 t]}. 481 R.Kollmann 1 3 The Phillips curve (7) implies that the output gap is a function of current and expected future infation: zt = 1 {t Ett+1}. Substituting this expression into the Euler Eq.(8) gives: I refer to (9) as the 'Euler-Phillips' equation. Assume that TFP and the discount rate shock follow stationary univariate AR(1) processes with autocorrelations 0 < 1 and 0 < 1, respectively: where t+1, t+1 are mean-zero innovations. Then, the natural real interest rate is given by Thus, the natural real interest rate is a decreasing function of TFP and an increasing function of the discount rate shock. Note that 0 < 1 implies that a positive shock to TFP lowers the expected future growth rate of TFP. In a fex-price economy, this entails a fall in the expected future growth rate of GDP and consumption, which lowers the natural real interest rate. Similar logic explains why a positive shock to the subjective discount rate between dates t and t+1 raises the natural real interest rate between t and t+1. 3.6 Liquidity trap This paper focuses on equilibria that obtain when the ZLB binds permanently, i.e. Rt = 1 t. A liquidity trap can, for example, arise when the central bank follows a Taylor-style interest rate rule. Then pessimistic household expectations about future infation and GDP can push the nominal interest rate to the ZLB (Benhabib etal. 2001a,b; Kollmann 2021a,b). The assumption of a permanent liquidity trap is solely made for analytical convenience. Kollmann (2021a,b) studies equilibria with self-fulflling (expectations-driven) equilibria in which, in each period, the economy can escape from the liquidity trap with positive probability. When the escape probability from a liquidity trap is sufciently small (i.e. when the liquidity trap is expected to last long), shock transmission is very similar to transmission in a permanent liquidity trap (Kollmann 2021a,b). The motivation for analyzing the efect of Covid using a model with a liquidity trap is that Covid hit the EA (and other advanced economies) in an environment of persistently ultra-low interest rates. The European Central Bank's (ECB) policy rate has been at (or very close to) the ZLB since November 2013; a departure from this low-interest rate policy does not seem to be on the agenda of ECB decision makers, as of this writing. In normal times, the ECB would be able to counteract (9) Rt = 1 t + (1 + 1+ )Ett+1 Ett+2 + Rnat t . t+1 = t + t+1, t+1 = t + t+1, R (10) nat t = (1 ) t + (1 )t. 482 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... adverse shocks by cutting the policy interest rate. This is not possible, in a liquidity trap.6 In a permanent liquidity trap, Rt = 0 holds.7 The Euler-Phillips Eq.(9) then becomes 0<<1 and >0 imply that one of the characteristics roots of this expectational diference is strictly larger than unity, while the other root is smaller than unity. This implies that Eq. (11) has multiple non-explosive solutions (Blanchard and Kahn 1980). Following the liquidity trap models of Mertens and Ravn (2014), Roeger (2015), Arifovic et al. (2018), Aruoba et al. (2018), Kollmann (2021a,b) and de Beaufort (2021), I consider minimal-state-variable (MSV) equilibria in which infation is a function of the contemporaneous fundamental forcing variables that drive the natural real interest rate, i.e. of TFP and the discount rate shock: where and are coefcients. Substitution of the infation decision rule (12) and of the formula for the natural real interest rate (10) into the Euler-Phillips Eq.(11) gives: This equation holds for arbitrary values of t and t if and only if It can readily be seen that (x) < 0 holds for 0 x < , and (x) > 0 for < x 1, where 0 < < 1 is a root of the polynomial (x), i.e. () = 0.8 Thus, 0 = (11) 1 t + (1 + 1+ )Ett+1 Ett+2 + Rnat t . (12) t = t + t, 0 = { 1 t + ( 1 + 1 + ) t ( ) 2 t } + { 1 t + ( 1 + 1 + ) t () 2 t } (1 ) t + (1 )t. = (1 )() and = (1 )(), (13) with (x) (14) 1 + (1 + 1+ )x x2. 6 The analysis here abstracts from unconventional monetary policies (such as Quantitative Easing, QE, or Negative Interest Rate Policy, NIRP) that have been conducted by the ECB since the global fnancial crisis of 2008-09. In March 2020, the ECB launched an asset purchases program (the "Pandemic Emergency Purchases Program", PEPP) that aims to counter the economic efects of the Covid crisis. Hohberger etal. (2019), Kabaca etal. (2020) and Altavilla etal. (2021) show that unconventional ECB policies have, to some extent, acted as a substitute for conventional interest rate policy, during the period of ultra-low policy rates. Wu and Zhang (2019) show that the efect of US QE can be captured with a 'shadow' federal funds rate that is not constrained by the ZLB, and that follows a Taylor-type rule. Explicitly modeling unconventional monetary policy is beyond the scope of the simple framework used in the paper here. However, below I consider a model variant in which the nominal interest rate is not constrained by the ZLB to address the possibility that unconventional monetary policies acted as a substitute for conventional interest rate policy, during the Covid crisis. 7 In an equilibrium with a permanent liquidity trap, R=1 holds in steady state. Linearization around the liquidity trap steady state thus implies Rt = 0 t. 8 = a2 {(a2) 2 1}0.5 with a (1 + + ). 483 R.Kollmann 1 3 This shows that a (sufciently) transitory rise in TFPlowers infation in a liquidity trap, while a persistent positive TFP shock raises infation. A transitory positive discount rate shock raises infation, while a transitory positive discount rate shock lowers infation. For intuition about the role of shock persistence for the response of infation in a liquidity trap, consider the case where the autocorrelation of shocks is close to unity. Then t Ett+1 Ett+2, so that the Euler-Phillips Eq.(11) implies that t Rnat t , i.e. a fall in the natural real interest rate raises infation. This explains why a persistent rise in TFP (that depresses the natural real interest rate; see (10)) triggers an increase in infation. Similar logic explains why a persistent positive taste shock (that raises the natural rate) lowers infation. Conversely, when shocks are i.i.d., then a date t shocks does not afect expected future infation, and the Euler-Phillips Eq. (11) implies t = Rnat t . Therefore, a purely transitory rise in TFP lowers infation, while a transitory positive discount rate shock raises infation. Expected future infation is As the output gap is given by zt = 1 {t Ett+1}, we fnd (from (12), (16)) that Therefore, a persistent positive TFP shocks raises the output gap, while a transitory TFP increase lowers the output gap. Conversely, a persistent positive discount rate shocks lowers the output gap, while a transitory positive discount rate shock raises the output gap. Note that GDP is given by Y t = zt + Y Flex t (see (6)). Thus, (17) implies A persistent TFP increase (with > so that > 0) always raises GDP; a transitory TFP increase (with < ) lowers GDP if prices are sufciently sticky, i.e. when the slope of the Phillips curve is small. A persistent positive discount rate shock lowers GDP, while a transitory positive discount rate shock raises GDP.9 (15) < 0, > 0 holds for , < ; and > 0, < 0 holds for , > . E (16) tt = t + t. zt = (17) 1 (1 ) t + 1 (1 ) t. (18) Y t = [1 + 1 (1 )] t + 1 (1 ) t. 9 (18) shows that a persistent negative TFP shock triggers an output contraction that is greater than the fall in TFP. Guerrieri etal. (2020) develop a multi-sector, incomplete-markets model in which a negative supply shock lowers output more than the shock; the authors refer to a supply shock with this feature as a "Keynesian" supply shock. The analysis here illustrates that "Keynesian" supply shocks arise in a standard liquidity trap model. 484 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... 3.7 Model solution withoutZLB constraint (Taylor rule) It is interesting to compare shock transmission in the liquidity trap to transmission when the ZLB constraint does not bind, so that the central bank can adjust the policy rate, in response to disturbances. This Section abstracts from the ZLB and assumes that the central bank sets the short-term interest rate as a function of the infation rate, according to a Taylor rule: where the parameter captures the response of the policy rate to infation. The 'Taylor principle' is assumed to hold (>1): a 1% rise in gross infation triggers a rise in the gross policy rate by more than 1%. When the monetary policy rule (19) applies, the Euler-Phillips Eq.(9) becomes. The Taylor principle >1 ensures that both characteristic roots of (20) are larger than unity (in absolute value), which ensures that (20) has a unique non-explosive solution of the form where and can readily be determined using the method of undetermined coefcients: >1 implies that + (x) < 0 holds 0x1. Thus, < 0 and > 0. GDP is now given by: Away from the ZLB, a positive TFP shock lowers infation, irrespective of the persistence of the shock; the shock raises GDP when the infation coefcient of the Taylor rule is sufciently large (which ensures that < 0 is sufciently small in absolute value, so that the coefcient of TFP in (23) is positive). Away from the ZLB, a positive discount rate shock raises infation and GDP irrespective of shock persistence (provided >1). 4 Interpreting Covid andtheEA macroeconomy throughthelens ofthemodel This Section discusses model calibration, presents simulated shock responses, and interprets the adjustment of the EA economy to Covid in 2020-2021 through the lens of the model. R (19) t = t, >1, (20) t = 1 t + (1 + 1+ )Ett+1 Ett+2 + Rnat t . (21) t = t + t, = (1 ){ + ()} and = (1 ){ + ()}. (22) (23) Y t = [1 + 1 (1 )] t + 1 (1 ) t. 485 R.Kollmann 1 3 4.1 Estimating Covidinduced TFP anddiscount rate shocks As the data in Table1 are annual, I use an annual model calibration.10 Covid was an unexpected event in 2020 that triggered persistent shifts in TFP and household preferences. I label the year 2020 as t=0. Let dxt denote the Covid-induced deviation of a variable xt from its no-Covid trajectory in period t0. From (7), dt = dzt + Etdt+1 for t0. As documented above, Covid had zero efect on EA infation in 2020, and a negligible efect on predicted infation in 2021. Because of the muted efect of Covid on EA infation, the model infers that the shock had (essentially) zero efect on the output gap: dz0 = 0. This implies that dY 0 = dY Flex 0 = d 0. The model thus infers that, in the EA, the Covid event of 2020 amounted to a negative TFP shock: d 0 < 0. From the model solution for infation, in a liquidity trap (see (12), (13)), we see that d0 = E0d1 = 0 imply: and Clearly, (24) and (25) imply and Because of the muted efect of Covid on actual infation in 2020 and on predicted infation in 2021, the model infers that the aggregate supply (TFP) and aggregate demand (discount rate) shifts in 2020 induced by Covid had exactly ofsetting efects on infation, and that these shifts had the same persistence (autocorrelation). The common autocorrelation of both forcing variables will be denoted by = . The subsequent analysis will be based on (26) and (27). It is straightforward to see 0 = {(1 (24) )()} d 0 {(1 )()} d0 0 = {(1 (25) )()} d 0 {(1 )()} d0. d (26) 0 = d0 (27) = . 10 Quarterly data show that the EA GDP contraction was strongest in 2020q1 (3.8% quarter on quarter, q-o-q, change) and 2020q2 (-11.6%); this was followed by a rebound in 2002q3 (+12.5% q-o-q), but there was a further GDP contraction in 2002q4 (0.7%) due to the second wave of the epidemic in the autumn-winter 2020-21. The q-o-q changes of the EA GDP defator were 0.5%, 1.0%,1.1% and 0.9%, respectively in 2020q1-q4. These q-o-q infation changes suggest that, at the quarterly frequency, aggregate demand and aggregate supply changes were not perfectly synchronized, by contrast to the perfect correlation between AD and AS shifts at the annual frequency (see below). However, the key stylized fact driving the results of the paper, namely that infation changes were more muted than the massive GDP changes during Covid, also holds in quarterly data. For simplicity, the paper focuses on annual data and an annual model calibration. A quarterly model would need to address that the second wave of the epidemic was possibly anticipated by householdsthis might require specifying a richer time series model of the Covid shocks than the simple AR(1) processes assumed in the annual calibration. 486 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... (from (21, 22)) that (26) and (27) are also implied by the model variant without ZLB constraint.11 The notion that EA frms sufered "technological" regress during Covid may seem debatable. The negative efect of Covid on aggregate supply can also refect partial or complete government-ordered frm shutdowns (to slow the spread of the virus), or a reduction in household labor supply (as workers fear infection while commuting to work or interacting in-person with co-workers and customers). The latter may be captured by replacing the household's period utility by ln(Ct) 1 1+1 (Ltt) 1+1, where t > 0 is an exogenous shock. Note that a fall in t raises the disutility of labor. It is straightforward to see that a 1% fall in t and a 1% fall in TFP t have identical efects on infation and GDP. The analysis of the role of TFP shocks for the EA macroeconomy during Covid can thus be rephrased in terms of labor supply shifts induced by Covid. Given the contraction of EA GDP by 7.8% in 2020, the model-inferred estimate of Covid-induced TFP and preference shifts in t=0 is(from (18), (26), (27)): When (27) holds, then the autocorrelation of GDP is = as can be seen from (18). The autocorrelation of GDP responses to Covid thus allows to obtain an estimate of the persistence of the Covid-induced aggregate supply and demand shifts. As discussed in Sect.2, Covid triggered a 4.7% revision in the predicted level of 2021 GDP, i.e. Covid is predicted to have a persistent negative efect on the level of future GDP. The ratio of the predicted 2021 GDP contraction to the 2020 GDP contraction is 0.6 (= (4.7%)(7.8%)). This suggests that the annual autocorrelation of the Covid-induced shift GDP is =0.6. The baseline model calibration below thus sets =0.6. Note that the estimated GDP autocorrelation =0.6 due to Covid is in the same range, but slightly smaller, than the autocorrelation of (detrended) EA GDP in preCovid times. The autocorrelation of detrended log EA GDP (annual) before Covid (1999-2019) is roughly 0.65.12 4.2 Calibrating structural model parameters The other model parameters are set at values that are standard in annual macro models. I assume = 0.99, which implies a 1% per annum steady state riskless real interest rate. The Frisch labor supply elasticity is set at unity, = 1, a conventional value in macro models. The slope coefcient of the Phillips curve (7) is calibrated by exploiting the observational equivalence between the linearized Phillips curve d 0 = d0 = 7.8%. 12 The autocorrelations of linearly detrended, quadratically detrended and HP fltered logged real annual GDP (1999-2019) are 0.67, 0.65 and 0.63, respectively. 11 The zero response of the natural real interest rate to the Covid-induced aggregate supply and demand shocks implies that a central bank that is unconstrained by the ZLB would not change its policy rate, in response to those shocks. 487 R.Kollmann 1 3 under price adjustment costs assumed here (see (4)) and the Phillips curve implied by Calvo-type (Calvo1983) staggered price setting. Empirical evidence, based on quarterly data for the EA, suggests that Calvo-equivalent price stickiness is about 4 quarters, i.e. the estimated probability that a frm does not re-optimize its price in a given quarter is about 0.75 (Kollmann 2001a; Giovannini etal. 2019). Based on this evidence, I set the Phillips curve slope at =2.9674, in the present calibration to annual frequency.13 13 Under Calvo price setting, the slope of the Phillips curve (4) is w = (1 D)(1 D)D, where D is the probability that an individual frm keeps its price unchanged in a given period. As estimates based on quarterly data suggest D=0.75, I set the probability of non-price adjustment at (0.75)4 , in the annual model calibration here. This implies w = 1.48373. The assumed labor supply elasticity (=1) then entails w(1 + ) = 2.9674. Less More Less More persistent persistent price price Baseline shocks shocks stickiness stickiness =0.6 =0.1 =0.9 =0.6 =0.6 =2.96 =2.96 =28.14 =0.59 (1) (2) (3) (4) (5) (a) Liquidity trap 1% TFP increase 0.72 -5.14 0.11 0.66 1.21 Y 1.10 -0.58 1.00 1.01 1.84 R 0.00 0.00 0.00 0.00 0.00 1% preference shock -0.72 5.14 -0.11 -0.66 -1.21 Y -0.10 1.58 -0.00 -0.01 -0.84 R 0.00 0.00 0.00 0.00 0.00 (b) Away from ZLB (Taylor rule) 1% TFP increase -0.41 -0.53 -0.16 -0.44 -0.34 Y 0.94 0.84 0.99 0.99 0.77 R -0.61 -0.80 -0.24 -0.66 -0.51 1% preference shock 0.41 0.53 0.16 0.44 0.34 Y 0.06 0.16 0.01 0.01 0.23 R 0.61 0.80 0.24 0.66 0.51 Table 2 Model-predicted impact responses to 1% TFP () and preference () shocks Notes: Impact responses of infation (), GDP (Y) and the nominal interest rate (R) to 1% innovations to TFP () and to the preference shifter () are shown. Responses of GDP are expressed in %; responses of infation and interest rate are in percentage points (ppt). Responses pertain to annual variables. : autocorrelation of shocks; : slope of Phillips curve. Panel (a) shows responses in a permanent liquidity trap; Panel (b) shows responses when the ZLB does not bind and the central bank follows a Taylor rule. Col. (1): baseline calibration (=0.6 and 4-quarter Calvo-equivalent price stickiness). Cols. (2, 3): less persistent shocks (=0.1) and more persistent shocks (=0.9), respectively, than in baseline (same price stickiness as in baseline). Cols. (4, 5): prices less sticky (2-quarter Calvo-equivalent) and more sticky (8-quarter Calvo-equivalent), respectively, than in baseline (same shock autocorrelation as in baseline) 488 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... 4.3 Simulated shock responses Table2 reports model-predicted impact responses of infation, GDP and the nominal interest rate (R) to a 1% TFP shock and to a 1% preference shock, respectively. Panel (a) shows predicted responses in the liquidity trap. Panel (b) shows responses that obtain when the ZLB does not bind and the central bank follows a Taylor rule; the infation coefcient of the interest rate rule (19) is set at the conventional value = 1.5. Column 1 of Table2 shows shock responses under the baseline calibration (shock persistence =0.6, 4-quarter Calvo-equivalent price stickiness). Col. (2) assumes less persistent shocks, =0.1, while Col. (3) assumes more persistent shocks, =0.9 (Cols. (2), (3) assume baseline price stickiness). Col. (4) lowers the Calvoequivalent price stickiness to two quarters, and Col. (5) sets the Calvo-equivalent price stickiness at 8 quarters (while assuming =0.6). Away from the ZLB, a Taylor-style monetary policy rule entails that the central bank cuts the policy rate, in response to a positive TFP shock, and that it raises the policy rate in response to a positive discount rate shock (see Panel (b), Table 2). Away from the ZLB, a positive TFP shock lowers infation, while a positive discount rate shock raises infation. In all 5 model variants, the Taylor-rule-based monetary policy (away from the ZLB) delivers GDP responses to TFP shocks that are positive, but smaller than the shock response under fexible prices; the GDP response to a positive discount rate shock is positive, but weak. In fact, predicted shock responses are close to the response under fexible prices, except when the shock is very transient (Col. (2)), or prices are very sticky (Col. (5)). (Nota bene: under fexible prices, a 1% TFP increase raises GDP by 1%, and a discount rate shock has zero efect on GDP.) In the liquidity trap, the interest rate cannot adjust to shocks (Panel (a), Table2). Under the baseline Phillips curve slope , the critical value for the shock autocorrelation (that is decisive for the sign of the infation response to shocks) is = 0.215 (see (14), (15)). The baseline shock autocorrelation =0.6 thus exceeds the critical persistence . Under the baseline calibration (Col. (1)), the model predicts hence that, in the liquidity trap, a positive TFP shock raises infation and the GDP gap, while a positive discount rate shock lowers infation and the GDP gap. However, quantitatively, the response of GDP, in the baseline liquidity trap model variant, is relatively similar to the fex-price GDP response: GDP rises by 1.1% in response to the TFP shock, and GDP falls by 0.1% in response to the discount rate shock; these responses are close to the 1% and 0% responses under fexible prices. The intuition for this is that persistent shocks (as assumed in the baseline calibration) have a muted efect on the natural real interest rate; those shocks thus have a relatively weak efect on infation, and hence their efect on GDP is close to the fex-price response. This logic explains why, when shocks are more persistent than in the baseline specifcation (see Col. (3) where =0.9 is assumed), then shock responses are even closer to the fex-price responses. As might be expected, the model variant with lower price stickiness too generates GDP responses (in the liquidity trap) that are close to the fex-price responses (see Col. (4)). By contrast, the GDP response to shocks is magnifed -- and it thus difers more from the fex-price response -- when 489 R.Kollmann 1 3 greater price stickiness is assumed (Col. (5)).14 The model variant with less persistent shocks (see Col. (2) where =0.1 is assumed) is the only model variant in Table 2 that deliver qualitatively diferent infation and GDP responses than the baseline calibration. This is so because < holds in Col. (2). In the liquidity trap, a transient TFP increase (=0.1) lowers infation and GDP, while a transient positive discount rate shock gives a big boost to infation and GDP. 4.4 Decomposing theGDP contraction duringCovid Remarkably, the size of the concomitant model-inferred AD and AS shocks d 0 = d0 = 7.8% that reproduce the 7.8% Covid-induced GDP contraction of 2020, at an unchanged infation rate, is invariant to shock persistence or to other model parameters; it is furthermore common to the liquidity trap model and to the "no ZLB" model variant (in which monetary policy follows a Taylor rule).15 However, the model-inferred relative contribution of Covid-induced TFP and discount rate changes to the GDP contraction, difers across model variants. In all model variants without ZLB constraint, the output contraction is largely attributed to the TFP shock. Away from the ZLB, the adverse Covid-induced discount factor shock contributes to the fall in GDP, but its infuence on GDP is weak. The model variants without ZLB constraint predict that if Covid had solely afected aggregate supply, the EA would have experienced a sharp rise in infation and a contraction in GDP that would have been smaller than the actual contraction. In the baseline liquidity trap model, the Covid-induced GDP change too is largely driven by the TFP shock; the simultaneous discount rate shock counterbalances the TFP-induced GDP change, but again the efect of the discount rate shock on GDP is weak. The role of the TFP shock is especially strong when prices are very sticky (Col. (5)). The only liquidity trap model variant in which the GDP change is dominated by the discount rate shock is the variant with very transitory shocks; see Col. (2) in Table2. The simulations in Table2 indicate thus that, for empirically plausible persistence of the Covid-induced AD and AS shifts, the efect of the AS shifts on GDP dominates clearly, in a liquidity trap. The analysis here suggests, hence, that the Covid-induced GDP contraction was largely due to the adverse efect of Covid on aggregate supply. However, aggregate supply and demand shifts both mattered equally for the observed stability of infation under Covid. In a liquidity trap, persistent adverse AS shifts tend to lower infation, while adverse demand shifts raise infation. The liquidity trap model predicts that, if Covid had solely afected aggregate supply, the EA would have experienced a sharp fall in infation and a contraction in GDP that would have been deeper than the actual 14 The critical shock persistence is 0.0332 in the low-price-stickiness model variant of Col. (4) and 0.4729 in the high-price-stickiness case of Col. (5). Thus, < holds in Cols. (4) and (5), which explains why the qualitative infation and GDP responses are the same as under the baseline calibration. 15 This helps to understand why, for all model variants, the sum of the infation responses to a 1% TFP shock and to a 1% preference shock is 0, while the sum of the GDP responses to both shocks is 1%, as can be seen in Table2. For example, in the baseline liquidity trap model version, a 1% TFP shock raises GDP by 1.1%, while a 1% preference shock lowers GDP by 0.1%. Thus the response of GDP to simultaneous 1% TFP and 1% preference shocks is 1.1%0.1%=1%. 490 1 3 Efects ofCovid19 onEuro area GDP andinfation: demand vs.... contraction; the contraction in aggregate demand thus had a partially stabilizing efect on EA GDP, during Covid. 5 Conclusion This paper has analyzed the macroeconomic efects of the Covid-19 epidemic on Euro Area (EA) GDP and infation, using a stylized New Keynesian model. Ofsetting aggregate demand and supply changes are shown to account for the stability of EA infation, in the face of Covid. The evidence presented here indicates that Covidinduced aggregate demand and supply shifts were persistent. An aggregate supply contraction is identifed as the dominant force driving the sharp fall of EA GDP in 2020.