Anticipated Growth and Business Cycles in Matching Models

41 Pages·2009·0.38 MB·English

Anticipated Growth and Business Cycles
in Matching Models
Wouter J. DEN HAAN and Georg KALTENBRUNNER
(cid:3)
February 14, 2009
Abstract
In a business cycle model that incorporates a standard matching framework, em-
ployment increases in response to news shocks, even though the wealth e⁄ect asso-
ciated with the increase in expected productivity reduces labor force participation.
The reason is that the matching friction induces entrepreneurs to increase investment
in new projects and vacancies early. If there is underinvestment in new projects in
the competitive equilibrium, then the e¢ ciency gains associated with an increase in
employment make it possible that consumption, employment, output, as well as the
investment in new and existing projects jointly increase before the actual increase in
productivity materializes. If there is no underinvestment then investment in existing
projects decreases, but total investment, consumption, employment, and output still
jointly increase.
Keywords: Pigou Cycles, Labor Force Participation, Productivity Growth
JEL Classi(cid:133)cation: E24, E32, J41
(cid:3)Den Haan: Department of Economics, University of Amsterdam, Roetersstraat 11, 1018 WB
Amsterdam, The Netherlands and CEPR, London, United Kingdom. Email: [email protected].
Kaltenbrunner: McKinsey & Company, Inc., Magnusstra(cid:223)e 11, 50672 K(cid:246)ln, Germany. Email:
[email protected]. The authors are grateful to an anonymous referee, Nir Jaimovitch,
Franck Portier, and Sergio Rebelo for insightful comments.
1 Introduction
1
Economists have long recognized the importance of expectations in explaining economic
2
(cid:135)uctuations. As early as 1927, Pigou postulated that (cid:145)the varying expectations of business
3
men ... constitute the immediate cause and direct causes or antecedents of industrial (cid:135)uc-
4
tuations.(cid:146)1 A recent episode where many academic and non-academic observers attribute
5
a key role to expectations is the economic expansion of the 1990s. During the 1990s,
6
economic agents observed an increase in current productivity levels, but also became more
7
optimistic regarding future growth rates of productivity. In fact, there was a strong sense
8
of moving towards a new era, the (cid:145)new economy(cid:146), of higher average productivity growth
9
rates for the foreseeable future. With the bene(cid:133)t of hindsight it is easy to characterize
10
the optimism about future growth rates as (cid:145)unrealistic(cid:146). At the time, however, the signals
11
about future productivity were in fact remarkable, and the view that a new era was about
12
to begin was shared by many experts, including economic policy makers such as Alan
13
Greenspan.2 Similarly, the question arises whether the downward adjustment of these
14
high expectations about future growth rates did not at least worsen, if not cause, the
15
economic downturn that took place at the beginning of the new millennium.
16
More formal empirical evidence that business cycles are caused by anticipated changes
17
in future productivity is provided by Beaudry and Portier (2006).3 They use changes in
18
stock prices to identify that fraction of future changes in productivity that is anticipated
19
and argue that this fraction is actually quite large. They show that innovations in tech-
20
nology are small, but initiate substantial future increases in productivity. Moreover, this
21
expectation shock leads to a boom in output, consumption, investment, and hours worked
22
1In Pigou (1927).
2See, for example, the following quote in Greenspan (2000): (cid:145)... there can be little doubt that not only
hasproductivitygrowthpickedupfromitsrathertepidpaceduringtheprecedingquarter-centurybutthat
the growth rate has continued to rise, with scant evidence that it is about to crest. In sum, indications
... support a distinct possibility that total productivity growth rates will remain high or even increase
further.(cid:146)
3Schmitt-GrohØ and Uribe (2008) estimate a model similar to the one in Jaimovich and Rebelo (2006)
allowing both for anticipated and non-anticipated shocks and document the importance of anticipated
shocks. They (cid:133)nd that anticipated shocks are responsible for 71% of the (cid:135)uctuations in output growth.
1
before the anticipated productivity growth actually materializes.
1
Beaudry and Portier (2007) analyze whether existing neoclassical models can generate
2
Pigoucycles. InaPigoucycle,output,consumption,investment,andhoursworkedjointly
3
increase in response to an anticipated increase in productivity and these variables decline
4
whentheanticipatedincreasefailstomaterialize. Theyconsideralargeclassofmodelsand
5
show that the answer is no.4 Instead, the typical response is an increase in consumption,
6
but a decrease in investment and hours worked. The reason is that the wealth e⁄ect
7
induces agents to increase consumption and leisure. It is not di¢ cult to generate an
8
increase in investment, because the anticipated increase in productivity also causes the
9
expected return on capital to go up.5 The problem is, however, that higher levels of
10
investment are typically (cid:133)nanced by a reduction in consumption, not by an increase in
11
hours worked. The real challenge is, therefore, to build a model in which hours worked
12
increase in response to an increase in anticipated productivity growth.
13
Recently, some models have been developed where an increase in expected productiv-
14
ity generates a business cycle boom. Exemplary papers are Beaudry and Portier (2004,
15
2007), Christiano, Motto, and Rostagno (2006), and Jaimovich and Rebelo (2006, 2007).
16
In Beaudry and Portier (2004, 2007) and Jaimovich and Rebelo (2006, 2007), the positive
17
co-movement of investment and consumption is generated by using alternative preferences
18
thateliminatethewealthe⁄ectonlaborsupplyand/orbymakingittoocostlyforvariables
19
to move in the (cid:145)wrong(cid:146)direction. The latter can be accomplished by complementarities
20
in the production technology or particular forms of capital adjustment costs. Christiano,
21
Motto, and Rostagno (2006) assume that nominal wages are sticky and argue that mon-
22
etary policy is expansionary when expected future productivity increases. The reason is
23
that the increase in the real wage caused by the expansion brings about a reduction in in-
24
(cid:135)ation when nominal wages are sticky. Since the expansion is anticipated, the news shock
25
leads to a reduction in expected in(cid:135)ation, which in turn leads to a reduction in interest
26
4Cochrane (1994) and Danthine, Donaldson, and Johnsen (1998) have made the same observation for
more speci(cid:133)c models.
5If the elasticity of intertemporal substitution is high enough, then the substitution e⁄ect dominates
the wealth e⁄ect, and investment increases.
2
rates when the central bank follows a Taylor rule.
27
This paper approaches the challenge to generate Pigou cycles from a di⁄erent angle by
1
considering a standard matching model augmented with endogenous labor force partici-
2
pation. There are no adjustment costs, except for the matching friction and the presence
3
of a matching friction is clearly not su¢ cient to generate Pigou cycles. The parameters
4
are chosen such that the matching model can generate enough employment volatility in
5
the presence of the usual unanticipated shocks and is not subject to the critique of Shimer
6
(2005). Inparticular,asinHagedornandManovskii(2008)itisassumedthattheentrepre-
7
neur receives on average a relatively small share of the surplus and it is also assumed that
8
wagesrespondlessthanproportionallytoincreasesinTFP.Theseassumptionsensurethat
9
investment in new projects increases sharply when productivity increases. The matching
10
friction makes it costly to quickly increase the number of new projects. Consequently, the
11
investment in new projects increases early in response to anticipated shocks.
12
Together with the increase in investment in new projects, vacancies robustly increase,
13
that is, the demand for labor increases. Just as in the standard RBC model, however, the
14
wealth e⁄ect associated with an increase in expected productivity growth has a downward
15
e⁄ect on labor supply. Nevertheless, employment strongly increases for the following
16
two reasons. First, the increase in the demand for labor dominates the reduction in
17
labor force participation. Second, with a matching friction, in order to bene(cid:133)t from the
18
increase in wages when they occur, workers have to start looking for a job early. The
19
di¢ culty in generating Pigou cycles is that the wealth e⁄ect (which reduces labor supply)
20
a⁄ects labor supply immediately, whereas the substitution e⁄ect (which increases labor
21
supply) only a⁄ects labor supply when wages actually increase. The matching friction
22
pulls the substitution e⁄ect forward in time. This dampens the reduction in labor force
23
participation.
24
The question arises whether consumption and the investment in existing projects also
25
increase. To shed light on this question, the analysis (cid:133)rst focuses on the question whether
26
the sum of consumption, C , and investment in existing projects, I , increases. C +I is
27 t t t t
equal to output minus the investment in new projects, which will be referred to as net
28
3
resources. When net resources increase, it is not di¢ cult to generate an increase in both
29
C and I , by choosing the right elasticity of intertemporal substitution.
1 t t
Net resources increase whenever the increase in output(cid:151)caused by the increase in
2
employment(cid:151)exceeds the cost of the increase in investment in new projects that induced
3
theincreaseinemployment. Inotherwords, theincreaseintheinvestmentofnewprojects
4
must(cid:151)from a social planner(cid:146)s point of view(cid:151)be self-(cid:133)nancing. For this to be possible,
5
theremustbeunderinvestmentinnewprojectsinthecompetitiveequilibrium. Inthiscase,
6
the sharp increase in investment in new projects in response to an anticipated shock leads
7
to e¢ ciency gains, which make it possible for net resources to increase.6 Underinvestment
8
happens when the share of the surplus the entrepreneur receives is su¢ ciently small.7 As
9
mentioned above, this is exactly the condition that make it possible for matching models
10
to generate a realistic amount of employment volatility.
11
In the benchmark calibration, the entrepreneur(cid:146)s share is indeed low enough so that
12
the e¢ ciency gains achieved in response to an anticipated shock make it possible that
13
consumption, both types of investment, employment, as well as output increase.
14
Inthealternativecalibration,theentrepreneur(cid:146)sshareisalsolow,butnotthatlowand
15
thereisnounderinvestmentinnewprojects. Outputnetofinvestmentinnewprojectsnow
16
decreases, but the model still generates Pigou cycles under a slightly weaker de(cid:133)nition of
17
Pigou cycles, namely one that only requires total investment to increase in response to an
18
anticipated shock and not both the investment in new and the investment in old projects.
19
The division of the surplus between entrepreneur and worker is chosen to match employ-
20
ment volatility in response to the usual unanticipated shocks. At these higher average
21
pro(cid:133)t levels, this requires a higher amount of wage stickiness. As in the benchmark cali-
22
bration, the division of the surplus is such that the competitive equilibrium is not Pareto
23
optimal. Since there is no underinvestment in new projects, the precipitous increase in
24
investment in new projects by the entrepreneurs during the anticipation phase is undesir-
25
6Althoughtherearee¢ ciencygains,aggregateTFPasmeasuredbytheSolowresidualisuna⁄ectedby
the news shock.
7Underinvestmentoccursbecausetheentrepreneurpaysthefullcostofcreatinganewproject,buthas
to share the revenues with a worker.
4
able from a social planner(cid:146)s point of view, there are no e¢ ciency gains, and output net
26
of investment in new projects displays a (moderate) decrease. The household could coun-
1
teract the undesirable sharp increase in investment in new projects with a sharp decrease
2
in investment in existing projects. This would result in an increase in consumption that
3
is closer to the socially desirable increase. The increase in employment leads, however, to
4
an increase in the expected return on the investment in existing projects. Consequently,
5
the increase in investment in existing projects decreases only slightly and by less than the
6
increase in investments in new projects; total investment as well as consumption increase.
7
2 Model
8
The economy consists of entrepreneurs and workers. Both can perfectly ensure idiosyn-
9
cratic risk, which is ensured by the following modelling device. At the end of the period,
10
all agents become part of a representative household and share the net revenues earned
11
during the period. The household decides how much to consume, how much to save, and
12
the level of labor force participation. The labor force consists of the mass of workers
13
searching for a job, i.e., the unemployed, plus the mass of workers returning to continuing
14
jobs. Workers can only become employed after they have searched for a job for at least
15
one period.
16
The key decision that is not made by the household is how many new projects to
17
start. This decision is made by individual entrepreneurs. In the planning phase, each
18
new project requires a periodic (cid:133)xed investment until production starts. Starting a new
19
projectalsoentailspostingavacancy. Thenumberofvacanciesandthenumberofworkers
20
searching for a job determine(cid:151)using a standard matching function(cid:151)the number of new
21
productive relationships. Exogenous separation occurs with probability (cid:26)x. Productivity
22
is high enough so that endogenous separation does not occur.
23
5
2.1 Production
24
Productiontakesplacewithinarelationshipconsistingofoneworkerandoneentrepreneur.
1
The production technology is given by:
2
y = Z k(cid:11); (1)
t t t
where Z stands for aggregate productivity, y for (cid:133)rm output, and k for (cid:133)rm capital.8
3 t t t
The law of motion for Z is given by
4 t
lnZ = (cid:26)lnZ +" : (2)
t t 1 t
(cid:0)
When analyzing whether this model can generate Pigou cycles, the assumption is made
5
that Z is known at t (cid:28) < t with (cid:28) > 0.
6 t
(cid:0)
Capital is rented by the (cid:133)rm at rate R . Each period the worker and the entrepreneur
7 t
divide revenues net of capital payments:
8
p = Z k(cid:11) R k : (3)
t t t t t
(cid:0)
The law of motion for the wage rate, W , is given by:
9 t
W = (1 !(cid:22))[!p +(1 !)E[p ]]; (4)
t t t
(cid:0) (cid:0)
where !(cid:22) and ! are (cid:133)xed parameters and E[p ] is the unconditional expectation of p . The
10 t t
parameter ! controls how the wage rate responds to changes in net revenues; wages are
11
(cid:133)xed when ! = 0; whereas wages are proportional to net revenues when ! = 1.9 The
12
average wage rate, E[W ], is equal to (1 !(cid:22))E[p ]. Thus, (1 !(cid:22)) determines the fraction
13 t t
(cid:0) (cid:0)
of net revenues the worker receives.
14
The (cid:133)rm chooses the capital stock that maximizes p . Thus:
15 t
Zt(cid:11) 1=(1(cid:0)(cid:11))
k = : (5)
t
R
t
(cid:18) (cid:19)
8Throughout this paper, (cid:133)rm level variables are denoted with lowercase and aggregate variables with
uppercase characters.
9If 0 ! < 1, then wages respond less than proportionally to changes in p ; such wage rules are
(cid:20) t
discussed in the section on strategic wage bargaining of Mortensen and NagypÆl (2007)
6
2.2 New projects
16
Entrepreneurs decide whether they want to start a new project. During the planning
17
phase, projects require an investment equal to each period. If the plan turns out to be
1
successful, production can start. During the planning phase, entrepreneurs also search for
2
a worker. The number of entrepreneurs with projects in the planning phase is determined
3
by the free-entry condition, that is, the cost, , has to equal the value of a successful
4
project times the probability of being successful.
5
Pro(cid:133)ts of successful projects, p , are equal to revenues (net of capital payments) minus
6 t
the transfer to the worker, i.e., p = p W . The value of a successful project to the
7 t t t
(cid:0)
entrepreneur is simply the discounted value of pro(cid:133)ts, taking into account that the project
8
is subject to the possibility of exogenous destruction in subsequent periods. Thus:
9
J = (cid:12)E Ct+1 (cid:0)(cid:13)(p +(1 (cid:26)x)J ) ; (6)
t t t+1 t+1
C (cid:0)
" t #
(cid:18) (cid:19)
where (C =C ) (cid:13) is the marginal rate of substitution. The free-entry condition can then
10 t+1 t (cid:0)
be written as:
11
f
= (cid:21) J ; (7)
t t
f
where(cid:21) istheprobabilitythataprojectintheplanningphaseissuccessfulandasuitable
12 t
worker is found. If J increases then an increase in the amount invested in new projects,
13 t
f
I , brings the economy back into equilibrium by lowering (cid:21) . Fujita (2003) models
14 N;t t
the planning and hiring phase of the project separately. For parsimony, the standard
15
convention is used here, planning and searching are subsumed under one phase, and the
16
probability (cid:21)f describes success on both counts.10
17 t
10For the calibration of , the interpretation of what is behind creating a new job is essential. If the
onlycostincreatinganewjobisthecostassociatedwithplacinganadvertisementforanewworker,then
entry would be so high that the matching friction would be non-existent. For the calibrated parameters,
the cost of starting a new project, , is equal to 17% of the (cid:133)rm(cid:146)s monthly output level and aggregate
investmentinnewprojects(successfulandnotsuccessful)isonaverageequalto1.4%ofaggregateoutput.
7
2.3 Matching market
18
On the matching market, entrepreneurs post vacancies and search for a worker. The
19
number of matches, M , is determined by the number of searching workers, i.e., the unem-
20 t
ployed, U , and the number of vacancies, V , which is equal to the number of projects in
1 t t
the planning phase, I = . The matching process is modeled with the standard constant
2 N;t
returns to scale matching function.11 That is:
3
Mt = (cid:22)(cid:22)Ut(cid:22)Vt1(cid:0)(cid:22); (8)
4
M M
(cid:21)w = t; and (cid:21)f = t: (9)
t U t V
t t
2.4 The household
5
The household chooses consumption, C , total labor supply, and next period(cid:146)s beginning-
6 t
of-period capital stock, K . Labor supply is equal to the sum of employed workers,
7 t+1
N , and workers searching for a job, U . The labor force, N + U , is assumed to be
8 t t t t
endogenous.12 Capital earns a rate of return R and depreciates at rate (cid:14).
9 t
Next period(cid:146)s beginning-of-period employment consists of those workers that have not
10
experienced exogenous separation, (1 (cid:26)x)N , and those workers that are matched during
11 t
(cid:0)
the current period, (cid:21)wN . Thus:
12 t t
N = (cid:21)wU +(1 (cid:26)x)N : (10)
t+1 t t t
(cid:0)
Searching is assumed to be a full-time activity. Consequently, the time spent on leisure
1
and home production, L , is equal to L U N .
2 t (cid:3) t t
(cid:0) (cid:0)
11Strictlyspeaking,thereisaconstraintthatM cannotbelessthaneitherU orV ,butthisconstraint
t t t
turns out not to be binding.
12In the matching literature, it is more common to model changes in the labor supply by means of
endogenoussearchintensity. Theadvantageofendogenizingthelaborforceisthatthereisaclearempirical
counterpart, which facilitates the calibration of the model.
8
The household(cid:146)s maximization problem is as follows:
max E 1 (cid:12)j Ct1+(cid:0)j(cid:13) (cid:0)1 +(cid:30)(L(cid:3)(cid:0)Ut+j (cid:0)Nt+j)1(cid:0)(cid:20)(cid:0)1 ; (11)
t
fCt+j;Ut+j;Nt+j+1g1j=0 j=0 " 1(cid:0)(cid:13) 1(cid:0)(cid:20) #
X
s.t.
N = (cid:21)w U +(1 (cid:26)x)N ; (12)
t+j+1 t+j t+j t+j
(cid:0)
C +I = W N +R K +P ; (13)
t+j t+j t+j t+j t+j t+j t+j
I = K (1 (cid:14))K : (14)
t+j t+j+1 t+j
(cid:0) (cid:0)
P = p Nw I is equal to total pro(cid:133)ts made by the entrepreneurs minus the costs
3 t t t N;t
(cid:0)
made by entrepreneurs in creating new projects, I = V . This is taken as given by the
4 N;t t
household.
5
Endogenous labor force participation. This speci(cid:133)cation of the utility function for
6
therepresentativeagentassumesthatthereisperfectrisksharing,notonlyintermsofcon-
7
sumption, but also in terms of leisure.13 An alternative would be to use the lottery setup
8
of Rogerson (1988), where agents use lotteries to insure consumption against unfavorable
9
labor market outcomes.14 This approach seems less suitable for a model with endogenous
10
labor force participation, since it indicates that labor force status is a random outcome. It
11
seems plausible that the employment status is not fully under the control of workers, but
12
it is more di¢ cult to justify that labor force entry is subject to randomization. Moreover,
13
Ravn (2008) shows that the implied linear utility function leads to a relationship between
14
aggregate consumption and labor market tightness, V =U , that is inconsistent with the
15 t t
empirical properties of smooth aggregate consumption on one hand and volatile tightness
16
on the other. The approach adopted here avoids Ravn(cid:146)s consumption-tightness puzzle.15
17
First-order conditions. Let (cid:17) be the Lagrange multiplier of the constraint of the law
18 t
of motion of N . This multiplier represents the shadow price for a worker in a productive
19 t
13AsimilarapproachisfollowedbyHornsteinandYuan(1999),ShiandWen(1999),andTripier(2003).
14Theutilityofleisurewouldthenbegivenby(cid:30) (L(cid:3) Ut Nt) 11(cid:0)(cid:20)+(Ut+Nt) 01(cid:0)(cid:20) =(1 (cid:20)),
(cid:2) (cid:0) (cid:0) (cid:2) (cid:2) (cid:0)
which is equal to (cid:30) [L(cid:3) Ut Nt]=(1 (cid:20)), i.e., ut(cid:2)ility would be linear in leisure. (cid:3)
(cid:2) (cid:0) (cid:0) (cid:0)
15See den Haan and Kaltenbrunner (2007) for details.
9