Understanding the Great Recession∗

(Preliminary and Incomplete.)

Lawrence J. Christiano† Martin S. Eichenbaum‡ Mathias Trabandt§

February 10, 2014

Abstract

We argue that the vast bulk of movements in aggregate real economic activityduring the Great Recession were due to financial frictions interacting with the zerolower bound. We reach this conclusion looking through the lens of a New Keynesianmodel in which firms face moderate degrees of price rigidities and no nominal rigiditiesin the wage setting process. Our model does a good job of accounting for the jointbehavior of labor and goods markets, as well as inflation, during the Great Recession.According to the model the observed fall in TFP and the presence of a working capitalchannel played critical roles in accounting for the small size of the drop in inflationthat occurred during the Great Recession.

∗The views expressed in this paper are those of the authors and do not necessarily reflect those of theBoard of Governors of the Federal Reserve System or of any other person associated with the Federal ReserveSystem.

†Northwestern University, Department of Economics, 2001 Sheridan Road, Evanston, Illinois 60208, USA.Phone: +1-847-491-8231. E-mail: l-christiano@northwestern.edu.

‡Northwestern University, Department of Economics, 2001 Sheridan Road, Evanston, Illinois 60208, USA.Phone: +1-847-491-8232. E-mail: eich@northwestern.edu.

§Board of Governors of the Federal Reserve System, Division of International Finance, Trade and Fi-nancial Studies Section, 20th Street and Constitution Avenue N.W, Washington, DC 20551, USA, E-mail:mathias.trabandt@gmail.com.

1. Introduction

This paper seeks to understand the key forces driving the U.S. economy in the wake of the

2008 crisis. Plausible inference requires that the model provide a good description of key

macro variables, including those describing labor market outcomes. To this end, we extend

the medium-sized DSGE model in Christiano, Eichenbaum and Trabandt (2013) (CET) to

endogenize the labor force participation rate. This extension is important in light of the

sharp drop in the labor force participation rate that occurred after 2008. To establish the

empirical credibility of our model, we estimate its parameters using pre-2008 data. We argue

that the model does a good job of accounting for the dynamics of fourteen key macroeconomic

variables over this period.

We use a simple method to quantify the business cycle movements of the macro variables

in the post-2008 period. We then characterize the role of four di§erent shocks in generating

the behavior of the economy during the post-2008 period. In particular, we introduce two

type of wedge shocks into our structural model. These wedges capture in a reduced form way

frictions which are widely viewed as having been important during the post-2008 period. The

first wedge is motivated by the literature stressing a reduction in consumption as a trigger

for a zero lower bound (ZLB) episode (see Eggertsson and Woodford (2003), Eggertsson

and Krugman (2011) and Guerrieri and Lorenzoni (2012)). For convenience we capture this

idea as in Smets and Wouters (2007) by introducing a perturbation to agents’ intertemporal

Euler equations associated with saving. Second, motivated by the sharp movements in credit

spreads observed in the post-2008 period, we introduce an additional wedge into households’

first order condition for optimal capital accumulation. Simple financial friction models based

on asymmetric information with costly monitoring imply that credit market frictions can be

captured in a reduced form way as a tax on the gross return on capital (see Christiano and

Davis (2006)). Also, motivated by models like Bigio (2012) and Kurlat (2012), we will allow

this wedge to impact on the cost of working capital. We also incorporate into our analysis

the observed decline in total factor productivity (TFP) as well as the initial rise and then

decline in government consumption.

We argue that, contrary to a widespread view, NK models can account for the key

features of the post-2008 US data with moderate degrees of price stickiness. The keys to

this result are (i) a prolonged slowdown in TFP growth during the Great Recession, and

(ii) the presence of a working capital channel on firms’ purchases of intermediate factors of

production that is subject to a wedge that rose in post-2008 period due to financial frictions.

At the same time we argue that the vast bulk of the decline in real economic activity is due

to the financial frictions as captured by the wedge shocks.

Significantly, our model accounts for the large decline in the labor force participation rate

2

and employment, as well as the persistent increase in unemployment. Our model is able to

do so, even though we do not allow for any nominal rigidities in the wage setting process.

All of the inertia in wages derives from the assumption by the alternating o§er bargaining

process proposed in Hall and Milgrom (2008) and extended in Christiano, Eichenbaum and

Trabandt (2013).

Finally, our results indicate that the rise in government consumption associated with the

American Recovery and Reinvestment Act of 2009 had a substantial expansionary e§ect with

a peak multiplier in excess of 1.5. However, based on our model we cannot attribute the

long duration of the Great Recession to the decline in government consumption that began

around the start of 2011.

2. The Model

In this section, we describe a medium-sized DSGE model whose structure is, with one im-

portant exception, the same as the one CET. The exception is that we modify the framework

to endogenize labor force participation rates.

2.1. Households and Labor Force Dynamics

The economy is populated by a large number of identical households. As in Andolfatto

(1995) and Merz (1996) we assume that each household has a unit measure of members.

Members of the household can be engaged in three types of activities: (i) (1− Lt) membersspecialize in home production in which case we say they are not in the labor force and that

they are in the non-participation state; (ii) lt members of the household are in the labor

force and are employed in the production of a market good, and (iii) (Lt − lt) members ofthe household are unemployed, i.e. they are in the labor force but do not have a job.

At the end of each period a fraction 1 − ρ of randomly selected employed workers is

separated from the firm they had been matched with. Thus, at the end of period t − 1 atotal of (1− ρ) lt−1 workers separate from firms and ρlt−1 workers remain attached to their

firm. Let ut−1 denote the unemployment rate at time t−1,so that the number of unemployedworkers at time t − 1 is ut−1Lt−1. The sum of separated and unemployed workers is given

by:

(1− ρ)lt−1 + ut−1Lt−1 = (1− ρ) lt−1 +Lt−1 − lt−1Lt−1

Lt−1

= Lt−1 − ρlt−1.

We assume that a separated worker and an unemployed worker have an equal probability,

1 − s, of exiting the labor force. It follows that s of separated and unemployed workers,

3

s (Lt−1 − ρlt−1) , remain in the labor force and search for work. We refer to s as the ‘staying

rate’.

The household chooses rt, the number of workers that it transfers from non-participation

into the labor force. Thus, the labor force in period t is:

Lt = s (Lt−1 − ρlt−1) + ρlt−1 + rt. (2.1)

By its choice of rt the household in e§ect chooses Lt. The total number of workers searching

for a job at the start of t is

s (Lt−1 − ρlt−1) + rt = Lt − ρlt−1. (2.2)

Here we have used (2.1) to substitute out for rt on the left hand side of (2.2).

It is of interest to calculate the probability, denoted et, that a non-participating worker

is selected to be in the labor force. We assume that the (1− s) (Lt−1 − ρlt−1) workers who

separate exogenously into the non-participation state do not return home in time to be

included in the pool of workers relevant to the household’s choice of rt. As a result, the

universe of workers from which the household selects rt is 1−Lt−1. It follows that et is givenby:1

et =rt

1− Lt−1=Lt − s (Lt−1 − ρlt−1)− ρlt−1

1− Lt−1. (2.3)

The law of motion for employment is:

lt = (ρ+ xt) lt−1 = ρlt−1 + xtlt−1. (2.4)

The job finding rate is the ratio of the number of new hires divided by the number of people

searching for work, given by (2.2):

ft =xtlt−1

Lt − ρlt−1. (2.5)

1We include the staying rate, s, in our analysis for a substantive as well as a technical reason. The substan-tive reason is that, in the data, workers move in both directions between unemployment, non-participationand employment. The gross flows are much bigger than the net flows. Setting s < 1 helps the model accountfor these patterns. The technical reason for allowing s < 1 can be seen by setting s = 1 in (2.3). In that case,if the household wishes to make Lt − Lt−1 < 0, it must set et < 0. That would require withdrawing fromthe labor force some workers who were unemployed in t − 1 and stayed in the labor force as well as someworkers who were separated from their firm and stayed in the labor force. But, if some of these workers arewithdrawn from the labor force then their actual staying rate would be lower that the fixed number, s. So,the actual staying rate would be a non-linear function of Lt − Lt−1 with the staying rate being below s forLt − Lt−1 < 0 and equal to s for Lt − Lt−1 ≥ 0. This kink point is a non-linearity that would be hard toavoid because it occurs precisely at the model’s steady state. Even with s < 1 there is a kink point, but itis far from steady state and so it can be ignored when we solve the model by perturbation methods.

4

2.2. Household Maximization

Members of the household derive utility from a market consumption good and a good pro-

duced at home. The home good is produced using the labor of individuals that are not in

the labor force, 1− Lt, and the labor of the unemployed, Lt − lt :

CHt = ηHt (1− Lt)1−αc (Lt − lt)

αc − F(Lt, Lt−1; ηLt ). (2.6)

The term F(Lt, Lt−1; ηLt ) captures the idea that is costly to change the number of peoplewho specialize in home production,

F(Lt, Lt−1; ηLt ) = 0.5ηLt φL (Lt/Lt−1 − 1)

2 Lt. (2.7)

We assume αc < 1 − αc, so that in steady state the unemployed contribute less to home

production than do people who are out of the labor force. Finally, ηHt and ηLt are processes

that ensure balanced growth. We discuss these processes in detail below. We included the

adjustment costs in Lt so that the model can account for the gradual and hump-shaped

response of the labor force to a monetary policy shock (see subsection 4.3).

Workers experience no disutility from working and supply their labor inelastically. An em-

ployed worker brings home the wages that he earns. Unemployed workers receive government-

provided unemployment compensation which they give to the household. Unemployment

benefits are financed by lump-sum taxes paid by the household. The details of how workers

find employment and receive wages are explained below. All household members have the

same concave preferences over consumption, so each is allocated the same level of consump-

tion.

The representative household maximizes the objective function:

E0

1X

t=0

βt ln(Ct), (2.8)

where

Ct =[(1− !)

(Ct − bCt−1

)χ+ !

(CHt − bC

Ht−1

)χ] 1χ .

Here, Ct and CHt denote market consumption and the consumption of a good produced at

home. The elasticity of substitution between Ct and CHt is 1/ (1− χ) in steady state. The

parameter b controls the degree of habit formation in household preferences. We assume

0 ≤ b < 1. A bar over a variable indicates its economy-wide average value.The flow budget constraint of the household is as follows:

PtCt + PI,tIt +Bt+1 (2.9)

≤ (RK,tuKt − a(u

Kt )PI,t)Kt + (Lt − lt)PtηDt Dt + ltWt +Rt−1Bt − Tt .

5

The variable Tt denotes lump-sum taxes net of transfers and firm profits, Bt+1 denotes

beginning-of-period t purchases of a nominal bond which pays rate of return, Rt at the start

of period t + 1, and RK,t denotes the nominal rental rate of capital services. The variable

uKt denotes the utilization rate of capital. As in Christiano, Eichenbaum and Evans (2005)

(CEE), we assume that the household sells capital services in a perfectly competitive market,

so that RK,tuKt Kt represents the household’s earnings from supplying capital services. The

increasing convex function a(uKt ) denotes the cost, in units of investment goods, of setting

the utilization rate to uKt . The variable PI,t denotes the nominal price of an investment good

and It denotes household purchases of investment goods. In addition, the nominal wage rate

earned by an employed worker is Wt and ηDt Dt denotes exogenous unemployment benefits

received by unemployed workers from the government. The term ηDt is a process that ensures

balanced growth and will be discussed below.

When the household chooses Lt it takes the aggregate job finding rate, ft, and the law

of motion linking Lt and lt,

lt = ρlt−1 + ft (Lt − ρlt−1) , (2.10)

as given. Relation (2.10) is consistent with the actual law of motion of employment because

of the definition of ft (see (2.5)).

The household owns the stock of capital which evolves according to,

Kt+1 = (1− δK)Kt + [1− S (It/It−1)] It. (2.11)

The function S(·) is an increasing and convex function capturing adjustment costs in invest-ment. We assume that S(·) and its first derivative are both zero along a steady state growthpath.

At time 0, the household chooses state-contingent sequences,CHt , Lt, lt, Ct, Bt+1, It, u

Kt , Kt+1

1t=0,

to maximize utility, (2.8), subject to, (2.6), 2.7), (2.9), (2.10) and (2.11). The household takes

K0, B0, l−1 the state contingent sequence of prices and wages, Rt,Wt, Pt, RK,t, PI,t1t=0 as

given.

2.3. Final Good Producers

A final homogeneous market good, Yt, is produced by competitive and identical firms using

the following technology:

Yt =

[Z 1

0

(Yj,t)1λ dj

]λ, (2.12)

where λ > 1. The representative firm chooses specialized inputs, Yj,t, to maximize profits:

PtYt −Z 1

0

Pj,tYj,tdj,

6

subject to the production function (2.12). The firm’s first order condition for the jth input

is:

Yj,t =

(PtPj,t

) λλ−1

Yt. (2.13)

2.4. Retailers

As in Ravenna and Walsh (2008), the jth input good is produced by a monopolist retailer,

with production function:

Yj,t = kαj,t (zthj,t)

1−α − ηφt φ. (2.14)

The retailer is a monopolist in the product market and is competitive in the factor mar-

kets. Here kj,t denotes the total amount of capital services purchased by firm j. Also, ηφt φ

represents an exogenous fixed cost of production, where φ is a positive scalar and ηφt is a

process, discussed below, that ensures balanced growth. We calibrate the fixed cost so that

retailer profits are zero along the balanced growth path. In (2.14), zt is a technology shock

whose properties are discussed below. Finally, hj,t is the quantity of an intermediate good

purchased by the jth retailer. This good is purchased in competitive markets at the price P htfrom a wholesaler. Analogous to CEE, we assume that to produce in period t, the retailer

must borrow P ht hj,t at the start of the period at the interest rate Rt. In this way, the marginal

cost of a unit of hj,t is

P ht (Rt + (1− )) , (2.15)

where is the fraction of the intermediate input that must be financed. The retailer repaysthe loan at the end of period t after receiving sales revenues. The jth retailer sets its price,

Pj,t, subject to the demand curve, (2.13), and the Calvo sticky price friction (2.16). In

particular,

Pj,t =

Pj,t−1 with probability ξPt with probability 1− ξ

. (2.16)

Here, Pt denotes the price set by the fraction 1− ξ of producers who can re-optimize. Note

that we do not allow for price indexation. So, the model is consistent with the observation

that many prices remain unchanged for extended periods of time (see Eichenbaum, Jaimovich

and Rebelo, 2011, and Klenow and Malin, 2011).

2.5. Wholesalers and the Labor Market

A perfectly competitive representative wholesaler firm produces the intermediate good using

labor only. Let lt−1 denote employment of the wholesaler at the end of t − 1. Consistentwith our discussion above, a fraction 1− ρ of these workers separates exogenously from the

wholesaler at the end of period. A total of ρlt−1 workers are attached to the wholesaler

7

at the start of period t. At the beginning of the period, the wholesaler pays a fixed cost,

ηκt κ, to meet a worker with probability one. Here κ is a positive scalar and ηκt is a process,

discussed below, that ensures balanced growth. To hire xtlt−1 workers, the wholesaler must

post xtlt−1/Qt vacancies. Here Qt denotes the aggregate vacancy filling rate which firms

take as given. Posting vacancies is costless. The wholesaler meets xtlt−1 new workers. In

equilibrium all meetings turn into job matches, so xt is the wholesaler’s hiring rate.

At the beginning of the period, the representative wholesaler is in contact with a total

of lt workers (see equation (2.4)). This pool of workers includes workers with whom the firm

was matched in the previous period, plus the new workers that the firm has just met. Each

worker in lt engages in bilateral bargaining with a representative of the wholesaler, taking

the outcome of all other negotiations as given. The equilibrium real wage rate,

wt ≡ Wt/Pt,

is the outcome of the alternating o§er bargaining process described below. In equilibrium all

bargaining sessions conclude successfully, so the representative wholesaler employs lt workers.

Production begins immediately after wage negotiations are concluded and the wholesaler sells

the intermediate good at the real price, #t ≡ P ht /Pt.

2.5.1. Wage Setting

Consistent with Hall and Milgrom (2008) and CET (2013), we assume that wages are deter-

mined according to the alternating o§er bargaining protocol proposed in Rubinstein (1982)

and Binmore, Rubinstein and Wolinsky (1986). Let wpt denote the expected present dis-

counted value of the wage payments by a firm to a worker that it is matched with:

wpt = wt + ρEtmt+1wpt+1.

Heremt is the time t discount factor which firms and workers view as an exogenous stochastic

process beyond their control.

Let Jt denote the value, denominated in units of the final consumption good, to a firm

of employing a worker in period t:

Jt = #pt − wpt .

Here #pt denotes the expected present discounted value of the marginal revenue product

associated with a worker to the firm:

#pt = #t + ρEtmt+1#pt+1. (2.17)

Because there is free entry into the labor market, firm profits must be zero. It follows that

ηκt κ = Jt. (2.18)

8

Let Vt denote the value to a worker of being matched with a firm that pays wt in period

t :

Vt = wt + Etmt+1[ρVt+1 + (1− ρ) s(ft+1Vt+1 + (1− ft+1)Ut+1

)(2.19)

+(1− ρ) (1− s)Nt+1].

Here, Vt+1 denotes the value of working for another firm in period t + 1. In equilibrium,

Vt+1 = Vt+1. Also, Ut+1 in (2.19) is the value of being an unemployed worker in period t+ 1

and Nt+1 is the value of being out of the labor force in period t + 1. The objects, s, ρ and

ft+1 were discussed in the previous section. Relation (2.19) reflects our assumption that an

employed worker remains in the same job with probability ρ, transits to another job without

passing through unemployment with probability (1− ρ) sft+1, transits to unemployment with

probability (1− ρ) s (1− ft+1) and to non-participation with probability (1− ρ) (1− s) .It is convenient to rewrite (2.19) as follows:

Vt = wpt + At, (2.20)

where

At = (1− ρ)Etmt+1

[sft+1Vt+1 + s (1− ft+1)Ut+1 + (1− s)Nt+1

](2.21)

+ρEtmt+1At+1.

According to (2.20), Vt consists of two components. The first is the expected present value of

wages received by the worker from the firm with which he is currently matched. The second

corresponds to the expected present value of the payments that a worker receives in all dates

and states when he is separated from that firm.

The value of unemployment, Ut, is given by,

Ut = ηDt Dt + Ut. (2.22)

Recall that ηDt Dt represents unemployment compensation at time t. The variable, Ut, denotes

the continuation value of unemployment:

Ut ≡ Etmt+1 [sft+1Vt+1 + s (1− ft+1)Ut+1 + (1− s)Nt+1] . (2.23)

Expression (2.23) reflects our assumption that an unemployed worker finds a job in the next

period with probability sft+1, remains unemployed with probability s (1− ft+1) and exitsthe labor force with probability 1− s.The value of non-participation is:

Nt = Etmt+1 [et+1 (ft+1Vt+1 + (1− ft+1)Ut+1) + (1− et+1)Nt+1] . (2.24)

9

Expression (2.24) reflects our assumption that a non-participating worker is selected to join

the labor force with probability et, defined in (2.3).

The structure of alternating o§er bargaining is the same as it is in CET.2 Each matched

worker-firm pair (both those who just matched for the first time and those who were matched

in the past) bargain over the current wage rate, wt. Each time period (a quarter) is subdivided

into M periods of equal length, where M is even. The firm makes a wage o§er at the start

of the first subperiod. It also makes an o§er at the start of every subsequent odd subperiod

in the event that all previous o§ers have been rejected. Similarly, workers make a wage o§er

at the start of all even subperiods in case all previous o§ers have been rejected. Because M

is even, the last o§er is made, on a take-it-or-leave-it basis, by the worker. When the firm

rejects an o§er it pays a cost, ηγt γ, of making a countero§er. Here γ is a positive scalar and

ηγt is a process that ensures balanced growth.

In subperiod j = 1, ...,M−1, the recipient of an o§er can either accept or reject it. If theo§er is rejected the recipient may declare an end to the negotiations or he may plan to make

a countero§er at the start of the next subperiod. In the latter case there is a probability, δ,

that bargaining breaks down and the wholesaler and worker revert to their outside option.

For the firm, the value of the outside option is zero and for the worker the outside option

is unemployment.3 Given our assumptions, workers and firms never choose to terminate

bargaining and go to their outside option.

It is always optimal for the firm to o§er the lowest wage rate subject to the condition that

the worker does not reject it. To know what that wage rate is, the wholesaler must know

what the worker would countero§er in the event that the firm’s o§er was rejected. But, the

worker’s countero§er depends on the firm’s counter o§er in case the worker’s countero§er

is rejected. We solve the firm’s initial o§er beginning from worker’s final o§er and working

backwards. Since workers and firms know everything about each other, the firm’s opening

wage o§er is always accepted. The firm must know what all the countero§ers would be

in each of the M − 1 future subperiods in order to determine what its opening o§er is.Our environment is su¢ciently simple that the solution to the bargaining problem has the

following straightforward characterization:

α1Jt = α2 (Vt − Ut)− α3ηγt γ + α4

(#t − ηDt Dt

)(2.25)

2We assume that the outside option for a worker is always unemployment and not out of the labor force.That is, when bargaining breaks down, workers are send to unemployment.

3We could allow for the possibility that when negotiations break down the worker has a chance of leavingthe labor force. To keep our anlysis realtively simple, we do not allow for that possibility here.

10

where βi = αi+1/α1, for i = 1, 2, 3 and,

α1 = 1− δ + (1− δ)M

α2 = 1− (1− δ)M

α3 = α21− δ

δ− α1

α4 =1− δ

2− δ

α2M+ 1− α2.

See the technical appendix for a detailed derivation of (2.25) and the procedure that we use

for solving the bargaining problem.

2.6. Market Clearing, Monetary Policy and Functional Forms

The total supply of the intermediate good is given by lt which equals the total quantity of

labor used by the wholesalers. So, clearing in the market for intermediate goods requires

ht = lt, (2.26)

where

ht ≡Z 1

0

hj,tdj.

The capital services market clearing condition is:

uKt Kt =

Z 1

0

kj,tdj.

Market clearing for final goods requires:

Ct + (It + a(uKt )Kt)/Ψt + ηκt κxtlt−1 +Gt = Yt. (2.27)

The right hand side of the previous expression denotes the quantity of final goods. The left

hand side represents the various ways that final goods are used. Homogeneous output, Yt,

can be converted one-for-one into either consumption goods, goods used to hire workers, or

government purchases, Gt. In addition, some of Yt is absorbed by capital utilization costs.

Finally, Yt can be used to produce investment goods using a linear technology in which one

unit of the final good is transformed into Ψt units of It. Perfect competition in the production

of investment goods implies,

PI,t =PtΨt.

We adopt the following specification of monetary policy:

ln(Rt/R) = ρR ln(Rt−1/R) (2.28)

+(1− ρR)

[0.25rπ ln

(πAtπA

)+ ry ln

(YtY∗t

)+ 0.25r∆y ln

(Yt

Yt−4µAY

)]+ σR"R,t,

11

where πAt ≡ Pt/Pt−4 and πA is the monetary authority’s inflation target. The object, πA isalso the value of πAt in nonstochstic steady state. The shock, "R,t, is a unit variance, zero

mean disturbance to monetary policy. The variable, Yt, denotes Gross Domestic Product(GDP):

Yt = Ct + It/Ψt +Gt,

where Gt denotes government consumption, which is assumed to have the following repre-

sentation:

Gt = ηgt gt. (2.29)

Here, ηgt is a process that guarantees balanced growth and gt is an exogenous stochastic

process. The variable, Y∗t , is defined as follows:

Y∗t = ηyt ι, (2.30)

where ηyt is a process that guarantees balanced growth and ι is a constant chosen to guarantee

that ln(Yt/Y∗t ) converges to zero in nonstochastic steady state. The constant, µAY , is the valueof Yt/Yt−4 in nonstochastic steady state. Also, R denotes the steady state value of Rt.We assume that the growth rate of neutral technology is the sum of a permanent (µP,t)

and a transitory component (µT,t) :

ln(µz,t) = ln (zt/zt−1) = ln(µz) + µP,t + µT,t. (2.31)

Here

µP,t = ρPµP,t−1 + σP "P,t (2.32)

and

µT,t = ρTµT,t−1 + σT ("T,t − "T,t−1). (2.33)

Here, "P,t and "T,t are mean zero, unit variance, iid shocks. To see why (2.33) is the transitory

component of technology, suppose µP,t ≡ 0 so that µT,t is the only component of technologyand (ignoring the constant term) ln(zt)− ln (zt−1) = µT,t, or

ln (zt)− ln (zt−1) = ρT (ln (zt−1)− ln (zt−2)) + σT ("T,t − "T,t−1).

Diving by 1− L, where L denotes the lag operator, we have:

ln (zt) = ρT ln (zt−1) + σT "T,t.

From this we see that a shock to "T,t has only a transient e§ect on ln (zt) as long as ρT < 1,

which we assume. By contrast, a shock, ∆"P,t to "P,t permanently displaces ln (zt) by the

amount, ∆"P,t/ (1− ρP ) .

12

We assume that when there is a shock to ln (zt) , agents do not know whether it reflects

the permanent or the temporary component. As a result, they must solve a signal extrac-

tion problem when they adjust their forecast of future values of ln (zt) in response to an

unanticipated move in ln (zt) . Suppose, for example, there is a shock to "P,t, but that agents

believe most fluctuations in ln (zt) reflect shocks to "T,t. In this case they will adjust their

near term forecast of ln (zt) , leaving their longer-term forecast of ln (zt) una§ected. As time

goes by and agents see that the change in ln (zt) is too persistent to be due to the transitory

component, the long-run component of their forecast of ln (zt) begins to adjust. It is well

known that the response to a shock is sensitive to whether it is temporary or persistent,

so the relative size of σT and σP has important implications for the dynamic response of

the model to technology shocks.4 As with the other parameters of the model, we will use

the pre-2008 data to help determine the relative size of these parameters. Our unobserved

components representation of the shocks will play an important role in our interpretation of

the post-2008Q2 data.

Finally, we assume that lnµΨ,t ≡ ln (Ψt/Ψt−1) follows an AR(1) process

lnµΨ,t = (1− ρΨ) lnµΨ + ρΨ lnµΨ,t−1 + σΨ"Ψ,t.

The sources of long-term growth in our model are neutral and investment-specific tech-

nological progress. The growth rate in steady state for the model variables is a composite,

Φt, of these two technology shocks:

Φt = Ψα

1−αt zt.

The variables Yt/Φt, Ct/Φt, wt/Φt and It/(ΨtΦt) converge to constants in nonstochastic

steady state.

If objects like the fixed cost of production, the cost of hiring, etc., were constant, they

would become irrelevant over time. To avoid this implication, it is standard in the literature

to suppose that such objects are proportional to composite technology, Φt. However, this

assumption has the unfortunate implication that technology shocks of both types have an

immediate e§ect on the vector of objects

Ωt =hηyt , η

gt , η

Dt , η

γt , η

κt , η

φt , η

Lt , η

Ht

i0. (2.34)

Such a specification seems implausible and so we instead proceed as in Christiano, Trabandt

and Walentin (2012) and Schmitt-Grohé and Uribe (2012). In particular, we suppose that

the objects in Ωt are proportional to a long moving average of composite technology, Φt :

Ωi,t = Φθt−1 (Ωi,t−1)

1−θ , (2.35)

4For an extensive discussion, see Christiano, Trabandt and Walentin (2011).

13

where Ωi,t denotes the ith element of Ωt, i = 1, ...,8. Also, 0 < θ ≤ 1 is a parameter to be

estimated. Note that the ratio,

Ωi,tΦt

=Φt−1Φt

(Ωi,t−1Φt−1

)1−θ,

so that Ωi,t has the same growth rate in steady state as GDP, i = 1, ...,8. When θ is very

close to zero, Ωi,t is virtually unresponsive in the short-run to an innovation in either of the

two technology shocks, a feature that we find very attractive on a priori grounds.

We adopt the investment adjustment cost specification proposed in CEE. In particular,

we assume that the cost of adjusting investment takes the form:

S (It/It−1) = 0.5 exphpS 00 (It/It−1 − µΦ × µΨ)

i

+0.5 exph−pS 00 (It/It−1 − µ× µΨ)

i− 1.

Here, µΦ and µΨ denote the steady state growth rates of Φt and Ψt. The value of It/It−1 in

nonstochastic steady state is (µΦ × µΨ). In addition, S 00 represents a model parameter thatcoincides with the second derivative of S (·), evaluated in steady state. It is straightforwardto verify that S (µΦ × µΨ) = S 0 (µΦ × µΨ) = 0. Our specification of the adjustment costs hasthe convenient feature that the steady state of the model is independent of the value of S 00.

We assume that the cost associated with setting capacity utilization is given by,

a(uKt ) = 0.5σaσb(uKt )

2 + σb (1− σa) uKt + σb (σa/2− 1)

where σa and σb are positive scalars. We normalize the steady state value of uKt to unity,

so that the adjustment costs are zero in steady state and σb is equated to the steady state

of the appropriately scaled rental rate on capital. Our specification of the cost of capacity

utilization and our normalization of uKt in steady state has the convenient implication that

the model steady state is independent of σa.

Finally, we discuss how vacancies are determined. We posit a standard matching function:

xtlt−1 = σm (1− ρlt−1)σ (lt−1vt)

1−σ , (2.36)

where lt−1vt denotes the total number of vacancies and vt denotes the vacancy rate. Given

xt and lt−1, we use (2.36) to solve for vt. Recall that we defined the total number of vacancies

by xtlt−1/Qt. We can solve for the aggregate vacancy filling rate Qt using

Qt =xtvt. (2.37)

The equilibrium of our model has a particular recursive structure. We can first solve all

model variables, apart from vt and Qt. These two variables can then be solved for using

(2.36) and (2.37).

14

3. Econometric Methodology

We estimate our model using a Bayesian variant of the strategy in CEE that minimizes the

distance between the dynamic response to three shocks in the model and the analog objects

in the data. The latter are obtained using an identified VAR for post-war quarterly U.S.

times series that include key labor market variables. The particular Bayesian strategy that

we use is the one developed in Christiano, Trabandt and Walentin (2011), henceforth CTW.

CTW estimate a 14 variable VAR using 14 variables quarterly data that are seasonally

adjusted and cover the period 1951Q1 to 2008Q4.5To facilitate comparisons, our analysis is

based on the same VAR that CTW use. As in CTW, we identify the dynamic responses to a

monetary policy shock by assuming that the monetary authority sees the current and lagged

values of all the variables in the VAR and a monetary policy shock a§ects only the Federal

Funds Rate contemporaneously. As in Altig, Christiano, Eichenbaum and Linde (2011),

Fisher (2006) and CTW, we make two assumptions to identify the dynamic responses to the

technology shocks: (i) the only shocks that a§ect labor productivity in the long-run are the

innovations to the neutral technology shock, zt, and the innovation to the investment-specific

technology shock, Ψt and (ii) the only shock that a§ects the price of investment relative to

consumption in the long-run is the innovation to Ψt. These assumptions are satisfied in our

model.6 Standard lag-length selection criteria lead CTW to work with a VAR with 2 lags.7

5There is an ongoing debate over whether or not there is a break in the sample period that we use.Implicitly, our analysis sides with those authors who argue that the evidence of parameter breaks in themiddle of our sample period is not strong. See for example Sims and Zha (2006) and Christiano, Eichenbaumand Evans (1999).

6Although shock to the permanent component of technology, "P,t, satisfies assumptions (i) and (ii), wehave not yet established a final identifying condition underlying the VAR analysis, the ‘invertibility condition’that "P,t can be represented as a linear combination of the VAR disturbances. We are currently studyingour model’s implication for this invertibility condition.

7See CTW for a sensitivity analysis with respect to the lag length of the VAR.

15

We include the following variables in the VAR:8

0

BBBBBBBBBBBBBBBBBBBBBB@

∆ ln(relative price of investmentt)∆ ln(realGDPt/hourst)∆ ln(GDP deflatort)unemployment ratetln(capacity utilizationt)

ln(hourst)ln(realGDPt/hourst)− ln(real waget)ln(nominal Ct/nominal GDPt)ln(nominal It/nominal GDPt)

ln(vacanciest)job separation ratetjob finding ratet

ln (hourst/labor forcet)federal funds ratet

1

CCCCCCCCCCCCCCCCCCCCCCA

. (3.1)

Given an estimate of the VAR we compute the implied impulse response functions to

the three structural shocks. We stack the contemporaneous and 14 lagged values of each

of these impulse response functions for 13 of the variables listed above in a vector, . We

do not include the job separation rate because that variable is constant in our model. We

include the job separation rate in the VAR to ensure the VAR results are not driven by an

omitted variable bias.

The logic underlying our model estimation procedure is as follows. Suppose that our

structural model is true. Denote the true values of the model parameters by θ0. Let (θ)

denote the model-implied mapping from a set of values for the model parameters to the

analog impulse responses in . Thus, (θ0) denotes the true value of the impulse responses

whose estimates appear in . According to standard classical asymptotic sampling theory,

when the number of observations, T, is large, we havepT( − (θ0)

) a

˜ N (0,W (θ0, ζ0)) .

Here, ζ0 denotes the true values of the parameters of the shocks in the model that we do

not formally include in the analysis. Because we solve the model using a log-linearization

procedure, (θ0) is not a function of ζ0. However, the sampling distribution of is a function

of ζ0.We find it convenient to express the asymptotic distribution of in the following form:

a

˜ N ( (θ0) , V ) , (3.2)

where

V ≡W (θ0, ζ0)

T.

8See section A of the technical appendix in CTW for details about the data.

16

For simplicity our notation does not make the dependence of V on θ0, ζ0 and T explicit. We

use a consistent estimator of V. Motivated by small sample considerations, that estimator

has only diagonal elements (see CTW). The elements in are graphed in Figures 3− 5 (seethe solid lines). The gray areas are centered, 95 percent probability intervals computed using

our estimate of V .

In our analysis, we treat as the observed data. We specify priors for θ and then compute

the posterior distribution for θ given using Bayes’ rule. This computation requires the

likelihood of given θ.Our asymptotically valid approximation of this likelihood is motivated

by (3.2):

f( |θ, V

)=

(1

2π

)N2

|V |−12 exp

[−1

2

( − (θ)

)0V −1

( − (θ)

)]. (3.3)

The value of θ that maximizes the above function represents an approximate maximum

likelihood estimator of θ. It is approximate for three reasons: (i) the central limit theorem

underlying (3.2) only holds exactly as T ! 1, (ii) our proxy for V is guaranteed to be

correct only for T !1, and (iii) (θ) is calculated using a linear approximation.Treating the function, f, as the likelihood of , it follows that the Bayesian posterior of

θ conditional on and V is:

f(θ| , V

)=f( |θ, V

)p (θ)

f( |V

) . (3.4)

Here, p (θ) denotes the priors on θ and f( |V

)denotes the marginal density of :

f( |V

)=

Zf( |θ, V

)p (θ) dθ.

The mode of the posterior distribution of θ can be computed by maximizing the value of the

numerator in (3.4), since the denominator is not a function of θ. The marginal density of is

required for an overall measure of the fit of our model. To compute the marginal likelihood,

we use the standard Laplace approximation. In our analysis, we also find it convenient to

compute the marginal likelihood based on a subset of the elements in (see Appendix B for

details).

4. Bayesian Inference

This section presents results for the estimated model. First, we discuss the priors and

posteriors of structural parameters. Second, we discuss the ability of the model to account

for the dynamic response of the economy to a monetary policy shock, a neutral technology

17

shock and an investment-specific technology shock. Finally, we discuss the macroeconomic

e§ects of an increase in government purchases of goods in ‘normal times’, that is, when the

ZLB on the nominal interest is not binding.

4.1. Calibration and Parameter Values set a Priori

We set the values for a subset of the model parameters a priori. These values are reported

in Panel A of Table 1. We also set the steady state values of five model variables, listed in

Panel B of Table 1. We specify β so that the steady state annual real rate of interest is three

percent. The depreciation rate on capital, δK , is set to imply an annual depreciation rate of

10 percent. The growth rates of composite technology, µΦ, is equated to the sample average

of real per capita GDP growth. The growth rate of investment specific technology, µΨ, is

set so that µΦµΨ is equal to the sample average of real, per capita investment growth. We

assume the monetary authority’s inflation target is 2 percent per year and that the profits

of intermediate good producers are zero in steady state. We set the steady state value of the

vacancy filling rate, Q, to 0.7, as in den Haan, Ramey and Watson (2000) and Ravenna and

Walsh (2008). We set the steady state unemployment rate, u, to the average unemployment

rate in our sample, 0.05. We set the parameter M to 60 which roughly corresponds to the

number of business days in a quarter. We assume ρ = 0.9, which implies a match survival

rate that is consistent with both HM and Shimer (2012a). Finally, we assume that the steady

state value of the ratio of government consumption to gross output is 0.20.

Two additional parameter pertain to the household sector. We set the elasticity of

substitution in utility between home and market produced goods, 1/ (1− χ) , to 3. This

magnitude is similar to what is reported in Aguiar, Hurst and Karabarbounis (2013).9 We

set the steady state labor force to population ratio, L, to 0.67.

To make the model consistent with the 5 calibrated values for L, Q, G/Y, u, and profits,

we select values for 5 parameters: the weight on market consumption in the utility function,

!; the constant in front of the matching function, σm; the fixed cost of production, φ; the cost

for the firm to make a countero§er, γ; the scale parameter, g, in government consumption.

The values for these parameters, evaluated at the posterior mode of the set of parameters

that we estimate, are reported in Table 3.

9We take our elasticity of substitution parameter from the literature to maintain comparability. However,there is a caveat. To understand this, recall the definition of the elasticity of substitution. It is the percentchange in C/CH in response to a one percent change in the corresponding relative price, say λ. From anempirical standpoint, it is di¢cult to obtain a direct measure of this elasticity because we do not have dataon CH or λ. As a result, structural relations must be assumed, which map from observables to CH and λ.Since estimates of the elasticity are presumably dependent on the details of the structural assumptions, it isnot clear how to compare values of this parameter across di§erent studies, which make di§erent structuralassumptions.

18

4.2. Parameter Estimation

The priors and posteriors for the model parameters about which we do Bayesian inference

are summarized in Table 2. A number of features of the posterior mode of the estimated

parameters of our model are worth noting. First, the posterior mode of ξ implies a moderate

degree of price stickiness, with prices changing on average once every 4 quarters. This value

lies within the range reported in the literature. Second, the posterior mode of δ implies that

there is a roughly 0.05% chance of an exogenous break-up in negotiations when a wage o§er

is rejected. Third, the posterior modes of our model parameters, along with the assumption

that the steady state unemployment rate equals 5.5%, implies that it costs firms 0.81 days of

marginal revenue to prepare a countero§er during wage negotiations (see Table 3). Fourth,

the posterior mode of steady-state hiring costs as a percent of gross output is equal to 0.5%.

This result implies that steady-state hiring costs as a percent of total wages of newly-hired

workers is equal to 7%.10 Silva and Toledo (2009) report that, depending on the exact costs

included, the value of this statistic is between 4 and 14 percent, a range that encompasses

the corresponding statistic in our model

Fifth, the posterior mode of the replacement ratio is 0.19. To put this number in per-

spective, consider the following narrow measure of the fraction of unemployment benefits to

wages. The numerator of the fraction is total payments of the government for unemploy-

ment insurance divided by the total number of unemployed people. The denominator of the

fraction is total compensation of labor divided by the number or employees, i.e. wage per

worker. The average of the numerator divided by denominator in our sample period is 0.14.

This fraction represents the lower bound on the average replacement rate because it leaves

out some other government contributions that unemployed people become eligible for. HM

summarize the literature and report a range of estimates from 0.12 to 0.36 for the replace-

ment ratio. It is well know that Diamond (1982), Mortensen (1985) and Pissarides (1985)

(DMP) style models require a replacement ratio in excess of 0.90 to account for fluctuations

in labor markets (see for example the extended discussion in CET). For the reasons stressed

in CET, alternating o§er bargaining between workers and firms mutes the sensitivity of real

wages to aggregate shocks. This property underlies our model’s ability to account for esti-

mated response of the economy to monetary policy shocks and shocks to neutral and capital

embodied technology with a low replacement ratio.

Sixth, the posterior mode of s implies that a separated or unemployed worker leaves the

labor force with probability 1− s = 0.2. Seventh, the posterior mode for αc is 0.02, implyingthat people outside of the labor force account for virtually all of home production. Eighth,

10Table 3 reports the hiring cost to gross output ratio in steady state which is defined as: sl = 100κnκxl/y.Here nκ is equal to Ωk,t/Φt evaluated at steady state. Given sl and the real wage, w, it is straightforwardto compute hiring costs as a share of the wage of newly hired workers: 100nκκ/w.

19

the posterior mode of θ which governs the responsiveness of the elements of Ωt to technology

shocks, is small (0.16). So, variables like government purchases and unemployment benefits

which are a§ected by those processes, are very unresponsive in the short-run to technology

shocks. Ninth, the posterior modes of the parameters governing monetary policy are similar

to those reported in the literature (see for example Justiniano, Primiceri, and Tambalotti,

2010).

Finally, we turn to the parameters of the unobserved components representation of the

neutral technology shock. According to the posterior mode, the standard deviation of the

shock to the transient component is roughly 5 times the standard deviation of the permanent

component. So, according to the posterior mode, most of the fluctuations (at least, at a short

horizon) are due to the transitory component of technology. This property of the posterior

seems to be heavily determined by the prior. The permanent component of neutral tech-

nology has an autocorrelation of roughly 0.7, so that a one percent shock to the permanent

component eventually drives the level of technology up by roughly 3 percent. The temporary

component is also fairly highly autocorrelated. Much of the literature concludes that the

growth rate of neutral technology follows a random walk. Our model is consistent with this

view. When we simulate a large sample of observations on ln (zt) we find that the first order

autocorrelation of ln (zt/zt−1) is −0.07, which is very close to zero. For discussions of how acomponents representation in which the components are both highly autocorrelated can nev-

ertheless generate a process that looks like a random walk, see Christiano and Eichenbaum

(1990) and Quah (1990).

4.3. Impulse Response Functions

The solid black lines in Figures 1-4 present the impulse response functions to a monetary

policy shock a permanent neutral-technology shock and an investment-specific technology

shock implied by the estimated VAR. The grey areas represent 95 percent probability in-

tervals. The solid lines with the circles correspond to the impulse response functions of our

model evaluated at the posterior mode of the structural parameters. Figure 1 shows that

the model does very well at reproducing the estimated e§ects of an expansionary monetary

policy shock, including the hump-shaped rises real GDP and hours worked, the rise in the

labor force participation rate and the muted response of inflation. Notice that real wages

respond by much less than hours worked to a monetary policy shock. Even though the

maximal rise in hours worked is roughly 0.14%, the maximal rise in real wages is only 0.06%.

Significantly, the model accounts for the hump-shaped fall in the unemployment rate as well

as the rise in the job finding rate and vacancies that occur after an expansionary monetary

policy shock. The model does understate the rise in the capacity utilization rate. The sharp

rise of capacity utilization in the estimated VAR may reflect that our data on the capacity

20

utilization rate pertains to the manufacturing sector, which probably overstates the average

response across all sectors in the economy.

From Figure 2 we see that the model does a good job of accounting for the estimated

e§ects of a negative shock to the permanent component of the neutral technology, "P,t. Note

that the model is able to account for the initial fall and subsequent persistent rise in the

unemployment rate. The model also accounts for the initial rise and subsequent fall in

vacancies and the job finding rate after a negative shock to the permanent component of

neutral technology. The model is consistent with the relatively small response of the labor

force participation rate to a technology shock.

Turning to the response of inflation, note that our VAR implies that the maximal response

occurs in the period of the shock.11 Interestingly, our model has no problem reproducing

this observation. As argued in CTW, this reflects two features of our model: (i) there is no

indexation of prices and (ii) the wealth e§ect associated with a negative shock to technology

is relatively modest. In the case of (ii) CTW point out that the very high autocorrelation

of technology growth estimated in Altig, Christiano, Eichenbaum and Linde (2011) triggers

such a strong wealth e§ect that the model is unable to reproduce the sharp VAR-based

estimate of the rise in inflation. To understand the role of wealth e§ects, recall that in

models with nominal rigidities, marginal cost is a key determinant of inflation. Recall also

that the marginal cost of production, MC, is the ratio of marginal cost of an input, Pinput,

to that input’s marginal productivity, MPinput:

MC =PinputMPinput

.

Other things the same, a negative technology shock drives marginal productivity, MPinput,

down and, hence, marginal cost and inflation up. The full e§ect of a negative technology

shock includes the general equilibrium impact on input costs, Pinput. A negative technology

shock that has a large negative wealth e§ect induces a drop in expenditures which induces

a slowdown in production and, hence a drop in Pinput. This latter e§ect attenuates (and,

maybe even reverses) the rise inMC. This is why it is that when the wealth e§ect associated

with a negative technology shock is large, it is hard to reproduce the VAR evidence that

inflation rises relatively sharply. In our components representation, a shock to the permanent

component of technology has a large wealth e§ect. However, agents who cannot distinguish

between the temporary and permanent components of technology are not aware of this fact.

They initially believe that a negative forecast error in technology is transient in nature. As a

result, the wealth e§ect associated with the response to a shock in the permanent component

of technology is small.11This finding is consistent with results in Christiano, Eichenbaum and Vigfusson (2005, 2006), Altig,

Christiano, Eichenbaum and Linde (2011), Paciello (2011) and Sims (2011).

21

Figure 3 reports the VAR-based estimates of the responses to investment-specific tech-

nology shocks. The figure also displays the responses to "Ψ,t implied by our model evaluated

at the posterior mode of the parameters. Note that in all cases the model impulses lie in the

95% probability interval of the VAR-based impulse responses.

Viewed as a whole, the results of this section provide evidence that our model does well

at accounting for the cyclical properties of key labor market and other macro variables, as

measured by their response, in the non-ZLB period, to a monetary policy shock, a neutral

technology shock and an investment specific technology shock.

4.4. A shock to government consumption

We conclude by discussing the model’s implications for government spending in ‘normal’

times, i.e. a period during which the ZLB on the nominal interest rate is not binding.

Figure 5 displays the response of the economy to a 1 percentage point increase in gt.The

solid and dotted lines display the impulse response functions of variables when gt follows an

AR coe¢cient, ρg, with 0.6 and 0.9,respectively. In both cases, the rise in gt induces a rise

hours worked, the labor force, hours worked, real GDP and the job finding rate. Real wages

and inflation rise but by relatively small amounts. At the same time the rise in gt leads to a

persistent fall in the unemployment rate. In both cases, consumption initially rises. When ρgis equal to 0.9, consumption eventually falls due to the stronger negative wealth e§ect from

the larger rise in taxes associated with larger rise in the present value of government spending.

In both cases, investment falls in response to an increase in government consumption, with

the fall larger when ρg is equal to .9.

The basic intuition for how a government spending shock a§ects the economy is similar

to the traditional NK model, except for the mechanism in the labor market. As in standard

NK sticky price models, an expansionary shock to government purchases leads to an increase

in the demand for final goods. This rise induces an increase in the demand for the output

of sticky price retailers. Since they must satisfy demand, the retailers purchase more of

the wholesale good. Therefore, the relative price of the wholesale good increases and the

marginal revenue product associated with a worker rises. Other things equal, this motivates

wholesalers to hire more workers and increases the probability that an unemployed worker

finds a job. The latter e§ect induces a rise in workers’ disagreement payo§s. The resulting

increase in workers’ bargaining power generates a rise in the real wage and provides an

incentive for the household to increase the size of the labor force. Given our assumptions

about parameter values, alternating o§er bargaining mutes the increase in real wages, thus

allowing for a large rise in employment, a substantial decline in unemployment, and a small

rise in inflation.

22

5. The Great Recession

In this section we analyze the behavior of the economy in the last 4 years. Our goal is to

assess which specific shocks drive that behavior. To do so, we must take a stand on what the

economy would have looked like in the absence of the shocks associated with the financial

crisis and the Great Recession. Given the resulting projection, we use our model to assess

which shocks account for the gap between what actually happened and our projection.

The section is organized as follows. First, we describe our characterization of how the

economy would have evolved absent the Great Recession. Second, we describe the shocks that

we subject our model to. In the third and fourth subsections below we describe the time series

representations for the shocks and our assumptions about monetary policy, respectively. In

the fifth subsection, we discuss our strategy for doing stochastic simulations with our model,

and how we take into account various nonlinearities in the model solution. Finally, we discuss

our empirical results.

5.1. Characterizing the Recession

The solid line in Figure 6 displays the behavior of key macroeconomic variables since 2001.

To assess how the economy would have evolved absent the large shocks associated with the

Great Recession, we adopt a very simple, transparent procedure. With four exceptions, we

fit a linear trend from 2001 to 2008Q2, represented by the dark-dashed line. For reasons

discussed below we include a measure of the spread between the corporate-borrowing rate

and the risk-free interest rate. The measure that we use corresponds to the one provided in

Gilchrist and Zakrajöek (2012) (GZ).12 With four exceptions, to characterize what the data

would have looked like absent the shocks that caused the financial crisis and Great Recession,

we extrapolate the trend line (see the thin dashed line) for each variable. The exceptions are

inflation, the federal funds rate, the unemployment rate and the job finding rate.13 There

are of course many alternative procedures for projecting the behavior of the economy, e.g.

assuming linear trends for all the variables, using separate ARMA time series models for each

of the variables, and adopting multivariate forecasting models. These alternatives would be

interesting to pursue in the future. We conjecture that our main qualitative conclusions

would be robust to these alternatives.

The projections for the labor force and employment after 2008Q2 are controversial be-

cause of ongoing demographic changes in the U.S. population. Our procedure attributes

12As Figure 6 shows, the spread was already unusually high in 2008Q2. Our projection as of 2008Q2 isthat the GZ spread falls to 1 percent, its value during the relatively tranquil period, 1990-1997.13For these variables, we assume a no-change trajectory after 2008Q2. Using a linear trend to extrapolate

the post 2008Q2 behavior for these variables led to very strange results. For example, the federal funds ratewould be projected to be almost six percent in the second quarter 2013.

23

roughly 1.5 percentage points of the 2.5 percentage point decline in the labor force par-

ticipation rate since 2008 to cyclical factors. Projections for the labor force to population

ratio made by the Bureau of Labor Statistics in November, 2007 suggest that the cyclical

component in the decline in this ratio was roughly 2 percentage points.14 The estimates in

Reifschneider, Wascher and Wilcox (2013) and Sullivan (2013) put the cyclical component of

the decline in the labor force to population ratio at 1 percentage point and 0.75 percentage

points respectively. We are roughly at the mid-point of existing estimates.

According to Figure 6, the employment to population ratio fell about 5 percentage points

from 2008 to 2013. According to our procedure only a small part, about 0.5 percentage

points, of this drop is accounted for by non-cyclical factors. An estimate of the non-cyclical

change in the employment to population ratio that focuses more explicitly on demographic

factors is three times larger, roughly 1.6 percentage points.15 These estimates are similar, in

that they both ascribe a small portion of the decline in the employment to population ratio

to non-cyclical factors.

The distance between the solid lines and the thin-dashed lines represents our estimate of

the economic e§ects of the shocks that hit the economy in 2008Q3 and later (see Figure 7).

Of course, the dynamics of the data over this period also reflect the e§ects of shocks that

occurred before 2008Q3. Our procedure assumes that those e§ects are relatively small.

5.2. The Shocks Driving the Great Recession

We suppose that the Great Recession was triggered by four shocks that occurred prior to

2008Q3. Two of these shocks are wedges which capture in a reduced form way frictions

which are widely viewed as having been important during the Great Recession. The other

sources of shocks that we allow are government consumption and technology.

Financial Shocks14See Erceg and Levin (2013), Figure 1.15A rough back-of-the-envelope calculation to assess the importance of demographic changes can be found

on Krugman’s blog post of February 3, 2014 (see http://krugman.blogs.nytimes.com/). He reports a BLSestimate that the share of the population aged 25 to 54 fell from 54 to 50 percent between 2007 and 2013.At the same time, the share of the population aged 55 to 64, 64 and above each increased by 2 percentagepoints (the share of the population in the 16-24 year range remain unchanged at 16 percent). The fractionof the people in each of these three groups that was employed in 2007 was 0.80, 0.62 and 0.16, respectively.If the employment to population ratio had remained unchanged in each of these three groups and only thepopulation shares had changed, then the change in the aggregate employment to population ratio wouldhave been:

−0.04× 0.80 + 0.62× 0.02 + 0.16× 0.02 = −0.016,

or −1.6 percentage points. These calculations suggest that demographics account for roughly 1.6 percentagepoints in the overall 5 percentage point decline in the employment to population ratio between 2007 and2013.

24

We begin by discussing the two financial shocks. The first is a shock to households prefer-

ences for safe and / or liquid assets.16 We capture this shock by introducing a perturbation,

∆bt , to agents’ intertemporal Euler equation associated with saving via risk-free bonds. With

this wedge, the Euler equation associated with the nominally risk free bond is given by:

1 = (1 +∆bt)Etmt+1Rt/πt+1.

The second shock represents a wedge to agents’ intertemporal Euler equation for capital

accumulation:

1 = (1−∆kt )Etmt+1R

kt+1/πt+1.

A simple financial friction model based on asymmetric information with costly monitoring

implies that credit market frictions can be captured as a tax, ∆kt , on the gross return on

capital (see Christiano and Davis (2006)). We refer to ∆bt and ∆

kt as the consumption wedge

and the financial wedge, respectively.

Recall that firms finance a fraction, , of the intermediate input in advance of revenues(see (2.15)). In contrast to the existing DSGE literature, we allow for a risky working capital

channel. In particular we suppose the financial wedge also applies to working capital loans.

So firms pay a premium, relative to the risk-free rate, for working capital loans. As a result,

we replace (2.15) with

P ht(Rt

(1 +∆k

t

)+ (1− )

), (5.1)

where = 1/2, as before. The risky working capital channel captures in a reduced form

way the frictions models in Bigio (2013) and Kurlat (2013).

We measure the financial wedge using the GZ interest rate spread. The latter is based

on the average credit spread on senior unsecured bonds issued by non-financial firms covered

in Compustat and by the Center for Research in Security Prices. The average and median

duration of the bonds in GZ’s data set is 6.47 and 6.00 years, respectively. We interpret the

GZ spread as an indicator of ∆kt . We suppose that the ∆

kt ’s are related to the GZ spread as

follows:

Γt = E

[∆kt +∆

kt+1 + ...+∆

kt+23

6|Ωt], (5.2)

where Γt denotes the GZ spread minus the projection of that spread as of 2008Q2 (see the

dashed line in Figure 6). Also, Ωt denotes the information available to agents at time t. In

(5.2) we sum over ∆kt+j for j = 0, ..., 23 because ∆k

t is a tax on the one quarter return to

16This shock is similar to the shock in the small scale DSGE model with no capital and frictionlesslabor markets considered in Christiano, Eichenbaum and Rebelo (2011), Eggertsson and Krugman (2012),Eggertsson and Woodford (2003), Guerrieri and Lorenzoni (2012 ). The shock is also similar to the ‘flightto quality’ shock found to play a substantial role in the start of the Great Depression in Christiano, Mottoand Rostagno (2003).

25

capital while Γt applies to t + j, j = 0, 1, ..., 23 (i.e., 6 years). Also, we divide the sum in

(5.2) by 6 to take into account that ∆kt is measured in quarterly decimal terms while our

empirical measure of Γt is measured in annual decimal terms.

We feed the sequence of Γt’s displayed in the 4,3 panel in Figure 7 for t ≥ 2008Q3 to ourmodel. However, we do not assume that agents have perfect foresight over the Γt’s. Instead,

we assume that at time t agents observe Γt−s, s ≥ 0 and that they forecast future values ofΓt using a mean-zero, first order autoregressive representation (AR(1)), with autoregressive

coe¢cient, ρΓ = 0.33.We chose this value of ρΓ, in conjunction with the shocks discussed

below, to help the model achieve its targets. This low value of ρΓ captures the idea that

agents thought the sharp increase in financial wedge was fairly transitory in nature. This

belief is consistent with the behavior of the GZ spread. Interestingly, if we increase the value

of ρΓ, the model generates a counterfactually large fall in investment

Total Factor Productivity (TFP)

We now turn to a discussion of total factor productivity (TFP), which is graphed in the

4,1 panel in Figure 6. In practice, TFP is measured by taking the ratio of a measure of

output to a Cobb-Douglas function of capital and labor, where each factor is raised to a

power that corresponds to its empirical income share. Di§erent empirical measures of TFP

vary according to whether they adjust for utilization of capital and/or labor, or whether they

pertain to the whole economy or just the business sector. Our measure of TFP does not

adjust for utilization, uses GDP as the measure of output and is constructed by the BLS.

Figure 7 displays the di§erence between the level of TFP and its linear trend computed

between 2008Q3 and 2013Q2. The detrended data are clearly very volatile. In our view

some of this volatility reflects measurement error because of the well known di¢culties of

correctly computing TFP at a quarterly frequency.

The principle, though not only, shock driving measured TFP according to our model

is the neutral technology shock. The log of TFP is not exactly the same as ln (zt) in our

model because GDP is not produced by a Cobb-Douglas production function. Instead, it is a

Cobb-Douglas production function minus a fixed cost that is on average about 30 percent of

GDP. Other, much smaller terms related to hiring costs and capital utilization costs are also

subtracted from the Cobb-Douglas production function to obtain GDP. When we compute

TFP in the model, we do so using the analog of the procedure used to compute GDP in the

data.

Recall that our neutral technology shock evolves according to the unobserved components

representation in (2.31) - (2.33). We set the values of the parameters to their posterior mode

from the pre-2008 estimation. We assume that there was a negative shock to the permanent

component of ln (zt) in 2008Q2 of size −0.75%. The persistence of this shock to the growth

26

rate of ln (zt) is given by the estimated value of ρP , 0.72. So the level of ln (zt) is eventually

roughly 2.5 percentage points below its pre-shock level. We think this a reasonable scenario

to entertain given that the value of TFP has not returned to its pre-crisis level. Recall that

according to our model, agents initially assign a high probability that negative shock to

ln (zt) is actually to the transient component of neutral technology. So they initially think

that ln (zt) will return its pre-shock level. Eventually, as agents see the persistence of the

drop in ln (zt), they begin to realize that the shock was actually to the permanent component

of ln (zt) . These forecasts are computed using standard Kalman filtering methods. Given

our estimates, in 2008Q3 agents think that the odds are one in five that the shock to ln (zt)

is to the permanent component. By the end of the recession, 2009Q2, agents think that the

odds are one to one that the 2008Q3 shock to technology was to the permanent component.

The Shock to Government Consumption

Next we consider the shock to government consumption. The variable ηgt defined in

(2.29) is computed using the simulated path of neutral technology, ln (zt) , using (2.34) and

(2.35).17 Then, gt is actual government consumption in Figure 6, divided by ηgt . Agents

forecast the period t value of ηgt using current and past realizations of the technology shocks.

For simplicity, we suppose as in Edelberg, Eichenbaum and Fisher (1999) and Schmitt-

Grohé and Uribe (2004), that in forecasting gt agents assume ln (gt/g) is the realization of a

zero-mean AR(1) process with coe¢cient, ρg = 0.9.

The Consumption Wedge

We do not have data on ∆bt . So, we suppose that at 2008Q2, agents think that ∆

bt

goes from zero to a constant value, 0.35 percent per quarter, for 20 quarters, after which

it is expected to return to zero. In fact, when faced with the fiscal cli§ and the sequester

in 2012Q3, agents revise their expectation of how long they expect ∆bt to remain at 0.35

percent. We posit that at this point they believe it will continue until 2015Q2. We chose the

value of ∆bt to allow the model to come as close as possible, given our other assumptions, to

roughly match the post-2008Q2 consumption targets.

5.3. Time Series Representations for post-2008 Shocks

Here, we describe the law of motion of the shocks that we assume were operating on the

economy after late 2008. We describe the law of motion in terms of a state space/observer

17For simiplicity in our calculations we assume that the investment specific technology shock simply remainson its steady state growth path after 2008.

27

representation. Let the state associated with the exogenous shocks be denoted by the 5× 1vector ξt. The law of motion of ξt has the following form,

ξt = F ξt−1 +D"t,

where F and D are 5 × 5 matrices and "t is a 5 × 1 vector of iid shocks, uncorrelated withξt−1. Let yt denote the 3× 1 vector of exogenous variables that are observed by agents:

yt =

0

@ln (gt/g)Γt

ln(µz,t/µz

)

1

A , (5.3)

where g and µz represent the steady state values of gt and neutral technology, µz,t (≡ zt/zt−1) ,respectively. We assume that the steady state value of Γt is zero. The vector, yt, is related

to the state by the 3× 5 matrix H :

yt = Hξt.

We posit that the first two elements of yt have a first order autoregressive (AR(1)) repre-

sentation with AR parameters ρg and ρΓ, respectively. In addition, the standard deviations

of the innovations are σg and σΓ. The third element of yt is assumed to have the unobserved

components representation specified in (2.31), (2.32) and (2.33).

We define the elements of the state-space/observer system as follows:

ξt =

0

BBBB@

log (gt/g)Γtµp,t

µτ ,t − στ"τ ,tστ"τ ,t

1

CCCCA, "t =

0

BB@

"g,t"Γ,t"p,t"τ ,t

1

CCA

F =

2

66664

ρg 0 0 0 00 ρΓ 0 0 00 0 ρp 0 00 0 0 ρτ ρτ − 10 0 0 0 0

3

77775, D =

2

66664

σg 0 0 00 σΓ 0 00 0 σp 00 0 0 00 0 0 στ

3

77775

H =

2

41 0 0 0 00 1 0 0 00 0 1 1 1

3

5 .

where µτ ,t and µp,t denote the temporary and permanent components of technology, respec-

tively.

We are able to compute P [yt+j|yt−s, s ≥ 0] for j > 0 at each date t using standard Kalmanfiltering formulas,

28

5.4. Monetary Policy

We make two key assumptions about monetary policy during the post 2008Q3 period. First,

we assume that the Fed initially followed a version of the Taylor rule that respects the ZLB on

the interest rate. Second, we assume that there is an unanticipated regime change in 2011Q3,

when the Fed switched to a policy of forward guidance. We model forward guidance as a

commitment to keep the Federal Funds rate close to zero until either the unemployment rate

falls below 6.5 percent or inflation rises above 2.5 percent. We assume that as soon as these

thresholds are met, the Fed switches back to our estimated Taylor rule. We refer to this type

of forward guidance policy as ‘threshold-based forward guidance’. The forward guidance

policy in the year after 2011Q3 is often referred to as ‘date-based forward guidance’ because

each Fed policy announcement specified a date when the Federal Funds rate was expected

to rise above zero (‘lift o§’). We interpret this policy as actually being threshold based. We

do so because the Fed repeatedly extended the date for lift o§, suggesting that the date was

a proxy for the expected state of the economy.

We now define our version of the Taylor rule that takes into account the non-negativity

constraint on the interest rate. Let Zt denote a gross ‘shadow’ nominal rate of interest, which

satisfies the following Taylor-style monetary policy rule:

ln(Zt) = ln(R)+rπ ln(πAt /π

A)+0.25ry ln (Yt/Y∗t )+0.25r∆y ln

(Yt/(Yt−4ι∆y

))+σR"R,t. (5.4)

The actual policy rate, Rt, is determined as follows:

ln (Rt) = max ln (R/a) , ρR ln(Zt−1) + (1− ρR) ln(Zt) (5.5)

Absent the ZLB constraint, the policy rule given by (5.4)-(5.5) coincides with (2.28), the

policy rule that we estimated using pre-2008Q2 data. We discuss the positive scalar, a,

below.

5.5. Solving the Model

Stochastic simulation of our model is challenging because of several factors. First, there are

the usual nonlinearities in the equilibrium conditions. Second, the equations that characterize

monetary policy switch depending on the realization of endogenous variables.

Standard solution procedures adopt a recursive representation of the economy and seek

a solution in the form of a time invariant policy rule. In contrast, we search for a solution

in the form of a sequence that satisfies the equilibrium conditions as stochastic di§erence

equations restricted by initial and end-point conditions. The approximation adopted by our

solution procedure is certainty equivalence. That is, wherever an expression like Etf (xt+j)

is encountered, we replace it by f (Etxt+j) , for j > 0.

29

We assume that the only stochastic shocks operating in the post-2008 period are the

ones in the vector yt, defined in (5.3). An additional source of variation comes from the

deterministic sequence of consumption wedges, ∆bt .

Let %t denote the N × 1 vector of period t endogenous variables. We express the equilib-rium conditions of the model as follows:

E[f(%t+1, %t, %t−1, yt, yt+1,∆

bt ,∆

bt+1

)|Ωt]= 0, (5.6)

where the information set is given by

Ωt =%t−1−j, yt−j, j ≥ 0

.

Our solution strategy proceeds as follows. Consistent with our discussion above we fix a

set of values for yt for the period after 2008Q2. We suppose that at date t agents observe

yt−s, s ≥ 0 for each t after 2008Q2. At each such date t, they compute forecasts, ytt+1, ytt+2,ytt+2, ..., of the future values of yt using the Kalman filtering techniques that are appropriate

given the state space - observer system described above. It is convenient to use the notation

ytt ≡ yt.We adopt an analogous notation for %t. In particular, denote the expected value of %t+j

formed at time t by %tt+j, where %tt+j ≡ %t for j = 0. The equilibrium value of %t is the

first element in the sequence, %tt+j, j ≥ 0. To compute this sequence we require ytt+j, j ≥ 0,and %t−1. For t greater than 2008Q3 %t−1 = %t−1t−1. For t corresponding to 2008Q3, we simply

set %t−1 to its non-stochastic steady state value. We now discuss how we computed %tt+j,

j ≥ 0. We do so by solving the equilibrium conditions and imposing certainty equivalence.

In particular, %tt must satisfy:

E[f(%t+1, %t, %t−1, yt, yt+1,∆

bt ,∆

bt+1

)|Ωt]

' f(%tt+1, %

tt, %

t−1t−1, y

tt, y

tt+1,∆

bt ,∆

bt+1

)= 0.

Evidently, to solve for %tt requires %tt+1. Relation (5.6) implies:

E[f(%t+2, %t+1, %t, yt+1, yt+2,∆

bt+1,∆

bt+2

)|Ωt]

' f(%tt+2, %

tt+1, %

tt, y

tt+1, y

tt+2,∆

bt+1,∆

bt+2

)= 0.

Proceeding in this way, we obtain a sequence of equilibrium conditions involving %tt+j, j ≥ 0.Solving for this sequence requires a terminal condition. We obtain this condition by imposing

that %tt+j converges to the non-stochastic steady state value of %t. With this procedure it is

easy to implement the monetary policy rule that we have assumed: a Taylor rule with a

potentially binding ZLB until 2011Q3, when there is an unanticipated switch to forward

guidance.

30

5.6. Results

Our results are reported in Figures 7-18. Figure 7 displays the simulation of our model when

the five shocks are chosen in the manner discussed above. The key result is that the model

does quite well at accounting for the behavior of 11 endogenous variables in the post-2008

period. Notice in particular that the model is able to account for the modest decline in

real wages despite the absence of nominal rigidities in wage setting. Also, notice that the

model accounts very well for the average level of inflation despite the fact that our model

incorporates only a moderate degree of price stickiness: firms change prices on average once

a year. In addition, the model also accounts well for the key labor market variables: labor

force participation, employment, unemployment vacancies and the job finding rate. The

model does not capture the extent of the drop in consumption after 2011.

Figures 8 through 12 decompose the impact of the di§erent shocks and the working

capital channel on the economy in the post 2008Q3 period. We determine the role of a shock

by setting that shock to its steady state value and redoing the simulations underlying Figure

7. The resulting decomposition is not additive because of the nonlinearities in the model.

The Role of Neutral Technology Shocks and the Working Capital Channel

Figure 8 displays the e§ect of the neutral technology shock on post-2008 simulations. For

convenience, the solid line reproduces the corresponding solid line in Figure 7. The dashed

line displays the behavior of the economy when neutral technology shocks are shut down (i.e.,

"pt = 0 in 2008Q3). Comparing the solid and dashed lines, we see that the neutral technology

slowdown had a significant impact on inflation. Had it not been for the decline in neutral

technology, there would have been substantial deflation, as predicted by very simple New

Keynesian models that do not allow for a drop in technology. This result is anticipated by

the VARs estimated in the pre-2008 period according to which a negative neutral technology

shock has a very substantial and sharply estimated positive impact on inflation. Since the

negative technology shocks induced more inflation and the ZLB constraint was binding, those

shocks also to lower real interest rates. Consequently, aggregate demand was higher than it

would have been absent the negative technology shocks. So employment and real wages are

higher than they would have been otherwise. Other things equal, higher real wages make

home production less attractive relative to work in the market thus inducing a drop in the

labor force participation rate and a decline the unemployment rate.

Medium sized DSGE models often abstract from the working capital channel. A natural

question is how important is that channel in allowing our model to account for the moderate

degree of inflation during the Great Recession. To answer that question, we redo the simu-

lation underlying Figure 7, replacing (5.1) with (2.15). The results are displayed in Figure

31

9. We find that the working capital channel plays a critical role in allowing the model to

account the moderate amount of inflation that occurred during the Great Recession. In the

presence of a working capital requirement, a higher interest rate due to a positive financial

wedge shocks directly raises firms’ marginal cost. Other things equal this leads to inflation.

Taken together the negative technology shocks and the working capital channel explain the

relatively modest disinflation that occurred during the Great Recession. Essentially they

exerted countervailing pressure on the disinflationary forces that were operative during the

Great Recession. The output e§ects of the working capital channel are much weaker than

those of the neutral technology shocks. In part this reflects the fact that the working capital

risk channel works via the financial wedge shocks and these are much less persistent than

the technology shocks.

Figures 10 and 11 report the e§ects of the financial and consumption wedges, respectively.

These shocks play a vital role in driving the economy into the ZLB. They also account for the

vast bulk of movements in real quantities. The financial wedge is overwhelmingly the most

important shock for investment. At the same time, the consumption wedge and financial

wedge play roughly equal roles in accounting for the drop in consumption. Notice that the

model attributes the substantial drop in the labor force participation rate almost entirely

to the consumption and financial wedges. This reflects that these wedges lead to a sharp

deterioration in labor market conditions: drops in the job vacancy and finding rates and in

the real wage. In this way, the model is consistent with the fact that labor force participation

rates are not very cyclical during normal recessions, while being very cyclical during the Great

Recession.

We now turn to Figure 12, which displays the role of government consumption in the

Great Recession. Government consumption passes through two phases. The first occurs

at the beginning and involves the expansion associated with the American Recovery and

Reinvestment Act of 2009. The second phase involves a contraction that began around the

beginning of 2011. The first phase involves a maximum rise of 3 percent in government

consumption (i.e., 0.6 percent of GDP) and a maximum rise of 1 percent in GDP. This

implies a maximum government consumption multiplier of 1/.6 or 1.67. In the second phase

it is clear that the government spending, while contractionary, has a very small multiplier

e§ect on output. It is di¢cult to attribute the long duration of the Great Recession to

the recent decline in government consumption. These findings are consistent with results

reported in Christiano, Eichenbaum and Rebelo (2011). They show that a rise in government

consumption that is expected to not extend beyond the ZLB has a large multiplier e§ect.

They also show that a rise in government consumption that is expected to extend beyond the

ZLB has a relatively small multiplier e§ect. A feature of our simulations is that the increase

in government consumption in the first phase is never expected by agents to persist beyond

32

the ZLB. But, the second phase in which there is a decrease in government consumption

does cause agents to expect that decrease to persist beyond the end of the ZLB.

Figure 16 documents the e§ects of government spending shocks in and out of the ZLB

referred to in the previous paragraph. The upper and lower panels report two model simula-

tions in which the ZLB is binding for three years, after which monetary policy reverts to the

Taylor rule. The top panel displays government spending in the two simulations. In each

case, agents in the model are assumed to know the path of government spending with perfect

foresight. The solid line corresponds to the case when government spending is expected to

remain high just during the three years when the ZLB is binding. The dashed line indicates

government spending when it is expected to also remain high for three years after the ZLB

ceases to bind. The bottom panel displays dGDPt/dGt at each t during the simulations.

These derivatives are computed by comparing simulations with and without the change in

government spending. The key thing to note in Figure 16 is that, as discussed in the previous

paragraph, the government spending multiplier is much larger when government spending is

expected to be high only while the ZLB lasts.

Figure 13 displays the impact of the switch to forward guidance in 2011. The dashed line

represents the model simulation with all shocks, when the Taylor rule is in place throughout

the period. Under the Taylor rule, there would have been some lift o§ during 2012 because of

the shrinking size of the fall in inflation. Our estimated Taylor rule assigns a relatively small

weight to output and no weight to unemployment, so the fact that these variables remain

depressed plays only a small role in the Taylor rule. But, forward guidance’s heavy emphasis

on unemployment exerts downward pressure on the interest rate, keeping it at the ZLB

throughout the period since 2008. Our estimates are that the switch to forward guidance

had a noticeable positive e§ect on unemployment, output and labor market variables.

Figure 14 displays the e§ect, in our simulations, of the unexpected extension in the

duration of the consumption wedge, ∆bt , in 2011Q3. The primary e§ect is that in the absence

of that extension the model would have predicted a return to steady state in inflation. In

addition, it would have predicted a lifto§ in inflation in the middle of 2014, rather than the

2015 lifto§ prediction in our baseline simulation.

Figure 15 displays the Beveridge curve in our model. In terms of the actual data, note

how vacancies and unemployment follow a negative sloped line between 2008Q3 and 2009Q4,

the o¢cial end of the recession. This negative slope is what is referred to as the ‘Beveridge

curve’. After 2009Q4, the curve seems to shift up, as vacancies rise but unemployment falls

less than expected based on the 2008Q3-2009Q4 period. This is sometimes interpreted to

reflect a shift in the Beveridge curve which in turn is supposedly due to greater di¢culties

in matching workers and firms. This has led to speculation that this increased di¢culty is

a symptom of an increased mismatch between the skills required by firms and the skills in

33

the workforce. Our simulation results suggest that although mismatch may well be a larger

version of today’s labor market, it does some seem to be the central force accounting for

the persistent high unemployment and low employment. According to Figure 15 our model

is able to account for the pattern of vacancies and unemployment since 2008Q3 while by

construction the technology whereby vacancies and unemployment result in matches has

remained constant in our simulations.

6. Conclusion

This paper argues that the vast bulk of movements in aggregate real economic activity during

the Great Recession were due to financial frictions interacting with the ZLB. We reach this

conclusion looking through the lens of a New Keynesian model in which firms face moderate

degrees of price rigidities and no nominal rigidities in the wage setting process. Our model

does a good job of accounting for the joint behavior of labor and goods markets, as well

as inflation, during the Great Recession. According to the model the observed fall in TFP

played a critical role in accounting for the small size of the drop in inflation that occurred

during the Great Recession.

34

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38

Table 1: Non-Estimated Model Parameters and Calibrated Variables

Parameter Value Description

Panel A: ParametersK 0.025 Depreciation rate of physical capital 0.9968 Discount factor 0.9 Job survival probabilityM 60 Maximum bargaining rounds per quarter

(1 )1 3 Elasticity of substitution market and home consumption100

A 1

2 Annual net ináation rate target

400ln () 1.7 Annual output per capita growth rate400ln ( ) 2.9 Annual investment per capita growth rate

Panel B: Steady State Valuesprofits 0 Intermediate goods producers proÖtsQ 0.7 Vacancy Ölling rateu 0.055 Unemployment rateL 0.67 Labor force to population ratioG=Y 0.2 Government consumption to gross output ratio

Table 2: Priors and Posteriors of Model Parameters

Prior Posterior

Distribution Mean,Std. Mode Std.

Price Setting ParametersPrice Stickiness Beta 0.66,0.15 0.737 0.022Price Markup Parameter Gamma 1.20,0.05 1.315 0.042

Monetary Authority ParametersTaylor Rule: Interest Rate Smoothing R Beta 0.70,0.15 0.794 0.017Taylor Rule: Ináation Coe¢cient r Gamma 1.70,0.15 1.730 0.126Taylor Rule: GDP Gap Coe¢cient ry Gamma 0.10,0.05 0.015 0.009Taylor Rule: GDP Growth Coe¢cient ry Gamma 0.25,0.10 0.231 0.095

Preferences and TechnologyMarket and Home Consumption Habit b Beta 0.50,0.15 0.894 0.013Capacity Utilization Adjustment Cost a Gamma 0.50,0.30 0.014 0.011Investment Adjustment Cost S

00Gamma 8.00,2.00 10.62 1.260

Capital Share Beta 0.33,0.03 0.257 0.017Technology Di§usion Beta 0.50,0.20 0.163 0.035

Labor Market ParametersProbability of Bargaining Breakup 100 Gamma 0.50,0.20 0.049 0.015Replacement Ratio D=w Beta 0.40,0.10 0.185 0.057Hiring Cost to Output Ratio sl Gamma 1.00,0.30 0.513 0.148Labor Force Adjustment Cost L Gamma 100,50.0 162.7 35.35Unemployed Share in Home Production cH Beta 0.03,0.01 0.019 0.006Probability of Staying in Labor Force s Beta 0.85,0.05 0.798 0.069Matching Function Parameter Beta 0.50,0.10 0.544 0.036

ShocksStandard Deviation Monetary Policy Shock R Gamma 0.65,0.05 0.644 0.035AR(1) Persistent Component of Neutral Techn. P Gamma 0.75,0.10 0.716 0.051Stdev. Persistent Component of Neutral Techn. P Gamma 0.10,0.05 0.071 0.012AR(1) Transitory Component of Neutral Techn. T Beta 0.75,0.10 0.864 0.047Stdev. Ratio Transitory and Perm. Neutral Techn. T =P Gamma 5.00,2.00 5.085 1.679AR(1) Investment Technology Beta 0.75,0.10 0.784 0.045Standard Deviation Investment Technology Shk. Gamma 0.10,0.05 0.096 0.015

Notes: sl denotes the steady state hiring to gross output ratio (in percent):

Table 3: Model Steady States and Implied Parameters

VariableAt EstimatedPosterior Mode

Description

K=Y 7.30 Capital to gross output ratio (quarterly)C=Y 0.56 Market consumption to gross output ratioI=Y 0.23 Investment to gross output ratiol 0.63 Employment to population ratioR 1.0125 Gross nominal interest rate (quarterly)Rreal 1.0075 Gross real interest rate (quarterly)mc 0.76 Marginal cost (inverse markup)b 0.036 Capacity utilization cost parameterY 0.87 Gross output=Y 0.32 Fixed cost to gross output ratiom 0.66 Level parameter in matching functionf 0.63 Job Önding rate# 1.013 Marginal revenue of wholesalerx 0.1 Hiring rateJ 0.07 Value of ÖrmV 204.0 Value of workU 200.0 Value of unemploymentN 192.4 Value of not being in the labor forcev 0.14 Vacancy ratee 0.06 Probability of leaving non-participation! 0.48 Home consumption weight in utilityCH 0.31 Home consumptionw 1.006 Real wage

=(#=M) 0.81 Countero§er costs as share of daily revenue

0 5 10−0.2

0

0.2

0.4

GDP (%)

0 5 10−0.2

−0.1

0

0.1

0.2

Unemployment Rate (p.p.)

0 5 10−0.2

−0.1

0

0.1

0.2

Inflation (ann. p.p.)

0 5 10−0.8

−0.6

−0.4

−0.2

0

0.2Federal Funds Rate (ann. p.p.)

0 5 10−0.2

0

0.2

0.4

Hours (%)

0 5 10−0.2

0

0.2

0.4

Real Wage (%)

0 5 10−0.2

0

0.2

0.4

Consumption (%)

0 5 10−0.1

0

0.1

0.2Labor Force (%)

0 5 10−1

0

1

Investment (%)

0 5 10−1

0

1

Capacity Utilization (%)

0 5 10−1

0

1

Job Finding Rate (p.p.)

Figure 1: Impulse Responses to an Expansionary Monetary Policy Shock

0 5 10−2

0

2

4

Vacancies (%)

Notes: x−axis in quarters.

VAR 95% VAR Mean Model

0 5 10−0.8−0.6−0.4−0.2

00.2

GDP (%)

0 5 10−0.2

−0.1

0

0.1

0.2

Unemployment Rate (p.p.)

0 5 10−0.2

00.20.40.60.8

Inflation (ann. p.p.)

0 5 10−0.2

0

0.2

0.4

Federal Funds Rate (ann. p.p.)

0 5 10−0.8−0.6−0.4−0.2

00.2

Hours (%)

0 5 10−0.8−0.6−0.4−0.2

00.2

Real Wage (%)

0 5 10−0.8−0.6−0.4−0.2

00.2

Consumption (%)

0 5 10

−0.4

−0.2

0

0.2Labor Force (%)

0 5 10−2

−1

0

1

Investment (%)

0 5 10−2

−1

0

1

Capacity Utilization (%)

0 5 10−2

−1

0

1

Job Finding Rate (p.p.)

Figure 2: Impulse Responses to a Negative Permanent Neutral Technology Shock

0 5 10−4

−2

0

2

Vacancies (%)

Notes: x−axis in quarters.

VAR 95% VAR Mean Model

0 5 10

−0.6

−0.4

−0.2

0

0.2

GDP (%)

0 5 10−0.2

−0.1

0

0.1

0.2

Unemployment Rate (p.p.)

0 5 10−0.2

00.20.40.60.8

Inflation (ann. p.p.)

0 5 10

−0.4

−0.2

0

0.2

0.4Federal Funds Rate (ann. p.p.)

0 5 10

−0.6

−0.4

−0.2

0

0.2

Hours (%)

0 5 10

−0.6

−0.4

−0.2

0

0.2

Real Wage (%)

0 5 10

−0.6

−0.4

−0.2

0

0.2

Consumption (%)

0 5 10

−0.2−0.1

00.10.2

Labor Force (%)

0 5 10−2

−1

0

1

Investment (%)

0 5 10−2

−1

0

1

Capacity Utilization (%)

0 5 10−2

−1

0

1

Job Finding Rate (p.p.)

Figure 3: Impulse Responses to a Negative Investment−Specific Tech. Shock

0 5 10

−4

−2

0

2

Vacancies (%)

Notes: x−axis in quarters.

VAR 95% VAR Mean Model

0 2 4 6 8 10 12 140

0.2

0.4

0.6

0.8

Response to Investment−Specific Technology Shock

0 2 4 6 8 10 12 14−0.2

−0.1

0

0.1

0.2

0.3

0.4

0.5Response to Permanent Neutral Tech. Shock

Figure 4: Impulse Responses of Relative Price of Investment

0 2 4 6 8 10 12 14

−0.25

−0.2

−0.15

−0.1

−0.05

0

0.05

Response to Monetary Policy Shock

Notes: x−axis in quarters, y−axis in percent

VAR 95% VAR Mean Model

0 5 100

0.5

1

GDP (%)

0 5 10

−0.8

−0.6

−0.4

−0.2

0Unemployment Rate (p.p.)

0 5 100

0.1

0.2

0.3Inflation (ann. p.p.)

0 5 100

0.1

0.2

0.3Federal Funds Rate (ann. p.p.)

0 5 100

0.5

1Hours (%)

0 5 100

0.05

0.1

0.15

0.2

Real Wage (%)

0 5 10

−0.1

0

0.1

Consumption (%)

0 5 100

0.05

0.1

Labor Force (%)

0 5 10−0.8

−0.6

−0.4

−0.2

0

Investment (%)

0 5 100

0.5

1

Capacity Utilization (%)

0 5 100

2

4

6

Job Finding Rate (p.p.)

Figure 5: Impulse Responses to a Government Consumption Shock

0 5 100

5

10

15

20

Vacancies (%)

Notes: x − axis in quarters. Government consumption rises by 1% of steady state output in t=0.

Model: Gov. Consumption AR(1)=0.6 Model: Gov. Consumption AR(1)=0.9

2002 2004 2006 2008 2010 2012

−2.8

−2.75

−2.7

Log Real GDP

2002 2004 2006 2008 2010 2012

1

1.5

2

2.5

Inflation (%, y−o−y)

2002 2004 2006 2008 2010 2012

1

2

3

4

5

Federal Funds Rate (%)

2002 2004 2006 2008 2010 2012

5

6

7

8

9

Unemployment Rate (%)

2002 2004 2006 2008 2010 2012

59

60

61

62

63

64Employment/Population (%)

2002 2004 2006 2008 2010 20124.54

4.56

4.58

4.6

4.62

4.64

Log Real Wage

2002 2004 2006 2008 2010 2012

−5.55

−5.5

−5.45

Log Real Consumption

2002 2004 2006 2008 2010 2012−5.9

−5.8

−5.7

−5.6

−5.5

Log Real Investment

2002 2004 2006 2008 2010 2012

64

65

66

67

Labor Force/Population (%)

2002 2004 2006 2008 2010 2012

50

60

70

Job Finding Rate (%)

2002 2004 2006 2008 2010 20127.8

8

8.2

8.4

Log Vacancies

2002 2004 2006 2008 2010 2012

234567

G−Z Corporate Spread (%)

2002 2004 2006 2008 2010 2012

4.55

4.6

4.65

4.7Log TFP

Figure 6: The Great Recession in the U.S.

2002 2004 2006 2008 2010 2012

−4.42

−4.4

−4.38

−4.36

−4.34

Log Gov. Cons.+Invest.

Notes: Gray areas indicate NBER recession dates.

Data2008Q2Linear Trend from 2001Q1 to 2008Q2Forecast 2008Q3 and beyond

2009 2011 2013 2015−10

−5

0GDP (%)

DataModel

2009 2011 2013 2015

−1.5

−1

−0.5

0

Inflation (p.p., y−o−y)

2009 2011 2013 2015−2

−1.5

−1

−0.5

0Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

1

2

3

4

Unemployment Rate (p.p.)

2009 2011 2013 2015−4

−3

−2

−1

0Employment (p.p.)

2009 2011 2013 2015

−1.5

−1

−0.5

0

Labor Force (p.p.)

2009 2011 2013 2015

−30

−20

−10

0Investment (%)

2009 2011 2013 2015−8

−6

−4

−2

0Consumption (%)

2009 2011 2013 2015

−4

−2

0Real Wage (%)

2009 2011 2013 2015−80

−60

−40

−20

0Vacancies (%)

2009 2011 2013 2015−20

−15

−10

−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015−5−4−3−2−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 7: The U.S. Great Recession: Data vs. Model

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

Notes: Data are the differences between raw data and forecasts, see Figure 6.

2009 2011 2013 2015

−10

−5

0GDP (%)

Baseline ModelNo Neutral Tech.

2009 2011 2013 2015

−3

−2

−1

0

Inflation (p.p., y−o−y)

2009 2011 2013 2015

−1.5

−1

−0.5

0

Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

2

4

6

Unemployment Rate (p.p.)

2009 2011 2013 2015

−5−4−3−2−1

0Employment (p.p.)

2009 2011 2013 2015

−1.5

−1

−0.5

0Labor Force (p.p.)

2009 2011 2013 2015

−30

−20

−10

0Investment (%)

2009 2011 2013 2015

−6

−4

−2

0Consumption (%)

2009 2011 2013 2015−3

−2

−1

0Real Wage (%)

2009 2011 2013 2015

−100

−50

0Vacancies (%)

2009 2011 2013 2015−25−20−15−10−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 8: The U.S. Great Recession: Effects of Neutral Technology

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

2009 2011 2013 2015−10

−5

0GDP (%)

Baseline ModelNo Work. Capital Spread

2009 2011 2013 2015

−3

−2

−1

0Inflation (p.p., y−o−y)

2009 2011 2013 2015

−1.5

−1

−0.5

0Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

1

2

3

4

Unemployment Rate (p.p.)

2009 2011 2013 2015

−3

−2

−1

0Employment (p.p.)

2009 2011 2013 2015

−1

−0.5

0Labor Force (p.p.)

2009 2011 2013 2015−30

−20

−10

0Investment (%)

2009 2011 2013 2015−6

−4

−2

0Consumption (%)

2009 2011 2013 2015−3

−2

−1

0Real Wage (%)

2009 2011 2013 2015−80

−60

−40

−20

0Vacancies (%)

2009 2011 2013 2015−20

−15

−10

−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 9: The U.S. Great Recession: Effects of Spread on Working Capital

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

2009 2011 2013 2015−10

−5

0GDP (%)

Baseline ModelNo Fin. Wedge

2009 2011 2013 2015

−1.5

−1

−0.5

0

Inflation (p.p., y−o−y)

2009 2011 2013 2015

−1.5

−1

−0.5

0Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

1

2

3

4

Unemployment Rate (p.p.)

2009 2011 2013 2015

−3

−2

−1

0Employment (p.p.)

2009 2011 2013 2015

−1

−0.5

0Labor Force (p.p.)

2009 2011 2013 2015−30

−20

−10

0Investment (%)

2009 2011 2013 2015−6

−4

−2

0Consumption (%)

2009 2011 2013 2015−3

−2

−1

0Real Wage (%)

2009 2011 2013 2015−80

−60

−40

−20

0Vacancies (%)

2009 2011 2013 2015−20

−15

−10

−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 10: The U.S. Great Recession: Effects of Financial Wedge

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

2009 2011 2013 2015−10

−5

0GDP (%)

Baseline ModelNo Cons. Wedge

2009 2011 2013 2015

−10123

Inflation (p.p., y−o−y)

2009 2011 2013 2015

0

2

4

Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

1

2

3

4

Unemployment Rate (p.p.)

2009 2011 2013 2015

−3

−2

−1

0Employment (p.p.)

2009 2011 2013 2015

−1

−0.5

0Labor Force (p.p.)

2009 2011 2013 2015−30

−20

−10

0Investment (%)

2009 2011 2013 2015−6

−4

−2

0Consumption (%)

2009 2011 2013 2015−3

−2

−1

0Real Wage (%)

2009 2011 2013 2015−80

−60

−40

−20

0Vacancies (%)

2009 2011 2013 2015−20

−15

−10

−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 11: The U.S. Great Recession: Effects of Consumption Wedge

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

2009 2011 2013 2015

−10

−5

0GDP (%)

Baseline ModelNo Gov. Cons.

2009 2011 2013 2015−2

−1.5

−1

−0.5

0

Inflation (p.p., y−o−y)

2009 2011 2013 2015

−1.5

−1

−0.5

0Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

2

4

Unemployment Rate (p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0Employment (p.p.)

2009 2011 2013 2015−1.5

−1

−0.5

0Labor Force (p.p.)

2009 2011 2013 2015−30

−20

−10

0Investment (%)

2009 2011 2013 2015

−6

−4

−2

0Consumption (%)

2009 2011 2013 2015−3

−2

−1

0Real Wage (%)

2009 2011 2013 2015

−80

−60

−40

−20

0Vacancies (%)

2009 2011 2013 2015

−20

−15

−10

−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 12: The U.S. Great Recession: Effects of Government Consumption and Investment

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

2009 2011 2013 2015

−10

−5

0GDP (%)

Baseline ModelNo Forward Guidance

2009 2011 2013 2015

−1.5

−1

−0.5

0

Inflation (p.p., y−o−y)

2009 2011 2013 2015

−1.5

−1

−0.5

0Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

1

2

3

4

Unemployment Rate (p.p.)

2009 2011 2013 2015

−3

−2

−1

0Employment (p.p.)

2009 2011 2013 2015−1.5

−1

−0.5

0Labor Force (p.p.)

2009 2011 2013 2015−30

−20

−10

0Investment (%)

2009 2011 2013 2015−6

−4

−2

0Consumption (%)

2009 2011 2013 2015−3

−2

−1

0Real Wage (%)

2009 2011 2013 2015−80

−60

−40

−20

0Vacancies (%)

2009 2011 2013 2015−20

−15

−10

−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 13: The U.S. Great Recession: Effects of Forward Guidance

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

2009 2011 2013 2015−10

−5

0GDP (%)

Baseline ModelNo 2012Q3 Cons. Wedge

2009 2011 2013 2015

−1.5

−1

−0.5

0

Inflation (p.p., y−o−y)

2009 2011 2013 2015

−1.5

−1

−0.5

0Federal Funds Rate (ann. p.p.)

2009 2011 2013 20150

1

2

3

4

Unemployment Rate (p.p.)

2009 2011 2013 2015

−3

−2

−1

0Employment (p.p.)

2009 2011 2013 2015

−1

−0.5

0Labor Force (p.p.)

2009 2011 2013 2015−30

−20

−10

0Investment (%)

2009 2011 2013 2015−6

−4

−2

0Consumption (%)

2009 2011 2013 2015−3

−2

−1

0Real Wage (%)

2009 2011 2013 2015−80

−60

−40

−20

0Vacancies (%)

2009 2011 2013 2015−20

−15

−10

−5

0Job Finding Rate (p.p.)

2009 2011 2013 20150

2

4

G−Z Corp. Bond Spread (ann. p.p.)

2009 2011 2013 2015

−4

−3

−2

−1

0TFP Level (%)

2009 2011 2013 2015

−8−6−4−2

02

Gov. Cons. & Invest. (%, exog.)

2009 2011 2013 20150

10

20

Fin. Wedge (quart. p.p., exog.)

Figure 14: The U.S. Great Recession: Effects of 2012Q3 Consumption Wedge Shock

2009 2011 2013 20150

0.1

0.2

0.3

Cons. Wedge (quart. p.p., exog.)

0.5 1 1.5 2 2.5 3 3.5 4 4.5 5−90

−80

−70

−60

−50

−40

−30

−20

−10

2008Q3

2009Q1

2009Q4

2010Q3

2011Q4

2013Q2

Unemployment Rate (p.p. dev. from 2008Q2 data or model steady state)

Vaca

ncie

s (lo

g de

v. fr

om d

ata

trend

or m

odel

ste

ady

stat

e)

Figure 15: Beveridge Curve: Data vs. Model

DataModel

0 1 2 3 4 5 6 70

0.2

0.4

0.6

0.8

1

Government Consumption (% of steady state GDP)

Years

3 Year Fiscal Stimulus6 Year Fiscal Stimulus

3 Year Fiscal Stimulus6 Year Fiscal Stimulus

Figure 16: Fiscal Multiplier in a 3 Year Zero Lower Bound Episode

0 1 2 3 4 5 6 70

0.5

1

1.5

2

2.5GDP (% dev. from steady state) − Multiplier

Years

Notes: Stimulus lasts for 3 or 6 years with AR(1)=0.6 thereafter. 3 years constant nominal interest rate. Perfect foresight.