Financial Markets and Unemployment∗
Tommaso Monacelli
Università Bocconi

Vincenzo Quadrini
University of Southern California

Antonella Trigari
Università Bocconi
December 29, 2011

Abstract
We study the importance of financial markets for (un)employment
fluctuations in a model with matching frictions where firms issue debt
under limited enforcement. Higher debt allows employers to bargain
lower wages which in turn increases the incentive to create jobs. The
transmission mechanism of ‘credit shocks’ is different from the typical credit channel and the model can explain why firms cut hiring
after a credit contraction even if they do not have shortage of funds
for hiring. The empirical relevance of these shocks is validated by
the structural estimation of the model. The theoretical predictions
are also consistent with the estimation of a structural VAR whose
identifying restrictions are derived from the theoretical model.
Keywords: Limited enforcement, wage bargaining, unemployment,
credit shocks.
JEL classification: E24, E32, E44.
∗

We thank Wouter Den Haan, John Haltiwanger, Nicolas Petrosky-Nadeau and Alan
Sutherland for insightful comments and seminar participants at Atlanta Fed, Boston Fed,
Ente Luigi Einaudi, European Summer Symposium in International Macroeconomics, European University Institute, Federal Reserve Board, NBER Summer Institute, New York
Fed, NYU Abu Dhabi, Ohio State University, Philadelphia Fed, Princeton University, St.
Louis Fed, Stanford University, University of Bonn, University of Cergy-Pontoise, University of Lausanne, University of Milano-Bicocca, University of Porto, University of Southern
California, University of Wisconsin.

1

Introduction

The recent financial turmoil has been associated with a severe increase in
unemployment. In the United States the number of unemployed workers
jumped from 5.5 percent of the labor force to about 10 percent and continued
to stay close to 9 percent after four years the beginning of the recession.
Because the financial sector has been at the center stage of the recent crisisand the growth rate in the volume of credit has dropped significantly from its
pick (see top panel of Figure 1), it is natural to ask whether the contraction of
credit has played some role in the unemployment hike and sluggish recovery.
One possible channel through which de-leveraging could affect the real
economy is by forcing employers to cut investment and hiring because of financing difficulties. This is the typical ‘credit channel’ formalized in Bernanke
and Gertler (1989) and Kiyotaki and Moore (1997). Although there is compelling evidence that the credit channel played an important role during thecrisis when the volume of credit contracted sharply, the liquidity dried up
and the interest rate spreads widened, there is less evidence that this channel
has been important for the sluggish recovery of the labor market after the
initial drop in employment. As shown in the bottom panel of Figure 1, theliquidity held by US businesses contracted during the crisis, consistent withthe view of a credit crunch. However, after the initial drop, the liquidity ofnonfinancial businesses quickly rebounded and shortly after the crisis firms
were holding more liquidity than before the crisis.1 This observation casts
some doubts that the main explanation for the sluggish recovery of the labormarket can be found in the lack of funds to finance investment and hiring.
Should we then conclude that de-leveraging is not important for understanding the sluggish recovery of the labor market? In this paper we argue
that, even if firms have enough funds to sustain hiring, de-leveraging can still
induce a decline in employment that is very persistent. This is not because
lower debt impairs the hiring ability of firms but because, keeping everythingelse constant, it places workers in a more favorable position in the negotiation of wages. Thus, the availability of credit affects the ‘willingness’, not(necessarily) the ‘ability’ to hire new workers.
To illustrate this mechanism we use a theoretical framework that sharesthe basic ingredients of the model studied in Pissarides (1987) where firms
1

A similar pattern applies to firms’ profits. Profits growth fell during the crisis, butthen quickly rebounded to the pre-crisis level, already a historically high peak.

1

Debt/GDP
85
80
75
70
65
60
55
50
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Liquid assets/GDP
8
7
6
5
4
3
2
1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009 2010

Figure 1: Liquidity and debt in the US nonfinancial business sector. Liquidity
is the sum of foreign deposits, checkable deposits and currency, time andsavings deposits. Debt is defined as credit markets instruments. Data isfrom the Flows of Funds Accounts.
are created through the random matching of job vacancies and unemployedworkers. We extend the model in two directions. First, we allow firms toissue debt under limited enforcement. Second, we introduce an additionalsource of business cycle fluctuation which affects directly the enforcement
constraint of borrowers and the availability of credit.
Because of the matching frictions and the wage determination process
based on bargaining, firms prefer to issue debt even if there is no fixed or2

working capital that needs to be financed. The preference for debt derives
exclusively from the wage determination process based on bargaining, whose
empirical relevance is shown in Hall and Krueger (2010). Higher debt reduces
the net bargaining surplus which in turn reduces the wages paid to workers.
This creates an incentive for employers to borrow, breaking the Modigliani
and Miller (1958) result. The goal of the paper is to study how changes inthe borrowing limit affect the dynamics of the labor market.
Central to our mechanism is the firm’s capital structure as a bargaining tool in the wage determination process. Both anecdotal and statisticalevidence point to this channel. Consider the anecdotal evidence first. An
illustrative example, also suggested in Matsa (2010), is provided by the caseof the New York Metro Transit Authority. In 2004 the company realized an
unexpected 1 billion dollars surplus, largely from a real estate boom. The
Union, however, claimed rights to the surplus demanding a 24 percent pay
raise over three years.2 Another example comes from Delta Airlines. The
company weathered the 9/11 airline crisis but its excess of liquidity allegedly
reduced the need to cut costs. This hurt the firm’s bargaining position withworkers and three years after 9/11 it faced severe financial challenges.3
The idea that debt allows employers to improve their bargaining positionis supported by several empirical studies in corporate finance. Bronars andDeere (1991) document a positive correlation between leverage and laborbargaining power, proxied by the degree of unionization. Matsa (2010) findsthat firms with greater exposure to (union) bargaining power have a capital
structure more skewed towards debt. Atanassov and Kim (2009) find that2

From The New York Times, Transit Strike Deadline: How extra Money ComplicatesTransit Pay Negotiations, 12/15/2005: “The unexpected windfall was supposed to be aboom[..] but has instead become a liability.[..] How, union leaders have asked, can theauthority boast of such a surplus and not offer raises of more than 3 percent a year? Why
aren’t wages going up more?”. In a similar vein: “The magnitude of the surplus [..] has
set this year’s negotiations apart from prior ones, said John E. Zuccotti, a former first
deputy mayor. It’s a much weaker position than the position the M.T.A. is normally in:
We’re broke and we haven’t gotten any money [..]. The playing field is somewhat different.
They haven’t got that defense”.
3
From The Wall Street Journal, Cross Winds: How Delta’s Cash Cushion Pushed
It Onto Wrong Course, 10/29/2004: “In hindsight, it is clear now that Delta’s pile ofcash and position as the strongest carrier after 9/11 lured the company’s pilots and top
managers onto a dire course. Delta’s focus on boosting liquidity turned out to be its
greatest blessing and curse, helping the company survive 9/11 relatively unscathed but
also putting off badly needed overhauls to cut costs”.

3strong union laws are less effective in preventing large-scale layoffs when firms
have higher financial leverage. Gorton and Schmid (2004) study the impact ofGerman co-determination laws on firms’ labor decisions and find that firmsthat are subject to these laws exhibit greater leverage ratios. Benmelech,
Bergman and Enriquez (2011) show that firms under financial distress areable to extract better concession from labor using a unique data set for theairline industry.
All the aforementioned studies suggest that firms may use financial leverage strategically in order to contrast the bargaining power of workers. Although there are theoretical studies in the micro-corporate literature thatinvestigates this mechanism (see Perotti and Spier (1993), and Dasgupta and
Sengupta (1993)), the implications for employment dynamics at the macroeconomic level have not been fully explored. The goal of this paper is toinvestigate these implications. In particular, we study how the labor market
responds to a shock that affects directly the availability of credit for employers. This shock resembles the ‘financial shock’ studied in Jermann andQuadrini (2012) but the transmission mechanism is different. While in Jermann and Quadrini the financial shock is transmitted through the standard
credit channel (higher cost of financing employment), in the current paper
the financing cost remains constant over time. Instead, the reduction in borrowing places firms in a less favorable bargaining position with workers and,as a result, they create fewer jobs.
Credit shocks can generate sizable employment fluctuations in our model.
Furthermore, as long as the credit contraction is persistent—a robust featureof the data—the impact on the labor market is long-lasting. In this vein, theproperties of the model are consistent with recent findings that recessions
associated with financial crisis are more persistent than recessions associatedwith systemic financial difficulties. See IMF (2009), Claessens, Kose, andTerrones (2008), Reinhart and Rogoff (2009). Models of the credit channel
where there are frictions in the substitution between equity and debt cangenerate large macroeconomic responses to credit contractions in the shortrun but, typically, they are not very persistent. In the short-run the responses
could be large because it is costly to replace debt with equity. However, oncethe substitution has taken place, which usually happens relatively quickly,
the lower debt is no longer critical for hiring and investment decisions.
There are other papers in the macro-labor literature that embed financial
mechanisms in search and matching models. Chugh (2009) and PetroskyNadeau (2009) are two recent contributions. The transmission mechanism
4

proposed by these papers is still based on the typical credit channel wherefirms could be financially constrained and the cost of financing new vacancies
plays a central role in the transmission of shocks. Also related is Wasmer
and Weil (2004), which considers an environment where bargaining is not
between workers and firms but between entrepreneurs and financiers. In thismodel financiers are needed to finance the cost of posting a vacancy and thesurplus extracted by financiers is similar to the cost of financing investments.
Thus, the central mechanism is still of the credit channel type.4
By emphasizing that other contributions are based on the typical credit
channel, we are not claiming that this channel is irrelevant or less important.
Furthermore, the credit channel could also play a role within our mechanism: if firms anticipate the possibility of future tighter constraints, they
may increase savings and hoard liquidity for precautionary reasons. Then,by holding more liquidity (and lower net liabilities), firms will be in less favorable bargaining position with workers. Although in our model firms do
not display precautionary behavior, we can capture the higher precautionarysavings in reduced form through a tightening of the enforcement constraint.5
In order to assess the empirical relevance of credit shocks for employment
fluctuations, we conduct a structural estimation of the model using Bayesian
methods. The estimation shows that credit shocks contribute significantly toemployment fluctuations in general and to the sluggish labor market recovery
experienced in the aftermath of the recent financial crisis. We also estimate astructural VAR where the shocks are identified using short-term restrictions
derived from the theoretical model. We find that the response of employment
to credit shocks is statistically significant and economically sizable. Although
the VAR analysis does not allow us to fully separate the standard credit
channel from the channel emphasized in this paper, the empirical results are
consistent with the predictions of the model.
4

Wasmer and Weil (2004) also discuss the possibility of extending the model with wage
bargaining. However, the analysis with wage bargaining is not fully explored in the paper.
5
More generally, we do not claim that our mechanism is the only possible explanation
for the sluggish recovery. As it is typically the case, business cycle fluctuations result frommultiple sources and possible explanations for the jobless recovery include the mismatch
between job openings and the skills of the idle labor force (Elsby, Hobijn, and Sahin (2010)
and Kocherlakota (2010)) and households de-leveraging (Mian and Sufi (2011)). Although
our paper emphasizes a different mechanism, in the estimation of the model we allow foralternative shocks that in principle could capture some of the alternative mechanisms.

5

2

Model

P
t
There is a continuum of agents of total mass 1 with lifetime utility E0 ∞t=0 β ct .
At any point in time agents can be employed or unemployed. They save in
two types of assets: shares of firms and bonds. Risk neutrality implies thatthe expected return from both assets is equal to 1/β − 1. Therefore, the netinterest rate is constant and equal to r = 1/β − 1.
Firms: Firms are created through the matching of a posted vacancy and aworker. Starting in the next period, a new firm produces output zt until thematch is separated. Separation arises with probability λ. An unemployedworker cannot be self-employed but needs to search (costlessly) for a job.
The number of matches is determined by the function m(vt , ut ), where vt
is the number of vacancies posted during the period and ut is the numberof unemployed workers. The probability that a vacancy is filled is qt =m(vt , ut )/vt and the probability that an unemployed worker finds a job is
pt = m(vt , ut )/ut .
At any point in time firms are characterized by three states: a productivity zt , an indicator of the financial conditions φt that will be described
below, and a stock of debt bt . The productivity zt and the financial state φt
are exogenous stochastic variables, common to all firms (aggregate shocks).
The stock of debt bt is chosen endogenously. Although firms could choose
different levels of debt, in equilibrium they all choose the same bt .
The dividend paid to the owners of the firm (shareholders) is defined by
the budget constraint
dt = zt − wt − bt +

bt+1
,
R

where R is the gross interest rate charged on the debt. As we will see, R isdifferent from 1 + r because of the possibility of default when the match isseparated.
Timing: If a vacancy is filled, a new firm is created. The new firm starts
producing in the next period and, therefore, there is no wage bargaining
in the current period. However, before entering the next period, the newly
created firm chooses the debt bt+1 and pays the dividend dt = bt+1 /Rt (theinitial debt bt is zero). There is no separation until the next period. Oncethe new firm enters the next period, it becomes an incumbent firm.
6

An incumbent firm starts with a stock of debt bt inherited from the previous period. In addition, it knows the current productivity zt and the financial
variable φt . Given the states, the firm bargains the wage wt with the worker
and output zt is produced. The choice of the new debt bt+1 and the payment
of dividends arise after wage bargaining. After the payments of dividends
and wages and after contracting the new debt, the firm observes whether
the match is separated. It is at this point that the firm chooses whether todefault. Therefore, each period can be divided in three sequential steps: (i)wage bargaining, (ii) financial decision, (iii) default. These sequential steps
are illustrated in Figure 2.

Separation withprobability λzt+1 , φt+1 , bt+1

zt , φt , bt
?

-

6

6

6

Wage
bargaining, wt

Payment of dividends, dt .
Choice of new debt, bt+1

Choice todefault

Figure 2: Timing for an incumbent firm

Few remarks: Before continuing, it will be helpful to emphasize the importance of some of our assumptions. As we will see, the sequential timingof decisions for an incumbent firm is irrelevant for the dynamic properties of
employment. For example, the alternative assumption that incumbent firms
choose the new debt before or jointly with the bargaining of wages will notaffect the dynamics of employment. For new firms, instead, the assumptionthat the debt is chosen in the current period while wage bargaining does nottake place until the next period is crucial for the results. As an alternative,
we could assume that bargaining takes place in the same period in which avacancy is filled as long as the choice of debt is made before going to the bargaining table with the new worker. For presentation purposes, we assumed
7

that the debt is raised after matching with a worker (but before bargaining
the wage). Alternatively, we could assume that the debt is raised before
posting a vacancy but this would not affect the results. What is crucial isthat the debt of a new firm is raised before bargaining for the first time with
the new worker.
The second point we would like to stress is that the assumption that wages
are bargained in every period is not important. We adopted this assumption
in order to remain as close as possible to the standard matching model (Pissarides (1987)). In Section 4 we show that the employment dynamics do notchange if we make different assumptions about the frequency of bargaining.
All we need is that there is bargaining when a new worker is hired.
Finally, the assumption that firms employ a single worker is not crucial.
As long as the production technology of a firm is linear in the number ofworkers and bargaining takes place collectively between the firm and its labor
force, the model displays the same properties.
Financial contract and borrowing limit: We assume that lending isdone by competitive intermediaries who pool a large number of loans. We
refer to these intermediaries as lenders. The amount of borrowing is constrained by limited enforcement. After the payments of dividends and wages,
and after contracting the new debt, the firm observes whether the match isseparated. It is at this point that the firm chooses whether to default. In
the event of default the lender will be able to recover only a fraction χt of
the firm’s value.
Denote by Jt (bt ) the equity value of the firm at the beginning of the period, which is equal to the discounted expected value of dividends for shareholders. This function depends on the individual stock of debt bt . Obviously,
higher is the debt and lower is the equity value. The latter also depends
on the aggregate states st = (zt , φt , Bt , Nt ), where zt and φt are exogenous
aggregate states (shocks), Bt is the aggregate stock of debt and Nt = 1 − ut
is employment. We distinguish aggregate debt from individual debt since, toderive the equilibrium, we have to allow for individual deviations. We use
the time subscript t to capture the dependence of the value function from theaggregate states, that is, we write Jt (bt ) instead of J(zt , φt , Bt , Nt ; bt ). We
will use this convention throughout the paper.
We begin by considering the possibility of default when the match isseparated. In this case the value of the firm is zero. The lender anticipates

8that the recovery value is zero in the event of separation and the debt will not
be repaid. Therefore, in order to break-even, the lender imposes a borrowing
limit insuring that the firm does not default when the match is not separated
and charges an interest rate premium to cover the losses realized when thematch is separated.
If the match is not separated, the value of the firm’s equity is βEt Jt+1 (bt+1 ),that is, the next period expected value of equity discounted to the current
period. Adding the present value of debt, bt+1 /(1 + r), we obtain the total
value of the firm. If the firm defaults, the lender recovers only a fraction χtof the total value of the firm. Therefore, the lender is willing to lend as longas the following constraint is satisfied:


bt+1
bt+1
+ βEt Jt+1 (bt+1 ) ≥
.
χt
1+r
1+r
The variable χt is stochastic and affects the borrowing capacity of the
firm. Henceforth, we will refer to unexpected changes in χt as ‘credit shocks’.
Thus, our interpretation of credit shocks is the one of exogenous variationsin the firm’s ability to borrow which are orthogonal to the value of the firm.
By collecting the term bt+1 /(1 + r) and using the fact that β(1 + r) = 1,
we can rewrite the enforcement constraint more compactly as
φt Et Jt+1 (bt+1 ) ≥ bt+1 ,(1)where φt ≡ χt /(1 − χt ). We can then think of credit shocks as unexpected
innovations to the variable φt . This is the exogenous state variable includedin the set of aggregate states st .
We now have all the elements to determine the actual interest rate that
lenders charge to firms. Since the loan is made before knowing whether
the match is separated, the interest rate charged by the lender takes into
account that the repayment arises only with probability 1 − λ. Assumingthat financial markets are competitive, the zero-profit condition requires thatthe gross interest rate R satisfies
R(1 − λ) = 1 + r.

(2)

The left-hand side of (2) is the lender’s expected income per unit of debt.
The right-hand side is the lender’s opportunity cost of funds (per unit ofdebt). Therefore, the firm receives bt+1 /R at time t and, if the match is notseparated, it repays bt+1 at time t + 1. Because of risk neutrality, the interest
rate is always constant, and therefore, r and R bear no time subscript.
9Firm’s value: Central to the characterization of the properties of themodel is the wage determination process which is based on bargaining. Before describing the bargaining problem, we define the value of the firm recursively taking as given the wage bargaining outcome. This is denote by
wt = gt (bt ). The recursive structure of the problem implies that the wage isfully determined by the states at the beginning of the period.
The equity value of the firm can be written recursively asbt+1+ β(1 − λ)Et Jt+1 (bt+1 )Jt (bt ) = max zt − gt (bt ) − bt +
bt+1
R

(3)

subject toφt Et Jt+1 (bt+1 ) ≥ bt+1 .
Notice that the only choice variable in this problem is the debt bt+1 . Also
notice that the firm takes the current wage as given but it fully internalizes
that the choice of debt bt+1 affects future wages. This is captured by thedependence of the next period value Jt+1 (bt+1 ) on bt+1 .
Because of the additive structure of the objective function, the optimal
choice of bt+1 does not depend neither on the current wage wt = gt (bt ) nor
on the current liabilities bt .
Lemma 1 The new debt bt+1 chosen by the firm is independent of bt and
wt = gt (bt ).
Proof 1 Since wt and bt enter the objective function additively and they do
not affect neither the next period value of the firm’s equity nor the enforcement constraint, the choice of bt+1 is independent of wt and bt 
As we will see, this property greatly simplifies the wage bargaining problem we will describe below.
Worker’s values: In order to set up the bargaining problem, we define theworker’s values ignoring the capital incomes earned from the ownership ofbonds and firms (interests and dividends). Since agents are risk neutral and10the change in the dividend of an individual firm is negligible for an individual
worker, we can ignore these incomes in the derivation of wages.
When employed, the worker’s value is
Wt (bt ) = gt (bt ) + βEt (1 − λ)Wt+1 (bt+1 ) + λUt+1 ,(4)which is defined once we know the wage function wt = gt (bt ). The function
Ut+1 is the value of being unemployed and is defined recursively as
Ut = a + βEt pt Wt+1 (Bt+1 ) + (1 − pt )Ut+1 ,where pt is the probability that an unemployed worker finds a job and a isthe flow utility for an unemployed worker.
While the value of an employed worker depends on the aggregate states
and the individual debt bt , the value of being unemployed depends only on theaggregate states since all firms choose the same level of debt in equilibrium.
Thus, if an unemployed worker finds a job in the next period, the value ofbeing employed is Wt+1 (Bt+1 ).
Bargaining problem: Let’s first define the following functions


bt+1
ˆ
+ β(1 − λ)Et Jt+1 (bt+1 )Jt (bt , wt ) = max zt − wt − bt +
bt+1
R


ct (bt , wt ) = wt + βEt (1 − λ)Wt+1 (bt+1 ) + λUt+1 .
W

(5)
(6)

These are the values of a firm and an employed worker, respectively, given
an arbitrary wage wt paid in the current period and future wages determinedby the function gt+1 (bt+1 ). The functions Jt (bt ) and Wt (bt ) were defined in(3) and (4) for a particular wage equation gt (bt ).
Given the relative bargaining power of workers η ∈ (0, 1), the current
wage is the solution to the problem
h
iη
1−η c
ˆ
Wt (bt , wt ) − Ut .
(7)
max Jt (bt , wt )wtThis problem maximizes the weighted product of the net values for thefirm and the worker. The net value for the firm is the equity value Jˆt (bt , wt )11since in the event of disagreement the firm would default on the debt (thethreat value is zero). The net value for the worker is the value of being
ct (bt , wt ), minus the value of quitting, Ut .
employed, W
Let wt = ψt (g; bt ) be the solution, which makes explicit the dependence
on the function g determining future wages. The solution to the bargaining
problem is the fixed-point to the functional equation gt (bt ) = ψt (g; bt ).
We can now see the importance of Lemma 1. Since the optimal debt
chosen by the firm after the wage bargaining does not depend on the wage,
in solving the optimization problem (7) we do not have to consider how the
choice of wt affects bt+1 . Therefore, we can derive the first order condition
taking bt+1 as given. After some re-arrangement this can be written as
Jt (bt ) = (1 − η)St (bt ),(8)

Wt (bt ) − Ut = ηSt (bt ),(9)where St (bt ) = Jt (bt ) + Wt (bt ) − Ut is the bargaining surplus. As it is typical in search models with Nash bargaining, the surplus is split between thecontractual parties proportionally to their relative bargaining power.
Choice of debt: Let’s first rewrite the bargaining surplus asbt+1+ (1 − λ)βEt St+1 (bt+1 ) − ηβpt Et St+1 (Bt+1 ). (10)R
Notice that the next period surplus enters twice but with different statevariables. In the first term the state variable is the individual debt bt+1 whilein the second is the aggregate debt Bt+1 . The reason is because the value ofbeing unemployed today depends on the value of being employed in the next
period in a firm with the aggregate value of debt Bt+1 . Instead, the valueof being employed today also depends on the value of being employed next
period in the same firm. Since the current employer is allowed to choose alevel of debt that differs from the debt chosen by other firms, the individualstate next period, bt+1 , could be different from Bt+1 . In equilibrium, ofcourse, bt+1 = Bt+1 . However, to derive the optimal policy we have to allow
the firm to deviate from the aggregate policy.
Because the choice of bt+1 does not depend on the existing debt bt (seeLemma 1), we have
∂St (bt )
= −1.
(11)
∂bt
St (bt ) = zt − a − bt +12

Before using this property, we rewrite the firm’s problem (3) asbt+1+ β(1 − λ)(1 − η)Et St+1 (bt+1 ) (12)Jt = max zt − gt (bt ) − bt +bt+1
Rsubject to(1 − η)φt Et St+1 (bt+1 ) ≥ bt+1 ,where we used Wt+1 (bt+1 ) − Ut+1 = ηSt+1 (bt+1 ) from (8) and the surplus isdefined in (10).
Denoting by µt the Lagrange multiplier associated with the enforcement
constraint, the first order condition isih(13)η − 1 + (1 − η)φt µt = 0.
In deriving this expression we used (11) and βR(1 − λ) = β(1 + r) = 1. We
can then establish the following result.
Lemma 2 The enforcement constraint is binding (µt > 0) if η ∈ (0, 1).
Proof 2 It follows directly from the first order condition (13)
A key implication of Lemma 2 is that, provided that workers have somebargaining power, the firm always chooses to maximum debt and the borrowing limit binds. Thus, bargaining introduces a mechanism through which
the original Modigliani and Miller (1958) result does not apply.
To gather some intuition about the economic interpretation of the multiplier µt , it will be convenient to re-arrange the first order condition as

 

1
1
1−η
µt =
×
−
.
1 + (1 − η)φt
R
R
|
{z
} |
{z
}
Total change
in debt

Marginal gainfrom borrowing

The multiplier results from the product of two terms. The first term is thechange in next period liabilities bt+1 allowed by a marginal relaxation of theenforcement constraint, that is, bt+1 = φt (1 − η)Et S(zt+1 , Bt+1 , bt+1 ) + ā,
13where ā = 0 is a constant. This is obtained by marginally changing ā. In1
t+1= 1+(1−η)φ, whichfact, using the implicit function theorem, we obtain ∂b∂āt
is the first term.
The second term is the net gain, actualized, from increasing the next
period liabilities bt+1 by one unit (marginal change). If the firm increases
bt+1 by one unit, it receives 1/R units of consumption today, which is paid
as dividends. This unit has to be repaid next period. However, the effective
cost for the firm is lower than 1 since the higher debt allows the firm to
reduce the next period wage by η, that is, the part of the surplus going to
the worker. Thus, the effective repayment incurred by the firm is 1 − η. This
cost is discounted by R = (1 + r)/(1 − λ) because the debt is repaid only if
the match is not separated, which happens with probability 1−λ. Therefore,
the multiplier µt is equal to the total change in debt (first term) multipliedby the gain from a marginal increase in borrowing (second term).
2.1

Firm entry and general equilibrium

So far we have defined the problem solved by incumbent firms. We now
consider more explicitly the problem solved by new firms. In this setup
new firms are created when a posted vacancy is filled by a searching worker.
Because of the matching frictions, a posted vacancy will be filled only withprobability qt = m(vt , ut )/vt . Since posting a vacancy requires a fixed cost
κ, vacancies will be posted only if the value is not smaller than the cost.
We start with the definition of the value of a filled vacancy. When avacancy is filled, the newly created firm starts producing and pays wages
in the next period. The only decision made in the current period is thedebt bt+1 . The funds raised by borrowing are distributed to shareholders.
Therefore, the value of a vacancy filled with a worker isbt+1+ β(1 − η)Et St+1 (bt+1 )(14)
Qt = max
bt+1
1+r
subject toφt (1 − η)Et St+1 (bt+1 ) ≥ bt+1 .
Since the new firm becomes an incumbent starting in the next period,
St+1 (bt+1 ) is the surplus of an incumbent firm defined in (10).
14

As far as the choice of bt+1 is concerned, a new firm faces a similar problem
as incumbent firms (see problem (12)). Even if the new firm has no initialdebt and it does not pay wages, it will choose the same stock of debt bt+1 as
incumbent firms. This is because the new firm faces the same enforcement
constraint and the choice of bt+1 is not affected by bt and wt as establishedin Lemma 1. This allows us to work with a ‘representative’ firm.
We are now ready to define the value of posting a vacancy. This is equal
to Vt = qt Qt −κ. As long as the value of a vacancy is positive, more vacancies
will be posted. Free entry implies that Vt = 0 in equilibrium. Therefore,
qt Qt = κ.

(15)

In a general equilibrium all firms choose the same level of debt and bt =Bt . Furthermore, assuming that the bargaining power of workers is positive,
firms always borrow up to the limit, that is, Bt+1 = φt (1 − η)Et St+1 (Bt+1 ).
Using the free entry condition (15), Appendix A derives the wage equation
wt = (1 − η)a + η(zt − bt ) +η[pt + (1 − λ)φt ]κ
.
qt (1 + φt )(16)

The wage equation makes clear that the initial debt bt acts like a reductionin output in the determination of wages. Instead of getting a fraction η ofthe output, the worker gets a fraction η of the output ‘net’ of debt. Thus,
for a given bargaining power η, the larger is the debt and the lower is thewage received by the worker.
3

Response to shocks

The goal of this section is to show how employment responds to shocks (credit
and productivity). We first provide some analytical intuition and then we
simulate the model numerically.
3.1

Analytical intuition

The key equation that defines job creation is the free entry condition qt Qt =κ. Once we understand how the value of a filled vacancy Qt is affected byshocks, we can then infer the impact of the shocks on job creation. Morespecifically, if the value of a filled vacancy Qt increases, the probability offilling a vacancy qt = m(vt , ut )/vt must decline. Since the number of searching15

workers ut is given in the current period, the decline in qt must derive froman increase in the number of posted vacancies. Thus, more jobs are created.
Because of the general equilibrium effects of a shock, it is not possible
to derive closed form solutions for the impulse responses. However, we canderive analytical results if we assume that the shock affects only a single(atomistic) firm. In this way we can abstract from general equilibrium effects
and provide simple analytical intuitions. This is the approach we take in thissection. The full general equilibrium responses will be shown numerically inthe next subsection.
Credit shocks: Starting from a steady state equilibrium, suppose that
there is one firm with a newly filled vacancy for which the value of φt increases. The increase is purely temporary and it reverts back to the steadystate value starting in the next period. We stress that the change involves
only one firm so that we can ignore the general equilibrium effects.
The derivative of Qt with respect to φt is∂Et St+1 (bt+1 ) ∂bt+1
1∂Qt+ β(1 − η)
=
.
∂φt
1+r
∂bt+1
∂φt
Applying the implicit function theorem to the enforcement constraint
holding with equality, that is, bt+1 = φt (1 − η)ESt+1 (bt+1 ), we can rewrite
the derivative as∂bt+1(1 − η)Et St+1 (bt+1 ).
=∂φt
1 − (1 − η)φt Et ∂St+1 (bt+1 )∂bt+1

Substituting ∂Et St+1 (bt+1 )/∂bt+1 = −1 (see equation (11)) we obtain∂Qtη(1 − η)βEt St+1 (bt+1 )=,∂φt
1 + (1 − η)φt(17)

where we have used β = 1/(1 + r).
From this equation we can see that an increase in φt raises the value of a
newly filled vacancy Qt , provided that the worker has some bargaining power,that is, η > 0. The intuition is straightforward. If the new firm can increase
its debt in the current period, it pays more dividends now and less dividends
in the future. However, the reduction in future dividends needed to repay
the debt is smaller than the increase in the current dividends because the16higher debt allows the firm to reduce the next period wages. Effectively, partof the debt will be repaid by the worker, increasing the firm’s value today.
In deriving this result we assumed that the change in φt was only for one
firm so that we could ignore the general equilibrium effects. However, since
φt is an aggregate variable, the change increases the value of a vacancy for all
firms and more vacancies will be posted. The higher job creation will havesome general equilibrium effects that cannot be characterized analytically.
The full general equilibrium response will be shown numerically.
Productivity shocks: Although the main focus of the paper is on credit
shocks, it will be helpful to investigate how the ability to borrow affects the
propagation of productivity shocks since this has been the main focus of alarge body of literature.6
In general, productivity shocks generate an employment expansion because the value of a filled vacancy increases. This would arise even if thelevel of debt is constant, which is the case in the standard matching model.
In the case in which the constant debt is zero we revert exactly to the standard matching model. However, if the debt is not constrained to be constantbut changes endogenously, then the impact of productivity shocks on employment could be amplified.
As for the case of credit shocks, we consider a productivity shock that
affects only one newly created firm and abstract from general equilibrium
effects. We further assume that the productivity shock is persistent. The
persistence implies that the new firm will be more productive in the next
period when it starts producing. If the increase in zt is purely temporary,
the change will not have any effect on the value of a new match.
The derivative of Qt with respect to zt is∂Et St+1 (bt+1 )1∂Et St+1 (bt+1 ) ∂bt+1∂Qt= β(1 − η)++ β(1 − η)
.
∂zt
∂zt
1+r
∂bt+1
∂zt
Applying the implicit function theorem to the enforcement constraint
bt+1 = (1 − η)φt Et St+1 (bt+1 ), we obtain(1 − η)φt Et ∂St+1∂z(bt t+1 )
∂bt+1
=
.
∂zt
1 − (1 − η)φt Et ∂St+1 (bt+1 )
∂bt+1

6

See, for instance, Shimer (2005) and related contributions.

17Since ∂Et St+1 (bt+1 )/∂bt+1 = −1 (see equation (11)), substituting in thederivative of the firm’s value Qt and using β = 1/(1 + r) we obtain!
∂Et St+1 (bt+1 )
(1
−
η)φ
β
∂Et St+1 (bt+1 )
∂Qt
t
∂zt
= β(1 − η)
+η
.
(18)
∂zt
∂zt
1 + (1 − η)φt
We now compare this expression to the equivalent expression we would
obtain if the borrowing constraint was exogenous. More specifically, we replace the enforcement constraint (1) with the borrowing limit bt+1 ≤ b̄ whereb̄ is constant. Under this constraint we have that ∂bt+1 /∂zt = 0. Therefore,∂Qt∂Et St+1 (bt+1 )= β(1 − η)
.
∂zt
∂zt

(19)

Comparing (18) to (19) we can see that, when the borrowing limit isendogenous, there is an extra term in the derivative of Qt with respect to
zt . This term is positive if η > 0. Therefore, the change in the value of afilled vacancy in response to a productivity improvement is bigger when the
borrowing limit is endogenous. Intuitively, the increase in productivity raises
the value of the firm. This allows for more debt which in turn increases thevalue of a filled vacancy Qt .
Of course, this does not tell us whether the amplification effect is large
or small. However, we can derive some intuition of what is required for theamplification effect to be large. In particular, as we can see from equation(18), we need that the value of a match is highly sensitive to the productivity(bt+1 )
to be large. This essentially requires large
shock, that is, we need ∂Et St+1
∂zt
asset price responses to productivity shocks. In this sense the model shares
the same features of the models proposed by Bernanke and Gertler (1989) andKiyotaki and Moore (1997) where the amplification of productivity shocks
depends on the response of asset prices.
3.2

Numerical simulation

We now show the responses to shocks in the general equilibrium throughnumerical simulation. Since the goal of the numerical simulation presented
in this section is only to illustrate the qualitative properties of the model,
we avoid a lengthy discussion of the parameter values which are reported inTable 1. A full quantitative analysis will be conducted in Section 5. As wewill see, the parameters used here are those estimated in Section 5.
18

Table 1: List of parameters
Description

Value

Discount factor for entrepreneurs, βMatching parameter, ξ¯Matching parameter, αRelative bargaining power, ηProbability of separation, λCost of posting vacancy, κUtility flow unemployed, aEnforcement parameter, φ̄

0.990
0.773
0.649
0.672
0.049
0.711
0.468
3.637

Responses to credit shocks: Figure 3 plots the responses of debt, employment, output and wages to a negative credit shock. The credit variable
φt is assumed to follow a first order autoregressive process with parametersρφ = 0.965 and σφ = 0.143. Since the model is solved by linearizing the
dynamic system around the steady state, the responses to a positive shock
will have the same shape but with inverted sign.
The response of employment is quite persistent, reflecting the persistenceof the shock. The mechanism that generates these dynamics should be clear
by now. Since firms are forced to cut their debt, workers are able to negotiate
higher future wages starting from the next period. The response of wages isplotted in last panel of Figure 3. At impact the wage falls below the steadystate but then, starting from the next period, it raises above the steadystate. Since new firms start paying wages in the next period, what mattersfor job creation is the response starting in period 1, that is, one period after
the shock. Thus, the anticipated cost of labor for new matches increases in
response to a negative credit shock and this discourages job creation.
The initial drop in the wage of incumbent workers can be explained asfollow. Besides the changes induced by general equilibrium effects, the new
debt does not affect the net surplus of existing matches since the debt will be
repaid in an exactly offsetting way: b0 − βR(1 − λ)b0 . But future wages willchange, implying that current wages need to change to keep their present
value (the surplus going to workers) unchanged.
The credit shock does not affect the value received by ‘incumbent’ workers and firms (besides, again, the impact coming from general equilibrium
19

Figure 3: Impulse responses to a negative credit shock.
effects). So it may appear counterintuitive why an incumbent firm chooses
to borrow up to the limit if, effectively, both the surplus and the divisionof the surplus do not change. This is due to the lack of commitment fromthe firm. Since the new debt is chosen unilaterally by the firm after bargaining the wage, the firm prefers higher debt to reduce future wages. This isanticipated by workers who demand higher wages today to compensate forthe lower wages expected in the future. If the firm could credibly commit
before bargaining the wage, it would agree not to raise the debt.7 We will return to the dynamics of wages in the next section where we consider possible
extensions of the model.
7

This mechanism has some similarities with the model studied by Barro and Gordon(1983): since workers anticipate that the central bank inflates ex-post, they demand higher
nominal wages today. Differently from that model, however, there are not real costs fromdeviating, at least from the point of view of an individual firm. As long as new firms canchoose the debt before bargaining with new workers, what happens after the firm becomesincumbent is irrelevant for the dynamics of employment.

20

Responses to productivity shocks: Figure 4 plots the impulse responses
to a negative productivity shock. The variable zt is assumed to follow a firstorder autoregressive process with parameters ρz = 0.944 and σz = 0.005. We
also report the response when the debt limit is exogenously fixed to the steady¯ wherestate value. In this case we impose the borrowing constraint bt+1 ≤ φ̄J,¯φ̄ and J are the steady state values of the financial variable φt and of thefirm’s value Jt (bt ).

Figure 4: Impulse responses to a negative productivity shock.
Productivity shocks are amplified when the borrowing limit is endogenous. However, the magnitude of the employment response is still small. In
general, the response of the economy to productivity shocks is similar to thestandard matching model. This is not surprising since the version of ourmodel with exogenous borrowing is the standard matching model.
4Model extension

In this section we propose two extensions of the model that could improvethe dynamics of wages. First we assume that each firm is a monopolistic
21

producer, that is, it produces a differentiated good used as an input in the
production of final goods. The second assumption is that, after the initial
wage bargaining for a new worker, wages are renegotiated infrequently. As wewill see, the new features will have very minor implications for the dynamics
of employment but will affect the dynamics of wages.
4.1

Monopolistic competition

In this section we assume that each firm/match is a monopolistic producerof a differentiated good. The differentiated goods produced by Reach firm,
1N
denoted by yi , contribute to aggregate output according to Y = ( 0 yiε di) ε ,where N is the total number of differentiated goods which is equal to employment. Furthermore, to make monopolistic competition relevant, we assume
that there is also an intensive margin for the production of good/firm i. The
production technology takes the form yi = zli where li is effort/hours supplied by the worker with dis-utility Ali1+ϕ /(1 + ϕ). The intensive margin
gives us additional flexibility in separating employment from output.
A well known feature of models with monopolistic competition is thatthe demand for the differentiated good and the profits of each producer are
increasing functions of aggregate production. In our model with equilibrium
unemployment, aggregate production depends on how many matches areactive which is also equal to the number of employed workers. Therefore,
higher is the employment rate and higher is the demand for each intermediate
good. Because of this, Appendix B shows that the revenues of an individual
firm can be written in reduced form as
πt = z̃t Ntν .

(20)

The variable z̃t is a monotone transformation of productivity zt and Nt isaggregate employment taken as given by an individual firm. We call this term
net surplus flow instead of output for reasons that will become clear below.
Therefore, the introduction of monopolistic competition only requires thereplacement of firm level production zt with the net surplus flows πt = z̃t Ntν .
We can now easily describe how a credit shock affects wages. Thanks to
the dependence of the surplus flow from aggregate employment, a positive
credit shock has two effects on the wages paid to newly hired workers. On
the one hand, taking as given aggregate employment, the higher leverage
allows firms to pay lower wages, which increases the incentive to hire moreworkers. On the other hand, the increase in aggregate employment, Nt , raises
22the surplus flow πt which, through the bargaining of the surplus, increases
wages. Therefore, whether a credit shock is associated with an increase or
decrease in the wages paid to newly hired workers depends on the relative
importance of these two effects.
Numerical simulation: There are only two new parameters, ε and ϕ.
The first determines the price mark-up and the second the elasticity of effort
or labor utilization. We set ε = 0.75 which implies a price mark-up of
1/ε − 1 = 0.33. Then we choose the value of ϕ so that the elasticity ofworkers’ effort is equal to 1, that is, 1/ϕ = 1.
Figure 5 plots the impulse responses to a credit shock. We first noticethat the responses of debt and employment are not very different from thebaseline model. The dynamics of wages, however, is different. In particular,
the wage falls on impact and, contrary to the baseline model, it does notraise above the steady state for several periods. What this means is that thewages of new hires are almost unaffected by the credit shock.

Figure 5: Impulse responses to a negative credit shock - Extended modelwith monopolistic competition and endogenous effort/hours.

23

4.2

Optimal labor contracts and infrequent negotiation

Although it is common in the searching and matching literature to assume
that wages are renegotiated every period, there is not a theoretical or empirical justification for adopting this assumption. An alternative approach is tocharacterize the optimal contract first and then design possible mechanisms
for implementing the optimal contract.
Suppose that, when the worker is first hired, the parties bargain an optimal long-term contract. The optimal contract chooses the sequence of wages
paid to the worker at any point in time, contingent on all possible contingencies directly related to the firm. The state-contingent sequence of wages maximizes the total surplus which is shared according to the relative bargaining
weight η. The sequence of wages must satisfy the participation constraints
for the firm and the worker. What this means is that, at any point in time,the value of the firm cannot be negative and the value for the worker cannot
be smaller than the value of being unemployed.
It turns out that the sequence of wages that characterizes the optimal
contract is not unique. The multiplicity has a simple intuition. Since production does not depend on wages, the choice of a different sequence does
not affect the surplus of the match. For example, the firm could pay slightly
lower wages at the beginning and slightly higher wages in later periods. Thisis also an optimal contract as long as the initial worker’s value is the sameand the participation constraints are not violated. The second condition istypically satisfied if η is not too close to 0 or 1 and shocks are bounded.
The assumption of risk neutrality plays a crucial role for this result. Withconcave utility of at least one of the parties, like in Michelacci and Quadrini(2009), the optimal sequence of wages would be unique.
Given the multiplicity, we have different ways of implementing the optimal
contract. One possibility is to choose a sequence of wages that is equal to thesequence obtained when the wage is re-bargained with some probability ψ.
As long as this sequence does not violate the participation constraints, it also
implements the optimal contract. Another way of thinking is that, when thefirm and the worker meet, they decide not only the division of the surplus(through bargaining) but also the frequency with which they renegotiate thecontract. Since the parties are indifferent, we could choose a frequency that
may appear more relevant empirically. Although the choice of a particularfrequency is arbitrary from a theoretical point of view, it cannot be dismissedon the ground that it is suboptimal.
24

Appendix C derives the key equations under the assumption that wage
contracts are renegotiated by each firm with probability ψ and wages stay
constant until they are renegotiated. The net surplus generated by a match
St (bt ) is still given by (10) while the net value of an employed worker when
the contract is renegotiated isWt (bt ) − Ut =wt − a+ Ωt (bt ),1 − β(1 − λ)(1 − ψ)(21)with the function Ωt (bt ) defined recursively asΩt (bt ) = ηβ[(1 − λ)ψ − pt ]Et St+1 (bt+1 ) + β(1 − λ)(1 − ψ)Et Ωt+1 (bt+1 ). (22)See Appendix C for the detailed derivation.
We can see from equation (21) that the worker’s value has two components. The first component derives from contingencies when the contract is
not renegotiated. The second component derives from contingencies when
the contract is renegotiated.
Numerical simulation: There is only one additional parameter to be calibrated, ψ, which we set to 0.25. If we think of a period as a quarter, this
implies that wages are renegotiated, on average, every year. This extension
does not affect the other parameters which we set to the same values used in
the previous subsection for the model with monopolistic competition.
Figure 6 plots the impulse responses to a credit shock generated by themodel with monopolistic competition and infrequent negotiation. The responses of debt and employment are not very different from the baselinemodel. Average wages, however, fall below the steady state for few quarters (thanks to monopolistic competition) and their volatility is significantly
smaller (thanks to infrequent negotiation). Therefore, the consideration ofmonopolistic competition and infrequent bargaining could allow the model
to generate more plausible dynamics of wages.8
8Gertler and Trigari (2009) assume infrequent negotiation not only for existing matches
but also for new matches. If in our model we allow for infrequent negotiations also fornew matches, the macroeconomic responses to credit shocks would be qualitative similar
but quantitatively smaller. However, as long as credit shocks are highly persistent, assuggested by the data, the quantitative differences will not be large.

25

Figure 6: Impulse responses to a negative credit shock - Extended modelwith monopolistic competition and infrequent negotiation.
5

Structural estimation

The analysis conducted so far has illustrated the dynamic responses of themodel to credit shocks numerically. The goal was primarily to show thequalitative properties of the model. In this and the next sections we try tobring the extended model (i.e., the one including monopolistic competition
and infrequent bargaining) to the data more systematically using two approaches. In this section we conduct a structural estimation using Bayesian
methods and in the next section we estimate a three-dimensional VAR whose
identifying restrictions are derived from the structural model.
Before proceeding with the structural estimation we add a third shock to
the model. In particular, we consider a shock to the efficiency of the matching
function mt = ξvtα u1−α
. The variables mt , vt , ut are, respectively, the newtmatches, the posted vacancies and the unemployed workers. In the previous
analysis ξ was a normalizing constant. Now we assume that it follows thefirst order autoregressive process ln ξt = ξ¯ + ρξ ln ξt−1 + ξ,t .
It is important to clarify that we do not have a particular interest in26

understanding the impact of this shock. Rather we interpret ξt as capturing
the potential impact of other shocks that are not explicitly modeled. In thisway we do not force the model to replicate the empirical series only withproductivity and credit shocks. As we show in Appendix D, innovations toξt may also capture the impact of shocks that are transmitted through thestandard credit channel as in Petrosky-Nadeau (2009).
5.1

Estimation with three shocks and three variables

With the matching shock we have three exogenous states: productivity, zt ,credit, φt , and matching efficiency, ξt . They all follow independent autoregressive processes characterized by the parameters ρj and σj , j ∈ {z, φ, ξ}.
Since we have three shocks, we use three empirical series: (i) real log-GDP;(ii) log-employment in the non-farm sector; (iii) net issuance of debt in thebusiness sector divided by business GDP. The estimation is performed using
first differences over the sample period 1984.I-2011.II. Later we will repeat
the estimation with additional shocks and empirical variables.
Five of the model parameters are pre-set. They are the discount factor β,
the frequency of negotiation ψ, the probability of separation λ, the average
efficiency of the matching function ξ¯ and the cost of posting a vacancy κ.
The discount factor is set to the standard quarterly value of β = 0.99 andthe frequency of negotiation to 1/ψ = 4 (annually on average). The reason
these two parameters are pre-set is because they do not affect the propertiesof the three variables included in the estimation set. The remaining threeparameters are pinned down using the following steady state targets: (i ) 5
percent unemployment rate; (ii ) 70 percent probability of filling a vacancy;(ii ) 93 percent probability of finding a job for an unemployed worker. Only
one of the three targets—the steady state unemployment rate—has somerelevance of the properties of the variables used in the estimation. However,since this number is standard in the literature, we pre-set it in advance.
All remaining parameters are estimated with Bayesian methods. Table 2reports the prior distributions, the mode and the thresholds for the bottom
and top percentiles of the posterior distributions.
The prior distributions are chosen based on the following considerations.
Direct estimates of the matching parameter α range from 0.3 to 0.7 (seePetrongolo and Pissarides (2001)). Thus, we assume that the mean of theprior distribution is the intermediate value of 0.5 with a sizable standard
deviation of 0.1. For the bargaining parameter η there is no direct evidence27

Table 2: Bayesian estimation with three variables.
Estimated parameter

Prior[mean,std]

Mode

Productivity shock persistence, ρz
Productivity shock volatility, σz
Credit shock persistence, ρφCredit shock volatility, σφMatching shock persistence, ρξMatching shock volatility, σξMatching share parameter, αBargaining power workers, ηUtility flow unemployed, aMean enforcement parameter, φ̄Mark-up parameter, εElasticity of effort, ϕBeta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.1]
Beta[0.5,0.1]
Beta[0.4,0.1]
IGamma[8,5]Beta[0.8,0.05]
Beta[1,0.2]

0.944
0.005
0.965
0.143
0.983
0.056
0.650
0.674
0.470
3.621
0.937
1.033

Posterior thresholds
Below 5%
Below 95%

0.937
0.004
0.954
0.135
0.977
0.052
0.638
0.676
0.433
3.607
0.932
1.002

0.968
0.006
0.970
0.155
0.987
0.062
0.656
0.696
0.463
3.654
0.954
1.035

and it is common to use a value of 0.5. This justifies our choice of a meanvalue of 0.5 and a sizable standard deviation of 0.1. A similar approach isused for the utility flow from unemployment. Since there is no agreementon the right value of a, we use a mean value of 0.4 and a sizable standard
deviation of 0.1. When evaluated at the mean value of all other parameters,
a = 0.4 implies that the period utility from being unemployed is 50 percent
the period utility from being employed.
The parameter φ̄ determines the ratio of debt over output. The value of 8
implies a debt-to-output ratio of 1 when evaluated at the mean values of allother parameters. At the same time, however, we allow for a large standard
deviation of 5. The mean value of ε is set to 0.8, implying a mark-up of
1/ε = 0.25, and the mean value of ϕ is set to 1, implying a unitary elasticity
of hours. Finally, for the parameters of the shock processes, we assign thesame values to each of the three shocks. The means, however, impose only
minor restrictions since they are associated with wide standard deviations.
As can be seen from Table 2, the estimated parameters fall into plausible ranges. For example, the mode values for the matching and bargaining
parameters are α = 0.65 and η = 0.674. The market power parameter isε = 0.937 implying a price mark-up of 6.5 percent. The elasticity of effort/hours is close to unitary. The mean of the enforcement parameter isφ̄ = 3.621 and the average debt-to-output ratio is 0.5. The unemployment
flow of utility is a = 0.47 and the period utility from being unemployed is28about 50 percent the utility flow from being employed.
The variance decomposition of several variables of interest are reported
in Table 3. Credit shocks contribute significantly to the volatility of employment. The contribution of productivity shocks is quite limited, which is
not surprising in light of the result of Shimer (2005). If we impose a higher
flow utility from unemployment along the lines of Hagedorn and Manovskii(2008) or allow for infrequent negotiation as in Gertler and Trigari (2009),
productivity could contribute more to employment fluctuations. However,productivity shocks are important determinants of output fluctuations. This
happens directly through the change in the productivity of each worker andthrough the change in effort/hours induced by the productivity improvement.
Finally, shocks to the matching efficiency are important contributors to thevariance of employment. As stressed above, however, we should not assign
a specific structural meaning to the contribution of the matching shocks.
They should be interpreted as capturing the impact of many other shocks
that have not been explicitly modeled in the paper. Some of these shocks
are those transmitted through a standard credit channel (see Appendix D).
Table 3: Variance decomposition. Estimation with three variables.

OutputEmployment
New debt/output
Hourly wage

TFP
shock
z

Creditshock
φMatching
shock
ξ

46.2
0.4
0.1
12.0

29.2
54.1
66.7
57.0

24.6
45.5
33.1
31.0

Figure 7 plots the time series contribution of productivity and credit
shocks to the empirical series of employment growth. The difference between
the actual data and the sum of the contributions of productivity and credit
shocks is the contribution of matching shocks. The series are constructed using the mode values of the parameters. As can be seen from the figure, credit
shocks contribute significantly to the fluctuation of employment growth. We
also observe that credit shocks contribute with some lag to the actual dynamics of employment. For example, during the last recession, credit shocks seemto have contributed to the decline in employment (negative growth) but not
at the pick of the recession. This is fully consistent with the view that our29channel contributes to the sluggish recovery after the crisis hit. The initial
drop was caused by something else including, perhaps, liquidity shocks propagated through the standard credit channel. As shown in Appendix D, theimpact of liquidity shocks propagated through the standard credit channel
could be captured in the model by the matching shock ξt .

Figure 7: Decomposition of employment growth, 1984.I-20011.I. Estimation
with three variables.

5.2

Estimation with four shocks and four variables

Since wages play a central role in our model, it would be desirable to include
empirical series of wages in the estimation. However, once we add wages,
we have four empirical series but only three shocks. Therefore, in order toperform the estimation we need to add a fourth shock. We choose to add iid
measurement errors in the empirical series of wages. This seems the mostnatural choice since the general view is that the wage series are imperfectly
measured. With this addition, we re-estimate the model using four empiricaltime series in first differences: (i) real log-GDP; (ii) log-employment in the
non-farm sector; (iii) net issuance of debt in the business sector divided bybusiness GDP; (iv) hourly real wages in non-farm business.
30

Table 4 reports the prior distributions, the mode and the thresholds forthe bottom and top percentiles of the posterior distributions. Compared tothe previous estimation we have two additional parameters: the standard
deviation of the measurement error, σw and the parameter that determines
the frequency of negotiation ψ. Since we include the wage series in theestimation, this parameter becomes relevant. The estimated mode is 0.182.
This implies that the negotiation of wages for incumbent workers takes place
on average every five/six quarters. The average debt-to-output ratio is about
0.45 and the period utility from unemployment is about 52 percent the period
utility from being employed.
Table 4: Bayesian estimation with four variables.
Estimated parameter

Prior[mean,std]

Mode

Productivity shock persistence, ρz
Productivity shock volatility, σz
Credit shock persistence, ρφCredit shock volatility, σφMatching shock persistence, ρξMatching shock volatility, σξMatching share parameter, αBargaining power workers, ηUtility flow unemployed, aMean enforcement parameter, φ̄
Negotiation frequency, ψ
Std measurement error wages, σw
Mark-up parameter, εElasticity of effort, ϕBeta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.1]
Beta[0.5,0.1]
Beta[0.4,0.1]
IGamma[8,5]Beta[0.25,0.05]
IGamma[0.001,0.05]
Beta[0.8,0.05]
Beta[1,0.1]

0.942
0.005
0.967
0.143
0.983
0.056
0.647
0.665
0.490
3.711
0.182
0.008
0.940
0.990

Posterior thresholds
Below 5%
Below 95%

0.923
0.004
0.964
0.130
0.976
0.050
0.614
0.644
0.477
3.698
0.170
0.008
0.938
0.980

0.944
0.006
0.978
0.145
0.987
0.068
0.648
0.666
0.496
3.727
0.195
0.009
0.956
0.994

Table 5 reports the variance decomposition for the variable of interest andFigure 8 plots the time series contribution of productivity and credit shocks
to employment growth. The estimation with the wage series reduces only
slightly the contribution of credit shocks to the volatility of employment. The
volatility of wages, however, is now mostly explained by measurement errors.
The contribution of credit shocks to quarter by quarter employment shownin Figure 8 is very similar to the contribution resulting from the previous
estimation without wages.

31

Table 5: Variance decomposition. Estimation with four variables

OutputEmployment
New debt/output
Hourly wage

TFP
shock
z

Creditshock
φMatchingshockξMeasure
error
wages

50.1
0.5
0.2
0.6

24.7
49.3
65.9
1.8

25.2
50.2
33.9
1.3

0.0
0.0
0.0
96.3

Figure 8: Decomposition of employment growth, 1984.I-20011.I. Estimation
with four variables.
5.3

Capital accumulation and concave utility

To facilitate the presentation of our theory, we have abstracted from two
popular features of standard business cycle models: capital accumulationand concave utility. In this section we extend the model along these twodimensions.
Although the addition of capital accumulation is straightforward, the extension with concave utility is more complex unless we make some simplifying
32

assumptions. In particular, we follow Merz (1995) and Andolfatto (1996) andassume that workers have the ability to insure the unemployment risk. With
this assumption we do not have to worry about the distribution of wealth.
As in Cooley and Quadrini (1999) we specify the utility function as

E0

∞
X

βt

i1−σ
h
Alt1+ϕct + (1 − χt )a − χt 1+ϕ
1−σ

t=0

.

The variable χt is a dummy variable that denotes the employment status of the agent. Since agents have access to full unemployment insurance,
they experience the same utility independent of the employment status. Thisimplies that the consumption ct differs between agents. In particular, employed workers have higher consumption in compensation for the dis-utilityof working.
Capital is accumulated by households and is rented to firms at the market
price rtk . Capital depreciates at rate δ. We assume that the firm and theworker split the net surplus from the match according to the share η. We
would like to clarify that the sharing rule is an assumption that is not derived
from Nash bargaining as in the case with risk neutral agents.9 The derivationof the surplus is very similar to the previous model with one importantchange: the discount factor is no longer constant. In particular, denoting
by Ut0 the derivative of the period utility with respect to consumption, the0/Ut0 . Also the risk-free interest rate is no
discount factor is Mt+1 = βUt+1
longer constant but is equal to rt = 1/Et Mt+1 − 1. The detailed derivation
is available upon request from the authors.
Once we have capital, we can add investment in the set of variables used
for the estimation of the model, which in turn requires the addition of a shock.
We add a shock to the investment technology since this is quite popular incomputable general equilibrium models. More specifically, the law of motionof capital is specified as
kt+1 = (1 − δ)kt + ζt it ,where ζt follows a first order autoregressive process with unitary mean.
9With risk averse agents, the Nash bargaining outcome is difficult to derive unless weassume that each worker belongs too a large family with an infinite number of members.
In this case the assumed sharing rule can be considered the result of Nash bargaining.

33

We estimate the model with five shocks—zt , φt , ξt , ζt and iid measurement errors on wages—and five time series—GDP, employment, investment,
wages and net issuance of debt in the business sector. The estimated parameters with associated statistics are reported in Table 6 and the variancedecomposition in Table 7. The contribution of credit shocks to employment
fluctuations is very similar to the contribution obtained in the model without
capital and linear utility. The quarter by quarter decomposition shown in
Figure 9 is also similar.
Table 6: Bayesian estimation with five variables.
Estimated parameter

Prior[mean,std]

Mode

Productivity shock persistence, ρz
Productivity shock volatility, σz
Credit shock persistence, ρφCredit shock volatility, σφMatching shock persistence, ρξMatching shock volatility, σξInvestment shock persistence, ρζInvestment shock volatility, σζMatching share parameter, αBargaining power workers, ηUtility flow unemployed, aMean enforcement parameter, φ̄Mark-up parameter, εElasticity of effort, ϕRenegotiation frequency, ψMeasurement error volatility, ψBeta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.20]
IGamma[0.001,0.05]
Beta[0.5,0.1]
Beta[0.5,0.1]
Beta[0.4,0.1]
IGamma[8,5]Beta[0.8,0.05]
Beta[1,0.2]
Beta[0.25,0.05]
IGamma[0.001,0.05]

0.912
0.009
0.972
0.145
0.982
0.057
0.966
0.001
0.661
0.636
0.445
3.488
0.825
1.110
0.168
0.009

Posterior thresholds
Below 5%
Below 95%

0.910
0.008
0.972
0.140
0.981
0.055
0.966
0.001
0.660
0.634
0.440
3.485
0.826
1.107
0.166
0.008

0.913
0.010
0.974
0.144
0.982
0.058
0.968
0.001
0.663
0.636
0.444
3.488
0.830
1.111
0.169
0.009

Table 7: Variance decomposition. Estimation with five variables

OutputEmployment
New debt/output
Investment
Hourly wage

TFP
shock
z

Creditshock
φMatchingshock
ξ

Investment
shockζMeasure
error
wages

64.9
0.3
0.1
16.5
0.4

16.9
51.8
64.0
22.6
2.5

16.2
47.9
35.9
16.0
1.7

2.0
0.0
0.0
44.9
0.2

0.0
0.0
0.0
0.0
95.2

34

Figure 9: Decomposition of employment growth, 1984.I-20011.I. Estimation
with five variables.
6

VAR estimation

In this section we further investigate the empirical relevance of credit shocks
using a structural VAR where the shocks are identified through short-term
restrictions that are derived from the theoretical model. Let’s start with thetheoretical model. The solution of the linearized system around the steadystate has the following representation,

 

 

zt
ρz 0
0
0
zt−1
z,t
 φt   0 ρφ 0

 

0 

=
  φt−1  +  φ,t  ,(23)
 bt   abz abφ abb abe   bt−1   0 etaez aeφ aeb aee
et−1
ξ,t
where zt is the aggregate productivity, φt is the variable that captures theaggregate financial conditions, et = 1 − ut is the employment rate, and bt isthe stock of debt at the beginning of the period. These four variables are thestates of the dynamic (linearized) system and z,t , φ,t , ξ,t are innovations
to productivity, credit and matching efficiency. For simplicity we assume
that the shock to the matching technology is iid. The analysis that follows
35will also go through with persistent matching shocks but with more complex
innovations to the reduced form system.
Ideally, we would like to estimate directly the above dynamic system
which is a first order VAR. This would be possible if we had data for each of
the four variables. The problem is that we have data for zt , bt , et , but not
for φt . Therefore, we have to use an alternative approach. The approach weuse is to substitute out φt and φt−1 using the third equation in system (23)evaluated at t and t + 1, that is,
bt = abz zt−1 + abφ φt−1 + abb bt−1 + abe et−1 ,bt+1 = abz zt + abφ φt + abb bt + abe et .
Using these two equations to eliminate the variables φt and φt−1 in thesecond and fourth equations of system (23) we obtain



 




ρz
0
0
0
0
0
z
zt
z
t−2
t−1


 bt+1  =  ψbz ψbb ψbe   bt  +  0 γbb 0   bt−1  ψez ψeb ψee etet−1
0 γeb 0
et−2



πzz 0
0
z,t
+  πbz πbb πbe   φ,t 
0
0 πee
ξ,t
This is a second order dynamic system in three observable variables. The
zeros in the matrix that multiplies the innovations z,t , φ,t , ξ,t provide therestrictions we use to identify the shocks. The first two restrictions imposethat zt is only affected by productivity innovations z,t , given the exogenous
nature of this variable. The additional two restrictions impose that shocks to
productivity and credit cannot affect employment at impact, which follows
from the property that employment responds with one period lag.
There are additional restrictions that the structural model imposes tothe VAR. However we only impose the short term restrictions just describedwhich are sufficient for the identification of the three shocks.
Data: The three dimensional VAR is estimated using quarterly growth
rates of TFP, Credit to the Private Sector and Employment over the period 1984.1-2009.3. TFP growth is based on the utilization-adjusted TFP
series constructed by John Fernald (2009). The growth in private credit is36

constructed using data from the Flow of Funds. Specifically, we use new borrowing (financial market instruments) for households and nonfinancial businesses dividend by the stock of debt (again, financial market instruments).
For employment we have three series: civilian employment from the BLS;
employees in private industries also from the BLS; employees in the nonfarm
sector from the Current Employment Statistics survey.
Impulse responses: We first estimate the VAR system with et measured
by ‘employment in the private sector’ and five lags. Results using the othertwo definitions of employment (not reported) are similar.
The impulse response functions of Private Credit and Employment tocredit and TFP shocks are plotted in Figure 10. As far as the credit shock
is concerned, we see that this generates an expansion in the growth rate ofprivate credit that lasts for many quarters. Therefore, these shocks tend
to generate long credit cycles. Credit shocks generate an expansion in thegrowth rate of employment that is statistically significant for four quarters.
IRF private credit to credit shock

IRF employment to credit shock

IRF private credit to productivity shock

IRF employment to productivity shock

1.5
1
.5
0
-.5

1.5
1
.5
0
-.5
0

2

4

6

8

0

2

4

6

8

Quarter

95% Confidence interval

Structural impulse response

Figure 10: Three variables VAR: TFP, private credit and employment.
TFP shocks also generate an expansion in the growth rate of private credit
but the impact is much less persistent. The growth rate of employment goes37

up but the overall impact is smaller than the impact of credit shocks.
Overall, the results presented in Figure 10 are consistent with the properties of the theoretical model. In particular, we see that credit shocks have astatistical significant impact on employment and TFP shocks lead to a credit
expansion. As long as a credit expansion allows for more job creation, thefinancial mechanism allows for some amplification of productivity shocks.
Separating the transmission through the credit channel: The VAR
analysis described above does not allow us to separate the transmission mechanism of credit shocks emphasized in this paper from the typical credit channel. Separating our mechanism from a standard credit channel is a difficult
task. Here we try a possible implementation which, however, is not strictly
derived from the theoretical model.
The idea is as follows. If the importance of the credit channel is reflected
in interest rate spreads, then a credit shock that changes the stock of debt
but does not affect the interest rate spread can be identified as a shock that istransmitted through our channel, not the credit channel. To pursue this idea
we extend the VAR by adding interest spreads. The short-term restrictions
are then given by the zeros in the matrix that multiplies the innovations(z,t , φ,t , ξ,t , r,t ):


πzz 0
0
0
 πbz πbb πbe πbr  00 πee 0 πrz 0 πre πrr
The variables in the system are now (zt , bt+1 , et , rt ) where rt is the interest
rate spread on corporate bonds. Therefore a credit shock is identified as aninnovation that affects the stock of debt but it does change, at impact, neither
employment nor the credit spread. As common in the literature we use thedifference in yields for Aaa and Baa rated bonds.
As can be seen from Figure 11, the response of employment to credit a
shock does not change significantly with the inclusion of interest rate spreads.
The estimation also suggests that credit spreads impact on employment but
this is in addition to our channel.

38

IRF private credit to credit shock

IRF employment to credit shock

IRF spread to credit shock

IRF private credit to productivity shock

IRF employment to productivity shock

IRF spread to productivity shock

IRF private credit to spread shock

IRF employment to spread shock

IRF interest rate spread to spread shock

2
1
0
-1

2
1
0
-1

2
1
0
-1
0

2

4

6

8

0

2

4

6

8

0

2

4

6

8

Quarter
95% CI

Structural impulse response

Figure 11: Four variables VAR: TFP, private credit, unemployment andcorporate interest rate spreads.
7

Conclusion

In this paper we have studied the importance of financial flows for employment (and unemployment) fluctuations. We have extended the basic matching model by allowing firms to issue debt under limited enforcement of financial contracts. Our approach goes beyond a mere cumulation of frictions,
respectively in financial and labor markets. Firms have an incentive to borrow in order to affect wage bargaining as emphasized in the corporate financeliterature. The paper embeds this mechanism in a general equilibrium environment and investigates its role for the dynamics of aggregate employment.
The ability to borrow can change exogenously in response to credit shocks
or endogenously in response to productivity shocks. Independently of thesources of credit expansion, higher debt allows firms to bargain more favorable wages. Through the structural estimation of the model we have shownthat the contribution of credit shocks to employment fluctuation is quantitatively important. This findings are also supported by the estimation of a
VAR whose identifying restrictions are derived from the structural model.
39

Appendix
A

Wage equation

Consider the value of a filled vacancy defined in (14). Using the binding enforcement constraint bt+1 = φt (1 − η)Et St+1 (Bt+1 ) to eliminate bt+1 , the value of afilled vacancy becomes
Qt = (1 + φt )β(1 − η)Et St+1 (Bt+1 ).
Next we use the free entry condition Vt = qt Qt − κ = 0. Eliminating Qt using
the above expression and solving for the expected value of the surplus we obtain
κ
Et St+1 (Bt+1 ) =.
(24)
qt (1 + φt )β(1 − η)Substituting into the definition of the surplus—equation (10)—and taking into
account that bt+1 = φt (1 − η)Et St+1 (Bt+1 ), we get
St (Bt ) = zt − a − bt +[1 − λ − pt η + φt (1 − λ)(1 − η)]κ.
qt (1 + φt )(1 − η)(25)

Now consider the net value for a worker,
Wt (Bt ) − Ut = wt − a + η(1 − λ − pt )βEt St+1 (Bt+1 )Substituting Wt (Bt ) − Ut = ηSt (Bt ) in the left-hand-side and eliminating
Et St+1 (Bt+1 ) in the right-hand-side using equation (24) we obtain
ηSt (Bt ) = wt − a +η(1 − λ − pt )κ
qt (1 + φt )(1 − η)(26)

Finally, combining (25) and (26) and solving for the wage we get
wt = (1 − η)a + η(zt − bt ) +η[pt + (1 − λ)φt ]κ
,qt (1 + φt )which is the expression reported in (16).
B

Monopolistic competition

Each firm, indexed by i, produces an intermediate good used in the production of
final goods. The production function for final goods is
Z N
Y =
0

40

 1ε

yiε di.

(27)

Notice that the integral is over the interval [0, N ] since there are N producers
equivalent to the number of employed workers. The inverse demand function is
Pi = Y 1−ε yiε−1 ,(28)

where Pi is the unit price for intermediate good i in terms of final goods and1/(1 − ε) is the elasticity of demand.
To make the monopolist structure relevant, we need to introduce some margin
along which the firm can change the quantity of intermediate goods produced.
One way to do this is to assume that there is also an intensive margin in the useof labor. Suppose that the production function for good i takes the form
yi = zli ,(29)

where li is efforts or hours supplied by the worker with dis-utility cost Al1+ϕ /(1 +ϕ). An alternative interpretation is that li represents costly utilization of labor.
The monopoly revenue is Pi yi , that is, the unit price multiplied by output.
Substituting the demand function (28) and the production function (29), the revenue can be written as Y 1−ε (zli )ε . The optimal input li solves the problem
(
)
1+ϕ
Al
max Y 1−ε (zli )ε − i
,
(30)
li
1+ϕ
with first order condition εY 1−ε z ε liε−1 = Aliϕ .
We can now impose the equilibrium condition li = L and individual production
1
becomes yi = zL. Aggregate production is equal to Y = zLN ε and the unit price1−εof intermediate goods is Pi = P = N ε . Finally, the individual revenue is equal
1−εto zLN ε .
Using these results in the first order condition for the intensive margin, we can 1 1−εϕsolve for L = εz
N ϕε . Then substituting in (30) and re-arranging, the revenueA
net of the dis-utility from working (net surplus flow) can be written as  1 (1−ε)(1+ϕ)
1+ϕ
ε ϕ
ε
ϕε
π=
1−
z ϕ N
.
(31)
A
1+ϕ
It is now easy to see the equivalencehbetween
this function
i 1+ϕand the net surplus
1 
ε ϕ
ε
flow reported in (20). If we define z̃ = A
1 − 1+ϕ z ϕ , which is a monotone function of z, and we define ν = (1−ε)(1+ϕ), the surplus flow defined in (31)ϕεis exactly equal to (20).

41

C

Model with infrequent negotiation

Suppose that wages are negotiated (bargained) when a new match is formed andthen they are renegotiated in future periods with some probability ψ. In theinterim periods wages are kept constant.
To avoid some unnecessary complications, we make the following assumption:
Assumption 1 The enforcement constraint takes the form φt Et Jt+1 (bt+1 ) ≥ bt+1 ,where Jt+1 (bt+1 ) is the next period equity value of the firm when the next period
wage is renegotiated with certainty.
This assumption insures that the borrowing limit is independent of the current
wage, which is different across firms depending on the renegotiation history. In
this way all firms continue to choose the same debt even if they pay different
wages. The assumption that the collateral value depends on the equity value ofthe firm when the next period wage is renegotiated with certainty can be justified
with the assumption that, in case of default, wages are always renegotiated. Since
the lender gets a fraction of the firm’s value, this assumption implies that thecollateral is a fraction φt of the equity value of the firm when the next period wageis renegotiated with certainty (since wages are renegotiated in case of default). See
Section 2 for the derivation of the enforcement constraint.
The value for a newly hired worker who bargains the first wage at time t ishi
Wt (bt ) = wt + βEt (1 − λ) ψWt+1 (bt+1 ) + (1 − ψ)W t,t+1 (bt+1 ) + λUt+1 , (32)where W t,t+1 (bt+1 ) is the value at time t + 1 if there in not renegotiation andthe worker receives the wage negotiated at time t. Therefore, the first subscript
denotes the last period in which the wage was negotiated and the second subscript
denotes the period in which the wage is paid.
The value of being unemployed is
Ut = a + βEt pt Wt+1 (Bt+1 ) + (1 − pt )Ut+1 .
(33)
Subtracting (33) to (32) and re-arranging we get( 
Wt (bt ) − Ut = wt − a + βEt (1 − λ) ψ Wt+1 (bt+1 ) − Ut+1 +(1 − ψ) W t,t+1 (bt+1 ) − Ut+1

− pt Wt+1 (Bt+1 ) − Ut+1



)

(34)

42

Since in equilibrium bt+1 = Bt+1 , we can rewrite the equation ashi Wt (bt ) − Ut = wt − a + β (1 − λ)ψ − pt Et Wt+1 (bt+1 ) − Ut+1 +β(1 − λ)(1 − ψ)Et W t,t+1 (bt+1 ) − Ut+1
(35)
To simplify notations, defineρ = β(1 − λ)(1 − ψ)hiδt = β (1 − λ)ψ − ptŴt (bt ) = Wt (bt ) − Ut
ˆ (b ) = W (b ) − U ,
W
τ,t t
τ,t t
t
where τ ≤ t is the time subscript for the last period in which the wage wasˆ (b ) = Ŵ (b ).
renegotiated. If τ = t we have W
τ,t t
t t
Using this notation, the net value of the worker can be written asˆŴt (bt ) = wt − a + δt Et Ŵt+1 (bt+1 ) + ρEt W
t,t+1 (bt+1 )(36)

The next period value without bargaining isˆˆWt,t+1 (bt+1 ) = wt − a + δt+1 Et+1 Ŵt+2 (bt+2 ) + ρEt+1 W t,t+2 (bt+2 )(37)
Substituting in (36) at t + 1, t + 2, t + 3,..., the net value for the worker can be
written asŴt (bt ) =wt − a+ Ωt (bt ),
1−ρ

(38)

where the function Ωt (bt ) is defined asΩt (bt ) = Et δt Ŵt+1 (bt+1 ) + ρEt δt+1 Ŵt+2 (bt+2 ) + ρ2 Et δt+2 Ŵt+3 (bt+3 ) + ...
The function Ωt (bt ) has a recursive structure and can be written recursively asΩt (bt ) = δt Et Ŵt+1 (bt+1 ) + ρEt Ωt+1 (bt+1 ).

(39)

Using the bargaining outcome Ŵt (bt ) = ηSt (bt ) in (38) and (39), we obtain
ηSt (bt ) =wt − a+ Ωt (bt ),
1−ρ

43

(40)

Ωt (bt ) = ηδt Et St+1 (bt+1 ) + ρEt Ωt+1 (bt+1 ).

(41)

Finally, the surplus is the same as in the baseline model, that is,
St (bt ) = zt − a − bt +
C.1

bt+1
+ (1 − λ − ηpt )βEt St+1 (bt+1 ).
R(42)Evolution of aggregate wages

Denote by w̄t−1 the average wage in period t − 1. Then the average wage in period
t is equal toi  m(v , u ) (1 − λ)Nt−1 h
t−1 t−1(1 − ψ)w̄t−1 + ψwt +
wt ,
(43)
w̄t =
Nt
Nt
where m(vt−1 , ut−1 ) is the number of new matches.
To determine the average wage at time t, we need to know the average wage
in the previous period and the share of employment that bargains a new wage attime t. This share is equal tost =ψ(1 − λ)Nt−1 + m(vt−1 , ut−1 ).
NtUsing st , the average wage equation can be written asw̄t = (1 − st )w̄t−1 + st wt .
C.2

Summary

The consideration of infrequent negotiation is captured by the following equations
ηSt (bt ) =wt − a+ Ωt (bt )1−ρΩt (bt ) = ηδt Et St+1 (bt+1 ) + ρEt Ωt+1 (bt+1 )w̄t = (1 − st )w̄t−1 + st wt
st+1 =

ψ(1 − λ)Nt + m(vt , ut )
Nt+1

(44)
(45)
(46)
(47)

Notice that equation (44) replaces the equation for the worker’s value in thebaseline model with period-by-period bargaining. Equations (45)-(47) are additional. The set of state variables is expanded with the new states st and w̄t−1 .

44

D

Costly financing and the credit channel

The paper has abstracted from frictions in financial markets that could affectmore directly job creation. The only channel through which financial markets
affect employment is the negotiation of wages. By doing so we have excluded
the standard credit channel which, according to recent contributions, could also
be important for the dynamics of the labor market. We now extend the model
to allow for a more direct role of financial markets and we show that the credit
channel cannot be easily separated from the efficiency of the matching function
ξt . Thus, fluctuations in ξt could also result from shocks that affect the cost of
external finance.
A typical feature of the matching model is that jobs are created through theposting of vacancies and this requires the payment of a cost κ. This cost has the
typical features of an investment whose return takes place over several periods.
We can then think of the debt raised by new firms as contributing to the financingof this investment. By further assuming that there are agency problems associatedwith the investment κ, we are able to introduce a more direct mechanism throughwhich financing affects job creation. This additional mechanism has the feature of
the standard credit channel.
Suppose that new firms raise debt before posting vacancy. In the baselinemodel we assumed that the debt was raised after knowing the outcome of thematch. However, this different timing for initial borrowing is inconsequential. If
the firm raises debt before posting a vacancy, the lender knows that the debt will
not be repaid if the vacancy is not filled and this happens with probability 1 − qt .
Anticipating this, the lender charges a higher interest but the expected cost of thedebt for the firm is still r = 1/β − 1. The timing in subsequent periods remain thesame.
As long as the lender can control the investment κ, that is, it can insure thatthe firm does post the vacancy and search for a worker, the different timing isirrelevant. The frictions arise if the lender has not full control over the use of theraised funds. In particular, we now assume that after receiving the loan, a new
firm has the ability to default before incurring the cost κ. If the firm defaults, itnretains the funds raised from the bank, that is, bRt+1
n , where R is the gross interest
rate charged by the bank. The firm raises funds to finance κ but after receiving
the funds it can default instead of investing. The value of default is the funds
received from the lender, that is, bRt+1
n .
Alternatively, the firm could post the vacancy whose expected value is
bt+1
Vt = − κ − n + qt β(1 − η)Et St+1 (bt+1 ).
(48)
RThe first term in parenthesis is the equity financing of κ. Since the firm raises

45

bt+1 /Rn with debt, the difference must be financed with equity.
Because of free entry, the value of posting a vacancy is zero in equilibrium,that is, Vt = 0. Therefore, the value of defaulting, bRt+1
n , is bigger than the valueof not defaulting, Vt . This implies that a new firm is unable to raise debt and theinvestment κ must be fully financed with equity.
Now suppose that the lender could enforce the investment κ with costly monitoring. Specifically, the lender can insure that the firm makes the investment by
incurring the cost %t κ, where %t is stochastic and captures time-varying frictions
in financial markets. This would make the cost of borrowing higher but allows thefirm to borrow. Since the cost of debt is now higher than the cost of equity, would
the new firm continue to borrow? As long as the monitoring cost %t is not too large
and the bargaining power of workers η sizable, the firm prefers debt over equity
because this allows to bargain lower wages in the event of a successful match.
Consider now the break-even condition for the lender which is equal to
bt+1
qt bt+1+ %t κ =.
nR
1+r
Using this condition to eliminate Rn in equation (48), the choice of debt for a
new firm can be written as
qt bt+1
Vt = max− (1 + %t )κ + β(1 − η)qt Et St+1 (bt+1 )
(49)
bt+1
1+r
subject toφt (1 − η)Et St+1 (bt+1 ) ≥ bt+1 ,Competition for entry then implies that Vt = 0 and the free entry condition
can be written asbt+1(1 + %t )κ = qt
+ β(1 − η)Et St+1 (bt+1 ) ,1+r
which is very similar to the free entry condition in the baseline model. The only
difference is the monitoring cost %t which was zero in the baseline model. Shocks
to %t are equivalent to an increase in the cost of posting a vacancy and are similar
to shocks studied in Petrosky-Nadeau (2009).
The new free entry condition makes clear that the monitoring cost cannot beeasily separated from the matching shock. Since the probability of filling a vacancy
is equal to qt = ξt (vt /ut )1−α , what matters for job creation is the ratio (1 + %t )/ξt .
It is in this sense that the matching shock ξt can be interpreted as also capturing
the impact of shocks that affect employment through the standard credit channel.

46

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