Modern Economy, 2011, 2, 163-168
doi:10.4236/me.2011.22021 Published Online May 2011 (http://www.SciRP.org/journal/me)
Copyright © 2011 SciRes. ME
Using Labor Market Stocks to Identify
Labor M arket Flow
Ben-David Nissim
Departm e nt of E c onomics an d Management, The North Academy, Emek Yezreel, Israel
E-mail: NissimB@yvc.ac. il
Received January 26, 2011; revised February 23, 2011; accepted Marc h 10, 2011
Abstract
A technique that p ermits the calculation of th e flow of agents between and with in labor market states i s pre-
sented. A statistical agency having collected data on those flows easiest to collect and together with data on
employment, unemployment and being out of the labor force, will be able to calculate the rest of the flows.
The contribution of this paper is in suggesting an easy process which overcomes the difficulties statistical
agencies usua lly have in collect ing flow data.
Keywords: Labor Market Flows, Labor Market Stocks
1. Introduction
Much of the interest in gross employment flow is due to
the work of [1] and, even more so, [2,3] and [4], who
exploited a large dataset based on U.S. manufacturing
plants. [5] presented a comprehensive view of the results
on U.S. data. Also notable are studies presenting results
for Germany by [6,7].
Starting with the work of [8], economists began to
make extensive use of micro-data to study employment
behavior at the firm level in order to explain the dynam-
ics of aggregate employment. Job flow measure the gross
creation and destruction of jobs, reflecting the expansion
and contraction of establishments. Within a certain time
period, a firm may employ new workers while separating
from other workers. This could arise from workers quit-
ting and being replaced, and/or simultaneous hiring and
firing by employers to improve the quality of their work-
force or to reconfigure their skill mix.
Statistical agencies in many countries mainly publish
data of labor market stocks, although in several countries
flow data are calculated by using a firms panel data-sets.
Although different authors have calculated American
labor market flows on the basis of raw CPS data, the
flows turn out not to be the same, and large disparities
across studies which use the same data source were
found (S ee [9]).
[10,11] found that the amplitude of fluctuations in the
flow out of employment is larger than that of the flow
into employment, implying that changes in employment
are dominated by movements in job destruction rather
than in job creation. [12] reported that the net drop in
employment during recessions is clearly dominated by
job separations. [13] too, stresses the importance of
separations for cyclical dynamics. [14] found that the
flow due to voluntary quits declines f airly sharply during
recessions, consistent with the notion that quits are
largely motivated by the prospects of finding another job.
Involuntaryseparations—both layoffs and termina-
tionsrise sharply during recessions and gradually taper
off during the expansions that follow.
Recently, [15] and [16] claimed that separation rates
are not as volatile as job-finding rates and that they can
be taken, roughly, as constant (in detrended terms).
Both concluded that the results contradict the con-
ventional wisdom of the last 15 years. If one wants to
understand fluctuations in unemployment, one must un-
derstand fluctuations in the transition rate from unem-
ployment to employment, not fluctuations in the separa-
tion rate. [15] reported that the job-finding probability is
strongly procyclical while the separation probability is
nearly acyclical, particularly during the last two decades.
[17] construct a decomposition of unemployment
variability which con tradicts [15] conclusions . They find
that separation rates are highly countercyclical under al-
ternative cyclical measures and filtering methods and
that fluctuations in separation rates contribute substan-
tially to overall unemployment variability. [18] show th at
even with [15] methods and data there is an important
role for countercyclical inflows into une mployment.
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164
The controversy over the strength of labor market
flows during the business cycle is surprising since flow
data are easy to analyze. However, since the flows are
calculated by using various data sets, different distin-
guished researchers do not agree which flows are domi-
nant during recession and prosp e rity.
The main aim in this paper is to present a technique
that will reduce the number of flows that should be col-
lected by a statistical agency. The statistical agency
should focus on collecting data about flows that are
highly accurate and calculate the rest of the flows ana-
lytically.
This paper is organized in the following manner: The
model structure and an example are laid down in Section
2, and Section 3 presents the summary.
2. The Model
2.1. Translating Stocks into Flows
Let us define three possible states for agents in the labor
market: employed, unemployed and out of labor force
agents. Within a certain time period, agents might move
from one state to another or stay in the same state, as
depicted in Figure 1.
In time 0 and in time 1 the statistical agencies publish
data of:
E0 - the number of employed workers in time 0.
U0 - the number of unemployed agents in time 0.
O0 - the number of out of labor force agents in time 0.
E1 - the number of employed workers in time 1.
U1 - the number of unemployed agents in time 1.
O1 - the number of out of labor force agents in time 1.
The agents in each state may stay in their position or
flow into another possible state.
The possible flows for agents employed in time 0 are:
FE-E staying employed, FE-U : moving out of a job into
unemployment or FE-O : moving out of a job into out of
labor force. We get:
Employed
Unemployed
Out of Labor Force
Figure 1. Labor market stocks and flows.
0- --
EE EUEO
EF FF
=++
(1 )
The possible flows for agents who are unemployed in
time 0 are: FU-E: a flow from unemployment into a new
job, FU-O: a flow from unemployment into out of the la-
bor for ce or FU-U: staying unemployed in time 1, and we
get:
0-- -UENUO UU
UFF F= ++
(2)
The possible flows for agents who are out of the labor
force in time 0 are: FO-E: a flow from out of the labor
force into a new job, FO-U: a flow from out of the labor
force into unemployment or FO-O: staying out of the labor
force in time 1, and we get:
0-- -
OEN OU OO
OFF F= ++ (3)
The agents in each position at time 1, arrived from a
certain position in time zero, or are agents newly of
working age.
Let us define:
L
The change in the number of agents of the work-
ing age.
1*
L
δ
The number of agents who become of work-
ing age and enter directly into a state of being employed,
(1
δ
).
2*
L
δ
The number of agents who become of work-
ing age and enter directly into a state of being unem-
ployed, (2
01
δ
≤≤
).
( )
12
1*
L
δδ
−− ∆
The number of agents who become
of working age and enter directly into a state of being out
of the labor force.
Summing up the flows that arrive, in time 1, into a
state of employment, into a state of unemployment and
into a state of out of the labor force we get:
1 ---1
*
EE UEOE
EF FFL
δ
=+ + +∆
(4)
1- --2
*
OUEU UU
UF F FL
δ
=+ + +∆
(5)
( )
1 ---12
1*
OOEO UO
OF F FL
δδ
=+ ++−−∆
(6)
Table 1 describes the possible flows:
The size of
1
δ
, the proportion of new agents of work-
ing age who go directly into employment within a certain
year may be considered as equal to 000 0
EE UO++,
Table 1. Labor market flows.
Time 0
Time 1
E1 U1 O1
E0 FE-E FE-U FE-O
U0 FU-E FU-U FU-O
O0 FO-E FO-U FO-O
L
1*L
δ
2*L
δ
( )
12
1*L
δδ
−− ∆
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165
while the size of 2
δ
, the proportion of new agents of
working age who go directly into unemployment within
a certain year may be considered as equal to
000 0
UE UO
++ 1.
2.2. Identification of the Flows
It is impossible to identify the 9 flows—FE-E, FE-U, FE-O,
FU-E, FU-U, FU-O, FO-E, FO-U, FO-O by directly solving Eq-
uations (1) to (6), since we have only 6 equations.
We must empirically measure some flows in order to
identify the rest.
Given that n is the number of possible stocks states we
must empirically measure
( )
2
21nn−−
flows in order
to identify all other flows.
In our case with n = 3 possible states in each period,
we must measure empirically
( )()
22
2132*3 14nn−−= −−=
flows.
Assuming that in each period we measure FU-U, FU-O,
FO-U, FO-O2 we can identify rest of the flows .
Using a matrix notation we can write Equations (1) -
(6) as follo ws:
1
2
12
111000000 0
000101100 0
000010011 0
100110000
010001010
0010001011
000001000 1
000000100 1
000000010 1
000000001 1
EE
EU
EO
UE
OE
UU
UO
OU
OO
F
F
F
F
F
F
F
F
F
L
δ
δ
δδ
 
 
 
 
 
 
 
 
−−
 
 
 
 
 
 

 
0
0
0
1
1
1
UU
UO
OU
OO
E
U
O
E
U
O
LF
LF
LF
LF








=

∆+


∆+

∆+


∆+

(7)
Or, AX = Y.
Notice that the last 4 rows of Equation (7) are auxil-
iary rows that assist in squaring X.
Given the vector Y and given
δ
, we get that:
1
X AY
=,
Table 2 presents U.S.A employment, unemployment
and out of labor force data, collected by the Bureau of
Labor Statistics.
Labor Force Statistics from the Current Population
Survey
Let assume, only for simulation purposes, that statisti-
cal agency collected data of the flows FU-U, FU-O, FO-U,
FO-O as is presented in Table 3.
I will apply the suggested technique on the data pre-
sented in Table 2 and Table 3 for calculating the matrix
A in (7) and then will calculate 1
X AY
=, where X is
the vector of calculated flow.
Assuming that
1 212
0.61,0.047,(1) 0.343
δ δδδ
==−− =
3
the matrix A is:
111000000 0
000101100 0
000010011 0
100110000 0.61
0 1 0 0 0 1 0 1 0 0.047
0 0 1 0 0 0 1 010.343
000001000 1
000000100 1
000000010 1
000000001 1








=







A
Table 2. Employment, Unemployment and out of labor
force in U.S.A.
E U O Year
134 523.00 5 653.00 68 730.11 12.1999
137 614.00 5 634.00 70 554.99 12.2000
136 047.00 8 258.00 72 044.33 12.2001
136 426.00 8 640.00 73 736.41 12.2002
138 411.00 8 317.00 75 924.50 12.2003
140 125.00 7 934.00 76 613.23 12.2004
142 783.00 7 219.00 77 273.76 12.2005
145 989.00 6 688.00 77 258.24 12.2006
146 294.00 7 541.00 79 248.33 12.2007
143 338.00 11 108.00 80 631.63 12.2008
1B
y using this ratio, we assume that the probability an out of labor force
agent joining employ ment is equal to the ratio between th e size of total
employment relative to the size of the working-
age population while
the probability s/he would join unemployment is equal to the ratio
between the size of total unemployment relative to the size of the
working-age population.
2We can choose to measure the flows that are easiest to meas
ure by the
statistical agencies.
3I assumed
12008200820082008
0.61EE UO
δ
= ++=
while
120082008200820080.61EE UO
δ
= ++=
B.-D. NISSIM
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166
Table 3. Assumed labor market flows.
FOO FOU FUO FUU
63 499.49 2822.20 563.40 1690.20
2000
64 839.89 2881.77 825.80 2477.40
2001
66 362.77 2949.46 864.00 2592.00
2002
68 332.05 3036.98 831.70 2495.10
2003
68 951.91 3064.53 793.40 2380.20
2004
69 546.38 3090.95 721.90 2165.70
2005
69 532.42 3090.33 668.80 2006.40
2006
71 323.50 3169.93 754.10 2262.30
2007
72 568.46 3225.27 1110.80 3332.40
2008
While its inverse is:
1
4.613.613.613.61 4.614.611 1 1 1
1.9531.9531.9531.9532.9531.9531 01 0
1.657 1.657 1.6571.6571.6572.6570101
212222 1100
2212220011
1 111111000
1111110100
1111110010
1 111110001
11
−−−
−−− −−
−−− −−
−− −−−
− −−−−
=−−−
−−−
−−−
−−−
−−−
A
1111 0000
















The vector Y for the period 12.1999 - 12.2000 is:
0
0
0
1
1
1
134 523.00
5653.00
68 730.11
137 614.00
5634.00
70 554.99
8840.67
5460.27
7719.07
68 396.36
UU
UO
OU
OO
E
U
O
E
U
O
LF
LF
LF
LF
















= =




∆+




∆+


∆+




∆+


Y
where
11100 0
4896.87LEOU E OU∆=+ +−−−=.
We get that the flows in year 2000 are:
B.-D. NISSIM
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167
Table 4. Calculated flows for the years 2001-2008.
FEE FEU FEO FUE FOE FUU FUO FOU FOO DL
128 819.08 891.45 4812.47 3399.40 2408.42 1690.20 563.40 2822.20 63 499.49 4896.87
2000
129 329.61 2779.15 5505.24 2330.80 2833.32 2477.40 825.80 2881.77 64 839.89 2546.34
2001
127 395.52 2983.25 5668.23 4802.00 2732.10 2592.00 864.00 2949.46 66 362.77 2453.09
2002
128 381.87 2603.97 5440.17 5313.20 2367.38 2495.10 831.70 3036.98 68 332.05 3850.09
2003
129 841.50 2394.34 6175.16 5143.40 3908.07 2380.20 793.40 3064.53 68 951.91 2019.73
2004
132 172.55 1839.98 6112.47 5046.40 3975.90 2165.70 721.90 3090.95 69 546.38 2603.53
2005
135 171.90 1466.27 6144.82 4543.80 4651.01 2006.40 668.80 3090.33 69 532.42 2659.48
2006
137 937.26 1960.81 6090.94 3671.60 2764.81 2262.30 754.10 3169.93 71 323.50 3148.09
2007
135 569.08 4456.60 6268.32 3097.80 3454.61 3332.40 1110.80 3225.27 72 568.46 1994.29
2008
1
4.613.613.613.61 4.614.611 1 1 1
1.9531.9531.9531.9532.9531.9531 01 0
1.657 1.657 1.6571.6571.6572.6570101
212222 1100
2212220011
1 111111000
1111110100
1111110010
1 111110001
1
−−−
−−− −−
−−− −−
−− −−−
− −−−−
= =−−−
−−−
−−−
−−−
X AY
134,523.00
5,653.00
68,730.11
137,614.00
5,634.00
*70,554.99
8,840.67
5,460.27
7,719.07
111110 0 0 068,396.36
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
−−
 
and
128 819.08
891.45
4812.47
3399.40
2408.42
1690.20
563.40
2822.20
63 499.49
4896.87
EE
EU
EO
UE
OE
UU
UO
OU
OO
F
F
F
F
F
F
F
F
F
L
 
 
 
 
 
 
 
 
= =
 
 
 
 
 
 
 
 
Y
In the same manner I calculated the flows for the years
2001-2008, as presented in Table 4.
3. Summary
The analysis of gross flows in the labor market has at-
tracted much attention by labor economists and macroe-
conomists in recent years. U.S. studies revealed a large
degree of job reallocation in all sectors, all regions and
all periods—a result which was confirmed by later Euro-
pean studies. The main advantage of looking at gross ra-
ther than net employment changes is that gross flows un-
cover patterns of job creation and job destruction and so
reveal important information about the underlying forces
that lea d to changes in employment i n t he aggregate.
Most statistical agencies publish data mainly on stocks
of employed, unemployed and out of the labor force
agents, at the beginning and end of each time period.
Data on flow between labor market states are rare be-
cause of the difficulties in collecting them.
This paper presents a technique that permits the calcu-
lation of flow between labor market states. Given stocks
at time 0 and at time 1, and given measurement of part of
the flows which are easiest to collect, the rest of labor
market flows can be calculated.
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