clR. rch,and Externd Affalr1 , ;
[.PAPERS
|National Economic Management
Economic Development Institute
The World Bank
June 1991
WPS 713
The Determination
of Wages
in Socialist Economies
Some Microfoundations
Simon Commander
and
Karsten Staehr
Wages are commonly assumed to be exogenously determined in
socialisteconomies But wages in socialisteconomies have been
determined by a combination of institutional and economic
factors.
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Policy, Research, and External Afflrs
Nlonal Economic Management
WPS 713
'T'his paper- aproduct of thc National Economic Management Division, Economic Development Institute
- is part of a larger effort in PRE to analyze the sources and dynamics of inflation in transitional socialist
economies. Copies are availablc free from the World Bank, 1818 H Street NW, Washington, DC 20433.
Please contact Olga Del Cid, room M7-047, extension 39050 (62 pages, with figures and tables).
Commander and S,aehr address the issue of how They interpret the partially reformed social-
wages are determined in socialist economies. ist economy as an attempt to refine the motiva-
tional ,tructure by introducing a manager
They distingL.sh between different types of between the planner and the workcrs. One
economic regime, in terms of how much decen- objective is to provide a framework in whichl
tralization is permitted and how extensive are workers and managers engage in a cooperative
market-based features or rules. game to determine wages and output with the
incentive structure given in effect by the planner.
Wages are commonly assumed to be exog- They show how this can yield undesired results,
enously given in socialist systems, regardless of when managers and workers cooperate, playing a
regime. Commander and Staehr show that this noncooperative game with the planner.
assumption is not warranted, given the use of
incentive-based systems in thcsc cconomies. They present a preliminary treatment of an
economic regime such as the one that existed in
Both the classical planned economy and the Poland after January 1990, where market-based
partially reformed regime face the problem of rules almost fully predominate. Their objective
motivating workers in thc absence of monitoring is to provide coherent foundations for wage
and of such conventional penalties as unemploy- equations that can be tested empirically.
ment. How do these regimes try to resolve the
incentive problem? They prepare estimates for the partially
reformed economies of Hungary and Poland.
In a centrally planned cconomy, the piece-
rate mechanism is an attempt to stimulate more Data and other limitations limit thc conclu-
effort among workers. But Commander and sions that can be drawn. But Commander and
Stachr show, using game-theorctic models, that Stachr show wages to be strongly associated
in cooperative settings the outcome can be lower with prices and rather less strongly associated
productivity than desired and that in noncoopera- with productivity. Hence, wages should not be
tive settings the outcome can be higher wages considered fully exogenous, even if institutional
than warranted. and other factors indicatc more exogeneity than
would exist in a standard market economy.
Thc PRE Working Papcr Series disseminates the findings of work under wiay in the Bank's Policy, Research, and External
AffaitsComplex. An objcctie eofthc scries is to getthcsc findings out quickly. cven ifprcsentations are less than fully polished.
The findings, interpretations, and conclusions in thcse papers do not necess.arily represent official Bank policy.
Produced by the PRE Dissemination Center
The Determinatlon of Wages in Socialist Economies:
Some Microfoundatlons
by
Simon Commander and Karsten Slaehr
Table of Contents
Section 1: Introduction 1
Section 2: Wage Determination in the Socialist Economy 3
2.1 Regime typology 3
2.2 The centrally planned economy 5
2.3 The partially reformed economy 6
2.4 The reiorm economy-second stage 1 0
Section 3: Wage Determination in the Centrally Planned Economy 1 0
3.1 Introduction 10
3.2 Framework and some assumptions 1 1
3.3 Cooperative wage bargaining: a dictatorial solution 1 3
3.4 The Stackelberg solution in a noncooperative game 1 7
3.5 Summary 20
Section 4: Wage Determination in the Reform 1 Economy 2 0
4.1 Introduction 2 0
4.2 A cooperative game 21
4.3 A cooperative game nested in a noncooperative game 2 6
4.4 Summary 31
Section 5: Wage Determination in the Reform 2 Economy 3 1
5.1 Introduction 31
5.2 A cooperative game between manager and workers 3 2
5.3 Concluding remarks 33
Section 6: Some Preliminary Empirical Results 34
6.1 Introduction 34
6.2 Hungary 35
6.3 Poland 38
6.4 Concluding comments 41
Section 7: Conclusion 41
References 4 2
Appendices 4 4
.Jction 1: Introduction
The inefficiencies particular to socialist economies have generally been
traced to the absence of market based discipline and most especially, the weights
given to full employment, price stability and low income dispersion. The
resulting trade-off was historically presented in terms of systemic or
macroeconomic rationality alongside microeconomic inefficiency 1. Yet
increasingly this distinction has appeared irrelevant. In some instances, the
extent of underlying macroeconomic imbalance was masked by recourse to heavy
external borrowing and/or accompanied by attempts at piecemeal economic reform
aimed at eliminating or reducing those imbalances. In general, the symptom of
tension was the presence of acute goods market shortages associated with an
excess demand regime. Less well perceived was the link between goods markets
disequilibria and the demand for factors of production. Guaranteed full
employment imposed excess demand for labour regimes generating some labour
hoarding by enterprises 2. Such hoarding could readily coexist with labour
shortages and indeed could exacerbate such shortages.
Clearly, persistent excess demand for labour and capital would appear to
rule out any of the behavioural relations, even correlation, between standard
macroeconomic variables. Thus, even the tendency toward wage expansion that
might be presumed to exist when labour reserves are exhausted might be absent in
the institutional setting of the classical socialist economy. Inflation could
in principle be eliminated by an ex ante balancing of incomes and expenditures.
An inability to balance revenues and expenditures could be expressed as open
inflation but equally as repressed inflation or simply be denied -- hidden
inflation <. The restrictions on the functioning of a labour market then
dissociate the maintenance of full employment through changes in the real wage,
imply further that labour allocation and sorting occurs independently of standard
signals and that with low wage dispersion a conventional intertemporal
accumulation of skills does not occur.
It is now evident with the benefit of hindsight that the coordination of
economic policies in a centrally planned system proved consistently more
difticult than anticipated. Incomes policies proved only partially effective as
a balancing mechanism with relatively rapid growth in open inflation in a numbe;
of economies, particularly those undertaking partial market-oriented reforms.
On the real side of the economy performance was very mixed with apparently
adverse dynamic outcomes. Table 1.1 demonstrates negative growth rates of
capital productivity for the entire sample from the mid-1970s onwards. In
addition, growth rates for labour productivity decelerated very significantly and
universally from the early 1970s onwards.
These adverse dynamics have commonly been attributed to the inappropriate
I Nuti (1988)
2 Bauer (1990); Kornai (1985)
3 Portes (1977)
-2-
incentive structure operating in the system with emphasis-on the lack of private
r- turns to effort. 'The incentive problem was widely recognized by planners and
Table 1.1
Labour and Capital Productivity (average annual growth rates), 1966-85
1966-70 1971-75 1976-80 1981-85
Lab Cap Lab Cap Lab Cap Lab Cap
Bulgaria 8.1 n.a 6.2 -0.6 4.4 -3.6 3.5 -3.1
Czechoslovakia 5.5 n.a 5.9 1.1 3.7 -1.5 1.3 -3.4
GDR 5.0 n.a 6.2 0.1 4.4 -1.0 4.3 -0.4
Hungary 5.1 n.a 6.1 -1.5 4.5 -4.3 2.3 -3.1
Poland 4.0 n.a 7.3 1.0 4.3 -4.2 -0.1 -3.4
Romania 7.3 n.a 6.2 -0.3 5.8 -0.8 4.0 -4.2
USSR 6.3 n.a 5.8 -1.1 2.8 -2.9 3.1 -2.7
Source: ECE-UN; cited in Nuti (1988), p367
academics in socialist economies. While high material intensity, low quality
capital goods and inflexible allocative mechanisms can explain part of this poor
performance, the institutional framework, motivational structure and remuneration
system are clearly central to explaining low productivity in the state sector.
At the same time, the attentuation of private ownership and thet reward structure
would exacerbate problems -- familiar also to a capitalist economy -- in
monitoring performance and information asymmetry. Among other results, the
absence of a conventional disciplinary mechanism -- su.:h as involuntary
unemployment -- might be expected to facilitate shirking.
Despite widespread recognition that the lack of a conventional
macroeconomic equilibrating mechanism in the system and the commitment to low
wage dispersion has tended to dilute productivity growth, exacerbate wage
pressures and been a component in the determination of the level of excess demand
in the system, limited attention has been directed to the particular processes
by which wages are determined in such economies. One assumption has been to view
wages as largely exogenous. Yet -- as this paper attempts to show -- this is
not appropriate once consideration of the incentive parameters is taken into
account. We also aim explicitly to introduce incentive features particu.lar to
a variety of socialist regimes where account is taken of the degree of ma-ket-
oriented reforms introduced into the system '.
This paper focusses on the issue of wage determination starting from the
case of a classical centrally planned economy and then progressively introducing
4 It should, of course, be mentioned that there is an extensive literature
on the Yugoslav experience with worker management/councils and more exotic
ownership forms; see, inter alia, Ward (1958); Tyson (1979); Horvat (1986); Jones
and Svejnar (1988). This paper explicitly does not concern itself wit) the
Yugoslav case.
-3-
market directed reforms. While such regime shifts have obviously to be
attributed to range of factors, we attempt to show that such reforms generally
represent attempts at changing the incentive and monitoring structure and hence
involve significant changes to the process by which wages are generated. We
approach the problem in a simple game theoretic framework and hence with regard
to the compatibility of interests among agents in these regimes. We relate the
wuge outcome to games involving, variously, workers, managers and the planner.
The players in these games differ by regime, as do the outcomes of the gamea.
An underlying concern of the paper is basically macroeconobaic as we wish to
extract a set of strictura. wage equations that could be cast in a macroeconomic
model. We further attempt to derive observable specifications. However, the
paper attempts to ground these equations by providing some simple micro-
foundations appropriate to the institutional and other arrangements
characterizing the socialist economy.
The organization of the paper is as follows. Section 2 presents a brief
dis,ussion of the institutional context in which wages and employment have been
determined in socialist economies. A simple typology of regimes is presented
that attempts to accomodate the features of the various reform measures
undertaken in a range of socialist economies over the past twenty years.
Sections 3 through 5 set up simple bargaining models feor the various regimes.
In Section 6, drawing on Hungarian and Polish experience and data, we present
some preliminary estimations of our wage equations and Section 7 concludes.
Section 2: Wage Determination in the Socialist Economy
2.1 Regime Typology
Tne discussion that follows aims to provide summary treatment of :he key
features of a range of socialist economy regimes with particular regard to the
wage determinati3n. Clearly many particularities are glossed over or ignored;
the objective is to encapsulate the basic regularities of the stylized regimes
with which we intend to work. The characteristics of the regimes are crudely
classified in Table 2.1. We distinguish four discrete regimes -- the classical
centrally-planned economy (CPE), the partially reformed socialist economy in a
first phase (RME), a reformed socialist economy in its second phase (R2E) and
a standard capitalist economy (CE). No strict linearity is implied by the
classification which is more aormative than theoretical. Rather, the typology
broadly captures a series of historical experiences among European socialist
economies. In general, however, the transformation has followed a linear
process. Movement away from the CPE has involved a transition to an economy with
RlE features. Hungary after 1968 and Poland from the early 1970s might be
considered as RlE economies. Advanced reform regimes (R2E) with features
increasingly akin to those of a standard capitalist economy have been a more
recent feature (for example Poland and GDR in 1990). The majority of countries
remain effectively located in RlE regimes.
For the purposes at hand, the distinction between the latter and the CPE
relates to the change in the rules determining wage fixing; the introduction of
new actors -- namely managers -- into the wage bargaining framework and the
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Table 2.1
CPE ... RIE R2E ... CE
1. Ownership of enterprises state owned state owned primarily largely private
state owned
2. Allocatio, of plan plan/free free frga
production inputs
3. Setting of plan plan/free market "riWt
factor prices
4. Allocation of plan plan/free free free
labor Lnput
5. Setting of wages plan free/rules markec / wage market
taxation
6. Allocation of plan plan/free free froe
consumer goods
7. Setting of plan plan/free market market
consumer prices
S. FLros. soft soft soft/hard hard
budget constraint
9. Unemployment goal no no accepts accepts
unemploymene unemployment unrnployment unemploymenc
10. Tax policy turn over tax turn-over tax incoms tax, income tax,
profit taxed VAT VAT
11. Sub#idled often often re-ove few
significant significant
12. Government * soft/hard soft/hard soft/hard soft/hard
budget constraint
13. Monetary policy passive rassive contingent concingent
14. Separate central bank no no/yes to some yea
and retail banks extent
15. Ownership of state state seate private
reeas1 banks
16. Retail banks' soft soft soft/hard hard I
budget constraint
17. securLties markets no no no yes
16. foreign trade state state + free free
monopoly enterprises
19. Exchange rate policy fixed, fixed, fixed/flexible fixed/flexible
rationed rationed
20. Convertibility no no yes (current yes
account)
general shift in planner's preference toward goals not strictly denominated in
quantity terms. However, no parametric shift occurs with regard to employment;
nor with regard to the budgec constraint facing enterprises. In short, the RlE
stage represents sele-tive market-oriented reforms with prices still largely
administratively determined and resource allocation driven by the planner or
central authority. To t'."Xt extent, both x 7orm economies (RlE and R2E) represent
degrees of decentralizacion with respect so the base CPE structure. While the
R2E economy bears most of the characteUistics of a capitalisr regime, the
thinness of financial institutions and the ownership structure continue to create
an effective distinction. Retention of the soft budget cons traint has potentially
powerful implications for the wage bargain.
2.2 The Centrally Planned Economy (CPE)
The CPE that was the characteristic organizational form for most socialist
regin;ss until the 1970s (and in some cases -- such as Bulgaria, Romania and
Soviet Union -- until almost the present day) was based on vertical controls,
with the planner coordinating economic decisions. Enterprise autonomy was
severely circumscribed and management was largely a transmission belt for orders
emanating from the planner. Trade unions lacked autonomy and full employment
was a given. Commands issued to agents and monitored essentially in quantities
proceeded on the basis of a theoretical balancing of input and output flows.
Similarly, revenues and expenditures were balanced with financial flows
accomodating planned physical flows. Wages were commonly set at low levels and
were compressed in their dispersion. A significant wedge between direct lrbour
costs to enterprises and household income emerged given the weight of transiers
and subsidies in total income. This generally implied low absolute wages but
relatively high aggregate household income. Wages were consistently subject to
centralized controls. These were critical for achieving balance between
aggregate revenues and expenditures as also for restraining the tendency for
labour market rents to be extracted out of a system where conventional ownership
and market disciplines were absent.
Several well-recognised tensions emerged from this system. In dynamic terms,
once labour reserves have been exhausted, the mechanism for output growth was
necessarily greater capital infusions. Growth depended on new investment with
higher capital-labour ratios and/or changing the product-mix toward more capital.
intensive goods. Depending on the income elasti 'r of consumer demand for
capital and labour-intensive goods, satisfying consum.L demand could have adverse
consequences for growth. By the same token, this could yield exaggerated
mismatch between consumer demand and the structure of aggregate output °. This
dynamic inefficiency reached down into the wage process. When labour shortages
emerged and the penalty that could be exacted by the planner from the worker for
inadequate effort was absent or difficult to enforce, the only feasible mechanism
for inducing greater worker effort remained piece-rate wage adjustment. The use
of piece-rates attempted to get round the monitoring problem. The issue turned
not only on the costs of monitoring individual effort but also, given the absence
One implication of this being that any shift in prefe,ence on the part
of the planner toward satisfying consumer demand would have a correspondingly
negative effect on output; see Weitzmann (1970).
-6
of a true management agency, in monitoring enterprise performance. To the extent
that an information constraint emerged, the planner would tend to select a
control 4.nstrument that, in principle, harmonized with the overall emphasis on
physical -- hence monitorable -- targets. This meant that regulation of the
wage-bill of enterprises became the other key control mechanism in the hands of
the planner 6. The enterprise wage-bill was in effect constructed as a base
wage with a piece-rate adjustment 7.
The use of above-ncrm payments as motivational devices became a widespread
feature of CPEs. By 1960 90-95% of Soviet industriel workers were paid some sort
of incentive wage and over 60% were on piece-r.tes 8, However, to the extent
that piece-rates resulted in aggregate demand effects, the likely consequence was
a further divergence of the planned supply of consumption goods from notional
demand, given limitations on factor substitutions and the higher c&pital/labour
ratios in production required to sustain growth. Shortage moreover induces
observable spillover effects in consumer markets 9. To the extent that the
leisure choices of workers are constrained 1', rising excess demand (assuming
that wage payments were not matched by availability of consumer goods), mirroild
in higher than desired money balances, would exert influence on the relative
effort applied by workers.
In short, the full employment regime imposed a weak incentive base.
Attempts to raise X-efficiency by piece-rate payments further tended to have
implications for balance In goods markets. Combined with the tendency fot
exhaustion of labour reserves to promote a structure of output- that worsen.d
consumer goods market disequilibria, this restrained the viability of sustair d"
use of piece-rstes to motivate workers.
2.3 The Partially Reformed Economy (RIE)
Characteristically, reforms to the CPE emphasized some measure of
decentralization of decision-making; the underlying objective being to simulate
some of the motivational features of a market economy while retaining the basic
ownership structure and redistributive traits of socialism. Generally, greater
autonomy for enterprises was accompanied by measures to associate domestic with
6 CPEs generally started out by regulating the average wage but fairly
rapidly moved to regulation of the wage-bill.
7 A wide variety of systems were tried at various stages; most aimed at
improving the incentive structure and/or providing enterprises with stimuli to
reduce labour absorption. In general, the wage-bill was defined as paid-out
wages and bonuses. In the late 1960s, separate bonus funds were established; see
Adam (1979) ppxviii/xix.
8 Kirsch (1972), pp41/42
9 See, for example, Podkaminer (1988)
10 Simply 'exiting' from work has generally not been feasible, as
legislation against 'parasitism' suggests.
.7
interv-ational pr'?Jes, to allow, in some caszs, enterprises to have ditect accers
to technology and other imports " and by greater tolerance for unofficial or
parallel markets in both goods and currency. Such measures were very tentatively
initiated (but then reversed) in Poland and Czerhoslovakia in the late 1950s and
more systematically in Hungary after 1968 and Pcland after 1.973/75.
Decentralization involved the central authorities relinquishing the right
to set physical output targets and centrally allocate inputs and materials.
Given concentration and market power, supervisory agencies were generally
retained with a view to containi.,g price expansion by monopolists. This also
cohered with the discretionary realloc-ation of resources by means of the tax
system, subsidies and refinancing credits issued through the Central Bank.
Despite specific country features, certain regularities can be isolated.
In general, devolution of controls implied some measure of worker self-
management, normally through enterprise councils or partially accountable
entitier. In Poland by the early 1980s workers' councils had been established
in over 6000 enterprises while in Hungary later measures resulted in around 73%
of state enterprises being transformed to management by councils 2. From the
perspective of this paper, this transition implies, first, the possible creation
of a new player in the game linking plant to planner. Under the partially
reformed system a diluted managerial role emerged, given the weakening of planned
outputs and allocations. This generated a more complex set of games between
enterprise and planner covering subsidy, tax eligibility and other negotiable
arrangements; it also generated the potential for firm-specific bargaining.
Decentralization also raised the issue of the manager's function and
motivation. Clearly, in a market economy, with a division between owner and
manager, motivation depends variously on labour market rewards, earnings based
incentives, share or stock options and any discipline exerted by external
valuation on the viability or independenc if the enterprise. rhese incentives
are largely absent in the RlE. In fact, the only consistent motivational
mechanism has been wage and performance-related bonus payments; themselves in
part constrained by the political acceptability of wider income dispersion ".
Further, precisely because of the horizons generatee by the system of social
ownership, the need to regulate the size of the incentive payments was
recognized. In general, the wage premia paid to enterprise managers was
explicitl' associated with performance or synthetic indicators with penalties
levied if wage expansion Was in excess of the growth in the performance
" With commonly disastrous consequences involving later socialization of
the debts incurred by unsatisfactorily regulated enterprise borrowing,
particularly in Poland.
12 However, central and party interference in the composition of management
committees remained widespread. For a summary of the inst :utioa%l changes, see
IMF (1989a and 1989b).
13 Political opposition to wage differentiation was one main reason for the
failure of the 1969 reforms in Hungary; see Soos (1987).
indicator 14. The same basic tension existed for managers as for workers with
respect to the possible appropriation of labour rents. Hence, :he external
imposition of wage and bonus norms on both mana3ers and workers. To that extort,
as we make explicit in Section 4, the manager and workers' interests might
coincide, allowing them to act coope.^atively against the planner.
Decentralization in RlE systems has normally been linked to some form of
tax-based incomes policy or method of wage regulation imposed on the enterprise.
The exact design of svch systems has varied widely, acting on either the wage
bill -- the sum of enterprise wages and bonuses -- or the rate of wage growth
with wages related to some measure of performance. The frequency of changes to
the system suggests the difficulty in isolating the appropriate synthetic
measures '. Tax-based incomes policies (TIP) were in principle designed to
achieve several objectives. )'ir3t, to restrain appropriation of labour rents;
second, to regulav..e effective demand and goods market imbalances and, third, to
regulate enterprise demand for labour and to achieve a moLe efficient allocation
of labour within the full employment constraint. The actual design o' the TIP
would then in part depend on the relative weights attache;' to these objectives.
Giving priority to regulating enterprise labour demand, for example, generally
implied control of the wag, 'ill.
The complexities in the design of wage controls are explored in detail
elsewhere "'. Several consistent, *nderlying tersions in the approach
characteristic of RlE regimes can be isolated from a raige of country
experiences.
* Associating the wage path to that given by productivity proved
problematic given the set of price distortions and offsetting taxes and subsidies
that remained in the system. Sound indicators of financial performance were not
transparent, necessitating frequent adjustments to wage control parameters.
* To the extent that wage formation was solidaristic and wage increases
converged to the upper limits, the outcome would be an acceleration in inflation
given the diluted discipline exerted on tradables prices by international prices.
Equally, inflation could be repressed via price controls.
a Reliance on plant-level productivity adjustment had the obvious
disadvantage that it could pull apart the wage distribution across industries
on the basis of no sound indicator; given the structure of distorted prices.
A preferable approach in any event would have been to link labour cost increasas
to economy-wide productivity expansion.
" Such premia could amount -- as in Hungary -- to as much as 50% of the
total wage; IMF (1989a).
" Between 1968 and 1989, there were seven major changes in the wage
regulatory system in Hungary while in Poland there were six s bstantive changes
in wage regulatior betwen 1981 and 1989.
'6 See, for example, Adam (1979) and (1982); Granick (1987); Marrese (1981);
IMF (1989a and 1989b)
-9-
* Using the wage bill to regulate labot demand would only f-end to change
the intra-firm ski.ll composition -- with a resulting bias toward unskilled, lower
wage categot:ies -- and hence have an impact on replacement policy. Little
efficiency gain might then be expected.
* Without basi" political acceptance of expanded wage differentials,
policies aimed at using wage diffentials as a motivational device have tended
to fail. Solidaristic wage outcomes likewise counter any presumed incentive
outcome. If decentralization proceeds alongside greater tolerance of the private
or parallel saczor, effo:t will be redirected to uncontrolled activities with
adverse productivity implications for the socialist sector.
* Soft budget constraints for enterprise managers and short-run wage
maximization objectives on the part of workers would tend to cluster wage demands
at the upper limits of the permissible payment irrespective of performance.
* Any incentive effects intended to be arsociated with productivitv and
skill related adjustments would tend to be diluted by a falling or low w
of wages to total earnings t.
* The effecti-_vness of any tax-based incomes approach depends on the
ability to enforce the penalties t8. To the extent that such 'control-by-
consjnt' is absent. more complex bargaining will emerge. This appears to fit
tba Polish RlE experience since the late 1970s. The outcome is accelerated wage
drift and the inefficacy of wage controls as a tool for demand management.
* Ther:e is an inevitable tension batween using wage controls for
macroeconomic objectives -- particularly excess demand in goods markets -- and
for incentive purposes if ex ante excess demand is significant (and monetary
overhang high) and supply elasticities low.
In summary, shifts to RIE regimes were attempts to address urtde '.ying
incentive problems in the CPE and thereby raise productivity. The outcomes were
inevitably ambiguous. Wage regulation could contain wage drift under certain
conditions, including passive unions. The Hungarian system appears successful
on this score over most of the 1980s. By contrast, where bargaining reflects
a basic argument ovez the wage level and political power -- as in Poland --
incomes policies tend to be ineffectual in managing lemand as also on
motivational grounds.
" It is instructive to note that for Hungary between 1984 and 1988 wages
averaged 38% of total cash receipts; social benefits in cash, 22% and other
receipts including Drivate economic activity, 24%. See; C.S.0 Monthly Bulletin
of Statistics.
1' Particularly problematic in a RlE where bargaining over exemptions and
special treatment remains endemic. See Gomulka and Rostowski (1984).
- 10 -
2.4 The Reform Economy - Second Stage (R2E)
Little experience is now available, given the recent nature of the changes
in Poland and former GDR. Broadly, the objective of the regime shift is to
induce lore completely market-based features in these economies through trade
liberalization, convertibility and the direct importation of international
prices. Fiscal discipline, autonomy of the monetary agency and elimination of
the conditions supporting a soft budget constraint for enterprises are other
components. Unemployment, wage dispersion and enterprise failures are tolerated.
In princivle, the R"E regime is supposed to behave 'ike a capitalist one; the
main obstacle being ownership righcs and budgetary transfers. In principle, the
latter can be addressed by pre-announcing a fiscal correction and pursuing a
restrictive monetary policy 19. The ownership issue is less tractable. Not
only is there high concentration but also a large weight of socialized
enterprises in total industrial activity. In Poland roughly 8000 state
enterprises account for about 90% of industrial output. Rapid divestiture raises
major questions regarding valuation, distributional and wealth effects. To the
extent that divestiture cannot be rapid, the question remains whether hard
enterprise budget constraints can be consistently enforced.
From the angle of wage regulation, this weight of the socialist sector
requires retention of certain wage controls, particularly in the context of a
stabilization. As usual, the design of the TIP is critical. For example,
maintaining controls on the wage bill -- as occurred in Poland in 1990 -- would
only tend to aggravate unemployment in this new context. Wage controls are also
likely to have undesired effects for an emerging private sector. For this
reason, private sector wages have been fully liberalized in Poland. The main
tension remains permitting wages to allocate labour and serve as a standard
incentive mechanism while maintaining macroeconomic balance in an environment
where the rules are not fully perceived as having changed. To the extent that
profit maximization and the associated penalties genuinely obtain, bargaining
models developed in t1e context of market economies are likely to be relevant.
fSction 3 Wagg Determination In the Centrally planned Ecom
3.1 Introduction
We now set up wage games appropriate for a CPE, incorporating an incentive
payment applied through a piece-rate, and establish the outcomes of these games
in both cooperative and non-cooperative settings 20. We are able to show that
the workers' reaction to an incentive payment can either result in reduced
productivity/effort or a higher than desired wage level and excess demand in good
markets.
19 Because of the ex ante structure of borrowing and inter-firm credits,
such an approach may be costly and a poor discriminator of underlying viability,
see Calvo and Coricelli (1990).
20 Throughout the paper wages refer to total remuneration including piece
rate, bonus and other fringe payments.
e 11 -
3.2 Framework and Some Assumptions
We assume that there are two important players in the CPE: the Planner and
the firms.a The latter are comprised of identical Workers; there is no distinct
management. There is a representative Worker's utility function. With no
unemployment in the CPE, this function includes effort and the expected real
wage. An increased expected real wage (W/P) increases consumption possibilities
either now or in the future and utility is hence a positive function of the real
wage. The relevant price index is the consumer price index 1. We assume that
the Workers form their expectation of this period's price level in terms of the
previous period so that PI can be considered an exogenous variable.
Utility is a negative function of the effort (Z) delivered.3 The
underlying argument is that the Workers face a trade off between work and leisure
and prefer less hard work. For convenience we choose an additive fo.mulation of
the utility function.
Uw - u(Z) + v(W/PF)
We assume that u'(Z) < 0, u"(Z) < 0, v'(W) > 0, and v"(W) < 0. That u"(Z) < 0
follows from the fact that the disutility associated with a high effort increases
with more effort. The indifference curves will be upward sloping in the 'effort
- wages space.
The Planner's role is to set economic targets and achieve them. In doing
so, the Planer might be concerned about a number of objectives, including the
volume of investment, private consumption, growth, income equality, price
stability, and the degree of excess demand on the goods markets. This can be
treated in the following way. The Planner has multiple objectives, the
rec ncilation of which consistently imposes a tension on the system. To achieve
the objectives, the Planner allocates the whole labor force, n, to production.
The output price level from the last period, P, is maintained. Finally, the
Planner sets a certain minimum wage calculated per time unit. We call this basis
wage, Wis.
2 In section 3-5 a closed economy is assumed.
2 It can be argued that in an economy with chronic excess demand for goods
the real wage is not a good measure for the consumption possibilities of a
certain nominal wage. However we have chosen not to include any measure of the
rationing at the goods market. The reason is that there is no a priori knowledge
of the way excess demand on the goods market influences the workers' desired
wage. One argument is that a rationed goods market will lead to less wage
pressure, cf. Ellis and Fender (1985), while another view is that the workers
will compensate for the present goods rationing by demanding .aigher wages (for
later effective consumption or for purchase of goods at the black markets).
Charemza and Gronicki (1983) call this last argument "wage illusion".
2 A formulation of the worker's utility function close to the one chosen
here can be found in Sokolovskii (1987), p5.
- 12 -
The Planner also seeks high production, hence growth. To yield these
targets a plan which sets the guniLty of the governments' investments and other
expenditures (I) along with the private consumption (C) is developed. Since the
economy is closed we have that the Planner will have a planned production target
(Ypw) equal to:
Yp,,, - I + C (3.1]
The Planner gives priority to fulfilment of Ypw and deviations from the target
leaves the Planner with the utility -00.
This model is a fixed price model and hence we can have that the Workers'
notional demand for goods can exceed the effective supply. If this is the case,
then we assume that the private consumption is rationed,2' We assume that the
Workers have no voluntary savings. This means that the Workers' notional demand
is equal to their income Wn. Excess demand can hence be written as:
X - Wn - PI - PY, (3.2]
where Y is the real production. We assume that the Planner prefers zero excess
demand and every deviation from this target decreases the Planner's utility.
We also assume that the economy is initially in a situation of excess demand
which implies that once Y>- is attained the Planner's utility increases as the
wage decreases.
The CPE has one firm managed by the Planner. The firm's production function
can be written as:
Y Zf(n)
The production is a function of the labour input and its technical productivity,
f(n), multiplied with the measure for the effort/productivity delivered by the
Workers, Z. It is assumed that f(n) > 0, f'(n) > 0, f"(n) < 0.
We have chosen a particular utility function for the Planner. Once the
production target is reached, utility decreases quadratically as the excess
demand deviates from its "optimal" value, zero. If we use the above formulation
of the utility function we can write the Planner's utility function as:
X00 if Y + Y
Up- [3.3]
L -Bj[PZf(n)-Wn-PI]a if Y - y33
We have assumed that n is exogenous, so the Planner will need an average
productivity equal to Zpt - Yp-/f(n) to fulfill the plan. Therefore, if the
productivity is Zp and the wage is W - (P/n)(Zpvf(n)-I) the Planner attains
maximum utility (equal to zero).
I In similar vein to Ellis and Fender (1985) and other fixed price
literature.
- 13 -
Due to the very centralized management of the firm the Planner has limited
possibilities for monitoring the work more and hence cannot rely on flexible or
nuanced payment schemes. Hence, to motivate Workers the Planner has recourse
to piece-rate payments ". We have chosen the following formulation for the
piece-rate payment:
W - W,, + CZ (3.4]
Wb. is the core wage determined by the Planner according to social and
distributional preferences, a denotes the piece-rate payment with Wale 2 0, a
0.
3.3 Cooperative Wage Bargaining: A Dictatorial Solution
In this section we look at the wage determination&as a cooperative game
with the wage (and the effort) being the result of bargaining between the Planner
and the Workers. For the time being, we assume that the Planner and the Workers
do not take into account systems for monitoring that the result of the bargain
is actually adhered to.
The Planner and the Workers have the utility functions Up and Uw. Let Up
denote the Planner's threat point and Uw the Workers' threat point." Let 0 (O
< e s 1) be the Planner's bargaining power. Hence 1-0 is the Workers' bargaining
power.
The Nash-Zeuthen-Harsanyi (NZH) solution to the cooperative game with two players
is found like this:"
Max ( [Up - Up IeUw - Uw]4 }
W.Z
We assume for the Workers' threat point; Uw - u(O)+v(W,w/P6), a situation where
the Workers choose not to deliver any effort at all and hence just receive Wb.
We assume that the Planner has an arbitrarily given threat point Up (< Up). We
get:
Max ( [Up - Up]e[Uw - (u(O)+v(WU./P))141 ) (3.5]
w,z
Equation (3.5] denotes the NZH solution to the bargaining between the Planner
and the Workers as a function of the bargaining power 0. The set of bargaining
I Extra-ordinary payments for above-norm effort have also been commonly
employed; see Adam (1979).
6 The threat point denotes the lowest utility the player will accept as
result of the bargaining.
2 See Friedman (1986) chp. 5 for a standard treatment of the cooperative
game. Svejnar (1986) contains a very good presentation of the Nash-Zeuthen-
Harsanyi solution for an asymmetric bargaining game.
14
solutions (as Q varies between 0 and 1) is the efficiency locus.
Let us discuss the shape of the efficiency locus. If the bargaining result
implies that the Workers' productivity is different from Zp,,, the PlaWer's
utility Up will be -0. The Planner will then stick to the threat point Up and
hence the product in [3.4] will be zero. To avoid this, the average productivity
must be Zp,. The Workers' utility can never get below u(Z)+v(Wb/P) since the
Workers' gain from the bargain in that case would be negative. From this we have
that the efficiency locus will be the points on the Z,. line lying above the
point where the Workers' indifference curve u(O)+v(W,./PE) intersects the Z7.,
line. If 0 is big (the Planner has large bargaining power) we will get a
solution near the intersection. As e becomes smaller the Whole line of solutions
will be traced. The efficiency locus (the NZH solutions) is drawn in figure 3.1
as a bold line. ThM point, D, is where the indifference curve u(O)+v(WM,/PO)
intersects the Zpm line.
Figure 3.1
W' \ / u(o)+v(Wb./r)
WhaI
ZIM
We now look at a special bargaining solution, namely the one where the
Workers' indifference curve u(O)+v(W"/P) intersects the Zp, line. This is the
NZH solution to the problem in equation (3.5] in the limit case where e -. 1.
We will call this particular solution the 'Dictatorial solution' since it is the
outcome of a bargaining where the Workers have no bargaining power and the
Planner dictates the result of the bargaining. It can be written as the vector
(WO,Z ), such that:
ze - t [3.6]
U(Z )+V(W/r) - U(O)+V(Wb/P0) [3.71
8 - . 1, but e + 1 (since if 8 was equal to 1 then the Workers would stick
to their threat point).
- 15 -
The Planner will choose to produce the planned output and pay a wage Just exactly
suffiLient to keep the Workers from delivering zero effort. The Dictatorial
solutlon can hence be interpreted as a solution where the Planner maxLmizes the
utility Up glven that the WorkersI utility is squeezed as much as possible.
We now return to the monitoring problem. How can the Planner be sure thet
the Workers will actually deliver the agreed upon effort, Zw,,, for the
DictatorLal solution? The only thing the Planner can monitor is the actual
production. To avoid the Workers receiving the payment W' but delivering, for
example, no effort, the Planner pays the Workers according to the pLece-rate
system described above. The Planner chooses a piece-rate a such that the sum
of the base wage and the piece-rate payment equals the agreed wage W;
Wb.+*Zp4,,, - W1 (3.81
This implementatione of the Dictatorial solution is illustrated in flgure 3.2.
The Planner will choose a piece-rate 0a such that the 1ine W - Wb+OZ passes
through the point D.
FLgure 3.2 u(O)+v(W>./P)
z-J,
zpw
The Dictatorial solution implemented via a piece-rate system (given by the
equations [3.5], [3.6], and [3.7]) is, however, unstable. In this set-up the
Workers de-ive nothing from the bargain yet have the possibility of reneging on
the outcome 3. Once the Workers realize that (a ,Zp1.) from equations [3.6]-
(3.8] is the outcome of the bargain they can react by playing the game in a non-
cooperative manner. This means that, given the piece-rate a the Workers will
S The piece-rate is a' - (W'-Wtw)/Z&,.
X Note that wb> is exogenous and predetermined. If this was not the case
the Planner could always adjust the base wage so as to make whatever combinatlon
of wage and productivity level a stable solution.
* 16 -
decrease their productivity (and their total wage) to increase their utility.
This behavior is illustrated in figure 3.3.
Flgure 3.3
Wb.+(4dZ
The point, D, again denotes the Dictatorial solution. The point D' will be the
Workers' optimal combination of wage and effort given that the Planner has chosen
the piece-rate a.
From the above discussion, it can be seen that the Dictatorial solution
tends to be unstable, since the Planner has not taken into account the Workers'
reaction on disclosure of the piece-rate a. This relates to the uneven nature
of the bargaining '. To the extent that the solution sticks, planned production
will always be attained, the wage will be relatively low and the likelihood
and/or the amount of excess demand will hence be relatively small.
We now examine the Dictatorial solution more closely. We know that the
productivity Z will be Zpw and that the wage can be found from equation [3.7].
By inserting Z - Zpt in equation [3.7] we find W* from: .
u(Zpn)+v(W'/P) - u(O)+v(W./P') [3.9]
From this we write the Workers' wage as a function of the base wage, the planned
productivity, the price expectations, and (formally) the Planner's threat point:
C,) (W) C? J
W- fn(Wb., ZPW, F, Up) (3.10]
The sign pattern i,s derived in Appendix 1 and '.ndicated by the signs above the
31 Note, however, that certain features of the CPE, make achieving a
dictatorial solution not wholly improbable. These features have included; an
absence of trade unions and a powerful repressive apparatus.
- 17 -
variables in equation (3.10]. An increased base wage will lead to a higher total
wage since it is now more attractive for the Workers to stick to their threat
point, i.e. not to work. When the planned productivity is increased, the total
wage rises; this follows from the curvature of the Workers' indifference curves.
Finally, an increase in the Workers' price expectations do not necessarily lead
to higher wages. A higher expected price means lower real wages which is not
desired. However, the real value of the threat point's W" also falls. The
resulting effect is uncertain. The Planner's threat point does not affect the
optimal wage.
3.4 The Stackelberg Solution in a Non-Cooperative Game
We continue by examining what the Planner can do to prevent the instability
shown above. The wage determination game is non-cooperative and we examine what
happens if the Workers' reaction is taken into account by the Planner. We work
with the same Planner and the same Workers as described in section 3.1. The
Planner is assumed to be a Stackelberg leader.
We assume the following "sequencing" of the non-cooperative game.
Basically the Workers produce the output and hence determine the effort while
the Planner pays wage to the Workers. The Workers decide on their productivity
given the offered wage. We assume they take into account that the Planner uses
a piece-rate remuneration system.
Workers' Reaction Curve
For every value of the piece-rate a which the Planner chooses, the Workers will
choose an effort maximizing their utility. The set of effort-wage combinations
derived in this way is the Workers' reaction curve. We find it by maximizing
the Workers' utility function subject to a given piece-rate. The Workers'
problem is:
lax ( u(Z) + v((Wb.4GZ)/P) 1
The first order condition leads to the reaction curve given implicitly by
equation [3.11]:
u'(Z) + v'((W.4+aZ)/r)(U/P) - 0 [3.113
Figure 3.4 gives a graphical illustration for the construction of the Workers
reaction curve. As regards the shape of the Workers' reaction curve, it will
always originate in the point (Z, W) - (0, Wb.). The reaction curve will tend
to move upwards being led by the increasing piece-rate. However, segments of
- 18 -
Figure 3.4
W
Workers' reaction curve
the curve can easily be backward bending, this being a consequence of the income
effect dominating the substitution effect.
Ti Planner as Stackelberg Leader
The Planner playing the non-cooperative game as a Stackelberg leader
regards the Workers' reaction curve as the possible combinations of effort and
wage. The Planner's problem is hence to maximize profit given the possibilities
depicted by the Workers' react'on curve and given that the Planner only can
change the piece-rate parametEr a. The Planner's problem can be written as:
Max Up s.t. u'(Z) + v'((Wb..4wZ)/PI)(a/PI) - 0 [3.121
As a Stackelberg leader the Planner maximizes Up by paying a total salary given
by the lowest point where the Workers' reaction curve crosses the Z*- line. That
is, the Planner chooses the piece-rate a where the line Wb.+a Z passes through
the lowest intersection point between the Workers' reaction curve and the Zpw,
line. This point is called S in figure 3.5 and is the Stackelberg solution.
From figure 3.5 we can derive two important results:
1) The Stackelberg solution is stable in the sense that none of the players have
any incentive to deviate from the solution. The Workers cannot get higher
m See Appendix 2 for a detailled discussion of the shape of the reaction
curve. There is nothing preventing the reaction curve from looking for example
like this:
fZ
-19-
Figure 3.5
>%w } Workers' reaction curve
WbI
utility given the piece-rate oa. (Their indifference curve just tangents the
point S). The Planner can not get higher utllity by lowerlng the piece-rate,
because then the production will fall short of the production target.
2) The wage will normally be higher for this solution than for the Dictatoital
solution found above. This makes sense given that in the case with the
Dictatorial solution the Planner squeezed the Workers as much as possLble, l.e.
to their threat point, while in the case of the Stackelberg solution the Planner
took the Workers' reaction into account.
However, as a consequence of the relative high wage payment implied by the
Stackelberg solution it is very likely that there will be significant excess
demand on the goods market. This is a frequently observed phenomenon in CPEs,
which (at least partially) can be explained by a high wage pressure stemming from
the non-cooperative functloning of the labour market 3. In conclusion, the
Stackelberg solution proved stable but had the drawback that the wage would tend
to be relatively high with a large excess demand on the goods market as the
result.
Because the Workers' reaction curve can contain backward bending segments
the multipliers cannot be calculated just by using the Implicit Function Theorem.
However, by adding one extra assumptlon (namely that v3(W) > 0) we can still
sign the multipliers.
The solution to the Planner's problem (expression [3.12]) is to choose the
procuctivity Z - Z and then the lowest piece-rate a satisfying the equation
for the Worker's reaction curve. That is, the Planner chooses a as the lowest
g satisfying
1' A special case can occur when the reaction curve is backward bendlng.
If the reaction curve bends backwards before it reaches the productivity target
(the ZO, line) the Planner will never be able to obtain the planned production.
- 20 -
u'(ZP,) + V'((Wb.,+oZp1.,)/P)(a/P9) - 0
If we assume existence of a Stackelberg Equilibrium, the Planner will choose the
wage (and hence the piece-rate) occuring at the lowest point where the Workers'
reaction curve intersects the Zw- line. By using this reasoning the multipliers
for the Dictatorial solution can be calculated (See Appendix 2).
(+) (+) C
W - fnW M., ZPh, P)
It should be noted that the wage initially will be higher in this situation than
in the earlier case. Furthermore, while the multipliers have the same signs as
for the cooperative game they will generally n= have the same size.
3.5 Summary
In our treatment of the CPE we find that the combination of centrally
determined production targets and piece-rate remuneration lead to either, (a)
unstable solutions with a tendency for under-attainment of production targets,
or (b), stable solutions with a likely high level of wages and significant excess
demand in the goods market.
Section 4: Wage Determination In the RefEL I Zggp=
4.1 Introduction
The main features of the RlE have been discussed in Section 2. The regime
might be considered a partial response to the incentive problems associated with
the CPE involving greater decentralization. In particular, the RlE has implied
greater autonomy for the workers and the managers in the setting of production,
investment and remuneration at their firms with explicit association of
remuneration to a performance indicator. One underlying argument for the reforms
that installed an RlE regime was that by imposing the 'right' incentive structure
on the managers the latter would balance the workers' demand for higher wages
and/or ensure that the workers deliver a high effort. To phrase it slightly more
technically, the reforms aimed to engage the workers and the managers in a
cooperative game determining production and remuneration. The government could
then choose the outcome of this game by imposing the 'right' i-centive structure
on the workers and the managers.
Our hypothesis is that the actual outcomes of the reforms deviated
significantly from intended outcomes. Especially in Poland, the government became
engaged in a game witV the workers and managers concerning the allocation of
resources in the economy. This game can be stylized as one where the workers
and managers played (more or less) together against the government or planner.
- 21 -
This section will model two games. Section 4.2 deals with a cooperative
game between the managers and t'te workers with an exogenous incentive structure
imposed by the planner. This game is in reality a two perso.. game with the
planner as nature. Section 4.3 sets up a three player game which is cooperative
between the managers and the workers and non-cooperative between these too and
the government or planner.
4.2 A cooperative game
There are two players, the Manager and the Workers. The Planner's
preferences do not appear directly but the Planner's policy and the institutional
arrangement influence the outcome of the co3perative game. Hence, the Planner's
behaviour represents nature and is exogenous to the Manager and the Workers.
We impose the same assumptions on the Workers in the RlE as for the CPE. To
simplify the calculations we have chosen to set the price expectation variable
r - 1. The Workers' utility function now reads;
Uw - u(Z) + v(W)
We use the same production function as in section 3 and assume employment at the
firm to be exogenously given by the Planner as n. The Manager's utility is
assumed to be a function of the remuneration received. The Manager's total
remuneration (R) is a fraction (a2) of the firm's profit (PZf(n)-Wn) and a
fraction (a3) of che value of the firm's production (PZf(n)).
R - a2(PZf(n)-Wn) + x,PZf(n)
We assume 0 c ok < 1 , 0 < a3 e 1. This arrangement for R broadly reflects the
incentive structure established in the RlE '. We simplify and obtain:
R - a,PZf(n) - a2Wn, where a, - a+a3.
The Manager's remuneration is expressed as a positive linear function of the
production value and a negative linear function of the total wage-bill, Wn, with
a linear band between them. We assume that the Planner can impose some penalty
on the Manager's remuneration if the Manager pays wages to the Workers above a
certain target. To ease the computations we choose a very simple formulation
of this tax. We assume that the Planner can change ao independently of ac. In
other words, the Planner can increase the deductions based on the wage-bill
without increasing the Manager's payment based on the value of the production.
Henceforth, we will interpret the 'incentive coefficients' in the following way
(a1 >0 , a > 0): a, < a2 implies a profit tax and an extra tax on the wage-bill;
3 As explained in section 2 the reforms also allowed the strengthening of
the private sector and often gave rise to dual pricing systems. These topics will
not be considered in this paper. See Commander and Coricelli (1990) for a
theoretical discussion of a dual pricing system in a RlE.
X The workers normally face economic incentives similar to the managers,
but the bonus payment constitutes a much smaller part of the workers' overall
salary than it does of the mnrnagers' salary.
22 -
, OI implies that only profit in taxed and a, > aa implies that profit and
production value are taxed.
For convenience, the expectation to the price level is taken as constant
and hence does not enter explicitly in the Manager's utility function. Finally,
we assume that the Manager's utility is directly proportional to the remuneration
received. The Manager is risk neutral. We can now write the Manager's utility
function, Ut, as:
UM - a,PZf(n) - %aWn.
For simplicity, 0 S a, 1 and 0 S 02 S 1. The Me.aager'c indifference curves are
straight lines with the slope (a,/%)(Pf(n)/n).
The Planner's utility function is somewhat modified in relation to the CPE
case. We assume that the Planner does not exclusively emphasize a production
target and instead concentrates equally on excess demand and the deviation from
the production target. The Planner prefers zero excess demand and every
deviation from this target decreases the Planner's utility. However, the formula
for excess demand (X) is now somewhat different, since the remuneration of the
Manager has to be taken into account. Below, the expression in the curled
bracket is the Manager's remuneration.
X - Wn + (cgPZf(n)-a2Wn) + PI - PY
X - PI - (l-a1)PZE(n) + (l-a2)Wn
We use an additive quadratic utility function where the utility decreases
quadratically as excess demand or production deviates from 'optimal' values.
The Planner's utility function is given by:
Up -1B[PI-(l-at)PZf(n)+(l-a2)Wn]2 - B2[y_y*-.2
The Planner needs an average effort/productivity equal to Z, - Y^m/f(n) to
fulfil the plan. Therefore, if the productivity is Zp and the wage is W -
(P/n)(Zp,f(n)-I) the Planner attains the maximum utility (equal to zero). This
point is called Op. The Planner's indifference curves are elliptical curves
around this optimal value and examples are given in figure 4.1.
The Planner still sets the employment n and the price level P. There is
no piece-rate system in this economy and hence no Wbm to set. Instead the
Planner sets the incentive parameters a, and a2.
23
Figure 4.1
z
The wage and effort are determined by bar&aining between the Workers and
the Manager. We call the Manager's threat point Um and the Workers' threat point
uw. e (O s e9 1) denotes the Manager's bargaining power and 1-8 is the Workers'
bargaining power. The NZH solution to the bargaining between the Manager and
the Workers is:
Max ( [UM - UM] [Uw - UW1 ) [4*.1]
w,z
If we insert UM - CtPZf(n)-%Wn and Uw u(Z)+v(W) in expression [4.1], we have:
Max ( [a,PZf(n)-OaWn - UM]¶[u(Z)+v(W) - U.w] 1 [4.2]
w,z
Expression [4.2] denotes the NZH solution to the bargaining between the Manager
and the Workers as a function of the bargaining power 0.
From the first order conditions for the problem in [4.2] we get the efficiency
locus." It can be written as:
a, Pf(n) u'(Z)
____ . D - [4.3]
a2 n v'(W)
The interpretation of expression (4.3] is that of a traditional efficiency
condition, namely that the marginal rate of substitution (between effort and
wage) for the Manager shall equal (minus) the marginal rate of substitution for
the Workers. The efficiency locus represents the set of the Nash-Zeuthen-
" See appendix 3 for the formal derivation of the efficiency locus.
- 24 -
HarsanyL solutions as e varies between 0 and 1. The slope of the efficiency
locus proves to be negative (Appendix 3). The intultion is that if the Manager
has a lot of bargainlng power the solution will be close to the Manager's optimal
choice, vlz, high effort and low wage (and hence the solutions will be in the
lower, right hand part of the efficlency locus). If the Workers have large
bargaining power we will have solutions with low effort and a high wage. The
indifference curves for the Manager and the Workers and the efficiency locus,
L, are drawn in Figure 4.2.
Figure 4.2
W _u
The actual outcome of the bargaining depends on the bargaining power 0 of
the two players. Later we will assume that the Managers and the Workers have
the same bargaining power. In this section we will briefly c.nsider what happens
to the efficiency locus as the Planner changes some of the exogenous variables.
We will examine what happens to the efficiency locus if the Planner changes the
incentive structure given to the Managers. Assume that the Manager's penalty
on the wage-bill, Wn, is zaised; i.e. q2 is increased. The Workers' indifference
curves are untouched, while the Manager's indifference lines will be flatter.
This means that the efficiency locus will move downwards and to the left. In
Figure 4.3 the original efficiency locus is called L and the one resulting from
an increase in c4 is called L'. That the efficiency locus.will move downward can
be verified directly from the expression for the efficiency locus, eq. (4.3].
dW/da2 (given Z) is found in Appendix 3.3 The sign is, as also argued above,
negative.
37 This exercise is inspired by McDonald and Solow (1981), p901.
- 25 -
Figure 4.3
W I
Uw
z
We now derive the multipliers for the change of the wage as a function of
changes in the exogenous variables. We assume that the two players have the same
bargaining power, e - 1. If we insert this in [4.2] and square the expression
in the curled bracket, the solution to the bargaining problem can be written
as30
Max ( [a,PZf(n)-%Wn - Um][u(Z)+v(W) - Uw] ) [4.4]
w,z
This is the symmetric Nash bargaining solution. Appendix 3 shows how the first
order conditions yield two equations having to be satisfied at the same time.
By using the Implicit Function Theorem on the first order conditions we obtain
a set of two equations for each exogenous variable. This set can be solved using
Cramer's rule providing the multipliers showing how each endogenous variable
influences W and Z. We write the Nash bargaining wage (W) as a function of all
the exogenous variables. Eq. (4.5] provides the basis for the estimations in
Section 6 of the paper.
Ws - fn(c1, a2, P, n, UM, Uw) (4.5]
An increase in the incentive parameter for production (a1) increases the wage.
The reason for this is that to make the Workers produce more the Manager has to
pay higher wages. An increase in the wage-bill tax (a2) decreases the wage. If
the price increases, the Manager's remuneration increases, this leading to higher
wages in this cooperative game. The sign for employment (n) is undetermined.
X To square the expression does not change the solutions to this
maximization problem, since X2 is a monotone transformation when x 2 0.
- 26 -
If the Manager's threat point, UM, increases the wage will falls, while an
increase in the Worker's threat point, Uw, will lead to an increased wage.
We continue this section with some remarks about the Planner. As mentioned
above thero is a combination of productivity and wage yielding the Planner
maximum utility. This can be attaineA by setting up an appropriate incentive
structure for the Manager, i.e. by regulating a,, o,. Appendix 3 contains the
calculations for dZ/da, and dZ/da2. One of the multipliers has undetermined
sign, but generally the multipliers dZ/da, and dZ/da2 will be linearly
independent of dW/da, and dW/da,. This means that we have two goals and two
linearly independent instruments and hence the Planner can always obtain the
desired productivity and wage just by adjusting a, and a2. Graphically the
changes in a, and Ga correspond to changes in the slope and the intercept (on the
W-axis) of the Manaser's isoprofit lines. By changing the slope and the
intercept of the isoprofit lines the Planner can ensure that the Workers' and
the Manager's Nash bargaining solution is just at the Planner's utility
maximizing point, Op (see Figure 4.4). Point B denotes the Nash bargaining
solution which coincides with Op.
Figure 4.4 Manager's isoprofit line
Workers'
indifference
curve
%Z
4.3 A cooperative game nested in a non-cooperative game
We now establish a three person game for the wage determination. Because
three person games are normally difficult to apply since the possibility of
coalitions has to be taken into account, we impose some restrictive assumptions.
The managers and the workers play a cooperative game, while these two players
" Note that if soft budget constraints hold and/or the Manager's
remuneration is ultimately weakly linked to performance, it might be expected
that the Manager's threat point would be very low.
- 27 -
play a non-cooperative game against the government or planner. We will show how
nesting the cooperative game in a non-cooperative setting changes the bargaining
and leads to some unexpected results.
There are three players in the game, the Manager, the Workers and the
Planner. The Manager's and the Workers' utility functions are the same as in
Section 4.2. When the Manager and the Workers cooperate we call these two
players, the Firm. We use the same quadratic utility function for the Planner
as the one described in section 4.2.
The following sequencing of the game is assumed. The Planner calls out
a certain wage target and the Manager and the Workers react to this by deciding
on a certain effort. The Planner reacts to this announcement of the Firm's
effort/productivity by offering another wage. However, this reaction will be
taken into account by the Manager and the Workers. The Firms' reaction will again
be taken into account by the Planner, and so on. This leads to a non-
cooperative Nash equilibrium. We assume that the Manager and the Workers maximize
the product of their utility gain subject to (the Planner's choice of) W. We
assume again that the two players have even bargaining power, e - ½. The problem
for the Firm can be written as:
Max ( [a1PZf(n)-oWn - UM][u(Z)+v(W) - U.] 1 (4.6]
z
Note that the above problem closely resembles the problem in expression (4.4].
However, in this case we maximize only with respect to Z, assuming that W is
given. This means that our solution will be a function relating the Firm's
optimal choice of Z to W.' The solution to the problem in (4.6] is found in
Appendix 4, The reaction curve is given (implicitly) by equation [4.7].
alPf(n) a,PZf(n)-%aWn
- _____ - -[(4.7]
u'(Z) u(Z)+v(W) -Uw
The interpretation of (4.7] is straightforward. The ratio of the Manager's
utility gain to that of the Workers' is equal to (minus) the ratio of the
marginal utilities resulting from an increase in productivity.
The reaction curve given by [4.7] is npt the same as the efficiency locu3
found as equation [4.3]. The reason is that the optimization problem required
to find the reaction curve is more restricted than the one required to find the
efficiency locus. This means on the other hand that the reaction curve will =
(generally) pass through the tangency point between the Manager's and the
Workers' indifference curves. In figure 4.5 the reaction curve is drawn in bold
(R) for the same indifference curves as used in figure 4.2. The slope of the
Firm's reaction curve is positive (Appendix 4).
1 In all the calculations in section 6 we have assumed that the threat
points are exogenous. This can be justified by pointing to the fact that the
"rules of the game" have determined the formation of coalitions a priori. Hence,
the players do not consider other coalitions than the one actually formed.
- 28 -
Figure 4.5
w Firms' reaction curve
The Planner reacts to the Firm's effort/productivity by choosing the
utility maximizing wage. To ootain the Planner's reaction curve we must maximize
the utility function Up with respect to W. We have:
Max ( -B[PI-(l-a1)PZf(n)+(l-a2)Wn]2 - B2(Y_y&,]2 1 [4.8]
w
The first order condition for the maximization problem leads after a little
simplifycation to eq. [4.9] which also can be written as in eq. (4.10].
PI-(l-a,)PZf(n)+(l-a2)Wn - 0 [4.9]
(l-eO)Pf(n) PI
W - - - Z - [4.10]
(1-oa) n (1-42)
We see from eq. [4.9] that the Planner's reaction curve simply is a relation
between wage and productivity such that excess demand is zero. The reason for
this is that given the Firm's choice of effort/productlvity, the only thing the
Planner can do ls to try to get as low excess demand as possible, viz; zero
excess demand. Further, the Planner's reaction curve can be expressed explicitly
and is linear (eq. [4.10]); a consequence of our choice of utility function for
the Planner. Finally, the slope of the reaction curve is positive.
The number of players is reduced to two, the Firm and the Planner. We find
the Nash equilibrium (N) as the intersection of the two players' reaction curves.
This is illustrated in figure 4.6. The Flrm's reaction curve is steeper than that
of the Planner. Thls is a necessary condition for the stability of the Nash
equilibrium.
29 -
Figure 4.6
Firms' reaction curve
Planners' reaction curve
In figure 4.7 are the same reaction curves as figure 4.6 but we have also
included indifference curves for the Planner and the Firm. The Firm's
indifference curves are constructed from the common utility function which is
maximized, i.e. the Firm's indifference curves are constructed by setting the
content of the curled bracket in expression [4.6] equal to a constant. Further,
the Firm has an utility maximizing combination of productivity and the wage; this
optimal point is Or. The Planner's optimal point is Op. As figure 4.7 is drawn
the Nash equilibrium implies higher wage and productivity than the Firm would
prefer and lower wages and productivity than the Planner would prefer. We see
that the Nash equilibrium implies solutions providing zero excess demand but a
Figure 4.7
Firms' reaction curve
r
Planners' reaction curve
- 30 -
very low productivity, i.e. solutions far away from the planned production
target. We also notice the non-Pareto optimality resulting from playing the
game in a non-cooperative way. The bold curve in figure 4.7 shows the part of
the efficiency locus Pareto dominating the Nash equilibrium.
We now derive the multipliers (see Appendix 4). The signs given below are
derived without further restrictions on the parameters of the model with the
exception of dW/dF where it is assumed that I is not too large.4'
fi3 0.) P aq (0) M 1+) _U O 1
i: - fn(at, ak, B,, B2, P, n, UM, Uw, I, ZpgAn) [4.11]
The multipliers derived from the non-cooperative model are rather surprising and
counterintuitive. Comparing with eq. [4.5] we see that, among the common
multipliers, only dW/dP has the same sign. The results from the nested game can
be interpreted as follows. Let us start with the multiplier dW/dU4 having a
negative sign, so that when the Workers' threat point increases the wage will
fall. When the Workers threat point increases the bargaining between the Workers
and the Manager will lead to lower effort given the wage.' The lower
effort/productivity will lead to a lower wage offered by the Planner, this again
leads to lower productivity and so on until a new stable Nash equilibrium is
reached. Graphically, this process can be described as a movement of the Firm's
reaction curve to the left.
Another surprising result is that an increase in the wage-bill tax results
in a wage increase, so that dW/da2 is positive. Several effects occur at the
same time. The Manager is penalized for wage expenses. Since the latter cannot
determine the wage in the bargaining with the Workers the only way the Manager
can compensate for this penalty is by increasing the productivity (at the given
wage). This corresponds to a shift of the Firm's reaction curve to the right
(see figure 4.8). However a change in a% also influences the Planner, since
(ceteris paribus) the revenue from the wage-bill tax will increase and hence an
excess supply on the goods market is created. The Planner will respond by paying
higher wages (at a given productivity level). This corresponds to an upward
shift in the Planner's reaction curve. The combined total effect of the
movements of the reaction curves implies a new Nash equilibrium with higher wage
and higher productivity, N', in figure 4.8. The remaining multipliers can be
interpreted in a similar vein.
41 (l+a,)Zf(n) > 2I is a sufficient condition for dW/dP to be positive.
I Remember that in this nested bargain the Workers and the Manager can only
settle on an effort/productivity given a certain wage. When the Workers' threat
point increases they will require an increase in their utility and this is
obtained by decreasing their productivity. In effect, the Workers "vote with
their feet".
- 31 -
Figure 4.8
W < / 0 Planners' reaction curvs
/ / Firms' reaction curves
// e ~~~~~~~~~~~Z
4.4 Summary
The above analysis has allowed us to trace out some of the implications
of wage bargaining in the RlE in both cooperative and non-cooperative settings.
The cooperative game inhibits a high degree of autonomy for the Planner and gave
usual signs for the multipliers. The nesting of the cooperative bargaining in
a non-cooperative game is an attempt to capture some of the stylized features
of an ecornomy marked by particular ownership, monitoring and information
constraints. This leads to a non-Pareto optimal outcome of the game and many
of the multipliers have unusual signs. Clearly a number of other crucial
characteristics -- such as the presence of a soft budget constraint and its
implications, in particular, for the Manager's threat point -- cannot be
adequately captured in this type of approach. It should also be noted that for
the non-cooperative setting the signs on the exogenous variables are obviously
sensitive to the sequence of the game and would be different if, say, the Planner
responded with a wage to a productivity given by the Manager and Workers.
Finally, it is expression [4.5] taken from the cooperative game that will provide
the basis for the later empirical work that we report in Section 6.
Section 5: Wage determination in the Reform 2 Economy
5.1 Introduction
We now present a very preliminary outline of a cooperative game between
the Manager and Workers in a context where unemployment is tolerated, where an
emerging private sector exists but where most of the enterprises are still state
owned. In principle, soft budget constraints are no longer present and the state
firm is instructed to act as a profit maximizer. However, it seems reasonable
to assume that R2E regimes are characterized by uncertainty over the rule changes
- 32 v
and by features -- including the limited size of the jrivate sector -- that
continue to distinguish them from a more conventional market economy. The model
elaborated below necessarily simplifies and is based on the standard efficiency
bargaining model developed in the context of a capitalist economy 4.
5.2 A cooperative game between Manager and Workers
There are two players, the Manager and the Workers. There is one firm
directed by the Manager and a given number of Workers (m) seeking employment in
the state owned sector. The individual Worker has the utility function defined
in section 3.2. Of the m Workers seeking employment in the state sector only
n (nrm) are employed. The effort delivered by Workers in the state sector is
assumed to be exogenous and equal to Z. " The utility for a Worker employed
in the state industry is:
UW - u(Z) + V(W).
Unemployment amounts to m-n. The utility for an unemployed Worker is:
Uw - u(B) + v(O),
where B denotes exogenous unemployment benefits. Involuntary unemployment
requires that u(Z) + v(W) > u(B) + v(O).
Using a utilitarian formulation of the utility function ^ for the group of
Workers seeking employment in the state industry we have:
Us - nv(W) + (m-n)v(B) + nu(Z) + (m-n)u(O)
The remuneration of the Manager is formulated as in section 4.2. That means that
if a, - a2 the state firm actually acts as a profit maximizer, but other choices
of a, and a2 will induce other incentives for the Manager.
The efficiency locus is found as the first order conditions to the
following problem:
Max ( [UM - UM][Us - Us]' ) (5.1]
W,n
In the R2E the threat point U8 is the remuneration the Worker can obtain by being
employed outside the state industry. (5.1] can be rewritten using the specific
4 McDonald and Solow (1981), Nickell (1982), Ellis and Fender (1985).
For an excellent survey, see Oswald (1985).
" Notice, n is now endogenous while the effort Z is exogenous. The
explanation for the latter assumption is that the Workers delivering a low effort
are laid off in the R2E.
a This way of aggregating utility functions is also used in Oswald (1985)
and McDonald and Solow (1981).
- 33 .
utility functions:
Max( (a,PZf(n)-a2Wn - UM]9[nv(W)+(m-n)v(B)+nu(Z)+(m-n)u(0) - U8]'.
W,n
The efficiency locus is found in Appendix 5. We have:
a,PZf (n) -oaW v(W)-v(B)+u(Z)-u(0)
Aa v' (W)
The interpretation of the efficiency locus is as usual: the Manager's marginal
rate of substitution between employment and wage shall equal (minus) the Workers'
marginal rate of substitution between employment and wage. Since v(W)-v(B)+u(Z)-
u(O) > 0 we have that a1PZfI(n)-%aW < 0. This indicates that the Manager employs
more labour than would be the case if the Manager was operating in a competitive
labour market. As shown in Appendix 5 the slope of the efficiency locus is
positive.
Static comparative analysis leads to many undetermined signs. The
following sign pattern is derived in Appendix 5.
WI - fn(a,, %a, P, m, B, Z, U., U,)
The three determined signs are intuitively sensible. An increase in the labour
force and hence in unemployment lowers the wage. An increase in the Manager's
threat point also lowers the wage, while an increase in the Workers' threat point
has the opposite effect. The remaining multipliers have undetermined signs.
With respect to a, an increase might be expected to motivate the Manager to hire
more workers and this would increase the wage. Offsetting this would be the fact
that the Manager's marginal remuneration as n increases would be negative,
motivating a lowering of the wage. It seems feasible to suppose that the former
effect will dominate I and this assumption would need to obtain if dir/da, and
dW*/dP are to be positive. It is also a sufficient condition for dW/dZ to be
positive. As regards dW/da2, an increase in the wage-bill tax a2 would lead the
Manager to reduce the wage-bill by lowering the wage. An indirect effect occurs
if the Manager reduces employment -- a likely outcome if a tax on total wages
is applied -- as this raises the Manager's utility at the margin and hence could
increase the wage. The overall effect is indeterminate. For dWC/dB, an increase
in unemployment benefits raises the utility pf Workers seeking employment in the
state sector. The direct effect is a fall in the wage; the indirect effect is
a fall in employment which could lead to a higher wage.
5.3 Concluding remarks
The model for an R2E outlined above illustrates the feature that since the
ownership of most of the enterprises still belongs to the state it can be
expected that the management of these will be carried out following rules from
I This means that 2(ajPZf'(n)-a2W)f'(n) > a,PZf I(n)f(n). See Appendix 5.
- 34 -
the Rlv.. If these rules stress a high productiont (a, is large) it is likely that
a high wage will be the outcome. Unemployment is in this model correlated with
the size of the labor force, m, and will tend to lower the wage in the R2E.
Finally, if the Workers have good income possibilities in the private sector
their threat point will be large leading to upward wage pressure in the state
sector.
However, the R2E regime raises a host of other interesting questions which
we are unable to address adequately using the above model. Among other issues
that need to be tackled will be the differences between the preferences of the
union/worker group as bargainer with private employers and as an employer in its
own right. The outcomes of that bargaining with respect to the wage and
employment are not however obvious, particularly given the overlay of structural
change imposed on the system by the transition to an R2E regime.
SectLmi 6: Some Preliminary Emixical ReIsults
6.1 Introduction
We now present in very preliminary form results from estimations of the
equation derived from the cooperative game setting for the RlE regime (see
Section 4.2). To that end we use quarterly data from both Hungary and Poland
covering the periods 1982(1)-1989(2) and 1982(l)-1989(4) respectively 47. Over
that time both systems could be stylized as RlE economies. The expression with
which we work is repeated below;
W+ I (+) M X0 L)
- fn(a,, o%, P, n, Um, Uw)
The parameter, a,, relates to the incentive for enhanced production. A rough
approximation for this incentive could be planned or realized productivity. a2
covers the wage bill tax. P is producer prices. In section 4 the Workers' and
the Manager's expectations to the consumer prices were ignored -- we choose now
to include consumer prices in our empirical analysis; n is employment. The
manager's threat point UM depends on the manager's alternative income sources
(see also section 4.2), and the workers' threat point Uw relates to the workers
income possibilities for example in the private sector. For the set-up presented
below, however, current data limitations have forced us to drop a number of terms
and concentrate in effect on the association between wages, prices and
productivity. We also incorporate simple error correction terms in the estimated
equations. The following notation is used throughout;
47 Data are taken from the IMF International Financial Statistics and are
more fully described in Appendix 6.
° 35 -
WAGE - index for average earnings.
CPI - consumer price index.
PPI - producer prices for the industry.
INEMP - index for industrial employment.
INPDN - index for industrial production.
PRO - index for industrial productivity (INEMP/INPDN).
L (as prefix) - natural logarithm of variable.
D (as prefix) - first difference of variable.
D4 (as prefix) - fourth difference of variable.
ECMH - correction term for Hungary (LWAGE-LCPI).
ECMP - correction term for Poland (LWAGE-LPPI-LPRO).
DUM* - dummy for period i.
6.2 Hungary
First difference changes in wages, prices and productivity presented in
Figure 6.1 pick out some particular features of the wage and price setting.
Wage changes appear clusteree in the first quarter up to and including 1985,
therafter an annual wage round appears absent with changes more randomly
distributed over the year. Intra-annual wage adjustments appear to have been
adopted as an institutional routine associated with the acceleration in consumer
prices over the later period. Consumer and producer price changes mostly track
each other closely, with some discrepancy at the start of the period. Again,
there is a consistent first quarter clustering of price changes. For
productivity (measured over the socialist material sector) changes are generally
concentrated in the second and fourth quarters. The spike in the fourth quarter
can in part be explained by the structure of the wage round and the use of the
wage tax to associate the wage and productivity paths. Reported productivity
increases in the fourth quarter likely reflect the incentive structure with a
tax-based wage policy. In short, there are clear institutional features that
yield particular regularities in the movement of the basic variables.
Table 6.1 reports the descriptive statistics. Several features stand out.
First, there is effective real wage stability over the period, as indicated by
the similarity in the mean of DLWAGE and DLCPI.
- 36 -
PIur 6.1.
Hungary
0.1oo . . 0 .
oœo~~ ~~ ~~ ~ ..... .. .A.... ....... . j....
0 .080 \ .......
0.000 ............. ...........
-0.025 ''" ' ! ! ; l ~.............. .. .......... . ............. . .. ..
-0.050
1883* 1884 188* Iw6 1987 198S
|_DLWA0O
0.100.
0.075. .... .... .. ...... .... .. .
905I... ,, -'., .....
0.025 ..... ...
0.000 . / .. .'
1983 1i98 19 8-5 98 1gi67 ti988
I DICPI DtP7I
0.10
-0101 ' 1 1985 1988 1987 1968
I-DURO|
- 37
There appears to be an indexation of wages to prices . The correction
term ECMH -- a real wage target -- is subsequently adopted in the estimation 1.
Consumer and producer prices have an expected coefficient. However, wage and
price changes are apparently very weakly correlated. The negative correlatlon
between consumer prices and productivity can be explained by the seasonal
features alluded to above. The productivity term is also marked by negeative
serial correlation, as indicated by the high DW statistic.
Table 6.1
Sample range: 1983(1) - 1989(2); number of observations: 26
Series Mean S.D. Maximum Minimum DW
DLWAGE 0.0245742 0.0351654 0.1183435 -0.0284606 2.192672
DLCPI 0.0235934 0.0251316 0.0966929 -0.0053410 2.513085
DLPPI 0.0148701 0.0344912 0.0945788 -0.0419526 2.132274
DLPRO 0.0078998 0.0403732 0.076r547 -0.0723430 3.172487
Covariance Correlation
DLWAGE,DLCPI 0.0000035 0.0041205
DLWAGE,DLPPI 0.0003322 0.2848057
DLWAGE,DLPRO 0.0004286 0.3139611
DLCPI,DLPPI 0.0005617 0.6739663
DLCPI,DLPRO -0.0002263 -0.2319340
DLPPI,DLPR0 0.0000690 0.0515244
The estimation presented in Table 6.2 relates wage changes to consumer
prices, productivity, a one lag correction term and dummies for 1984(4) and
1988(1). The constant is suppressed; its inclusion exerted little effect on the
coefficients and their standard errors 1. The size of price and productivity
coefficients enter with roughly the same magnitudes as for market economies while
the correction term suggests a rapid adjustment speed. There is a clear
underlying relationship linking price, productivity and wage changes. However,
the equation is clearly under-identified and lacks adequate stability. This can
be attributed in part to the institutional features of the economy and the many
changes over this period in those arrangements. Nevertheless, a reasonably
robust conclusion would be that wage formation has marked endogenous attributes
and that the wage does not enter as a purely exogenous variable.
4 More fully explored in Commander and Coricelli (1990).
4 The correction term is an observed relation between wage and price
variables during the 1980s and is not to be interpreted as a long run equilibrium
relationship.
a0 See Appendix 6 for actual and fitted values as well as residuals.
- 38 -
Table 6.2
Dependent Variable is DLWAGE
Sample range: 1983(1) - 1989(2); number of observatiorns: 26
VARIABLE COEFFICIENT STD. ERROP T°STAT. 2-TAIL SIG.
DLCPI 0.7908919 0.1673248 4.7266867 0.000
DLPRO 0.3075491 0.1237486 2.4852732 0.021
ECMH(-l) -0.6369975 0.1410623 -4.5157170 0.000
DUM844 -0.0635518 0.0252779 -2.5141279 0.020
DUM881 -0.0733555 0.0295827 -2.4796703 0.022
R-squared 0.603610 Mean of dependent var 0.024574
Adjusted R-squared 0.528107 S.D. of dependent var 0.035165
S.E. of regression 0.024157 Sum of squared resid 0.012254
Durbin-Watson stat 1.811326 F-statistic 7.994525
Log likelihood 62.68714
6.3 Poland
First difference changes for wage, prices and productivity are reported
in Figure 6.2. The pattern of wage change is clear; adjustment is in the first
quarter with the exception of 1987(1) 5'. Producer price changes exhibit a
similar first quarter pattern with consumer price changes clustered generally
in the second quarter. Productivity also exhibits first quarter spikes with a
deceleratiou over the last eight quarters of the sample. For both wages and
prices, there are sharp accelerations toward the end of the period, particularly
from 1989(2) onward as a set of upward adjustments to administered prices occurs
and the economy enters into a short high inflation period.
Tne descriptive statistics presented in Table 6.3 indicate a high and
predictable correlation between wage and price changes, particularly for producer
prices. The mean of wages is somewhat lower than of the cons'tmer prices while
the sum of the producer price and productivity variable almost equals the mean
for the wage. This motivates the insertion of a correction term relating wages
to production values (LUAGE-LPPI-LPRO). It should also be noted that the low
DW point to non-stationarity in some variables, particularly consumer prices.
°' There was a significant real wage fall as a result of a price surprise
in 1987.
- 39-
FIgue 6.2
Poland
0.4
0.4 . ..... .... ''''''''' ................. '...... ''"''''''''il'''''/
002 .. ..... .. .... .. .... ... .... ............ ............ ......
0.3 ... ...
0V.8
-0.1
000
1983 1064 IMS 9i8 1987 IS88 1989
10. .. . ..
0.50 ......
=045~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~/
|_ DICPI .... D .PI
0.100
-0-075' ....: ....
0.07'5 . ,. ,.
-0.020
19S3 1984 1985 1986 1987 ' 1988 1989
|_ DLPRO
- 40 -
Table 6.3
Sample range: 1983(1) - 1989(4); number of observations: 28
Series Mean S.D. Maximum Minimum DW
DLWAGE 0.1031135 0.1352018 0.4486949 -0.0153958 1.164384
DLCPI 0.1165299 0.1880734 0.9145840 -0.0054556 0.316326
DLPPI 0.0870261 0.1242070 0.4987389 0.0000000 1.358728
DLPRO 0.0108672 0.0280915 0.0927196 -0.0444890 1.724336
Covariance Correlation
DLWAGE,DLCPI 0.0177138 0.7224306
DLWAGE,DLPPI 0.0148153 0.9149054
DLWAGE,DLPRO 0.0009634 0.2630659
DLCPI,DLPPI 0.0169464 0.7523111
DLCPI,DLPRO -0.0008803 -0.1727925
DLPPI,DLPRO 0.0009282 0.2758756
The estimation reported in Table 6.4 relates wage changes to consumer and
producer prices, productivity, a dummy being 1 for all quarters of 1987, and the
correction term '. The constant is suppressed. The first quarter adjustment
structure for the key variables prompts fourth differencing of the data. Unlike
for Hungary, both consumer and producer prices enter jointly and significantly
and their coefficients sum to near unity. Producer price increases that
translate into consumer price increase appear to have direct and full
transmission through to the wage. The productivity term has a rather high
Table 6.4
Dependent Variable is D4LWAGE
Sample range: 1983(1) - 1989(4); number of observations: 28
VARIABLE COEFFICIENT STD. ERROR T-STAT. 2-TAIL SIG.
D4LCPI 0.3745738 0.1421613 2.6348511 0.015
D4LPPI 0.6178990 0.2258889 2.7354108 0.012
D4LPRO 0.6408179 0.2495559 2.5678332 0.017
ECMP(-4) -0.8597551 0.2577528 -3.3355802 0.003
DUM87 -0.0976912 0.0286817 -3.4060427 0.002
R-squared 0.975054 Mean of dependent var 0.342996
Adjusted R-squared 0.970716 S.D. of dependent var 0.303656
S.E. of regression 0.051964 Sum of squared resid 0.062105
Durbin-Watson stat 1.461380 F-statistic 224.7482
log likelihood 45.82553
' See Appendix 6 for actual and fitted values.
- 41 -
coefficient. While the fit is reasonable for the period 1984-1987, the residuals
for 1988/89 suggest inclusion of dummies. Their insertion did not however
materially improve the performance of the estimation.
6.4 Concluding Comments
Both the Hungary and Poland estimations presented above represent very
preliminary attempts at modelling wages in RlE regimes. Data and other
limitations mean that the equations are evidently under-identified. The wage
variable itself may not capture components of wage income committed to workers
under other titles. These factors naturally limit the conclusions that can be
derived. Nevertheless, it is clear that in both economies wage changes have been
strongly associated with prices and somewhat less with productivity suggesting
that wages should not be taken as strictly exogenous. More satisfactory
empirical investigation presupposes the construction of new series allowing
inclusion of the full set of variables denoted in expression 4.5 above.
Section 7: onclusion
This paper has addressed the issue of how wages are formed in socialist
economies. It has done so on the basis of a number of stylized regimes
characterized by their degree of decentralization and introduction of market-
based features or rules. The paper shows that one 'traditional treatment
involving a strong assumption of exogeneity for the wage is not warranted. Both
the classical planned economy and the partially reformed regime (RlE) are faced
with the joint problem of motivating workers in the absence of conventional
penalties -- particularly unemployment -- and of monitoring effort. The paper
indicates the manner in which these regimes attempt to resolve the incentive
problem. For the CPE the piece-rate mechanism is applied. We show how under
cooperative and non-cooperative settings the outcome can be either lower than
desired productivity or higher than warranted wages. The RlE regime can be
interpreted as an attempt to refine the motivational structure by introducing
another player, the manager. One underlying objective is to provide a framework
where workers and managers engage in a cooperative game to determine wages and
output with the incentive structure in effect given by the Planner. We attempt
to show how this can yield other-than-intended results if workers and managers
cooperate, playing a non-cooperative game with the Planner. This type of outcome
might broadly typify recent Polish experience over the 1980s. From the
bargaining model that we set up in Section 5.2 we derive an equation that can
be estimated for the RlE regime and some preliminary results are reported. The
assumption of exogeneity is shown to be untenable, even if institutional and
other factors indicate a greater degree of exogeneity than would be the case for
a standard market economy.
- 42 -
Referencea
Adam, J. (1979), Wage control and inflation in the Soviet bloc countries;
Praeger Publishers.
Adam, J. (ed.), (1982), Employment policies in the Soviet Union and Eastern
Europe; MacMillan Press.
Bauer, T., (1990), The Microeconomics of Inflation uxder Economic Reforms:
Enterprises and Their Environment; mimeo.
Calvo, G. and Coricelli, F. (1990), Stagflationary effects of stabilization
programs in reforming socialist countries: supply side vs. demand side factors;
The World Bank.
Central Statistical Office, Monthly Bulletin of Statistics; Budapest, Hungary.
Charemza, W. and Gronicki, M., (1983), Rational expectations, wage illusion and
consumption excess demand: an empirical investigation for Poland; Birkbeck
College Discussion Paper, no. 143.
Commander, S. and Coricelli, F., (1990), Levels, rates and sources of inflation
in socialist economies: a dynamic framework; The World Bank, mimeo.
Commander, S. and Coricelli, F., (1990) The macroeconomics of price reform in
socialist countries: A dynamic framework; The World Bank, mimeo.
Ellis, C.J. and Fender, J., (1985), Wage bargaining in a macroeconomic model with
rationing; Quarterly Journal of Economics.
Friedman, J.W., (1986), Game theory with applications to economics; Oxford
University Press.
Granick, D., (1987), Job rights in the Soviet Union: their consequences;
Cambridge University Press.
Gomulka, S. and Rostowski, J., (1984), The Reformed Polish Economic System, 1982-
83; Soviet Studies, 36,3.
Horvat, B., (1986), The theory of the Worker-Managed Firm revisited; Journal
of Comparative Econtales, 10.
International Monetary Fund, (1989a) Economic Reform in Hungary since 1968;
Washington, mimeo.
International Monetary Fund, (1989b) Economic Reform in Poland since 1981;
Washington, mimeo.
Jones, D., and Svejnar, J.,(eds),(1988), Advances in the Economic Analysis of
Participatory and Labour Managed Firms; JAI Press.
- 43 -
Kirsch L.J., (1972), Soviet wages; changes in structure and administration since
1956; MIT Press.
Kornai, J.,(1980) The Economics of Shortage; North Holland.
Kornai, J.,(1985) Contradictions and Dilemmas; MIT Press, Cambridge.
Marrese, H., (1981), The evolution of wage regulation in Hungary; in Hare, P.G.,
Radice, H.K., and Swain, N. (eds.), Hungary: a decade of economic reform, George
Allen and Unwin.
McDonald, I.M. and Solow, R.M., (1981), Wage bargaining and employment; The
American Economic Review.
Nickell, S.J., (1982), A bargaining model of the Phillips curve; Discussion
paper no. 130, Centre for labour economics, London School of Economics.
Oswald, A.J., (1985), The economic theory of trade unions: an introductory
survey; Scandinavian Journal of Economics.
Podkaminer, L., (1988), Disequilibria in Poland's Consumer Markets: Further
Evidence on Inter-Market Spillovers; Journal of Comparative economics, 12,1.
Portes, R., (1977), The control of inflation: lessons from East European
experience; Economica.
Sokolowskii, L.E., (1987), On individual and collective forms of labor
organization and incentives; Matekon.
Soos, K.A. (1987), Wage bargaining and the 'policy of grievances': a contribution
to the explanation of the first halt in the reform of the Hungarian economic
mechanism 1969; Soviet Studies.
Svejnar, J., (1986), Bargaining power, fear of disagreement, and wage
settlements: theory and evidence from US industry; Econometrica.
Tyson, L., (1979), Incentives, income sharing, and institutional innovation in
the Yoguslav self-managed firm; Journal of Comparative Economics.
Ward, B., (1958), The firm in Illyria: market syndicalism; American Economic
Review.
Weitzmann, M., (1970), Soviet post-war economic growth and Capital-Labour
Substitution, American Economic Review, 60, 4.
-44-
AnuendIS 1: The Dictatorial soluation ia She CPE
Multipliers
To simplify the expression the following notational simplifications are
made for Appendix 1 and 2; the stars indicating the optimal value are dropped;
Wb - Wb., and Zp - Zpw.
The wage as a function of the base wage
To find dW/dWb we use the Implicit Function Theorem (IFT). Define F as:
F - u(Zp)+v(W/P)-u(0)-v(Wb/P)
From equation (3.91 In section 3.3 we have that the wage for the Dictatorial
solution is W implying F - 0. From IFT, the multiplier dW/dWb is given as:
dW dF/dWb - v'(Wb/F^)(l/P)
dWb dF/dW V (W/t) ( /r)
dW v'(W/P^)
- _ > 0
dWb v° (W/r)
If we use vw < 0, then v'(Wb/P) > v'(W/P) and hence dW/dWb > 1.
The wage as a function of the planned productivity
dW dF/d7Zp uI (Z)
_ m - _ -
dZp dF/dW vI(W/")(11P)
dW u'(ZP)
_ . p s > O
dZp v' (W/PF)
The wage as a function of price expectations
dW dF/d^ v'(W/pe)(-W/Po) - v'(Wb/PE)(Wb/e)
dPF dF/dW VI Mr)(1/t)
We get after simplification:
- 45 -
dW v'(WI/r)(W/P ) - v'(Wb/P )(Wt/P')
dr v' (WMr)
dW/dr cannot be signed because of two opposite effects as the result of an
increase in P. The real value of the whole salary (W) decreases which tends
to increase the wage. On the other hand, the real value of the base wage Wb
decreases such that the alternative (to deliver zero effort and receive Wb)
becomes less attractive. The combined effect is uncertain.
Th- wage as a function of the Planner's threat point
Up does not appear in F and hence dW/dUp - 0.
AD1endix 2: The non-cooperative Same
Slope of the Workers' reaction curve
As argued in section 3.4 the reaction curve can be backward sloping, i.e.
the reaction curve constitutes a correspondance and we can not use IFT straight
away. However, as a first step we can find the elope of the inverted reaction
function. This means we are now going to find dZ/dW (instead of dW/dZ); using
the Chain Rule we have:
dZ dZ do
dW da dW
dZ/do can be found from the implicit form of the reaction curve (eq. (3.111 in
section 3.4): 1
F - u'(Z) + v9((Wb..+aZ)/PO)(a/P6) - 0
Using IFT gives us:
dZ dF/da v"(W/P*)(ZIPe)(aIPe) + v'(W/PO)(L/P)
do dF/dZ u"(Z) + v"(W/P')(a/Pp)2
The denominator is always negative, while the numerator can be positive or
negative.
a We generally use the notation F for the function used to derive
multipliers via the Implicit Function Theorem. The F used in this appendix has
no relationship to the F used in appendix 1.
- 46 -
The piece-rate is a - (W-Wb)/Z. This gives the derivative da/dW - I/Z. We can
find the slope of the inverted reaction curve for the Workers.
dZ v"(W/P)(Z/P@)(a/P) + v'(W/P@)(1/1') I
dW u"(Z) + v"(W/PO)(a/P)2 Z
Again the denominator is negative, while the numerator can be positive or
negative. If the term v"(W/P')(Z/P')(a/P') is smaller than v'(W/P)(1/P) the
numerator is positive and dZ/dW is hence positive. If vt(W/P)(Z/P)(air*) >
v'(W/PO)(1/P) the inverted reaction curve is downward sloping. Since we have no
a priori knowlodge about v" we cannot sign the numerator and hence we cannot
determine the slope of the inverted reaction curve. In the figure below an
example of a possible reaction curve in an inverted 'effort - wage' space is
drawn.
z
Workers' reaction curve
Wt..W
Multipliers for the Stackelberg equilibrium
We know that the Planner chooses the smallest piece-rate which satisfies
equation (3.13] in section 3.4. This means that the Planner will always choose
a wage (and effort) on the upward sloping parts of the reaction curve. However,
the upward sloping parts on the original reaction curve will also be upward
sloping on the inverted reaction curve. This means that only the upward sloping
parts of the inverted reaction curve are of interest. As argued above, the
inverted reaction curve slopes upward when v"(W/P) (Z/P) (a/PI) < v'(W/P)(l/P).
Therefore, when we calculate the Stackelberg equilibrium we know that it is going
to be found where v"(W/P')(Z/P@)(a/Pe) < v'(W/P")(1/P).
However, as illustrated above, we can say very little about the behavior
of the reaction curve, and by just considering the upward sloping parts of the
reaction curve we very easily risk working with overlapping "pieces" of
continuous functions. To avoid this we assume that the second order derivative
- 47 -
of v is upward sloping, that is vm > 0. This condition secures that the
inverted reaction curve will be bell-shaped, i.e. the original reaction curve
will contain only one bend. This again means that the part where
v"(W/P)(Z/P`)(v/P`) < v'(W/Pr)(l/Pr) will be a continuous, differentiable, and
upward sloping function. The intersection between the Worker's reaction curve
and the Planner's Zp, line will then be unique and we can find it just by using
IFT (on equation (3.13]).
The wage as a function of the base wage
The (total) wage is given as:
W - Wb + OZp
We have:
dW da
_ 1 + - z
dWb dWb
To find da/dWb we use IFT on equation (3.13J. From equation [3.13] we have
that the function Fp defined below is equal zero.
F- uI(Z.) + v'((W+aZp)/PI)(a/P) - 0
Using IFT we find the multiplier da/dWb as:
do dFp/dWb v"(W/P) ( /P) (alp")
dWb dFp/da v"(W/P^)(ZM/P)(a/p) + v'(W/P)(l/r)
We insert the expression for da/dWb into the formula for dW/dWb and obtain:
dW v' (W/P) (1/P)
dWb v" (W/P") (Zp/Pr) (O/P") + v' (W/r) (l/P)
Since v" < 0 we have that dW/dWb > 1.
The wage as a function of the planned productivity
Again using the Chain Rule:
dW do
_~ _ Zp + a
dZp dZp
- 48 -
To find do/dZp we use IFT:
do dFp/dZp u" (Zp) + v" (W/P) (/P) (/P*)
dZp dFp/dr V"(W/P)(Z4/r)(0/P) + v'(W/r)(l/r)
We insert da/dZp into the expression for dW/dZp:
dW u"(Zp) + v"(W/r) (C/rP)(a1/)
_ - . zp + o
dZp v" (W/r) (ZP/r) (alp") + v ' (W/r) (l/r)
dW v'(W/r)(q/r) - un(Zp)Zp
_ , . . ~~~~~~~> O
dZp v"(W/r)(ZP/PO)(o/r) + v'(W/P)(l/P)
The vage as a function of the price ezpectations
dW dO
dPr dr
da dFp/dP v"(W/P)(-W/P)(a/lp) + v'(W/p)(-o/p2)
dPr dFp/da v" (W/P) (ZP/P) (a/p) + v (W/P) (l/P)
We Insert in formula for dW/dP and get after simplification:
dW dFp/dPr v"(W/p*)(_W/Pd)(a/r)Zp + V'(U/p6)(_a/p)Zp
dPe dFp/dG v"(W/P1)(Z,/r) (a/PI) + v (W/P) (1/P^)
We cannot sign the multiplier dW/dP.
ApvendiS 3: The cooperative game In the RIE
The efficiency locus
The NZH solution to the cooperative game is given by:
t~i ( [a,PZf(n)-a°Wn - UM]([u(Z)+v(W) - Uw]'
For computational ease we take the logarithm of the expression in the curled
brackets. We differentiate with respect to W and Z and obtain the following
first order conditions:
- 49 -
-a2n v'(W)
e + (l-e) - o0
a1PZf(n)-a%Wn - UM U(Z)+V(W) - UW
a,pf(n) u'(Z)
e + (1-e) - o
a,PZf(n)-%aWn - UM u(Z)+v(W) - UW
By isolating the denominator for the first fraction in the first equation and
inserting it into the second equation we get that the efficiency locus can be
written as:
a, Pf(n) u'M
- ~~ m -
a2 n v'(W)
Slope of efficiency locus
Let us write the equation for the efficiency locus in a somewhat different
way and call the expression on the left hand side F.
F - a,Pf(n)v'(W) + %anu'(Z) - 0
Using IFT we have the following expression:
dW dF/dZ %anu"(Z)
dZ dP/dW a,Pf(n)v"(W)
Since both the second order derivatives are less than zero (cf. section 4.2) we
have that dW/dZ c 0.
Change of wage-bill tax
dW dF/d%a nu'(Z)
d4, J dF/dW a,Pf(n)v"(W)
The denominator is, as before, negative; the numerator is negative and the whole
expression is negative.
Multipliers
The first order conditions for the Nash bargaining solution can also be
found without taking logs of the utility gain function first. By differentiating
the expression in the curled bracket in [4.41 with respect to W and Z we get the
following first order conditions:
- 50 -
F. ( t,PZf(n)-%2Wn -UM]V(W) - a2n(u(Z)+v(W) - UW] - 0
FZ - c,tPZf(n)-a2Wn - M1u'(Z) + c1Pf(n)(u(Z)+v(W) - Uw] - 0
Subscript W respective Z denotes that the objective function is differentiated
with respect to W respective Z. Let us call the Manager's gain from the
bargaining 6M, 6M - a,PZf(n)-%aWn - UM, and the Workers' gain 6w, 8w - u(Z)+v(W) -
UW. Using this notation the above system can be written as:
Fw - 6MV'(W) - oan6w 0 ° .
Fz - SMu'(Z) + al1Pf(n)6w 0 °
We can find the multipliers via IFT for a set of simultaneous equations. The
multipliers dW/dai and dZ/da, can be found from the following syst9mg
(dFw/dWIEdW/dcz] + [dFw/dZJ(dZId(xJ - (dFw/da,1
[dFz/dW][dW/da,] + [dFz/dZ][dZ/da1 8 - [dFz/dall
The solutions to this system can be found using Cramers Rule:
dW [dFw/dZ1[dFz/da1 - (dFz/dZ1fdFw/da,]
dai tdFw/dW](dFz/dZ] - (dFw/dZ][dFz/dW]
dZ tdFz/dWJ[dFw/daI1 - (dFw/dW3(dFz/da,c
de4 [dFw/dW]ldFz/dZ] - (dFw/dZ]ldFz/dWJ
Call the common denominator D3. From the second order conditions for the
maximization problem we know that D3 - (dFw/dW] [dFz/dZ] - (dFw/dZ]2 > 0 (as well
as dFw/dW < 0 and dFz/dZ < 0).
For convenience we calculate the partial derivatives for later use:
dFw/dW - -2a2nv'(W) + 6wv"(W) < 0
dFw/dZ - a,Pf(n)v'(W) - a2nu'(Z) - 2C1Pf(n)v'(W) - - a2nu'(Z)
(dFw/dZ - dFz/dW > 0. The last two equality signs are derived using the condition
for the effeciency locus).
dFz/dZ - 2a,Pf(n)u'(Z) + 6Mu"(Z) < 0
Let us first look at the impact of the exogenous variables on the wage.
- 51 -
dW/df, - (1/D3)( [dFz/dW][dFw/dXi] - [dFz/dZ][dF/dal])
- (1/D3)( [2c,Pf(n)v'(W)][PZf(n)u'(Z) + Pf(n)6w]
- [2a,Pf(n)u'(Z) + 6mu"(Z)J[PZf(n)v'(W)] 4
(1/D3)( 2a,Pf(n)v'(W)u'(Z) - 6mu"(Z)PZf(n)v'(W) ) > 0
dW/da2 - (1/D3)( [dFz/dW][dFw/doa2 - (dFz/dZ][dFz/dQ]1
- (1/D3)( [2c,Pf(n)v'(W)][-Wnu'(Z)l
- (2aiPf(n)u'(Z) + 6mu"(Z)J(-Wnv'(W) - n6w] )
- (1/D3)( 2a,Pf(n)u'(Z)n6w + 6mu"(Z)[Wnv'(W) + n6w] ) < 0
dW/dP - (1/D3)( (dFd/dW][dFw/dP] - [dFz/dZ][dFz/dP] )
- (1/D3)( (2a1Pf(n)v'(W)ICa,Zf(n)u'(Z) + a,f(n)6w]
- (2a,Pf(n)u'(Z) + 6mu"(Z)]falZf(n)vI(W)]
- (1/D3)( 2c,Pf(n)v'(W)a,f(n)6w - 6u"(Z)alZf(n)v'(W) ) > 0
dW/dn - (1/D3)( [dFz/dW][dFw/dnl - [dFddZ][dFz/dn]
- (1/D3) ( [2ctPf(n)v' (W) j [,PZf ' (n)u'(Z) + a,PfI(n)6w]
- [2a,Pf(n)u'(Z) + 6mu"(Z)][((rlPZf'(n)-q2W)v'(W) - %6w]
a (1/Da)( 2a,Pf(n)v'(W)aPf'(n))w + 2acPf(n)u'(Z)oa[Wv (W)+6w3
- 6Mu"(Z)f(alPZf'(n)-oaW)v'(W) - q26w]
dW/dn has undetermined sign.
dW/diUm - (1/D,)( [dFz/dW][dFw/dUm] - [dFz/dZ][dFz/dUc]
- (1/D3)( (2a,Pf(n)v'(W)][-u'(Z)]
- [2a,Pf(n)u'(Z) + Smu"(Z)J[-v'(W)] )
- (1/D3)( 2a,Pf(n)u'(Z)v'(W) ) < 0.
- 52 -
dW/dUw - (l/D.)( (dFz/dW][dFw/dUW]- [dFz/dZJfdF/dUw]
- (1/D3)( (-q2nu'(Z)J[-a1Pf(n)3
- [2a,Pf(n)u'(Z) + Smu"(Z)1a[n]1
- (l/D3)l - anmu" (Z) ) > 0.
We calculate how the o dtLvitx Z depends on the incentive parameters
a and a:
dZ/dzt - (1/D3)( [dFz/dW][dFw/dC,J - [dFw/dW][dF2/dj] I
- (1/D3)( 1-qnu1(Z)][PZf(n)v'(W)]
- [-2qanv'(W) + 6wv"(W)I[PZf(n)u'(Z) + Pf(n)6w]
- (1/Do) ( 2a2nv'(W)Pf(n)6w - Jwv"(W)HPZf(n)u'(Z)+Pf(n)6wl 1
dZ/da1 has undetermined sign.
dZ/dM2 - (1/D3)( [dFz/dW] dFw/da] - [dFw/dWI[dFz/d42]j
- (1/D3)( [-q2nu'(Z)j[-Wnvm(W) - n6w]
- [-2Ganv'(W) + Ewv"(W))[-Wnu'(Z) I
- (1/D3)( a2nu'(Z)n6w + 6wv"(W)Wnu'(Z) ) < 0.
AaRendix 4: A cooneritive gsAme nested in i non-C or5at1L gft
The Firm'e reaction curve
If we take logs to the content of the curled bracket in [4.63 and
differentiate with respect to Z we get:
-ct,Pf (n) u'SZ)
+ -0
a,PZf(n)-oWn - u(Z)+v(W) -
This can only be simplified a little; we obtain the reaction curve:
a,Pf(n) a,PZf(n)-&aWn -
u'(Z) u(Z)+v(W) - Uw
The first order condltion for the Flrm can also be written as:
FF - C1tPZf(n)-q.Wn - Um1u'(Z) + *,Pf(n)[u(Z)+v(W) - Uw] - 0
- 53 -
The second order condition for a maximum requires that dFF/dZ < 0, which is
satisfied. To aimplify the notation we call the Manager's utility &ain 6m, 6m
- a,PZf(n)-qWn-Ufm, and the Workers' utility gain 6w9 8w - u(Z)+v(W)-UW. Fp can
then be written as:
FF -MU '(Z) + -1Pf(n)6W - 0
To find the slope of the Firm's reaction curve we use IFT:
dW dFF/dZ a,Pf(n)u;(Z) + 6mu"(Z) + a,Pf(n)u'(Z)
dZ dFF/dW -%nu'(Z) + a,Pf(n)v'(W)
dW 2a,Pf(n)u'(Z) + 6Mu"(Z)
dZ 2nu'(Z) - a,Pf(n)v'(W)
Both numerator and denominator are negative, so dW/dZ is positive. The Firm's
reaction curve is upward sloping.
The Planner's reaction curve
We differentiate the content of the curled bracket in expression (4.8]
in section 4.3. We obtain:
Fp - -2(1-a,)Bln(PI-(1-',)PZf(n)+(l-%)Wn3 - 0
This can, provided (1-%)B1n . 0, be simplified to equation 14.9] in section
4.3.
Multipliers
At the Nash equilibrium both the Firm's and the Planner's reaction
curves are satisfied at the same time. (The intersection between the two
reaction curves is the NE).
The Firm's and the Planner's reaction curves:
FF - LMu (Z) + a,Pf (n)6w - 0
Fp - -2(1-%)Bln[PI-(1-a1)PZf(n)+(l-ca)Wn] - 0
We have two simultanous equations. As in Appendix 3 we use IFT and Cramer's rule
to obtain the following formula for the multiplier showing the change in W as
a, changes.
- 54
dW [dFF/dZJjdFPz/da,1 - (dFp/dZ3(dFF/da,1
dal, [dFF/dW][dFp/dZ] - (dFF/dZl(dFp/dW]
Call the denominator D40 that is, D4 - (dFF/dWJ(dFp/dZJ - [dFF/dZjCdFp/dW]. Let
us sign this expression. For the NE to be stable (and unique) we require that
the slope of the Firm's reaction curve is bigger than the slope of the Planner's
reaction curve. The slope of the reaction curves can be found using IFT on the
equation for FF and Fp.
Slope (Firm's reaction curve) > Slope (Planner's reaction curve)
(dFF/dZ] (dFp/dZ]
(dFF/dW] [dPF/dWJ
(dFF/dW][dFp/dZ] - dFF/IdZH[dFp/dW] < 0.
The denominator D4 must be negative for the NE to be stable.
For convenience we calculate the partial derivatives for later use:
dFF/dZ - 2a,Pf(n)u'(Z) + 6Mu"'(Z) c 0 (Firm)
dFa/tZ - 2(1-a,)(I-%)B,nPf(n) > 0 (Planner)
Let us look at the impact of the exogenous variables on the wage.
dW/dI, - (1/D4){ [dFF/dZ3(dFp/dajj - (dFp/dZ](dFF/da,l }
- (1/D4){ t2aPf(n)u'(Z)+&yu'(Z)][-2(1-a2)3,nPZf(n)]
- (2(1-cl)(1-a2)B,nPf(n)][PZf(n)u'(Z)+Pf(n)6w] }
a (1/D4){2(1-a2)3,nPf(n)}
( -(1+a,)PZf(n)u'(Z) - Z6Mu"(Z) - (1-a1)Pf(n)6w )
dW/da, cannot be signed.
- 55 -
dW/d4 - (1/D4)( (dFp/dZ][dFp/dM2] - [dFp/dZ1[dFF/da
(1/D4)( (2a,Pf(n)u'(Z)+6mu"(Z)j[2BtnX + 2(1-qg)B,nWn]
- [2(1-a1)(1-a)8,nPf(n)][-Wnu'(Z)I )
- (1/D4)( 2(l-)2)B,n2W)((lfa1)Pf(n)u'(Z)+5uu"(Z) ) > 0.
dW/dB, - (1/D4)( [dFF/dZ](dFp/dB,] - (dFp/dZ][dFF/dBiJ )
- (1/D4)( [2a,Pf(n)u'(Z)+6muu(Z)][-2(1-a2)nX] ) - 0.
Excess demand is always zero.
dW/dI6 is zero since S2 does not occur in neither Fp nor FF.
dW/dP - (1/D4) ( [dFF/dZ][dFp/dP] - [dFp/dZ][dFF/dP] )
- (1/D4)( [2atPf(n)u'(Z)+6mu"(Z)](2(1-4)Bln(Zf(n)-I)]
- [2(1-al)(1-a2)8,nPf(n)J[a,Zf(n)u'(Z)4a,f(n)5wI
- (1/D4)( 2(1-aa)Bln)(2a,Pf(n)u'(Z)(Zf(n)-I)+8mu"(Z)(Zf(n)-I)
- (1-a,)Pf(n)a,Zf(n)u'(Z)-(l-a1)Pf(n)a1f(n)6w )
- (1/D4)( 2(1-2)B1n)( a,Pf(n)u'(Z)[(1+a1)Zf(n)-2I]
+ 6mu"(Z)(Zf(n)-I) - (l-a,)PZ(n)a,f(n)6W]
A sufficient condition for dW/dP being positive is that (14*,)Zf(n)-21 > 0.
dW/dn - (1/D4)( [dFF/dZ][dFp/dn] - [dFp/dZ][dFF/dn] )
- (1/D4)( (2a¶Pf(n)u'(Z)+6mu"(Z)][-2(1-2)B¶n(PZf'(n)-(l-a,)W]
- [2(1-ai)(1-a2)B,nPf(n)][(a,PZf'(n)-a4W)u'(Z)+a,Pf(n)Sw1 )
dW/dn has undetermined sign.
dW/dUm - (l/D4)( [dFF/dZ][dFp/dUmj - [dFp/dZ][dFF/dUM )
- (1/D4)(- [2(1-a,)(l-ak)B,nPf(n)](-u'(Z)) )
- (1/D4)( 2(l-a,)(l-a2)BjnPf(n)u'(Z) ) > 0.
- 56 -
dW/dUw - (I/D.)( [dFF/dZ1[dFp/dUw] - [dFp/dZ1[dFF/dUw]
° (1/D4)( - [2(l-a1)(l-a2)B,nPf(n)][-alPf(n)] )
- (1/D4)( 2(1-aj)(l-a)BjnPf(n)alPf(n) ) < 0.
dW/dI - (l/D4)( (dFF/dZ][dFp/dIj - [dFp/dZ][dFp/dI] )
- (l/D4)( [2csPf(n)u'(Z)+6uu"(Z)][-2(l-oi)8in(-P)] < 0.
A&Mendix 5: A coooeratLve Same in the R2F
The efficiency locus
The NZH solution is the solution to the following problem:
jax(([a,PZf(n)-aaWn - UM]9[nv(W)+(m-n)v(B)+nu(Z)+(m-n)u(0) - UeP)
We take logs of the expressions in the curled brackets, differentiate with
respect to W and n, and obtain:
-a2n nv (W)
e o + (1-0) _
a1PZf(n)-a2Wn - Um nv(W)+(m-n)v(B)+nu(Z)+(m-n)u(0) - Us
-tjPZf I(n) -a,?W v(W)-v(B)+u(Z)-u(0)
e + (1-0) -o
a,PZf(n)-a2Wn - U. nv(W)+(m-n)v(B)+nu(Z)+(m-n)u(O) - U8
C1PZf ' (n) -a2W v(W) -v(B)+u(Z) -u(O)
V'(W)
The slope of the efficiency locus can be found using IFT if we write the
condition for the efficiency locus this way:
F - (ajPZf'(n)-a2W)v'(W) + a2(v(W)-v(B)+u(Z)-u(O))
dW dF/dn aQPZf"(n)v'(W)
dn dF/dW a2v'(W) + (a,PZf'(n)-a2W)v"(W) + a2v'(W)
- 57 -
dW a1PZf"(n)v'(W)
_ _ * > 0
dn (t,PZf' (n) -a2W)v"(W)
The efficiency locus is upward sloping.
multipliers
The first order conditions for the Nast. bargaining solution leave two
simultaneous equations.
Fw- - ans + 6mnv'(W) - 0
F. (a,PZf'(n)-UW)68 + 6m(v(W)-v(B)+u(Z)-u(0)) - 0
The Manager's gain from the bargaining is 6m - aPZf(n)-q2Wn - Um and the Workers'
gain is 69 - nv(W)+(m-n)v(B)+nu(Z)+(m-n)u(0) - Us.
IFT for two simultaneous equations gives the multiplier:
dW [dFw/dn][dFA/dCl1 - (dF./dn][dFw/da,]
da1 [dFw/dW ([dFn/dn] - [dFw/dn [(dF./dW]
The denominator is called D5 and is positive according to the second order
conditions.
We calculate the partial derivative needed in all the multipliers.
dFw/dn - - M8s - a2n(v(W)-v(B)+u(Z)-u(0)) + (a,PZf'(n)-o%W)nv'(W) + 6mv'(W)
- 2n(CtPZf'(n)-%W)v'(W) - - 24n(v(W)-v(B)+u(Z)-u(0))
dF,/dn - a,PZf"(n)69 + 2(a,PZf'(n)-2W)(v(W)-v(B)+u(Z)-u(O))
_ a,PZfn(n)68s - 2(l/%)(a1PZf'(n)-q2W)2vI(W)
- a,PZf"(n)69 - 2o(v(W)-v(B)+u(Z)-u(O))2(l/v'(W))
These derivatives have been simplified using the first order condition for the
Nash bargaining solution and the condition for the efficiency locus.
dW/da, - (l/Do)( [dFw/dn][dF./da,] - (dFf/dn][dFw/dai]
- (l/D8)( [2n(a1PZf'(n)-q2W)v'(W)]
[PZf'(n)66 + PZf(n)(v(W)-v(B)+u(Z)-u(0))]
- [a,PZf-(n)8s v 2(1/a2)(a,PZf'(n)-oW)2v'(W)][PZf(n)nv'(W)]
- (1/Do)( 2n(a,PZf'(n)-%W)v'(W)]PZf'(n)69 - a0PZf"(n)68PZf(n)nv'(W) )
- 58 -
(1/Da)( nv'(W)PZ8s)(2(a,PZf'(n)-a2W)f'(n) - a,f"(n)PZf(n)
dW/da1 > 0 if 2(a,PZf'(n)-o%W)f'(n) > a,f " (n)PZf(n).
dW/daa - (1/D5)( [dFw/dn][dFdd4] - [dF./dn][dFw/da]
- (1/D5)( [2n(a1PZf'(n)-%W)v'(W)][-W68 - Wn(v(W)-v(B)+u(Z)-u(O))J
a[,PZfn(n)66 - 2(1/a,)(a,PZf'(n)-a2W)2v'(W)][-n68 - Wnnv'(W)]
- (1/De)( -2n(a,PZf' (n)-%W)v' (W)W6S + @1PZf"(n)6s[n6s+Wnnv (W)]
- 2(1/2)(ajPZf'(n)-QaW)2vl(W)n68 )
ajPZf'(n)-aoW > 4W is a sufficient condition for dW/d42 < 0.
dW/dJJa, - (1/Do) { dFw/dnl[dFn/dUM] - [dFn/dnl[dFw/d(l )
- (I/Da)( [2n(t,PZf'(n)-a2W)v'(W)][-(v(W)-v(B)+u(Z)-u(O))I
[ (a1PZf"(n)69 - 2(1/oh)(G1PZfE(n)-a2W)gv"(W)][-nv'(W)]
- (1/Do) C,PZf"(n)6Snv'(W) < 0
dW/ZdU - (l/Do) ( (dFw/dnI [ dF./dUg] - [dF./dn] (dFw/dU8s I
- (1/Da)( (2n(a,PZf' (n)-a2W)v'(WU)] [-(a,PZf' (n)-a2W)]
a, (PZf'n(n)66 - 2(1/c,)(t,PZf'(n)-ahW)2v'(W)][-a2n(-1)]
- (l/D5)( -a1a2PZf"(n)n6S ) > 0
dW/dP - (l/D.) (dFw/dn] [dF./dP] - (dFf/dn dFw/dP] I
- (1/Da)( [2n(a1PZf'(n)-a2W)v'(W)]
[a,Zf (n)Sg + a,Zf(n) (v(W) -v(B)+u(Z) -u(O))]
- [a,PZf"(n)6s - 2(l/o)(a1PZf'(n) -2V)'v'(W)]fa,Zf(n)nv (W)]
- (l/Do)( 2n(a1PZf'(n)-a2W)v'(W)]a,Zf'(n)6g - Ck,PZf"(n)6ea,Zf(n)nv (W))
dW/dP > 0 if 2(ajPZf'(n)-a2W)f'(n) > a,f"(n)PZf(n).
- 59 -
dW/dm - (11D5)( (dFw/dnl[dFn/dml - [dF"/dn](dFw/dm] )
- (1/Da)( [2n(a,PZf'(n)-a2W)v'(W)3[(a,PZf'(n) + a2W)(v(B)-u(O))J
- [a,PZf"'(n)6s - 2(1/a2)(a1PZf'(n)-a2W)2v'(W)](-an(v(B)-u(O)I
- (1/D5){ a1a2PZf''(n)n6S(v(B)-u(O) ) c 0.
dW/dB - (1/D5)( [dFw/dn][dFi/dB] - [dFn/dn]3dFw/dB] )
- (l/D.)( [2n(a1PZf'(n)-%aW)v'(W)]
((C1PZf'(n)-a2W)(m-n)v (B) + 6M(-V' (B))]
- (a1PZf''(n)68 - 2(1/a2)(a1PZf'(n)-oW)2v'(W)][-a2n(m-n)v'(B)]
- (GMD){ -2n(a1PZf'(n)-%aW)v'(W)6Mv'(B) + ,PZf"(n)6Sa2n(m-n)v'(B) )
dW/dB > 0 if 2(a,PZf'(n)-a2W) > (m-n)a1pzf''(n).
dW/dZ - (1/Do){ (dFw/dn](dF"/dZ3 - CdFn/dn][dFw/dZJ }
- (1/D5){ [2n(a,PZf'(n)-a2W)v' (W)J
[a,PZf'(n)68 + (a1PZf'(n)-t2W)nu'(Z)
+ a1PZf(n)(v(W)-v(B)+u(Z)-u(O)) + 6uu'(Z)J
- [a,PZf"(n)68 - 2(1/a2)(a1PZf'(n)-a2W)V' v(W)J
(-a2nnu'(Z) + a,Pf(n)nv'(W)J )
- (l/D5){ 2n(a,PZf'(n)-a2W)v'(W)a,Pf'(n)68 - a,PZf"(n)6sa1PZf(n)nv'(W)
+ 2n(ca,PZf'(n)-a2W)v' (W)6Mu'(Z) - a1PZf"(n)6M2nnu' (Z))
2(a1PZf'(n)-a2W)f'(n) > alf"(n)PZf(n) is a sufficient condition for dW/dZ being
positive. If there was no disutility associated by delivering a higher effort
u'(Z) would be zero and the stated condition would be a necessary condition.
Appendlx 6t Preliminary empirical results
Date
The data printed below are from the IMF, International Financial
Statistics. The Hungarian data is extracted from the database IMFGES in BESD
up to Sept. 1990. The Polish data is from IMFGES and the GUS Bulletin
(Statistical Office, Warsaw). The employment index for Poland before 1985 is
based on a yearly series from IMF IFS adjusted for seasonal variation using
estimates for the period, 1986(1) - 1989(4).
- 60 -
Legend (for both countries)
WAGE - index for average earnings.
CPI - consumer price index.
PPI m producer prices for the industry.
INEMP - index for industrial employment.
INPDN - index for industrial production.
Hungary
obs WAGE CPI PPI INEMP INPDN
1982.1 0.817021 0.781467 0.892857 1.036720 0.950820
1982.2 0.818440 0.799846 0.854037 1.038880 0.973588
1982.3 0.812766 0.823429 0.847826 1.037800 0.930783
1982.4 0.784397 0.828660 0.864130 1.032400 0.962659
1983.1 0.837589 0.847112 0.944876 1.008640 0.950820
1983.2 0.857447 0.853103 0.906056 1.012960 0.982696
1983.3 0.857447 0.866523 0.895186 1.014040 0.950820
1983.4 0.837589 0.873712 0.907609 1.018360 0.979053
1984.1 0.900709 0.921399 0.977484 1.001080 0.994535
1984.2 0.921986 0.931943 0.944876 1.007560 1.004550
1984.3 0.909929 0.944884 0.944876 1.011160 0.958106
1984.4 0.884397 0.939851 0.943064 1.015120 1.010930
1985.1 0.969503 0.987778 1.000000 0.997840 0.997268
1985.2 0.999291 0.993769 1.000000 1.002160 1.012750
1985.3 0.995745 1.006230 1.000000 1.003240 0.989071
1985.4 1.031210 1.012460 1.000000 1.006480 1.000910
1986.1 1.046100 1.045770 1.041000 0.993521 0.995446
1986.2 1.084400 1.041460 1.029000 0.995680 1.051000
1986.3 1.081560 1.055600 1.011000 0.995680 0.989071
1986.4 1.082980 1.068060 1.000000 0.998920 1.012750
1987.1 1.116310 1.105440 1.043000 0.975162 1.027320
1987.2 1.154610 1.126770 1.056000 0.973002 1.075590
1987.3 1.178720 1.163670 1.063000 0.967603 1.000000
1987.4 1.222700 1.182600 1.063000 C.969762 1.081970
1988.1 1.193620 1.302660 1.095000 0.947084 1.036430
1988.2 1.230500 1.299540 1.096000 0.943844 1.063750
1988.3 1.292200 1.338370 1.109000 0.941685 0.987249
1988.4 1.454540 1.361370 1.119000 0.944924 1.057380
1989.1 1.451000 1.489190 1.230000 0.918000 1.021000
1989.2 1.486000 1.530330 1.272000 0.910000 1.042000
m^,. "" . " .. mmmm.__ ..i n._ _.,,..._.,. w .
61 -
Poland
obs WAGE CPI PPI INEMP INPDN
1982.1 0.543000 0.524000 0.652000 1.021840 0.843000
1982.2 0.539000 0.626000 0.652000 1.018810 0.849000
1982.3 0.538000 0.650000 0.652000 1.021780 0.838000
1982.4 0.575000 0.672000 0.652000 1.022000 0.858000
1983.1 0.720000 0.729000 0.752000 1.011840 0.932000
1983.2 0.709000 0.785000 0.752000 1.008810 0.922000
1983.3 0.701000 0.785000 0.752000 1.011780 0.909000
1983.4 0.734000 0.803000 0.752000 1.012000 0.914000
1984.1 0.781000 0.845000 0.861000 1.004840 0.971000
1984.2 0.793000 0.902000 0.861000 1.001810 0.969000
1984.3 0.795000 0.919000 0.861000 1.004780 0.959000
1984.4 0.834000 0.914000 0.861000 1.005000 0.964000
1985.1 0.913000 0.938000 0.963000 0.999846 0.978000
1985.2 0.953000 0.996000 0.969000 0.996810 0.990000
1985.3 0.953000 1.017000 0.979000 0.999780 0.986000
1985.4 1.000000 1.042000 1.000000 1.000000 1.000000
1986.1 1.124000 1.096000 1.126000 1.004000 1.029000
1986.2 1.151000 1.164000 1.130000 1.000000 1.044000
1986.3 1.150000 1.169000 1.144000 1.000000 1.033000
1986.4 1.211000 1.225000 1.178000 1.002000 1.042000
1987.1 1.279000 1.301000 1.409000 1.004000 1.054000
1987.2 1.378000 1.467000 1.418000 0.999000 1.079000
1987.3 1.378000 1.523000 1.439000 0.998000 1.068000
1987.4 1.470000 1.591000 1.492000 0.997000 1.075000
1988.1 2.147000 1.866000 2.028000 0.990000 1.133000
1988.2 2.188000 2.273000 2.142000 0.984000 1.149000
1988.3 2.297000 2.458000 2.233000 0.983000 1.130000
1988.4 2.704000 2.700000 2.384000 0.981000 1.127000
1989.1 4.182000 3.274000 3.432000 0.977000 1.169000
1989.2 4.722000 4.204000 3.751000 0.969000 1.159000
1989.3 6.587000 7.034000 4.528000 0.972000 1.112000
1989.4 10.31700 17.55500 7.456000 0.963000 1.096000
~~~~~~0 .................
...................... ......... ..
0 - 4. -4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~............. ..
94~~~~~~~~~~~~~~~-
4J~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~49
.4. 1~~~~~~4
II II~~~~~~~~~~~~~~~~~II6-444
PRE Working Eaper Series
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