- Email: [email protected]
Reallocation shocks, persistence and nominal rigidities
Accepted Manuscript Reallocation shocks, persistence and nominal rigidities Francesco Furlanetto, Nicolas Groshenny PII: DOI: Reference:
S0165-1765(16)30058-1 http://dx.doi.org/10.1016/j.econlet.2016.02.029 ECOLET 7093
To appear in:
Economics Letters
Received date: 7 January 2016 Revised date: 24 February 2016 Accepted date: 24 February 2016 Please cite this article as: Furlanetto, F., Groshenny, N., Reallocation shocks, persistence and nominal rigidities. Economics Letters (2016), http://dx.doi.org/10.1016/j.econlet.2016.02.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights
Unemployment and vacancies are strongly negatively correlated in the data. The literature argues that reallocation shocks are not important because they generate a positive correlation. Reallocation shocks do not always generate a positive correlation between unemployment and vacancies. The sign of the correlation depends on the degree of price rigidity and on the persistence of the shock. A non-negligible role for reallocation shocks cannot be dismissed on theoretical grounds.
*Manuscript Click here to view linked References
Reallocation Shocks, Persistence and Nominal Rigidities Francesco Furlanettoy
Nicolas Groshennyz
February 2016
Abstract We reconsider the role of reallocation shocks in a simple New Keynesian model with search and matching frictions. The sign of the conditional correlation between unemployment and vacancies depends on the degree of price rigidity and on the persistence of the shock. Therefore, a non negligible role for reallocation shocks in driving business cycle ‡uctuations cannot be ruled out on theoretical grounds. Keywords: Search and Matching Frictions; Matching E¢ ciency; Reallocation Shocks. JEL codes: E32, C51, C52 This paper should not be reported as representing the views of Norges Bank. The views expressed are those of the authors and do not necessarily re‡ect those of Norges Bank. This paper is a revised and shortened version of Norges Bank Working Paper 7/2012 with title "Matching e¢ ciency and business cycle ‡uctuations". We are indebted to our discussants Tim Kam, James Hansen and Ian King for their extremely valuable feedback. For useful comments, we thank one anonymous referee, Regis Barnichon, Larry Christiano, Marco Del Negro, Punnoose Jacob, Nicolas Jacquet, Alejandro Justiniano, Per Krusell, Francois Langot, Ellen McGrattan, Espen Moen, Federico Ravenna, Kjetil Storesletten, Fabien Tripier, Anders Vredin, Mirko Wiederholt and Jake Wong. y Corresponding Author. Address: Norges Bank, Bankplassen 2, PB 1179 Sentrum, 0107 Oslo, Norway. E-mail: [email protected]. Telephone number: +47 22316128. z Address: University of Adelaide, School of Economics. E-mail: [email protected].
1
1
Introduction
In this paper, we reconsider the debate on the importance of reallocation shocks initiated by Lilien (1982) and we highlight the link between the degree of nominal rigidity and the propagation of persistent shocks to the matching e¢ ciency in the labor market. Following the seminal paper by Andolfatto (1996), these shocks can be interpreted as reallocation shocks, as long as they capture some form of mismatch in skills, in geography or in other dimensions. In particular, we use a simple New Keynesian model with equilibrium search unemployment to investigate how variations in the e¤ectiveness of the labor market matching process a¤ect the correlation between unemployment and vacancies. According to Lilien (1982), reallocation shocks could explain up to 50 percent of unemployment ‡uctuations in the postwar period. The empirical regularity underlying this result is a positive correlation between the dispersion of employment growth rates across sectors and the unemployment rate. However, Abraham and Katz (1986) show that this positive correlation is consistent not only with reallocation shocks but also with aggregate demand shocks. According to Abraham and Katz (1986), the use of data on unemployment and vacancies is more useful and lead to dismiss the importance of reallocation shocks. In fact, they argue that reallocation shocks, unlike aggregate demand shocks, deliver a positive correlation between unemployment and vacancies, while the two series are strongly negatively correlated in the data along the well-known Beveridge curve. We contribute to the literature on the relationship between reallocation shocks and the conditional correlation between unemployment and vacancies by using a fully speci…ed general equilibrium model. Furthermore, we show that the conditional correlation between unemployment and vacancies discussed in Abraham and Katz (1986) is positive only when prices are su¢ ciently rigid and the shock is highly persistent. When nominal rigidities are present, as in our baseline model, a negative shock leads to an increase in vacancies and creates a positive correlation. However, as we reduce the degree of nominal rigidities, the response of vacancies to a negative disturbance becomes less and less positive and eventually turns negative when prices are highly ‡exible. Hence, the conditional correlation between unemployment and vacancies declines substantially and can
2
even become negative when the shock has limited persistence. Interestingly, this …nding is reminiscent of Galí’s (1999) result on the role of nominal rigidities for determining the sign of the employment response to a technology shock. We conclude that a non-negligible role for reallocation shocks cannot be ruled out on theoretical grounds. Importantly, while other studies have considered shocks to the matching e¢ ciency (cf. Lubik 2009, Krause, Lubik, and López-Salido 2008, and Justiniano and Michelacci 2011, among others), the link between the degree of nominal rigidities, the shock’s persistence and the sign of the correlation between unemployment and vacancies is a novel contribution of this paper. Hosios (1994) has also made the point that reallocation shocks do not necessarily generate a positive correlation between unemployment and vacancies in the context of a partial equilibrium model with ‡exible prices and temporary layo¤s driven by a shock to the relative price dispersion across …rms. We conduct our analysis in a general equilibrium model with nominal rigidities driven by a matching e¢ ciency shock. The paper proceeds as follows: Section 2 brie‡y describes the model, Section 3 presents our results and Section 4 concludes.
2
The Model
The model relies largely on Kurozumi and Van Zandweghe (2010) and is purposely simple. The representative household is a large family, made up of a continuum of individuals of measure one. Family members pool their income before allowing the head of the household to choose its optimal per capita consumption. Each period, Nt family members are employed. Each employee works a …xed amount of hours and earns the nominal wage Wt . The remaining (1
Nt ) family members are
unemployed and each receives nominal unemployment bene…ts b, …nanced through lumpsum nominal taxes Tt so that the government budget is always balanced. Unemployment bene…ts b are proportional to the steady-state nominal wage: b = W . The representative household owns retail …rms and receives each period the accumulated pro…ts (Dt ).
3
The family’s period t budget constraint is given by
Pt Ct +
Bt Rt
Bt
1
+ Wt Nt + (1
Nt ) b
(1)
Tt + Dt ;
where Ct represents a Dixit-Stiglitz aggregator of retail goods purchased for consumption purposes, Pt is the corresponding price index, Bt refers to the quantity of bonds purchases by the family and Rt denotes the gross nominal interest rate. The family’s lifetime utility P s is described by Et 1 ln Ct+s , where 0 < < 1. s=0
Each intermediate good-producing …rm i 2 [0; 1] enters in period t with a stock
of Nt
1
(i) employees. New matches become productive in the period, as in Ravenna
and Walsh (2008). The job destruction rate
is constant. The workers who have
lost their jobs start searching immediately and can possibly still be hired in period t with a probability given by the job …nding rate. Employment at …rm i evolves according to Nt (i) = (1
) Nt
1
(i) + Mt (i) where the ‡ow of new hires Mt (i) is given by
Mt (i) = Qt Vt (i) : The term Vt (i) denotes vacancies posted by …rm i in period t and Qt t is the aggregate probability of …lling a vacancy, de…ned as Qt = M . The expressions Vt R1 R1 Mt = 0 Mt (i) di and Vt = 0 Vt (i) di denote aggregate matches and vacancies respecR1 tively. Aggregate employment, Nt = 0 Nt (i) di, evolves according to
Nt = (1
) Nt
1
(2)
+ Mt :
The matching process is described by an aggregate constant-returns-to-scale Cobb Douglas matching function,
Mt = Lt St Vt1
(3)
;
where St denotes the pool of job seekers in period t given by St = 1
(1
) Nt 1 ; and Lt
is a time-varying scale parameter that captures the e¢ ciency of the matching technology. It evolves exogenously following the autoregressive process,
ln Lt = (1
L ) ln L
+
L
ln Lt
1
+ "Lt ; 4
(4)
where L denotes the steady-state value of the matching e¢ ciency, while persistence of the shock, and "Lt is i:i:d:N (0; The job-…nding rate (Ft ) is de…ned as Ft = 1
L
measures the
2 L ). Mt St
and aggregate unemployment is Ut
Nt : Firms face hiring costs measured in terms of the …nished good (Ht (i)). Those
costs depends linearly on the number of vacancies posted by the …rm, Ht (i) = where the parameter
N
N Vt
(i),
governs the magnitude of the (pre-match) hiring cost.
Each period, …rm i uses Nt (i) homogeneous employees to produce Yt (i) units of intermediate good i according to the constant-returns-to-scale technology described by Yt (i) = Nt (i) : Each intermediate good-producing …rm i 2 [0; 1] chooses employment and vacancies to maximize pro…ts and sells its output Yt (i) in a perfectly competitive market at a price Zt (i) that represents the relative price of the intermediate good in terms of the …nal good. The …rm maximizes
Et
1 X s=0
where
t
s
t+s+1
Zt+s (i)Yt+s (i)
t+s
Wt+s (i) Nt+s (i) Pt+s
Ht+s (i) ;
(5)
represents the marginal utility of consumption.
The nominal wage Wt (i) is determined through surplus sharing,
Wt (i) = arg max
where 0 <
t
(i) Jt (i)1
(6)
;
< 1 represents the worker’s bargaining power,
t
(i) is the worker’s surplus
and Jt (i) is the …rm’s surplus. There is a continuum of retail goods-producing …rms indexed by j 2 [0; 1] that transform the intermediate good into a …nal good Ytf (j) that is sold in a monopolistically competitive market at price Pt (j). Cost minimization implies that the real marginal cost is equal to the real price of the intermediate good (Zt ) that is common across …rms. Demand for good j is given by Ytf (j) = Ct (j) = (Pt (j)=Pt ) Ct , where
represents the
elasticity of substitution across …nal goods. Firms choose their price subject to a Calvo scheme in which every period a fraction
is not allowed to re-optimize, whereas the
5
remaining fraction 1
Et
1 X
t+s
)s
(
chooses optimally its price (Pt (j)) by maximizing:
t
s=0
Pt (j) Pt+s
f Zt+s Yt+s (j) :
(7)
The central bank adjusts the short-term nominal gross interest rate Rt by following a Taylor-type rule,
ln
Rt R
=
r
ln
Rt 1 R
+ (1
The degree of interest-rate smoothing output growth (
and
y)
r)
"
r
ln
Pt Pt 4
1=4
+
y
ln
Yt Yt 4
1=4
#
:
(8)
and the reaction coe¢ cients to in‡ation and
are all positive.
Our parameterization is based on the US economy. A …rst set of parameters is taken from the literature on monetary business cycle models. The discount factor is set at = 0:99; the elasticity of substitution across …nal goods at
= 11 implies a steady-state
markup of 10 percent. The parameters in the monetary policy rule are y
= 0:8;
= 1:5,
= 0:5. The average degree of price duration is four quarters, corresponding to
= 0:75.
r
A second set of parameter values is taken from the literature on search and matching in the labor market. The degree of exogenous separation is set at
= 0:08, while the
steady-state value of the unemployment rate is U = 0:06. The elasticity in the matching function is
= 0:5, in the range of plausible values used in the literature. In the absence
of convincing empirical evidence on the value for the bargaining power parameter , we set it equal to 0.5 to satisfy the Hosios condition. The vacancy …lling rate Q is set equal to 0:70. We set
N
such that total hiring costs in the steady state are equal to one percent
of steady state output. The value of unemployment bene…ts
is derived from the steady-
state conditions. These choices are common in the literature and avoid indeterminacy issues, as discussed in Kurozumi and Van Zandweghe (2010). Finally, as there is no clear guidance from the literature, we choose an intermediate value for the persistence of the shock process. We set it at 0.6 in the baseline parameterization and we consider the full range of values between 0 and 1 in the next Section. Additional details on the model (including the list of the order conditions, the analysis
6
of the steady state and the log-linearized equations) are provided in the working paper version of this letter (Furlanetto and Groshenny, 2012).
3
The Role of Nominal Rigidities and Persistence
We now discuss how the degree of price rigidity a¤ects the vacancy response to a matching e¢ ciency shock (cf. Figure 1). Under sticky prices (solid lines) …rms do not increase prices as much as they would prefer in response to a less e¢ cient matching process in the labor market. Therefore, the decrease in output and in hiring is limited. When matching e¢ ciency declines, the probability of …lling a vacancy is also reduced and …rms need to post more vacancies to achieve their hiring target. This e¤ect dominates despite the decline in hiring (that would call for reduction in vacancy posting) as long as prices are su¢ ciently rigid. When prices are ‡exible (dashed lines in Figure 1), …rms can increase prices optimally, so as to keep markups constant. The fall in aggregate demand is more pronounced and …rms need a larger contraction in hiring. To achieve this goal, …rms cut posted vacancies. The relationship between the sign of the vacancy response and the degree of nominal rigidity can also be shown analytically in the extreme (but still instructive) case where monetary policy is exogenous (instead of having an interest rate rule) and prices are …xed (instead of sticky), closely following Galí (1999). The derivation is provided in the Appendix. Interestingly, the mechanisms that govern the response of hours worked to a technology shock in a standard New Keynesian model (with a Walrasian labor market) and the response of vacancies to a matching e¢ ciency shock in our model with search and matching frictions are the same. In Figure 2 we appreciate that the sign of the correlation between unemployment and vacancies does not depend on the degree of autocorrelation in the shock process in our baseline model that features four quarters of average price rigidity. However, this result is not as general as the previous literature has taken for granted. In fact, it relies on the presence of nominal rigidities. From the grey dots in Figure 2 we see that in a ‡exible price version of our model ( = 0), the correlation between unemployment and vacancies depends on the degree of autocorrelation in the shock process. When the shock process 7
Matching efficiency shock
Vacancy filling rate
0
1 sticky prices flex prices
0 -0.5 -1 -1
0
10 Vacancies
-2
20
0.2
0.2
0
0.1
-0.2
0
10 Output
0 0
20
0
10 Unemployment
20
10 Inflation
20
10
20
0.2
-0.1
-0.2
0
0
0
10
-0.2
20
0
Figure 1: Impulse responses to a negative matching e¢ ciency shock in the model with sticky prices (bold lines) and with ‡exible prices (dashed lines). The standard deviation of the shock is set equal to 1 percent. Impulse responses are expressed in percentage points.
is very persistent, we con…rm the …nding in Abraham and Katz (1986): the reallocation shock generates a positive conditional correlation between unemployment and vacancies, even when prices are fully ‡exible. But for lower degrees of persistence, the correlation between unemployment and vacancies declines and becomes negative for values of
L
lower
than 0.6. When the shock is i.i.d, the conditional correlation between unemployment and vacancies is -0.52, meaning that the sign of the conditional correlation is in line with the one for the unconditional correlation. Nevertheless, the unconditional correlation in the data is about -0.9, more negative than even our most favorable model calibration delivers. With i.i.d shocks, the variables revert quickly to steady state and the sign of the conditional correlation is largely determined by the co-movement on impact, which is positive under sticky prices and negative under ‡exible prices. In this case, matching e¢ ciency shocks generate ‡uctuations along the Beveridge curve rather than shifts of the curve. Notice that these results are consistent with the fact that matching e¢ ciency
8
play a limited role in estimated New Keynesian models (Furlanetto and Groshenny, 2015) whereas they explain 92 percent of unemployment and 38 percent of vacancy ‡uctuations in the ‡exible price model estimated by Lubik (2009).1 ρ =0
ρ = 0.3
ζ
ζ
20
20 sticky prices, corr = 0.53 flex prices, corr = -0.36 Vacancy rate
Vacancy rate
sticky prices, corr = 0.39 flex prices, corr = -0.52
0
-20 -20
0 Unemployment rate ρ = 0.6
0
-20 -20
20
ζ
20 sticky prices, corr = 0.97 flex prices, corr = 0.88 Vacancy rate
sticky prices, corr = 0.72 flex prices, corr = -0.02 Vacancy rate
20
ζ
20
0
-20 -20
0 Unemployment rate ρ = 0.9
0 Unemployment rate
0
-20 -20
20
0 Unemployment rate
20
Figure 2: Simulated series for vacancies and unemployment conditional on matching e¢ ciency shocks in the model with sticky prices (black dots) and with ‡exible prices (grey dots) for di¤erent values of persistence in the shock process.
We now investigate how the conditional correlation between unemployment and vacancies changes when we vary at the same time the degree of price rigidity and the persistence of the shock (cf. Figure 3). We see that a negative conditional correlation (blue areas) 1
In line with our argument, Krause, Lubik, and López-Salido (2008) estimate a sticky price version of the model in Lubik (2009) and …nd a more limited role for matching e¢ ciency shocks. Notice that nominal rigidities dampen also the propagation of technology shocks. In addition, Krause and Lubik (2007) and Van Zandweghe (2010) show that the presence of real wage rigidity and job search a¤ect the correlation between unemployment and vacancies in response to technology shocks. These features may have an impact also on the transmission of matching e¢ ciency shocks.
9
1
Corr(V,U)
0.5
0
-0.5
-1 1 1 0.8
0.5
0.6 0.4 0.2
Shock persistence
0
0 Calv o probability
Figure 3: Conditional correlation between unemployment and vacancies (vertical axis) as a function of the degree of shock persistence (horizontal axis on the left) and of the degree of nominal rigidity (horizontal axis on the right).
emerges in a non-negligible share of the parameter space where the persistence is limited and the degree of nominal rigidity is lower than two quarters. An important question is whether the combination of low persistence and limited nominal rigidity, featured by the blue areas in Figure 3, may be empirically relevant. We believe that a few recent papers point in that direction, in particular for recent years. Galí and Gambetti (2009) provide a series of stylized facts that are consistent with a lower importance of nominal rigidities for economic dynamics (or with a more aggressive response of the monetary policy authority to in‡ation in the monetary policy rule). We have no direct evidence of a reduction in the persistence of matching e¢ ciency shocks. Nevertheless, Pancrazi and Vukotic (2015) document a large decline in the persistence of wage mark-up shocks in the Great Moderation period that may capture also a decline in the persistence of matching e¢ ciency shocks, given the near observational equivalence between wage mark-up shocks and matching
10
e¢ ciency shocks discussed in Foroni, Furlanetto and Lepetit (2015). Finally, Foerster, Sarte, and Watson (2011) document a more prominent role for sectoral shocks in recent years: these shocks explain up to 50 percent of the variability in industrial production during the period 1984-2007 in the context of a structural factor analysis. All these …ndings lead us to the conclusion that reallocation shocks cannot be dismissed a priori and that the combinations of parameters leading to a negative conditional correlation between unemployment and vacancies may have become more relevant in recent years.
4
Conclusion
Abraham and Katz (1986) dismiss the role of reallocation shocks because, they argue, these shocks generate a positive correlation between unemployment and vacancies. In this paper we …nd support for their statement in the context of a general equilibrium model but only when nominal rigidities are pervasive. When the average duration of prices is lower than two quarters and the shocks exhibit limited persistence, the conditional correlation between unemployment and vacancies becomes negative and a more relevant role for reallocation shocks cannot be ruled out on theoretical grounds. References Abraham, K., Katz, L.F., 1986. Sectoral shifts or aggregate disturbances? Journal of Political Economy 94, 507-522. Andolfatto, D., 1996. Business cycles and labor market search. American Economic Review 86, 112-132. Foroni, C., Furlanetto, F., Lepetit, A., 2015. Labor supply factors and economic ‡uctuations. Norges Bank Working Paper 7/2015. Foerster, A., Sarte, P.D., Watson, M.W., 2011. Sectoral versus aggregate shocks: a structural factor analysis of industrial production. Journal of Political Economy 119, 1-38. Furlanetto, F., Groshenny, N., 2015. Mismatch shocks and unemployment during the Great Recession. Journal of Applied Econometrics, forthcoming. 11
Furlanetto, F., Groshenny, N., 2012. Matching e¢ ciency and business cycle ‡uctuations. Norges Bank Working Paper 7/2012. Galí, J., 1999. Technology, employment and the business cycle: Do technology shocks explain aggregate ‡uctuations? American Economic Review 89, 249-271. Galí, J., Gambetti, L., 2009. On the sources of the Great Moderation American Economic Journal Macroeconomics 1, 26-57. Hosios, A.J., 1994. Unemployment and vacancies with sectoral shifts. American Economic Review 84, 124-144. Justiniano, A., Michelacci, C., 2011. The cyclical behavior of equilibrium unemployment and vacancies in the US and Europe. NBER International Seminar on Macroeconomics 2011, The University of Chicago Press. Krause, M.U., López-Salido, D., Lubik, T.A., 2008. In‡ation dynamics with search frictions: a structural econometric analysis. Journal of Monetary Economics 55, 892-916. Krause, M.U., Lubik, T.A., 2007. The (ir)relevance of real wage rigidity in the New Keynesian model with search frictions. Journal of Monetary Economics 54, 706-727. Kurozumi, T., Van Zandweghe, W., 2010. Labor market search, the Taylor principle and indeterminacy. Journal of Monetary Economics 57, 851-858. Lilien, D.M., 1982. Sectoral shifts and cyclical unemployment. Journal of Political Economy 90, 777-793. Lubik, T.A., 2009. Estimating a search and matching model of the aggregate labor market. Federal Reserve Bank of Richmond Economic Quarterly 95, 101-120. Pancrazi, R., Vukotic, M., 2015. Has monetary policy maintained its e¤ectiveness? Manuscript, University of Warwick. Ravenna, F., Walsh, C., 2008. Vacancies, unemployment and the Phillips curve. European Economic Review 52, 1494-1521. Van Zandweghe, W., 2010. On-the-Job Search, Sticky Prices, and Persistence. Journal of Economic Dynamics and Control 34, 437-455. 12
Appendix Following Galí (1999) step-by-step, we consider the case of exogenous monetary policy (instead of an interest rate rule) and …xed prices (instead of sticky prices) and we postulate the money demand equation mt
pt = yt (in log-linear terms).
The assumptions of exogenous money and …xed prices imply that output is …xed in the period. According to our simple production function, …xed output implies that employment is also …xed. Then, from the law of motion for employment (2), we see that there will be no job creation in response to the shock. Finally, the response of vacancies to matching e¢ ciency shocks can be derived by using the matching function (3). Being new hires …xed in the period and searchers a predetermined variable, the following is true in log-linear terms:
vt =
1 (1
)
lt :
According to our calibration ( = 0:5), a one percent decrease in the matching e¢ ciency will be accompanied by a 2 percent increase in vacancies. Therefore, under the extreme case of exogenous money and …xed prices, the vacancy response will be always positive. In our model results are more muted, since monetary policy is endogenous and prices are not …xed. Nevertheless, the larger the degree of price rigidity is, the more positive the vacancy response will be (as the more negative the e¤ect of a positive technology shock on the labor input will be).
13
S0165-1765(16)30058-1 http://dx.doi.org/10.1016/j.econlet.2016.02.029 ECOLET 7093
To appear in:
Economics Letters
Received date: 7 January 2016 Revised date: 24 February 2016 Accepted date: 24 February 2016 Please cite this article as: Furlanetto, F., Groshenny, N., Reallocation shocks, persistence and nominal rigidities. Economics Letters (2016), http://dx.doi.org/10.1016/j.econlet.2016.02.029 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.
*Highlights (for review)
Highlights
Unemployment and vacancies are strongly negatively correlated in the data. The literature argues that reallocation shocks are not important because they generate a positive correlation. Reallocation shocks do not always generate a positive correlation between unemployment and vacancies. The sign of the correlation depends on the degree of price rigidity and on the persistence of the shock. A non-negligible role for reallocation shocks cannot be dismissed on theoretical grounds.
*Manuscript Click here to view linked References
Reallocation Shocks, Persistence and Nominal Rigidities Francesco Furlanettoy
Nicolas Groshennyz
February 2016
Abstract We reconsider the role of reallocation shocks in a simple New Keynesian model with search and matching frictions. The sign of the conditional correlation between unemployment and vacancies depends on the degree of price rigidity and on the persistence of the shock. Therefore, a non negligible role for reallocation shocks in driving business cycle ‡uctuations cannot be ruled out on theoretical grounds. Keywords: Search and Matching Frictions; Matching E¢ ciency; Reallocation Shocks. JEL codes: E32, C51, C52 This paper should not be reported as representing the views of Norges Bank. The views expressed are those of the authors and do not necessarily re‡ect those of Norges Bank. This paper is a revised and shortened version of Norges Bank Working Paper 7/2012 with title "Matching e¢ ciency and business cycle ‡uctuations". We are indebted to our discussants Tim Kam, James Hansen and Ian King for their extremely valuable feedback. For useful comments, we thank one anonymous referee, Regis Barnichon, Larry Christiano, Marco Del Negro, Punnoose Jacob, Nicolas Jacquet, Alejandro Justiniano, Per Krusell, Francois Langot, Ellen McGrattan, Espen Moen, Federico Ravenna, Kjetil Storesletten, Fabien Tripier, Anders Vredin, Mirko Wiederholt and Jake Wong. y Corresponding Author. Address: Norges Bank, Bankplassen 2, PB 1179 Sentrum, 0107 Oslo, Norway. E-mail: [email protected]. Telephone number: +47 22316128. z Address: University of Adelaide, School of Economics. E-mail: [email protected].
1
1
Introduction
In this paper, we reconsider the debate on the importance of reallocation shocks initiated by Lilien (1982) and we highlight the link between the degree of nominal rigidity and the propagation of persistent shocks to the matching e¢ ciency in the labor market. Following the seminal paper by Andolfatto (1996), these shocks can be interpreted as reallocation shocks, as long as they capture some form of mismatch in skills, in geography or in other dimensions. In particular, we use a simple New Keynesian model with equilibrium search unemployment to investigate how variations in the e¤ectiveness of the labor market matching process a¤ect the correlation between unemployment and vacancies. According to Lilien (1982), reallocation shocks could explain up to 50 percent of unemployment ‡uctuations in the postwar period. The empirical regularity underlying this result is a positive correlation between the dispersion of employment growth rates across sectors and the unemployment rate. However, Abraham and Katz (1986) show that this positive correlation is consistent not only with reallocation shocks but also with aggregate demand shocks. According to Abraham and Katz (1986), the use of data on unemployment and vacancies is more useful and lead to dismiss the importance of reallocation shocks. In fact, they argue that reallocation shocks, unlike aggregate demand shocks, deliver a positive correlation between unemployment and vacancies, while the two series are strongly negatively correlated in the data along the well-known Beveridge curve. We contribute to the literature on the relationship between reallocation shocks and the conditional correlation between unemployment and vacancies by using a fully speci…ed general equilibrium model. Furthermore, we show that the conditional correlation between unemployment and vacancies discussed in Abraham and Katz (1986) is positive only when prices are su¢ ciently rigid and the shock is highly persistent. When nominal rigidities are present, as in our baseline model, a negative shock leads to an increase in vacancies and creates a positive correlation. However, as we reduce the degree of nominal rigidities, the response of vacancies to a negative disturbance becomes less and less positive and eventually turns negative when prices are highly ‡exible. Hence, the conditional correlation between unemployment and vacancies declines substantially and can
2
even become negative when the shock has limited persistence. Interestingly, this …nding is reminiscent of Galí’s (1999) result on the role of nominal rigidities for determining the sign of the employment response to a technology shock. We conclude that a non-negligible role for reallocation shocks cannot be ruled out on theoretical grounds. Importantly, while other studies have considered shocks to the matching e¢ ciency (cf. Lubik 2009, Krause, Lubik, and López-Salido 2008, and Justiniano and Michelacci 2011, among others), the link between the degree of nominal rigidities, the shock’s persistence and the sign of the correlation between unemployment and vacancies is a novel contribution of this paper. Hosios (1994) has also made the point that reallocation shocks do not necessarily generate a positive correlation between unemployment and vacancies in the context of a partial equilibrium model with ‡exible prices and temporary layo¤s driven by a shock to the relative price dispersion across …rms. We conduct our analysis in a general equilibrium model with nominal rigidities driven by a matching e¢ ciency shock. The paper proceeds as follows: Section 2 brie‡y describes the model, Section 3 presents our results and Section 4 concludes.
2
The Model
The model relies largely on Kurozumi and Van Zandweghe (2010) and is purposely simple. The representative household is a large family, made up of a continuum of individuals of measure one. Family members pool their income before allowing the head of the household to choose its optimal per capita consumption. Each period, Nt family members are employed. Each employee works a …xed amount of hours and earns the nominal wage Wt . The remaining (1
Nt ) family members are
unemployed and each receives nominal unemployment bene…ts b, …nanced through lumpsum nominal taxes Tt so that the government budget is always balanced. Unemployment bene…ts b are proportional to the steady-state nominal wage: b = W . The representative household owns retail …rms and receives each period the accumulated pro…ts (Dt ).
3
The family’s period t budget constraint is given by
Pt Ct +
Bt Rt
Bt
1
+ Wt Nt + (1
Nt ) b
(1)
Tt + Dt ;
where Ct represents a Dixit-Stiglitz aggregator of retail goods purchased for consumption purposes, Pt is the corresponding price index, Bt refers to the quantity of bonds purchases by the family and Rt denotes the gross nominal interest rate. The family’s lifetime utility P s is described by Et 1 ln Ct+s , where 0 < < 1. s=0
Each intermediate good-producing …rm i 2 [0; 1] enters in period t with a stock
of Nt
1
(i) employees. New matches become productive in the period, as in Ravenna
and Walsh (2008). The job destruction rate
is constant. The workers who have
lost their jobs start searching immediately and can possibly still be hired in period t with a probability given by the job …nding rate. Employment at …rm i evolves according to Nt (i) = (1
) Nt
1
(i) + Mt (i) where the ‡ow of new hires Mt (i) is given by
Mt (i) = Qt Vt (i) : The term Vt (i) denotes vacancies posted by …rm i in period t and Qt t is the aggregate probability of …lling a vacancy, de…ned as Qt = M . The expressions Vt R1 R1 Mt = 0 Mt (i) di and Vt = 0 Vt (i) di denote aggregate matches and vacancies respecR1 tively. Aggregate employment, Nt = 0 Nt (i) di, evolves according to
Nt = (1
) Nt
1
(2)
+ Mt :
The matching process is described by an aggregate constant-returns-to-scale Cobb Douglas matching function,
Mt = Lt St Vt1
(3)
;
where St denotes the pool of job seekers in period t given by St = 1
(1
) Nt 1 ; and Lt
is a time-varying scale parameter that captures the e¢ ciency of the matching technology. It evolves exogenously following the autoregressive process,
ln Lt = (1
L ) ln L
+
L
ln Lt
1
+ "Lt ; 4
(4)
where L denotes the steady-state value of the matching e¢ ciency, while persistence of the shock, and "Lt is i:i:d:N (0; The job-…nding rate (Ft ) is de…ned as Ft = 1
L
measures the
2 L ). Mt St
and aggregate unemployment is Ut
Nt : Firms face hiring costs measured in terms of the …nished good (Ht (i)). Those
costs depends linearly on the number of vacancies posted by the …rm, Ht (i) = where the parameter
N
N Vt
(i),
governs the magnitude of the (pre-match) hiring cost.
Each period, …rm i uses Nt (i) homogeneous employees to produce Yt (i) units of intermediate good i according to the constant-returns-to-scale technology described by Yt (i) = Nt (i) : Each intermediate good-producing …rm i 2 [0; 1] chooses employment and vacancies to maximize pro…ts and sells its output Yt (i) in a perfectly competitive market at a price Zt (i) that represents the relative price of the intermediate good in terms of the …nal good. The …rm maximizes
Et
1 X s=0
where
t
s
t+s+1
Zt+s (i)Yt+s (i)
t+s
Wt+s (i) Nt+s (i) Pt+s
Ht+s (i) ;
(5)
represents the marginal utility of consumption.
The nominal wage Wt (i) is determined through surplus sharing,
Wt (i) = arg max
where 0 <
t
(i) Jt (i)1
(6)
;
< 1 represents the worker’s bargaining power,
t
(i) is the worker’s surplus
and Jt (i) is the …rm’s surplus. There is a continuum of retail goods-producing …rms indexed by j 2 [0; 1] that transform the intermediate good into a …nal good Ytf (j) that is sold in a monopolistically competitive market at price Pt (j). Cost minimization implies that the real marginal cost is equal to the real price of the intermediate good (Zt ) that is common across …rms. Demand for good j is given by Ytf (j) = Ct (j) = (Pt (j)=Pt ) Ct , where
represents the
elasticity of substitution across …nal goods. Firms choose their price subject to a Calvo scheme in which every period a fraction
is not allowed to re-optimize, whereas the
5
remaining fraction 1
Et
1 X
t+s
)s
(
chooses optimally its price (Pt (j)) by maximizing:
t
s=0
Pt (j) Pt+s
f Zt+s Yt+s (j) :
(7)
The central bank adjusts the short-term nominal gross interest rate Rt by following a Taylor-type rule,
ln
Rt R
=
r
ln
Rt 1 R
+ (1
The degree of interest-rate smoothing output growth (
and
y)
r)
"
r
ln
Pt Pt 4
1=4
+
y
ln
Yt Yt 4
1=4
#
:
(8)
and the reaction coe¢ cients to in‡ation and
are all positive.
Our parameterization is based on the US economy. A …rst set of parameters is taken from the literature on monetary business cycle models. The discount factor is set at = 0:99; the elasticity of substitution across …nal goods at
= 11 implies a steady-state
markup of 10 percent. The parameters in the monetary policy rule are y
= 0:8;
= 1:5,
= 0:5. The average degree of price duration is four quarters, corresponding to
= 0:75.
r
A second set of parameter values is taken from the literature on search and matching in the labor market. The degree of exogenous separation is set at
= 0:08, while the
steady-state value of the unemployment rate is U = 0:06. The elasticity in the matching function is
= 0:5, in the range of plausible values used in the literature. In the absence
of convincing empirical evidence on the value for the bargaining power parameter , we set it equal to 0.5 to satisfy the Hosios condition. The vacancy …lling rate Q is set equal to 0:70. We set
N
such that total hiring costs in the steady state are equal to one percent
of steady state output. The value of unemployment bene…ts
is derived from the steady-
state conditions. These choices are common in the literature and avoid indeterminacy issues, as discussed in Kurozumi and Van Zandweghe (2010). Finally, as there is no clear guidance from the literature, we choose an intermediate value for the persistence of the shock process. We set it at 0.6 in the baseline parameterization and we consider the full range of values between 0 and 1 in the next Section. Additional details on the model (including the list of the order conditions, the analysis
6
of the steady state and the log-linearized equations) are provided in the working paper version of this letter (Furlanetto and Groshenny, 2012).
3
The Role of Nominal Rigidities and Persistence
We now discuss how the degree of price rigidity a¤ects the vacancy response to a matching e¢ ciency shock (cf. Figure 1). Under sticky prices (solid lines) …rms do not increase prices as much as they would prefer in response to a less e¢ cient matching process in the labor market. Therefore, the decrease in output and in hiring is limited. When matching e¢ ciency declines, the probability of …lling a vacancy is also reduced and …rms need to post more vacancies to achieve their hiring target. This e¤ect dominates despite the decline in hiring (that would call for reduction in vacancy posting) as long as prices are su¢ ciently rigid. When prices are ‡exible (dashed lines in Figure 1), …rms can increase prices optimally, so as to keep markups constant. The fall in aggregate demand is more pronounced and …rms need a larger contraction in hiring. To achieve this goal, …rms cut posted vacancies. The relationship between the sign of the vacancy response and the degree of nominal rigidity can also be shown analytically in the extreme (but still instructive) case where monetary policy is exogenous (instead of having an interest rate rule) and prices are …xed (instead of sticky), closely following Galí (1999). The derivation is provided in the Appendix. Interestingly, the mechanisms that govern the response of hours worked to a technology shock in a standard New Keynesian model (with a Walrasian labor market) and the response of vacancies to a matching e¢ ciency shock in our model with search and matching frictions are the same. In Figure 2 we appreciate that the sign of the correlation between unemployment and vacancies does not depend on the degree of autocorrelation in the shock process in our baseline model that features four quarters of average price rigidity. However, this result is not as general as the previous literature has taken for granted. In fact, it relies on the presence of nominal rigidities. From the grey dots in Figure 2 we see that in a ‡exible price version of our model ( = 0), the correlation between unemployment and vacancies depends on the degree of autocorrelation in the shock process. When the shock process 7
Matching efficiency shock
Vacancy filling rate
0
1 sticky prices flex prices
0 -0.5 -1 -1
0
10 Vacancies
-2
20
0.2
0.2
0
0.1
-0.2
0
10 Output
0 0
20
0
10 Unemployment
20
10 Inflation
20
10
20
0.2
-0.1
-0.2
0
0
0
10
-0.2
20
0
Figure 1: Impulse responses to a negative matching e¢ ciency shock in the model with sticky prices (bold lines) and with ‡exible prices (dashed lines). The standard deviation of the shock is set equal to 1 percent. Impulse responses are expressed in percentage points.
is very persistent, we con…rm the …nding in Abraham and Katz (1986): the reallocation shock generates a positive conditional correlation between unemployment and vacancies, even when prices are fully ‡exible. But for lower degrees of persistence, the correlation between unemployment and vacancies declines and becomes negative for values of
L
lower
than 0.6. When the shock is i.i.d, the conditional correlation between unemployment and vacancies is -0.52, meaning that the sign of the conditional correlation is in line with the one for the unconditional correlation. Nevertheless, the unconditional correlation in the data is about -0.9, more negative than even our most favorable model calibration delivers. With i.i.d shocks, the variables revert quickly to steady state and the sign of the conditional correlation is largely determined by the co-movement on impact, which is positive under sticky prices and negative under ‡exible prices. In this case, matching e¢ ciency shocks generate ‡uctuations along the Beveridge curve rather than shifts of the curve. Notice that these results are consistent with the fact that matching e¢ ciency
8
play a limited role in estimated New Keynesian models (Furlanetto and Groshenny, 2015) whereas they explain 92 percent of unemployment and 38 percent of vacancy ‡uctuations in the ‡exible price model estimated by Lubik (2009).1 ρ =0
ρ = 0.3
ζ
ζ
20
20 sticky prices, corr = 0.53 flex prices, corr = -0.36 Vacancy rate
Vacancy rate
sticky prices, corr = 0.39 flex prices, corr = -0.52
0
-20 -20
0 Unemployment rate ρ = 0.6
0
-20 -20
20
ζ
20 sticky prices, corr = 0.97 flex prices, corr = 0.88 Vacancy rate
sticky prices, corr = 0.72 flex prices, corr = -0.02 Vacancy rate
20
ζ
20
0
-20 -20
0 Unemployment rate ρ = 0.9
0 Unemployment rate
0
-20 -20
20
0 Unemployment rate
20
Figure 2: Simulated series for vacancies and unemployment conditional on matching e¢ ciency shocks in the model with sticky prices (black dots) and with ‡exible prices (grey dots) for di¤erent values of persistence in the shock process.
We now investigate how the conditional correlation between unemployment and vacancies changes when we vary at the same time the degree of price rigidity and the persistence of the shock (cf. Figure 3). We see that a negative conditional correlation (blue areas) 1
In line with our argument, Krause, Lubik, and López-Salido (2008) estimate a sticky price version of the model in Lubik (2009) and …nd a more limited role for matching e¢ ciency shocks. Notice that nominal rigidities dampen also the propagation of technology shocks. In addition, Krause and Lubik (2007) and Van Zandweghe (2010) show that the presence of real wage rigidity and job search a¤ect the correlation between unemployment and vacancies in response to technology shocks. These features may have an impact also on the transmission of matching e¢ ciency shocks.
9
1
Corr(V,U)
0.5
0
-0.5
-1 1 1 0.8
0.5
0.6 0.4 0.2
Shock persistence
0
0 Calv o probability
Figure 3: Conditional correlation between unemployment and vacancies (vertical axis) as a function of the degree of shock persistence (horizontal axis on the left) and of the degree of nominal rigidity (horizontal axis on the right).
emerges in a non-negligible share of the parameter space where the persistence is limited and the degree of nominal rigidity is lower than two quarters. An important question is whether the combination of low persistence and limited nominal rigidity, featured by the blue areas in Figure 3, may be empirically relevant. We believe that a few recent papers point in that direction, in particular for recent years. Galí and Gambetti (2009) provide a series of stylized facts that are consistent with a lower importance of nominal rigidities for economic dynamics (or with a more aggressive response of the monetary policy authority to in‡ation in the monetary policy rule). We have no direct evidence of a reduction in the persistence of matching e¢ ciency shocks. Nevertheless, Pancrazi and Vukotic (2015) document a large decline in the persistence of wage mark-up shocks in the Great Moderation period that may capture also a decline in the persistence of matching e¢ ciency shocks, given the near observational equivalence between wage mark-up shocks and matching
10
e¢ ciency shocks discussed in Foroni, Furlanetto and Lepetit (2015). Finally, Foerster, Sarte, and Watson (2011) document a more prominent role for sectoral shocks in recent years: these shocks explain up to 50 percent of the variability in industrial production during the period 1984-2007 in the context of a structural factor analysis. All these …ndings lead us to the conclusion that reallocation shocks cannot be dismissed a priori and that the combinations of parameters leading to a negative conditional correlation between unemployment and vacancies may have become more relevant in recent years.
4
Conclusion
Abraham and Katz (1986) dismiss the role of reallocation shocks because, they argue, these shocks generate a positive correlation between unemployment and vacancies. In this paper we …nd support for their statement in the context of a general equilibrium model but only when nominal rigidities are pervasive. When the average duration of prices is lower than two quarters and the shocks exhibit limited persistence, the conditional correlation between unemployment and vacancies becomes negative and a more relevant role for reallocation shocks cannot be ruled out on theoretical grounds. References Abraham, K., Katz, L.F., 1986. Sectoral shifts or aggregate disturbances? Journal of Political Economy 94, 507-522. Andolfatto, D., 1996. Business cycles and labor market search. American Economic Review 86, 112-132. Foroni, C., Furlanetto, F., Lepetit, A., 2015. Labor supply factors and economic ‡uctuations. Norges Bank Working Paper 7/2015. Foerster, A., Sarte, P.D., Watson, M.W., 2011. Sectoral versus aggregate shocks: a structural factor analysis of industrial production. Journal of Political Economy 119, 1-38. Furlanetto, F., Groshenny, N., 2015. Mismatch shocks and unemployment during the Great Recession. Journal of Applied Econometrics, forthcoming. 11
Furlanetto, F., Groshenny, N., 2012. Matching e¢ ciency and business cycle ‡uctuations. Norges Bank Working Paper 7/2012. Galí, J., 1999. Technology, employment and the business cycle: Do technology shocks explain aggregate ‡uctuations? American Economic Review 89, 249-271. Galí, J., Gambetti, L., 2009. On the sources of the Great Moderation American Economic Journal Macroeconomics 1, 26-57. Hosios, A.J., 1994. Unemployment and vacancies with sectoral shifts. American Economic Review 84, 124-144. Justiniano, A., Michelacci, C., 2011. The cyclical behavior of equilibrium unemployment and vacancies in the US and Europe. NBER International Seminar on Macroeconomics 2011, The University of Chicago Press. Krause, M.U., López-Salido, D., Lubik, T.A., 2008. In‡ation dynamics with search frictions: a structural econometric analysis. Journal of Monetary Economics 55, 892-916. Krause, M.U., Lubik, T.A., 2007. The (ir)relevance of real wage rigidity in the New Keynesian model with search frictions. Journal of Monetary Economics 54, 706-727. Kurozumi, T., Van Zandweghe, W., 2010. Labor market search, the Taylor principle and indeterminacy. Journal of Monetary Economics 57, 851-858. Lilien, D.M., 1982. Sectoral shifts and cyclical unemployment. Journal of Political Economy 90, 777-793. Lubik, T.A., 2009. Estimating a search and matching model of the aggregate labor market. Federal Reserve Bank of Richmond Economic Quarterly 95, 101-120. Pancrazi, R., Vukotic, M., 2015. Has monetary policy maintained its e¤ectiveness? Manuscript, University of Warwick. Ravenna, F., Walsh, C., 2008. Vacancies, unemployment and the Phillips curve. European Economic Review 52, 1494-1521. Van Zandweghe, W., 2010. On-the-Job Search, Sticky Prices, and Persistence. Journal of Economic Dynamics and Control 34, 437-455. 12
Appendix Following Galí (1999) step-by-step, we consider the case of exogenous monetary policy (instead of an interest rate rule) and …xed prices (instead of sticky prices) and we postulate the money demand equation mt
pt = yt (in log-linear terms).
The assumptions of exogenous money and …xed prices imply that output is …xed in the period. According to our simple production function, …xed output implies that employment is also …xed. Then, from the law of motion for employment (2), we see that there will be no job creation in response to the shock. Finally, the response of vacancies to matching e¢ ciency shocks can be derived by using the matching function (3). Being new hires …xed in the period and searchers a predetermined variable, the following is true in log-linear terms:
vt =
1 (1
)
lt :
According to our calibration ( = 0:5), a one percent decrease in the matching e¢ ciency will be accompanied by a 2 percent increase in vacancies. Therefore, under the extreme case of exogenous money and …xed prices, the vacancy response will be always positive. In our model results are more muted, since monetary policy is endogenous and prices are not …xed. Nevertheless, the larger the degree of price rigidity is, the more positive the vacancy response will be (as the more negative the e¤ect of a positive technology shock on the labor input will be).
13