Government policy, real wage resistance and the resolution of conflict

European Economic Review 19 (1982) 181-212. North-Holland

Publishing Company

GOVERNMENT POLICY, REAL WAGE RESISTANCE THE RESOLUTION OF CONFLICT

AND

Rick van der PLOEG* Unioersity

of Cambridge,

Cambridgq

CB3

9DE,

UK

Received February 1981, final version received November 1981 A theory of bargaining with K players is proposed to reconcile the multitude of conflicting interests in an econometric model. This Nash strategy corresponds to a non-zero sum differential dynamic game and is established either by rational anticipation of linite conflict or pre-play round-table discussion. The theory is illustrated with an analysis of conflict between government, trade unions and entrepreneurs. All results are calculated from a large-scale multisectoral dynamic model of the U.K. economy developed by the Cambridge Growth Project.

1. Introduction Various complaints have been lodged about the logical problems involved in econometric policy evaluation [Lucas (1976)]. The critique is that when the government implements a new strategy the private sector will anticipate this and vice versa. The conventional econometric model is invariant to the policy rule adopted by the public sector, whereas typically the structure of the economy alters in reaction to government policy. This critique implies that econometric models may serve for conditional forecasting exercises, but that the results of quantitative policy evaluation should be treated with suspicion unless account is taken of the reactions to the policy under investigation. These problems are suitably illustrated with an analysis of a collective bargain between a trade union and government. The public sector (trade union) can only forecast the response of the economy when the trade union (state) is taken into confidence. The purpose of such a collective bargain is to provide sufficient information to ensure that both parties are able to choose an unregrettable equilibrium ‘strategy. The concept of, a dynamic Nash equilibrium is proposed as the best approximation to a collective bargain. The author considers the Stackelberg strategy, with one dominant agent and the other agents as followers, as unrealistic in the *I would like to thank members of the Cambridge Growth Project, participants of seminars at Oxford and Cambridge University and delegates of the Third Economics and Control Conference for many helpful comments. The paper has benefited from suggestions made by J. Waelbroeck and an anonymous referee. The financial support of the SSRC is gratefully acknowledged.

0014-2921/82/0CKXMOOO /%02.75 0 1982 North-Holland

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context of a collective bargain. Instead of the static micro-economic approach of bilateral monopoly with one employer and one union maximising profits and the real wage surplus respectively [de Menil (1971)], our analysis focuses on inter-temporal issues of macro-economic policy and conflict. This paper denies the existence of an explicit trade-off between inflation and unemployment (Phillips-curve), but accepts the notion of pure real wage resistance [Coutts et al. (1976)] except in cases of severe depression. An endogenous theory of wage inflation is proposed, where unions base nominal wage claims on the actual rate of price inflation, resist redundancies, fight public spending cuts and aspire a certain growth in real wages. The pursuit of a modified real wage resistance strategy provokes government reaction, since it violates the government targets of macro-economic policy. Similarly demand management involves an incomes policy and elicits a reaction of the trade unions. Such issues of conflict are best resolved within the context of a collective bargain. The paper shows that, despite the non-cooperative nature of the collective bargain, there is considerable scope for discretionary demand management. A theory of the collective bargain for the reconciliation of conflict between non-cooperative agents is developed in section 2. The same section gives an implementable algorithm for calculating such bargains from nonlinear dynamic econometric models. The results of section 2 are subsequently applied to the analysis of inter-temporal conflict between government, trade unions and entrepreneurs in the U.K. economy. It is assumed that all agents adhere to a common view of Britain’s economic prospects, that is as forecast by the Cambridge multisectoral dynamic model described in section 3. The preferences of the three competing pressure groups are discussed in section 4 and the corresponding strategies (including the collective bargain) are described in section 5. The paper concludes with section 6. 2. Theory of the collective bargain 2.1. Competing pressuregroups

In conventional policy formulation exercises with one central decisionmaker the current policy, say u,, depends on the model structure, the means and covariances of the model parameters, the expectations of all current and future modelling errors, the reliability of available sources of information, and the preferences and degree of risk-aversion of the central decision-maker [se& Theil (1964), Pindyck (1973) and Chow (1975)]. The problem of economic policy is therefore usually viewed as a struggle’ against unpredictable nature. However, many interesting problems are due to conflict between competing pressure groups. For example, inflation and excessive

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fluctuations may arise when trade unions, government, entrepreneurs and foreigners struggle for a share in the national income. In such a situation of more than one, say K, decision-makers the current policy of decision-maker k, say u:, also depends on his expectations at time t of current and future policies planned by the other pressure groups. This last property gives the framework of economic policy the characteristics of a dynamic game, for each player must take account of the unpredictability of future manipulations of the other agents. In general the first-order optimal change in the current policy of player k, say Su:, is given by the linear expression

su: =8UfOL - zt[izk{G$’ Ek(6uf,,)} +J’:,, Ek(~,,,;l, where 6& denotes the deviation of the open loop compromise strategy for player k from the benchmark policy, Ek(Guf,,) is the expectation of player k at time t of the change in policy of player i at time I, and Ek(s,,J is the expectation of player k at time t of the modelling errors due to unknown exogenous shocks at time 1.’ The strategies (1) may be considered to be derived from maximising a welfare criterion, specific to each agent, subject to the constraints of a dynamic stochastic model of the economy. They inform each decision-maker what to do when all future exogenous shocks and policies of the other players are known. The decision-makers typically experience difficulties in forming expectations of the future manipulations of the other pressure groups, because preferences and the view of the economy adopted by the other agents may not be known. A collective bargain may be established with the aid of pre-play round-table discussion to reveal preferences and intended strategies. This process should be interpreted as cooperation in the provision of information, but not as cooperation in strategy. This may be called a non-cooperative collective bargain with no secrecy. When all players perfectly anticipate future policies of the other players one speaks of a bargaining equilibrium, This satisfies the Nash equilibrium property [cf. Starr and Ho (1969) and Ho (1970)] wk(&!,,,

. . ., 6Uk,.

. ., 6&)

5

w,@t+?J,,

. . ., C-h&-,

. . ., c%&),

Vk,

where W, denotes the welfare criterion of agent k, 6& denotes the string of all current and future equilibrium policies adopted by player k, and 6uk is any ‘other string of policy implemented by player k. At the equilibrium none of the players has an incentive to deviate from the anticipated bargain. Hence, it does not pay to cheat when the other agents stick to the bargain. It must be emphasised that often the players could gain from cooperation, since ‘The subscript OL indicates open loop, so that the corresponding changes in the strategies of the other agents or exogenous shocks.

policies

do not react

to

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policy and real

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many economic situations are described by a non-constant sum game [see Bacharach (1976)]. Cooperation in strategy only works when the various pressure groups trust each other and any acceptable change in policy must satisfy Pareto efficiency and interpersonal non-comparability [see Lute and Raiffa (1957)]. Equilibria derived from (1) are hard to find as perfect foresight of all future errors and manipulations is required. The next section therefore adopts a framework with a finite planning horizon. This allows the derivation of noncooperative bargains from large-scale econometric models. 2.2. Rational anticipation offinite conflict

Assume a dynamic econometric parameters in final form, say, y=y”+6y+&=

mode1 of the economy

yO+~(M’&4’)+&, I

with known (3)

where the target variables are y=(y;,, . . ., y>)‘, the policy instruments of player k are uk =(u;, . . ., I&)‘, the modelling discrepancies are E= (E;, . . ., E;)‘, o denotes the benchmark view, 6uk=uk-u”, and T is the length of the planning horizon. All players influence current and future prospects of the economy (y) and the effectiveness of each agent is measured by the dynamic multipliers (Mk=ay/8uk). Fqr-simplicity all agents have the same view of the economy and access to identical sources of information, but aspire different objectives and have control over different policies. Suppose the members of pressure group k attempt to manipulate the Folicy instruments at their disposal (uk) to steer the economy towards the view they desire, say yk*. Assume therefore that each agent minimises a quadratic welfare loss criterion of the form [cf. Theil (1964)] Zk=(y-yk*)‘Qk(pyk*),

(4)

where the semi-positive definite matrix Q’ contains the relative trade-off weights (priorities) for each of the target variables. The first-order optimal change in the policy of player k is given by

dUk= G& - i$k (Gi’k 6~‘) - Fk Ek(&), where Fk = (Mk’

Giik = Fk Mi

6&

Mk) - 1 Mb Qk,

Qk

3

= Fk6yk*.

(1’)

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The optimal policy feed backs information about past and future strategies undertaken by the other agents. An agreement is reached when no player has an incentive to change policy, given that the other players stick to the bargain [cf. (2)]. This equilibrium is found from solving 6U=6V,N+H6V,

(5)

Ek(s)] where V = (u”, . : ., uk’)r, the kth sub-vector of 6V,, is given by [&&-Fk and the coordinated reaction matrix H consists of sub-matrices Hki= - Gijk and H,,=O. The pre-play round-table negotiations on the counter-moves each player would take in reaction to a change in policy of the other pressure groups may be formalised by

where each element of the power series expansion in the haggling process. (The haggling commences for policy, that is 6VIN.) When the bargaining singular the negotiations converge to an agreement 6V=(I-H)-‘6V,N=B-1bV,N.

corresponds to one stage with the initial proposals matrix, B=IH, is nonof the form (6)

Because the collective bargain is invariant to scaling of the penalty matrices Qk, interpersonal non-comparability is satisfied. At the equilibrium each policy-maker reacts to environmental disturbances (E) with the aid of feedback rule (6). The feedback of realised exogenous shocks does not alter the nature of the equilibrium. For known linear models with separable quadratic preferences certainty .equivalence holds and this provides a justification for assigning expected values to future (unknown) errors. However strategy (6) is open loop with respect to policy. Strategy (5) is closed loop with respect to environmental uncertainty and policy, since it employs the coordinated reaction matrix (H) to feed back the evolving and expected strategies of other players. Our closed loop strategy (5) is conceptually different from Kydland’s (1975) feedback strategy. Kydland restricts policy to a function of the current state of the economy, but this is an inferior strategy and (6) generally yields higher welfare. In a sense our approach is an alternative to the time-decomposed solution, based on joint Riccatti systems, proposed by Pindyck (1977) and extends .Pindyck’s analysis to non-causal nonlinear models with K players and non-separable preferences. It is trivial to modify (2)-(6) to allow for a situation where players adopt a different view of the economy and future exogenous shocks. The derivation of the collective bargain also extends to non-causal economic models whose structure is not invariant to the policy rules. This

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case arises when some agents form rational expectations of future states of the economy [cf. Wallis (1980)]. It’follows by induction that in the final form of such models the current state not only depends on the past history of policy and exogenous shocks, but also on the anticipation of all future strategies. The matrices of dynamic multipliers (Mk) simply loose the lower block-triangular structure, but the equilibria (5)-(6) remain optimal. Under rational expectations the fundamental dynamic programming principle breaks down and any policy which merely feedbacks the current state of the economy is time-consistent but not optimal [e.g. Kydland and Prescott (1977, 1980)]. This does not prevent the calculation of optimal but timeinconsistent equilibria, so that the problems raised in Lucas (1974) are resolved. 2.3. Bargaining strength and singular games

The resolution of conflict does not necessarily converge. Consider a dynamic game with two players, say T and G, influencing economic prospects by manipulation of strategy t and g, respectively. Assume both players have an identical view of the world, then the bargaining matrix is given by B=

where B,

= (M’

The determinant

Q’ M’)

- 1 j,,f”

Qi Mi.

of B follows from Schur’s formula and is given by

det(B) = det(l- B,,B,,) = det(l - B,,B,,). The game is singular when this determinant is zero. One important case is when one player, say 7; adopts a targets-instruments approach [Tinbergen (1952)].’ Then, Brg = M; ’ M,,

BBAg = 1,

and the game is singular. No collective bargain is found, because one of the players insists and is able to attain under all circumstances its desired values 2One speaks of a targets-instruments approach when a decision-maker attempts to attain the specified values for a number of target variables exactly by manipulating an equal number of policy variables. Tinbergen has shown that this is possible only when the matrix of multipliers, that is M, is invertible.

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exactly and is not prepared to compromise. An example of this type of singularity is when trade unions claim an increase in nominal wages, compatible with a desired growth in real wages, without taking account of the disastrous effect a growth in real wages higher than growth in labour productivity may have on future unemployment. When the game is singular the outcome must depend on the relative bargaining strengths of the various parties. Suppose r(B)= k, dim(U)= n, and that the parties negotiate, the n-k undetermined variables. In the above example these may be the wage rates. The outcome of the negotiations depend on the skill and intensity of bargaining of each pressure group and may be formalised by

SGU=s,

(7)

where r(S’:B’)=n. The collective bargain subject to (7) yields an unique negotiated equilibrium. An extreme case is when one player, say i, is strong enough to achieve his goals exacly, so that he is able to pursue a targetsinstruments approach. In this case S =JM and s = J(6yi* -P(a)), where J denotes a (n-k) x dim(y) matrix for selecting the relevant target variables of player i from the vector y. 2.4. An open loop algorithm for nonlinear econometric models

The algorithm must minimise the quadratic welfare criterion (4) for each of the K players subject to the constraints of a nonlinear dynamic econometric model with known parameters. The outcome is an open loop equilibrium for a K player non-constant sum non-cooperative dynamic game. An efficient numerical algorithm is described by the following steps: (1) Select a benchmark view on policy, corresponding target variables, say y”.

say U”,

and

calculate

the

(2) Use the adjoint variable technique [e.g. Nepomiastchy and Ravelli (1977/78)] or numerical perturbation to calculate an initial estimate of the dynamic multipliers, say MO. Set the iteration counter (n) to zero. (3) Calculate a Gauss-Newton policy correction (6U”) in the direction of the collective bargain from the asymmetric set of simultaneous equations [(M”‘xQ)M”]6U”=(M”‘xQ)x[Y*-Y”-E(s)], where Q=(Q’,..

., Q?, M=(W

,..., Mk), Y*=(y*“,..

., Yap’)‘, Yn=(yn’ ,..., JP’),

E(E)= (El(s)‘, . . ., Ek(s)‘)‘, and x denotes direct multiplication matrices.

of partitioned

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(4) Perform a coordinated line-search by gradually diminishing the steplength parameter a” (starting with CL”= 1) until the length of the coordinated reduced gradient, that is t#(a”)=ll(M”‘xQ)x[Y(U”+a”6U”)-Y*]ll, is reduced sufficiently below 4(O). Set U”+ ’ = U” + a” 6U” and simulate the econometric model to obtain Y”+l. (5) Re-evaluate the dynamic multipliers with the adjoint variable technique or numerical perturbation. Alternatively, update the dynamic multipliers with the aid of the Broyden (1965) and Schubert (1970) variable metric revision formula to obtain IV”+‘. (6) Check for convergence. When 4 is zero or the change in U and y is insignificant stop, otherwise set n=n+ 1 and go to 3. The evaluation of the closed loop policy rules (1’) is avoided; instead the problem is solved with coordinated Gauss-Newton reduced gradient algorithm. Account is also taken of agents with different expectations of future exogenous shocks. The algorithm is an extension of Myoken (1975) and based on Rustem and Zarrop (1979). It provides an alternative to Pau (1975). Section 5 of this paper discusses the application of the above algorithm, using numerical perturbation in step 2 and the variable metric revision formula in step 5, to the Cambridge multisectoral dynamic model. 3. The Cambridge multisectoral

dynamic model of the U.K. economy

This section describes a large multisectoral dynamic model (MDM) of the British economy,3 which is used in section 5 to analyse conflict between state, unions and firms. The model was originally developed as a static Leontief input-output model suitable for analysing the equilibrium impact of structural change on the industries in the U.K. economy. It has subsequently been extended, by introducing dynamics in the econometric relationships for the components of final demand, imports, employment and wages, to allow the year by year projection of transient paths. The dynamic version of the model therefore does not ensure equilibrium in the labour market or in the market for foreign exchange and, although total demand and supply for each commodity will be balanced, it is not necessary that the individual %is is the model developed by members of the Cambridge Growth Project under direction of Sir Richard Stone and Terence Barker. More details of this model may be found in Barker et al. (1980).

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components of final demand will be in equilibrium. The present model may be viewed as a hybrid model which combines the desirable features of the structural Leontief input-output model with the dynamic properties of today’s aggregate econometric models. The hybrid approach to model building facilitates the synthesis of economic policy, for it is possible to discuss at the same time the appropriate timing of changes in the policy instruments and a suitable disaggregated implementation of aggregate policy measures. Similarly, the industrial implications of macro-economic policy may be analysed. MDM is much larger than the average aggregate time-series econometric model, for it contains more than 15,000 estimated coefficients and 3,000 endogeneous, 850 policy and more than 4000 other predetermined variables. The tremendous detail modelled in MDM does not imply that the logical structure is more complicated than the conventional Keynesian macroeconomic model, because the specification of the sectoral equations often follows from the disaggregation of the corresponding macro-relationship. The equations of MDM are organised around a social accounting matrix (SAM), both in constant and current prices, so that the economy is modelled as a complete and consistent set of national accounts. The core of MDM is that part of the SAM which represents the Leontief-Keynesian identities between total demand and supply. Total demand for each of the 57 commodities is found from equations for exports, separate relationships for the domestic components of final demand and from intermediate demand. The intermediate demands are determined by a traditional input-output model, extended to allow for joint production in the 40 industries. The import-share functions are then used to divide total demand between domestic output and imports of commodities. The make matrix transforms domestic commodity output into domestic industry output which then enters the employment, investment and stockbuilding equations. The model recognises that investment and employment decisions may be interdependent. This implies that labour productivity is endogeneous and determined by the composition and growth of investment and labour supply. Hence, the growth rate may be increased, not only by an increase in capacity utilisation, due to higher effective demand, but also by extra investment and reallocation of labour to more productive industries. The equations in MDM have been restricted to ensure internal and price homogeneity of degree zero in the long-run. The first property ensures that an x% increase in domestic wages, compensated for by an x% depreciation of the exchange rate and a corresponding revaluation of all assets and liabilities, has no long-run effect on real flows. The second property implies that if a change in foreign prices is compensated by an equal change in the exchange rate the real variables and foreign trade should eventually adjust to their original values. However, the adjustment process may permanently improve

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competitiveness, since the model allows for irreversible increases in labour productivity. In summary, MDM is essentially a multisectoral Keynesian model with no supply constraints, except for the production of North Sea oil, and relatively little monetary feedbacks to the real sector. Hence, it is assumed that there is suflicient labour mobility across industries, the supply of funds to firms is not rationed, importers can obtain the foreign exchange they require, etcetera. Furthermore, the supply of money is assumed to be sufficient to cover the demand for money and does not enter as a policy instrument. The enormous size of MDM is due to its industrial nature and provides an ideal challenge to the optimal control and bargaining algorithms proposed in section 2 of this paper. 4. Preferences of competing pressure groups4 4.1.

Objectives

of macro-economic policy

The main macro-economic goals are well known and not controversial, although some might argue on the relative priorities of the various targets and on the way the economy operates. The targets of a hypothetical administration for the U.K. economy are, in decreasing order of priority, to attain lower levels of unemployment (1.5 million) and higher annual growth of the domestic economy (3.5x), to improve competitiveness, to gradually reduce the public sector borrowing requirement and to ensure that foreign reserves do not diminish. The target for competitiveness ensures that this government desires an acceptable rate of price inflation, that is in line with the rate of world inflation. These aims must be achieved by a feasible manipulation of the standard rate of income tax, the exchange rate and the level of government expenditures. This administration also considers it desirable to gradually reduce direct taxation and withdraw public spending in line with HMSO (1980) and to have the exchange rate close to the value which maintains competitiveness. Finally, this government is not shortsighted and adopts a planning horizon of eleven years. The objective function implicit in table 1 allows one to deduce certain marginal rates of substitution, that is how far to sacrifice one target in order to attain an improvement in another target and remain at the same welfare contour. For example, it implies, for 1983 and thereafter, a decision-maker who is prepared to substitute a 1% drop in the public sector borrowing ratio for an additional 448,000 jobs. This particular indifference statement is only locally valid, that is at an original 5% public sector borrowing ratio and unemployment level of 4 million.5 4A summary of the preferencesof the state, trade unions table 1. ‘MRS=aYdaY,=

-qso11-Y:)/(q2(Y2-Y:))=

-($5%5-

and entrepreneurs

1.5)/((10/42)(4-

1.5))=

is presented -0.448.

in

R. oan der Ploeg, Government

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Preferences Target

variable

of competing Desired

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1 pressure

groups.

value

Priority

GOVERNMENT Balance of trade (Em 1970 export prices) Unemployment

0

(million)

1.5

Ratio of public sector borrowing requirement to gross domestic product Growth

in gross domestic

product

Competitiveness factor (unit value of U.K. exports of manufactures divided by the unit value of competitiors’ exports of manufactures, both in U.S. S) Standard

rate of income

1

tax

10

4.75% for 1980, 3.5% for 1981, 2.5% for 1982, and 1.5% for 1983 and thereafter

5

3.5%

8

1.0 29.2% for 1980, 30.0% for 1981,28.0% for 1982, and 25% for 1983 and thereafter

Exchange rate in dollars per pound (1971= 1.0)

Compatible with maintaining competitiveness

40

Level of current (excluding defence) and capital (excluding housebuilding) government expenditures

HMSO (1980) for 1980-83 and fixed at 1983 level for each year from 1984 onwards

20

TRADE Annual

UNIONS growth

of real wage

3%

10

Redundancies

0

10

Annual growth of current (excluding defence) and capital (excluding housebuidling) government expenditures

1.5%

10

ENTREPRENEURS Share of profits

Function utilisation

Industrial

n.a.

prices

of capacity co 0

4.2. Trade union policy

Roughly 50% of the labour force was unionised in 1978 and this proportion has been rising for some time. Many of the remaining sections of the labour force follow the outcome of the unionised sector. It may therefore EER-

B

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be not too unrealistic to consider the complex of trade unions in the U.K. economy as one monopolistic organisation with complete control over the nominal wages of its members. It therefore does not seem appropriate to lrelate the rate of wage inflation to some proxy for excess demand for labour. Wage increases could take place at any level of demand, if the trade union SO desires. The trade union wishes to be compensated for all increases in the cost of living. It therefore argues in terms of real wages, since it perfectly anticipates the rate of price inflation. The trade union decides on nominal wages to secure a desired growth in real wages. This aspiration level of growth in real wages is presumably determined by past successes in wage settlements and possibly some compensation for the introduction of new technology. When real wages are the only target variable adopted by the trade union, there is no scope for compromise and no collective bargain. Such a strategy ignores the feeling of unease spread by redundancies. 2erefore this paper postulates a trade union, which does not only pursue high growth in real wages but is also concerned with avoiding present and future redundancies. This is an extremely rational trade union, since it is prepared to sacrifs some growth in real wages today when it anticipates a significant future fall in redundancies. Unions only suffer from money illusion when they genuinely fear redundancies. If prospects for employment are bright, money illusion, is non-existent. This specification implies that depreciation need not necessarily lead to an inflationary spiral which destroys any beneficial impact on the real economy. Since the trade union values employment and realises that a depreciation could raise labour productivity and stimulate demand for domestic products, it may persuade its . members to put up with a temporary reduction in the growth of real wages. When the union anticipates that an incomes policy has a beneficial effect on preserving trade union membership, it might impose a rational and voluntary incomes policy. An excellent discussion of the history of incomes policy in Britain may be found in Tarling and Wilkinson (1977). There is some evidence that unions resist the burden of higher taxation [Johnston and Timbre11 (1973) and Coutts et al. (1976)]. An increased share for the state (or foreign suppliers) is an unrequited transfer from the trade union to the government (or abroad) and usually leads to conflict and higher wage inflation. An alternative interpretation of the above hypothesis is that workers prefer to spend money themselves rather than the state spending it on their behalf. In this exercise the union adopts a pre-tax real wage target, but fights public spending cuts. Ideally, one requires an evaluation of the social utility of each type of government expenditure. Perhaps, the trade union prefers expenditure on health and social services to defence. Our analysis is based on tax illusion and denies the possibility of an inflationary spiral induced by an increased role for the state. This stems from our belief that the trade union values public services and is prepared to pay for it.

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The trade union is modelled as an agency with asymmetric preferences. This downward inflexibility is obtained by setting ambitious targets. The union is not concerned with unemployment per se. This is the task of a paternalistic government who wishes to avoid social unrest. In this exercise the workers adopt a horizon of eleven years. This is clearly unrealistic, but not necessarily undesirable. In practice trade unions are much more more myopic and may urge for immediate rises in real income. The consequences of such a strategy could be, calculated from a sequence of collective bargains at (say) three yearly intervals [cf. Athans et al. (1975)], but unfortunately limitations to our computer codes prevented us from doing this at this stage. When no weights are attached to the redundancy and public spending targets this trade union policy reduces to a pure real wage resistance strategy [Coutts et al. (1976) or Landesmann and Lawson (1980)]. Wage determination is represented as the outcome of periodic negotiated wage settlements composed of compensation for past and current increases in the cost of living due to higher prices or taxation. It follows that wage inflation is more rapid when settlements occur more frequently. Coutts et al. (1976) point out that the correct variable to consider is of course a specially devised wage settlement index and not an aggregate index of wage rates. This is a lesson our analysis has failed to attend to. 4.3. Strategy of entrepreneurs

and other agents

For simplicity, assume that the sole aim of producers is to attain a desired share of profits (d*) by setting industrial prices. The desired price is given by a mark-up (l/(1 -A*)) on unit labour costs and entrepreneurs immediately revise prices to these aspiration levels. This corresponds to a cost-push theory of inflation, for when the state, workers or foreigners manage to increase their share of value added producers simply recover their share by raising prices. Price inflation is therefore caused by real wages rising faster than the productivity of labour. It is assumed that the desired share of profits is an increasing function of the degree of capacity utilisation. This implies that firms with large amounts of excess capacity are inclined to pursue a cautious pricing policy for fear of losing their markets. Firms operating near full capacity tend to press for higher profit margins, since it is unlikely tha’ other firms will invade their markets [cf. Rowthorn (1977)]. Becausl: entrepreneurs only alter their pricing policy when the cost of producing normal output varies, demand and supply are balanced via shortening and lengthening of order books. The money supply is regarded as entirely passive, for it is fully determined by fiscal policy, interest rates and external flows, and does not constrain inflation. Effectively, entrepreneurs pursue a targets-instruments exercise and are not prepared to trade off one objective against another. This excludes entrepreneurs from the collective bargain. A

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more realistic exercise may allow producers to take some time in marking up, to defend themselves against reductions in the expected levels of turnover and sales and more generally to adopt a less myopic strategy. Entrepreneurs and all other agents, excluding workers and. the state, behave according to the assumed econometric relationships. These adopt a passive targets-instruments strategy and do not participate in the collective bargain. The policy-invariant part of the economy is therefore defined by the accounting identities, the technological relationships and the passive behavioural equations and does not respond to future changes in macroeconomic or trade union policy. 5. Frustration

of macro-economic

policy6

5.1. The benchmark view

The standard view provides a sketch of the development of the U.K. economy over the next decade conditional on no changes in intended policies and a stable political and institutional environment. For this forecast we assume that whatever government is in office is able to pursue an effective anti-inflationary policy consistent with our assumption of about 18% wage inflation in 1980 gradually ,tapering off to 8.8”/d.in 1990. The benchmark view also assumes that the current administration is able to cut the general level of real public spending by 6.3% over the period 1980-83, but will increase public consumption by 1.7% per annum thereafter. The standard rate of income tax is gradually reduced to 25% in 1983 and remains at that level thereafter, whereas the value-added tax system remains as it exists in 1980. We assume that the level of world inflation fluctuates around 8% and that the exchange rate is gradually depreciated until U.K. competitiveness is restored. Finally, we assume that the production of North Sea oil and gas gradually rises to 120m.t.o.e. in 1982 and remains at this level thereafter. With these assumptions MDM predicts a depressed future for the U.K. economy. Britain becomes gradually more and more de-industrialised and suffers from slow growth in gross domestic product. Unemployment rises to nearly 4 million in 1990. These alarming levels of unemployment coincide with large surpluses on the balance of payments account. These surpluses sketch too optimistic prospects, for without the benefits of North Sea oil production the level of foreign reserves deteriorates rapidly. The above picture of Britain’s future is not wholly realistic and its passive nature must be rejected as politically infeasible. No government is prepared 6All results of this section are calculated with the aid of a large-scale multisectoral dynamic model of the U.K. economy (see section 3). The results of the benchmark view and the various strategies based on the preferences given in table 1 are reviewed in this part of the paper and presented in figs. 1-12.

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to let unemployment rise above .say 2.5 million, when simultaneously many (temporary) advantages are accruing due to North Sea oil. The government in power is likely to reverse these contractionary policies, sooner or later, and will attempt to reflate the economy without having to worry too much about the balance of payments constraint. 5.2. A repationary

mix with passive unions’

In view of the undesirable features of the benchmark projection the government may attempt to formulate a reflationary package. At first the government will have little idea of the strategy of the trade union. Suppose therefore that the state formulates an initial plan conditional on workers settling for the same nominal wages as in the standard run. The optimal policy requires major and immediate changes from the benchmark policy. Substantial increases in public spending, large reductions in direct taxes and a significant depreciation constitute the reflationary package. The structure of this demand management strategy is due to the Keynesian nature of MDM. The revised projection is clearly more desirable, since unemployment is reduced from 4 to 2.2 million by 1990, competitiveness is improved and the economy grows at a faster rate. This has been done without too much strain on public sector borrowing and a feasible manipulation of the three policy variables. This reflationary package recognises the appropriate timing of changes in policy. This is demonstrated most clearly in the different type of policy mix recommended for the period 1979-82, when the world economy experiences a severe depression and Great Britain faces even greater problems, and for the period 1983-90, when world inflation is under control, world trade picks up again and the U.K. receives substantial benefits from North Sea ail production. The implication is that in the initial periods public sector borrowing must rise to boost employment. During this period income taxes are raised to finance part of the increase in government expenditure and the defence of the exchange rate. After 1983 the British economy revives and public sector borrowing becomes a minor constraint, for higher activity and less redundancies imply receipts of more taxes and payment of less unemployment benefits. Hence, from 1983 onwards direct tax cuts and devaluation are feasible options for demand management and complement the public spending stimulus. The depreciation improves the terms of trade, but raises domestic prices. This causes a reduction in the real wage and lower levels of consumers’ spending as the value of real wealth declines. The improvement in competitiveness combined with the rise in activity create a much more open economy. The result is an export-led ‘This section considers one centralised decision-maker only, since the other agents do not react to the policies of this decision-maker. A special case of the algorithm for calculating the non-cooperative bargain given in section 2, that is the case with K = 1, has been used.

196

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growth, since the policy stimulates exports by a greater amount than it raises imports. The industrial implications of this macro-economic policy are discussed in van der Ploeg (1980). In the introduction the methodology employed to formulate this reflationary mix has been criticised, for it fails to take account of the reactions of the private sector. The state achieved its objectives by depressing the share of labour in value-added. This was accomplished with a reduction in real wages after introducing higher prices. Economies of scale and the reduction in unit labour costs, due to a rise in labour productivity, caused prices to drop, but these effects were completely swamped by higher import costs caused by the large depreciation. Because the state borrows from the private sector, this inflation is a tax and represents an unrequited transfer. Individual members of the trade union probably refuse to accept this attack on living standards, even though real personal disposable income for the whole population has been raised. Trade union action is therefore unavoidable and should be accounted for. 5.3. Eflects of real wage resistance

The incompatibility of the preferences of a typical trade union and the preferences of the state are highlighted in this section. Suppose that the trade union under consideration attaches equal priority to 3% growth in real wages, no redundancies and 1.5% growth in public spending. Then the best claims for nominal wages conditional on the benchmark proposals for government policy and the MDM view of the structure of the U.K. economy are presented in fig. 1. Average annual growth in real wages (2.13%) is much higher than in the benchmark view (1.15x), but less than the aspiration growth (3%). Real earnings also rise faster than the productivity of labour in the standard view (1.56%). This causes a further drop in growth of output per man (1.31x), a gradual rise in unemployment to more than 5 million by 1990 and a slow growth in gross domestic product (0.95%). Wage inflation accelerates and is on average 14.5% per annum. The result is a rapid deterioration in the terms of trade, significant balance of payments deficits (despite North Sea oil) and public sector borrowing rising to an alarming 12.1% of gross domestic product by 1990. Although output has been reduced, real personal income is raised as the share of labour increases from 48% in the standard view to 53% in 1990. Observe that the trade union is prepared to suffer a temporary drop in real wages during 1982, for fear of redundancies caused by the world depression. As soon as activity picks up again (1983 onwards) the union presses for large increases in the real wage. The corresponding pure real wage resistance strategy with no weight on the redundancy target [cf. Landesmann and Lawson (1980)] resulted in even higher unemployment, decline, excessive state borrowing and hyper-inflation.

R. van der Ploeg, Government

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197

The consequences of this type of ambitious trade union strategy violate the targets of the public sector on all scores. Government reaction is inevitable. 5.4. The coIZectioe bargain’ It should be obvious by now that the preferences of the state and trade union are incompatible and, unless conflict is allowed to perpetuate, some form of collective bargain is desirable. The outcome of these negotiations must be fair and voluntary, that is the two parties should have no incentive to deviate from the equilibrium strategy and be much better off than not bargaining at all. The collective bargain is established when each party perfectly anticipates the current and future actions of the other. The roundtable discussion reconciles the competing preferences without cooperation in strategy. The framework may aid a process of free collective bargaining, where the government agrees to adopt policies favoured by the trade union in exchange for unregrettable wage control. Legal sanctions and statutory powers have seen growing opposition from the trade union movement [Tarling and Wilk.inson (1977)], but are unnecessary for this type of bargain. The outcome based on the preferences of table 1 are presented in fig. 1-12. In the bargain the state raises direct taxes and moderates growth in public spending, from 1.63% under passive union strategy to 1.05’% per annum, in order to finance the increase in the nominal wages of public sector employees. The sensible macro-economic policy is to increase direct taxation much more than the slow-down of public expenditure, because unions argue on a pre-tax base and actually value high annual growth in government expenditure. The government depreciates sterling even further and thereby raises productivity, avoids redundancies and operates a kind of incomes ._policy by raising prices. The extent of these depreciations is probably infeasible and inconsistent with balance in external monetary and capital flows. The union considered the disastrous effect of aspiration growth in real wages on redundancies. Therefore, growth in nominal wages is reduced from 14.5% to 12.7% per annum and growth in real earnings per man from 2.13% to 1.09% per annum. This moderation in labour’s claim on real income combined with the economies of scale induced by demand management causes a rise in labour productivity from 1.31% per annum under the union strategy to 1.67% in the bargain. The growth in output per man is above growth in real wages, hence the share of labour is reduced from 52.9% tb 48.5% by 1990. This causes a reduction in the rate of domestic inflation (below the rate of world inflation) and therefore improves tiompetitiveness and eliminates the huge losses of foreign reserves caused by the union strategy. The export-led growth stimulates demand for home products and *This

section

uses the algorithm for calculating the collective bargain between competing K = 2, from a large nonlinear econometric model (see section 2).

pressuregroups,with

198

e

R. van der Ploeg,

Government

policy

and

real

wage

resistance

20,000’

Union / 1 :’

19,000,.: 18.000i ,.*.

17,00017,000-

8.’

16,000-

15,000-

14,000-

13,000-

11,000Ii,00

10,000IO,00

9,0009,00

8.00

7.00 I

6.00

4.00

I 1980

I 1981

I 1982

Fig.

1983

1. Average

1984

I 1985

earnings

I 1986

per man.

I 1987

I I988

I 1989

I 1990

R. van der

Ploeg,

Government

policy

and

real

wage

resistance

199

32r

.z

31-

30 -

29 -

28 -

27-

26-

25

24-

23-

22-

21-

zo-

19-

I

I

I

I980

1981

I

1

I

1982

1983

1984

I l9i5

I 1986

I 1987

Fig. 2. Standard rate of income tax.

I I988

I I989

GOV~KlllP,fXlt 1 1990

200

R. van der Ploeg, Government

policy and real wage resistance

1971-100.0 9a

80

75

70

65

60

Bargain 55;

/

45

I

I

I

I

I

1980

1981

1982

I

i

1983

1984

I985

1986

1987

Fig. 3. The exchange rate (dollars per pound).

1906

1989

1990

R. van

der Ploeg,

policy

Government

and

real

wage

201

resistance

E million 12,o

Government II.5

II,0

10.5

IO.0

9.5

9,0(

state target

8,5(

I

I980

I

1981

I

1982

I

I

1983

I904

I

1985

I

1986

I

1987

Fig. 4. Government expenditure (1970 prices).

I

1908

I

1989

I

1990

202

R. van der Ploeg, Government

policy

and real wage resistance

Fig. 5. Balance of trade (in 1970 export prices).

R. van der Ploeg, Government

policy

203

and real wage resistance

thoueends 55

50

40

301

20(

IO<

I

I

I

I

I

I

I 1980

Fig. 6. Unemployment.

I

I

I

I

204

R. van der

Ploeg, Government

policy and

real wage resistance

Fig. 7. Ratio of public sector borrowing requirement to gross domestic product.

R. van der Ploeg,

Government

policy

and

real

wage

205

resistance

f million 7s.000

-

65.000

-

/

‘\ ‘\

55.000

c

I 1980

l.

I

..

* .\rCCLd. I

----I

_**I

4

C’

/

I 1985

I

I

Fig. 8. Gross domestic product (1970 prices).

I

I 1

206

R. van der Ploeg,

Gouernment

policy

and

real

wage

resistance

E million 60,000 -

.‘Beachmark 50,000

40.000,

-

I 1980

I

I

I

Fig. 9. Real personal

I 1985

disposable

I

1

I

income (1970 prices).

I

I 1990

R. van der Ploeg, Government

Fig.

10. Terms

policy

of trade

and real wage resistance

(1970=

100.0).

207

208

R. van der Ploeg, Government

policy and real

wage resistance

f I80 0’

170 o-

160 O-

150

140 oJ

,:

1X 10 1980

1

1

I

Fig.

I

I 1985

11. Real earnings

I

I

I

I

I 1990

per man (1970 prices).

R. uan der Ploeg, Government

Fig.

12. Productivity

policy

of labour

and real wage resistance

(1970 prices).

209

210

R. van der Ploeg, Government policy and real wage resistance

avoids many redundancies. The state and union agree on preserving jobs, hence unemployment is only 46i),OOOhigher than under the government strategy with passive unions. Higher profits, higher rates of income tax and less redundancies ensure that public sector borrowing is dramatically reduced, despite the costs of public work programmes. The switch of resources from consumption to investment and exports accompanies a transfer of income from workers to the state and capitalists. This attacks price inflation (only 6% per annum), raisesproductivity and employment and at-the sametime guaranteesa moderate growth in real earnings per man.

5.5. Implications

for economic

policy

The appeal of the Phillips-curve is that internal and external balance automatically secure that growth in real wages is in line with the rate of labour-augmenting technical progress. The job of the government is then to steer the economy towards the natural rate of unemployment, determined by frictions in the labour market, and this cures the problems of inflation at the sametime. The market forces underlying the Phillips-curve imply an explicit trade-off between inflation and unemployment, for the state could buy more jobs at the expenseof accelerating prices. This story does not hold when real wage resistance applies. In this case an additional instrument of’ policy is required to raise growth in productivity9 to the aspiration growth in real wages, since a natural rate without inflation does not exist. In the above bargain productivity was raised by conventional reflationary means. This was only feasible, becausethe union was prepared to accept a temporary cut in living standards (caused by significant depreciations) to avoid redundancies. The modified real wage resistance hypothesis corresponds to an implicit trade-off between inflation and changes in unemployment. The natural rate is not caused by frictions in the labcur market, but varies over time and is determined by past history and the rate of unemployment prevailing at the time that growth in real wages equals the rate of labour-augmenting technical progress.When workers adopt real wages as their only target this implicit trade-off disappears and the job of raising productivity is much harder. Traditional macro-economic policy will need to be supplemented with alternative strategies, such as import controls [Cripps and Godley (1976)] or public investment in highly innovative industries, otherwise an involuntary incomes policy is required to reduce private sector aspirations.

‘The only other alternative, for maintaining a constant share of labour, is to enforce a perpetual depreciation of the pound at a rate equal to the difference between growth in real wages and growth in labour productivity, but this is paid for by excessive domestic intlation.

R. van der

Ploeg,

Government

policy

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real

wage

resistance

211

6. Concluding remarks

The resolution of conflict is obtained with the aid of a collective bargain, whose purpose is to provide round-table discussion to aid the rational anticipation of conflict. The bargain respects the principle of policydependent parameters for the state and trade union and is calcuated from large-scale econometric models by solving simultaneously for all current and future anticipated variables. It corresponds to a dynamic game between rational pressure groups each one of which implements an unregrettable strategy. There is scope for discretionary demand management as long as the trade union is consulted and secrecy is avoided, since preferences of the private and public sector need not be diametrically opposed. A democratic decision process is essential to establish a bargain and secure effective government policy. Depreciation is effective and inuuces only a moderate inflationary spiral, since the union anticipates this raises productivity and reduces redundancies. To eliminate all conflict labour productivity must rise as fast as the aspiration growth in real wages. The conventional reflationary mix did not completely full3 the aspiration of workers. Perhaps, it should be complemented by import restrictions or a disaggregated investment plan financed by North Sea oil revenues. A more realistic exercise distinguishes many participants in the collective bargain. For example, central. government, local authorities, the Bank, foreign lenders, a few leading trade unions, employers, consumers’ organisations et cetera. These participants presumably adhere to different views on the economy, say a monetarist cabinet or Bank and Keynesian unions or local authorities. References Athans, M. et al., 1975, Sequential open loop optimal control of a nonlinear macroeconomic model, IEEE Transactions on Automatic Control AC-19, no. 5, 518-523. Bacharach, M., 1976, Economics and the theory of games (Macmillan, London). Barker, T.S., V.K. Borooah, F. van der Ploeg and L.A. Winters, 1980, The Cambridge multisectoral dynamic model: An instrument for national economic policy analysis, Journal of Policy Modeling 2, 319-344. Broyden, C.G., 1965, A class of methods for solving nonlinear simultaneous equations, Mathematics of Computation 21, 368-381. Chow, G.C., 1975, Analysis and control of dynamic economic systems (Wiley, New York). Coutts, K.J., R.J. Tarling and SF. Wilkinson, 1976, Wage bargaining and the inflation process, in: Economic policy review no. 2 @epartment of Applied Economics, Cambridge University, Camb.Idge). Cripps, F. and W. Godley, 1976, A formal analysis of the Cambridge economic policy group model. Economica 43,335-348. Desai, M., 1973, Growth cycles and inflation in a model of the class struggle, Journal of Economic Theory 6, no. 6, 527-545. Ho, Y.C., 1970, Differential games, dynamic optimization and generalized control theory, Journal of Optimization Theory and Applications 6, no. 3, 179-209. Johnston, J. and M. Timbrell, 1973, Empirical tests of a bargaining theory of wage rate determination, The Manchester School of Economic and Social Studies, 141-167.

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wage

resistance

Kydland, F.E., 1975, Noncooperative and dominant player solutions in discrete dynamic games, International Economic Review 16, no. 2, 321-335. Kydland, F.E. and E.C. Prescott, 1977, Rules rather than discretion: The inconsistency of optimal plans. Journal of Political Economy 85, 473-491. Kydland, F.E. and E.C. Prescott, 1980, Dynamic optimal taxation, rational expectations and optimal control, Journal of Economic Dynamics and Control 2, 79-91. Landesmann, M. and T. Lawson, 1980, Reflation, devaluation and import controls, Paper presented to the conference on industry, energy and the economy (Christ’s College, Cambridge). Lucas, R.E. Jr., 1976, Econometric policy evaluation: A critique, in: K. Brunner and A.H. Meltzer, eds., The Phillips curve and labor markets (North-Holland, Amsterdam). Lute, R.D. and H. Raiffa, 1957, Games and decisions (Wiley, New York). Menil, G. de, 1971, Bargaining: Monopoly power versus union power (MIT Press, Cambridge, MA). Myoken, H., 1975, Non-zero sum differential games for the balance of payments adjustment in an open economy, International Journal of Systems Sciences 6, no. 6, 501-511. Nepomiastchy, P. and A. Ravelli, 1977/78, Adapted methods for solving and optimizing quasitriangular econometric models, Annals of Economic and Social Measurement 6, 555-582. Pau, L.F., 1975, A dilIerentia1 game among sectors in a macroeconomy, Automatica 11, 473-485. Pindyck, R.S., 1973, Optimal planning for economic stabilization (North-Holland, Amsterdam). Pindyck, R.S., 1977, Optimal economic stabilization policies under decentralized control and conflicting objectives, IEEE Transactions on Automatic Control AC-22, no. 4, 517-530. Ploeg, F. van der, 1980, The formulation of economic policy from medium-term econometric models, Paper presented at the 2nd economics and control conference (Princeton, NJ). Rowthom, R.E., 1977, Conflict, inflation and money, Cambridge Journal of Economics I, 215239. Rustem, B. and M.B. Zarrop, 1979, A Newton-type algorithm for a class of N-player dynamic games using nonlinear econometric models, PROPE discussion paper no. 35 (Imperial College of Science and Technology, London). Schubert, L.K., 1970, Modihcation of a quasi-Newton method for nonlinear equations with a sparse Jacobian, Mathematics of Computation 24, 27-30. Starr, A.W. and Y.C. Ho, 1969, Non-zero sum difFerentia1 games, Journal of Optimization Theory and Applications 3, no. 3, 184-206. Tarling, R.J. and S.F. Wilkinson, 1977, The social contract: Post-war incomes policies and their inflationary impact, Cambridge Journal of Economics 1, no. 4, 395-414. Theil, H., 1964, Optimal decision rules for government and industry (North-Holland, Amsterdam). Tinbergen, J., 1952, On the theory of economic policy (North-Holland, Amsterdam). U.K. Chancellor of the Exchequer, 1980, The government’s expenditure plans 198&81 to 198384, Cmbd. 7841 (HMSO, London). Wallis, K.F., 1980, Econometric implications of the rational expectations hypothesis, Econometrica 48,49-73.