The new Sovietincentive
model
Martin L. Weitzman
Professorof Economics
of Technology
MassachLisettsInstitLite
Suppose y is a "performanceindicator"for an enterprise.As examples, y mightstandfor output,profits,cost savings, orfactorproductivity.Withstandard piecework reward systems the manager of an
enterprisewilltryto convince his superiorsthaty is likelyto be small,
therebyentitlinghim to a lower targetwhichis easier tofulfill.A new
reformin the Soviet economy is aimed at stimulatingmore ambitious
plans by making the bonus size depend on the plan targetas well as
the degree to whichit has been fulfilled.This novel incentivescheme
is modelled in thepresentpaper and its basic propertiesare analyzed.
Some applications and extensions are proposed.
* Designinga good systemof incentivesis a problemthat has been
withus fora long time. In principle,such a systemought to encourage individualsto do what is rightby rewardingthemforcarryingout
socially desirable policies. Unfortunately,it is not easy to make an
incentivesystemwhich is altogetherflawless. Sometimes the defects
are not evident at first,but they almost always make themselves
known eventually.
While the incentiveproblemis by no means unique to a planned
economy, it does take on special relevance in that context. Soviet
plannershave had mixed degrees of success in grapplingwithit over
the years. Justrecentlythere has been a major reformof the Soviet
incentivestructure.' The new system is quite unlike what went before. It is relativelysophisticatedand has some intriguing
properties.
In the presentpaper I would like to stress the theoreticalside, rather
than concentrateon specificadministrativeor historicaldetails. My
hope is that an analysis of the Soviet model may be of interestto a
wide audience, since similarproblemsof motivationand coordination
occur in many contexts. Quite possibly this incentive scheme or a
variant of it mightbe applicable to the internalmanagementof a
multidivisionalcapitalistfirmor to the regulationof public enterprises
in a mixed economy.
The authorwould like to thankJoseph Berliner,Michael Manove, Leif Johansen,
Evan Kwerel, a referee, and the editor of this journal for useful comments and
suggestions.
I This reformwas intendedto be institutedduringthe Ninth Five-Year Plan and
was inauguratedin 1971. Conversion over to it seems to have been spread throughout
the plan period, and there are reports even now of enterpriseschanging over. An
excellentdetailed surveyof the new reform,as well as of the backgroundto it, is given
in Berliner(1975). Veselkov (1968) contains a good descriptionof the precedingdebate
about incentivesystems. One of the earliest proposals was that of Liberman (1962).
1. Introduction
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2. The model
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* My aim is to focus directlyon the analytical essence of the new
reward structure.Naturallya great many otherconsiderationsnot of
direct relevance are going to be abstracted away in doing this.
Suppose for simplicitythe planners are concerned with but a
single performanceindicator, denoted y. Usually y will symbolize
output,but sometimesprofits,or perhaps productivity,or even cost,
dependingon the context.2
There are two basic incentiveproblems associated with standard
piecework schemes which reward quota overfulfillmentand/or
penalize quota underfulfillment.
The immediate (and probably most
important)difficulty
is essentiallya static problem. It is in the interest
of the manager(or worker)to convince his superiorsthaty is likelyto
be small, therebyentitlinghim to a lower targetand a bonus whichis
easier to attain.
The static incentiveproblem thus creates a built-intendencyfor
target misrepresentation.Planners and enterprisesfind themselves
locked into the tense roles of adversariesin a gamingsituation.Fixing
targetsis a costly procedure and the planners will typicallyneed to
hire a team of expert assessors. Even then, there will be bickering
about standardson both sides. If the quota is set too low or too high,
it has bad consequences all around (and the plannersare never really
sure, beforehand,what it ought to be).
This bringsus to the second or dynamicincentiveproblem,arising
out of the tendency of planners to use currentperformanceas a
partialbasis for settingfuturetargets.Enterprisesmay be temptedto
hold back outputin hopes of inducinga smaller quota next time. A
targetwhichis set too low will not ordinarilylure enterprisemanagers
to overfulfillby a conspicuous margin because next period's plan
target may start off with this period's performanceas a point of
departure(the well-known"ratchet principle"). Even if above-plan
outputis not adversely affected,such outputis of littleuse unless it
has been anticipated. Setting overtaut targets is also undesirable.
Aside from the all around bad morale such action engenders, the
ratchetprinciplemay temptenterprisesto fail badly. Then therewill
be the inevitable supply foul-ups as the plan breaks down, with
secondary and tertiarylosses multiplying
throughoutthe economy.3
Note thatthe staticincentiveproblembiases enterpriserepresentationsof productionpossibilitiesdownwardto induce a lower quota,
whereas the dynamic incentive problem biases enterprise performance towardJlower
fulfillment
levels, given the quota. One could try
to argue that both'incentiveproblems would be eliminatedby doing
away altogetherwith the notion of a targetand instead just setting
rewardsin some fixedrelationto realized y. This mightbe all rightfor
a situationwhere economic planningis superfluousin the firstplace,
because no coordinationis necessary. The primaryreason for planningis the need forcoordination.In orderto have tightlycoordinated
plans, it really is indispensibleto know (at least approximately)who
will be producing what. This is especially critical for intermediate
goods, where too littlecan be a disaster, and too much is practically
2 In the Soviet contextthereare currently
threemajor success indicators:value of
output,profitrate, and labor productivity.In what follows we implicitlyassume that
inputsand the productmix are fixed,so thatthe issue of changingthemdoes not arise.
I Manove (1973) and Weitzman (1971) contain discussions of this problem.
worthless.So in planningsituationsthereis a genuineneed to have an
enterprisereveal beforehandapproximatelywhaty will be. Hence the
unavoidabilityof dealing with targetsor quotas.
By making the bonus size depend on the plan target, the new
reformproposes to counter the built in tendency for managers to
underrepresenttheir potential in seeking low assignments. Analytically the new system works as follows.4
There are three stages. In the firstor preliminaryphase the planners (on the basis of theirown best currentknowledge) assign to the
enterprisea tentative targety and a tentative bonus fund5B for
meetingthatquota. Also made available is a set of bonus coefficients
a, j3, and y, whose role will be explained.6
In the second or planning phase, the enterprisehas the option of
selecting a larger (or smaller) plan targety with a correspondingly
larger(or smaller)planned bonus fundfor meetingit, B, accordingto
the formula:
A = B + ,(3-y).
(1)
However, B is only theplanned bonus fund(which the enterprise
would receive if it actually ended up producingthe targetedamount
&). In the thirdor implementationstage, when the enterpriseends up
producingamount y it actually receives the bonus fund
B B + sa(y-'):
B-(2
B - y(y-y)
y?9
: y<
(overfulfillment)
(2)
(underfulfillment).
The final stage is thus similar to the old system except for one
importantdifference.In the old system B and y were fixed by the
planners,in consultationwiththe enterprise(thus temptingthe latter
to understatepossibilities). Now ' and, by formula(1), B are selected
by the enterpriseaccordingto the multistageprocedurejust outlined.
4The description is based primarilyon the supplement to Ekonomicheskaya
Gazeta, No. 22 (1971), and an article in the same journal, No. 23 (1972, pp. 15-16).
While the Soviet authoritiesare obviously serious about thisreform(it is mandatoryfor
in
every enterprise,and in no sense voluntaryor recommended), there is difficulty
assessing the actual economic impact. Sporadic reportsindicate that some enterprises
may be having trouble understandingor implementingthe procedure. There is also
journalisticevidence that Soviet planners, themselves,are sometimesuncertainabout
how strictlythe new bonus paymentstructureshould actually be applied ex post when
unforeseencontingenciesarise. My overall impressionis thatthe formulationexpressed
here is a fairabstractionor idealization of what is essentiallya real life procedure. It
Tenth Five-Year Plan documentforclues
will be interestingto look at the forthcoming
on the currentadministrativestatus of this incentive model.
5 The fond material'nogo pooshchreniia, which can be used for a variety of
purposes, includingpaying out bonuses to managersand workers. See Berliner(1975)
for more details.
6 In principle,the numbersforeach year are all set at the beginning
of the five-year
plan and are intended not to be altered later. This is the situation analyzed -inthe
present paper. It remains an open question what will actually happen, e.g., if the
planners see that the economic environmenthas changed. The instructionscontain
vague provisionsabout the possibilityof reassigningtargetsin extraordinarysituations.
Althoughall coefficientsare clearlyintendedto be fixedbeforehandand unalteredover
to know for sure thatthisis,
the five-yearplan, we do not yet have enoughinformation
in fact, what is generallyhappening. In the past, authoritieshave sometimestinkered
withincentiveschemes to reduce disparitiesin bonus fundsamong enterprises.If thisis
done in a systematicway, it of course changes the natureof the incentivesthemselves
and thwartstheiroriginalpurpose.
WEITZMAN
/ 253
For the new systemto have theproperincentiveeffects,a,
y must be set so that
O < a < ,8 < y.
p, and
(3)
This conclusion has not escaped the attentionof Soviet planners7and
the standardsin Ekonomicheskaya Gazeta specifythat y shall be at
least 30 percent greaterand a at least 30 percent less than 8.
Notice thatthe dynamicincentiveproblemis not altogethereliminated by the new model. There is stilla multiperiodgamingproblem
associated withthe tendencyof plannersto use recentperformanceas
a partialbasis for settingfutureindicators. As under the old scheme,
an enterprise suspects that if it performsconspicuously well, its
burden will probably be greater later on. The dynamic incentive
problem, however, is made considerablyless acute in the new system, since the lag between presentperformanceand futuretargetor
coefficientsettinghas been greatlylengthened.In the formalanalysis
all such multiperiodgamingconsiderationsare suppressedforthe sake
of analyticsimplicity(the dynamicproblemis very messy). An enterprise is assumed to act as if it were concerned only about the present
period (or as iffuturetargetsand coefficientsare set independentlyof
presentachievements).This allows us to concentratemoredirectlyon
the abilityof the new model to induce correctrevelationsin the short
run, which is the essence of the static incentiveproblem.
Now a very basic question which the enterprisemust answer is
this.8 What is the optimal self-selectedtarget5^? In their turn, the
planners would like to know the answer to the followingquestion.
What relationdoes the optimalself-selectedtargety bear to the actual
outputy?
First note thatif the enterpriseknows for sure how muchy can be
produced, it will always get the maximumbonus by setting9 equal to
thatvalue. This follows directlyfromexaminingthe consequences of
over or underreporting
the targetwhen (3) holds. Thus, there is an
incentive to be truthfulin the case of perfectcertainty.
Now suppose a small amount of uncertaintyin y, small enough to
permit us to use the expected value hypothesis. The probability
densityfunctionofy is f(y). By hypothesis,the enterprisewill choose
3yto maximize the expected bonus:
J [B +
+ {x[B +
3(y-y) + y(y-y)] f(y)dy
3-y)
+ a(y-3')]f@y)dy.
(4)
Differentiating
(4) withrespect tob and settingthe resultequal to
zero yields (aftercancelling out terms)
{(Y- 13 f(y)dy =
Using the fact that
254 / OF ECONOMICS
(5)
f(y)dy = 1, the above expression becomes
Veselkov (1973), for example, lays great stress on it.
There have been otherstudies of the new Soviet incentivesystem(forexample:
Ellman (1973), Fan (1975), Leeman (1970), Sokolovsky (1974)). I thinkit is fairto say
that they have not been so explicit as this one in modelingthe analytic side.
7
8
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__
K(a- a) f(y)dy.
= 7
P(y ?)- Y)
ya
(6)
where
P(y
2 Y) -
J, f(y)dy.
Thus, the optimalself-selectedtargetis such thatthe probabilityof ex
post plan fulfillment
is the ratio of the differencein the coefficients
(y-,8)/(y-a). Note that it is only the relative (to each other) magnitudes of the coefficientswhich count in determiningy.
Out of what looked like a complicated problem comes a simple
solution. An optimal plan target lies somewhere between the
minimumand maximumpossible output levels, at a point where the
incentivecoefficientsdeterminethe percentilelevel forthe probability
thatit can be met. With a less than ,3 by the same percentagewhich y
is greaterthan /3, would be chosen as the median value of y. By
raising a, lowering p, or raising y, the planners can induce more
conservative (lower) plan targets,y, which are more likely to be
fulfilled.By doing the opposite they can stimulatemore ambitious
targets.
A
* If we introduce risk aversion in the form of a concave utility 3. Extensions and
conclusions
function,we get an analogous set of results; only now the first-order
condition(5) would contain marginalutility(of the bonus) under the
integral sign. If the center does not know the enterprise's utility
function,in place of strictequality (6) it could only conclude that
p (y 2Y y) 2:-
:
(7)
y a
due to the concavityof utility.The more pronouncedthe decrease in
marginal utility,the more conservative the proposed plan target.
Otherwisethe qualitativepropertiesof a solutionare more or less the
same as for the expected value hypothesis.
Thus far,output has been treatedas if it were a random variable
entirelybeyond the control of the enterprise.This is a simple case
which most easily reveals the analyticalessence of the basic incentive
problems. But in realityeffortcan also influenceoutput.9Withextra
effort,an enterprisemay be able to increase its production possibilities. The effectis to stabilize realized output closer to the announced targetlevel. This helps make the outputquota a more meaningfulconcept to the planners because they can count on it more.
To see this effectmost clearly, consider the followingsimplified
scenario. Assume once again a degree of uncertaintysufficiently
small
to justifylinear approximationsand the expected value hypothesis.If
the enterpriseexpends no extra effort,or the "usual' effort,the
densityfunctionof output will be f(y) (as before). But now suppose
outputcan be increased fromany level by expendingextra effort.Let
the expenditureof extra effortrequired to increase output by a unit
give disutilityequivalent to a loss of y' fromthe bonus. If y' - y, it
does not pay the enterpriseto exert the extra effortneeded to bring
below-targetoutput up to the targetlevel, and we are back in the
9 For more on this point see Keren (1972).
WEITZMAN
/ 255
world of last section's model. If y' < y, the enterprisewill want to
raise what would otherwisebe below-targetoutputup to 5 by expending extra effortbecause the benefitof so doing outweighsthe cost. In
this case y is chosen by the enterpriseexactly as before,except that
ry'replaces y in all the formulae.Withthe new interpretation
'y'(@-y)
representsthe psychic cost of raising output fromy to y, whereas
beforey (5-y) stood forthe penaltycost of fallingbelow the targetby
amount 9-y. Althoughthe interpretationof the model is somewhat
different(since realized output will always be at least y), the
mathematicsis identical.
What are the best levels of a, ,x,and y fromthe center's point of
view? They should be proportional10to: the real social value of
having an extra unit which has been prepromised(for ,3); the real
social value of having an extra unit unexpectedlydelivered (for a);
the real social cost of being unexpectedlycaught short by one unit
(for y). Setting the incentive coefficientsthis way guarantees the
enterprisewill choose that targetlevel which is socially optimal (in
the sense of maximizingthe enterprise's contributionto expected
national product when the center treats the targetex ante as if it
standsforthe actual outputwhich will be forthcoming).Note thatthe
various social costs and values will differaccording to the situation.
For example, y will probablybe relativelyhighforbasic intermediate
goods and raw materials far back in the productionprocess due to
multiplierloss effects.1"As of the moment, there seems to be no
evidence thatSoviet plannershave seriouslyanalyzed how the incentive coefficientsought to be set.
This seems to be about as far as one can go witha simple model.
My own tentativeconclusion is thatthe new Soviet incentivescheme
looks like a clever innovation. And it seems to have some nice
theoreticalproperties.But we shall have to wait to see how it works
in practice before passing finaljudgment.12
References
J. S. Innovation in Soviet Indlustry.Chapter 14, "General Incentives and
Decision Rules." Cambridge: M.I.T. Press, 1975.
M. "Bonus Formulae and Soviet Managerial Performance: A Further
ELLMAN,
Comment." Southern Economic Journal (April 1973), pp. 652-653.
BERLINER,
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256/ OF ECONOMICS
10The proportionality
factorshould be the same for all of the parameters.When
effortis irrelevant,the magnitudeis arbitrarybecause of the linearityof the enterprise's
objective functionunder the expected value hypothesis.But when effortmatters,the
proportionality
factor ought to be unityto elicit the socially optimal target.
II See Manove (1973) for a full discussion of this sort of thing.
12 An interesting
applicationof thisanalysis in our own economyis to the contracting of projects on what is basically a cost-plus formula.In many cases the contractor
would like very much to know beforehandwhat the realized cost of a project will turn
out to be. For example, the U.S. governmentmay engage a firmto build and operate a
pilot breederreactorprimarilyto determinecost and feasibility.Some importantpolicy
issues mightdepend on the magnitudeof constructionand operatingcosts, which the
governmentdoes not reallyknow beforehandnearlyso well as the firm.Naturally,the
governmentwould like to have the relevantinformationas soon as possible. Unfortunately, the static incentive problem encourages a misrepresentationof initial cost
estimatesby the firmso long as it assumes some fractionof cost overrunswhile sharing
a (smaller) fractionof cost savings. But let a three-stageincentive scheme like the
model of thispaper be used (where y now stands forthe (negative of) costs). Then the
firmis induced to reveal at the very beginningits own best estimate of futurecosts.
FAN, L. S. "On the Reward System." The American Economic Review, Vol. 65, No.
1 (March 1975), pp. 226-229.
KEREN, M. "On the Tautness of Plans." Review of Economic Studies (October 1972),
pp. 469-486.
LEEMAN, W. A. "Bonus Formulae and Soviet Managerial Performance." Southern
Economic Journal (April 1970), pp. 434-445.
LIBERMAN, E. "Plan, Pribil, Premia" in Pravda. (September 9, 1962).
MANOVE, M. "Non-Price Rationing of Intermediate Goods in Centrally Planned
Economies." Econometrica, (September 1973), pp. 829-852.
L. H. "Stimulirovanye Naprazhonikh Planov v Usloviakh Neopredelonosti." Ekonomika i MatematicheskiyeMetodi, Vol. 10, No. 4 (July 1974),
pp. 802-804.
VESELKOV, F. S. Stimnuly
VysokikhPlanovykh Zadan ii. Moscow, 1968.
. "StimulirovanyeNaprazhonikh Planov." Voprosi Ekonomiki, Vol. 10 (1973),
pp. 3-13.
Journal of
WEITZMAN, M. L. "Material Balances under Uncertainty." Qular-terly
Economics (May 1971), pp. 262-282.
SOKOLOVSKY,
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/ 257