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The Effects of Uncertainty Shocks on the Labor Market:
A Search Approach ∗
Elisa Guglielminetti
†
June, 2013
Abstract
Uncertainty has recently become a major concern for policymakers and academics.
Spikes in uncertainty are often associated to recessions and potentially have detrimental
effects on the aggregate economy. This paper analyzes the effects of uncertainty on
firms’ hiring decisions, both empirically and theoretically. First, I provide new evidence
on the negative effects of uncertainty on the economic performance and in particular
on the labor market. The VAR specification allows to distinguish the autonomous role
of uncertainty from standard technological shocks. Second, I build a DSGE model with
search and matching frictions in the labor market and stochastic volatility and I study
the response of the economy to an uncertainty shock. The model is able to replicate the
observed negative co-movement among consumption, output, employment, vacancies,
the labor market tightness and the job finding rate. The specific role of the labor
market structure in the propagations of uncertainty shocks is investigated through a
sensitivity analysis.
Keywords: Uncertainty Shocks, Labor Market, DSGE Model, Business Cycle, Survey
Data.
JEL classification: E21, E23, E24, E32.
∗
I owe a special thank to Etienne Wasmer for the supervision of this work and to Magali Marx for
her help. I am also grateful to Nicolas Coeurdacier and to my Ph.D colleagues in Sciences Po for useful
comments.
†
Sciences Po and La Sapienza University. E-mail: [email protected]
Introduction
After the 2008 Great Recession, economic agents, policymakers and academics are increasingly concerned about uncertainty and its potentially detrimental effects on the aggregate
economy. Uncertainty is not directly quantifiable; different measures have been proposed,
ranging from stock market volatility to survey and newspaper-based indexes. Regardless
of the measure being used, however, the negative correlation between uncertainty and economic performance is a well established stylized fact. The October 2012 World Economic
Outlook, documents that uncertainty surged at the onset of the Great Recession and remained high ever since. The report also identifies some channels through which uncertainty
can negatively affect the economic performance1 .
At the same time, small businesses ranked uncertain economic conditions as the second
most severe problem and the vast majority of the respondents to a survey administered
by the National Association for Business Economics agreed that uncertainty about fiscal
policy was holding back economic recovery 2 .
This evidence motivates a newly blossoming area of research on the relationship between
uncertainty and the business cycle. This paper contributes to this literature and asks the
following questions: Is there any empirical evidence on the effects of uncertainty on the
labor market? What kind of model can account for this empirical observation? What
characteristics of the labor market do amplify or attenuate the effects of uncertainty shocks?
To answer these questions, in the first part I conduct an empirical investigation. In the
second part I present a model that is able replicate some of the empirical evidence.
Both theoretically and empirically, it is not straightforward to establish the direction
of causality between uncertainty and the business cycle. In principle, uncertainty can be
either an impulse or a consequence of recessions. Evidence on this is sparse and far from
conclusive 3 .
To test the two hypothesis, I perform VAR estimates which are suited to assess the
significance and the quantitative implications of increases in uncertainty once TFP shocks
are taken into account. I use a survey-based measure of uncertainty which is consistent
with the specification of the model, allowing me to draw a map between the empirical and
the analytical part. Although not entirely new in the literature, this measure has been less
employed than, say, stock market volatility. Survey-based measures potentially incorporate
more noise: I thus view the significant results of the empirical part as a confirmation of the
importance of uncertainty in shaping economic outcomes. The Cholewsky ordering I adopt
allows me to identify an autonomous role of uncertainty on the aggregate economy. More
specifically, I focus on the impact of uncertainty on several labor market variables, which
1
See Kose and Terrones 2012 and Bloom, Kose, and Terrones 2013.
See NFIB 2012 and Economic Policy Survey.
3
Bachmann and Moscarini 2012 argue that the direction of causality runs from recessions to increased
observed cross-sectional dispersion. In contrast, Bloom et al. 2012 find that TFP shocks seem not to drive
countercyclical uncertainty at the micro level.
2
1
have received little attention by the literature in the field. I find that a 1 SD increase in
uncertainty does have significant negative effect on employment, the number of vacancies
posted by firms and the job finding rate.
Motivated by the empirical findings, I thus analyze the effect of exogenous spikes in
uncertainty, rather than consider it as a by-product of the business cycle. Much work has
been devoted to explore the linkages between uncertainty and firms’ investment choices.
As I show in the empirical section, however, uncertainty is likely to have strong implications also on the labor market. Moreover, the sharp and persistent rise in unemployment
observed during the last recession is a major concern of policymakers and economists. It
is thus important to have analytical tools to study the reaction of firms’ hiring decisions
to uncertain economic conditions like the ones characterizing the actual economic environment.
To examine the impact of uncertainty shocks, I adopt a dynamic general equilibrium
framework: some previous contributions, including the seminal paper by Bloom (Bloom
2009) have partial equilibrium models, which neglect price dynamics that can potentially
offset the real effects.
Reproducing the negative co-movement of output, consumption and labor market variables generated by the VAR estimates is not straightforward. In a standard real business
cycle model, risk-averse households react to uncertainty shocks by increasing saving and
labor supply. If prices can perfectly adjust, firms employ greater amounts of inputs (capital
and labor). Uncertainty shocks thus determine a decline in consumption and a contemporaneous rise in investment, output and employment, in sharp contrast with the empirical
evidence.
Solutions to this puzzle have been proposed in previous works, but mainly regarding
the effects of uncertainty on investment. This literature shows that uncertainty negatively
affects investment when it raises the real option value of waiting for the firm: this happens
when physical investment is partially or totally irreversible and/or when financial frictions
reduce firms’ funding ability. The intuition carries over to the hiring decisions. Hiring a
worker is a costly activity. Firms are willing engage in the match only if they believe that
it will be enough productive to compensate them for the hiring cost. Uncertainty reduces
firms’ confidence in the future, thus leading them to adopt a cautious attitude and to pause
from hiring.
A natural candidate to test this intuition is the search and matching framework à la
Mortensen-Pissarides. I thus build a real DSGE model featuring search and matching
frictions in the labor market and stochastic volatility. Uncertainty shocks are defined
as unexpected exogenous variations in the volatility of the technological process4 . This
facilitates comparisons with the standard RBC framework, which is the core of modern
macro models. Furthermore, I give support to the view that uncertainty shocks can provide
4
In this setting, uncertainty affects only the supply side of the economy. However, this should not
be regarded as a shortcoming of the model. A related contribution (Leduc and Liu 2013) shows that the
response of the economy is independent of the specific source of uncertainty (demand, supply, policy)
2
an alternative explanation to business cycle fluctuations, helping to overcome the critique
that TFP declines are rarely observed.
By contrasting the IRFs of the economy in the competitive and in the search model,
I highlight the role of labor market frictions in propagating uncertainty throughout the
economy. To get some insights on the relevant forces at work, I then conduct a sensitivity analysis on the parameters affecting the labor market structure. The results are
the following. First, the model with search and matching frictions is able to match the
empirical negative co-movement among consumption, output, employment, vacancies, the
labor market tightness and the job finding rate. Second, the effects of uncertainty on the
economy are amplified the greater the firms’ bargaining power. Firms which are entitled a
larger fraction of the surplus are more concerned about the evolution of productivity and
they thus have a stronger reaction. Third, if matches are highly responsive to vacancy
posting activity, households’ reaction is amplified, whereas firms’ response is attenuated.
This occurs because the economy is less (more) sensitive to households’ (firms’) decisions,
implying that they must take a stronger (weaker) stance to achieve the desired result. Finally, I consider the implications of the Hosios-Pissarides efficiency rule: I find no direct
evidence that labor market reactions are differently affected whether the Hosios-Pissarides
condition holds. Indeed, the firms’ bargaining power and the elasticity of the matching
functions play distinct roles.
The rest of the paper is organized as follows: Section 1 reviews the related literature;
Section 2 presents the empirical evidence; Section 3 provides the economic intuition of
the effects of uncertainty in different settings; Section 4 introduces the model; Section 5
outlines the solution method and the calibration strategy; Section 6 presents the results;
Section 7 concludes.
1
Related literature
This paper is mainly related to three strands of literature. First, I contribute to recent
empirical and theoretical works which consider the effects of stochastic volatility in different
settings. Second, I build on the numerous papers which analyze the behavior of the labor
market under the presence of search and matching frictions. More specifically, I refer to
works which incorporate the Diamond-Mortensen-Pissarides (DMP) framework in DSGE
models. I am not the first in combining these two branches: in independent works, Schaal
2012 and Leduc and Liu 2013 consider models which feature both stochastic volatility
and search frictions in the labor market. However, there are noticeable differences that I
highlight below. I start by reviewing the literature on uncertainty shocks; then, I briefly
mention papers belonging to the search literature which are more related to mine. The
economic intuition of the different approaches is explored in more detail in Section 3.
The role of uncertainty shocks in explaining business cycle facts is a newly blossoming area of research. Some empirical works estimate a sizable effect of uncertainty on the
3
aggregate economy, whereas theoretical contributions explore the channel through which
uncertainty propagates to the economy. For the empirical studies, both micro and macro
measures of uncertainty have been employed, reflecting different propagation channels explored in the theoretical models. However, as documented by Bloom 2009, micro uncertainty measures are strongly correlated with macro uncertainty and both of them are
counter-cyclical. For this reason, in what follows I will not explicitly distinguish between
the two approaches, leaving the discussion on the most recurrent uncertainty indicators to
Section 2.
The effects of uncertainty have been firstly and more extensively investigated in relation
to investment. The relationship between uncertainty and investment is ambiguous. An
example of this older empirical literature, is the influential work by Leahy and Whited
1996. In this paper, the authors empirically test the implications of different economic
theories on the effect of uncertainty on firms’ investment decisions. They document a
strong negative influence of uncertainty on investment, thus pleading in favor of theories
of investment irreversibility.
In more recent times, many researchers got interested in the effects of uncertainty on
a broader spectrum of economic variables. Alexopoulos and Cohen 2009 find that uncertainty shocks are able to explain a non-trivial fraction of the total variance of industrial
production, output, employment, consumption and investment. Knotek II and Khan 2011
focus on households’ response to changes in uncertainty. They adopt the same indicator
as in Alexopoulos and Cohen 2009. By disentangling households purchases by different
categories, their empirical findings suggest that households’ spending reduction are modest and delayed. These results emerge when other possibly important explaining factors
are accounted for in a multivariate VAR. In addition, uncertainty shocks account fo only
a small portion of the total fluctuations in households’ spending.
Bachmann, Elstner, and Sims 2012 compare the effects of uncertainty on the German
and US economy, finding that an increase in uncertainty causes a negative response of
output. In Germany this response quickly rebounds, while in the US it is more persistent.
The so-called "volatility overshoot" (a drop followed by a quick rebound and an overshoot
of the steady state level ) is also documented by Bloom 2009 for the US economy.
Gilchrist, Sim, and Zakrajsek 2012 show that uncertainty has a strong and significantly
negative economic impact on corporate bond spreads and real variables. By using different
identification schemes they argue that financial frictions are an important channel of transmission of uncertainty shocks to the economy. They also provide further empirical evidence
on the importance of uncertainty in explaining firm-level credit spreads and investment.
Many works have recently come to the forth, highlighting different propagation channels of uncertainty and providing different explanations for the empirical evidence reported
above. The literature on the relationship between investment and uncertainty goes back
to the works by Bernanke 1983, Dixit and Pindyck 1994 and Abel and Eberly 1999. These
authors stress that when physical investment is irreversible, agents must trade off the extra
4
returns from early commitment against the benefits from waiting for more information. Increased uncertainty about future returns increase the value of waiting for more information,
thus dampening investment and economic activity.
More recently, a rapidly growing strand of literature explicitly motivate exogenous
innovations in uncertainty and study their impacts on the economy. Uncertainty shocks
are generally modeled as exogenous innovations to the standard deviation of first-moment
shocks. The recent contributions in this field have focused on different first-moment shocks
whose volatility is allowed to vary, mirroring the variegated empirical evidence and the
different propagation channels at work.
Bloom, Bond, and van Reeenen 2007 shows that if investment is only partially reversible, firms which face higher level of uncertainty are less responsive to demand shocks.
This effect arises because uncertainty enlarges the inaction region, in which the firms neither invest nor disinvest. Bloom 2009 and Bloom et al. 2012 build a model in which
non-convex labor and capital adjustment costs interact with stochastic volatility determining a cautionary attitude in investing and hiring decisions when firms are confronted
with more uncertain times. These models differ from mine in that they focus on micro
uncertainty, that is the dispersion of idiosyncratic productivity at the establishment level,
and consider different propagation mechanisms, namely non-convex adjustment costs.
Other authors study how financial frictions can amplify the detrimental effects on uncertainty on the economy. Christiano, Motto, and Rostagno 2010 estimate a large-scale
DSGE model where financial frictions combine with shocks to the dispersion of idiosyncratic returns on investment, defined as risk shocks. They find that risk shocks are one
of the major business cycle driving force, explaining 60 percent of the volatility of investment in the US. Arellano, Bai, and Kehoe 2012 build a DSGE model with heterogeneous
firms and financial intermediaries. If financial markets are incomplete, firms cannot issue
state-contingent bonds to insure themselves against the risk of default. As a consequence,
hiring labor is a risky activity because it increases the probability of default. It follows that
shocks to the volatility of idiosyncratic demand make firms more reluctant to hire workers. In Gilchrist, Sim, and Zakrajsek 2012 fluctuations in economic uncertainty influence
corporate bond prices and investment. An essential feature of this model is the interaction
between the agency cost associated with external finance and the capital capacity overhang
problem caused by irreversible investment. As in Bloom, Bond, and van Reeenen 2007, the
partial irreversibility of investment increases the real-option value of waiting after positive
volatility shock, while financial frictions amplify the negative response.
These models are generally more complex than mine and focus on the role of financial
frictions which are absent in my setup.
The effects of nominal rigidity are analyzed by Basu and Bundick 2012. The authors
show that price stickiness is able to generate responses to uncertainty shocks that are
consistent with the business cycle.
Time varying volatility is a distinctive feature of a variety of time series, as documented
5
by Fernandez-Villaverde and Ramirez 2011. Motivated by this observation, FernandezVillaverde et al. 2011 postulate a stochastic volatility process for the real interest rate
at which small open emerging economies borrow and show how uncertainty shocks have
a quantitatively important effect on real variables like output, consumption, investment,
and hours worked. Justiniano and Primiceri 2008 estimate a DSGE model along the lines
of Smets and Wouters 2007 and Christiano, Eichenbaum, and Evans 2005 introducing
stochastic volatility for each type of shock. My focus is instead on stochastic volatility of
the aggregate productivity shock and I am mainly interested in understanding the effect
on labor markets.
Finally, policy uncertainty is the focus of ongoing research5 .
The assumption underlying the models reviewed until now is that changes in uncertainty are exogenous to the economic environment, very much like standard productivity
shocks in the the RBC literature. Even if the counter-cyclical behavior of both micro and
macro uncertainty measures seems to be robust, there is less consensus on the direction
of causality6 . Other authors have thus take another route, explaining how uncertainty
can endogenously arise following more conventional first-moment shocks (the so called "byproduct hypothesis", since uncertainty is a by-product of the cycle). Some of the exponents
of this strand of literature are Bachmann and Moscarini 2012, D’Erasmo and Boedo 2013
and van Nieuwerburgh and Veldkamp 2006. Different mechanisms are at play: imperfect information about the elasticity of demand faced by each firms in Bachmann and
Moscarini 2012, possibility of diversifying market-specific shocks in D’Erasmo and Boedo
2013 and learning about the true level productivity in van Nieuwerburgh and Veldkamp
2006. These papers are different from mine, because I consider uncertainty as an exogenous
driving force.
My paper is also related to the vast strand of literature regarding the presence of search
and matching frictions in the labor market. The Diamond-Mortensen-Pissarides (DMP)
framework7 has been incorporated in the RBC model by Merz 1995 and Andolfatto 1996.
Since than, it has been widely used in larger DSGE models to study how the presence
of labor market frictions affects the economic response to a wide range of shocks. In this
field, the papers most related to mine are den Haan, Ramey, and Watson 2000, Walsh 2005
and Blanchard and Galì 2010. With respect to den Haan, Ramey, and Watson 2000 I do
not consider endogenous separation and I have a different matching technology; moreover
households’ derive disutility from working. My model differentiate to Walsh 2005 and
Blanchard and Galì 2010 because I do consider capital accumulation but I abstract from
monetary issues, my focus being on real effects.
By the best of my knowledge, two other independent works explore the effects of uncer5
See Fernández-Villaverde et al. 2011 and Baker, Bloom, and Davis 2013
Bloom et al. 2012 addresses this point. He finds no evidence that first-moment shocks drive microeconomic uncertainty but rather argues that higher uncertainty leads to a TFP slowdown.
7
See Pissarides 1990a for an explanation of the search and matching framework.
6
6
tainty shocks in a model with search. Schaal 2012 considers the effects of volatility shocks
in a partial equilibrium search model with heterogeneous firms. Firms are hit by both aggregate and idiosyncratic productivity shocks but only the last ones feature time-varying
volatility. The author aims at replicating the pattern of output, unemployment and many
other labor variables during the NBER-dated crisis and more specifically during the last
Great Recession. He thus calibrates a combination of productivity and volatility shocks
that allows him to approximate the empirical time series. The model and the focus are
quite different from mines: I have a general equilibrium approach and I consider capital
accumulation. Furthermore, I adopt a representative firm approach: this does not allow
me to tackle issues related to cross-variations in establishments and to consider the effects of idiosyncratic shocks. More importantly, I focus on uncertainty shocks as the main
business-cycle driving force and I am interested in the co-movement among consumption,
output and labor variables on a much longer horizon. The mechanisms which are at work
in the two models are substantially different: the IRFs to uncertainty shocks I focus on
display opposite sign to those got by Schaal 2012.
Leduc and Liu 2013 embeds stochastic volatility in a model which is similar to mine.
However, there are some noticeable differences: I do not allow for nominal rigidities while
I consider capital accumulation with investment adjustment costs. Moreover, their focus is
somewhat different: they highlights the role of price stickiness, while I examine in greater
details the specific role of labor market rigidities by comparing my model with a competitive
labor market setup. We both provide empirical evidence on the effects of uncertainty shocks
on the aggregate economy, but we employ different measures and I provide some results
also for variables which are more specific to the search literature, like vacancies, the labor
market tightness and the job finding rate. Despite these differences, our results on the
effects of uncertainty on unemployment are remarkably similar. Our simulated IRFs are
both able to replicate the empirical result that unemployment significantly rises after a
volatility shock: this suggest that labor market frictions are a key ingredient to explain the
effects of uncertainty on the labor market.
2
Empirical evidence
2.1
Measuring uncertainty
In this section I present some empirical evidence on the effect of uncertainty on the aggregate economy and more specifically on the labor market. As uncertainty indicator I
use a measure of disagreement drawn bu the Survey of Professional Forecasters (SPF).
The SPF is a quarterly survey administered by the Philadelphia Fed, starting in 1968Q4
and still conducted roughly in the same format. Professional forecasters8 are asked to
disclose their best predictions about several macroeconomics indicators on different hori8
These include members of financial institutions, banks, consulting firms and researchers in the academy.
7
zons. The Philadelphia FED itself compute a measure of forecast dispersion, which consists
of the difference between the 75th percentile and the 25th percentile of the forecasts. I
use this measure computed for the forecast on nominal GDP for the quarter immediately
following the survey date. This measures the ex-ante disagreement among professionals
and thus captures the uncertainty surrounding future economic conditions. Other surveybased measures of uncertainty have been previously employed in the empirical literature
(see Bachmann, Elstner, and Sims 2012 and references therein). Bachmann, Elstner, and
Sims 2012 use forecast dispersion from the Business Outlook Survey, administered by the
Philadelphia Fed. Since I focus on economy-wide measures of economic activity (all the
variables I include in the VAR analysis are not industry-specific and are taken at the country level) I rather choose data drawn from SPF, which cover different sectors throughout
the United States.
As a robustness test, I also consider other two measures of uncertainty, namely stock
market volatility and the variance of the TFP growth rate obtained from a GARCH(1,1)
model (in logs). Previous contributions have claimed stock market volatility to be a good
proxy for uncertainty. Schwert 1989 argues that financial asset volatility helps to predict
future macroeconomic volatility and both of them increase during recessions. Bloom 2009
shows that stock market volatility is highly correlated with other cross-sectional measures
of uncertainty at the micro-level and takes it as a basis to build a volatility indicator
that has significant effects in VAR estimates. Alexopoulos and Cohen 2009 use stock
market volatility and a newspaper-based indicator to assess the effect of uncertainty on a
wide range of variables, including industrial production, consumption goods, employment,
unemployment and productivity.
The other measure I consider is the conditional heteroskedasticity series, estimated
using a GARCH(1,1) on the TFP growth rate computed by Fernald 20129 . This measure has been introduced by Bloom et al. 2012, who only shows the coincidence between
spikes in macroeconomic volatility and NBER recession dates, but does not use it in VAR
estimates10 .
Other commonly used measures of uncertainty are corporate bond spread (Bachmann,
Elstner, and Sims 2012), newspaper or google-based indicators (Alexopoulos and Cohen
2009, Bachmann, Elstner, and Sims 2012, Knotek II and Khan 2011) and cross-sectional
measures of dispersion in TFP growth and level, profit and sales at the sector, industry
9
The series is downloadable from John Fernald’s website:
http://www.frbsf.org/economics/economists/staff.php?jfernald. The series I employ is called dtfp.
10
More specifically, I estimate the following GARCH model:
¯ = c + σt t
dtfpt − dtfp
2
σt2 = k + α1 2t−1 + β1 σt−1
¯ is the mean of the dtfp series. As a measure of uncertainty I consider the estimated conditional
where dtfp
heteroskedasticity series represented by σt .
8
and firm level (Bloom 2009, Bloom et al. 2012, Kehrig 2011). Gilchrist, Sim, and Zakrajsek
2012 use high-frequency stock market data at the firm level to construct a novel proxy for
idiosyncratic uncertainty.
2.2
VAR estimates
Despite of the wider use of stochastic volatility as a proxy for macroeconomic uncertainty
I take forecast dispersion as favorite measure, since it is the closest concept to the specification of time-varying volatility I adopt in the model11 . All the results stay significant
when I consider stock market volatility and TFP growth rate volatility.
I present estimates for tri-variate VARs, including, in order, the TFP growth rate
(dtfp), my measure of uncertainty (forecast dispersion in the preferred specification) and a
measure of economic activity. VAR estimates are based on United States data at quarterly
frequency spanning from 1968q4 (the first available date for the SPF) to 2012q4. The order
reflects the assumption that both TFP shocks and volatility shocks contemporaneously
affect economic activity, while volatility impacts TFP growth only with a lag. The trivariate specification allows me to take into account shocks to the technological level, and
provide more conservative estimates with respect to the bi-variate case (i.e. only with
the uncertainty and the economic measure). Moreover, the Chowlesky ordering in which
uncertainty is ordered second implies that the IRFs to uncertainty shocks have already
been purged from the effects of TFP shocks. Results hold true also in the multivariate
VARs in which I include the effective federal funds rate and the consumption price index
(not shown in the text)12 .
Figure 1 plots the impulse response functions of industrial production, consumption and
investment to a 1 SD uncertainty shock (measured by forecasts’ dispersion). Uncertainty
negatively affects economic activity, leading to a drop in the main macro variables for about
4 quarters followed by a rebound and an overshooting after about 10 periods.
Figure 2 shows that uncertainty has a significant negative impact on different labor
market variables, that are not generally included in the empirical studies cited above. In
particular, uncertainty causes a drop in two variables most studied in the search literature,
namely vacancies (i.e. the composite help-wanted advertising index computed by Regis
Barnichon) and the job finding rate (computed by Robert Shimer). Forecast dispersion also
have a negative impact on hours worked (not shown in the figure) and causes a temporary
rise in unemployment. The major effect shows up between three and five quarters, with a
labor market then reverting back to previous levels and eventually overshooting them.
11
In the context of future inflation uncertainty, Bomberger 1996 indicate a clear relationship among
forecasters disagreement and conditional variance of ex-post forecast errors. He thus concludes that the
survey-based measure based on Livingston data are a potentially usefully proxy for uncertainty.
12
In the multivariate case the fraction of the variance explained by uncertainty shocks is reduced
9
3
Intuition
Before introducing the model and formally discussing the results, I provide the economic
intuition of the dynamic reactions triggered by an uncertainty shock. To this aim, I find
useful to compare a DMP type of model, like the one I develop in Section 4, with a model
featuring a competitive labor market.
First consider a standard RBC model: agents’ utility is defined over consumption and
leisure and firms use capital and labor to produce a homogeneous good which is sold to
households. Under the assumption of risk aversion, we can draw quite easy and intuitive
predictions about agents’ reaction when facing more uncertain economic conditions. By
definition, risk-averse households desire to self-insure themselves against risk: higher uncertainty about the future state of the world lead them to save more for precautionary
motives. For the same reason, they increase labor supply. With perfectly competitive
capital and labor market, the interest rate and the wage fall to clear the respective markets; in equilibrium, inputs are employed in a greater amount and production increases. If
no other shock occurs and assuming that the rise in volatility is temporary, the following
period agents realize that no change has intervened in altering their consumption possibilities. First order effects prevail on the volatility effect, which is only second-order and
is vanishing out by assumption. Given the fundamentals, which have not changed, households are away from their optimal consumption choice; they thus start consuming again:
all variables quickly revert to their steady state values.
In this context the uncertainty effect is completely "households’ driven": risk aversion determines a precautionary reaction and the market clearing is ensured though price
adjustment. Given the absence of frictions, firms fully absorb the increased capital and
labor supply; production increases. Firms are assumed to be risk neutral. The optimization problem they cope with is actually static: they maximize actual profits by equating
the price of the factors to their marginal productivity. Because uncertainty regards future
shocks dispersion, it does not play any role in firms’ investment and hiring decisions. Firms
are thus "passive", limiting to go along with households’ desires.
The mechanism at work in this simple framework is clearly at odds with the empirical
evidence presented in Section 2. More specifically, the only prediction consistent with
the data is the fall in consumption, which triggers the positive response of investment,
employment and output. This happens because results are driven only by households’
risk aversion; the supply side of the economy, instead, faces a static problem which is not
concerned by a rise in uncertainty.
To understand the empirical results, two different propagation channels can be considered: i) price rigidity either in factor markets or in the final good market, and ii)
modifications of the firms’ optimization problem. I will loosely refer to these two cases by
saying that the effects of uncertainty shocks are "price driven" and "firms’ driven", respectively. This distinction can be simplified in this way: either i) firms are willing to expand
employment and capital, but excess supply is not absorbed because prices are not allowed
10
to adjust to clear the market, or ii) despite of the (possible) price adjustment, firms are
not willing to hire more labor and/or use more capital.
The first mechanism is explored by Basu and Bundick 2012, who consider Rotemberg
price adjustment costs in the final good market. In this New-Keynesian type of model,
output is demand-determined and the mark-up counter-cyclically adjusts to clear the market. In this way, the authors are able to generate the negative observed co-movement of
consumption, output and investment. Basu and Bundick 2012 also show that the effects of
uncertainty shocks are amplified when the monetary policy is constrained by the zero-lower
bound. This result is not surprising: the impossibility for the interest rate to fall shuts
down another price adjustment channel and magnifies the quantitative response for the
same size of the shock.
The second type of mechanism rather concerns the structure of the firm’s problem.
Firms may be concerned by the rise in uncertainty as well as households even maintaining
the risk neutrality assumption. This happens when firms do not face a purely static
problem but the actions they undertake today are subject to a real cost that they are
willing to bear only if they generate sufficient expected profits both in the present and
in the future periods. This feature of the firms’ problem generates a real option value to
postpone decisions. It follows that firms are more reluctant to employ productive factors
when future economic conditions are more uncertain, even when prices can perfectly adjust.
Many contributions in the literature which are interested in the effects of uncertainty
shocks, actually exploit this intuition. As already mentioned in Section 1, various modifications to the firms’ optimization problem make investment and hiring decisions risky,
thus inducing a cautious attitude when economic volatility increases. These mechanisms
include, among others, irreversibility (like in Bloom, Bond, and van Reeenen 2007, Bloom
2009 and Bloom et al. 2012) and uninsurable default risk (Arellano, Bai, and Kehoe 2012).
In either case, current actions have irreversible and potentially harmful effects on firms’
perspectives. Profit maximization thus requires to take into account the stochastic distribution of future shocks. Higher variance of the distribution of the exogenous processes
makes extreme shocks more likely to occur. Firms, however, are more concerned about the
lower tail of the distribution, that is the occurrence of bad shocks. In fact, they can always
take advantage of good shocks when they eventually realize, while they cannot optimally
reduce inputs when they need to do it.
The same considerations apply to hiring decisions when the labor market is characterized by search frictions. Firms trade off the fixed cost of posting a vacancy against the
expected return of the productive match. Their decisions are thus conditioned to the expected continuation value, which depends on the shock realizations in the future periods.
Heightened uncertainty increases the risk that future returns are too low to compensate
the vacancy costs, thus depressing hiring. Frictions characterizing the labor market do not
directly impact the capital market. A negative effect can arise indirectly because of the
lowered return to capital induced by the reduction in labor. However, this negative force is
largely overcome by the drop in the interest rate determined by the increase in households’
11
precautionary savings. It follows that search frictions alone are not sufficient to account
for the observed drop in investment triggered by an uncertainty shock. However, I avoid to
introduce additional imperfections in the capital market which would deliver the desired
outcome but would obscure the basic economic intuition. I thus get a positive response of
investment which does not match the empirical evidence; this is certainly a shortcoming
of the model. Having provided a unified framework to explain the effects of uncertainty
shocks, I can focus on the role of search frictions on unemployment, vacancies, the labor
market tightness and the job finding rate, a much more unexplored topic in the literature.
Notice also that, despite of the positive response of investment, the drop in employment
determines a negative effect on output. The model is thus able to generate the negative
co-movement among output, consumption and labor market variables, a robust empirical
prediction.
4
The model
The benchmark model combines features of the standard RBC setting, search frictions à
la Mortensen-Pissarides in the labor market and stochastic volatility of the technological
process.
Time is discrete. The economy is populated by households and firms. Households
consume, invest in the bond market and supply labor. I distinguish between wholesale
firms and retailers. Wholesale firms employ capital and labor to produce a homogeneous
good sold to retailers in a perfect competitive market. Workers are recruited on a frictional
labor market and wages are the outcome of a Nash bargaining process between workers
and firms. Retailers owe a technology which allows them to differentiate the good without
nay other input. The differentiated good is then sold to households under monopolistic
competition.
Technology follows an exogenous AR(1) process. The volatility of the technological
shocks is itself stochastic.
4.1
Households
The economy is populated by a continuum of identical households of mass 1. They consume
a composite good Ct which incorporates all the varieties produced by the retailers, hold
bonds and supply labor. Since in any period workers are either employed or unemployed
(i.e. matched or unmatched), a distributional problem may arise. As in Merz 1995, I assume
that households pool consumption (they behave like a big family which fully insures each
member against unemployment).
12
The consumption program solves13 :
max
Ct ,Nt ,Bt+1
s.t.
E0
∞
X
t
β U (Ct , 1 − Nt ) = E0
t=0
Ct +
∞
X
"
β
t=0
t
Ct1−σc
N 1+σn
−ψ t
1 − σc
1 + σn
#
Bt wt
Bt+1
= Rt
+ Nt + Ft
Pt
Pt
Pt
where σc is the relative risk aversion and σn is the inverse of Frisch elasticity. Households can allocate their income between consumption and nominal bonds, which pay the
nominal (gross) interest rate Rt . In addition households’ supply labor: the labor income
is represented by the real wage paid to the household’s members who are employed during
the period (Nt ). Finally, households’ own firms, whose profits are denoted as Ft .
Ct is the Dixit-Stiglitz aggregator:
"Z
1
Cit
Ct =
−1
# −1
di
0
where is the demand elasticity.
The first order condition are the following:
Ct−σc = λt
"
βEt
(1)
λt+1 Pt
Rt+1
λ Pt+1
#
(2)
where λ is the marginal value of wealth.
Moreover, the demand for variety i is
Cit =
P −
it
Pt
Ct
(3)
1
The aggregate retail price index is: Pt = 01 Pit 1− di 1− .
Labor supply decisions must take into account the frictions characterizing the labor
market and are derived in Section 4.2.1. Notice that, with perfectly competitive labor
markets, the following condition would hold:
R
wt
= ψCtσc NtσN
Pt
(4)
Eq. (4) states that, absent any friction, households supply labor by equating the wage
to the intratemporal marginal rate of substitution.
13
Notice that I adopt a "stock at the beginning at the period" time convention.
13
4.2
The labor market
Labor market clearing is prevented by search and matching frictions à la MortensenPissarides (see Mortensen and Pissarides 1994). Demand and supply conditions (number of
vacancies posted and job-seekers, respectively) and labor market characteristics (matching
efficiency) jointly determine the employment level.
In order to hire workers, firms must post vacancies on the labor market, incurring the
real cost k f . The realized number of matches is the outcome of a Cobb-Douglas technology,
which depends on the number of vacancies (Vt ) and searchers (ut ): Mt (Vt , ut ) = Vtη (ut )1−η .
The probability that a firm matches with a worker is pft = Mt (VVtt ,ut ) . qtw = Mt (Vutt ,ut )
expresses the job-seeker’s probability of being hired. Labor market tightness is defined as
θt = Vutt . It is easy to show that pf is a decreasing function of θ, while q w is an increasing
function of θ. Furthermore, there exists the following relationship: q w (θ) = θpf (θ).
In each period, timing is the following: i) workers and firms search on the labor market
and matches are formed, ii) shocks realize, iii) production occurs, iv) matches exogenously
severe and separated workers enter the unemployment pool.
Employment dynamic is thus given by:
Nt+1 = (1 − s)Nt + Mt
(5)
where s is the exogenous separation rate. The first term in the r.h.s of eq. (5) represents
workers matched in the previous period who do not separate (surviving matches); the second term represents new matches realized at the beginning of the period before production
occurs. As a consequence, the number of searchers is
ut = 1 − (1 − s)Nt−1
that is, all the currently unmatched workers. Unemployment is simply Ut = 1 − Nt .
4.2.1
Workers
Workers can be either employed or unemployed. I now characterize their value function in
both cases. The value function of an employed worker is:
(
i
wt
λt+1 h
w
w
Wt =
− ψCtσc Ntσn + βEt
(1 − s)Wt+1 + s qt+1
Wt+1 + (1 − qt+1
)Ut+1
Pt
λt
)
(6)
where w is the real wage. The second term in r.h.s. of eq. (6) is the marginal rate
of intratemporal substitution, which expresses labor disutility in terms of consumption
goods. The term in brackets is the continuation value of the match: the match continues
with probability 1 − s, while with probability s the worker enters the unemployment pool.
w , otherwise
In the latter case, in the following period she rematches with probability qt+1
she remains unemployed.
14
With a little abuse of notation, let Ut be the value of unemployment at time t:
(
Ut = βEt
λt+1 w
w
q Wt+1 + (1 − qt+1
)Ut+1
λt t+1
)
(7)
The value function of an unemployed worker is defined when the current period matches
have already been formed. It is thus represented by a weighted average of the values
attached to each employment status, where the weights are the probabilities of finding a
job and staying unemployed, respectively.
The surplus which accrues to an employed worker is thus given by:
StW = Wt − Ut =
(
wt
λt+1
w
H
=
− ψCtσc Ntσn + (1 − s)βEt
(1 − qt+1
)St+1
Pt
λt
4.2.2
)
(8)
Wholesale firms
Wholesale firms must take decision on capital, labor and investment. To study the optimal
investment decision, I set up the firm’s maximization problem:
max
Kt+1 ,It ,Nt
s.t.
E0
∞
X
β
t λt+1
t=0
λt
"
#
h
I i
wt
Ptw
t
Yt − k f Vt − Nt − It 1 + S
Pt
Pt
It−1
Yt = At Ktα Nt1−α
Kt+1 = (1 − δ)Kt + It
Pw
where Ptt is the relative price of the wholesale good in terms of the final good, k f is
the real costs of posting a vacancy.
Investment is subject to positive convex adjustment costs, represented by the function
S(·). I adopt the following functional form:
S
It
It−1
!
κ It
=
2 It−1
!2
−κ
It
It−1
!
+
κ
2
It is easy to verify that S(1) = S 0 (1) = 0 and S 00 = κ, so that the steady state does not
depend on κ14 .
14
Christiano, Eichenbaum, and Evans 2005 and Smets and Wouters 2007 adopt similar specifications.
15
Optimization with respect to Kt+1 and It yields:
(
qt = βEt
h
qt 1 − S
"
w
λt+1 Pt+1
α−1 1−α
αKt+1
Nt+1 + qt+1 (1 − δ)
λt Pt+1
I i
t
It−1
= qt S
0
I I
t
t
It−1 It−1
(
− βEt
#)
(9)
I
I
λt+1
t+1
t+1 2
qt+1 S 0
λ
It
It
)
+1
(10)
where q is Tobin’s q. Eq. (9) is the standard Euler equation in presence of investment
adjustment costs, while eq. (10) expresses the optimal choice in terms of investment.
In order to hire workers, firms must post vacancies on the labor market, by paying the
fixed real cost k f . The value of a vacancy is:
JtV
f
=k +
pft JtF
+ (1 −
pft )βEt
λt+1 V
J
λt t+1
!
(11)
Eq. (11) states that with probability pft the firm fills the vacancy and gets the value of
the match (JtF ) and with a complementary probability the vacancy remains unfilled. Free
entry implies:
kf
JtF = f
(12)
pt
The value of a productive match is represented by the following equation:
(
JtF
)
i
λt+1 h
Pw
wt
F
V
+ βEt
(1 − s)Jt+1
+ sJt+1
= t (1 − α)At Ktα Nt−α −
Pt
Pt
λt
(13)
where the first term is the productivity on an additional worker given the current level
of employment and capital stock, wt is the real wage and the term in brackets represents
the continuation value of the match, which ends with probability s.
Eq. (13) and free entry lead to the job creating condition:
(
kf
)
Ptw
wt
λt+1 h
kf i
α −α
=
(1
−
α)A
K
N
−
+
βE
(1
−
s)
t t
t
t
Pt
Pt
λt
pft
pft+1
(14)
Eq. (14) says that firms keep posting vacancies until the real cost they bear (which
depends on the fixed cost and the search spell) equates the current productivity gains and
the savings on future vacancy costs. Eq. (14) is the key transmission channel of uncertainty
shocks. Search frictions distort firms’ optimization condition on hiring. To see this, rewrite
eq. (14) as follows:
(
)
Ptw
wt k f
λt+1 h
kf i
(1 − α)At Ktα Nt−α =
+ f − βEt
(1 − s) f
Pt
Pt
λt
pt
pt+1
16
The distortion introduced by labor market frictions is represented by the two last terms of
the r.h.s.. Heightened uncertainty impacts the continuation value of the match, reducing
expected profits represented by the last term and thus impairing job creation.
4.2.3
Nash bargaining
Wages are established through Nash bargaining, thus implying:
StW =
γ
SF
1−γ t
where StW is defined in eq. (8), γ is the worker’s bargaining power and StF = JtF is the
firm’s surplus.
After some algebra, I obtain this expression for the real wage which prevails in equilibrium:
"
#)
(
wt
λt+1
γ
kf
kf
σc σn
w
− (1 − s)βEt
(15)
= ψCt Nt +
(1 − qt+1 ) f
Pt
1 − γ pft
λt
pt+1
Eq. (15) shows that workers must be compensated for the disutility of working (as in
the competitive framework) but, as long as they have a positive bargaining power, they can
also extract part of the firm’s surplus (the first term inside the brackets). The last term
inside the brackets represents the expected future gains from employment, which enter
with a negative sign: if, say, the worker expects the future surplus to be high, she is willing
to accept a lower wage in the current period.
4.3
Retailers
The homogeneous wholesale good is sold to retail firms, which differentiate it at no cost and
sell them to households. Retailers maximize their profits subject to the demand schedule
for each individual good i:
max
Pit
s.t.
E0
∞
X
t=0
Yit =
β
t λt+1
λt
Pit
Pt
!
Pi t − Ptw
Yit
Pt
!−
With flexible prices, retailers just impose a mark up on the wholesale price:
Pt = µPtw
where µ =
−1 .
17
4.4
The monetary authority
The monetary authority follows a standard Taylor rule:
"
Rt =
ρr
Rt−1
1 Yt
β Ȳ
!δy
Pt
Pt−1
!δπ #1−ρr
where β1 is the steady state interest rate, ρr is the degree of monetary policy inertia
and δy and δπ express the monetary policy reaction to the output gap and to inflation,
respectively.
4.5
Exogenous processes and market clearing
The aggregate resource constraint implies:
"
Yt = Ct + It 1 + S
I t
It−1
#
+ k f Vt
The model features two exogenous processes for the log(technology) and the log(volatility)
of the technological shocks:
ln At+1 = ρa ln At + σt at+1 ,
ln σt+1 = (1 − ρσ ) ln σ̄ + ρσ ln σt + (σ
σ
)σt+1 ,
at+1 ∼ N (0, 1)
(16)
σt+1
(17)
∼ N (0, 1)
where σ̄ is the steady state standard deviation of a and ρa and ρσ represent the
persistence of technological and volatility shocks, respectively. a is a shock to the (log)level
of technology: for this reason I will sometimes refer to it a first moment shock. σ is instead
a shock to the (log)volatility of technology: I will refer to it equivalently as volatility shock,
uncertainty shock or second moment shock. The log-specification of the volatility process
ensures that the standard deviation remains positive even when hit by negative shocks.
This is the same specification adopted by Justiniano and Primiceri 2008.
The process described by eq. (17) is the true innovation with respect to an otherwise
standard search framework. In what follows, I am interested in studying the response of
the economy to a pure uncertainty shock, that is the response to σt . It is worthy to stress
that σt is a mean preserving shock, meaning that it does not have any impact on the level
of technology. This implies that agents’ reactions are not motivated by a change in the
fundamentals, as it would be in the case for any type of first moment shock15 .
15
This approach is rather different from the one taken by Schaal 2012, who combines technological and
volatility shocks to replicate the times series behavior during the recent crisis and the following sluggish
recovery in unemployment.
18
I choose to focus on the stochastic volatility of aggregate technology to establish a
useful comparison with the RBC literature, which constitutes the core of widely used
macro models. Leduc and Liu 2013 who consider stochastic volatility in the demand shock
and in the government spending shock in a similar setup. They show that results stay
unchanged irrespective of the type of uncertainty being considered. This suggests that the
results can be interpreted as the effects of a more general form of economy-wide uncertainty
which is not specific to productivity and in general to supply shocks.
5
Solution method and calibration
5.1
Solution method
The model is calibrated and then solved through perturbation. Aruoba, Fernandez-Villaverde,
and Rubio-Ramirez 2006 and Caldara et al. 2012 show that higher than first order perturbation performs well in terms of speed and accuracy. Due to certainty equivalence, the
volatility of the technological process does not play any role in the first order approximation
of the policy functions. I thus employ a third order perturbation around the deterministic
steady state 16 , which allows me to analyze the effects of second moments shocks.
The presence of volatility in higher order approximations move the economy away
from its deterministic steady state17 . This implies that impulse responses computed as
deviations from the deterministic steady state (as it is usually done with log-linearized
models) do not converge. By looking at these responses it is thus not possible to distinguish
the true effect of a volatility shock from the convergence to the new steady state.
To overcome this problem, take the deterministic steady state as a starting point and I
simulate the model for 2000 periods shutting off any shock. I consider the values reached
by the variables after the simulation period as the "stochastic steady state". The stochastic
steady state is defined as the state where agents choose to stay when they expect future
risk and the realization of the shocks is 018 . In what follows , all impulse response are
computed by imposing a 1 SD volatility shock after the 2000 periods simulation and plotted
as deviations from the stochastic steady state.
5.2
Calibration
In order to confront the outcomes of the model with the empirical evidence presented
in Section 2, I calibrate the model on US quarterly data. Calibration of preferences,
monetary policy, the technological process and the labor market parameters is based on
16
The latest version of Dynare allows pruning also for third order perturbation algorithms.
In a second-order approximation, for instance, the effect of volatility shows up in a constant which
adds to the policy and transition functions. See Jin and Judd 2002 and Schmitt-Grohé and Uribe 2004 for
a formal proof.
18
This is the same definition as in Coeurdacier, Rey, and Winant 2011.
17
19
standard values widely employed in the previous literature and on the data. This facilitates
comparisons and make sure that results are not driven by the extreme parametrization
strategies.
However, the literature on uncertainty shocks provide ambiguous and quite dispersed
estimates on the specification of the exogenous volatility process. I thus choose to adopt
an original strategy based on the data I use in the VAR analysis.
The benchmark calibration is reported in Table 1. β is 0.99, so that the annual steady
state interest rate is around 4 %. Capital depreciation is 10 % on a annual basis. I
adopt a utility function log-linear in consumption and leisure (this implying σc = 1 and
σn = 0.5). For the investment adjustment costs I retain a value of S 00 (·) = κ = 2, which
is quite conservative19 . I assume a steady state unemployment of 7 %, which is in the
range of the values employed in the literature. It is slightly above the average of the
unemployment in the period I consider in my empirical analysis (1968q4-2012q4)20 . The
exogenous separation rate is 10 %: this is consistent with the evidence reported by Davis,
Faberman, and Haltiwanger 2006. For the job finding rate (pf ) I take a value of 0.7, as
in den Haan, Ramey, and Watson 2000. This implies a job finding rate of 0.57. For the
benchmark calibration I retain a value of 0.5 for η, the elasticity of the matching function.
I also take a conservative stand in imposing the same value on the workers’ bargaining
power (γ). The Hosios efficiency condition thus holds in the benchmark calibration. I
then relax this hypothesis to perform a sensitivity analysis on these two parameters. As in
f
Walsh 2005 and Blanchard and Galì 2010, the total vacancy expenditure on GDP ( kYV ) is
1 %. I calibrate α in order to obtain a labor share of 2/321 . The mark up is calibrated at
1.2. I adopt a standard specification of the monetary policy rule, with quite high inertia
(ρr = 0.8), and monetary policy reactions which respect the Taylor principle (δy = 0.5
and δπ = 1.5). For the exogenous process of technology I use the standard values in King,
Plosser, and Rebelo 1988: 0.9 of persistence and steady state volatility (σ̄ a ) equal to 0.007.
The persistence of the volatility process, is generally assumed to be quite high: I thus
adopt a value of 0.8, as in Basu and Bundick 2012 and Gilchrist, Sim, and Zakrajsek 2012.
As regards the standard deviation of the volatility shock, there is no general consensus.
I thus calibrate it to match the empirical standard deviation of my uncertainty indicator
(forecast dispersion) which is around 16 times higher than GDP volatility22 .
19
See Christiano, Eichenbaum, and Evans 2005 and Smets and Wouters 2007 and Sala, Söderström, and
Trigari 2008 for an estimate in a search model.
20
I abstract from labor market participation: since I only consider two employment status (namely
employed and unemployed), population is intended to be active labor force. Other authors like Andolfatto
1996 address this issue by including in the definition of U both people out of the labor force and unemployed.
They accordingly calibrate U on much higher values.
21
In presence of labor market frictions α is no more equal to the labor share. For the retained calibration,
α turns out to be 0.322.
22
To get this value I must impose σσ = 0.45.
20
Table 1. Benchmark calibration
Definition
Calibrated value
Notes
Preferences and technology
β
discount factor
0.99
S.s. annual interest rate of ' 4 %
δ
capital depreciation rate
0.025
Annual rate 10 %
κ
Inv. adj. cost elasticity
2
Sala, Söderström, and Trigari 2008
σc
relative risk aversion
1
Log-utility
σn
inverse of Frisch elasticity
0.5
µ
mark-up over wholesale price
1.2
Utility log-linear in leisure
Labor market parameters
U
Unemployment
0.07
s
Separation rate
0.1
Davis, Faberman, and Haltiwanger
2006
pf
Job filling rate
0.7
den Haan, Ramey, and Watson
2000
qw
Job finding rate
0.57
Labor share
2/3
Vacancy costs/GDP
0.01
Walsh 2005, Blanchard and Galì
2010
η
Elasticity of the match. func.
0.5
Blanchard and Galì 2010
γ
worker’s bargaining power
0.5
Hosios condition respected
WN
Y
f
k V
Y
Monetary Policy
ρr
Monetary policy inertia
0.8
δy
Reaction to output gap
0.5
δπ
Reaction to inflation
1.5
Exogenous processes
ρa
Persistence of the tech. process
0.9
σ̄ a
S.s. SD of the techn. process
0.007
ρσ
Persistence of the volatility
process
0.8
Basu and Bundick 2012; Gilchrist,
Sim, and Zakrajsek 2012; Arellano,
Bai, and Kehoe 2012
σσ
SD of the volatility process
0.45
SD(σa )/SD(log(y)) ' 16, as in the
data
21
King, Plosser, and Rebelo 1988
6
The effects of uncertainty shocks
To facilitate comparisons with the RBC literature and to highlight the role of labor market
frictions, I first report and discuss the IRFs to a 1 SD volatility shock in a model identical
to the one I described but which features a perfect competitive labor market23 . Calibration
is the same discussed in Section 5. I then show the results for the model with search in the
labor market.
6.1
The competitive labor market
Let first discuss the results in the case where the labor market is perfectly competitive.
Figure 3 plots the IRFs to a 1 SD volatility shock. The desire for precautionary saving drives
a drop of consumption on impact, together with a rise in investment. Risk aversion also
leads to precautionary labor supply, which causes a rise in employment. The combination
of higher investment and labor supply leads to a rise in production. Factor prices, i.e.
the wage and the shadow price of installed capital drop to ensure market clearing. All
variables quickly revert to steady state as soon as the higher risk does not materialize into
more disperse technological shocks. The model is not thus able to reproduce the empirical
co-movement among consumption, employment and output.
With different calibrations, responses may change: for instance, with lower investment
adjustment costs and/or with lower risk aversion, agents may prefer to consume more as
uncertainty raises. However, with a perfect competitive labor market, employment, output
and investment always exhibit a dynamic which is opposite to consumption. The intuition is
as follows. As economic conditions become more uncertain, agents who are sufficiently risk
averse decide to consume less to precautionary save for the "rainy days". However, if their
risk aversion is very low, they prefer to consume more to smooth consumption in the case of
positive realizations of the technological shock24 . Households’ decision about consumption,
investment and employment are, de facto, one unique decision. Consider the benchmark
calibration and the responses depicted in Figure 3 (the reverse argument applies to a
calibration which yields opposite results). Risk-averse households facing higher uncertainty
desire to self-insure against bad shock realizations that may occur in the future. Their
action are thus jointly directed towards this goal: consumption falls, directly translating
into a drop in investment, and labor supply increases. Price adjustment ensures labor and
capital market clearing; more inputs are used in production, which thus rises above its
steady state level.
23
With a perfectly competitive labor market, the wage is equal to the marginal rate of substitution
between consumption and labor and to the marginal productivity of labor.
24
Intuitevely, the higher the risk aversion the more agents are inclined to save for precautionary purposes.
For the same RRA, the higher the investment adjustment costs, the more difficult is to profit from good
investment opportunities in case of positive technological shocks. It follows that agents’ ability to smooth
consumption in case of positive realizations of the shocks is dampened, thus leading them to save more.
22
6.2
Search in the labor market
Figures 5, 4 and 6 report the IRFs to a 1 SD volatility shock in the model with search on
the labor market. From Figure 5 we can observe a drop in both consumption and output
on impact. The drop in consumption is more abrupt, reaching the through in the second
period and then quickly reverting to steady state. The fall in production is less pronounced
and smoother: the lower values is reached after four quarters and the recession is more
persistent. The dynamic of output is explained by investment, which follows the opposite
pattern of consumption, thus reducing the negative effect on output and smoothing its
response.
Labor market responses are reported in Figure 4. An unexpected rise in uncertainty
induces firms to post less vacancies and causes labor market tightness to fall. Less vacancies
translate into less job positions and a rise in unemployment, which is of the same magnitude
as the drop in vacancies (as in the data). The fall in the job finding rate follows as a direct
consequence. The timing of the simulated and the empirical responses matches quite well:
the through (peak) is overall attained after 3 periods, which is in line with the VAR
estimation. In Figure 6 I also report the responses of the factor prices, i.e. the wage
and the price of installed capital: they both fall to clear the respective markets. This
notwithstanding, the drop in the wage is not enough to overcome the inefficiency due to
the presence of frictions. The wage reduction does compensate only in part the fall in the
continuation value of the firm due to the increase in uncertainty.
The model is thus able to replicate the empirical responses, except for investment. This
is due to the fact that the model incorporates only convex adjustment costs which smoothly
vary with investment changes and are not sufficient to generate a real option value for the
firm in postponing investment decisions.
These findings are summarized in Proposition 1:
Proposition 1 The combination of uncertainty shocks and search frictions in the labor
market generate a contemporaneous drop in consumption, output, employment, vacancies,
the labor market tightness, the job finding rate and wages.
6.3
The role of labor market frictions
Because the aim of this paper is to analyze the role of labor market frictions in the transmission of uncertainty shocks, I now perform a sensitivity analysis on the parameters
characterizing the matching function and the bargaining process. The two parameters I
focus on are the workers’ bargaining power (γ) and the elasticity of the matching function
(η)25 . First, I explore the role of γ and η separately, retaining the benchmark calibration
for all other parameters. I then perform a further analysis by jointly varying γ and η,
to investigate the possibility that the variation in the responses comes from the difference
25
Changes in the vacancy posting costs do not significantly affect the results.
23
between the two, rather than from the variation of each parameter singularly taken. It
turns out that both γ and η do play a specific and distinguishable role and I discuss the
economic intuition behind my findings.
I now provide a general explanation of the mechanism of the model and on the effects
of uncertainty shocks on agents’ decisions depending on the calibration. This will be useful
later on to interpret the results under different parametrizations. In the competitive labor
market described in Section 6.1, the employment level is mainly "households’ driven",
with wages adjusting to clear the market. In the search model, instead, employment
adjusts according to firms’ hiring decisions and the matching technology. After a volatility
shock, the response of vacancies as well as labor market tightness are influenced only by
firms’ posting decisions. The job finding rate as well as unemployment also depend on
the matching technology, that is on η 26 . Intuitively, if vacancies drop, the job finding rate
should drop too, but the size of the drop would also depend on the elasticity (η). The same
applies to the response of new matches and thus of unemployment.
As regards the reaction of the other variables, it should be noted that households
optimize by intra-temporally substitute consumption and labor. A fall in consumption is
associated to a fall in the intra-temporal marginal rate of substitution which leads to a
lower equilibrium wage. Given the absence of non-convexities in firms’ investing decisions,
each variation in consumption translates in an opposite reaction of investment. Markets
clearing is ensured by the adjustment of the wage and the price of installed capital (Tobin’s
q). Finally, output response is determined by both investment and employment.
I now discuss how firms’ and households decisions are affected by changes in parameters.
As we saw in Section 6.2, after a volatility shock firms react by reducing the posting
activity. The size of the drop in vacancies depends on both 1 − γ and η. 1 − γ represents
the fraction of the match surplus which accrues to firms: if this fraction is high, firms’
profitability is strongly affected by variations in the match surplus. The firms’ bargaining
power can thus be regarded as a measure of firms’ sensitiveness to everything that potentially affects the value of the productive match. We should thus expect a sharper reduction
in vacancies when firms hold a higher bargaining power.
Households cut consumption expenditure to save for precautionary purposes. Low
values of γ imply that it is more difficult to accumulate resources, because households’
benefit less from the match surplus. It follows that the drop in consumption and the rise
in labor supply is more pronounced when the workers’ bargaining power is low. Wages and
the price of investment adjust accordingly.
Another natural candidate in influencing model responses to uncertainty shocks is the
elasticity of the matching function. Higher values of η imply that the number of new
matches is marginally more affected by the number of vacancies rather than by the number
of searchers. This means that little variation in vacancies may have stronger implications
for the number of matches and thus for the overall employment level. η can thus be regarded
26
Remember that qtw = θη .
24
as an index of firms’ need to reduce vacancies to attain a certain level of employment: firms
that want to reduce employment, need to reduce vacancies by less when η is higher. We
should thus expect a weaker reaction of vacancies when η is calibrated at high values. On
the supply side of the labor market, we can apply the reverse argument: households’ who
want to save for precautionary motives cut consumption by more and are willing to accept
lower wages when the number of hirings is less responsive to the number of searchers (i.e.
when η is high).
I now present the Figures which graphically show the mechanism I have discussed.
Figures 8, 7 and 9 show the IRFs of the variables of interest for three different values of the
workers’ bargaining power (γ = 0.3, γ = 0.5 and γ = 0.7), while all the other parameters
are fixed at the values reported in Table 1. The blue solid line represents the benchmark
(γ = 0.5).
Let first consider labor market responses, depicted in Figure 7. The response of vacancies directly mirrors firms’ decisions. Firms react more strongly when workers’ relative
bargaining power is low, meaning that they are more concerned by the variation in uncertainty. Everything else equal, larger productivity shocks would have worse consequences
on firms’ profitability when they are assigned a larger share of the surplus. The sharpest
firms’ reaction drives all the other outcomes: the increase in unemployment and the drop in
the labor market tightness and in the job finding rate. As we can notice from Figure 8, low
values of γ have a stronger effect on consumption too: households must cut consumption
by more in order to attain the desired level of savings. The intra-temporal optimization
implies a larger fall in the wage (cfr. Figure 9). Output response is driven by the rise in
unemployment. Since both households and firms’ reactions are stronger for low values of γ,
we can infer a monotonic relationship between γ and the magnitude of the response of the
overall economy to uncertainty shocks. This is summarized by the following proposition:
Proposition 2 Everything else equal, the magnitude of the response of the economy to an
uncertainty shock is a positive function of the firms’ bargaining power (1 − γ).
Let now discuss the effects of uncertainty shocks for different values of the elasticity of
the matching function. I compare the benchmark calibration (η = 0.5) with a 0.2 decrease
and increase in the value of η. I thus focus on a meaningful range (from η = 0.3 to η = 0.7)
according to the estimates provided by the literature 27 .
Figures from 11 to 12 plot the IRFs to a 1 SD uncertainty shock for the three different
calibrations; the benchmark is the blue solid line plot.
The drop in vacancies is more pronounced when elasticity is at its bottom value: to get
the same effect on employment, firms must reduce vacancies by more. This triggers the
sharper response in labor market tightness. However, the job finding rate and unemployment exhibit the sharpest response when η = 0.5. In fact, even if the drop in vacancies
27
See Petrongolo and Pissarides 2001 for a survey on the estimates of the elasticities of the aggregate
matching function.
25
is larger for η = 0.3, the job finding rate and the employment level are less responsive
because of the low elasticity.
When η is low, the economy is more responsive to households’ decision. They thus need
to cut consumption by less; it follows that the wage and the Tobin’s q IRFs are attenuated.
Investment mirrors consumption response with the opposite sign, as usual. Output drops
by more when the elasticity of the matching function is at the benchmark. This is the
consequence of the stronger effect on employment discussed above.
Conversely, when η = 0.7 households need to cut consumption by more to get the
desired level of savings (cfr. Figure 11). Capital and labor market clearing requires a
larger drop in the wage and in Tobin’s q (Figure 12). From Figure 10 we can see that
the responses of all labor variables are attenuated, because of the weaker firms’ reaction.
Moreover, we can observe a tiny impact response which goes in the opposite direction of
what expected. This can be explained by first order effects that counterbalance the effect of
increased uncertainty, which is only second-order. On impact, the huge wage drop induces
firms to benefit from the higher surplus and to post more vacancies. As soon as wages start
to revert back to equilibrium, the uncertainty effect dampens vacancies response, which
becomes negative. All other labor market variables responses plotted in Figure 10 and
output behavior are direct consequences of the mechanism just described.
Because of the complex interactions between households’ and firms’ decisions and between firms’ decision and the implications of the matching technology, it is not possible to
derive a monotonic relationship between η and the response of the economy to uncertainty
shocks. The previous findings are summarized in the following proposition:
Proposition 3 Everything else equal, it is not possible to derive a monotonic relationship
between the elasticity of the matching function w.r.t. vacancies (η) and the response of the
economy to uncertainty shocks.
Low values of η tend to attenuate consumption, investment and input prices response
(which depend on households’ decisions).
At the same time, low values of η amplify firms’ reaction and thus the drop in vacancies.
However, this does not necessarily implies a larger drop (rise) in (un)employment because
of the weaker responsiveness caused by the low elasticity.
The effects on γ and η on the strength of firms’ and households reaction to a volatility
shock, is summarized in Table 2. To facilitate comparisons with the following section, the
firms’ bargaining power (1 − γ) is reported. The plus (minus) sign must be interpreted as
the amplification (attenuation) of the response of the row variable to uncertainty shocks
as 1 − γ and η respectively increase. The first line of Table 2, for instance, means that the
response of vacancies to an uncertainty shock (which is negative), is amplified for higher
values of 1 − γ and attenuated for higher values of η.
The search literature has emphasized the importance of the so-called Hosios-Pissarides
condition (Pissarides 1990b). The Hosios-Pissarides rule states that search frictions are
26
Table 2. Attenuation and amplification effects of labor market frictions on the
responses to a volatility shock
1−γ
η
Firms’ decision
Vacancies
Labor market tightness
+
+
-
Firms’ decision + matching tech.
Job finding rate
Unemployment
+
+
?
?
Households’ decisions
Consumption
Investment
+
+
+
+
Derived responses
Wage
Tobin’s q
Output
+
+
+
+
+
?
a
The plus (minus) sign expresses the amplification (attenuation) effect of 1 − γ and η,
respectively, on the response of each row variable following a positive uncertainty shock.
The first line, for instance, means that the response of vacancies to an uncertainty shock
(which is negative), is amplified for higher values of 1 − γ and attenuated for higher
values of η.
minimized and the constrained social optimum is achieved when the firms’ bargaining power
is equal to the elasticity of the matching function with respect to vacancies. As shown in
Petrosky-Nadeau and Wasmer 2012, deviations from the Hosios-Pissarides condition, may
have important implications. Since in this framework uncertainty shocks propagate to the
economy through search frictions, one may ask to which extent the previous results are
due to a departure from the efficiency rule.
To investigate this issue, I simulate the model by setting both 1 − γ (firms’ bargaining
power) and η to the same value. This allows me to distinguish whether the variation in the
responses discussed above is due to the departure from the optimality condition or rather
to a specific effect of each one of the two parameters. Results are shown in Figures 14, 13
and 15. It can be immediately observed that the three different calibrations yield closer
responses ar regards vacancies and the labor market tightness, but very different outcomes
for all the other variables. The interpretation is straightforward, given the previous analysis
on the separate effects of γ and η summarized in Table 2. 1 − γ and η have opposite
effects on firms’ decision. On one side, a higher bargaining power induces firms to reduce
vacancies more sharply; on the other side, a higher elasticity reduces the need to do that.
The offsetting nature of these two parameters is evident in the top panels of Figure 13:
different parameterizations do not seem to generate significant differences in the responses
of vacancies and θ. The implications for the job finding rate and the unemployment level,
27
however, are very different. For the same drop in vacancies, the labor market reacts
more strongly when the elasticity is higher. This drives also the difference in the output
response. Furthermore, consumption, investment and prices exhibit very different reactions
depending on the calibration. In the highest calibration, consumption drops more than two
times compared to the lowest one. This huge difference depends on the reinforcing effect
of η and 1 − γ, which both magnify households’ reaction.
As an additional check I report the IRFs when the Hosios condition is violated, that
is when η and 1 − γ depart from one to another. The simulated responses are plotted in
Figures 17, 16 and 18. As expected, the responses of consumption, investment and prices
are much closer one to another, while the differences in firms’ reaction are magnified.
The implications of the violations of the Hosios-Pissarides rule are summarized in the
following proposition:
Proposition 4 The Hosios-Pissarides condition (η = 1 − γ), does not affect, per se, the
response of the economy to an uncertainty shock. The elasticity of the matching function
and the firms’ bargaining power do play a distinct role on firms’ and households’ decisions,
namely:
• η and 1 − γ both have an amplifying effect on households’ decision and thus on
consumption, investment and prices. It follows that the responses of these variables
to an uncertainty shock have different magnitudes when the Hosios conditions holds
for different calibrated values.
• η and 1 − γ have opposite effects on firms’ decisions, and thus on vacancies and the
labor market tightness. It follows that the responses of these variables to an uncertainty shock have similar magnitudes when the Hosios condition holds for different
calibrated values.
7
Conclusions
This paper examines the impact of uncertainty shocks on the labor market, both empirically
and theoretically. In the empirical part, I proxy uncertainty with forecasts dispersion in
the Survey of Professional Forecasters. I perform VAR estimates including both the TFP
and the uncertainty indicators and different measures of economic activity. I show that
uncertainty plays an autonomous and significant role, negatively affecting the aggregate
economy. I provide new evidence on the negative impact of uncertainty on the labor market,
especially on employment, vacancies, the labor market tightness and the job finding rate.
In the theoretical part, I build a DSGE model featuring search and matching frictions
à la Mortensen-Pissarides in the labor market and stochastic volatility. Uncertainty shocks
are defined as unexpected increases in the volatility of the technological process. In contrast
to the standard RBC framework, the model is able to generate the observed co-movement
28
of output, employment, vacancies, the labor market tightness and the job finding rate.
The sensitivity analysis allows me to identify the propagation forces of uncertainty shocks
throughout the economy. The firm’s bargaining power has an amplifying effect on the
impact of uncertainty. The role of the elasticity of the matching function with respect
to vacancies is instead twofold: from one side, it attenuates households’ reaction (thus
reducing the response of consumption, investment and input prices), while from the other
side it induces a stronger cautionary attitude from the firms’ part (thus magnifying the
response of the labor market). Finally, the Hosios-Pissarides condition does not seem to
play an autonomous role in shaping the economic outcomes after an uncertainty shock.
These findings can be interpreted in the light of previous research and suggest that
uncertainty is likely to play a detrimental role on the overall economy when frictions prevent
firms to smoothly adjust their investment and hiring decisions in line with the current
economic conditions. In this case, the real option value of waiting increases as future
becomes more uncertain and firms adopt a cautious attitude. The search and matching
framework naturally embeds this mechanism and indeed proves to explain the negative
impact of uncertainty on the labor market observed in the data.
29
References
Abel, A.B. and J.C. Eberly (1999). “The Effects of Irreversibility and Uncertainty on
Capital Accumulation”. In: Journal of Monetary Economics 44, pp. 339–377.
Alexopoulos, M. and J. Cohen (2009). “Uncertain Times, Uncertain Measures”.
Andolfatto, D. (1996). “Business Cycles and Labor-Market Search”. In: American Economic Review 86 (1), pp. 112–132.
Arellano, C., Y. Bai, and P.J. Kehoe (2012). Financial Frictions and Fluctuations in Volatility. Research Department Staff Report 466. Federal Reserve Bank of Minneapolis.
Aruoba, S.B., J. Fernandez-Villaverde, and J.F. Rubio-Ramirez (2006). “Comparing Solution Methods for Dynamic Equilibrium Economies”. In: Journal of Economic Dynamics
and Control 30, 2477–2508.
Bachmann, R., S. Elstner, and E.R. Sims (2012). Uncertainty and Economic Activity:
Evidence from Business Survey Data. Working Paper 014. University of Notre Dame.
Bachmann, R. and G. Moscarini (2012). “Business Cycles and Endogenous Uncertainty”.
Baker, S.R., N. Bloom, and S.J. Davis (2013). Measuring Economic Policy Uncertainty.
Working Paper 13-02. Chicago Booth.
Basu, S. and B. Bundick (2012). Uncertainty Shocks in a Model of Effective Demand.
Working Paper. Boston College.
Bernanke, B. (1983). “Irreversibility, Uncertainty and Cyclical Investment”. In: Quarterly
Journal of Economics 98 (1), pp. 85–107.
Blanchard, O. and J. Galì (2010). “Labor Market and Monetary Policy: a New-Keynesian
Model with Unemployment”. In: American Economic Journal: Macroeconomics 2 (2),
pp. 1–30.
Bloom, N. (2009). “The Impact of Uncertainty Shocks”. In: Econometrica 77 (3), pp. 623–
685.
Bloom, N., S. Bond, and J. van Reeenen (2007). “Uncertainty and Investment Dynamics”.
In: Review of Economic Studies 74 (2), 391–415.
Bloom, N., M.A. Kose, and M.E. Terrones (2013). “Held Back by Uncertainty”. In: Finance
and Development (March).
Bloom, N. et al. (2012). Really Uncertain Business Cycles. Working Paper 18245. NBER.
Bomberger, W.A. (1996). “Disagreement as a Measure of Uncertainty”. In: Journal of
Money, Credit and Banking 28 (3), pp. 381–392.
Caldara, D. et al. (2012). “Computing DSGE Models with Recursive Preferences and
Stochastic Volatility”. In: Review of Economic Dynamics 15, pp. 188–206.
Christiano, L., R. Motto, and M. Rostagno (2010). Financial Factors in Economic Fluctuations. Working Paper 1192. European Central Bank.
Christiano, L.J., C.M. Eichenbaum, and C.L. Evans (2005). “Nominal Rigidities and the
Dynamic Effects of a Shock to Monetary Policy”. In: Journal of Political Economy 113
(1), pp. 1–45.
30
Coeurdacier, N., H. Rey, and P. Winant (2011). “The Risky Steady-State”. In: American
Economic Review Papers and Proceedings.
D’Erasmo, P.N. and H.J. Moscoso Boedo (2013). “Intangibles and Endogenous Firm Volatility over the Business Cycle”.
Davis, S.J., R.J. Faberman, and J. Haltiwanger (2006). The Flow Approach to Labor Markets: New Data Sources and Micro-macro Links. Working Paper 12167. NBER.
Dixit, A. and R. Pindyck (1994). Investment under Uncertainty. Ed. by Princeton University Press. New Jersey.
Fernald, J. (2012). A Quarterly, Utilization-Adjusted Series on Total Factor Productivity.
Working Paper 2012-19. Federal Reserve bank of San Francisco.
Fernandez-Villaverde, J. and J.F. Ramirez (2011). “Macroeconomics and Volatility: Data,
Models, and Methods”. In: Advances in Economics and Econometrics: Theory and
Applications. Tenth World Congress of the Econometric Society. Ed. by Cambridge
University Press.
Fernandez-Villaverde, J. et al. (2011). “Risk Matters: The Real Effects of Volatility Shocks”.
In: American Economic Review 101.6, pp. 2530–61.
Fernández-Villaverde, J. et al. (2011). Fiscal Volatility Shocks and Economic Activity.
Working Paper 17317. NBER.
Gilchrist, S., J.W. Sim, and E. Zakrajsek (2012). “Uncertainty, Financial Frictions, and
Irreversible Investment”.
Jin, H. and K.L. Judd (2002). “Perturbation Methods for General Dynamic Stochastic
Models”.
Justiniano, A. and G. Primiceri (2008). “The Time-Varying Volatility of Macroeconomic
Fluctuations”. In: American Economic Review 98 (3), 604–641.
Kehrig, M. (2011). The Cyclicality of Productivity Dispersion. Working Paper CES-WP11-15. US Census Bureau Center for Economic Studies.
King, C., C.I. Plosser, and S.T. Rebelo (1988). “Production, Growth and the Business Cycle. I. The basic Neoclassical Model”. In: Journal of Monetary Economics 21, pp. 195–
232.
Knotek II, E.S. and S. Khan (2011). “How Do Households Respond to Uncertainty Shocks?”
In: Kansas FED Economic Review (2).
Kose, M.A. and M. Terrones (2012). “How Does Uncertainty Affect Economic Performance?” In: World Economic Outlook. Ed. by IMF, pp. 49–53.
Leahy, J.V. and T.M. Whited (1996). “The Effect of Uncertainty on Investment: Some
Stylized Facts”. In: Journal of Money Credit and Banking 28 (1).
Leduc, S. and Z. Liu (2013). Uncertainty Shocks are Aggregate Demand Shocks. Working
Paper 2012-10. Federal Reserve Bank of San Francisco.
Merz, M. (1995). “Search in the Labor Market and the Real Business Cycle”. In: Journal
of Monetary Economics 36, pp. 269–300.
Mortensen, D.T and C.H. Pissarides (1994). “Job Creation and Job Destruction in the
Theory of Unemployment”. In: Review of Economic Studies 61, pp. 397–415.
31
NABE, US National Association for Business Economics, ed. Economic Policy Survey.
NFIB, US National Federation of Indipendent Businesses, ed. (2012). Small Business Problems and Priorities.
Petrongolo, B. and C.A. Pissarides (2001). “Looking into the Black Box; A Survey of the
Matching Function”. In: Journal of Economic Literature 39 (2), pp. 390–431.
Petrosky-Nadeau, N. and E. Wasmer (2012). “The Cyclical Volatility of Labor Markets
under Frictional Financial Markets”.
Pissarides, C. (1990a). Equilibrium Unemployment Theory. Ed. by MIT Press.
— (1990b). Equilibrium Unemployment Theory. Ed. by Oxford: Basil Blackwell.
Sala, L., U. Söderström, and A. Trigari (2008). “Monetary Policy under Uncertainty in an
Estimated Model with Labor Market Frictions”. In: Journal of Monetary Economics
55, 983– 1006.
Schaal, E. (2012). “Uncertainty, Productivity and Unemployment in the Great Recession”.
Schmitt-Grohé, S. and M. Uribe (2004). “Solving Dynamic General Equilibrium Models
Using a Second-order Approximation to the Policy Function”. In: Journal of Economic
Dynamics and Control 28, 755–775.
Schwert, G.W. (1989). “Why Does Stock Market Volatility Change Over Time?” In: Journal
of Finance 44 (5), pp. 1115–1153.
Smets, F. and R. Wouters (2007). Shocks and Frictions in US Business Cycles: a Bayesian
DSGE Approach. Working Paper Research 109. National Bank of Belgium.
Walsh, C.E. (2005). “Labor market search, sticky prices, and interest rate policies”. In:
Review of Economic Dynamics 8, 829–849.
den Haan, W.J, G. Ramey, and J. Watson (2000). “Job Destruction and Propagation of
Shocks”. In: American Economic Review 90 (3), 482–498.
van Nieuwerburgh, S. and L. Veldkamp (2006). “Learning Asymmetries in Real Business
Cycles”. In: Journal of Monetary Economics 53, 753–772.
32
Industrial Production
Consumption
.5
.2
0
0
Investment
1
0
−1
−.5
−.2
−2
−1
−.4
0
5
10
periods
95% CI
15
orthogonalized irf
20
−3
0
5
10
periods
95% CI
15
20
0
orthogonalized irf
Figure 1. Macro variables: IRFs to 1 SD uncertainty shock
5
10
periods
95% CI
15
20
orthogonalized irf
a
a
Trivariate VAR on United States data from 1968q4 to 2012q4.
Series included
are,
in
order:
TFP
growth
(dtfp
series
from
John
Fernald’
website
http://www.frbsf.org/economics/economists/staff.php?jfernald), the uncertainty indicator (i.e.
the
cross-sectional dispersion of forecasts on nominal GDP in the next quarter from the Philadelphia FED’s
SPF) and one variable proxying economic activity.
The variables included in each subfigure are, respectively: log(industrial production index) (FRED’S
ID: INDPRO), log(real personal consumption expenditures) (FRED’S ID: PCECC96) and log(real gross
private domestic investment) (FRED’S ID: GPDIC96). Variables enter with four lags, selected according
to the Akaike criterion.
All variables are expressed as percentage deviations from the hp-filtered series with smoothing parameter
1600. The figure plots the response of each macro variables ordered last to 1 SD shock to the uncertainty
indicator.
33
Vacancies
Labor market tightness
2
2
0
0
−2
−2
−4
−6
−4
0
5
10
periods
15
20
0
5
Unemployment
10
periods
15
20
15
20
Job finding rate
3
.5
2
0
1
−.5
0
−1
−1
0
5
95% CI
10
periods
15
20
0
orthogonalized irf
5
10
periods
95% CI
Figure 2. Labor variables: IRFs to 1 SD uncertainty shock
a
orthogonalized irf
a
Trivariate VAR on United States data from 1968q4 to 2012q4.
Series included
are,
in
order:
TFP
growth
(dtfp
series
from
John
Fernald’
website
http://www.frbsf.org/economics/economists/staff.php?jfernald), the uncertainty indicator (i.e.
the
cross-sectional dispersion of forecasts on nominal GDP in the next quarter from the Philadelphia FED’s
SPF) and one labor market variable.
The variables included in each subfigure are, respectively:
the log of the composite
help-wanted advertising index (from the Conference Board and Regis Barnichon’s website https://sites.google.com/site/regisbarnichon/research),
labor market tightness defined as
log(hwi)-log(unemployment), log(unemployment) (thousands of people, from CPS) and the
job finding rate (series constructed by Robert Shimer and downloadable from his website
https://sites.google.com/site/robertshimer/research/flows).
The VAR specification with the labor market tightness and unemployment is estimated with 2 lags,
whereas the others with 4 lags, all selected according to the Akaike criterion. All variables are expressed
as percentage deviations from the hp-filtered series with smoothing parameter 1600. The figure plots the
response of each macro variable ordered last to 1 SD shock to the uncertainty indicator.
34
·10−2
8
Consumption
·10−2
Output
10
Investment
0.6
6
5
0.4
4
0
0.2
2
−5
0
0
0
5
10
15
Unemployment
20
−10
0
5
·10−2
10
Wage
15
−0.2
20
0
0.5
2
0
0
0
−2
−2
−4
−4
−6
−6
−0.5
−1
−1.5
0
5
10
15
20
−8
0
·10−2
2
5
10
15
20
−8
5
0
Figure 3. Competitive labor market: IRFs to a 1 SD volatility shock
5
10
15
Tobin’s q
10
15
20
20
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations
of log(output), log(consumption), log(investment), log(unemployment), wage and Tobin’s q from their
stochastic steady state, as defined in the main text.
a
35
·10−2
0
Vacancies
0
−5
−5
−10
−10
−15
−15
−20
0
5
10
15
20
Unemployment
·10−2
10
−20
8
0
0
5
10
15
Jof
finding
rate
·10−2
20
−1
6
−2
4
−3
2
0
Labor
market tightness
·10−2
0
5
10
15
20
−4
0
5
10
15
20
a
Figure 4. Search in the labor market: IRFs to a 1 SD volatility shock
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
log(vacancies), log(θ), log(unemployment), and the job finding rate (q w ) from their stochastic steady state,
as defined in the main text.
a
·10−3
0
Output
Consumption
·10−2
0
·10−2
Investment
4
−0.5
−2
2
−1
−4
−1.5
0
5
10
15
20
0
0
5
10
15
20
0
5
Figure 5. Search in the labor market: IRFs to a 1 SD volatility shock
10
15
20
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
log(output), log(consumption), and log(investment), from their stochastic steady state, as defined in the
main text.
a
36
·10−2
0
Wage
·10−2
Tobin’s q
0
−2
−0.5
−4
−1
0
5
10
15
20
0
5
10
15
Figure 6. Search in the labor market: IRFs to a 1 SD volatility shock
20
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
wage and shadow price of installed capital (Tobin’s q) from their stochastic steady state, as defined in the
main text.
a
Labor market tightness
Vacancies
0
0
−0.1
−0.1
−0.2
−0.2
0
5
10
15
20
Unemployment
·10−2
20
15
0
0
5
10
15
Job
finding
rate
·10−2
20
γ =0.3
γ =0.5
γ =0.7
−2
10
−4
5
0
0
5
10
15
20
−6
0
5
10
15
20
Figure 7. The role of labor market frictions: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
log(vacancies), log(θ), log(unemployment), and the job finding rate (q w ) from their stochastic steady state
(as defined in the main text), for different values of the workers’ bargaining power.
a
37
Consumption
·10−2
Output
·10−3
0
·10−2
0
4
−1
2
Investment
γ =0.3
γ =0.5
γ =0.7
−2
−4
−6
0
−2
−8
0
5
10
15
20
0
5
10
15
20
−2
0
5
10
Figure 8. The role of labor market frictions: IRFs to a 1 SD volatility shock
15
20
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations
of log(output), log(consumption), and log(investment) from their stochastic steady state (as defined in the
main text), for different values of the workers’ bargaining power.
a
·10−2
Wage
·10−2
0
0
−2
−0.5
−4
−1
−6
Tobin’s q
γ =0.3
γ =0.5
γ =0.7
−1.5
0
5
10
15
20
0
5
10
15
20
Figure 9. The role of labor market frictions: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
wage and shadow price of installed capital (Tobin’s q) from their stochastic steady state (as defined in the
main text), for different values of the workers’ bargaining power.
a
38
Labor market tightness
Vacancies
0
0
−0.1
−0.1
−0.2
0
5
10
15
20
Unemployment
·10−2
15
−0.2
0
·10
5
10
15
Job
finding
rate
−2
20
η =0.3
η =0.5
η =0.7
0
10
5
−2
0
−5
0
5
10
15
20
−4
0
5
10
15
20
Figure 10. The role of labor market frictions: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
log(vacancies), log(θ), log(unemployment), and the job finding rate (q w ) from their stochastic steady state
(as defined in the main text), for different values of the elasticity of the matching function.
a
·10−3
Consumption
·10−2
Output
·10−2
η =0.3
η =0.5
η =0.7
8
0
0
Investment
6
−2
−1
−4
−2
4
2
0
5
10
15
20
0
0
5
10
15
20
0
5
10
Figure 11. The role of labor market frictions: IRFs to a 1 SD volatility shock
15
20
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations
of log(output), log(consumption), and log(investment) from their stochastic steady state (as defined in the
main text), for different values of the elasticity of the matching function.
a
39
·10−2
Wage
·10−2
Tobin’s q
η =0.3
η =0.5
η =0.7
0
0
−0.5
−2
−1
−4
−1.5
−6
0
5
10
15
20
0
5
10
15
20
Figure 12. The role of labor market frictions: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
wage and shadow price of installed capital (Tobin’s q) from their stochastic steady state (as defined in the
main text), for different values of the elasticity of the matching function.
a
40
·10−2
0
Vacancies
0
−5
−5
−10
−10
−15
−15
−20
0
5
10
15
20
Unemployment
·10−2
20
−20
Labor
market tightness
·10−2
0
0
5
10
15
Job finding rate
·10−2
20
15
−2
10
5
0
−4
0
5
10
15
20
0
5
10
15
20
η, 1-γ = 0.3
η, 1-γ = 0.5
η, 1-γ = 0.7
Figure 13. The Hosios-Pissarides rule: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
log(vacancies), log(θ), log(unemployment), and the job finding rate (q w ) from their stochastic steady state
(as defined in the main text), when the Hosios-Pissarides rule holds for different calibrations.
a
41
·10−3
Consumption
·10−2
Output
0
0
−2
−1
−4
−6
0
5
10
15
20
Investment
0.15
0.1
−2
5 · 10−2
−3
0
0
5
10
15
20
0
5
10
15
η, 1-γ = 0.3
η, 1-γ = 0.5
η, 1-γ = 0.7
Figure 14. The Hosios-Pissarides rule: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations
of log(output), log(consumption), and log(investment) from their stochastic steady state (as defined in the
main text), when the Hosios-Pissarides rule holds for different calibrations.
a
·10−2
Wage
·10−2
0
Tobin’s q
η, 1-γ = 0.3
η, 1-γ = 0.5
η, 1-γ = 0.7
0
−2
−4
−1
−6
−2
−8
0
5
10
15
20
0
5
10
15
20
Figure 15. The Hosios-Pissarides rule: IRFs to a 1 SD volatility shock
a
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
wage and shadow price of installed capital (Tobin’s q) from their stochastic steady state (as defined in the
main text), when the Hosios-Pissarides rule holds for different calibrations.
42
20
Labor market tightness
Vacancies
0
0
−0.1
−0.1
−0.2
−0.2
−0.3
−0.3
−0.4
0
5
10
15
20
Unemployment
−0.4
0.2
0
0
5
10
15
Job finding rate
·10−2
20
0.15
−2
0.1
5 · 10−2
0
−4
0
5
10
15
20
0
5
10
15
20
η = 0.3; 1-γ = 0.7
η = 0.7; 1-γ = 0.3
Figure 16. The Hosios-Pissarides rule: IRFs to a 1 SD volatility shock
a
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
log(vacancies), log(θ), log(unemployment), and the job finding rate (q w ) from their stochastic steady state
(as defined in the main text), when the Hosios-Pissarides rule is violated for different calibrations.
43
·10−3
Consumption
·10−2
Output
0
0
−2
−0.5
−4
−1
−6
−1.5
0
5
10
15
20
·10−2
6
Investment
4
2
0
0
5
10
15
20
−2
0
5
10
15
20
η = 0.3; 1-γ = 0.7
η = 0.7; 1-γ = 0.3
Figure 17. The Hosios-Pissarides rule: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations
of log(output), log(consumption), and log(investment) from their stochastic steady state (as defined in the
main text), when the Hosios-Pissarides rule is violated for different calibrations.
a
·10−2
Wage
·10−2
0
Tobin’s q
0
−2
−0.5
−4
−6
0
5
10
15
−1
20
0
5
10
15
20
η = 0.3; 1-γ = 0.7
η = 0.7; 1-γ = 0.3
Figure 18. The Hosios-Pissarides rule: IRFs to a 1 SD volatility shock
a
IRFs to a 1 SD deviation shock to σ a occurred in period 0. The figure plots percentage deviations of
wage and shadow price of installed capital (Tobin’s q) from their stochastic steady state (as defined in the
main text), when the Hosios-Pissarides rule is violated for different calibrations.
a
44