Runge, Dale, "The Reference Mode as a Guide to Transparent Causal Structure", 1976

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THE REFERENCE MODE ‘TABLE OF CONTENTS

AS A GUIDE TO TRANSPARENT CAUSAL STRUCTURE

%, INTRODUCTION

TI. ILLUSTRATIVE CASE: DEVELOPMENT OF A MODEL 458
OF THE LABOR MARKET

by
Dale Runge

Massachusetts Institute of Technology

Cambridge, Massachusetts 02139, USA A. Purpose of the Model 458
B, Evolution of Baste Causal Structure n60
This paper establishes the importance and usefulness of a vell~defined ©, Causal Influences on Model Rates of Flow * ow
reference mode aa a guide to developing transparent causal structures for 1, hitting nate -
system dynamics models. The importance of a transparent causal structure NIB
fa tvofold: it enhances understanding the model dynamice, and 4t facili~ | 2 Separation Rate 16
tates conaunicating to others the model and the insights derived from a AeeEvere dacReeBse e
wodel simulations. . 0
: ; 4, Departures from Sector ho
The paper offers as a fundamental guideline for selecting transparent :
causal structures the following: strive for as highly-aggregated and as 5. Change in Wages w8L
simple a structure that will generate the dynamics of interest. Ability
to follow the guideline depends on a well-defined reference mode, which ‘THE. EVALUATING THE CHOSEN STRUCTURE 48h
in turn requires a clear model purpose. F drs comnustons ae
. To illustrate how a well-defined reference mode can guide the selec~ . BRFERENCES . how

tion of a transparent causal structure, the paper traces the development
of a model of the labor market. First, the model purpose is described.
Next, the evolution of the basic causal etructure is discussed, utilizing
the reference mode embodied in the model purpose to select a transparent
structure. Finally, the causal influences on model rates of flow are
highlighted.

To establish the suitability of the selected structure, the paper
then summarizes the results of model tests. As the paper shows, the
relatively transparent causal structure chosen for the model appears
capable of providing insight into the real-world labor market, and of
enhancing Jabor-market policy analysis.

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= 455 -

I, INTRODUCTION

A critical etep in developing any systen dynanices model is to
“choose the baste caueal structure of the model, The term “causal struc~
ture” refers principally to the set of levels and rates that comprise
the model. Deciding which levels, and their associated rates, to include
4n a model is rarely a straightforvard matter. Commonly, questions
about a desirable degree of aggregation, and about an explicit versus
implicit treatment of certain processes, cloud the matter and make select~

ic causal structure an agonizing phase of model development.

ing 4

Models of population provide a ready example: often the modeler encounters

difficulty in deciding how fine a representation of the aging process
(which determines the basic set of levels and rates in the model) should
be used.

hia paper asserte that difficulties encountered in selecting
a basic causal structure can be traced to an inadéquate formulation of the
reference mode for which the model is designed, The uncertainty resulting
from an inadequate statement of the reference mode most commonly leads to
more detail in model structure than is desirable.

The importance of a clear reference mode for a model cannot be
overstated, Only if the modeler has a clear reference mode in mind can
he or she hope to evolve a "transparent" causal structure for the model.
‘The transparency of a model's causal structure has importance for two
principal reasons. First, only if the model is significantly less com

plex than the real world can the modeler hope to understand its dynamtce

+ hs -

and attain any enduring inaights into the real-vorld syatem being
modeled, . The absence of a relatively transparent causal structure, en—
suing from an ill-defined reference mode, means the modeler may have
Entned Lfttle by building the model. Second, even 4£ modeler can cope
with an unnecessarily detailed model, his or her ab{lity to communtcate
to others the model itself, and ineights derived from model simulations,
ite greatly diminished, The intellectual effort required of others to
wade through a labyrinth of deteiled structure greatly reduces the impact
of a modeling effort,

Transparency of causal structure, then, is an important aim in
developing a model, What guidelines exist for achieving transparent
causal structures? The fundamental’ guideline appeara to bet strive for
as highly aggregated and as eiuple a atructure that will generate the
dynamics of interest. The dynamics of interest, of course, revolve around
“the reference mode, which 1s in turn a function of the model's purpose.

The reference mode of a model under development can be stated

by drawing a graph of the expected behavior of major variables of interest.

Doing so alao helps define nore clearly which variables must appear in the
model. The reference node may aleo be stated descriptively, by a discus~
sion of the phenomena the model is meant to portray, Often, the refer-
ence mode encompasses different possible specific time paths for model
variables, and a descriptive treatment of the reference mode may actually

convey more of the purpose of the model than a graph of expected behavior,

:
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i

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= 457 -

‘An unfortunate aspect of many treatments of methodology ie
that tha generalities and guidelines offered lack concrete meaning to
the reader, For example, the guideline that one should “strive for as
highly aggregated and as aimple a structure" as possible may be of little
use to the reader when attempting to implement it. A concrete i1lus-
tration of how the guideline has actually been folloved in practice is
worth more than repeated exhortations. Accordingly, the remainder of
this paper traces the process by which a clear notion of model purpose
and the consequent reference mode led to a relatively transparent model
causal atructure. As the discussion will reveal, a leas well-defined
reference mode could have led to a considerably more complex--arid
consequently less useful—causal structure, To demonstrate that the
transparent causal structure is still adequate for generating the dynamics

of interest, the paper will also sumarize the results of model testing,

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‘I, ILLUSTRATIVE CASE: DEVELOPMENT OF z

A MODEL OF THE LABOR MARKET
To provide a concrete illustration of how the reference mode

a guide to transparent causal structure, this section relates
tha development of a system dynantes model of the labor market, The pro
‘cedure will be first to digcusa the purpose of the labor-market model,

in which tha reference mode of the structure under development is de:

eribed, then to trace the selection of levels and rates, and finally to

highlight the causal influences on the rates.

A. Purpose of the Model

‘The labor-market model comprises one sector, called the labor

" gector, of a larger nodel of national socto-economic behavior.” The

* terms “laboremarket model" and "labor sector of the National Model" refer -

interchangeably to the structure described in this paper. The purpose

of the labor-market model is twofold: first to increase understanding of

Jabor-market dynamics, and second, in conjunction with the larger National

Model,’ to analyze labor-market policies,

Jthe model discussed here is developed fully in the. author's Ph.D. disser-
tation (Rung? 1976a), The dissertation research was carried out under
several gra-!7, including those from the Rockefeller Brothers und and
the Natfonal fence Foundation,

2the larger model, the System Dynamics National Model, is being developed
by the System Dynamics Group, Alfred P. Sloan School of Management, MIT.
For a description of the scope and purpose of the National Model, see
Forrester, Mass, and Ryan (1976).

ee ITT

Vidllean .

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+ The Syatem Dynamics National Model incorporates the major features of
national socto-economte behavior as endogenous variables. The interaction of
these variables will generate the economfe growth, instability, and inflation
that characterize the United States econoay. The National Model will address i‘

such ae the causes of businese-cycle

short-range and medium-range issue!
(3-7 year period), Kuznets-cycle (15-20 year period), and Kondratteff-cycle
(45-60 year period) fluctuationa, and long-term desues such as the one-tine
transition from growth to equilibrium. The National Model consista of six dis-
tinct model sectors: the production, labor, demographic, household, f1nanctal,
and government sectors. . The labor sector--the “labor-uarket model" discussed
in this paper--receives inputs from other sectors on the demand for workers,
worker incone and assets, transfer payments, and the size of the workforce.

The labor sector supplies workers to the production sector of the National
Model. The production sector, in turn, contains a standard set of equations,

uch as capital gooda

which are replicated for different sectors of the econony,

OF services. For each replication of the standard production sector, the labor

sector determines worker hiring and quite, vhich along with layoffs comprise

the flow of workers between employment and unemployment. In addition, the Labor

sector captures worker mobility between sectors. Wages are also generated in

the labor sector for workers in each replication of the standard production sector.
A major short-term isaue treated in the Natfonal Model will be the apparent

tradeoff between inflation and unemployment. When coupled with the other sectors

‘of the National Model, tha labor sector will exhibit short-term variations in

‘employment and wage changes. The avatlability and willingness to work of

RA UREA AILEY SARANRERNNE IED “URL IRLRMCNLCREANNRRY NEEDS ARIA ~ ii aN

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\ ‘tneaployed workers in the labor sector will atgnificantly influence both the
8 of policies

short-term inflation/unemployment tradeoff and the effective:
ained at altering the tradeoff. - The vage-change equation in the labor sector *
does not

seeks to incorporate the actual pressures that bear on wage-setting proces:

@ a tradeoff between unemployment and wage changes; rather, ‘it.

euch as the difficulty employers have in filling job vacan-

in the real worl
cles. : \

Among the long-term issues treated by the National Model 1s the indus-
trialization process, and cohatraints arising from shortages of capital,
technology, and Labor. When enbedded in the Nattonat Model, the labor sector
will display long-term changes in employment patterns among sectors of the
‘economy, The labor sector will aleo demonstrate the effect of the availability
fot workers on such long-term changes. Any restriction in the flow of workers
among sectors would constrain the growth of sectors attempting to expand.
Moreover, higher vages needed to attract workers to growing sectors can contri-

4 bute to {nflation.

B. Evolution of Basic Causal Structure
"Representing worker atocka and. their interconnecting rates of
flow in a multi~sector economy 1s a potentially formidable undertaking.
Because labor is a factor of production in each replication of the
standard production sector of the Nations! Model, the pool of employed
workers in each sector must necessarily be represented. From that
predeternined starting point, one is faced with a wide array of possible
representations of unemployed worker pools, and the flow of vorkers

between unemployed and employed pools.

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Firat, one must settle the question of how to define the
“unemployed” stock or stocks of workers, To be classified by the United
States Bureau of Labor Statistics as "unemployed", but still in the labor
force, a worker must be actively seeking work. In terms of the actual
nunber of jobless workers available for hiring, such a definition under-
atates the size of the pool of workers from which employers can draw
labor. Accordingly, jobless workers in the labor-market model are as~
sumed to include the "passive" unemployed, or those not actively seeking
work. To avoid confusion with the Bureau of Labor Statistics concept,
Jobless workers in the labor-market model are termed "nonemployed", rather
than “unemployed, to reflect the inclusion of the "passive" as well as
“active” unemployed.

Figure 1 shows one obvious alternative for handling nonemployed
workers in the model structure. In the figure, nonemployed workers are
aggregated into a single pool, and hiring for the sector employed pools
of all sectors drava on workers from the single general nonemployed pool.
Such a structure offers a staple, transparent representation of the labor
market. Wowever, brief reflection reveals its inadequacy. Regardless of
the total number of nonemployed workers at any time, the number of vorkers
available to a given production sector 4a limited, Whether by tradition,
training, or lack of information, each sector faces a constraint of
limited worker availability, The real-world segmentation of the labor

market, which leads to the existence of "nonconpeting groups" (Kerr 1954),

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atrongly suggests the inability of the structure tn Figure 1 to capture _
Jnbor-market dynantes adequately, Figure 1 appears to enhance sinplicity
at the expense of dynamte, capability; accordingly, a more complicated
representation appears necessary.

tor General Sector
Employed |Nonemp Loyed| Employed

Sector
Enployed

Figure 1, Labor-Market Structure with One Nonemployed Pool.

ae

Whidblean o:.

~ 463 - ~ h6h =

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Figure 2 depicts an attempt to incorporate. labor-market seg-
mentation by introducing one pool of nonemployed workers, called the
“sector nonemployed" pool, for each production sector, The atructura

in Figure 2 clearly satisfies the need to incorporate the real-world ie

Limitation of worker availability faced by each production’ sector.
Sector Sector Sector e-m Sex
Moreover, by associating a nonemployed pool of workers with each produc= raployed employed onan pleved Psepately

tion sector, the structure potentially allows examination of policy

issues arising from inter-sectoral differences in the economic well-being
of nonemployed workers. For example, such a structure can aid examina~ ak

or
tion of the effect of an increase in nonemployment compensation on ‘ Nonemployed

nonenployed workers willingness to accept vork in a sector, or to move

to a different sector,
Sector
Employed
é A significant question the structure depicted in Figure 2 e

Jeaves unanswered is how to represent the intersectoral flow of workers.
Data on the United States labor market strongly suggest the need to
incorporate intersectoral worker flows, The long-term movement ‘of

workers out of agriculture and into manufacturing and services provides

one example, Even on a short-term basis, intersectoral worker
flows‘are significant, According to Gallaway (1967, p. 29), at least ® > Pool Tor each Eeployed Pool. meneneeree
25% of the employeea in one industry in 1957 were employed in another in- ®

dustry in 1960. Data from Bancroft and Garfinkle (1963, pp. 1-10) show

bs = hes =
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, that over one-half of the Job changes in 1961 involved « movement from
one of fourteen industry classifications to another, While the need to
incorporate intersectoral worker flows 1s clear, the means of doing so
1s perhaps the crucial unanswered question faced in developing a struc~
ture for modeling the labor market.

Figure 3 presente one alternative for representing intersectoral
vorker flows, In the figure, all logically possible flove—from each
pool to every other pool--are depicted. The flovs in Figure 3 capture
flows that actually occur in the real world. A amauaenayed worker in
one sector may move to a second sector, either by being hired directly out
of the first sector's nonemployed pool or by moving to the second sector's
nonemployed pool and there looking for work. Simflarly, an employed
worker in one sector may leave his Job and go to the nonemployed pool in
a second sector to seek work, Moreover, he may go directly to a new job
4n another sector. In fact, direct job-to-job flow is more than a logical

“possibility: Bancroft and Garfinkle (1963, p. 1) show that in 1961 ap-

+ proximately 40% of all job’ changes occurred without an intervening period
of unemployment.

From the above considerations, the network of worker flows in
Figure 3 vould appear necessary for a realistic representation of the
labor market, However, vhile an accurate literal portrait of worker
movements, the network of flows in Figure3 presents a tremendous burden

to the analyst, first in specifying the determinants and parameters for

= N66 -

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all the flow rates, and second in interpreting the dynamics inherent in

euch a complicated structure, Testing and understanding the model struc-
ture implied in Figure 3 would require such a devotion of attention to
detat2 that the model behavior would likely be as conceptually impenetrable
aa the real world, Figure 3 clearly illustrates the tradeoff entailed in
detailed representation of the real world in a model: one quickly be-
comes immersed in a task that is unlikely to generate insight and under-
standing because of the amount of detail. Consequently, some alternative
to Figure 3 appears desirable, What ts needed 4e a atructure for inter-
sectoral vorker movenents that gains in simplicity over Figure 3, yet

does not lose its basic dynamic characteristica,

~ Gt =
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Sector Sector
Eaployed jonemployed
Sector
Nonemployed|
Sector
Employed
Figure 3. Potential Intersectoral Worker Flows.

Sector
jonemployed

VbOT bam ise:

Sector
Nonemployed

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Figure 4 shows tha basic structure of worker pools and their

interconnecting flow rates used for the Labor-market model. The struc~
ture in Figure 4 conbines features of Figure 1, in vhich all workers

were dravn from one general nonemployed pool (meaning that intersectoral
flows occurred implicitly), and Figure 2, in which workers for a sector
were drawn from a local, and limited, supply. In Figure 4, workers for

a given sector are hired from the nonemployed pool associated with that

sector; The general nonemployed pool in Figure 4 now provides a channel

for worker movement between sectors. ALL intersectoral flows are repre-
‘sented in Figure 4 as the result of movement out of the sector nonemployed
pool of one sector, into the general nonemployed pool, and from there to
tha sector nonemployed pool of another sector.

The structure in Figure 4 retains the important feature in
Figure 2 of constraining at any one time the availability of workers for
hiring in a particular sector, But vhat of the pattern of intersectoral
movements in Figure 4? Clearly, the structure in Figure 4 i@ less rich
than that in Figure 3, where all the real-world flowa were shown, How

can euch a simplification be justified?

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~ Weg =

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The key to accepting the conceptual adequacy of the basic
structure shown in Figure 4 lies in a grasp of the aggregation such «
structure embodies, The structure in Figure 4 asserts that even @
direct real-vorld flow from a job in one sector to a job in a second
sector 1s constrained to flow successively through the nonemployed
pool in the first sector, the general nonemployed pool, and finally the
nonemployed pool in the second sector. The worker Flows through each

nonemployed pool have associated time constants, which represent the

erage duration of stay in each pool, The average duration of stay in
a given pool derives from a vide distribution of individual durations
of stay; some workers stay in each pool much longer than the average, some

stay much less than the average time. Direct job-to-job movement can be

interpreted as a flow through the intervening nonemployed pools in

Figure 4 with a zero duration of stay. Therefore, while on first glance
the structure of Figure 4 appears to omit important real-world worker
flows, closer consideration of the aggregation embodied in such a structure

suggests that it is nonetheless capable of exhibiting the same dynamics

as the real-world labor market.

= 40 -

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Sector Sector General Sector | J Sector
Employed | |Nonemployed|” |Nonemployed|  |Nonemployed Employed

Sector
Employed

Figure 4, Labor-Market. Structure that Combines Use
of General and Sector Nonemployed Pools.

rt

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lies . ; - We -
D-2460 a
Figure 5 shows a nore refined veraion of the basic causal ‘ : N * . x / °
structure selected by the above reasoning. Figure 5 illustrates a typi< : \ sector 3. 7
cal arm of the star-shaped network of Anbor-market flove first seen oo Ng Oo v4 “7
in Figure 4, The general nonemployed pool connects with a5 many sector ~~. NO ry : Yo 7
nonemployed pools as there are production sectors in‘a given version SOS : 1 ao Yo
of the National Model, The flow of workers from the general nonemployed 4, # \ aaa Wie
to the sector nonemployed pools 1s called arrivals in sector; the . ¥
oppasite flow is dermed departures from sector. The hiring rate and the SECTOR: 1 ~ RONEMPLOYED { AEETOR
separation rate connect the sector noneuployed and the sector eaployed ; x _t——.. XY
pools within each production sector. oe = ex cK —~ os .
ALL production sectors are treated in a standard way in the 2 oo (7 DEPARTURES ARRIVALS SN,
Jabor-market modelt the sane mobility equations operate for each produc~ co FROM SECTOR yi sector NOUS

.tion sector, with parameter values set to represent the particular . 7

. 2 SECTOR NN
/ NONEMPLOYED
characteristics of each sector. In other worda, the labor-market model : \

f

in Figure 5, ,One additional rate in Figure 5 represents the change in ‘ Rare oTION bx i) Rae?

epatures all worker mobility in the four flow rate equations indicated

wages in each sector, These five equations form the core of the labor= | |
market model, r waces
SECTOR
EMPLOYED
PRODUCTION
SECTOR
SECTOR |

Figure 4. Basic structure of the labor-market model .

A OTE LARA SEES D EES ELE cats ~ trae ma uamannsnoe~anabtnaenmnes-~canuemmunanannnay ~anenesiietsiant eis
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\
€. Causal Influences on Model Rates of Flow ‘ ° The disposable income of sector employed also influences the hiring rate.

Having selected the basic causal structure shown in Figure 4 As disposable income of sector employed increases, the hiring rate also rises £
and refined in Figure 5, the remaining tasks of formulating rate equa- due to the greater attractiveness of holding a job in the sector. However, the :
tions and interpreting model behavior are vastly simplified, Instead of net effect of disposable income of sector employed on the hiring rate depends
the multitude of flows implied in Pigure 3, all vorker movementa in the on the length of week for labor. For a given.income, a longer length of week
Jabor-market model are captured in only four generic flow equations. The for labor tends to depress the hiring rate. If the length of week for labor i
remainder of this section highlights the influences on those four mobility in a sector 1s too long, workers are discouraged from accepting work in the sec- :
equations and on the equation for the change in wages, to facilitate inter- tor. |
pretation of the teat results in the section that follows. In Figure 6, the hiring rate is negatively affected by the well-being of

the sector nonemployed. The well-being of the sector nonemployed increases as
1. Hiring rate : : transfer payments to the sector nonemployed increase, duration of transfer pay- E

Pigure 6 showa the influences on the hiring rate, As depicted ments lengthen, and assets per worker grow; well-being decreases as the dura~ 4
on the right side of Figure 6, an increase in the backlog for workers tion of stay in the sector nonemployed pool (equal to sector nonemployed divided
(analogous to job vacancies) raises the hiring rate. However, a higher by hiring rate plus departures from sector) lengthens. An increase in the
backlog for workers also reduces the relative availability for hiring, . . fut

well-being of sector nonemployed reduces the economic incentive tc work and
defined as the ratio of the sector nonemployed to the backlog for workers,

tends to depress the hiring rate, and vice versa.?
The probability that a given Job opening is f11led in a given time period ; .

decreases as the relative availability for hiring declines, Therefore,

a higher backlog for workers decreases the probability of filling a given

Job opening in a given time period, thereby making any rise in the hiring

rate less than proportional to the increase in backlog.

3 the positive effect that a long duration of unemployment has on a worker's _
willingness to accept a job is a cornerstone of the job vacancy-turnover 3
theory of the labor market. ‘The effect of transfer payments on job-search
activity are revurced, for example, in Myers and Schultz (1951).

- semesys sosranoel ssa 5
SR OE ALL A AT SINT RELA CLR IEB I ices see
* Whdieaa a...

~ 415 =: , P :
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,
_— . +

aeuaTe

Fon vinwe” : .
* ‘BACKLOG #
Fon wonee

$ecToR
EmPLoreo

DISPOSABLE mcome
OF SECTOR EMPLOYED

WELL ~ BEING OF

guearion oF SECTOR NONEMPLOYED
av tv SECTOR =
+ NONEMPLOVED i:
perantures
Rom sect — TRANSFER Parents 10
aa SECTOR NONEMPLOYED
— DURATION OF TRANSFER a
PAYMENTS: ware
ASSETS PER WoRKER

Figure 6, Influences on hiring rate

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D-2460

2. . Separation rate
Figure 7 shows the influence.on the separation rate, The sepa-
ration rate is the aum of the quit rate and the layoff rate. The quit
rate 49 basically proportional to. the number of sector employed workers,
but fa also influenced by the well-being ef sector nonemployed, the dis~
posable income of sector employed, and the length of week for labor.
Whenever job openings increase, and the hiring rate consequently rises,
the duration of stay in sector nonemployed decreases, As a result,
the well-being of sector nonemployed increases due to the reduced need
to consume assets while not employed. Higher well-being of sector
nonemployed tends to increase the quit rate.” on the other hand, high
disposable income of sector employed tends to diminish the quit rate
by making present jobs more attractive.” The length of week for labor
also affects the quit rate. If the length of week for labor exceeds
ite traditional length (at a given income) or becomea excessively fatiguing,
thé quit tate rises,
The layoff rate in Figure 7—determined in the production sector
of the National Model—is governed by a comparison between the desired

and the actual, number of sector employed, An excess of desired over actual

sector employed leads to fewer layoffs; conversely, if actual sector

employed is greater than desired, a higher layoff rate results.

The response of quits to increased demand and hiring is discussed in
Behman (1964), pp. 261-262.

Spureon and Parker (1969) discuss empirical evidence for the negative

influence of :

2s (and therefore income) on quite.

neers ae vn = -

LAYOFF mare

SECTOR
NONEMPLOYED

+
DK + —-- = separation nate
+

SECTOR
EMPLovEO
‘Qui rare,
ro pty
LENGTH OF
UI WEEK FOR
‘tagon
: DISPOSABLE INCOME .
. OF SECTOR EMPLOYED

WELL-BEING OF
SECTOR NONEMPLOYEO

Figure 7, Influences on separation rate

3. Arrivala in sector
Figura 8 showa the’ influence on‘arrivals in sector, “Arrivals ta
sector are proportional to the size of the workforce in the sector (the™
aun of sector employed and sector nonemployed). As discussed in Myers and
Schultz (1951, pp. 70-71), @ large portion of Job information 4s trans-
mitted by word-of-mouth therefore, the larger the sector, the more non-
enployed workers outaide the sector are likely to work there, Arrivale
in sector are affected aa well by the size of the general nonemployed pools

a smaller (larger) general non-employed pool means a lower (higher) flow

= 478 -

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out of the pool. The duration of stay in the general nonemployed pool (equal
to a general nonemployed divided by total arrivals in sector) algo influences .
arrivals in sector. A lengthening duration of stay in general nonemployed in-
creases the financial hardship of, those remaining in the general nonemployed
pool and raises the incentive to seek work, Therefore, in Figure 8, an increase
in the duration of stay in general nonemployed raises the relative duration in
general nonemployed, which then increases arrivala in sector, Transfer pay-
ments to the general nonemployed also influence arrivals in sector through their
effect on the "acceptable" duration of stay in the general nonemployed pool.
An increase in transfer paymente to general nonemployed shortens the relative
duration in general nonemployed, corresponding to greater economic well-being,
which lessens the incentive to seek work and thereby depresses arrivals in sector.
Aside from the size of the workforce in a sector, the major sector~ .
specific influences on arrivals in sector are the perceived income ratio and
the relative perceived hiring delay. The perceived income ratio reflects the
perception by workers in the general nonemployed pool of the income of workers
in the sector. relative to the avetage income of all workers in the economy. An
increase in the income of vorkere in a sector tends to raise arrivals in sector
because of the attractiveness of the greater earning potential there. The rela-
tive perceived hiring delay indicates the perception by workers in the general
nonemployed pool of the hiring delay in the sector relative to the average hir-

ing delay in the economy. The hiring delay measures the average time required

to find vork in a sector. A short hiring delay, signaling favorable demand con~

ditions in a sector, increas arrivals in sector because the likelihood of

finding work there is high.

YIDEERA bine

= 479 -
D260 . ,
TRANSFER pavweNTs TO,
Enema NONEMPLOVED
. guration or .
jONEMPLOVED *
Maat ACcEPTALE
- Sunation OF
Stari cenena,
NONENPLOVED

RELATIVE DURATION IN
GENERAL NONEMPLOYED

cewenan,
ONEMPLOYED’

Ld
: ‘sector

WONEMPLOYED
PERCEIVED
income
natio

WoAKFORCE
+ wisecton
+
eter,
MPLOVED.

Figure 8. Influence on arrivals in sector

4. Departures from sector
Figure 9 shows the influence on departures from sector. Normally, some
fraction of the sector nonemployed can be expected to depart to the general

nonemployed pool for a variety of reasons, such as dissatisfaction or upward

A St ERASER A SORES NERS NITES NINETIES SE

~ 480 %
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mobility; therefore, departures from sector are proportional to the size

of the sector nonemployed pool, Departures from sector are also influenced
-by the well-being of sector nonemployeds the higher the well-being of see~
ter nonemployed, the less impetus for leaving the sector to seek work
elsewhere, Departures from sector are also tempered by perceived average
fncome, a measure of the perception by the sector nonemployed of the average
income elsewhere in the economy, High average income elsewhere increases

the attractiveness of leaving a sector.

In Pigure 9, the mob{Ltiy of workers through the general noneuployed pool
also influences departures from sector, A short relative duration in general
nonenployed suggeata high mobiitty, an encouragement for departures, and vica
versa. The effect of the relative duration in general nonemployed on depar-

ture thus indtrectly reflects the ease of finding work elsewhere.

©, comparison of the sector-specifiec influences on arrivals in sector

(Figure 8) and departures from sector (Figure 9) indicates that arrivals are
Feaponsive to such particular conditions in the sector as income and

hifing ‘delay, In contrast, departures are influenced only by the well-being
of sector nonemployed, The concept of asymmetrical influences on arrivals
and departures is consistent with the main thread of recent migration studies
as discussed in Morrison and Relles (1975, pp. 1-4).

- he -

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+

RELATIVE DURATION
IN GENERAL NONEMPLOYEO

Generar
NONEMPLOVED |

DK ———oerantunes FROM SECTOR

F

sector
NONENPLOYEC'

Figure 9, Influences on departures from sector,

, 5; Change in wages

Figure 10 showa the influences on the change in wages in each sector. The
change in wages 1s proportional to existing wages. In other words, the abso~
ute change. in wages. due to a given percent change depends on the ‘level of
wages. The other influences on the changes in wages, when multiplied by the
level of wages, determine the absolute change in wages.

Relative wages--wages in the sector relative to average wages in the
economy--influence the change in wages. If average wages outaide the sector
increase, relative wages within the sector decline, creating upward pressure

on the change in wages. The impact of relative wages on the change in wages

~ hae =
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captures the effect of “secondary wage drift" discussed in Phelps Brown (1962).
Secondary wage drift describes the influence that wage changes in one part of
the éconony have on wage changes elsevhere, :

Perceived inflation in the nation also influences the change in wages.
the perceived inflation in nation represents worker and employer perception
of the rate of inctease in prices.

Another influence on the change in wages 1 the delivery delay for workers.
The delivery delay for workers, a measure of the average time needed to fill
a Job opening, provides the principal influence on the change in wages from
the worker eupply-demand balance in the model. A short delivery delay for
workers reflects a slack Labor market where Job openings are easy to fill; a
long delivery delay for workers, on the other hand, reflects tight labor-market
conditions where job openings take a long time to fill. The use of delivery
delay for vorkers as an influence on the change in wages in the labor-market
model deatvaske wrth the dominant practice in empirical economics. In a tra~

dition established by Phillips (1958), model equations for the change in wages

typically incorporate the unemployment rate as an indicator of the worker
supply-demand balance. The unemployment rate is frequently used because
data ts lacking on other, more realistic indicators of the worker supply-
denand balance. In the labor-market model, on the other hand, the delivery
delay for workers indicates the relative difficulty employers have in filling
Job openings; the delivery delay for workers comes much closer to capturing
real-world pressures on wage changes than the unemployment rate.

Figure 10 also shows an influence on the change in wages from the employ=

ment ratio in sector, which is the ratio of the actual to the desired nunber

“cessor” ~esteneanroneomemmcntoe

VIQEEGA tars,

= 483 =
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of sector employed, When the desired exceeds the actual number of sector
employed, upward pressure is placed on the change in wages, and vice versa.

pesinco
Secron
ESLoreo
DS eurcovuen
gio
PEMIWERY ofc ay
Workers
ar
an cHaNce In aces
\ panceweo
INFLaT
1 RATION
waces,

AELATIVE WAGES
tye

AVERAGE WAGES.
aa

Figure 10, Influences on the change in wages

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THI, EVALUATING THE CHOSEN STRUCTURE

Elegant verbal justifications for a particular causal structure aside,
the true test of a model's ability to generate the dynamice of interest and
to foster underatanding of the real world lies in its response to inputs,
Accordingly, this section reviews and briefly highlights the results of initial
teste of the labor-market model, The test results suggest that the transpa~
rent causal structure developed in Section II indeed fulfills its dual role

of generating both appropriate behavior and insight.

<The Labor-sarket model, in both one- and two-eector versions, has been
tested extensively for validation purposes. The model has been subjected
to two classes of test inputa: simple (that is, step and fluctuating) inputs,
and tine-sertes inputs. Intttal teste utilized a step tnerease in, and a
fluctuating level of, desired employment, The inttial test results showed a
plausible model response to teat inputs, and a relative insensitivity to
afzeable parameter changeo, “The test reaults have permitted comparions be~
tween the behavior of the model and the real-world labor market. Moreover,
the model structure has provided explanatory tnetghts into numerous features
characterizing both the model and real-world Labor marketa,

‘The model has also deen subjected to inputs derived from real-vorld data.

A two-sector version of the model, representing the enttre US labor market,
Proved capable of replicating real-world worker mobility and wages over the
Period 1954-1973, when driven by time series inputa.

ae
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Selected resulta of subjecting a one-sector version of the model to
simulated business-cycle conditions will be reviewed below, The model was
subjected to a 410% fluctuation in desired employment, with a period of
4 years, to approximate US business~cycle fluctuations in the denand for
workers. The test provided a wealth of material for comparing model behavior
“to tha real world, However, due to space Limitations, only certain phase
relations and correlations in the model will be treated here.

In Figure lla, the hiring rate, the backlog for workers, and the levels
o£ sector employed and sector nonemployed all fluctuate over amplitude ranges
that agree with US business-cycle Eluctuations.” The backlog for workers in
Figure 11a leads the sector employed, peaking about 3/4 year before sector
employed. A comparable phase relation exists between nonagricultural job
openings and nonagricultural employment in the United States.®

Figure 11b shows the behavior of wages in the labor-market model, Wages
fluctuate, 4n response to changing demand for and supply of workers, about
an average value greater than their initial value, The tendency for wages to
increase on the average arises from the greater flexibility of wages upward
than downward. In the one-sector model used for Figures 11a and 1b,
average wages in the economy are assumed to be constants they therefore exert

downward preasure whenever wages in the sector rise, Wages in Figure 11b

Tyhe simulation shown in figures 11a and 11b spans 20 years. The figures
show only year 10 to year 20, however, to reveal more detail and facili-
tate examination of phase relations and correlations,

®see Moore and Shiskin (1967, p. 55).

~ 486 - . H

D-2460

fluctuate about @ value where the downward prassure from the effect of rela-
tive wages offeets the greater upvard flexibility of wages in the sector.

If wages were increasing elsewhere in the model, the downvard pressure on
wagea in the sector vould diminish and wages would exhibit a secular rise in
their average value, Such a tendency in.the labor-market model—-as in the
real world—can be an important component of inflation. Wages in Figure 11b
leg behind sector employed in Figure lla by about 5 months. The lag of wages
behind sector employed agrees with the real-world lag of wages behind employ~
ment fn manufacturing, as noted in Gordon (1961, p. 289).

Figures 1a ond 11h show correlations betveen model varlables that cor~
respond to real-world correlations. For example, Figure lla shows that the
backlog for workers and the sector nonemployed are ‘negatively correlated; an
increase in the backlog for workers is accompanied by a decline in sector
nonemployed, and vice versa. Figure 12 shows annual values-of the backlog for
workers-and sector nonemployed from the simulation in Figure lla plotted as
Percenta of the workforce in the sector, On the vertical axis, the backlog
fraction in sector 1s defined as the backlog for workers divided by the work-
force in sector. The horizontal axis shows the nonemployed fraction in sector

expreased in percent terms.

SEUEEM bare

© = 4BT - a? = 498 -

260 D-2460

,
20 E
. 4 :
oan
gz 8 soe v. i
i |. , ;
= . H
i 49. . i ga Age
E “e4
3 : j o
o :
i J ‘|
°
1 o 2 4 6 6 . iO a ry . © 1
secon nae veneer
HONEMPLOYED FRACTION IW BECTOR (%) FIGURE & VACANCIES AND UNEMPLOYMIENT, U.6 OATA: 1947-1968.
Figure 11, Response of Labor-market model .
to fluctuating desired employment, 2a, Backlog fraction in sector Figure 12b, Vacancy rate versus
nonemployed fraction in sector unemployment rate in United States,

. from simulation in Figure lla.
Figure 12b shows real-world data comparable to that in Figure 12a? In

Figure 12b, the number of vacancies pending at the US Employment Service as a
Percent of the labor force, called the vacancy rate, is plotted against un-

employment as a percent of the labor force. A comparison of figures 12a and

9
‘Figure 12b reproduces Figure 6 in Holt et al, (1971, p. 40).

- 489 -

D-2460

12 shows the qualitative agreement between the correlations in the two fir
sures: the structure of the labor-market model explains why such a correr
Jation should extat in both the model and the real world. An increase in
the backlog for workers, by tncreasing the hiring rate, tenda to decrease the
number of sector noneaployed, and vice versa, thereby inducing a negative cor~
relation between backlog for workers and sector nonemployed.?+

Figure 1b reveala a second correlation of interest. The nonemployad
fraction in sector and the fractional change in wages tend to be negatively
correlated; an increase in the nonemployed fraction in sector is ‘accompanied

by a decline in the fractional change in waj

» and vice versa, Figure 13a
graphs data from the simulation shown in Figure 11b on the fractional change

in wages versus the nonemployed fraction in sector, both expressed in percent

terms. The curve through the data in Figure 13 expresses a regression of the
‘fractional change in wages (FCW) on the reciprocal of the nonemployed frace

tion in sector (NFS), in an equation of the form FCW = A + B/NFS.

re vertical ecales are different between. figures 12a and 12b because.
vacancy data used for Figure 12b understates the actual number of vacancies
in the economy, Even if the data in Figure 12b did report all job
vacancies, the scales would still differ because backlog for workera is a
more inclusive measure of demand than officially defined job vacancies,
(For example, “backlog for workers" includes demand for workers being re-
called from layoff, but "job vacancies" does not.) The difference in verti-
cal scale between two figures only alters the slope of the negative correla<
tionj the underlying qualitative agreement between the two correlations ie
not affected,

"ane model also displays a shift in the correlation between backlog for workers

and sector nonemployed vhen transfer payments to the sector nonemployed increases,

Gujarati (1972) found the same results in the real world.

= hgo =

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Figure 13b reproduces the original Phillips curve that relates’ the rate
of changa‘of money wages to the unemployment rate in the United Kingdom.22
Comparison of figures 13a and 13b reveals close agreement between the correla-
tions in the two figures, Both show that the rate of wage change tends to
accelerate aa the unemployment rate declines. Conversely, as the unemployment
rate increases, the rate of wage change falls with decreasing steepness,
Moreover, the values of the fractional change in wages in Figure 13a agree
well with those in Figure 13b for corresponding values of the nonemployed
fraction in sector. The Jabor-narket model structure explains the negative
correlation between the fractional change in wages and the nonemployed frac-
tion‘in sector: when the nonemployed fraction in sector declines, the
increased competition for workers raises the difficulty of matching workers
with Jobs in a given time period, as manifested in a longer delivery delay
for workers. The resulting upward pressure on wages from a longer delivery
delay for workers induces a wage increase that correlates with the decline in
the nonemployed fraction in sector.

The correspondence between model and real-world labor markets reveals the

ability to capture labor-market dynamics realistically. Among other . -
features, the model also shows a positive correlation between hiring and wage
changes that agrees with the correlation shown in Behman (1964, p. 259), More=
over, the model structure explains the negative correlation coumonly found be-
tween wage changes and the rate of change of unemployment!? on the basis of

stock-flow interactions in the labor market, 4
ir
eteure 13b reproduces Figure 1 in Phillips (1958, P. 285).

500 Bowen and Berry (1963) for exanple.

4,

Space limitations preclude full discussion of such features here.
See Runge (1976a, Chapter IV).

,

PRACTIONAL CHANGE IN WAGES T% YR) y
° oe 3

o

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NONEMPLOYED FRACTION IM SECTOR (4)

Figure 13a, Phillips curve
derived from simulation in
Figure 11b,

> bon,

MEET Care

Figure 13b, Original Phillips curve
relating the rate of change of money
wages and employment.

= ge -

D-2460

TV. CONCLUSIONS
This paper has shown the usefulness and importance of a well~

defined reference mode as a guide to transparent causal structure. The

value of a transparent causal structure was seen to lie in two areas:
first, it enhances the modeler's ability to understand the model's dyna—
mica and acquire enduring insights about the real world; second, it
facilitates communication to others of the model, and of insights derived
from model simulations. |

The fundamental guideline offered for achieving transparency in
a model's causal structure was: to strive for as highly-aggregated and as
simple a structure that will generate the dynamics of interest. Further-

more, the paper argued that without a clearly-

ated purpose of the model,
and a consequently well-formulated reference mode, the chances of achiev~
ng a transparent model causal structure were slight.

To illustrate how a well-defined reference mode can guide the
modeler in developing a transparent causal structure, the paper traced the
development of a model of the labor market. The basic causal structure
selected vas significantly less complex than a literal representation of
Jabor-market stocks and flows would have been. The aggregation and simpli~
city embodied in the model structure was defended verbally by describing
how it could capture the essential dynamice of the real-world labor market.
The key to accepting the plausibility of the model structure lay in under~ ,
atanding that the time constants of flow through the nonemployed poole were

average values, Consequently, real-world flows that were not explicitly

seco

= 493 -

‘D-2460

represented in the model were implictly captured in the averaging process,
‘The ultimate evaluation of a causal structure, transparent or
not, Jies in its behavior when tested. Accordingly, the paper summarized
some results of tests of the labor-market model to show that ‘ee trans~
Parency of its structure did not detract from ite dynamic capabilities,
The model tests to date have provided a solid initial basis for confidence

in the model, The model's response to simple step and fluctuating inputs,

as well as ite performance when subjected to time-series inputs, yield

many areas of congruence between the model and the real world, The model
structure also sheds light on the dynamics of the real-world labor market.
While further testing 19 required, the labor-market model, whose transparency
“derives from a well-defined reference mode, appears to promise a means of
better understanding labor~market dynamics and of better formulating labor-

market policies,

D-2460

= igh =

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Behman (1964)

Bowen and Berry (1963)

Burton and Parker (1969)

Forrester, Ha:
Ryan (1976)

Gallavay (1967)

Gordon (1961) +

Gujaratt (1972)

Bolt (1970)

"1961," Monthly Labor Review, August 1963,

Behman, S. “Labor Mobility, Increasing Labor Demand,
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Bowen, W., and R. Berry. "Unemployment Conditions
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Burton, J.F., Jr., and J.E. Parker. "Interindustry
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