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Macroeconomics 2Lecture 7 - Labor markets: Introduction & the search model
Zsofia L. Barany
Sciences Po
2014 March
The neoclassical model of the labor market
central question for macro and labor: what determines the level ofemployment and unemployment in the economy?
1. theoretically can not deal with unemploymentI there is supply and demand only
demand determined by technology or by demand for outputsupply driven by inter-temporal substitution
I there can be under-employment due to wage stickiness, butthere is no unemployment in equilibrium
I or unemployment as leisure
⇒ does not fit the statistical definition of unemployment
2. empirically can not explain fluctuations in employmentI shifting the demand curve according to the business cycle,
employment and wage movements do not fit the data
Some facts about the labor market
I unemployment is a persistent phenomenon→ can wage/price stickiness be the reason?
I large flows of workers between employment, unemploymentand non-participation states
I
∆u = inflow− outflow
inflow: due to job loss or new entry from non-participationoutflow: due to job finding or exit into non-participation(retirement, school, inactivity)
I employed workers often change jobs – with a wage gain orwage reduction
Search theory
I main postulate: there are frictions in the labor marketI source of frictions:
I heterogeneity of workers and firmsI imperfect information: invest resources in locating firm/workerI mobility costs
neoclassical model ⇔ search modelsemployment is employment is a state,
a control variable flows are the controls
Why is search theory important?
→ Can we learn more about the macro equilibrium of the labormarket by introducing frictions, studying the flows?→ Is getting information about the stocks through the flows moreuseful than studying the stocks directly?
I Search theory provides a coherent, dynamic theory that canbe used to analyze
I labor supply and demand in a more satisfactory way than inthe perfectly competitive models
I the nature of unemployment, workers and vacancy flowsI the efficiency / optimality of the level of unemploymentI the distribution of workers’ wagesI the dynamic of workers’ wages depending on their labor market
history
Why is search theory important?
I provides a strong theoretical background for quantitativequestions
I why was unemployment around 4-5% in the US until the1970s?
I why did it increase in the 1970s, 1980s, and then decline againin the late 1990s?
I why did European unemployment increase in the 1970s, andremain high since then?
I why is the composition of employment so different acrosscountries?male vs female, young vs old, high vs low wages
I useful tool for policy analysis
How should labor market frictions be modeled?
I incentive problems, efficiency wages
I wage rigidities. bargaining, non-market clearing prices
I search frictions
search and matching: costly process for workers (firms) to find theright jobs (workers)
→ how do markets function without a Walrasian auctioneer?
→ for empirical analysis we need to develop a tractable and richmodel
Facts about job flows
I job creation is mildly pro-cyclical
I job destruction is strongly counter-cyclical
I job destruction leads job creationit is the driving force of the business cycle – especially ineconomies with flexible labor markets
I job creation seems to be the main cause of long-run changesin unemployment
Facts about worker flows
I worker turnover about three times as large as job turnover
I worker quits are strongly pro-cyclical↔ offset by the counter-cyclical job destruction raterecession → job destruction increases
→ voluntary quitting decreases⇒ inflow to unemployment increases, but less
I unemployment changes driven mainly by the outflow fromunemployment
I in monthly data: employment ↔ non-participation flows ≈employment ↔ unemployment flows
Key labor market statistics US
0.0
2.0
4.0
6.0
8.0
10.0
12.0
14.0
16.0
18.0
20.0
50.0
52.0
54.0
56.0
58.0
60.0
62.0
64.0
66.0
68.0
70.0 Jan-‐48
Aug-‐49
Mar-‐51
Oct-‐52
May-‐54
Dec-‐55
Jul-‐5
7 Feb-‐59
Sep-‐60
Apr-‐62
Nov-‐63
Jun-‐65
Jan-‐67
Aug-‐68
Mar-‐70
Oct-‐71
May-‐73
Dec-‐74
Jul-‐7
6 Feb-‐78
Sep-‐79
Apr-‐81
Nov-‐82
Jun-‐84
Jan-‐86
Aug-‐87
Mar-‐89
Oct-‐90
May-‐92
Dec-‐93
Jul-‐9
5 Feb-‐97
Sep-‐98
Apr-‐00
Nov-‐01
Jun-‐03
Jan-‐05
Aug-‐06
Mar-‐08
Oct-‐09
May-‐11
Dec-‐12
employment-‐populaEon raEo (%)
labor force arEcipaEon rate (%)
unemployment rate (%, right scale)
Source: Bureau of Labor statistics, monthly, seasonally adjusted data
Inflow and outflow
40 The Labor Market in the Great Recession
Figure 5. Age-Adjusted Unemployment Rate
Figure 6. Unemployment Inflow and Outflow Rates
0
2
4
6
8
10
12
1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008
Percent of Labor Force
Published Unemployment Rate
Age Adjusted Unemployment Rate
Source: Bureau of Labor Statistics. Adjusted for 16-24, 25-34, 35-44, 45-54, and 55+ age groups
0.00
0.01
0.02
0.03
0.04
0.05
0.06
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1948 1953 1958 1963 1968 1973 1978 1983 1988 1993 1998 2003 2008Source: Bureau of Labor Statistics and authors' calculations. Quarterly averages of monthly data.
Outflow Rate, f Inflow Rate, s
Outflow rate (left axis)
Inflow rate (right axis)
Source: Elsby, Hobijn, Sahin (2010), Figure 6.
Inflow and outflow in recessions
1. outflow rate from unemploymentI markedly pro-cyclicalI prolonged downswings during recessions
2. inflow into unemploymentI countercyclicalI sharp upswings at the onset of recessions, but tend to subside
quickly by the end of the recessions
3. in the 1990 and 2001 (relatively mild) recessions, the increasein the inflow rates was relatively muted
Inflow rates by reason
44 The Labor Market in the Great Recession
Figure 9. Unemployment Flows by Reason for Unemployment
Figure 10. Separation vs. Employment to Unemployment Transition Rates
0.00
0.01
0.02
0.03
0.04
1968 1973 1978 1983 1988 1993 1998 2003 2008Source: Bureau of Labor Statistics and authors' calculations based on Elsby, Michaels, and Solon (2009)
Inflow Hazard
Layoff Inflow Rate
Quit Inflow Rate
Entrant Inflow Rate
0
0.005
0.01
0.015
0.02
0.025
0.03
0.035
0.04
0.045
0.05
1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 2009Source: Bureau of Labor Statistics and authors' calculations. Monthly rates based on CPS and JOLTS data.
Monthly Rate
Total Separation Rate
E-U Transition Rate
Source: Elsby, Hobijn, Sahin (2010), Figure 9.
Shimer’s exercise
the change in the unemployment rate is
ut+1 − ut = st(1− ut)− ftut
I st – separation rate
I ft – job finding rate
I ignore exit from the labor force, and entry from out of laborforce
denote average rates by:
s =T∑t=1
stT
and f =T∑t=1
ftT
Shimer’s exercise
Compare the actual unemployment rate with
1. a hypothetical unemployment rate constructed using theaverage (a constant) separation rate:
ut+1 − ut = s(1− ut)− ftut
2. a hypothetical unemployment rate constructed using theaverage (a constant) job finding rate:
ut+1 − ut = st(1− ut)− f ut
The role of the job finding rateholding the separation rate constant at s
0
0.02
0.04
0.06
0.08
0.10
0.12Job Finding Rate
Actual Unemployment RateHypothetical Unemployment Rate
0
0.02
0.04
0.06
0.08
0.10
0.12
1945 1955 1965 1975 1985 1995 2005
Employment Exit Rate
Actual Unemployment RateHypothetical Unemployment Rate
Figure 2: Contribution of Fluctuations in the Job Finding and Employment Exit Rates toFluctuations in the Unemployment Rate, 1948Q1–2007Q1, quarterly average of monthly data.The job finding rate ft is constructed from unemployment and short term unemployment ac-cording to equation (4). The employment exit rate xt is constructed from employment,unemployment, and the job finding rate according to equation (5). The top panel showsthe hypothetical unemployment rate if there were only fluctuations in the job finding rate,x/(x+ft), and the bottom panel shows the corresponding unemployment rate with only fluc-tuations in the employment exit rate, xt/(xt+f). Both panels show the actual unemploymentrate for comparison. Employment, unemployment, and short term unemployment data areconstructed by the BLS from the CPS and seasonally adjusted. Short term unemploymentdata are adjusted for the 1994 CPS redesign as described in Appendix A.
30
Source: Shimer (2005)
The role of the separation rateholding the job finding rate constant at f
0
0.02
0.04
0.06
0.08
0.10
0.12Job Finding Rate
Actual Unemployment RateHypothetical Unemployment Rate
0
0.02
0.04
0.06
0.08
0.10
0.12
1945 1955 1965 1975 1985 1995 2005
Employment Exit Rate
Actual Unemployment RateHypothetical Unemployment Rate
Figure 2: Contribution of Fluctuations in the Job Finding and Employment Exit Rates toFluctuations in the Unemployment Rate, 1948Q1–2007Q1, quarterly average of monthly data.The job finding rate ft is constructed from unemployment and short term unemployment ac-cording to equation (4). The employment exit rate xt is constructed from employment,unemployment, and the job finding rate according to equation (5). The top panel showsthe hypothetical unemployment rate if there were only fluctuations in the job finding rate,x/(x+ft), and the bottom panel shows the corresponding unemployment rate with only fluc-tuations in the employment exit rate, xt/(xt+f). Both panels show the actual unemploymentrate for comparison. Employment, unemployment, and short term unemployment data areconstructed by the BLS from the CPS and seasonally adjusted. Short term unemploymentdata are adjusted for the 1994 CPS redesign as described in Appendix A.
30
Source: Shimer (2005)
Lessons from Shimer’s exercise
I separation rate not so important in the evolution ofunemployment
I job finding rate is a more important determinant ofunemployment
I why?separation rates do increase during recessionsBUT the job finding rate is high in the US, even duringrecessionseven if more workers get laid off, they find a job quickly →job separation rate not so important
But countries are different536 THE REVIEW OF ECONOMICS AND STATISTICS
Figure 1.—Average Inflow and Outflow rates across countries
more acute problem. These important sources of heterogene-ity cannot be gleaned from data on the duration structure ofunemployment that we use throughout the paper. Uncoveringthe differential role of time aggregation across different sub-groups of the labor market is therefore an important avenuefor future research.
C. Evidence from OECD Data
The average unemployment inflow and outflow hazardsover the sample periods for the whole sample of countries arereported in table 2. A striking observation from these resultsis the substantial cross-country variation in both st and ft .A particularly useful illustration of this point is in figure 1,which displays the average values of st and ft from table 2 ingraph form. Interestingly, one can discern a natural partitionof developed economies between Anglo-Saxon, Nordic, andcontinental European economies.
Figure 1 reveals very high outflow rates among the Anglo-Saxon and Nordic economies. Among these countries, theaverage monthly unemployment outflow hazard exceeds20%. The economies of continental Europe stand in starkcontrast. Unemployment outflow rates in these economies liebelow 10% at a monthly frequency. A similar picture developsfor the estimates of the inflow rates in figure 1. We observehigh unemployment inflow hazards among the Anglo-Saxonand Nordic economies, which typically lie above 1.5% on amonthly basis. Likewise, inflow rates among the Europeaneconomies are again much lower, at around 0.5% to 1% permonth.23
23 It is important to remember that while estimates of average flow ratesin continental Europe are very low in comparison to their Anglo-Saxon
Figure 1 also shows that there are both extremes andintermediate cases that are understated in this Anglo-Saxon/Nordic/continental Europe taxonomy. For Japan,while the average unemployment outflow rate of 19% issimilar to those in Anglo-Saxon and Nordic economies, itsinflow rate is more comparable to those of continental Europe.Another intermediate case is the United Kingdom, whichdisplays unemployment flows that lie halfway between theAnglo-Saxon and the continental European models. Perhapsthe most striking observation is the outlier status of the UnitedStates. With an average monthly unemployment outflow rateof nearly 60% and an average inflow rate of 3.5%, it exhibitstransition rates at least 50% larger than the remainder of oursample of countries.
Figures 2 and 3 display the time series for the inflow andoutflow hazards for each country in our sample. The transitionrates are plotted on log scales since, as emphasized in theliterature on unemployment flows and as we will confirm inwhat follows, it is the logarithmic variation in st and ft thatplaces them on an equal footing with respect to fluctuationsin the unemployment rate.
Figures 2 and 3 reveal that in addition to significantcross-country variation in unemployment flows, also sub-stantial variation in unemployment flow hazards over timewithin countries. Although a great deal of information is con-tained in these figures, a number of observations come to
counterparts, there is likely to be a great deal of underlying heterogeneityin worker flows among some European economies. For example, the use oftemporary, or fixed-term, contracts in France and Spain is widely thoughtto have given rise to a subgroup of the labor force within each countrythat experiences very high rates of turnover. See Bentolila et al. (2008) andBlanchard and Landier (2002).
Source: Elsby, Hobijn, Sahin (2013), Figure 1.
Shimer’s exercise for other countries
changes in unemployment are due to
I UK: 71% inflow rate, 29% outflow rate(Elsby, Smith, Wadsworth (2010))
I Spain: 57% inflow rate, 43% outflow rate(Petrongolo and Pissarides (2009))
An overview of search models
I First generation: one-sided searchI focuses on the workersI exogenous wage distribution: F (w)I exogenous job arrival rate: aI worker’s optimal decision
I Second generation: two-sided searchI endogenous job arrival
somebody has to create the job – active job creation by firmsI matching function m = m(u, v)
u – stock of unemployed, state variablev number of vacancies, control variable
I arrival rate: m(u, v)/uI endogenous wage: reached through bargaining→ no wage distribution
I value of match endogenousI exogenous job destruction, λ
I Third generationI endogenous job destruction
destroy job, if its productivity is not high enough → Rreservation productivity
I match output from G (x) distribution⇒ there is a wage distribution, which depends on G (x)
I Fourth generationI endogenous wage distribution
Short, informal introduction to dynamic programmingConsider the following consumption-saving problem:
∞∑t=0
βtu(ct)
s.t. at+1 = (1 + r)at − ct for all t ≥ 0
at+1 ≥ 0 for all t ≥ 0, for a given a0 > 0
direct approach: set up the Lagrangian, and find the two infiniteoptimal sequences {at+1}∞t=0 and {ct}∞t=0
dynamic programming approach: find a time-invariant policyfunction h mapping wealth at the beginning of period t intooptimal consumption in period t, s.t. the sequence {ct}∞t=0
generated by iterating
ct = h(at)
at+1 = (1 + r)at − ct
starting from a0 solves the consumption-saving problem
Potential advantages of dynamic programming
while it is unclear that finding a policy function is easier thanfinding an infinite sequence, but it has three advantages:
1. sometimes we can find a closed-form solution for the policyfunction h
2. sometimes we can characterize theoretical properties of thepolicy function h
3. various numerical methods are available to solve dynamicprograms
The value function
we first need to solve for an auxiliary function called the valuefunction, V (a), which measures the optimal lifetime utility fromconsumption starting with an initial wealth a:
V (a0) ≡ max{ct ,at+1}∞t=0
∞∑t=0
βtu(ct)
such that for all t ≥ 0
at+1 = (1 + r)at − ct
at+1 ≥ 0
we need to determine the value function
To determine the value function:
I we show that the value function is the solution to a particularfunctional equation called the Bellman equationnote: not all optimization problems can be represented with aBellman equation
I the problem must satisfy the Principle of Optimality
I which applies only to problems with a recursive structure
The value function can be expressed as:
V (a0) = max{0≤ct≤(1+r)at}∞t=0
∞∑t=0
βtu(ct)
such that for all t ≥ 0
at+1 = (1 + r)at − ct
let Γ(a) ≡ [0, (1 + r)a]
Heuristic procedure
V (a0) = max{at+1∈Γ(at)}∞t=0
∞∑t=0
βtu((1 + r)at − at+1)
V (a0) = max{at+1∈Γ(at)}∞t=0
[u((1 + r)a0 − a1) + β
∞∑t=1
βt−1u((1 + r)at − at+1)]
V (a0) = max{at+1∈Γ(at)}∞t=0
[u((1 + r)a0 − a1) + β
∞∑t=0
βtu((1 + r)at+1 − at+2)]
V (a0) = maxa1∈Γ(a0)
[u((1 + r)a0 − a1)+
max{at+2∈Γ(at+1)}∞t=0
β
∞∑t=0
βtu((1 + r)at+1 − at+2)]
V (a0) = maxa1∈Γ(a0)
[u((1 + r)a0 − a1) + βV (a1)]
V (a0) = maxc0∈Γ(a0)
[u(c0) + βV ((1 + r)a0 − c0)]
The recursive formulation
I this heuristic procedure seems reasonable
I formally it is valid, because the Principle of Optimality appliesto the problem
I the Principle of Optimality tells us that the value functiondefined before can be rewritten as
V (a) = maxc∈[0,(1+r)a]
[u(c) + βV ((1 + r)a− c)]
→ recursive formulation of the optimization problem→ once we determine the value function V (a), we can solve forthe optimal consumption level:
c∗ = arg maxc∈[0,(1+r)a]
u(c) + βV ((1 + r)a− c)
→ c∗ is a function of a: h(a) ≡ c∗
Solving the optimization problem with dynamicprogramming
This has 5 steps:
1. write down the Bellman equation (the definition of the valuefunction)
2. write down the first order conditions of the optimizationproblem
3. write down the Benveniste-Scheinkman equation (theenvelope condition) to determine the derivative of the valuefunction wrt wealth
4. apply the envelope condition to the next period’s valuefunction and wealth
5. derive the Euler equation, which summarizes the optimalintertemporal behavior of consumption
Step 1: the Bellman equation
V (a) = maxc∈[0,(1+r)a]
[u(c) + βV ((1 + r)a− c)]
I a functional equation, the unknown is the function V itselfthis is the Bellman equation, let’s assume for now that asolution to this problem exists
I a is a state variable: it contains all the information from thepast that is needed to solve the forward-looking optimizationproblem
I c is a control variable: this is to be chosen in the currentperiodit determines the state variable’s next period value, a′,according to the transition equation
a′ = (1 + r)a− c
Step 2: the FOC
first rewrite the Bellman equation → we choose a′ rather than c
V (a) = maxa′∈[0,(1+r)a]
[u((1 + r)a− a′) + βV (a′)]
→ this is useful for the envelope condition→ let’s assume V exists and is differentiable
The FOC wrt to a′:
dV
da′(a) = −∂u
∂c((1 + r)a− a′) + β
∂V
∂a(a′) = 0
∂u
∂c(c) = β
∂V
∂a(a′)
Step 3 & 4: the Envelope Condition & one step forward
we need to determine ∂V /∂a for the first order condition
V (a) = maxa′∈[0,(1+r)a]
[u((1 + r)a− a′) + βV (a′)]
∂V
∂a(a) =
∂u
∂c(c)
((1 + r)− da′
da
)+ β
∂V
∂a(a′)
da′
da
=∂u
∂c(c)(1 + r) +
da′
da
(−∂u∂c
(c) + β∂V
∂a(a′)
)︸ ︷︷ ︸
=0 due to the FOC
∂V
∂a(a) =
∂u
∂c(c)(1 + r)
this holds in all periods, so forwarding by one period:
∂V
∂a(a′) =
∂u
∂c(c ′)(1 + r)
Step 5: the Euler equation
we plug∂V
∂a(a′) =
∂u
∂c(c ′)(1 + r)
into∂u
∂c(c) = β
∂V
∂a(a′)
to get
∂u
∂c(c) = β
∂u
∂c(c ′)(1 + r)
u′(c) = β(1 + r)u′(c ′)
the optimization problem can thus be reduced to finding h(a) forall a such that:
∂u
∂c(h(a)) = β(1 + r)
∂u
∂c(h((1 + r)a− h(a)))
First generation models
The search model
based on McCall partial equilibrium search model (1968)
I the simplest model of search frictions
I people get draws from a given wage distribution
I decision: which jobs to accept and when to start work
I jobs are sampled sequentially
Environment
I people are risk neutral → utility function?
I continuous time (very similar in discrete time)
I a worker’s objective is to maximize expected discountedlifetime utility
I every worker starts as unemployed
I all jobs are identical, except for their wageswages are drawn (iid) from an exogenous stationarydistribution F (w)with bounded support w ∈ [0,A]
The search model
I an unemployed workerI receives income b per unit of time
I the value of leisure and home production activitiesI unemployment benefitI net of search costs
I actively searches for a job→ jobs arrive according to a Poisson process with rate a > 0
I if a job offer arrives, the worker has to decide whether toaccept it or not
let Ut denote the expected present discounted value of a unitof unemployed labor at time t– the value of an unemployed worker
I let Wt(w) be the value of an employed worker at wage wI employment is an absorbing state: once accepts a job with
wage w , remains employed at that wage foreverI alternative: allow for on-the-job search
Arrival rate – Poisson process
I in each period of length δt a worker can potentially receiven = 0, 1, 2, ... offers, with probability a(n, δt)
I let N(t) denote the number of offers received by time t ≥ 0,such that N(0) = 0
I a(n, δt) follows a Poisson distribution:
a(n, δt) =eaδt(aδt)n
n!
I the number of offers received is independent across periods
I ⇒ {N(t), t ≥ 0} is a Poisson process with rate a > 0
P(N(δt) = 1) = aδt + O(δt)
P(N(δt) ≥ 2) = O(δt)
a function f is O(δt) if limδt→0f (δt)δt = 0
The value of an unemployed worker
assuming
I infinite horizon
I constant discount rate, r
I the length of a period is δt ≥ 0, but small
Ut satisfies the Bellman equation:
Ut =bδt
1 + rδt+aδt
max(Wt+δt ,Ut+δt)
1 + rδt+(1− aδt)
Ut+δt
1 + rδt
I very similar to the evaluation of an asset
I dividend yield
I option arrives → expectation of the capital gain
I option does not arrive → continuation value
The value of an unemployed worker
rearranging terms and dividing by δt
rUt = b + a (max(Wt+δt ,Ut+δt)− Ut+δt) +Ut+δt − Ut
δt
taking the limit as δt → 0 and omitting subscripts for convenienceyields:
rU = b+a (max(W ,U)− U)+U
this is an arbitrage equation for the valuation of human capital:
I investing the value at a safe returnI if you leave the asset in the labor market
I flow returnI expected capital gain from change of stateI capital gains from changes in evaluation – in the steady state,
b, a, r are all constant + infinite horizon ⇒ stationarysolutions to the valuation equations, i.e. U = 0
Closing the model
assume that
I employment is an absorbing state
I a worker earns forever the wage, w , that he/she was hired at
W =w
r
and the stationary solution to U staisfies
rU = b + a(
max(wr,U)− U
)
When does the unemployed take a job?
W ≥ Uw
r≥ U
w ≥ rU
⇒ optimal stopping rule: reservation wage, the minimumacceptable wage
ξ ≡ rU
if you stay unemployed, you can never be worse off than rU, sounless someone pays at least this, you won’t start working
For a known wage offer distribution
assume that offers arrive from a known wage distribution, F (w)
rU = b + a
(∫ A
0max
(wr,U)dF (w)− U
)wages under the reservation wage, ξ = rU are rejected:
rU = b + a
∫ A
ξ
(wr− U
)dF (w)
collecting terms and solving for the reservation wage
ξ =r
r + a(1− F (ξ))b +
a
r + a(1− F (ξ))
∫ A
ξwdF (w)
a(1− F (ξ)) is the transition from unemployment to employment
On-the-job search
this is critical for understanding the difference between worker andjob flows
assume that
I employed workers get job offers at rate aeI unemployed workers get job offers at rate au
new reservation rules for an offer of wage w
I unemployed, accept if W (w) ≥ U → ξ
I employed with wage w1, accept if W (w) ≥W (w1) → ξ(w1)
Value of the employed and the reservation wage
value of an employed worker with wage w1
rW (w1) = w1 + ae
∫ A
ξ(w1)(W (w)−W (w1)) dF (w)
I W ′(w) > 0
I for w = w1, W (W ) = W (w1)
⇒ the reservation wage for on-the-job search is the current wage
ξ(w1) = w1
note the absence of job changing costs
Value of unemployed
let ξ be the reservation wage if unemployed
rU = b + au
∫ A
ξ(W (w)− U) dF (w)
the value of a job with wage w = ξ is
rW (ξ) = ξ + ae
∫ A
ξ(W (w)−W (ξ)) dF (w)
note that W (ξ) = U, hence
ξ = b + (au − ae)
∫ A
ξ(W (w)− U) dF (w)
The reservation wage of the unemployed
ξ = b + (au − ae)
∫ A
ξ(W (w)− U) dF (w)
the reservation wage for the unemployed depends on the arrivalrates:
I if au = ae , then ξ = b
I if au > ae , then ξ > b
I if au < ae , then ξ < b
note that with on-the-job search there is a much bigger flow ofworkers than jobsworkers quit for a better job, and leave behind a vacancy, which isfilled by someone further down the chain⇒ vacancy chains, with the unemployed at the bottom
