Asymmetric unemployment fluctuations and monetary policy trade-offs

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.1 (1-17)

Review of Economic Dynamics ••• (••••) •••–•••

Contents lists available at ScienceDirect

Review of Economic Dynamics www.elsevier.com/locate/red

Asymmetric unemployment fluctuations and monetary policy trade-offs Antoine Lepetit 1 Board of Governors of the Federal Reserve System, Division of Research and Statistics, 20th St. and Constitution Ave., NW, Washington, DC 20551, United States of America

a r t i c l e

i n f o

Article history: Received 19 March 2018 Received in revised form 15 July 2019 Available online xxxx JEL classification: E24 E32 E52 Keywords: Optimal monetary policy Unemployment asymmetries Steady-state distortions Fundamental surplus

a b s t r a c t I show that a quantitatively significant trade-off between inflation and unemployment stabilization arises in New Keynesian models with search and matching frictions in the labor market when both steady-state distortions and the elasticity of labor market tightness with respect to productivity are large. The first condition implies that variations in average unemployment matter for welfare outcomes. In combination with the unemployment asymmetries built in the search and matching framework, the second condition entails that average unemployment is substantially higher in an economy with business cycles than in steady state. In this environment, the central bank has an incentive to tolerate some inflation volatility in response to shocks since doing so reduces unemployment volatility and average unemployment. Most of the welfare gains obtained by the optimal policy derive from this effect on the average level of unemployment. Published by Elsevier Inc.

1. Introduction How much weight should policymakers place on inflation, and how much on employment? In practice most central banks seem to assign a non-negligible role to the stabilization of real activity. Most notably, in the United States, the Federal Reserve pursues the dual objective of promoting price stability and maximum sustainable employment. This behavior of central banks is at odds with the recommendations that have emerged from a literature that seeks to describe optimal monetary policy in dynamic stochastic general equilibrium models featuring nominal and real rigidities. These studies generally find that an exclusive focus on inflation stabilization is close to optimal (Walsh, 2014). In models incorporating search and matching frictions in the labor market, wage distortions create a trade-off between stabilizing inflation and addressing labor market inefficiencies (Faia, 2009), but this trade-off was found to be quantitatively small in calibrated models (Faia, 2008 and 2009; Thomas, 2008; Ravenna and Walsh, 2011 and 2012). I revisit this conclusion by showing that a significant trade-off between inflation and unemployment stabilization arises when both steady-state distortions and the elasticity of labor market tightness with respect to labor productivity are large. The first condition implies that linear terms, notably the average unemployment level, show up in second-order approximations to the utility function and matter quantitatively for welfare outcomes. The second condition obtains when the fraction of a job’s output

E-mail address: [email protected]. I would like to thank the Associate Editor and two anonymous referees for their comments and suggestions that have greatly improved the paper. I also thank Florin Bilbiie, Pierrick Clerc, Nicolas Dromel, Francesco Furlanetto, Jordi Galí, Jean-Olivier Hairault, Eleni Iliopulos, Jesper Lindé, Espen Moen, Taisuke Nakata, Federico Ravenna, Jordan Roulleau-Pasdeloup, as well as participants in various seminars and conferences for helpful comments. 1

https://doi.org/10.1016/j.red.2019.07.005 1094-2025/Published by Elsevier Inc.

JID:YREDY AID:953 /FLA

2

[m3G; v1.260; Prn:8/08/2019; 16:08] P.2 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

that the invisible hand can allocate to vacancy creation—what Ljungqvist and Sargent (2017) call the fundamental surplus—is small, and implies that labor market fluctuations are large. Because of the unemployment asymmetries built in the search and matching framework, it also entails that average unemployment is substantially higher in an economy with business cycles than in steady state. In this environment, the central bank has an incentive to tolerate some inflation volatility in response to shocks since doing so reduces unemployment volatility and average unemployment. The bulk of the welfare gains obtained by the optimal policy derive from this effect on the average level of economic activity. I use a standard New Keynesian model with search and matching frictions in the labor market. In this setting, inflation volatility is costly as producers face quadratic price adjustment costs. This gives rise to a Phillips curve that relates firms’ markups to inflation and gives monetary policy some leverage over job creation. Moreover, positive shocks reduce unemployment less than negative shocks increase it. In the model, fluctuations in technology lead to about symmetric shifts in the job-finding probability. However, because of the negative covariance between the job-finding probability and the unemployment rate, a notable feature of U.S. data, these fluctuations in the job-finding probability have an asymmetric effect on employment (Hairault et al., 2010; Jung and Kuester, 2011). In an expansion, the positive impact on employment of an increase in the job-finding probability is dampened by the decrease in the size of the pool of job seekers. In a recession, the negative impact on employment of the decrease in the job-finding probability is amplified by the increase in the size of the pool of job seekers. This asymmetric nature of unemployment fluctuations implies that aggregate fluctuations lead to a potentially costly increase in average unemployment. In this setting, the central bank may use inflation over the business cycle to influence markups, with the goal of affecting job creation. The adoption of different monetary policy rules leads to different outcomes in terms of average unemployment. In the baseline calibrated version of the model, average unemployment is higher than steady-state unemployment by 0.21 percentage points when the monetary authority responds to both inflation and output. However, under a policy of price stability, this gap doubles to 0.42 percentage points. More generally, holding the response to output constant, average unemployment is increasing in the central bank’s response to inflation. The intuition for this result is as follows. When responding mildly to inflation and/or strongly to output, the monetary authority engineers procyclical markups in response to technology shocks. This behavior of markups limits the procyclicality of firms’ real revenues and the volatility of job creation. Under a policy of price stability, markups are constant over the business cycle and real revenues and job creation are accordingly more volatile. This larger volatility of job creation translates in larger unemployment fluctuations, and because the latter are asymmetric, in higher average unemployment. Thus, the model features a long-run relationship between inflation volatility and average unemployment—the central bank can reduce average unemployment by tolerating some inflation volatility. In order to understand under which conditions the central bank should actually do so, I compute the Ramsey optimal monetary policy and decompose welfare outcomes as a function of the first and second-order moments of inflation and several labor market variables. When steady-state distortions are large and the fundamental surplus is small, business cycle costs under a policy of price stability are substantial and mostly accounted for by a term involving the covariance between the unemployment rate and the job-finding probability. The small fundamental surplus implies that this covariance is sharply negative, and the large steady-state distortions entail that it receives a large weight in welfare. By deviating from price stability, the Ramsey policy can stabilize labor market fluctuations and reduce the covariance between the unemployment rate and the job-finding probability (in absolute value). In doing so, it pushes average unemployment down, which leads to sizeable welfare gains. When one of two above-mentioned conditions fails to hold—that is, when steady-state distortions are small, or when the fundamental surplus is large—business cycle costs under a policy of price stability are reduced. As steady-state distortions become smaller, the weight attached to the covariance between unemployment and the job-finding probability tends towards zero—unemployment is still significantly higher than in steady state but this has a limited impact on welfare outcomes. As the fundamental surplus grows, labor market volatility declines and the covariance between unemployment and the job-finding probability is reduced (in absolute value)—average unemployment is not significantly different from steady-state unemployment. In both cases, the welfare gains that can be achieved by stabilizing labor market activity are limited and the Ramsey policy focuses instead on stabilizing inflation. Related literature. Several papers have showed that the asymmetric unemployment dynamics generated by a simple search and matching model of the labor market can lead to substantial business cycle costs (Hairault et al. (2010), Jung and Kuester (2011) and Petrosky-Nadeau and Zhang (2013)). Benigno et al. (2015) show that the relationship between macroeconomic volatility and average unemployment implied by such a model can be found in U.S. data. Ferraro (2018) also documents that the employment rate fluctuates asymmetrically over the business cycle in the U.S. and proposes an alternative explanation, based on endogenous job destruction and worker heterogeneity in skills. I build on these studies and draw the monetary policy implications of the presence of this asymmetry in unemployment fluctuations. My results contribute to a large literature on the optimal design of monetary policy. The conclusion that monetary policy should focus exclusively on stabilizing inflation is robust in the models generally used for monetary policy analysis, regardless of the different frictions that are included (Walsh, 2014). A large literature has focused on the specific case of labor market frictions. Faia (2008 and 2009) shows that a trade-off between inflation and unemployment stabilization arises in the presence of search and matching frictions as a central bank can use inflation to correct for an inefficient level of labor market activity. However, just like Thomas (2008) and Ravenna and Walsh (2011), she finds that the gains of adopting this policy rather than a policy of price stability

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.3 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

3

are small.2 Ravenna and Walsh (2012) also find that the incentives to deviate from price stability are small, unless wages are perfectly rigid and set at an inefficient level. Compared with this literature, the contribution of this paper is twofold. First, I provide general conditions under which a significant trade-off between inflation and unemployment stabilization arises. In particular, following Ljungqvist and Sargent (2017), I emphasize that wage rigidity is neither necessary nor sufficient to deliver a large elasticity of labor market tightness with respect to productivity. Such a large elasticity obtains when wages are flexible if the fundamental surplus is small. Conversely, wage rigidity on its own will not be able to generate large labor market fluctuations if the fundamental surplus is large. This implies that a small fundamental surplus—not wage rigidity—is key to obtaining a significant trade-off between inflation and unemployment stabilization. Given these conditions, one can understand why the literature finds that policies of price stability are nearly optimal. In Thomas (2008) and Ravenna and Walsh (2011), the steady state is efficient. In Faia (2008 and 2009), the elasticity of labor market tightness with respect to productivity is small, although wages exhibit some rigidity in Faia (2008). In three of the four cases considered by Ravenna and Walsh (2012), the steady state of the economy is efficient and/or the elasticity of labor market tightness with respect to productivity is small. In the fourth case, these authors identify a particular situation in which a significant trade-off arises—the steady state is inefficient and both their calibration and the introduction of perfectly fixed wages result in a small fundamental surplus.3 Second, I outline the mechanism through which such a trade-off arises. Because of the presence of labor market asymmetries, business cycles drive a wedge between average unemployment and steady-state unemployment. When this wedge is large and costly from a welfare perspective, monetary policy should deviate from price stability to stabilize labor market fluctuations and bring about a reduction in average unemployment. Finally, this paper is related to a literature that discusses how to properly evaluate the linear terms appearing in second-order approximations to welfare when steady-state distortions are large (Schmitt-Grohé and Uribe, 2004; Benigno and Woodford, 2005; Kim et al., 2008). It provides an example of a model economy in which moving from an efficient steady state to a distorted one drastically changes policy recommendations. Structure of the paper. Section 2 develops the model. Section 3 undertakes a comparative statics exercise to understand the origin of the asymmetry in unemployment fluctuations. Section 4 calibrates the model and studies the inflation volatility and average unemployment outcomes under alternative monetary policy rules. Section 5 examines under which conditions the Ramsey optimal monetary policy should deviate from price stability. Section 6 proposes two robustness exercises involving: i) an alternative wage-setting mechanism; ii) the introduction of alternative shocks. Section 7 concludes. 2. A New Keynesian model with search and matching frictions This section develops a model with sticky prices in which monetary policy has a meaningful role to play. It departs from the standard New Keynesian model in several ways. The labor market is not perfectly competitive but is characterized by search and matching frictions. The surplus of a match is divided between the worker and the firm according to an exogenous rule that determines the real wage. The economy consists of two sectors of production. Wholesale firms operate in perfectly competitive markets. They use labor as the sole input in the production process and have to post vacancies in order to match with workers. Their output is sold to monopolistically competitive retail firms which transform the homogeneous goods one for one into differentiated goods and must pay a quadratic adjustment cost to change their prices. 2.1. Labor market The size of the labor force is normalized to unity. Workers and firms need to match in order to become productive. The number of matches in period t is given by a Cobb-Douglas matching function mt = χ stα v t1−α , st being the number of job seekers and v t the number of vacancies posted by firms. The parameter χ reflects the efficiency of the matching process. Define θt = vs t as labor market tightness. The probability qt for a firm to fill a vacancy and the probability pt for a worker to t

= χ θt1−α . At the beginning of each period t, a fraction ρ of existing employment relationships N t −1 is exogenously destroyed.4 Those ρ N t −1 newly separated workers and the 1 − N t −1 workers unemployed in the previous period form the pool of job seekers st = 1 − (1 − ρ ) N t −1 . Job seekers have a probability pt of find a job are, respectively, qt =

mt vt

= χ θt−α and pt =

mt st

finding a job within the period. The law of motion of employment N t is accordingly given by

N t = (1 − ρ ) N t −1 + pt (1 − (1 − ρ ) N t −1 )

(1)

2 Blanchard and Galí (2010) find that an exclusive focus on inflation yields welfare losses several times larger than the optimal policy when wages are rigid. However, they normalize welfare losses under the optimal policy to one and all welfare losses under alternative policies are reported relative to that implied by the optimal policy. It is thus impossible to tell whether these welfare losses are big or small in consumption units. 3 A more extensive discussion of the results of these studies is provided in Section 5.3.2 and online Appendix 4. 4 The hypothesis of an exogenous separation rate is made to ensure comparability with the rest of the optimal monetary policy literature. Two elements are worth emphasizing. First, as discussed in Pissarides (2009), introducing endogenous destruction along the lines of Mortensen and Pissarides (1994) would have no effect on job creation decisions. Second, as discussed in Hairault et al. (2010), comovements between the job separation rate and the unemployment rate are unlikely to have a significant effect on average unemployment. However, asymmetries in the job separation rate itself may substantially affect average unemployment. Thus, this could provide another channel through which monetary policy can influence average unemployment.

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.4 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

4

The number of unemployed workers in period t is ut = 1 − N t . 2.2. Households Household members receive a real wage w t when employed and a value b when unemployed. b can be interpreted either as home production, or as the value of leisure while unemployed expressed in consumption units. I assume that consumption risks are fully pooled within the household. Household members have expected intertemporal utility

E t0

∞ 

C t1−σ

β t −t0

(2)

1−σ

t =t 0

where β is the household’s subjective discount factor, σ the coefficient of relative risk aversion and C t the consumption level of each household member. Households receive profits tr from retail firms, pay lump-sum taxes T t , and invest in risk-free bonds B t +1 that promise a unit of currency tomorrow and cost (1 + I t )−1 today, where I t is the nominal interest rate. They face the following per period budget constraint

P t C t + (1 + I t )−1 B t +1 = P t [w t N t + b(1 − N t )] + B t + P t tr − P t T t Consumption of market goods is given by C tm = C t − b(1 − N t ). C tm ≡ the different varieties of goods produced by the retail sector and

 1 0

(3)

C tm ( j )

 −1 −1 dj

is a Dixit-Stiglitz aggregator of

is the elasticity of substitution between the different

varieties. The optimal allocation of income on each variety is given by C tm ( j ) =



P t ( j) Pt

−

C tm , where P t =

 1 0

P t ( j)

 −1 −1 dj

is the price index and P t ( j ) is the price of a good of variety j. Households choose bonds holding so as to maximize (2) subject to (3). The household’s optimal consumption path is governed by a standard Euler equation

β Et

1 + It



C t +1 Ct

t +1

where t +1 =

 −σ

P t +1 Pt

=1

(4)

is the gross inflation rate between periods t and t + 1.

2.3. Wholesale firms A measure one of wholesale firms, indexed by i, produce according to the following technology

Y itw = Z t N it

(5)

where Z t is a common, aggregate productivity disturbance. Wholesale firms sell their output in a competitive market at a price P tw . Posting a vacancy comes at a cost κ . Firm i chooses its level of employment N it and the number of vacancies v it in order to maximize the expected sum of its discounted profits

E t0

∞ 

β

C t−σ

t −t 0



C t−0 σ

t =t 0

P tw Pt

Z t N it − κ v it − w t N it

(6)

subject to its perceived law of evolution of employment N it = (1 − ρ ) N it −1 + v it q(θt ), a nonnegativity constraint on vacancies V it ≥ 0, and taking the wage w t and the vacancy filling probability q(θt ) as given. In equilibrium all firms post the same number of vacancies and employ the same number of workers. I therefore drop individual firm subscripts i. After rearranging the first-order conditions, the following job creation equation obtains

κ − ψt q(θt )

=

Zt

μt

C

 − w t + E t βt +1 (1 − ρ ) −σ

κ − ψt +1 q(θt +1 )

 (7)

where βt +1 = β Ct +1 is the stochastic discount factor of households between periods t and t + 1, μt = PPwt is the t t markup of retail over wholesale prices, and ψt is the multiplier associated with the V t ≥ 0 constraint. This equation is an arbitrage condition for the posting of vacancies. It states that the marginal costs of hiring must be equal to the marginal benefits of having an extra employee for the firm. These benefits consist of the revenues from output, net of wages, plus savings on future hiring costs. Finally, the optimal firm policy also satisfies the Kuhn-Tucker conditions

ψt V t = 0,

V t ≥ 0,

ψt ≥ 0

(8)

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.5 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

5

2.4. Retail firms There is a large number of retailers, indexed by j, who buy the goods produced by wholesale firms at a price P tw and transform them one for one into differentiated goods. The real marginal cost of production for retailers is given by mct = They face quadratic costs of adjusting prices t ( j ) =

φp 2



P t ( j) P t −1 ( j )

2

−1

P tw Pt

.

Y t , which are measured in terms of aggregate output

Y t , and their revenues are subsidized at the constant rate τ . This subsidy is employed in order to ensure that steady-state inefficiencies arise only from search frictions, and not from monopolistic competition. Retail firms choose P t ( j ) in order to maximize

E t0

∞ 

β t −t0

t =t 0

C t−σ C t−0 σ



(1 + τ ) P t ( j ) − P tw Pt

Y t ( j ) − t ( j )

subject to the demand for each variety Y t ( j ) = ( P t ( j )/ P t )− Y td where Y td is aggregate demand for final goods. Noting that in the symmetric equilibrium P t ( j ) = P t , we obtain

(1 + τ )(1 − ) +

Z t +1 N t +1 − φ p t (t − 1) + E t βt +1 φ p t +1 (t +1 − 1) =0 μt Z t Nt

(9)

This equation is a nonlinear expectational Phillips Curve linking marginal cost and inflation. Because of the presence of sticky prices, inflation has an influence on markups. Importantly, lower markups (and higher marginal costs) for retail firms imply higher relative prices for wholesale firms and greater benefits from a filled vacancy. Thus, by engineering an increasing path for inflation, monetary policy can encourage firms to hire more workers and thereby reduce unemployment. 2.5. Wage setting For simplicity, I choose to model wages in the form of the wage schedule proposed by Blanchard and Galí (2010) γ

wt = ω Zt

(10)

where γ ∈ [0, 1] is the elasticity of wages with respect to technology. In order for the costs arising from the asymmetry in unemployment fluctuations to be significant, one needs a model which generates sizeable fluctuations in labor market activity. As first emphasized by Shimer (2005), the baseline Mortensen-Pissarides model is unable to account for the volatility of labor market variables observed in U.S. data. Several solutions to this problem, involving a different calibration in the case of Nash-bargained wages (Hagedorn and Manovskii, 2008) or a modification of the wage-setting mechanism (Hall, 2005; Hall and Milgrom, 2008) have been proposed. Ljungqvist and Sargent (2017) show that these solutions have in common that they restrict the fraction of a job’s output that the invisible hand can allocate to vacancy creation, what they call the fundamental surplus. As these authors emphasize, wage rigidity is neither a necessary nor a sufficient condition to generate large labor market fluctuations. In order to show this, consider the steady-state elasticity of labor market tightness with respect to productivity changes ηθ, Z . Abstracting from the nonnegativity constraint on vacancies, it writes

ηθ, Z =

1

α



1

μ

− ωγ Z γ −1



Z

(11)

Z

γ μ − ωZ

Z When the steady-state wage ω is large, the fundamental surplus μ − ω Z γ is small and the size of the elasticity is mainly determined by the last term, the fundamental surplus fraction. In that case a large elasticity of labor market tightness with respect to productivity changes is consistent with a high degree of wage flexibility.5 Conversely, when the steady-state wage ω is small, the fundamental surplus is large and a small elasticity of labor market tightness with respect to productivity changes is consistent with fully rigid wages (γ = 0). I focus here on steady-state comparative statics, but the same intuition applies in a dynamic setting. In order to generate sizeable labor market fluctuations while being consistent with the empirical evidence on the flexibility of the wages of new hires, the model is calibrated to feature a large γ and a small fundamental surplus, as detailed in Section 4.1. While the simple wage equation (10) is chosen for analytical convenience, it has the undesirable property of being invariant to the conduct of monetary policy. This gives the central bank more leverage over job creation as movements in markups affect the real revenues of intermediate firms with no offsetting movements in real wages. In Section 6.1, I check that my results hold under alternative wage-setting arrangements in which wages are endogenous to the conduct of monetary policy, such as Nash bargaining.

5

This holds as long as

γ < 1. When γ = 1 and Z = 1, ηθ, Z =

1 α is invariant to the value of the steady-state wage.

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.6 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

6

2.6. Monetary policy and equilibrium Monetary policy adjusts interest rates in response to movements in inflation and output growth according to the following rule

log(

1 + It 1+I

) = φr log(

1 + I t −1 1+I



) + (1 − φr ) φπ log (t ) + φ y log (Y t /Y t −1 )

(12)

where Y t = Z t N t is aggregate output. The economy-wide resource constraint is obtained by aggregating the budget constraints of households. Final output and home production can be used for consumption or to cover the deadweight costs of changing prices and posting vacancies

 C t = Z t Nt

1−

φp 2

 (t − 1)2 + b(1 − N t ) − κ v t

(13)

We can now define an equilibrium. Definition. A competitive equilibrium is a set of plans {C t , I t , N t , μt , θt , πt , w t , V t , ωt } satisfying equations (1), (4), (7), (8), (9), (10), (12), (13), as well as the definition of vacancies V t = (1 − (1 − ρ ) N t −1 ) θt , given a specification for the exogenous process { Z t } and initial conditions N −1 and I −1 . Technology is modeled as a first-order autoregressive process Z t − Z = δ Z ( Z t −1 − Z ) + εtZ where 0 < δ Z < 1 and N (0, σε2Z ) is a white noise innovation.

εtZ 

3. Steady-state analysis: uncovering the asymmetry in unemployment fluctuations This section undertakes a comparative statics exercise in order to understand the origin of the asymmetry in unemployment fluctuations. I solve for the zero-inflation steady-state equilibrium of the model. In that case, markups are constant and the equilibrium consists of three endogenous variables: labor market tightness, unemployment and consumption. In the following equations, steady-state variables are indicated by the absence of a time subscript. For expositional purposes, I abstract from the nonnegativity constraint on vacancies. Equilibrium labor market tightness is given by the job creation equation

κ q(θ) When

=

1



1 − (1 − ρ )β

Z

μ

 − ωZγ

α = 0.5, we have that p (θ) = p=

χ2



Z

κ (1 − (1 − ρ )β) μ

χ2 q(θ)

, hence the previous equation can be rewritten in the following way

 − ωZγ

The job-finding probability p is entirely determined by the level of productivity Z . In the (u , p ) plane of Fig. 1, the job creation curve is a horizontal line. Now that we have obtained the job-finding probability, we can deduce the unemployment rate from the steady-state version of equation (1)

p=

ρ (1 − u ) 1 − (1 − ρ )(1 − u )

This employment-flow curve is decreasing and convex in the (u , p ) plane of Fig. 1. We can see that shifts in productivity lead to almost symmetric shifts in the job-finding probability, but asymmetric shifts in unemployment. When Z = 1, steady-state unemployment is equal to 6%. When productivity increases by 2.5%, steady-state unemployment decreases by 4%. However, when productivity decreases by 2.5%, steady-state unemployment increases dramatically and reaches 14.5%. The intuition behind this result is simple. In an expansion, the impact on unemployment of an increase in the job-finding probability is dampened by the fact that the pool of job seekers is shrinking. In a recession, the impact on unemployment of a decrease in the job-finding probability is amplified by the fact that the pool of job seekers is expanding. In other words, in a search and matching model of the labor market, unemployment losses in recessions tend to be greater than unemployment gains in expansions. Unemployment fluctuations are asymmetric, and mean unemployment is higher in an economy with business cycles than in steady state. Following Jung and Kuester (2011), we can obtain an analytical expression for E (ut ) − u, where E (ut ) denotes the unconditional average of unemployment in an economy with aggregate fluctuations. Assuming that all variables in the employment-flow equation (1) are covariance stationary, E (ut ) − u is given by

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.7 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

7

Fig. 1. Steady-state equilibrium of the model. The solid blue line represents the steady-state version of the employment-flow equation. The red dashed line represents the steady-state version of the job creation equation for Z = 1. The red circled line represents the steady-state version of the job creation equation for Z = 1.025. The red pointed line represents the steady-state version of the job creation equation for Z = 0.975. The calibration required to obtain the figure is detailed in Section 4.1.

E (u t ) − u = −

1−ρ

ρ + (1 − ρ ) p

 cov ( pt , ut −1 ) +



ρ 1−ρ

 + E (u t ) ( E ( p t ) − p )

(14)

The proof of this result is presented in online Appendix 1. The mechanism described above is captured by the first term and involves the covariance between the job-finding probability and the unemployment rate. The second term E ( pt ) − p captures the extent to which fluctuations in the job-finding probability are asymmetric. In this comparative statics example, fluctuations in the job-finding probability are symmetric only if γ = 0 or γ = 1. Out of steady state, fluctuations in the stochastic discount factor and markups will also drive a wedge between E ( pt ) and p. However, as shown in the following sections, in the baseline version of the model, fluctuations in the job-finding probability are nearly symmetric and the bulk of unemployment losses due to business cycles is accounted for by the negative covariance between the job-finding probability and the unemployment rate. The analysis carried out so far suggests that an increase in the volatility of the job-finding probability leads to higher average unemployment. Through its influence on firms’ markups, monetary policy has the ability to influence job creation and labor market volatility. The next section explores in a quantitative manner how different monetary policy rules can lead to different outcomes in terms of mean unemployment. 4. Monetary policy, labor market volatility and mean unemployment 4.1. Calibration and solution method I calibrate the model to U.S. data. I take one period to be a quarter. Table 1 gives a summary of parameter values. A few parameters are calibrated using conventional values. The discount factor is set to β = 0.99, which yields an annual interest rate of 4%. The elasticity of substitution between goods is set to = 6 and the subsidy τ is fixed to ensure that the steady-state markup is equal to 1. I choose a coefficient of relative risk aversion σ = 1.5. The price adjustment cost parameter φ p is chosen according to the following logic. The linearized Phillips Curve of the model is observationally equivalent to the one derived under Calvo pricing, and structural estimates of New Keynesian models find an elasticity of (ε −1)(1+τ ) inflation with respect to marginal cost ω of 0.5 (Lubik and Schorfheide, 2004). In my model ω = , which implies φp

that φ p = 12. Alternatively, assuming an average contract duration of 4 quarters, the coefficient ω under Calvo pricing would be equal to 0.0858. This implies φ p = 70. I choose an intermediate value φ p = 40. This is also the value chosen by Krause and Lubik (2007). Next, I calibrate labor market parameters. I set the elasticity of matches with respect to unemployment at α = 0.5, within the range of plausible values proposed by Petrongolo and Pissarides (2001). I set the steady-state values of unemployment and labor market tightness to their empirical counterparts. I use the seasonally-adjusted monthly unemployment rate constructed by the Bureau of Labor Statistics (BLS) from the Current Population Survey (CPS). Labor market tightness is computed as the ratio of a measure of the vacancy level to this measure of unemployment. The measure of the vacancy level is obtained by merging the composite Help-Wanted index constructed by Barnichon (2010) for 1951-2001 and the seasonally-adjusted monthly vacancy level constructed by the BLS from JOLTS for 2001-2018. Over the period 1951-2018, the mean of the unemployment rate is 5.8% and the mean of labor market tightness is 0.61. For practical purposes, my targets will be 6% and 0.6 respectively. The separation probability is set to 0.08. These targets imply through the steady-state

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.8 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

8

Table 1 Calibrated parameters.

β φp

σ ε α ρ u

θ

κ b

γ δZ

σε Z φr φπ φ y

Parameter/SS value

Justification

0.99 40 1.5 6 0.5 0.08 6% 0.6 0.1282 0.4 0.8 0.9 0.009 0.69 1.35 0.26

Corresponds to an interest rate of 4% annually Intermediate value Conventional value Steady-state markup of 20% Petrongolo and Pissarides (2001) Conventional value Mean over the period 1951-2018 Mean over the period 1951-2018 Hiring costs = 14% of quarterly compensation Ad-hoc choice Haefke et al. (2013) Matches U.S. standard deviation and persistence of labor productivity Galí and Rabanal (2005) Galí and Rabanal (2005) Galí and Rabanal (2005)

employment flow equation a quarterly job-finding probability of 0.56, and through the definition of the job-finding probability, a matching efficiency of 0.7181. Silva and Toledo (2009) report that the number of hours spent by company employees to hire one individual amounts to about 4% of quarterly employee compensation. This figure jumps to 14% when expenses such as advertisement costs, agency fees, or travel costs for applicants are also accounted for. Thus, the vacancy posting cost is assumed to be equal to κ = 0.14qw. This results in vacancy posting costs κ v equal to 1.1% of output in steady-state. I can 1

then back out the steady-state value of the real wage from the job creation equation. I obtain ω = 1+0.14(1μ−β(1−ρ )) = 0.9877 and κ = 0.1282. Thus, this high value of the steady-state real wage stems from the calibration of hiring costs, and results in a small fundamental surplus.6 Pissarides (2009) and Haefke et al. (2013) emphasize that job creation depends on the expected net present value of wages over the entire duration of the newly-created jobs. Since wages in existing matches are known to be unresponsive to changes in aggregate conditions, it is the elasticity of the wages of new hires with respect to technology that matters for job creation. Following estimates in Haefke et al. (2013), I set this elasticity γ to 0.8. Finally, I choose a value of home production b equal to 0.4 in the baseline calibration. However, given that this parameter controls the level of steady-state distortions and is therefore critical in the analysis of monetary policy trade-offs, I also report results for alternative values in Section 5. The parameters of the technological process, δ Z and σε Z , are chosen in order to match U.S. labor productivity standard deviation and persistence. Finally, in order to mimic reasonably well the behavior of U.S. monetary policy, estimates from Galí and Rabanal (2005) are used to fix the parameters of the Taylor rule, φr = 0.69, φπ = 1.35 and φ y = 0.26.7 The model is solved by taking a second-order approximation to the equilibrium conditions around the deterministic steady state. The solution method is explained in Schmitt-Grohé and Uribe (2004). Using a second-order approximation to the equilibrium conditions rather than a first-order approximation is crucial to capture the nonlinearities induced by matching frictions. However, perturbation methods may not be appropriate if the lower-order derivatives evaluated at the deterministic steady state do not accurately capture the global behavior of the policy functions that are solved for. For this reason, I also solved the model with a global projection method. The algorithm and results are reported in online Appendix 5. The main messages of the paper are not only confirmed but strengthened in that case. 4.2. Labor market volatility and unemployment losses under alternative monetary policy rules Table 2 shows that the model generates a significant amount of labor market volatility when monetary policy is conducted according to the Taylor rule specified in the previous section. Labor market volatility is, however, lower than in the data, which seems reasonable given that technology is the only source of uncertainty in the model. Unemployment losses due to business cycles are modest in the baseline economy—average unemployment is only 0.21 percentage points higher than steady-state unemployment. As expected from the analysis carried out in Section 3, this is due to two factors. First, the model generates a negative covariance between the unemployment rate and the job finding probability equal to −4.15, measuring both rates in percentage points. Second, the mean job-finding probability in the fluctuating economy is lower than the steady-state job-finding probability p = 0.5562. This job-finding probability gap is mostly driven by the positive comovement between technology and markups, which tends to reduce average real revenues and depress job creation. Table 3 presents some simulated moments of the model under a policy of price stability (that is, φr = φ y = 0 and an arbitrarily large weight is put on inflation).

6 This direct relationship between small vacancy expenditures and a small fundamental surplus no longer holds with Nash bargaining. In that case, a small fundamental surplus necessary implies small hiring costs, but the opposite does not hold (Ljungqvist and Sargent, 2017). 7 Similar results obtain when the original Taylor (1993) rule is used.

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.9 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

9

Table 2 Moments of several labor market variables, in the data and simulated from the model. On the first line, u, v, θ , and p are quarterly averages of monthly series. The data sources for u, v, and θ are detailed in Section 4.1. The job-finding probability p is reconstructed according to the methodology detailed in Shimer (2012). All standard deviations are reported in logs as deviations from an HP trend with smoothing parameter 105 .

Standard deviation - Data Standard deviation - Taylor Rule Mean - Taylor Rule

u

v

θ

p

0.204 0.139 0.0621

0.201 0.199 0.0805

0.395 0.196 0.5886

0.141 0.098 0.5479

Table 3 Moments of several labor market variables. Simulated from the model. All standard deviations are reported in logs as deviations from an HP trend with smoothing parameter 105 .

Standard deviation - Price Stability Mean - Price Stability

u

v

θ

p

0.301 0.0642

0.217 0.0812

0.306 0.6175

0.153 0.5536

The labor market is much more volatile under this policy. The standard deviation of unemployment doubles and mean unemployment is higher by about 0.42 percentage points than in steady state. This increase in average unemployment is essentially accounted for by the increase in the volatility of the job-finding probability. Indeed, the value of the covariance between the job-finding probability and the unemployment rate jumps at −14.9. The asymmetry in job-finding rate fluctuations does not contribute to the increase in average unemployment. Because markups are constant under price stability, average real revenues are not affected by business cycles and the average job-finding probability is actually higher than in the baseline economy. We can understand why hiring is more volatile under a policy of price stability by solving forward the job creation equation

κ − ψt q(θt )

=

∞  j =0

 Et β j

 C t + j −σ Ct

(1 − ρ ) j (

Zt+ j

μt + j

γ

− ω Zt+ j )

(15)

This equation states that vacancy posting today is driven by the sum of future expected discounted real revenues net of wage payments. Since the paths of labor productivity and real wages are identical under all policies, the differences in vacancy posting activity must come from differences in the path of markups. As emphasized previously, markups are influenced by monetary policy as they depend on current inflation and future expected inflation. Thus, through its impact on markups, monetary policy has some control on the reaction of labor market activity to technology shocks. Under a Taylor rule, the monetary authority deviates from price stability and engineers procyclical markups, which dampens the impact of the shock on labor market tightness and employment. Under a policy of price stability, markups are constant and the effect of the shock on labor market tightness and employment is consequentially much larger. This is illustrated in Fig. 2, which plots the response of several variables to a positive productivity shock under the two policies. Thus, by engineering procyclical markups, the monetary authority can limit the impact of technology shocks on hiring. This will tend to reduce the magnitude of fluctuations in the job-finding probability and the unemployment rate, and because unemployment fluctuations are asymmetric, lead to lower average unemployment. However, in order to generate procyclical markups, the central bank must tolerate deviations from price stability. Therefore, this analysis suggests that the monetary authority faces a choice between inflation volatility and average unemployment. This intuition can be confirmed with a simple exercise. I assume that the monetary authority responds to inflation with coefficient φπ and to deviations of employment from steady state with coefficient φ N and compute E (ut ) for different values of φπ ranging from 1.5 to 10 and φ N ranging from 0 to 1. I thus consider both policies of price stability, for which φπ = 10 and φ N = 0, and policies that put a heavy emphasis on limiting employment volatility (for example φπ = 1.5 and φ N = 1). Fig. 3 plots the standard deviation of inflation and average unemployment under those different monetary rules. It shows that there is a clear relationship between inflation volatility and average unemployment. A higher standard deviation of inflation is associated with a lower level of unemployment. This section has established that deviating from price stability to reduce average unemployment is possible. The next section explores when it is optimal to do so. 5. When should the monetary authority deviate from price stability? In order to answer the question contained in the title, I first examine the sources of inefficiency in the flexible-price equilibrium that monetary policy can attempt to correct for by deviating from price stability. Second, I decompose welfare outcomes as a function of several first and second-order moments involving the job-finding probability, the unemployment

JID:YREDY AID:953 /FLA

10

[m3G; v1.260; Prn:8/08/2019; 16:08] P.10 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

Fig. 2. Impulse responses of selected variables following a positive productivity shock of one standard deviation under different rules: (1) Taylor rule, (2) Price Stability. The IRFs that are reported are average IRFs. I compute different IRFs for different initial conditions and different sequences of future shocks and average them.

Fig. 3. Standard deviation of inflation and average unemployment under alternative monetary policy rules.

rate, the inflation rate, and the level of technology. This helps understand through which margins the optimal policy improves on the flexible-price allocation. This exercise reveals that significant deviations from price stability are optimal when two conditions are met: 1) steady-state distortions are large; and 2) the fundamental surplus is small. 5.1. Sources of inefficiency in the flexible-price equilibrium I compare the flexible-price decentralized equilibrium with the allocation that a planner would achieve. The job creation equation in the planner equilibrium writes (see online Appendix 2.1)

  κ − ψt 1−α κ − ψt +1 = ( 1 − α )( Z − b ) + E β ( 1 − ρ ) 1 − αχ θ t t t + 1 t +1 χ θt−α χ θt−+α1

(16)

This equation should be compared with the job creation equation in the decentralized equilibrium, equation (7). In the flexible-price equilibrium, μt is constant and equal to one, its steady-state value, when the subsidy on the revenues of retail firms is in place. This makes it clear that inefficiencies in the decentralized equilibrium necessarily arise from wage disγ ef f tortions. While the actual wage is equal to w t = ω Z t , the efficient wage is given by w t = α ( Z t + E t βt +1 (1 − ρ )κ θt +1 ) + 8 (1 − α ) b. For given β, μ, α , ρ , κ , ω, Z , and given that steady-state labor market tightness θ is a function of these param8 The multiplier ψt +1 does not show up in this expression since the complementary slackness condition ψt V t = 0 and the requirement that N t ≤ 1 imply that ψt θt = 0.

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.11 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

Fig. 4. Coefficients

11

υ1 , υ2 , υ3 as a function of the value of home production b.

eters, the degree of steady-state distortions is thus summarized by the value of home production b. There is a threshold value of b¯ such that w = w e f f

b¯ =

ω − α (1 + β(1 − ρ )κ θ) 1−α

(17)

¯ the wage is too high relative to the efficient one and too few vacancies are posted in steady state. The When b < b, ¯ the reverse holds. Even when the steady state is efficient, job creation unemployment rate is inefficiently high. When b > b, ef f

will generally be inefficient in response to shocks as w t differs from w t . This is where monetary policy comes into play. By manipulating markups, the central bank can influence firms’ incentives to post vacancies and correct for inefficient labor market fluctuations. This comes at the cost of non-zero inflation volatility. 5.2. Decomposing welfare outcomes In order to lay the groundwork for the comparison between the optimal policy and the policy of price stability, I decompose conditional welfare U t0 = E t0 the utility function gives

U t0 = E t0

∞ 

∞

t =t 0

β t −t0

C t1−σ 1−σ

in a level effect and a volatility effect. A second-order approximation to

β t −t0 C −σ [Levelt + Volatilityt ] + O 3 + t .i . p .

(18)

t =t 0

where O 3 is terms of third and higher order, t.i.p. is terms independent of policy, and

Levelt = C˜t = υ1 p˜ t + υ2 p˜ t2 + υ3 u˜ t −1 p˜ t − Volatilityt = −

σ ˜2 Ct = −

2C

σ

2C

1 2

˜ t2 − Z˜ t u˜ t Nφ p

υ4 ut2−1 + υ5 p˜ t2 + υ6 u˜ t −1 p˜ t + υ7 Z˜ t p˜ t + υ8 Z˜ t u˜ t −1

(19)

 (20)

where the tilde sign ∼ indicates deviations from steady state X˜t = X t − X and the coefficients υ1 to υ8 depend on parameters of the model and steady-state values of endogenous variables. All derivations as well as the expressions for υ1 to υ8 are presented in online Appendix 2.4. Equation (19) shows that the level of consumption decreases with inflation volatility and the covariance between technology and unemployment. The impact of the other terms depends on the values of υ1 , υ2 and υ3 , which are plotted in Fig. 4 as a function of b. All else equal, an increase in the volatility of the job-finding probability always leads to an increase in the level of consumption regardless of the degree of steady-state distortions (υ2 > 0 ∀b), as it lowers vacancy posting costs. Decreases in the level of the job-finding probability p˜ t and in the covariance between unemployment and the job-finding probability u˜ t −1 p˜ t lead to decreases in both employment and vacancy posting costs. As long ¯ the output loss due to the decrease in employment is larger than the decrease in vacancy posting costs, and conas b < b, ¯ these two effects perfectly offset each other and p˜ t and u˜ t −1 p˜ t drop out of equation (19). It sumption declines. When b = b, is well known in the literature that linear terms show up in second-order approximations to welfare when the steady state is distorted. In the context of the standard New Keynesian model, expected utility depends on the expected level of output (Benigno and Woodford, 2005). In the model considered in this paper, which incorporates search and matching frictions in the labor market, expected utility depends on expected levels of employment and vacancies, which appear in equation (19)

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.12 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

12

Table 4 Moments of several variables under the optimal policy for different values of b. Simulated from the model. Standard deviations are reported in logs as deviations from an HP trend with smoothing parameter 105 .

Standard deviation - Unemployment Standard deviation - Inflation

λ

b=0

b = 0.4

b = b¯ = 0.905

0.036 0.40% 0.41%

0.077 0.33% 0.17%

0.239 0.07% 0.002%

through the terms p˜ t and u˜ t −1 p˜ t .9 As shown in Fig. 4, the importance of these terms rises with the extent of steady-state distortions. 5.3. The optimal policy I now derive the Ramsey optimal policy, defined as the process { I t } associated with the competitive equilibrium that yields the highest level of conditional welfare U t0 , and study its properties. In what follows, I define the welfare costs of adopting a regime of price stability instead of the Ramsey regime λ as the fraction of the Ramsey consumption process that a household would be willing to give up to be as well-off under the price stability regime as under the Ramsey regime. 5.3.1. The role of steady-state distortions Table 4 reports the standard deviations of unemployment and inflation under the optimal policy, as well as the welfare costs of price stability λ, for different values of b. Focusing first on the middle column, which corresponds to the baseline calibration, one can see that unemployment volatility is much lower than under a policy of price stability. This lower volatility is reflected in the value of the covariance between the unemployment rate and the job-finding probability, which stands at −0.98. Because the average job-finding probability is sensibly equal to its value under price stability, the unemployment losses due to business cycles are much lower—average unemployment is equal to 6.12%. This reduction in average unemployment compared to the price stability case is achieved by allowing the standard deviation of net inflation to rise to 0.33%. The Ramsey policy reaps substantial welfare gains by doing so—λ is equal to 0.17% in the baseline calibration. Focusing now on the other columns, it is apparent that the behavior of the Ramsey policy varies systematically with the degree of steady-state distortions. When the steady state is efficient or nearly so, the Ramsey policy is comparable to a policy of price stability. The central bank puts a strong emphasis on stabilizing inflation at the expense of unemployment volatility. For lower values of home production—that is, when the steady state is more distorted—the Ramsey policy becomes more stabilizing. It uses inflation volatility to reduce unemployment volatility and average unemployment. This results in large welfare gains compared to the price stability case. I now use the decomposition of conditional welfare to understand these results. Fig. 5 plots the business cycle costs arising from the different terms appearing in (19) and the volatility term (20) as a whole, as a function of the value of home production b. The top panel shows welfare outcomes under a policy of price stability and the bottom panel shows welfare outcomes under the optimal policy. In the top panel, it is immediately apparent that the welfare costs of business cycles under a policy of price stability rise dramatically with the degree of steady-state distortions, and that this rise is mostly accounted for by the term involving the negative covariance between the unemployment rate and the job-finding probability. This reflects the increase in υ3 as b decreases. Indeed, the cyclical properties of the model, and the size of the covariance between the unemployment rate and the job-finding probability, are largely independent of b. Turning to the bottom panel, one can see that most of the welfare gains obtained by the Ramsey policy can be traced back to the decrease (in absolute value) in the covariance between unemployment and the job-finding probability (the green dotted line). To a lesser extent, the reduction in consumption volatility (the red plus signs) also contributes to the improvement in welfare outcomes. This comes at a cost, an increase in inflation volatility (the black arrows). Thus, as steady-state distortions grow, deviations of average unemployment from its steady-state value—proxied by the size of the covariance between unemployment and the job-finding probability—loom larger in welfare, and business cycle costs increase. The monetary authority then finds it optimal to use some inflation volatility to reduce average unemployment. 5.3.2. The role of the fundamental surplus, and the limited relevance of wage rigidity The preceding analysis has been conducted under the assumption that the calibrated economy features a small fundamental surplus, and therefore that the model generates a significant amount of labor market volatility in response to shocks.

9 I seek to obtain a welfare measure that is accurate to second order in order to compare the welfare consequences of different policies. In an economy with a distorted steady state, this implies solving for a second-order approximation to the complete evolution of the endogenous variables under each contemplated policy, and then use this solution to evaluate (18) in combination with (19) and (20) (Kim et al., 2008). This is what is done here. Alternatively, following Benigno and Woodford (2005), it would be possible to express p˜ t as a function of quadratic terms only by taking second-order approximations to the job creation equation (7) and the Phillips Curve (9). In that case, policies and their welfare consequences could accurately be ranked by minimizing a version of equations (18), (19), and (20), in which the expression of p˜ t as a function of quadratic terms has been substituted, subject to a first-order approximation of the equilibrium conditions. I stop short of this last step as it involves tedious algebra, without clear benefits in terms of interpretation.

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.13 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

13

Fig. 5. Business cycle costs arising from the different terms appearing in the decomposition of conditional welfare under a policy of price stability (top panel) and the optimal policy (bottom panel). These costs are measured as the fraction of steady-state consumption that agents would have to give up to be as well-off in steady state as in an economy in which business cycle costs arise only from the term under consideration. Positive values indicate a welfare cost, while negative values indicate a welfare gain.

I now consider a version of the model with a larger fundamental surplus. This is achieved by recalibrating hiring costs to be equal to 30% of quarterly employee compensation. In that case the steady-state wage ω is lower and steady-state efficiency now dictates that b = b¯ = 0.805. Compared to the baseline calibration, the standard deviation of unemployment under a policy of price stability is approximately halved and average unemployment lower by 0.3 percentage points for all values of b. Fig. 6 reproduces the decomposition of conditional welfare under this new calibration. It shows that the assumption of a small fundamental surplus is critical to generating large business cycle costs under a policy of price stability. With lower labor market volatility, the covariance between the unemployment rate and the job-finding probability is smaller (in absolute value), and the costs arising from it much more modest (the green dotted line). This results in less incentives to deviate from price stability for the policymaker; inflation volatility is lower under the optimal policy (the black arrows). Even when steady-state distortions are large, for example when b = 0, the welfare costs of adopting a regime of price stability instead of the Ramsey regime λ = 0.075% remain modest. Conversely, similar simulations show that the welfare costs of price stability increase as the size of the fundamental surplus decreases.10 I have thus far kept the degree of wage rigidity γ fixed. As shown in equation (11), for a given fundamental surplus, a lower γ is associated with a larger elasticity of labor market tightness to productivity. For example, when hiring costs are equal to 30% of quarterly employee compensation, a similar elasticity of labor market tightness with respect to productivity than in the baseline calibration is obtained if γ = 0.55. When hiring costs are equal to 50% of quarterly employee compensation, such an elasticity is obtained if γ = 0.25. Conversely, with hiring costs equal to 7% of quarterly employee compensation, this elasticity is obtained if γ = 0.9. In all cases, deviations from price stability are substantial, provided the

10

Results are available upon request.

JID:YREDY AID:953 /FLA

14

[m3G; v1.260; Prn:8/08/2019; 16:08] P.14 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

Fig. 6. Business cycle costs arising from the different terms appearing in the decomposition of conditional welfare under a policy of price stability (top panel) and the optimal policy (bottom panel). These costs are measured as the fraction of steady-state consumption that agents would have to give up to be as well-off in steady state as in an economy in which business cycle costs arise only from the term under consideration. Positive values indicate a welfare cost, while negative values indicate a welfare gain. Calibration with a larger fundamental surplus: hiring costs are equal to 30% of quarterly employee compensation.

degree of steady-state distortions is kept constant.11 Thus, for a given size of the fundamental surplus, the presence of wage rigidity can help deliver a significant trade-off between inflation and unemployment stabilization. However, as emphasized in Ljungqvist and Sargent (2017), wage rigidity is neither necessary nor sufficient to obtain a large elasticity of labor market tightness with respect to productivity. If the fundamental surplus is large, labor market fluctuations can be small although wages are rigid. If the fundamental surplus is small, large labor market fluctuations obtain although wages are flexible. This last point is further developed in Section 6.1, which looks at monetary policy trade-offs when wages are set according to the Nash bargaining solution. A comparison with the literature confirms the importance of the fundamental surplus and the limited relevance of wage rigidity.12 In Faia (2008), the elasticity of labor market tightness with respect to productivity is small, although wages exhibit some rigidity. This is because the fundamental surplus is large; unemployment benefits and the steady-state real wage are significantly below the steady-state value of firms’ real revenues. Ravenna and Walsh (2012) consider two cases in which the steady state is inefficient; one in which wages are set according to the Nash bargaining solution, another in which they are fixed at their steady-state value. They find that a significant trade-off between stabilizing inflation and stabilizing labor market activity only arises in the second scenario. Indeed, in the first case, their calibration implies that the outside option of workers is significantly below the marginal product of a worker—the fundamental surplus is large. In the second case, the introduction of perfectly rigid wages entails that the size of the fundamental surplus is directly related to the size of

11 12

¯ this implies readjusting the value of b. Given that an increase in hiring costs leads to a decrease in b, The following results are shown formally in online Appendix 4.

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.15 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

15

hiring costs, which are calibrated to be small. As a result, the fundamental surplus is divided by a factor of ten compared to the case with Nash-bargained wages. 6. Robustness 6.1. An alternative wage-setting mechanism One limitation of the preceding analysis is that the wage is invariant to the conduct of monetary policy. When markups decrease, the increase in real revenues is not offset by an adjustment in wages. This makes the central bank much more effective at influencing real activity and may thus push the benefits of deviating from price stability upwards. In order to address this concern, I now check whether my results still hold when wages are instead given by the Nash bargaining solution. This example also serves to further emphasize that a significant trade-off between inflation and unemployment stabilization can arise even when the elasticity of wages with respect to productivity is close to one—in what follows, it is equal to 0.93. The derivations are presented in online Appendix 3. The real wage becomes



wt = η

Zt

μt

 + E t βt +1 (1 − ρ )κ θt +1 + (1 − η)(b + w u )

(21)

where η is the bargaining power of workers and w u is unemployment benefits. In this setting, the steady-state elasticity of labor market tightness with respect to productivity is equal to κ

ηθ, Z =

Z

θ q(θ ) (1 − β(1 − ρ )) + ηβ (1 − ρ ) κ

κ

μ

θ q(θ ) α (1 − β(1 − ρ )) + ηβ (1 − ρ ) κ μ Z

(22)

− b − wu

Since the first term is bounded above by 1/α , the size of this elasticity mainly depends on the second term, the fundamental Z surplus fraction. In turn, the fundamental surplus μ − b − w u depends on the value of non-market activity b + w u . In order

to generate a small fundamental surplus, I calibrate b + w u to 0.95. I also set the bargaining power η equal to 0.5. The value of vacancy posting costs κ is then determined through steady-state relationships. The resulting hiring costs are equal to 7% of quarterly compensation, which lies in the interval proposed by Silva and Toledo (2009). Given that η = α , the degree of steady-state distortions is still usefully pinned down by the value of home production b (or inversely, by the value of unemployment benefits w u )

b¯ − b = w u =

w − wef f

(23)

1−η

When w u = 0 and b = b¯ = 0.95, the flexible-price allocation coincides with the efficient allocation. As b decreases and w u increases, the steady state becomes more distorted. Table 5 reports the standard deviations of unemployment and inflation under the optimal policy, as well as the welfare costs of price stability λ, for different values of b. The results obtained in the ¯ the Ramsey policy sticks to a policy of price stability in order to baseline specification are largely confirmed. When b = b, replicate the flexible-price allocation. However, as the degree of steady-state distortions increases, the optimal policy relies more and more on inflation volatility to stabilize unemployment fluctuations. This strategy generates large welfare gains, which are mostly accounted for by the decrease (in absolute value) in the covariance between the unemployment rate and the job-finding probability, as shown in Fig. 1 in the online Appendix. Table 5 Moments of several variables under the optimal policy for different values of b. Simulated from the model with Nash bargaining. Standard deviations are reported in logs as deviations from an HP trend with smoothing parameter 105 .

Standard deviation - Unemployment Standard deviation - Inflation

λ

b=0

b = 0.4

b = b¯ = 0.95

0.1442 0.81% 0.44%

0.182 0.61% 0.19%

0.344 0.00% 0.00%

6.2. Other shocks Another limitation of the analysis is that it is conditional on a single shock to technology. This shock is generally the only source of uncertainty in studies analyzing optimal monetary policy in models with search and matching frictions in the labor market. Nevertheless, it could be interesting to see whether similar results obtain in response to other disturbances, especially those which play a large role in estimated New Keynesian models. One such disturbance is a shock to the desired

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.16 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

16

Table 6 Moments of several variables under the optimal policy for different values of b. Simulated from the model with price-markup shocks. Standard deviations are reported in logs as deviations from an HP trend with smoothing parameter 105 .

Standard deviation - Unemployment Standard deviation - Inflation

λ

b=0

b = 0.4

b = b¯ = 0.905

0.0506 0.32% 0.24%

0.0478 0.27% 0.11%

0.1013 0.12% 0.006%

price markup of retail firms, which can be introduced by making the elasticity of substitution between goods time varying. I now assume that this elasticity follows an autoregressive process of order one

t − = δ ( t −1 − ) + εt

(24)

where 0 < δ < 1 and εt  N (0, σε2 ) is a white noise innovation. Abstracting from technology shocks, I set δ = 0.9 and cal-

ibrate σε2 such that the standard deviation of unemployment under the Taylor rule is similar to that reported in Section 4.2. Table 6 shows that the Ramsey policy tolerates more inflation volatility and less unemployment volatility as the degree of steady-state distortions becomes larger. The welfare gains of deviating from price stability also increase with the level of steady-state distortions and can be quite significant. They are mostly accounted for by the decrease (in absolute value) in the covariance between the unemployment rate and the job-finding probability achieved by the Ramsey policymaker, as shown in Fig. 2 in the online Appendix. Thus, the results are comparable to those obtained in the case of technology shocks. A significant trade-off between inflation and unemployment stabilization arises under the same conditions, and for the same reasons. 7. Conclusion An important literature seeks to describe optimal monetary policy in dynamic economies featuring nominal and real rigidities. This paper adds to this literature by showing that a significant trade-off between inflation and unemployment stabilization arises in the presence of search and matching frictions in the labor market when both steady-state distortions and the elasticity of labor market tightness with respect to labor productivity are large. The first condition implies that variations in average unemployment matter for welfare outcomes. The second condition obtains when the fraction of a job’s output that the invisible hand can allocate to vacancy creation, what Ljungqvist and Sargent (2017) call the fundamental surplus, is small, and implies that labor market fluctuations are large. Because of the labor market asymmetries built in the search and matching framework, it also entails that average unemployment is substantially higher in an economy with business cycles than in steady state. In this environment, the central bank has an incentive to tolerate some inflation volatility in response to shocks since doing so reduces unemployment volatility and average unemployment. The welfare gains of adopting such a dual mandate policy instead of a policy of price stability are large. Appendix A. Supplementary material Supplementary material related to this article can be found online at https://doi.org/10.1016/j.red.2019.07.005. References Barnichon, Regis, 2010. Building a composite help-wanted index. Economics Letters 109 (3), 175–178. Benigno, Pierpaolo, Woodford, Michael, 2005. Inflation stabilization and welfare: the case of a distorted steady state. Journal of the European Economic Association 3 (6), 1185–1236. Benigno, Pierpaolo, Ricci, Luca A., Surico, Paolo, 2015. Unemployment and productivity in the long run: the role of macroeconomic volatility. Review of Economics and Statistics 97 (3), 698–709. Blanchard, Olivier J., Galí, Jordi, 2010. Labor market frictions and monetary policy: a New Keynesian model with unemployment. American Economic Journal: Macroeconomics 2 (2), 1–30. Faia, Ester, 2008. Optimal monetary policy rules with labor market frictions. Journal of Economic Dynamics and Control 32, 1600–1621. Faia, Ester, 2009. Ramsey monetary policy with labor market frictions. Journal of Monetary Economics 56, 570–581. Ferraro, Domenico, 2018. The asymmetric cyclical behavior of the U.S. labor market. Review of Economic Dynamics 30, 145–162. Galí, Jordi, Rabanal, Pau, 2005. Technology shocks and aggregate fluctuations: how well does the RBC model fit postwar U.S. data? In: NBER Macroeconomics Annual 2004, vol. 19, pp. 225–318. Haefke, Christian, Sonntag, Marcus, van Rens, Thijs, 2013. Wage rigidity and job creation. Journal of Monetary Economics 60 (8), 887–899. Hagedorn, Marcus, Manovskii, Iourii, 2008. The cyclical behavior of equilibrium unemployment and vacancies revisited. The American Economic Review 98, 1692–1706. Hairault, Jean-Olivier, Langot, François, Osotimehin, Sophie, 2010. Matching frictions, unemployment dynamics and the costs of business cycles. Review of Economic Dynamics 13, 759–779. Hall, Robert E., 2005. Employment fluctuations with equilibrium wage stickiness. The American Economic Review 95, 50–65. Hall, Robert E., Milgrom, Paul, 2008. The limited influence of unemployment on the wage bargain. The American Economic Review 98, 1653–1674. Jung, Philip, Kuester, Keith, 2011. The (un)importance of unemployment fluctuations for the welfare cost of business cycles. Journal of Economic Dynamics and Control 35, 1744–1768.

JID:YREDY AID:953 /FLA

[m3G; v1.260; Prn:8/08/2019; 16:08] P.17 (1-17)

A. Lepetit / Review of Economic Dynamics ••• (••••) •••–•••

17

Kim, Jinill, Kim, Sunghyun, Schaumburg, Ernst, Sims, Christopher A., 2008. Calculating and using second-order accurate solutions of discrete time dynamic equilibrium models. Journal of Economic Dynamics and Control 32, 3397–3414. Krause, Michael U., Lubik, Thomas A., 2007. The (ir)relevance of real wage rigidity in the NK model with search frictions. Journal of Monetary Economics 54, 706–727. Ljungqvist, Lars, Sargent, Thomas J., 2017. The fundamental surplus. The American Economic Review 107 (9), 2630–2665. Lubik, Thomas, Schorfheide, Frank, 2004. Testing for indeterminacy: an application to U.S. monetary policy. The American Economic Review 94 (1), 190–217. Mortensen, Dale T., Pissarides, Christopher A., 1994. Job creation and job destruction in the theory of unemployment. The Review of Economic Studies 61, 397–415. Petrongolo, Barbara, Pissarides, Christopher A., 2001. Looking into the black box: a survey of the matching function. Journal of Economic Literature 39, 390–431. Petrosky-Nadeau, Nicolas, Zhang, Lu, 2013. Unemployment Crises. NBER Working Paper Series 19207. National Bureau of Economic Research, Cambridge, Mass., July. www.nber.org/papers/w19207. Pissarides, Christopher A., 2009. The unemployment volatility puzzle: is wage stickiness the answer? Econometrica 77, 1339–1369. Ravenna, Federico, Walsh, Carl E., 2011. Unemployment, sticky prices, and monetary policy: a linear-quadratic approach. American Economic Journal: Macroeconomics 3, 130–162. Ravenna, Federico, Walsh, Carl E., 2012. Monetary policy and labor market frictions: a tax interpretation. Journal of Monetary Economics 59, 180–195. Schmitt-Grohé, Stephanie, Uribe, Martin, 2004. Solving dynamic general equilibrium models using a second-order approximation to the policy function. Journal of Economic Dynamics and Control 28, 755–775. Shimer, Robert, 2005. The cyclical behavior of equilibrium unemployment and vacancies. The American Economic Review 95, 25–49. Shimer, Robert, 2012. Reassessing the ins and outs of unemployment. Review of Economic Dynamics 15 (2), 127–148. Silva, Jose I., Toledo, Manuel, 2009. Labor turnover costs and the cyclical behavior of vacancies and unemployment. Macroeconomic Dynamics 13, 76–96. Taylor, John B., 1993. Discretion versus policy rules in practice. Carnegie-Rochester Conference Series on Public Policy 39, 195–214. Thomas, Carlos, 2008. Search and matching frictions and optimal monetary policy. Journal of Monetary Economics 55, 936–956. Walsh, Carl E., 2014. Multiple Objectives and Central Bank Trade-Offs Under Flexible Inflation Targeting. CESifo Working Paper 5097. CESifo Group Munich.