Imen Ben Mohamed
email: imen.benmohamed@univ-paris1.fr

Marine Salès

Credit Imperfections, Labor Market Frictions and Unemployment: a DSGE approach

Keywords: JEL classication: E12, E24, E32, E44 new-Keynesian model, labor and credit market frictions, vacancies and unemployment dynamics

This paper investigates the impact of credit market imperfections on unemployment, vacancy posting and wages. We develop and simulate a new-Keynesian DSGE model, integrating sticky prices in goods market and frictions in labor and credit markets. A search and matching process in the labor market and a costly state verication framework in the credit market are introduced. Capital spending, vacancies costs and wage bill need to be paid in advance of production and thus require external nancing in a frictional credit market.

The theoretical model demonstrates how the procyclicality of the risk premium impacts the vacancy posting decisions, the wage and unemployment levels in the economy. Higher credit market frictions are the source of lower posting vacancies and higher unemployment level. Asymmetric information in the signing of a loan pushes up wholesale rms' marginal costs, as well as hiring costs by a nancial mark-up charged by nancial intermediaries. This nancial mark-up is then transmitted by these rms on prices. Thus, it aects their hiring behavior, the wage and employment levels, as well as ination in the economy. Then, the theoretical model is simulated by using quarterly United-States (US) data for the sample period 1960:Q1 to 2007:Q4. We nd that employment rates and vacancy posting increase following positive credit, net worth and uncertainty shocks. Dierent channels of propagation from the nancial sphere of the economy to the labor market are investigated and the results appear to be consistent with our theoretical model.

Introduction

Credit market imperfections are suspected of playing a key role in the worsening of the situation on the labor market. In recent years, especially following the Great Recession, there has been an increasing interest in analyzing the interaction between credit and labor markets. Questions have been raised about the fact that higher credit imperfections may be the cause of a slowdown of the economy, and not its consequence. By themselves, nancial frictions could destabilize the whole economy. The research to date has tend to focus either on the impact of nancial frictions on overall macroeconomic performances (Bernanke and Gertler (3), Bernanke and Gertler (4), Carlstrom and Fuerst [START_REF] Carlstrom | Agency costs and business cycles[END_REF], Kiyotaki and Moore (26), Bernanke et al. [START_REF] Bernanke | The nancial accelerator in a quantitative business cycle framework[END_REF], Carlstrom and Fuerst (11), Gertler et al. [START_REF] Gertler | Financial intermediation and credit policy in business cycle analysis[END_REF] and Fiore and Tristani (18)), either on the impact of labor market frictions (Merz (33), Andolfatto [START_REF] Andolfatto | Business cycles and labor-market search[END_REF], Walsh [START_REF] Walsh | Labor market search, sticky prices, and interest rate policies[END_REF], Krause et al. [START_REF] Krause | Ination dynamics with search frictions: A structural econometric analysis[END_REF], Gertler and Trigari (24), Thomas and Zanetti [START_REF] Thomas | Labor market reform and price stability: An application to the euro area[END_REF], Trigari (46), Christoel et al. (15), Lechthaler et al. (31), Blanchard and Galí (6), Galí et al. (20), Campolmi and Faia (9), Christiano et al. [START_REF] Christiano | Unemployment and business cycles[END_REF]). However, far too little attention has been paid to the impact of nancial frictions on labor markets, being themselves imperfect (Thomas and Zanetti (44), Christiano et al. [START_REF] Christiano | Introducing nancial frictions and unemployment into a small open economy model[END_REF], Zanetti and Mumtaz (50) and Petrosky-Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF]).

Figures 1 and2 shed light on the possible causal relationships that we propose to study and highlight in this paper. The evolution of unemployment rate, Baa-Aaa spread and default rate between 1970-Q1 and 2007-Q4 for the United-States (US) is represented in gure 1. The unemployment rate is the ratio of civilian unemployed persons to the civilian labor force. The default rate is the default rate for Moody's rated US speculative-grade corporate bonds. The Baa-Aaa spread is the Moody's seasoned Baa-Aaa corporate bond yield. A correlation is observed among these variables, especially for the unemployment rate and the Baa-Aaa spread (0.76). The higher the unemployment rate is, the higher the Baa-Aaa spread is and conversely. For the default rate, the correlation is less explicit, due to plausible structural forces between 1971 and 1982, linked to the monetary policy. However, some periods of correlation exist: 1979-Q1 until 1985-Q4 (0.6) and from 1990 (0.32). Then, the negative correlation between the labor market tightness and the Baa-Aaa spread is shown on gure 2. The negative correlation among 1970.Q1 and 2007.Q4 is quite huge (-0.84). It induces that the higher are vacancy posting relative to unemployment, the lower is the Baa-Aaa spread and conversely. Based on these basic empirical correlations, we construct and simulate a new-Keynesien model integrating credit and labor market frictions, so as to gure out possible causal links among this kind of variables.

The model is a monetary new-Keynesian model with asymmetric information in the credit market à la Bernanke et al. [START_REF] Bernanke | The nancial accelerator in a quantitative business cycle framework[END_REF] and a search and matching process in the labor market à la Mortensen and Pissarides [START_REF] Mortensen | Job creation and job destruction in the theory of unemployment[END_REF].

Capital spending, wage bill and vacancies costs are assumed to be paid partially by external funds (Petrosky- 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 Quaters

Unemployment rate Default rate Baa-Aaa spread 1970 1973 1976 1979 1982 1985 1988 1991 1994 1997 2000 2003 2006 Quarters

Labor market tightness Baa-Aaa Spread Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF] consider that only vacancies costs are paid in advance). The costly state verication (CSV) approach (Townsend (45)) is used because of its tractability and the facility that it oers to embed informational frictions in a general equilibrium analysis. Moreover, this approach was chosen because it generates a wedge between the cost of internal and external nance, with a nancial accelerator mechanism. The propagation and amplication mechanism come from the uctuation of entrepreneurs' net worth, while in collateral constraints framework (Kiyotaki and Moore [START_REF] Kiyotaki | Credit Cycles[END_REF]), it comes from uctuations in asset prices.

Our model, based on these features, provides an explanation of cyclical uctuations in key labor market variables (unemployment, vacancies, hours worked per employee and wages) and in credit market central variables (risk premium and default rate). We nd that the procyclicality of the risk premium (the cost of external over internal funds) impacts vacancy posting decisions, the wage bill and unemployment levels in the economy, as well as the level of ination. In period of downturns, the risk premium increases and the net worth of entrepreneurs decreases. It increases their dependence on external funds, making job posting more expensive. So, less vacancies are posted and a higher equilibrium unemployment is obtained. More precisely, asymmetric information in the credit market pushes up marginal costs and prices, as well as hiring costs by a nancial mark-up, depending on the levels of monitoring cost and idiosyncratic shock threshold. This nancial mark-up is made to overcome the agency problem between nancial intermediaries and entrepreneurs. But it will be charged in return by wholesale rms on prices and will aect their hiring behavior, as well as wage, employment and ination levels in the economy.

A simulation exercise, based on parameters calibration, is then chosen to investigate the impact of a net worth shock, a credit shock and an uncertainty shock on macroeconomic variables, such as vacancies, unemployment rate, real wages, intensive and extensive margins. Quarterly US data for the sample period 1960:Q1

to 2007:Q4 are used. The most striking result to emerge from the simulation is that employment rates and vacancies posting increase well following positive credit, net worth and uncertainty shocks. Dierent channels of propagation from the nancial sphere of the economy to the labor market are investigated and appear to be consistent with our theoretical model. The key mechanism behind this result is that following positive shocks on the credit market, the nancial mark-up decreases, leading to lower real marginal costs paid by wholesale rms, that is pass through prices in the economy, and inducing rms to post more vacancies. The unemployment as a consequence decreases. Furthermore, after a positive net worth shock, a substitution eect appears between hours worked per employee and the number of employees, either between the intensive and the extensive margins. This element is veried in the data, in the sense that the extensive margin is always more reactive that the intensive one. This substitution eect does not appear following a positive credit shock, or a positive uncertainty shock, resulting in a higher positive impact on the whole economy.

Section 2 consists of a related literature review. The theoretical model is developed in Section 3. In Section 4, we outline the simulation exercise and present the consequent results. Section 5 summarizes and concludes.

Related literature

As explained in the previous section, the paper is at the intersection of dierent lines of research. Firstly, a number of research papers introduce search and matching frictions on labor markets in real business cycle (RBC) models or in new-Keynesian (NK) models. Other articles highlight the role of nancial frictions for macroeconomic dynamics, without taking into account search and matching frictions on labor markets. Finally, more recent studies embody simultaneously frictions in labor and credit markets in partial equilibrium models or in dynamic stochastic general equilibrium (DSGE) models, to study interactions and implications of these two types of frictions.

The assumption of Walrasien labor markets is considered as a weakness of standard RBC and NK models.

Indeed, these models do not take into account variations in the number of unemployed, the extensive margin that never changes. They allow only to study variations in hours worked per employee, the intensive margin. This may seem annoying to the extent that unemployment is an important indicator of performances of the economy in its use of resources and it is a major policy issue. Furthermore, this kind of models is ineective to explain the eect of various shocks on unemployment dynamics. As a consequence, many articles have introduced search Papers, as those of Merz [START_REF] Merz | Search in the labor market and the real business cycle[END_REF] and Andolfatto [START_REF] Andolfatto | Business cycles and labor-market search[END_REF], study implications of search and matching frictions for economic uctuations in a standard RBC model. Both model show that labor market frictions are a mechanism of amplication and persistence for technology shocks. These frictions improve the empirical performance of RBC models, compared to a standard one, even if they do not predict enough cyclical movements in vacancies and output compared to data. Moreover, Andolfatto (2), by introducing extensive and intensive margins, nds that most of the variability of total hours worked is due to changes in unemployment level rather than hours worked per employee.

Then, several papers in the same spirit (Walsh (47), Trigari (46), Thomas and Zanetti (44), Lechthaler et al. [START_REF] Lechthaler | Monetary persistence and the labor market: A new perspective[END_REF] and Campolmi and Faia (9)) examine the role of matching frictions in new-Keynesian models. For example, Walsh [START_REF] Walsh | Labor market search, sticky prices, and interest rate policies[END_REF] develops a new-Keynesien DSGE model with labor market frictions and with dierent potential sources of persistence (habit persistence, price stickiness and policy inertia). He founds through a calibration exercise that his model amplies for US data the output response and decreases the ination response to a monetary policy shock, as well as it generates persistence in output and ination as observed in data and as standard NK models do not succeed to generate. In the same idea, Trigari [START_REF] Trigari | Equilibrium unemployment, job ows, and ination dynamics[END_REF] considers cyclical uctuations of output, ination and labor market variables following a monetary shock. She studies the possibility of endogenous separation between rms and workers, as well as extensive and intensive margins. Her estimated model is able to replicate well for US data the observed responses of output, ination and labor market data to a monetary policy shock. Using a VAR, she nds as observed in data that in a model with labor market frictions, the response of ination is less volatile and response of output more persistent after a monetary policy shock than in a standard NK model.

However, these Mortensen-Pissarides search and matching models of unemployment remaines unable to match important stylized facts observed in data. In particular, these types of models are not performing well to explain high volatility and persistence of unemployment and vacancies, as well as the relative smooth behavior of real wages found in data. The framework of wage Nash bargaining appears to lead to an exaggerated procyclical movements in wages after a positive productivity shock for example, that dampens the rm's incentives to hire. can resort to external nancing to raise capital at a risk-free interest rate. With credit market frictions, information asymmetry appears in the form of moral hazard between the lender and the borrower. Borrower will indeed be induced to report to the lender a lower real output produced than their true level. As a consequence, this type of asymmetric information can lead rst to borrowing restrictions for borrowers on the amount of external nancing available, based on the existence of collateral constraints to cover their potential inability to reimburse loans as in Kiyotaki and Moore [START_REF] Kiyotaki | Credit Cycles[END_REF]. In this framework, agents face endogenous credit limits determined by the value of collateralized assets. Collateral constraints always bind but default never occur at the equilibrium.

Wages

Then, asymmetric information between a lender and a borrower can lead to a second type of nancial frictions (Bernanke and Gertler (3), ? ), Bernanke et al. ( 5)), namely a higher cost of external nancing compared to internal nancing opportunity cost (the risk-free interest rate), that to say an external nance premium or a risk premium, paid by entrepreneurs. Agency costs are here endogenous over the business cycle and default emerges as an equilibrium phenomenon. The canonical RBC model of ? ) introduce informational asymmetry between lenders and borrowers and show that it leads the economy to return more slowly to the steady-state after being hit by a shock (propagation mechanism). The mark-up distorts factor markets, so wages and capital rental rates are below their corresponding productivity. Thus, an increase in the net worth of a rm reduces agency costs and hence the mark-up. Debt arises as the optimal nancial contract between rms and banks, and rms must borrow at a premium over the risk-free rate. The nancial contract is designed to minimize the expected agency costs. It species returns when bankruptcy or success occurs and a monitoring threshold as developed in our model. The threshold is a decreasing function of borrower's net worth and an increasing function of the deposit risk free-rate (opportunity cost).

Fiore and Tristani [START_REF] Fiore | Optimal monetary policy in a model of the credit channel[END_REF] show also, by adopting the costly state verication set-up, that nancial market conditions are important to explain macroeconomic outcomes because its aects rms' marginal costs. Higher credit spreads increase lending rates and marginal cost of credit for rms, which leads to increase prices and as a consequence, it aects output.

All these previous papers assume standard Walrasien labor markets. Only few papers consider both credit and labor markets frictions, as the ones of Christiano et al. [START_REF] Christiano | Introducing nancial frictions and unemployment into a small open economy model[END_REF], Zanetti and Mumtaz (50) and Petrosky-Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF]. Labor market frictions imply that it is costly to hire new workers. The functioning of frictional labor markets prevents the competitive allocation of labor resources, and thus it will interact with nancial frictions to impact production, unemployment, investment and capital accumulation. [START_REF] Petrosky-Nadeau | Macroeconomic dynamics in a model of goods, labor and credit market frictions[END_REF], who assume search frictions on both labor and credit markets. Search frictions and agency costs are both credit market imperfections but we decide to focus on agency costs by a costly-state verication framework. Note also that our work is included in the spirit of researches about the impact of credit market imperfections on investment ows but on our side, we decide to focus on their impact on employment and vacancies ows, hours worked and wages.

3 The model

Model overview and timing summary

The model is populated by seven types of agents: households, wholesale-good rms managed by entrepreneurs, retailers, nal-good rms, banks and a government that conducts monetary and scal policies.

The household sector is represented by a continuum of identical households of length unity. Each household is constituted of members who are either working or unemployed. All members are supposed to be risk-averse.

They supply labor, consume, rent capital and save through money holding and through their deposits in a nancial intermediary.

Entrepreneurs are risk-neutral and have nite lifetime. Following Bernanke et al. [START_REF] Bernanke | The nancial accelerator in a quantitative business cycle framework[END_REF], each entrepreneur is as-sumed to have a given probability to survive to the next period. They manage wholesale rms, that produce wholesale goods using a constant return-to-scale technology using labor and capital as inputs. Surviving entrepreneurs carry their prots as a part of their net worth. Dying entrepreneurs consume everything. After deciding on the number of new workers they need, entrepreneurs, based on their net worth amount and their expected production and returns, borrow funds from banks to post vacancies (and recruit workers), to pay capital spending and the wage bill in advance. However, wholesale-good production is subject to an idiosyncratic shock, privately observed by entrepreneurs, while banks need to pay a monitoring cost to check the real output produced, as well as the eciency of the recruitment process. This agency problem will alter the marginal cost of production and the real recruitment costs of wholesale rms.

As soon as funds are obtained, entrepreneurs enter the labor market, match with their potential employees and bargain on wages. Whenever it happens, the match is assumed to keep going on until it is exogenously costlessly destroyed.

Finally, the production sector has three dierent layers in the spirit of Bernanke et al. [START_REF] Bernanke | The nancial accelerator in a quantitative business cycle framework[END_REF]. At the rst layer,

where agency problem and search and matching frictions occur, a continuum of perfectly competitive wholesale rms produce homogeneous goods using capital and labor. At the second layer, where price stickiness arises, wholesale goods are dierentiated costlessly by a continuum of monopolistic rms. The realized prots are rebated lump-sum to households. The nal good is then homogeneous and can be used for consumption, capital accumulation and government spending.

The seven agents are thus interacting in seven dierent markets (labor market, capital market, credit market, liquidity market, wholesale-good market, intermediate and nal-good markets), where the timing is given by the following sequence of events.

Firstly, monetary policy and aggregate shocks are realized. The liquidity market opens. Then, a given fraction of entrepreneurs are born so as to ensure a constant fraction of entrepreneurs at each period. An exogenous endowment is given to all entrepreneurs, to be sure that they remain entrepreneurs. Given all expected prices and revenues in the economy, households decide on their level of consumption, deposits, money holding, investment and on the capital rate of utilization.

The credit market opens. Banks accumulate the deposited amounts by households at the end of period t -1 in order to grant them as loans at the beginning of the current period t. The credit market clears when the amount of deposits and money injected in the economy equals the amount of granted loans.

Entrepreneurs own and manage the wholesale production sector. They enter period t with a net worth, either composed by the exogenous endowment and the accumulated net worth at the end of period t -1 for the last period not dying solvent entrepreneurs. Or they enter the period t with a net worth given by the exogenous endowment for the entrepreneurs who died or went bankrupt last period. They all borrow from banks using a nominal nancial contract, in order to cover their expected production bill (labor and capital costs) and vacancies costs. Indeed, these elements are assumed to be paid in advance.

After, the labor market opens. Entrepreneurs post vacancies at a real unit cost and recruit a given number of workers. The wage is established after a Nash bargaining process and new hired employees start working immediately. The Nash bargained wage and the vacancies costs have to be paid immediately by entrepreneurs, using their loans.

The capital market opens, where households are assumed to own the capital stock of the economy. They rent eective capital to entrepreneurs at a perfectly competitive price. They accumulate capital at the end of the period t -1 to lend it during the current period t to entrepreneurs. The capital market clears when the amount of eective capital supplied by households is equal to the amount demanded by entrepreneurs. Entrepreneurs have to pay immediately their capital costs to households, using their loans.

The three production markets can now opened. First, wholesale goods are produced by wholesale-good rms thanks to labor and capital. Entrepreneurs sell it to retailers and declare either being solvent or bankrupt, after having observed privately their own idiosyncratic shocks. Solvent entrepreneurs, characterized by a suciently high idiosyncratic shock, pay back their loan and keep the remaining amount to use it at the end of the period t (to consume and/or to accumulate net worth). For bankrupt entrepreneurs, the bank spends a monitoring cost, proportional to the realized rm's value, in order to check the output they produced and conscates the proceeds of production left by these entrepreneurs. These later can neither consume nor carry over net worth to the coming period. Then, banks reimburse households' deposits. The role of the nancial intermediary is well dened: it allows to mitigate the monitoring cost and to avoid its duplication.

Retailers, that are a set of monopolistically competitive rms owned by households, buy the wholesale good and dierentiate it costlessly. However, only a given fraction of retailers are able to fully re-optimize their prices.

All the realized prots are transferred to households at the end of the period t.

Final goods are then sold to households (to consume and to accumulate capital), to the government (government spending) and to solvent dying entrepreneurs (to consume), at a consumer's price index.

Finally, households consume, invest, make their deposits and their money holding. Solvent entrepreneurs decide either on their consumption or on their net worth, depending on their probability of death in the current period t: those exiting the economy at the end of the period t consume all their net worth just before death, and those keeping in the economy will accumulate totally their net worth thanks to money.

To make it more understandable, the gure 3 represents the previous timing of events in a synthetic way.

Then, the gure 4 reports the ow of funds between agents in the economy characterized by the previous timing.

Households

Households consume, save through deposits, hold money, invest in capital and supply passively labor to entrepreneurs. At the beginning of the period t, given all expected prices and revenues in the economy, households decide how much they want to consume, to save through deposits and money and how much they want to invest nal goods to accumulate capital. This capital will be rented at the next period t + 1 to entrepreneurs on a perfectly competitive capital market. Households decide also the capital utilization rate for the current period t, which will determine the eective capital submitted for rent in this period t.

To make their decisions, households expect as resources, wages earned after the matching process of the period t by workers, and unemployment benets earned by unemployed at the end of period t. They earn also incomes from the rental of capital and prots from retailers, as they own them. Finally, they receive from banks, after loans reimbursement by wholesale-good rms, the last period risk-free interest rate, multiplied by the amount of deposits decided last period. This revenue is sure because nancial intermediation is assumed to be realized through a large number of atomistic risk-neutral banks, holding enough large and diversied portfolios to ensure perfect risk pooling for their main creditors, the households.

Then, when the labor market opens, unemployed households members supply passively labor to entrepreneurs.

A fraction of them is matched with entrepreneurs and begins to work immediately. The other fraction is not matched and stays unemployed. Newly matched workers and workers who have been matched without exogenous destruction in the period t -1 receive their wages immediately after the wage bargaining. The unemployed have to wait the end of the period to receive unemployment benets.

At the end of the period, after the production of nal goods, households have to pay lump-sum taxes to the government, that will nance unemployment benets and government spending. Finally, households consume eectively, invest nal goods to accumulate capital, hold money and make their deposits to banks.

Employed and unemployed members

After obtaining a loan from a bank, a wholesale rm i posts actively V it job vacancies at a real unit cost, γ, to attract unemployed workers, U t , who are searching passively for a job.

Assumption 1. Only the unemployed workers can search passively for a job and can be hired. Current employed workers are not allowed to look for another job. Job-to-job transition is not considered.

Job creation occurs when an entrepreneur and an unemployed worker meet on the labor market after a search and matching process à la Mortensen and Pissarides [START_REF] Mortensen | Job creation and job destruction in the theory of unemployment[END_REF], and when they agree on a Nash bargaining wage. At the end of this process, a wholesale rm i employs n it workers at a real hourly wage W it . As there exists a continuum of wholesale rms represented by the unit interval, the total number of vacancies during the matching process of period t, and the total number of employed workers after the matching process of period t, are:

V t = 1 0 V it di n t = 1 0 n it di
As the labor force is normalized to one, the number of unemployed searching for a job during the matching of the period t corresponds to:

U t = 1 -(1 -δ)n t-1 (1)
where δ is the exogenous job destruction rate.

Assumption 2. A job is assumed to be destroyed at an exogenous rate, δ. According to our timing, the exogenous destruction of a match can occur only between the end of the matching process of period t and the end of the period t.

Assumption 3. There is a full participation of workers. They are either employed or unemployed workers looking for a job. The transition between in and out the labor force is ignored.

Formally, total vacancies, V t , will be lled by unemployed workers, U t , via an aggregate constant return to scale matching function, m(U t , V t ), specied by 1 :

m(U t , V t ) = U ρ t V 1-ρ t ( 2
)
where ρ ∈ (0, 1) is the elasticity of matches to unemployment. Moreover, as standard in the literature, the matching technology is assumed to be concave and increasing in both arguments. It represents the aggregate ows of hires in period t.

Assumption 4. As soon as the matching happens, new hired workers start working immediately 2 . Employed 1 Gertler et al. [START_REF] Gertler | An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining[END_REF] use the same specication. The Cobb-Douglas matching function is used in almost all macroeconomic models with search and matching frictions. Furthermore, the constant returns to scale assumption (homogeneity of degree one) seems to be supported empirically according to Petrongolo and Pissarides (37).

2 Following Krause and Lubik (29), Gertler et al. ( 23), Thomas and Zanetti ( 44) and Blanchard and Galí [START_REF] Blanchard | Labor markets and monetary policy: A new keynesian model with unemployment[END_REF], workers are assumed workers for whom the matching ends exogenously during period t are allowed to search for a new job in the same period 3 . But a new matching is only possible after nancial contracts and loans are decided and obtained, so only at the opening of the labor market at the next period.

The ratio of total vacancies to unemployed workers, θ t , denes the labor market tightness during the matching process of the period t from the rm point of view, so that:

θ t ≡ V t U t
The probability for a rm to ll a vacancy job during the matching process of the period t, p t , is given by:

p t = m(U t , V t ) V t = m(θ -1 t , 1) (3)
And the probability for an unemployed worker to nd a job during the matching process of the period t, q t , is

given by:

q t = m(U t , V t ) U t = m(1, θ t ) (4)
Therefore, the number of hired workers during the matching of the period t, ψ t , is given by:

ψ t = p t V t = m(U t , V t ) (5)
Note that q t = θ t p t and ∂p t /∂θ t < 0, ∂q t /∂θ t > 0. The higher vacancies on unemployment (or the higher the labor market tightness from the rm point of view), the higher the probability for an unemployed worker to nd a job and the lower the probability for a rm to ll a job. Both unemployed workers and rms are assumed to take q t and p t as given.

Finally, the total number of employed workers after the matching process of the period t, n t , is dened as the sum of the surviving workers from the exogenous separation at the end of period t -1, (1 -δ)n t-1 , and the new hires from the matching of the period t, ψ t :

n t = (1 -δ)n t-1 + ψ t (6)
to be immediately productive after being hired. 3 Many papers on searching and matching literature are considering the same assumption. See Blanchard and Galí ( 6) for example.

So the level of unemployment in the economy after the matching process of period t is 1 -n t , as the labor force is normalized to one. Then, since workers who discontinue their match during the period t are assumed to be allowed to search passively for a new job in the same period, the number of unemployed searching workers at the end of the period t is 1 -(1 -δ)n t , which will be used as the denition of unemployment for the next period t + 1.

Household behavior

Households are seen as a large representative family represented by the unit interval, consisting of a continuum of members, either employed or unemployed. As in Merz [START_REF] Merz | Search in the labor market and the real business cycle[END_REF] and Andolfatto (2), there is a full risk sharing of consumption in order to avoid distributional issues due to heterogeneity in incomes among family members. So, the family pools its income such that a perfect consumption is fully insured for all members.

The same notation is then used for the consumption of the representative household and for the consumption of each member 4 .

After a search and matching process à la Mortensen and Pissarides [START_REF] Mortensen | Job creation and job destruction in the theory of unemployment[END_REF] on the labor market, the number of employed family members is n t ∈ (0, 1), whereas the remaining members, 1-n t , are unemployed. Each employed worker supplies labor at a real Nash bargaining wage, W t . Entrepreneurs set unilaterally eective hours of work, H t , at the time of the nancial contract establishment. Therefore, the total number of hours worked by a representative household, N t , is given by:

N t = n t H t
In addition to the real wage income, W t N t , earned by employed workers and real unemployment benets, b5 , received by unemployed workers, the representative family has a diversied ownership stake in monopolistic retailers, paying out a nominal lump-sum prot, Π t . The family receives also from banks the last period riskfree interest rate, R t-1 , multiplied by the amount of deposits decided last period, D t-1 . Then, households hold an amount M t-1 of money carried from the previous period. As the household owns the capital stock of the economy, he rents eective capital, K t , to wholesale rms at a real interest rate, r K t . He has also to make a nominal lump-sum transfer for a nominal amount T t to the government.

Finally, this total income is used to consume a real amount C t of nal goods, to invest a real amount I t , to save a nominal amount D t of bank deposits remunerated at a risk free rate, R t , and to accumulate a nominal amount of money M t . Thus, the representative household budget constraint is given by:

W t n t H t + (1 -n t )b + R t-1 D t-1 P t + r K t ν t -Υ(ν t ) K p t-1 + Π t P t + T t P t = M t -M t-1 P t + C t + I t + D t P t (7)
where P t is the nominal aggregate price level.

Households are assumed to own the economy's stock of physical capital, K p t-1 , and so, they choose the capital utilization rate, ν t , which transforms physical capital into eective capital, K t . The amount of eective capital that households rent to wholesale rms in period t is given by:

K t = ν t K p t-1 (8)
Υ(ν t ) is the real cost of capital utilization per unit of physical capital 6 . We assume that, at the steady state, the following conditions hold:

ν t = 1 and Υ (1) Υ (1) = σ a .
By investing I t units of nal goods in period t, the representative household increases the physical capital stock, K p t , available during period t + 1 according to:

K p t = (1 -δ K )K p t-1 + 1 -Λ I t I t-1 I t (9)
where δ K is the capital depreciation rate and Λ(.) is the real cost of investment adjustment. Λ(.) is an increasing and convex function 7 . Since the aggregate productivity shock is then assumed to be stationary, Λ(.) satises the following conditions at the steady state: Λ(.) = Λ (.) = 0 and Λ (.) = κ > 0.

Conditional on {H t , n t } ∞ t=0 and taking as given the set of prices

{P t , W t , R t , r K t } ∞ t=0 , the household chooses the streams of consumption of nal goods {C t } ∞ t=0 , nominal money balances {M t } ∞ t=0 , deposits {D t } ∞ t=0 , investment {I t } ∞ t=0 , capital utilization rate {ν t } ∞ t=0 and physical capital {K p t } ∞ t=0
, maximizing the following discounted utility 6 Υ(νt) is specied as follow:

Υ(νt) = rK σa [exp (σa(νt -1)) -1] ,
where rK is the steady state value of the renting capital interest rate and σais dened as the capital adjustment cost elasticity. 7 The following specication is used for Λ(xt):

Λ(xt) = 1 2 exp[ √ κ(xt -1) + exp - √ κ(xt -1) -2 , where xt = It It-1 .
function 8 subject to the budget constraint [START_REF] Blanchard | The Beveridge Curve[END_REF] and the physical capital law of motion ( 9):

E 0 ∞ t=0 β t log(C t -hC t-1 ) + ξ log M t P t - H 1+τ t n t 1 + τ (10)
where 0 < β < 1 is the intertemporal discount factor, h is a habit persistence parameter, ξ is a money preference parameter and τ denotes the inverse of the Frisch elasticity of labor supply. When h > 0, the model allows for habit persistence in consumption preferences to take into account the necessary empirical persistence in the consumption process.

The rst-order conditions of the representative household's problem are given by:

(C t ) λ t = 1 C t -hC t-1 -βhE t 1 C t+1 -hC t ( 11
)
(D t ) 1 = βE t λ t+1 λ t R t π t+1 (12)
(ν t ) r K t = Υ (ν t ) (13)
(I t ) Q t 1 -Λ I t I t-1 = 1 + Q t I t I t-1 Λ I t I t-1 -βE t λ t+1 λ t Q t+1 I t+1 I t 2 Λ I t+1 I t (14)
(K p t ) Q t = βE t λ t+1 λ t (1 -δ K )Q t+1 + r K t+1 ν t+1 -Υ(ν t+1 ) (15)
(M t ) M t P t = ξ λ t -βE t λ t+1 π t+1 -1 (16)
where π t ≡ P t P t-1 is the ination rate, λ t is the Lagrange multiplier associated to the household's budget constraint and Q t is the value of an additional unit of physical capital in terms of nal goods units. Q t represents more precisely the ratio between the Lagrange multiplier associated to the capital evolution law [START_REF] Campolmi | Labor market institutions and ination volatility in the euro area[END_REF] and λ t .

Equation 11 denes the marginal utility of consumption when there is habit formation. It states that the Lagrange multiplier equals the marginal utility of consumption. Equations 12, 13, 14 and 15 correspond to the household choice in terms of deposits, rate of capital utilization, investment and physical capital. Equation 16denotes the household's demand for real balances.

Wholesale-good rms

Wholesale-good rms, indexed by i ∈ (0, 1), need labor and capital to produce. Y ws it is the quantity of wholesale goods produced by a rm i using N it total hours of labor and K it units of eective capital, according to the following production function:

Y ws it = A t K α it N 1-α it ( 17
)
where α is the capital share in production and A t is the aggregate technology shock, realized at the beginning of each period, source of systematic risk. This shock is assumed to be stationary and evolves according to:

log(A t ) = ρ A log(A t-1 ) + u A t , ρ A ∈ (0, 1) where u A t iid ∼ N (0, σ 2 A )
Eective capital, K it , is rented from households at a competitive price, r K t . Total hours worked, N it , are paid to employed workers through the wage, W it . Needed new hires, ψ it , are obtained through a matching process on the labor market, implying vacancy posting costs, γV it . The expected production bill, W t N it + r t K it , and vacancy posting costs, γV it , are assumed to be paid prior to production.

Each wholesale rm is managed by a nite lived risk-neutral entrepreneur, who may die at each period with a probability (1 -ς t ). This assumption is made to be sure that entrepreneurs will not accumulate net worth and that they will borrow from banks at each period 9 . Intra-period entry into and exit out of wholesale rms at each period are ruled out. Entrepreneurs have a net worth, composed by a real exogenous entrepreneurial wage, W e , and for the one solvent and not exiting the economy last period, by the net worth accumulated from the previous period. But this net worth will not be sucient to cover the total production bill, as well as the vacancy posting costs. Entrepreneurs have to borrow from banks. Thus, a nancial intermediation is realized through a large number of atomistic risk-neutral banks. They receive deposits from households at the end of period t -1, that they use to lend to entrepreneurs in period t. Furthermore, entrepreneurs are subject to idiosyncratic shocks, privately observed by them, but not observed by banks. So banks have to monitor wholesale rms, which declare themselves bankrupt after the production occurs. The monitoring is costly and has to be integrated in the nancial contract. An optimal nancial contract is thus determined between banks and entrepreneurs, maximizing the entrepreneur's expected returns, subject to the bank's participation constraint.

Hiring decision

Before the nancial contract conclusion, based on the rm's expected net returns, the number of needed new hires, ψ it , is determined by the human resources department of each rm. Indeed, wholesale rms are assumed to be composed by dierent departments. In particular, there are a human resources department, which is in charge with the recruitment process, and a management department, directed by the entrepreneur, which is in charge with the borrowing process. The human resources department decides on the labor needs of the rm in order to maximize its discounted value of future prots. To do so, this department determines the price of a new worker, or to be more precise, the expected net value of this new worker for the rm. Each new worker is thus evaluated through this value. It enables then the management department to go to negotiate to the bank, based on this implicit worker price. At the end, the net recruitment cost or the replacement cost of a new worker, integrating nancial costs, will be obtained.

To sum up, just before the nancial contract establishment, wholesale rms set up their hiring decision, based on the workers' expected net returns. They determine the number of new workers, ψ it , they have to take on, knowing the given probability for a rm to ll a vacancy job, p t . Then, the hiring section of the rm post vacancies, V it , on the labor market at the real unit cost, γ, partially externally nanced. The level of Z t , the net recruitment cost of a new worker, is nally derived.

Precisely, the hiring decision of a wholesale rm i is the optimal solution to the following bellman equation:

Ψ it = max ψ it P ws t P t Y ws it -W it N it - Z t P t ψ it + βE t λ t+1 λ t Ψ it+1 subject to n it = (1 -δ)n it-1 + ψ it N it = n it H it (18)
where P ws t is the wholesale-good price and β λ t+1 λ t is the rm's discount factor 10 .

Conditional on {H it } ∞ t=0 and taking as given the set of prices {P t , W it , Z t , P ws t } ∞ t=0 , the human resources department of a wholesale rm chooses rst the number of hirings, ψ it , and consequently the number of employees sought, n it , so as to maximize the rm's discounted value of future prots. An univariate optimization problem can be obtained in n it by embedding both constraints into the problem, since by choosing n it , the human resources department determines implicitly ψ it . So that the following rst-order condition can be derived:

Z t P t = P ws t P t (1 -α)Y ws it n it -W it H it + βE t λ t+1 λ t Ψ n it ,it+1 (19)
Using the envelop theorem, one obtains:

Ψ n it-1 ,it = (1 -δ) Z t P t (20)
By taking equation ( 20) one period forward and plugging it in equation ( 19), the following Euler equation is derived:

Z t P t = P ws t P t (1 -α)Y ws it n it -W it H it + (1 -δ)βE t λ t+1 λ t Z t+1 P t+1 (21)
The expected real total cost of hiring a new worker, Z t , is equal to the real expected net value of a match. The real marginal value of a new hire is the sum of the net real return of a worker, which corresponds to its real marginal productivity net of the real marginal labor cost that is dened as the hourly wage, plus the real value of the continued relationship with the same worker, realized with the probability (1 -δ). Therefore, the hiring decision of wholesale rms is such that the expected prot from maintaining a match with an existing worker is equal to the expected real total cost of hiring a new worker. This expected cost will be now determined explicitly trough the nancial contract establishment.

Optimal nancial contract

A nancial contract is established between a nancial intermediary and an entrepreneur, who needs to pay in advance its production bill and vacancies posting costs. The nancial intermediation is realized through a large number of atomistic risk-neutral banks. Banks are assumed to hold enough large and diversied portfolios to ensure perfect risk pooling for their main creditors, the households, carrying deposits to banks. 11 .

Although we use the same costly state verication framework (CSV) used in Carlstrom and Fuerst (10), Bernanke et al. ( 5) and others, asymmetric information is introduced between wholesale-good producers, called entrepreneurs, and banks. Financial intermediaries and banks are used interchangeably in the model. They are operating in a competitive market, so that only the behavior of a representative bank will be considered below.

Then, by dierence to Carlstrom and Fuerst [START_REF] Carlstrom | Agency costs and business cycles[END_REF], credit contracts are here nominal. These contracts stipulate one-period loans, established after the aggregate shock, A t , has occurred. Indeed, in order to eliminate aggregate uncertainty from the lender-borrower relationship, the aggregate technology shock, A t , is assumed to be observed by all agents in the economy and it is realized before any loan contract is established. On the other hand, an idiosyncratic shock, ω it , is privately observed by the entrepreneur i after the production takes place and it can be veried by the lender only at a monitoring cost, µ t , proportional to the realized value of the rm. Thus, this private information creates a moral hazard problem as the entrepreneur may be encouraged to under-report the true value of its production at the time of loan's repayment.

Finally, under a costly state verication framework, the perfectly competitive nancial intermediaries' setting ensures that each rm-bank pair writes the borrowing contract that maximizes the expected return of the borrower, the entrepreneur, under the constraint that the expected return to the lender, the bank, exceeds its opportunity cost, namely the risk free interest rate, R t . So the optimal incentive-compatible nancial arrangement is just a standard risky debt contract, whose terms are the optimal solution to a standard principle-agent problem between entrepreneurs and banks 12 .

After the wholesale-good production takes place, each entrepreneur observes its idiosyncratic shock, ω it , dened as a productivity and management eciency shock, reecting its management skills, recruitment eciency, hires' quality and input utilization skills. This idiosyncratic shock is the source of wholesale rms' heterogeneity. ω it is i.i.d. with a continuous distribution function, Φ(.), and a density function, φ(.). ω it is dened over a nonnegative support, has a mean of unity and Φ(0) = 0. Moreover, its variance, reecting the shock's volatility and the entrepreneurs' riskiness, is time-varying and its standard deviation, σ ω,t , follows a rst-order auto-regressive process given by:

log(σ ω,t ) = (1 -ρ σ ) log(σ ω ) + ρ σ log(σ ω,t-1 ) + u σ t , ρ σ ∈ (0, 1) where u σ t iid ∼ N (0, σ 2 σ )
σω is the steady-state value of the standard deviation, σ ω,t . A shock on this standard deviation is called in our simulation exercise an uncertainty shock, representative of a variation in the degree of uncertainty concerning the idiosyncratic eciency of entrepreneurs.

To justify the recourse to external funding, entrepreneurs are assumed to pay their real production bill, r K t K it + W it N it , as well as the real vacancy posting costs, γV it , prior to production 13 . But due to idiosyncratic shocks, rms face a default risk on their debt. For low values of ω it , some entrepreneurs may not be able to reimburse their credit. Let B it be the total expected real amount of the production bill, including vacancy posting costs, for a rm i, so that: 12 See Townsend [START_REF] Townsend | Optimal contracts and competitive markets with costly state verication[END_REF] and Gale and Hellwig [START_REF] Gale | Incentive-compatible debt contracts: The one-period problem[END_REF]. 13 Recall that entrepreneurs have a probability to die at each period, 1 -ςt, that ensures that they do not accumulate net worth and have to borrow from banks at each period.

B it = W it N it + r K t K it + γV it
The entrepreneur of each rm borrows a nominal amount of P t (B it -X it ) from the bank at an implicit interest rate, R l t , where X it is its real net worth. The entrepreneur and a representative bank agree on a nancial contract specifying a break-even entrepreneur-specic productivity level, ωit , satisfying R l t P t (B it -X it ) = ωit (P ws t Y ws it + Z t ψ it ). Indeed, if ω it ≥ ωit , the entrepreneur pays back the value ωit (P ws t Y ws it + Z t ψ it ), either the loan amount augmented with interest, R l t P t (B it -X it ).

If ω it < ωit , the rm is insolvent and the bank conscates the proceeds of the production. The bank can observe this state of nature at a monitoring cost µ t ∈ (0, 1), proportional to the realized value of the rm. After the realization of shocks and production occurrence, this rm's value is given by ω it (P ws t Y ws it + Z t ψ it ). The monitoring is non-stochastic and the lender actions are pre-committed.

Formally, the expected return earned by the wholesale rm i, E f it , is given by:

E f it = (P ws t Y ws it + Z t ψ it ) ω>ω it (ω -ωit )φ(ω, σ ω )dω (22)
Using the statistic properties of the random idiosyncratic shock, equation ( 22) can be developed to see that the expected return of the wholesale rm is a fraction of its realized value:

E f it = (P ws t Y ws it + Z t ψ it )f (ω it , σ ω,t ) (23)
where 14 and

f (ω it , σ ω,t ) = ω>ω it ωφ(ω, σ ω )dω -ωit [1 -Φ(ω it , σ ω,t )]. Note that f (ω it , σ ω,t ) ∈ (0, 1)
f (ω it , σ ω,t ) = Φ(ω it , σ ω,t ) -1 ≤ 0.
The wholesale rm's expected return is a decreasing function of ωit . This result is quite intuitive since an increase of the default rate, Φ(ω it , σ ω,t ), reduces the gross share of return going to the rm.

Similarly, the expected return earned by the bank, E b it , is given by:

E b it = (P ws t Y ws it + Z t ψ it ) ω>ω it ωit φ(ω, σ ω )dω + (1 -µ t ) ω<ω it ωφ(ω, σ ω )dω (24)
It is straightforward to show that lender's expected return is also a fraction g(ω it , σ ω,t ) ∈ (0, 1), of the total realized value of the wholesale rm 15 . Then,

E b it = (P ws t Y ws it + Z t ψ it )g(ω it , σ ω,t ) (25)
where g(ω it , σ ω,t ) = 1 -f (ω it , σ ω,t ) -µ t Γ(ω it , σ ω,t ) and Γ(ω it , σ ω,t ) = ω<ω it ωφ(ω, σ ω )dω. So, an amount of the realized rm's value is lost due to monitoring in cases of declaring bankruptcy by the borrower. In this context, the monitoring cost spending is a synonym of bankruptcy and it is spent in terms of currency so that bankruptcy has no impact on the real output. The proportion of the total amount recovered by the bank in case of bankruptcy is nally (1 -µ t )Γ(ω it , σ ω,t ). (1 -µ t ) is thus interpreted as the recovery rate. Following Livdan et al. [START_REF] Livdan | Financially constrained stock returns[END_REF] and Petrosky-Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF], this recovery rate is assumed to be time-varying and to have the following specication:

1 -µ t = s 0,t exp s 1 (ω it -1) (26)
s 1 is the elasticity of the recovery rate to the entrepreneurial productivity level and s 0,t is interpreted as a credit shock, following a rst-order auto-regressive process:

log s 0,t = (1 -ρ s0 ) log s0 + ρ s0 log s 0,t-1 + u s0 t , ρ s0 ∈ (0, 1) where u s0 t iid ∼ N (0, σ 2 s0 )
s0 is the steady-state value of the credit shock, s 0,t .

Finally, the optimal debt contract is a solution to a maximization problem, where the entrepreneur maximizes its expected return subject to the bank's participation constraint (Paustian (36)), knowing the level of n it decided by the human resources department in the previous step. The bank is willing to lend funds only and only if the contract yields an expected return greater or equal to the riskless rate of return, R t : The rst-order conditions for the wholesale rm's problem are summarized by the three following equations:

max K it ,H it ,V it ,ω it [P ws t Y ws it + Z t ψ it ]f (ω it , σ ω,t ) subject to [P ws t Y ws it + Z t ψ it ]g(ω it , σ ω,t ) ≥ R t P t (W it N it + γV it + r K t K it -X it ) ψ it = p t V it N it = n it H it (
Y ws K (K it , H it | n it ) = P t P ws t r K t R t S it (28)
Y ws H (K it , H it | n it ) = P t P ws t n it W it R t S it (29)
Z t P t = γ p t R t S it (30)
where

S it = {1 -µ t [Γ(ω it , σ ω,t ) + ωit h(ω it , σ ω,t )f (ω it , σ ω,t )]} -1
, with h(ω it , σ ω,t ) the hazard rate 16 dened by

h(ω it , σ ω,t ) = φ(ω it , σ ω,t ) 1 -Φ(ω it , σ ω,t )
.

In order to keep the representative-rm context, we assume that the threshold value of the entrepreneurial productivity, ωit , is the same for all wholesale rms. This assumption guarantees a constant capital-labor ratio across rms. At the equilibrium, this is an important assumption since all rms will have the same nancial mark-up, S it , and they will bargain the same wage, W it . Consequently, according to our assumption, the subscript i is dropped in what follows.

From rst-order conditions, asymmetric information in the credit market generates ineciencies in both markets, the wholesale-good market and the labor market. On the one hand, the marginal productivity of labor (and capital) is higher than its corresponding marginal cost without nancial frictions. Then, the nal real price of the wholesale good is augmented by a nancial mark-up, S t > 117 , used to overcome the agency problem between entrepreneurs and banks. As a consequence, credit market conditions matter because they aect rms' marginal costs and are transmitted to the rest of the economy through the selling price's mark-up.

Banks have a margin behavior, that will pass trough the rest of the economy by the wholesale-good price. This framework breaks down the Modigliani-Miller theorem and makes the rms' external borrowing costs higher than internal funds opportunity costs. Indeed, rms must borrow at a premium over the risk-free rate.

Aggregating over entrepreneurs and embedding equations ( 28)- [START_REF] Kydland | Time to build and aggregate uctuations[END_REF] in the lender's break even constraint, the rms' leverage ratio, L t , is given by:

L t ≡ B t X t = 1 1 -S t (ω t , σ ω,t )g(ω t , σ ω,t ) (31)
with L ω > 0. For a given level of net worth X t , a higher leverage ratio is associated with a higher default rate.

Indeed, the probability of default increases as the loan amount raises (Stiglitz and Weiss ( 43)).

It is straightforward to show that, at the optimum, the constraint (27) is binding. Using this result with the condition on ωt , the risk premium, ∆ t , dened as the ratio of the lending rate to the risk free rate, R l t /R t , is given by:

∆ t = ωt g(ω t , σ ω,t ) (32)
Figure 5 shows the evolution of the risk premium as a convex increasing function of the entrepreneurial productivity threshold, ω. This result is quite familiar in the nancial accelerator literature. A higher default probability of rms induces a higher cost of lending for banks and consequently, a higher loan spread.

On the other hand, from equation 30, the cost of a new hire, Z t , depends also on the nancial contract conditions. Besides the unit cost stemming from hiring, γ, and the average duration of vacancies, 1/p t , the total cost of recruitment is augmented by the same nancial mark-up, S t . Financial contract conditions aect the labor market eciency through the total vacancies posting cost, that becomes here an endogenous variable.

This relation is represented by gure 6, where the real job posting cost is also an increasing and convex function of ω and its slope raises with monitoring costs, µ. For a higher default likelihood (higher ω), banks charge a higher risk premium, ∆, so that entrepreneurs obtain their credit at a higher lending rate, R l . External Then, an increase of µ shifts the real vacancies posting cost upward. For a xed level of ω, the real cost of a new hire raises with monitoring costs. As these costs are expressed in terms of currency, and not in terms of physical goods, they do not generate a loss of resources through a destruction of goods, which could have been used for consumption. However, they generate an additional cost taken into account by banks when agreeing on an appropriate interest rate on loans. Fluctuations in monitoring costs and bankruptcy rates have an impact on welfare only indirectly, through their implications on the mark-up pricing. Now, by making use of the optimal nancial contract conditions derived below and the hiring condition given by equation ( 21), the job creation condition under nancial frictions in the credit market is obtained:

γ p t R t S t = W t H t [R t S t -1] + (1 -δ t )βE t λ t+1 λ t γ p t+1 R t+1 S t+1 (33)
For any positive monitoring cost, nancial frictions increase as expected the average cost of lling a vacancy.

The evolution of credit market conditions changes the opportunity cost for resources used to create new jobs.

Thus, it alters the dynamics of job vacancies. Credit spreads are a key element to understand the cyclical behavior of job creation and the general dynamics of labor markets. Thus, agency problems on credit markets aect the performance of labor markets.

Wage bargaining

Once entrepreneurs decided the number of new workers they need and once they obtained a loan covering their production bill, as well as vacancies costs, they enter the labor market to post vacancies, match with unemployed workers and bargain on wages. The real hourly wage, W t , is assumed to be determined on a period-by-period basis and through a Nash bargaining between a representative entrepreneur and a representative household.

Bellman equations

The Nash real hourly wage splits by denition the joint surplus of the employment relationship between a representative entrepreneur and a representative household, depending on their respective bargaining power, η.

The discounted value of employment for a worker in terms of current consumption is given by:

W n t = W t H t - H 1+τ t (1 + τ )λ t + βE t λ t+1 λ t 1 -δ(1 -q t+1 ) W n t+1 + δ(1 -q t+1 )W U t+1 (34)
The discounted value of a job for a worker in terms of current consumption is the sum of the total real wage earned, reduced for the marginal disutility of working and the expected discounted gain from being either employed or unemployed during the subsequent period. A worker will be again employed at the period t + 1 if the match has not been destroyed, with a probability (1 -δ), after the matching of the period t ; or if the match has been destroyed with the probability δ after the matching of the period t, but that another matching occurs at the period t + 1 with the probability q t+1 . And a worker will become unemployed at the period t + 1 if the match is destroyed after the matching of the period t and if he or she does not nd a job at the period t + 1, that to say with the probability δ(1 -q t+1 ).

The discounted value of unemployment for a worker in terms of current consumption is given by:

W U t = b + βE t λ t+1 λ t q t+1 W n t+1 + (1 -q t+1 )W U t+1 (35)
In the same spirit, the discounted value to be unemployed for a worker in terms of current consumption is the sum of real unemployment benets and the expected discounted gain from being either employed (with probability q t+1 ) or unemployed (with probability 1 -q t+1 ) after the matching of the period t + 1.

Therefore, the worker's surplus of an employment relationship is given by:

W n t -W U t = W t H t - H 1+τ t (1 + τ )λ t -b + βE t λ t+1 λ t (1 -δ)(1 -q t+1 )(W n t+1 -W U t+1 ) (36)
For a rm, the discounted value of an employed worker in terms of current consumption is dened as:

J n t = P ws t P t (1 -α)Y ws t n t -W t H t + βE t λ t+1 λ t (1 -δ)J n t+1 (37)
This discounted value is equal to the current prots from an employed worker, plus the expected discounted continuation value. The job is still provided at the period t + 1 if the match has not been destroyed with a probability (1 -δ) after the matching of the period t. And if the job is not provided at the period t + 1, the continuation value will be equal to zero.

Then, the discounted value of an open vacant job for a rm in terms of current consumption is given by:

J V t = - Z t P t + βE t λ t+1 λ t p t+1 J n t+1 + (1 -p t+1 )J V t+1 ( 38
)
The discounted value of an open vacancy job for a rm in terms of current consumption is equal to the real total hiring costs of the vacancy job, plus the expected discounted gain to ll or not the vacant job during the following period. The vacancy job is lled at the period t + 1 with a probability p t+1 , if a match occurs during the matching of the period. Otherwise, with a probability (1-p t+1 ), the job remains vacant in t+1.

Nash bargaining and wage setting

The Nash wage bargaining consists of maximizing the net surplus of the employment relationship for a representative rm, (J n t -J V t ), and a representative household, (W n t -W U t ), depending on the households' bargaining power, η. As a consequence, the chosen real hourly wage is the one that maximizes 18 :

max Wt (W n t -W U t ) η (J n t -J V t ) (1-η)
Since there is a free-entry condition on the labor market, at the equilibrium, J V t = 0 is satised. Indeed, if J V t > 0, a rm has an incentive to post vacancies as the value of a vacant job is positive. As the number of vacancies increases relative to the number of unemployed workers, the probability to ll a vacancy job, p t , decreases. Indeed, the labor market tightness, θ t , increases and p t decreases since ∂p t /∂θ t < 0. That reduces the incentive to post vacancies and diminishes the value of J V t , until it equals zero. Therefore, the rst-order necessary condition for the Nash bargaining solution is given by:

ηJ n t = (1 -η)(W n t -W U t ) (39)
The following Nash real hourly wage is then obtained:

W t H t = η P ws t P t (1 -α)Y ws t n t + (1 -δ) Z t P t E t (θ t+1 ) + (1 -η) b + H 1+τ t (1 + τ )λ t (40)
The real wage shares costs and benets from the match between households and entrepreneurs according to the parameter η. Workers are compensated for a fraction (1 -η) for the disutility they suer from supplying hours of work and for the foregone unemployment benets. And they obtain a fraction η of the rm's revenues, as well as a fraction η of the rm's saving of total hiring costs, depending on the probability that the match will not be destroyed exogenously until the end of the period t and the expected labor market tightness of period t + 1. If the matching is broken, entrepreneurs have to look for another partner in the next period, which is costly. This cost is thus incorporated in the wage. Final goods are produced using a standard constant return to scale technology given by:

Y t = 1 0 Y -1 j,t dj -1 (41)
where > 1 is a parameter governing the degree of monopolistic competition in the intermediate good sector

(or the elasticity of substitution between intermediate goods).

Each competitive nal-good rms choose their own input demand functions for each variety of intermediate goods, Y j,t , so as to maximize their nominal prot, Π t , dened as: Then, as we are in a competitive setting, the zero-prot condition applies at the equilibrium for nal-good rms and it yields:

Π t = P t Y t - 1 0 P j,t Y j,
P t Y t = 1 j=0 P j,t Y j,t dj
From this condition, the nominal output price or the consumer's price index can be easily derived by plugging the demand function into the zero-prot condition:

P t Y t = 1 j=0 P j,t P j,t P t - Y t dj
which gives:

P t = 1 j=0 P (1-) j,t dj 1 1- (43)
Looking now to the intermediate-good sector, there is a continuum of monopolistically competitive retailers.

These retailers are owned by households. They buy from entrepreneurs homogeneous wholesale goods at the price P ws t . They dierentiate costessly each unit of these goods into a unit of retail goods, Y j,t . These rms are assumed to have no other inputs or costs than the homogeneous good. Following Yun (49), Christiano et al. [START_REF] Christiano | Nominal rigidities and the dynamic eects of a shock to monetary policy[END_REF] and Trigari [START_REF] Trigari | Equilibrium unemployment, job ows, and ination dynamics[END_REF], a price stickiness for these rms is formulated in the spirit of Calvo [START_REF] Calvo | Staggered prices in a utility-maximizing framework[END_REF]. Every period, only a random fraction (1 -) ∈ (0, 1) of rms is able to fully re-optimize their nominal prices knowing the aggregate shock, A t . The hazard rate, , is constant across rms and time. And prices are thus xed on average for 1 1periods. The remaining fraction of rms does not re-optimize their prices and following Christiano et al. [START_REF] Christiano | Unemployment and business cycles[END_REF], they keep their prices unchanged. So the price set by a retailer j, P j,t , corresponds to:

P j,t =     
P j,t-1 with probability

P * t with probability 1 - (44)
where P * t is the optimal price set by the fraction of retailers who are able to re-optimize their prices at time t. Note that P * t does not depend on j because all rms that can re-optimize their prices at time t choose the same price as they are assumed to be symmetric. Then, for rms not able to re-optimize their prices, there is no price indexation to replicate the observation that many prices can remain unchanged over time ((author?) (Eichenbaum and Rebelo) and (author?) (Klenow and Malin)). So, the price index, P t , is thus given by:

P t = 1 0 P 1- j,t dj 1 1-= (1 -) P * t 1-+ P t-1 1- 1 1- (45)
The price index is a CES aggregate of all retail goods' prices in the economy at period t. The sum in equation [START_REF] Townsend | Optimal contracts and competitive markets with costly state verication[END_REF] can then be transformed into a convex combination of two prices because rms of each type are assumed to be respectively symmetric. A costless price regulation mechanism is assumed, which guarantees that a consumer pays the same price whatever the rm at which she or he realizes his purchases 20 . So, the price index corresponds to a weighted average price of the fraction of rms who can re-optimize their prices after the aggregate shock, A t , and the fraction (1 -) of rms who can not.

Firms that can re-optimize their price, maximize the expected discounted value of their prots given the demand for the good they produce, since rms expect to keep this price for more than the current period. They take into account that the price may be xed for many periods. If the expected probability of price stickiness is high, rms able to re-optimize their price at the period t will be relatively more concerned about the future when they make their current pricing decisions.

Thus, these rms face the following problem, subject to the total demand (42) it faces: Note that is integrated in the discount rate because there is a probability s that the price chosen is still applied in s periods time.

max P j,t E t ∞ s=0 ( β)
The rst-order condition of the problem is given by:

E t ∞ s=0 ( β) s λ t+s λ t P ( -1)
t+s Y t+s P ws t+s P * (--1) + (1 -)P * (-) t = 0

The optimal price, P * t , sets by rms who are able to re-optimize their prices is thus given by:

P * t = -1 E t ∞ s=0 ( β) s λ t+s λt P ws t+s P t+s Y t+s E t ∞ s=0 ( β) s λ t+s λt P -1 t+s Y t+s (46)
These rms set their price such that it equals the present discounted value of marginal costs. The optimal price is a mark-up over a weighted average of future marginal costs. The size of the mark-up depends negatively on the degree of monopolistic competition in the intermediate good sector, . If there is no price-stickiness, = 0, 20 The matching of consumers and rms is ignored.

the monopoly standard mark-up formula is derived:

P * t = -1 P ws t+s , where -1 > 1 (47)
The nal-good market clearing condition implies that nal goods, Y t , may be consumed by households, C t , and entrepreneurs, C e t , or be used as investment, I t , as government expenditures, G t , or as capital utilization costs,

Υ(ν t )K p t-1 .
The following aggregate resource constraint is thus obtained:

Y t = C t + C e t + I t + G t + Υ(ν t )K p t-1 (48)

Entrepreneurs

Entrepreneurs own wholesale-good rms. At the beginning of period t, they borrow from banks to cover hiring costs, wage bill and renting capital because they have to pay them prior to the production. Then, after receiving the amount borrowed from the bank, they rent and pay immediately capital from households on a perfectly competitive capital market. At the same time, vacancies are posted and matches take place with workers. Entrepreneurs pay also immediately vacancies costs and wages of workers hired and of workers already hired in previous periods. Finally, after the wholesale-good sale, some entrepreneurs will be declared solvent or bankrupt, depending on their production and idiosyncratic shock levels. Entrepreneurs declared bankrupt are not able to reimburse their entire loan. The bank will conscate the proceeds of the production. As a consequence, bankrupted entrepreneurs will not consume, nor accumulate net-worth. But at the beginning of the next period t + 1, entrepreneurs are assumed to receive an exogenous endowment, W e , which will be used as collateral or net worth to borrow from banks at the beginning of the next period, in order to be sure that this kind of agents, specialized in managing production, will be able to continue their activities. Entrepreneurs declared solvent reimburse their entire loan to banks. Then, they have to wait the production of the nal good to consume or accumulate a net worth. To ensure that entrepreneurs do not accumulate net worth, such that they could be able to self-nance their production at the next period, we assume that each entrepreneur has a constant probability, 1 -ς t , to die at the end of the period. It will limit the size of aggregate net worth in an innite horizon set up. Indeed, since the rate of return on internal funds is higher than the one of external funds, due to asymmetric information on credit markets, risk neutral entrepreneurs may be willing to postpone consumption and would only accumulate funds.

So solvent entrepreneurs who exit the economy at the end of the period will consume all their net worth. Thus, the aggregate entrepreneurial consumption, C e t , is given by:

C e t = (1 -ς t ) P ws t P t Y ws t f (ω t ) (49)
To be sure however to have a constant fraction of entrepreneurs in the economy in every period, we assume that the birth of rate of entrepreneurs at the beginning of each period ensures this constant fraction.

Solvent entrepreneurs who do not exit the economy at the end of the period will keep accumulating net worth using their realized returns. Consequently, the evolution of the aggregate entrepreneurial real net worth is:

X t+1 = W e + ς t P ws t P t Y ws t f (ω t ) (50)
ς t is interpreted as a shock to entrepreneurs' net worth. It evolves according to:

ς t = ς ς t (51) log( ς t ) = ρ ς log( ς t-1 ) + u ς t , ρ δ ∈ (0, 1) where u ς t iid ∼ N (0, σ 2 ς )
where ς is the steady state value of the shock to entrepreneurs' net worth, ς t .

Monetary and scal policy Monetary policy

The monetary policy is decided and carried out by the central bank following an interest rate Taylortype rule 21 . The nominal interest rate of each period will be set depending on deviations in output, ination and nominal interest rate from their steady-state levels:

R t+1 R = R t R ρr π t π ρπ Y t Ȳ ρ Y 1-ρr (52)
where ρ R is the degree of interest rate smoothing, ρ Y and ρ π are the response coecients to output and ination variables and variables without a time subscript are steady state values. R t+1 is the interest rate decided today by the government, that will pay o in period t + 1. So this interest rate is known at time t. Then, knowing this nominal interest rate, the government adjusts the money supply so as to achieve the equilibrium in the money market.

Fiscal policy

The scal policy is decided and carried out by the government at the end of the period t. After the nal-good production, households pay nominal lump-sum taxes, T t , to the government. Then, we assume that the government earns mainly revenue through printing of real money. Basically, the central bank returns this revenue back to the scal authority. With these taxes and seignoriage revenue, M t+1 -Mt Pt , the government nance the real exogenous government spending, G t , and the amount of real unemployment benets, (1 -n t )b, for unemployed workers. The level of the unemployed is known by the government at the end of the matching process on the labor market.

So the government budget constraint is the following:

G t + (1 -n t )b = T t P t + M t+1 -M t P t (53)
where G t is the exogenous government spending.

Model simulation

This section demonstrates how both nancial and labor market frictions aect the response of unemployment and vacancies to shocks originating in the credit market.

First a positive shock on the net worth of entrepreneurs is considered. We next represent a positive shock on credit conditions, through an increase in monitoring costs. Finally, we consider a positive uncertainty shock on the idiosyncratic eciency's standard deviation of wholesale rms, inducing that it is more risky for banks to lend to wholesale rms.

Data

Quarterly US data are used for the sample period 1960:Q1 through 2007:Q4. Output is dened as the real gross domestic product; consumption as the real personal consumption expenditures; the nominal interest rate is dened as quarterly averages of Federal Funds rate; ination is dened as the growth rate of the GDP deator; unemployment and employment are dened as the civilian unemployment and employment rate (as a percentage of the civilian labor force); real wages are dened as the nonfarm business sector real compensation per hour and hours worked per employee are nonfarm business sector average weekly hours worked per employee. Investment is dened as the real private xed investment. Vacancy job data are obtained from the Help Wanted OnLine (HWOL) dataset provided by the Conference Board (TCB). They are used by Sahin et al. [START_REF] Sahin | Mismatch unemployment[END_REF]. This data covers online advertised vacancies posted on internet job board in newspapers online editions.

More precisely, it is the number of new, rst-time online jobs and jobs reposted from the previous month for over 16,000 Internet job boards, corporate boards and smaller job sites. This data set is constructed to avoid double-counting (a same ad can appear on multiple job boards), by using an unduplication algorithm that identies unique advertised vacancies on the basis of a combination of company name, job title, city or state 22 . Finally, government expenditures are dened as the real government consumption expenditures and gross investment 23 .

The data are demeaned, seasonally adjusted when necessary and the output, consumption, investment and government expenditures series are expressed in per capita terms, in the sense of the labor force as in Smets and Wouters [START_REF] Smets | An estimated dynamic stochastic general equilibrium model of the euro area[END_REF].

Our simulation period ends in 2007:Q4 as justied by Galí et al. (20) in order to prevent our simulation from being disturbed by nonlinearities induced by the lower bound on the Federal Funds rate and binding downward nominal wage rigidity during the Great Recession.

Calibration

Parameter values are chosen to be consistent with those standard in literature and especially with estimated new-Keynesian models. The household discount factor, β, is set to 0.99 implying an annual real interest rate of 4 %. The capital depreciation rate, δ K , is xed to 0.025 corresponding to an average annual depreciation rate of 10 per cent. For the wholesale-good sector, the capital share in output, α, is standard at 0.36. This value is based on calculation of Kydland and Prescott (30) using US time series data.

The elasticity of matches to unemployment, ρ, is set to 0.72 as in Shimer [START_REF] Shimer | The consequences of rigid wages in search models[END_REF] and Petrosky-Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF]. This value is almost within the range of values of 0.5 to 0.7 reported by Petrongolo and Pissarides [START_REF] Petrongolo | Looking into the black box: A survey of the matching function[END_REF] in their survey of the literature on the estimation of matching function 24 . The conventional value, 0.5, is given to the 22 Like The Conference Board's long-running Help Wanted Advertising Index of print ads (which was published for over 55 years and discontinued in July 2008), the HWOL series measures help wanted advertising, i.e. labor demand. The HWOL data series began in May 2005. It replaces the Help-Wanted Advertising Index of print advertising maintained by the TCB (the Conference Board surveys help-wanted print advertising volume in 51 major newspapers across the country every month, until 2008). Since the online ads are a direct indication of hiring intent by employers, the ads serve as a measure of labor demand. For more detailed information and comments on survey coverage, concepts, denitions and methodology, see the Technical Notes at https://www.conferenceboard.org/data/helpwantedonline.cfm. 23 More details about data used are available in Appendix 5. 24 Others values are used such as 0.4 in Blanchard and Diamond [START_REF] Blanchard | The Beveridge Curve[END_REF], Merz (33), Andolfatto (2) and Mortensen and Nagypal (34) or 0.5 in Gertler et al. [START_REF] Gertler | An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining[END_REF].

bargaining power, η, as in [START_REF] Gertler | An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining[END_REF]. The vacancy posting cost, γ, is set to 0.14, and the destruction rate parameter, δ, is set to 0.08. It is compatible with those used in the literature which range from 0.07 in Merz [START_REF] Merz | Search in the labor market and the real business cycle[END_REF] to 0.15 in Andolfatto [START_REF] Andolfatto | Business cycles and labor-market search[END_REF]. The unemployment benets, b, is equal to 0.71 also as in Petrosky-Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF].

The inverse of the elasticity of worked hours to real hourly wage (or the Frish elasticity), τ , is equal to 10 as in Trigari (46), who has extensive and intensive margin in her paper. The external habit persistence parameter, h, is xed to 0.5 as in Gertler et al. [START_REF] Gertler | An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining[END_REF].

For the intermediate-good sector, the monopolistic mark-up or the elasticity of substitution across inputs, , is xed to 11 to have a conventional price-mark-up on marginal costs at 10 % as in Walsh [START_REF] Walsh | Labor market search, sticky prices, and interest rate policies[END_REF] and Trigari [START_REF] Trigari | Equilibrium unemployment, job ows, and ination dynamics[END_REF]. The Calvo stickiness of prices, , is set to 0.66 as in Gertler et al. [START_REF] Gertler | An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining[END_REF]. The steady state entrepreneurial survival rate, ς, is equal to 0.9728 in line with Bernanke and Gertler (4) and Zanetti and Mumtaz [START_REF] Zanetti | The eect of labor and nancial frictions on aggregate uctuations[END_REF]. The gross external nance premium, s 1 , is set to 4.97307139522323, and the steady state value of credit shock, s0 , is set to 7.3678.

For the Taylor rule, conventional value are also taken. The interest rate smoothing coecient, ρ R , is set to 0.75. Coecients for the responses of interest rate to ination, ρ π and to the output gap are xed respectively to 1.7 and 0.125 as in Gertler et al. [START_REF] Gertler | An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining[END_REF].

Results

Our simulation exercise is a Taylor approximation around the steady state of order one.

Net worth shock

Let us assume that there is an expansionary shock to the entrepreneurs net worth. According to our model, it means a positive increase in ς t . The aggregate real net worth is increasing as the probability of dying for each entrepreneur is decreasing. A positive net worth shock induces that all entrepreneurs will carry on to the next period t + 1 a higher real amount of net worth. Recall that in our model, surviving solvent entrepreneurs carry their prots as a part of their net worth. And entrepreneurs, based on their net worth amount and their expected production and returns, borrow funds from banks to post vacancies, to pay capital spending and the wage bill in advance. So the net worth is a mean for entrepreneurs to lower their use of external nancing.

Figure 7 shows impulse responses to a positive net worth shock. According to our simulation exercise, rstly, an increase in the aggregate real net worth has a positive eect on the nancial sphere. By a positive eect, we mean that it decreases the nancial mark-up, highlighting a nancial accelerator mechanism. The higher is the level of the aggregate real net worth, the lower is the nancial markup charged by banks to entrepreneurs, as found by Zanetti and Mumtaz [START_REF] Zanetti | The eect of labor and nancial frictions on aggregate uctuations[END_REF]. As a consequence of the real aggregate net worth increase and of the nancial mark-up decrease, the default rate is also decreasing. This decrease induces an increase in the gross share of returns going to the rm according to our model.

These results on the nancial sphere will impact the real sphere of the economy, especially the labor market.

An increase in the aggregate real net worth of entrepreneurs leads to a decrease in the unemployment rate, following a negative hump-shaped, thanks to an easing in their nancing costs. Indeed, entrepreneurs are now able to nance by themselves a higher part of their production and vacancies costs, and for the part nanced by loans, the nancial mark-up charged by banks is reduced. So the aggregate real wholesale rm's marginal costs are reduced according to our model. This reduction induces entrepreneurs to post more vacancies, and the unemployment rate decreases as a consequence, as found in the estimation of Zanetti and Mumtaz (50).

The job nding rate for workers increases as expected and the labor market tightness from the rm point of view decreases.

More precisely, a substitution eect between hours worked per employee and the amount of employed workers appears for the labor market in our simulation, as in the estimation of Christiano et al. (14). This phenomenon highlights the interaction between intensive and extensive margins on labor markets. As a consequence of the easing of nancing costs, entrepreneurs are willing to hire more workers, but they decrease their demand for hours worked per employee. This fact is also observed in data in the sense that extensive margin is more reactive than the intensive margins when the economy is hit by a shock.

Furthermore, the link from the nancial market to the labor market goes through wages. An easing in nancial real marginal costs is pass through prices according to our model, leading to a lower ination rate as observed in the simulation exercise. These two facts contribute to an increase of the real wage in the economy. However, these results are not found in the estimation of Zanetti and Mumtaz [START_REF] Zanetti | The eect of labor and nancial frictions on aggregate uctuations[END_REF]. It could be linked to the fact they integrate only the capital stock as the production cost to be paid in advance.

Obviously, the previous results on the nancial sphere have also an impact on goods market. An increase in the net worth of entrepreneurs generates a positive hump-shaped in consumption, through according to our model, the higher wages, more vacancies posted and less unemployment. The net worth positive shock induces also a positive hump-shaped, larger than the one for consumption, in investment. This increase in investment can be explained by our model as the consequence of more employed workers and higher wages for households that are able to invest more, and through a higher demand for capital expressed by entrepreneurs, as net worth and nancial mark-up decrease (Zanetti and Mumtaz ( 50)). The conjunction of higher consumption and higher investment leads to an increase of output, after a rst decrease, possibly due to the existence of investment adjustment costs and higher wages.

So the economy is better o, at least in terms of consumption and employment, when all rms are able at the aggregate level to self-nance a higher part of their production and vacancies costs. Financial frictions are indeed less at stake as a consequence, through a decrease in the amount of loans demanded by rms and a decrease in the level of marginal costs, realized by a lower nancial mark-up. The most important impact appears to be on the labor market, where vacancies increase and unemployment rate decreases, as expected by our model.

Credit shock

A positive credit shock is realized in the economy through a decrease in the monitoring costs, µ t . More precisely, the recovery rate dened in our model following Livdan et al. [START_REF] Livdan | Financially constrained stock returns[END_REF] and Petrosky-Nadeau and Wasmer [START_REF] Petrosky-Nadeau | Macroeconomic dynamics in a model of goods, labor and credit market frictions[END_REF] increases (so the monitoring cost decreases), by an increase of s 0,t , interpreted as a credit shock. Recall that in our model monitoring costs appear because wholesale-good production is subject to an idiosyncratic shock, observed privately by entrepreneurs. Thus, banks have to pay a monitoring cost for bankrupt entrepreneurs to check the real output produced and the eciency of the recruitment process. This monitoring cost is assumed to be proportional to the realized rm's value. Furthermore, it is spent in terms of currency.

Figure 8 shows impulse responses to a positive credit shock. As for the net worth shock, a positive credit shock has an impact on the nancial sphere. A decrease of the monitoring cost leads to a reduction of the default rate. It was strongly expected as in our model, the monitoring cost spending is a direct synonym of bankruptcy.

The lower are the monitoring costs, the lower is the default rate according to our framework. Then, the positive credit shock leads to a reduction of the nancial mark-up charged by banks to entrepreneurs. It could be easily explained through our model by the expression of the nancial mark-up, S t , that depends negatively on the recovery rate. A positive credit shock means that the recovery rate for banks increases. The proportion of the real amount recovered by banks is higher. So banks do not need to charged, everything else equal, the same amount of nancial mark-up to entrepreneurs. For the real part of the economy, following our model, the agency problem between banks and entrepreneurs alter the real recruitment cost and the marginal cost of production for wholesale rms. We observe in our simulation exercise that it is the case: a positive credit shock induces an increase of vacancies and a decrease of unemployment, following a negative hump-shaped with a peak at one year and half. Petrosky-Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF] nds in the same spirit following a negative credit shock a positive hump-shaped for unemployment with a peak just over a year after the shock, that is considered as comparable to the research of Jermann and Quadrini ( 25), but with a specic insight into the labor market. Eckstein et al. (16) identify also this impact, through a called ow prot and vacancy cost channels. So, lower marginal costs, thanks to lower nancial mark up, induce rms to recruit more, to post more vacancies. The labor market tightness from the rm point of view increases, and the job nding rate for households increases as a consequence, as in Petrosky-Nadeau [START_REF] Petrosky-Nadeau | Credit, vacancies and unemployment uctuations[END_REF]. In our model, we nd as well that the slope of the real posting cost raises with the monitoring costs. The real cost of a new hire raises with monitoring costs, everything else equal.

The substitution eect between hours worked per employee and number of employed workers does not appear here after a positive credit shock. On the contrary, a complementary eect is observed: employed workers are more, and each of them are working more. That is a rst reason why we could observe a positive impact on the output compared to the previous case.

Concerning the output, in the model, we assume that the monitoring cost spending, synonym of bankruptcy is spent in terms of currency, and not in terms of physical goods. Bankruptcy has no direct impact on the real output. However, the simulation shows a clear indirect impact on output. Indeed, monitoring costs are additional costs taken into account by banks when agreeing on an appropriate interest rate on loans. A reduction in monitoring costs and bankruptcy rates has an impact on welfare indirectly, through their implications on the mark-up pricing. The simulation illustrates this phenomenon: the decrease in monitoring costs reduce real marginal costs of rms, reducing the level of ination in the economy, as well as the level of nominal interest rate.

It generates an increase in consumption and investment that in turns increase the output level. Then, a slow decrease in the level of the real wages can be observed probably as the consequence of the ination rate decrease.

Finally, the entrepreneurial consumption and the aggregate real net worth increase as a consequence of the reduction of the monitoring cost, and of marginal costs. Solvent dying and not dying entrepreneurs have indeed a larger share of the net output to consume and to save to the next period.

Thus, a positive credit shock pushes down marginal costs and prices, as well as hiring costs by a nancial markup, depending on the level of monitoring cost. A reduction of monitoring costs in an economy has a strong impact on the vacancies and employment levels, as expected in our model.

Uncertainty shock

An uncertainty shock is dened as a variation in the variance of the idiosyncratic shock concerning entrepreneur's eciency. According to our model, this variance reects the degree of entrepreneurs' riskiness for banks. As a consequence, banks are facing a higher risk when they decide to lend to entrepreneurs. Recall that in our model, banks do not observe rm's idiosyncratic shocks, but they only know the cumulative and density functions of these idiosyncratic shocks. Figure 9 shows impulse responses to a positive uncertainty shock. As expected, after an increase in the level of uncertainty for banks about the idiosyncratic shock of rms, banks charge a higher nancial mark-up to protect them against the asymmetric information. The default rate increases in quite huge proportion, due to the increase of uncertainty in the economy, and due to the increase in the nancial mark-up that increases rm's real marginal costs. On the real side, a higher uncertainty decreases employment, output, consumption and investment. As a consequence, labor market tightness from the workers' point of view increases. Indeed, rms are posting fewer vacancies. The reason is linked to the increase of the nancial mark-up. After an increase in the level of uncertainty, according to our model, the increase of the nancial mark-up is passing through real marginal costs and prices in the economy. Firms are induced to post fewer vacancies, to hire fewer workers because of this increase in nancing costs. Furthermore, ination increases, as well as the nominal interest rate. Intensive and extensive margins appear here to move in the same direction. Hours worked per employee decrease also. So, fewer workers are employed in the economy and each employed workers are working less. According to our model, it could explain why consumption and investment are going down. Households have a less amount of resources to invest and the demand for capital by rms decreases, due to the increase of the nancial mark-up. Thus, the economy reaches a negative position after an increase in the uncertainty concerning the idiosyncratic shock of wholesale rms. Facing higher risks, banks need, to overcome the agency problem they face with entrepreneurs, to increase the nancial mark-up that they charge to them. The real marginal nancing costs of entrepreneurs increase. It reduces as a consequence the value of a new hire, and leads to lower vacancies. The unemployment goes down. Furthermore, the higher marginal costs are passed through prices to the rest of the economy, leading to higher ination, less consumption, and less output.

By moving three dimensions involving dierent degrees of nancial frictions, we observe through our simulation exercise a clear impact from the nancial market to the labor market. Increasing asymmetric information in nancial markets (through higher monitoring costs, higher uncertainty or lower entrepreneurial net worth) leads clearly to higher unemployment in the economy, through dierent channels. These channels converge all to the role of the nancial mark-up that is charged by banks to overcome agency problems. This nancial mark-up is pass through the rest of the economy by higher marginal costs, and higher ination. That in turn reduces the levels of vacancies posting, employment, wages and consumption, and nally, the level of output. The evolution of credit market conditions changes the opportunity cost for resources used to create new jobs. Thus, it alters the dynamics of job vacancies and unemployment. For our three shocks, the unemployment jumps up or goes down to its highest level in the rst period and then slowly converges back to its steady state level.

Conclusion

We construct a new-Keynesien DSGE model integrating sticky prices, nancial frictions on the credit market and asymmetric information on the labor market. We nd that credit market frictions may be the source of lower posting vacancies and higher unemployment level. Asymmetric information pushes up wholesale rms'

By making the change of variables, we get x 1,t and x 2,t dened by:

x 1,t = ln(ω t ) + 0. • Derivatives computation 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Quarters 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Quarters 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Quarters 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Quarters 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Quarters 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Quarters 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 1960 1963 1966 1969 1972 1975 1978 1981 1984 1987 1990 1993 1996 1999 2002 2005 2008 Quarters 1960196319661969197219751978[START_REF] Stiglitz | Credit rationing in markets with imperfect information[END_REF]1984198719901993199619992002[START_REF] Walsh | Labor market search, sticky prices, and interest rate policies[END_REF]2008 Quarters Quarters

Log H Log W V 1 0 -1 - 2

Figure 1 :

 1 Figure 1: Unemployment, Baa-Aaa Spread and Default Rate between 1970-Q1 and 2007-Q4 for the United-States

Figure 2 :

 2 Figure 2: Labor-market tightness and Baa-Aaa Spread between 1970-Q1 and 2007-Q4 for the United-States

  and matching frictions in labor markets, based on Mortensen and Pissarides (35) framework, in RBC models or in NK models (Merz (33), Andolfatto (2), Walsh (47), Krause et al. (28), Gertler and Trigari (24), Thomas and Zanetti (44), Trigari (46), Christoel et al. (15), Lechthaler et al. (31), Blanchard and Galí (6), Galí et al. (20), Campolmi and Faia (9), Christiano et al. (13)).

  absorb much of the change in the expected benet to a new worker induced by uctuations in labor productivity. As a consequence, several papers try to tackle this issue by introducing wage rigidity mechanisms(Shimer (41),Gertler and Trigari (24) and Christiano et al. (13)) or hiring and ring costs. Firstly, Blanchard and Galí[START_REF] Blanchard | Labor markets and monetary policy: A new keynesian model with unemployment[END_REF] nd that while search and matching frictions modify the level of unemployment but the unemployment rate stays invariant to productivity shocks. Thus, they study alternative wage-setting (Nash bargaining wage and more rigid real wages) and show that rigid wages enable to have inecient uctuations in unemployment after a productivity shock. Lechthaler et al.[START_REF] Lechthaler | Monetary persistence and the labor market: A new perspective[END_REF] introduce in a new-Keynesian model labor market frictions, through hiring and ring costs but no wage rigidity. They nd trough a calibration on a given European country, more persistence in output and unemployment in response to real and monetary policy shocks and in ination in response to real shocks, as well as a strong amplication eect of these shocks on unemployment and on the job nding rate. Gertler and Trigari[START_REF] Gertler | Unemployment uctuations with staggered nash wage bargaining[END_REF] reproduce by calibration, in a standard Mortensen-Pissarides search and matching framework with a staggered multiperiod Nash wage, the relative volatile behavior of unemployment and the relative smooth behavior of real wages over the business cycle as observed in data.On the other hand, frictions have been also studied on the credit market side (Bernanke and Gertler (3), Bernanke and Gertler (4), Carlstrom and Fuerst (10), Kiyotaki and Moore (26), Bernanke et al. (5), Carlstrom and Fuerst (11), Gertler et al. (22) and Fiore and Tristani (18)). They have been devoted to understand the relationship between nancial markets and overall macroeconomic performances. Financial factors are indeed suspected to amplify and increase persistence of macroeconomic variables responses to aggregate shocks. The idea behind is that deteriorating credit conditions could be the source of poor economic activity and not the consequence of a declining real economy. Bernanke and Gertler (3), ? ), Kiyotaki and Moore (26) and Bernanke et al. (5) develop the concept of a nancial accelerator in DSGE models integrating money and price stickiness. Without credit frictions, an entrepreneur

Figure 3 :P o s t in g v a c a n c ie s Figure 4 :

 34 Figure 3: Timing of events

27) 15 Since 1 -

 151 f (ω, σω) ∈ (0, 1) and by denition, we have ω< ωit ωφ(ω, σω)dω ∈ (0, 1) and ω> ωit ωitφ(ω, σω)dω + ω< ωit ωφ(ω, σω)dω ∈ (0, 1), then g(ω, σω) ∈ (0, 1), lim ω→0 g(ω, σω) = 0 and lim ω→∞ g(ω, σω) = 1 -µ.

Figure 5 :Figure 6 :

 56 Figure 5: The risk premium as a function of ω

Figure 7 :

 7 Figure 7: IRF to a positive networth shock

Figure 8 :

 8 Figure 8: IRF to a positive credit shock

Figure 9 :

 9 Figure 9: IRF to a positive uncertainty shock

  fω = Φ(ω, σω ) -1 fσω = ωf σω (ω, σω ) -Γ σω (ω, σω ) ḡω = 1 -Φ(ω, σω ) -μωφ(ω, σω ) ḡσω = -f σω (ω, σω ) -μΓ σω (ω, σω )

  Those models enhance the Bernanke et al. (5) framework with a more realistic labor market. Christiano et al. (14) show in a new-Keynesian model that nancial and employment frictions are able to change the model dynamics in an open economy setting, and improve the forecasting properties of the model for Swedish data, in particular for ination. Zanetti and Mumtaz

	(50) demonstrate through a Bayesian estimation that labor and nancial frictions are supported by the data and
	that they play together to amplify or reduce the variables' reaction to various shocks. Firms have in their model
	to paid only capital in advance. Petrosky-Nadeau (38) considers that rms nance only their vacancies costs
	with external nancing on frictional credit markets. He nds that the easing of nancing constraints during
	an expansion (a productivity shock) reduces the opportunity cost for resources allocated to job creation (cost
	channel), because rms are able to accumulate net worth. Credit market frictions generate persistence in the
	dynamics of labor-market tightness and have a moderate eect on amplication.
	The research to date has tended to focus on technological or monetary policy shocks. No paper tries to
	investigate direct shocks from the nancial sphere, such as credit, net worth or uncertainty shocks. Furthermore,
	no paper takes into account that production costs, as well as vacancies costs are paid in advance in a DSGE
	framework. Our paper tries to bring the gap. Besides, note that our framework is dierent from the one of
	Acemoglu (1) or Wasmer and Weil (48), Petrosky-Nadeau and Wasmer

  The wholesale-good production takes place, once capital and labor inputs are obtained. The production process is then split into two dierent sectors, in the spirit of what it is standard in medium scale DSGE models, a competitive nal goods sector and a monopolistically competitive intermediate-good sector, that use wholesale goods as inputs.3.4 Intermediate and nal-good productionFinal-good rms proceed in a perfectly competitive market and are owned by households. They purchase a continuum of dierentiated intermediate goods indexed by j ∈ (0, 1) and aggregate theses varieties to produce Y t units of nal good. They have no other cost, except the one to buy to intermediate-good rms the dierent varieties.

  t dj where P t is the bundler's technology price-index that corresponds to the nominal aggregate consumer's price index. The solution to the maximization problem19 yields the following demand function for the intermediate

	good of variety j:	Y j,t =	P j,t P t	-	Y t	(42)
	So, the demand for each variety of intermediate good is a downward sloping demand curve, which will give to
	the intermediate-good rms some pricing power.

Table 1 :

 1 Baseline calibration

	Parameter	Value	Description
	Preferences
	β	0.99	Households discount factor
	Technology
	α	0.36	Capital share in production
	δ K	0.025	Capital depreciation rate
	σ A	0.05	Cost of capital utilization
	κ	4	Investment adjustment cost
	Preferences
	τ	10	Inverse of the elasticity of worked hours to real wage
	h	0.5	External habit persistence
	Job market
	ρ	0.72	Elasticity of matches to unemployment
	γ	0.14	Unit cost of job vacancies
	b	0.71	Unemployment benets
	η	0.5	Bargaining power parameter
	δ	0.08	Job destruction rate
	Entrepreneurs and nancial market
	s 1	4.97307139522323 Gross external nance premium
	s0	7.3678	Steady-state value of credit shock
	ς	0.9728	Steady-state value of net worth shock
	W e	0.01	Entrepreneurial endowment
	Intermediate-good market
		0.66	Calvo stickiness of prices
		11	Monopolistic mark-up
	Monetary policy
	ρ R	0.75	Interest rate smoothing coecient
	ρ π	1.7	Response to ination
	ρ Y	0.125	Response to output
	Shocks
	ρ s0	0.95	Credit shock persistence
	ρ ω	0.97	Uncertainty shock persistence
	ρ ς	0.5	Net worth shock persistence
	σ s0	0.15	Standard deviation of credit shock
	σ ω	0.15	Standard deviation of uncertainty shock
	σ ς	0.15	Standard deviation of net worth shock

  5 ln(1 + σ 2 ω,t ) ln(1 + σ 2 ω,t ) then ω t = exp ln(1 + σ 2 ω,t )x 1,t -0.5 ln(1 + σ 2 ω,t ) x 2,t = ln(ω t ) -0.5 ln(1 + σ 2 ω,t ) ln(1 + σ 2 ω,t ) then ω t = exp ln(1 + σ 2 ω,t )x 2,t + 0.5 ln(1 + σ 2 ω,t )Substituting ω t by x 2,t and applying the substitution rule in integration, we get:Γ(ω t , σ ω,t ) =Given the obtained results, we get the following:f (ω t , σ ω,t ) = 1 -F ln(ω t ) -0.5 ln(1 + σ 2 ω,t ) ln(1 + σ 2 ω,t ) -ωt 1 -F ln(ω t ) + 0.5 ln(1 + σ 2 ω,t ) ln(1 + σ 2 ω,t ) g(ω t , σ ω,t ) = (1 -µ t )F ln(ω t ) -0.5 ln(1 + σ 2S(ω t , σ ω,t ) = 1 -µ t Γ(ω t , σ ω,t ) + ωt h(ω t , σ ω,t )f (ω t , σ ω,t )

								ω,t )	+ ωt 1 -F	ln(ω t ) + 0.5 ln(1 + σ 2 ω,t )
					ln(1 + σ 2 ω,t )	ln(1 + σ 2 ω,t )
								2
	with	h(ω t , σ ω,t ) =	dx 1 = dx 2 = exp -ωt 2π ln(1 + σ 2 1 ω,t ) 1 -F	1 ω ln(1 + σ 2 ω ) ln(ωt)+0.5 ln(1+σ 2 dω ω,t ) 2 ln(1+σ 2 ω,t ) ln(ωt)+0.5 ln(1+σ 2 ω,t ) ln(1+σ 2 ω,t )
	and							-1
			lim ωt→0	x 1,t = -∞,	lim ω→ωt	x 1,t =	ω,t ) ln(1 + σ 2 ln(ω t ) + 0.5 ln(1 + σ 2 ω,t )	.
			lim ωt→0	x 2,t = -∞,	lim ω→ωt	x 2,t =	ln(ω t ) -0.5 ln(1 + σ 2 ω,t ) ln(1 + σ 2 ω,t )
			ln( ωt )+0.5 ln(1+σ 2 ω,t ) √ ln(1+σ 2 ω,t ) -∞	1 √ 2π	exp -	x 2 1 2	dx 1 = F	ln(ω t ) + 0.5 ln(1 + σ 2 ω,t ) ω,t ) ln(1 + σ 2	(55)
	where F(.) is the cumulative distribution function of a standard Normal distribution.
	Similarly,we know that:
								ωt
					Γ(ω t , σ ω,t ) =	ωφ(ω, σ ω,t )dω
								0
				ln( ωt )-0.5 ln(1+σ 2 ω,t ) √ ln(1+σ 2 ω,t ) -∞	1 √ 2π	exp -	x 2 + ln(1 + σ 2 ω,t ) 2	2	ωdx 2
			=	ln( ωt )-0.5 ln(1+σ 2 ω,t ) √ ln(1+σ 2 ω,t ) -∞	1 √ 2π	exp -	x 2 1 2	dx 2
			=	ln( ωt )-0.5 ln(1+σ 2 ω,t ) √ ln(1+σ 2 ω,t ) -∞	1 √ 2π	exp -	x 2 1 2	dx 1
			= F	ln(ω t ) -0.5 ln(1 + σ 2 ω,t )
					ln(1 + σ 2 ω,t )

.

Substituting ω t by x 1,t and applying the substitution rule in integration, we get:

Φ(ω t , σ ω,t ) =

The family optimally allocates the same consumption for each member, regardless their respective individual income.

b can be interpreted as home production or as unemployment benets, as we do, provided by the government and nanced by lump-sum taxes.

The form of the utility function is based on the ones used by (5) and[START_REF] Gertler | An estimated monetary DSGE model with unemployment and staggered nominal wage bargaining[END_REF].

The same assumption is made by Bernanke et al.[START_REF] Bernanke | The nancial accelerator in a quantitative business cycle framework[END_REF] and Paustian[START_REF] Paustian | Welfare eects of monetary policy rules in a model with nominal rigidities and credit market frictions[END_REF]. Carlstrom and Fuerst (10) make the dierent assumption, that consumers and entrepreneurs have dierent time-discount factors, with entrepreneurs less impatient than consumers.

Since all rms are owned by households in this economy, prots are evaluated in terms of utility brought to them.

Innitely-lived households are risk averse, but they become risk neutral for the nancial contract. Carlstrom and Fuerst[START_REF] Carlstrom | Agency costs and business cycles[END_REF] explain this fact by the absence of uncertainty about the term of the one-period contract since the aggregate uncertainty is realized before the contract establishment. Furthermore, by the law of large numbers as banks are nancing a continuum of dierent entrepreneurs, households know they will receive the expected return of the idiosyncratic shock.

f (ω, σω) ≤ 0, ∀ ω ∈ [0, ∞). In addition, limω→0 f (ω, σω) = 1 and limω→∞ f (ω, σω) = 0. Then, f (ω, σω) ∈ (0, 1).

We assume that ωh(ω, σω) is increasing in ω in order to ensure the concavity of the lender's net share of return, g(ω, σω), and avoid any credit rationing at the equilibrium. This regularity condition is without loss of generality and it is satised by most of the continuous probability distributions. See Bernanke et al.[START_REF] Bernanke | The nancial accelerator in a quantitative business cycle framework[END_REF] for details.

See appendix A for the proof.

Recall that by assuming an identical threshold value of entrepreneurial productivity for all wholesale rms, we keep a representative-rm context.

Final-good rms maximize their expected stream of prots, which is equivalent to maximizing their prot period-by-period since they purchase intermediate goods at the same frequency.

The same kind of Taylor rule is used by (21), Krause et al.[START_REF] Krause | Ination dynamics with search frictions: A structural econometric analysis[END_REF] and Trigari[START_REF] Trigari | Equilibrium unemployment, job ows, and ination dynamics[END_REF].

marginal costs, as well as hiring costs by a nancial mark-up charged by nancial intermediaries. This nancial mark-up is then transmitted by these rms on prices. Thus, it aects their hiring behavior, as well as wage and employment levels in the economy. Then, we simulate the model by using quarterly US data for the sample period 1960:Q1 to 2007:Q4. We consider three shocks: a net worth shock, a credit shock and an uncertainty shocks. We nd that employment rates and vacancies posting increase following positive credit, net worth and uncertainty shocks. Dierent channels of propagation from the nancial sphere of the economy to the labor market are investigated and appear to be consistent with our theoretical model. All these channels appear to converge to the key role of what we called, a nancial mark-up charged by banks to overcome agency problems.

Appendices Appendix A

In this appendix, we prove that

Using the assumption that ωt h(ω t ) is increasing in ωt and taking derivatives, we obtain

Given this result, S t is an increasing function of ωt .

Now taking limits of Γ(ω t ) and ωt h(ω t )f (ω t ) at the lower bound of ω, we get

Combining the previous results,

Appendix B: Log-normal distribution and nancial contract

Financial contract: Technical issues

The idiosyncratic shock ω t has a log-normal distribution with mean 1 and standard error σ ω,t . In order to resolve the model numerically, some simplications and analytic expressions regarding f (ω t , σ ω,t ), g(ω t , σ ω,t ) and S(ω t , σ ω,t ) are needed. Since E(ω t ) = 1 and V (ω t ) = σ 2 ω,t , then the parameters of the log-normal distribution are given by -0.5 ln(1 + σ 2 ω,t ), ln(1 + σ 2 ω,t ) . So that the density function φ(ω t , σ ω,t ) can be expressed by:

• Finding Φ(ω t , σ ω,t ) and Γ(ω t , σ ω,t ) . We know that: