A dynamic model of the interaction between the state and the private sector

A dynamic model of the interaction between the state and the private sector

Journal of Public Economics A DYNAMIC 16 (1981) 53-86. North-Holland Publishing Company MODEL OF THE INTERACTION BETWEEN STATE AND THE PRIVATE...

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Journal

of Public

Economics

A DYNAMIC

16 (1981) 53-86.

North-Holland

Publishing

Company

MODEL OF THE INTERACTION BETWEEN STATE AND THE PRIVATE SECTOR* Frans

Economic

Institute,

Centre for Research

in Public

VAN WINDEN**

Utrecht

Bernard

Received

September

THE

Unioersity,

Utrecht,

The Netherlands

VAN PRAAG

Economics,

Leyden

University,

1979, revised version

Leyden,

received August

The Netherlands

1980

The main characteristic of the micro model developed in this paper is the endogenous behaviour of the state. The state is treated as an organization in its own right, made up of politicians and bureaucrats. Its behaviour is related to the interests of these agents and their relative power within the state organization. The economic consequences of this interest representation by the state, and the impact of structural coercion (constraints), originating from the private sector, on these consequences, are our main concern. A particular feature of the model is that it allows for the fact that technology may be dependent on the state’s activities.

1. Introduction In this paper we develop and analyze a dynamic model of the interaction between the state and the private sector in a capitalist economy. The interdependence of these two sectors has always been of great significance to the functioning and understanding of capitalist economies,’ although its intensity and, say, visibility has fluctuated over time (think of war periods) and across countries [see Shonfield (1970)]. Since the World War II a general, steady, and remarkable increase in this intensity has occurred.2 The state has not only become more and more *This paper was abstracted in Economics Letters, vol. 1, 1978, pp. 225-229. An earlier version was presented at the European Meeting of the Econometric Society, Geneva, 1978. **The authors are grateful to Ben van Velthoven for valuable discussions and comments, and to Bruno S. Frey and two anonymous referees of this Journal who commented on a previous version of this paper. Thanks are also due to Joost Cohen Tervaert and Huib van de Stadt who did the computer programming, and to Maja Banck, Marl&e Sopers, and Jo& Kooijman for their secretarial assistance. At the time of writing Frans van Winden was affiliated with the Centre for Research in Public Economics, Leyden University. ‘An example that readily comes to mind is the Mercantilist period. ZSymptoms are: state expenditures growing faster than GNP and in some countries approaching or even exceeding a 50 percent share; industrial sectors being widely dependent on the state for product demand, basic research or highly qualified labour; an increasing number of tax-incentives and regulatory activities by the state. The recently revived interest in subjects like

0047-2727/81/0000-0000/$02.50

0

1981 North-Holland

54

F. van Winden and B. van Praag, The state and the private sector

involved in activities by its own initiative - in order to stimulate and to sustain technological developments, for example, or to canalize international influences but it is also forced or manipulated into such greater involvement by powerful organizations.3 In spite of the importance of the subject, the systematic and non-normative analysis of the behaviour of the state is by and large of quite recent date. Roughly speaking, there are two approaches: the Marxist Approach and the Public Choice Approach.4 As yet only a few formal politico-economic models - in which the activities of the state are directly related to the interests of the agents that make up the state organization, and in which they constitute an endogenous part of an economic model - have been developed, however; all within the Public Choice Approach. Nevertheless, in our opinion at least, a formal approach seems desirable in this highly intricate field of research where the thrust of an argument is very often dependent on the exact specification of relationships. The model presented below is part of a series of studies by the first author on the interaction between state and private sector, or Political Economics for short [see Van Winden (1976, 1979a, 1979b, 1980, 1981)]. Two sets of problems are addressed by these studies: (1) The impact of representation, structural coercion, and pressure on the character and behaviour of the state. By representation is meant the representation of interests by agents within the state. Structural coercion denotes the behavioural constraints - including instrumental constraints - on the actions of the state that stem from its environment (the private sector); that is, insofar as these do not result from deliberate influence attempts by agents (such as political parties, voters, big corporations) in that environment, in which case we speak of pressure. (2) The impact of different types of states on the behaviour of private sector participants (workers, firms, voters, etc.). the limits to taxation, tax capacity, and the restrictions on the size of the non-market sector is one of the outgrowths of this state of affairs; see Bacon and Eltis (1978), Hadjimatheou and Skouras (1979), OECD (1978), O’Connor (1973). As important developments in the private sector may be mentioned: concentration and globalization of economic activities, giantism, technological development, and organization (pressure groups); see, e.g., Jacquemin and De Jong (1976). 3See, e.g., Lindbeck (1975) on the increased importance of bargaining. “For the Marxist Approach, see Foley (1978), Gold, Lo and Wright (1975), Jessop (1977), and the literature mentioned there. The Public Choice Approach can be subdivided in studies on representative government [see Frey (1978) and Mueller (1976) for references], bureaucracy [see Blankart (1975) and Orzechowski (1977) for references], and the interrelations between government and bureaucracy [Breton (1974), Davis, Dempster and Wildavsky (1966), Miller (1977), Niskanen (1971)]. Although such branches of mainstream economics as Welfare Economics, the Theory of Economic Policy, Public Finance/Economics, and Industrial Organization are also concerned with this research area, these studies are, on the whole, normative in character and/or ignore politics.

F. van Winden and B. van Praag,

The state and the private sector

55

The state is thereby considered as an organizational unit. Its behaviour is supposed to be determined by the interests of politicians (who make up the government, which comprises cabinet and legislature) as well as bureaucrats (who make up the bureaucracy, which comprises the judiciary, the military, the administration, and so on). The behaviour of different types of states characterized by the relative strength with which interests are represented by politicians and bureaucrats within the state organization is analyzed within a micro-framework. The characteristics of the private sector (the behaviour of workers, firms, political agents, etc.) shape the degree of structural coercion on the state, and determine, for example, the maximum feasible state size. As there is no immediate identification with only one particular form of political participation or political system, these studies take a more basic approach to the analysis of the interaction between the state and the private sector, compared with the Public Choice models which main purpose has been to show the possibility of an economic cycle induced by elected politicians that are preoccupied with their re-election (the political business cycle). The scope of these models is very limited, which also shows up in the rather abstract macro-framework in which they are cast, and the fact that, as regards the state organization, only the actions of cabinet officials are focussed upon.’ In this paper, the aforementioned sets of problems will be tackled by means of a simple, somewhat truncated, politico-economic model. As it would lead too far, within the confines of a single article, to give an adequate account of the influence of pressure on the behaviour of the state, we propose to restrict attention to the impact of representation and structural coercion. Thus, it will be assumed that there are no influential political actions emanating from outside the state sector. The complicating effects of activities such as voting in case of a capitalist economy with a democratic political system and periodic elections are studied elsewhere [see Van Winden (1979a, 1981)]. A particular feature of the model is that it allows for the fact that technology may be dependent on the state’s activities. Although the empirical determination of technological change is fraught with many difficulties6 it is generally recognized that the state has a significant part in it through its ‘It may be useful to note that the almost exclusive attention that voting in elections has obtained in the Public Choice Approach obscures the fact that voting is just one means of political action. Between elections that is, most of the time ~ other forms of political participation are relied upon, such as lobbying, social movements, strikes, etc. [see Breton (1974, ch. 5), Milbrath and Goel (1977, ch. 1); see also Foley (1978, pp. 226225)]. Moreover, many and perhaps even most capitalist economies do not have real free elections. A rough calculation from a table presented by Dahl (1971, pp. 232-234), shows that in around 50 percent of the ‘capitalist economies’ over 90 percent of adult citizens were eligible to vote, while in circa 59 percent of those countries there was at least some positive percentage eligible to vote. %ee, e.g., Dougherty (1974) Rees (1980).

F. van Winden and B. van Praag, The state and the private sector

56

activities in such areas as health, education, infrastructure, research and development.’ The importance of this for the relationship between the state and the private sector is clear. Nevertheless, little attention has been paid to it in formal economic models.8 The paper is arranged as follows. The model is presented in section 2. Section 3 deals with the characteristics of equilibria. Section 4 is concerned with the dynamics of the model, and section 5 concludes. Throughout the paper the word ‘state’ will be used in a political sense only.

2. The model The model comprises: (1) a private production sector, which produces a (marketed) good that can be used for investment as well as consumption; (2) a state, which levies an income tax on and pays unemployment benefits to households; the bureaucracy consists of one department which produces a (non-marketed) good that influences the technology of the private production sector; (3) households, which supply one homogeneous labour service to the private production sector and the state, and are the sole consumers of private output; (4) a rudimentary bank, which supplies loans to the private production sector (firms) and the state; it employs neither capital goods nor labour. Time is treated as a discrete variable. The assumed sequence of events per period in the economy is shown in table 1. This sequence will also be followed in the exposition of the model. We introduce the following notational convention: a tilde (-) indicates expected values of variables, a superscript d stands for demanded or desired (planned), a superscript s for supplied, a superscript t for transacted, a subscript p for private or business, and a subscript s for state.

‘See, e.g., OECD (1978, p. 8); instructive are also the governmental reports on innovation [for The Netherlands, see Tweede Kamer (1979)]. In addition to the activities mentioned in the text we could further point at the importance of the maintenance of internal and external order (think of labour productivity). *See, however, Aarrestad (1978), Johnston (1975), McMillan (1978). For empirical studies, see Denison (1967), Griliches (1964). One justification for this neglect may be that the size of the state may also have unfavourable consequences for technology because of the possible impact of private production and investment through so-called ‘Verdoorn effects’ [Verdoorn (1952)] and ‘learning by doing’ [Arrow (1962)]. However, although this matter cannot be settled without much more empirical research, it should be noted that these effects may also occur in the state sector. Moreover, private production and investment need not be hampered if there is a positive influence of state activities on technology [see the critique of Hadjimatheou and Skouras (1979, p. 399) on Bacon and Eltis (1978)].

Labour demand

)emand jr tbour

supply

Labour

Wage bargaining

Labour

‘ax rate nnounced

ltate

tart

Transactions

market

Loans for wages and doles

‘Bank

on

Taxes over wage related income

Firms’ outlays labour

State outlays on labour

State/firms

Sequence

Table 1

Investment demand

Consumption demand

Product

t.

Transactions

market

of events for period

Price decision

Investment decision + Reservation of funds

Firms

Dividend

taxes

Distribution of excess funds by firms

State/firms

Debt account adjustment for firms and state

‘Bank

end

58

F. van Winden and B. van Praag, The state and the private sector

2.1. The behaviour

of the state: Bureaucrats

and politicians

Interests. It is assumed that bureaucrats ~ whatever their ultimate goals may be - are interested in a continuous and gradual expansion of the stateorganization. As a first approach this is a plausible assumption to make, and it seems to be in line with hypotheses and the scarce empirical findings put forward by students of bureaucracy (see the references in footnote 4). The expansion will be represented by the growth rate of the number of state employees. The interests of politicians are - again, whatever their ultimate goals may be, and as a first approach - taken to be divided between private output and state output. This assumption allows for the common distinction between ‘left-wing’ governments that are supposed to have a preference for state expenditures, and ‘right-wing’ governments, that are pro private sector and try to curb state expenditures. In order to take account of power processes within the state organization in yet a simple way it is further assumed that the state acts as if it maximizes (at the start of a period) the expected value of a variable P,, specified as

+ (1 -~)[~lnZ~(t)+

(1 -~)lnZ,(t)],

where E denotes the number of employees, t is a time index (when not used as a superscript), 8 is the state employment growth target of the bureaucrats and X stands for output. The relative strength of the different interests of politicians within the government is denoted by p; ~1characterizes the type of government. The relative strength of the interests of the bureaucrats uersus the interests of the politicians within the state is indicated by K. A type of state is characterized by (rc,~). Given the lack of evidence on the time horizon of state officials, and since politicians are generally believed to be rather short-sighted, a future time horizon of one period is simply assumed.’ The state has two instruments at its disposal: its demand for Instruments. labour E:(t) and a uniform income tax rate z(t). The relations determining the relationship between P,(t) and Constraints. both instrumental variables of the state - together making up the economic model that is implicitly or explicitly employed by the state - will now be given, in addition to some constraints on the use of the instruments. We start with some objective relations that hold in reality and not just in the state’s conception of the economy. They will be presented without tildes. The state’s demand for labour, Et(t), is restricted by, on the one hand, the size of a fixed total labour force, E,, and, on the other hand, a minimum state employment ‘The implications

of a longer time horizon

are studied

in Van Winden

(1979b).

F. van Widen

level E;

and B. van Praag, The state and the private sector

(>O): E; SEf(t)5EE,.

(2)

Labour is the sole input in the production (>O) is assumed to be constant:”

of state goods;

its productivity

X,(t)=@,@). For &(t), see (14). A linear production As will become clear in subsection firms. Private labour productivity, subsection 2.4);”

CC,

(3) technology is postulated. 2.4, there will be no idle labour in the a,(t), is taken to be variable (see

X,(~)=~,W,(O For E,(t) and E,(t), see (14) and (15). Private equal production plus stocks s(t):

(4) product

supply

is supposed

to

(5)

x;(t)=x,(t)+s(t). Assuming voluntary exchange and exhaustion of all mutually transactions in the product market equal: transactions,12 X’,(t)=min{Xd,(t),X;(t)}. For x:(t),

59

advantageous

(6)

see (15). Stocks are equal to S(t)=XS,(t-1)-X#-1).

(7)

The state is supposed to strive after a balanced budget (see below). State expenditures consist of wage payments and unemployment benefits, for which loans - free of interest - can be contracted with the bank. Loans have to be paid off as soon as possible. State revenues are derived from the income tax on wages, unemployment benefits and dividends. Dividends are equal to the firms excess funds F(t) adjusted for reservations made for investment. The funds F(t) comprise the difference between sales revenues on the one hand, and wage costs and accumulated debts, II,(t), on the other, augmented by the money reserved for “‘This assumption rests on the common view that labour hardly be changed; see Spann (1977) for some evidence. “A constant productivity is not excluded, however. “Cf. Barro and Grossman (1976, p. 40).

productivity

in the state sector can

60

F. van Winden and B. van Praag,

unfulfilled investment orders, if that value of this remainder, see (15)] :

The state and the private sector

should

be the case

[for the expected

F(t)=p(t)X’,(t)--w,(t)E,(t)--D,(t)+p(t)CX~(t)--~(t)l, where p(t) denotes the product price, w,(t) the private wage rate, superscript i stands for investment. For p”(t) and G’,(t) see (15). The firms’ debt burden equals: D,(t)=max{O, The state’s debt burden,

63) and the

-F(t-1)).

(9)

defined for t+ 1 for notational

convenience,

equals:

o,(t+l)=ws(t)E,(t)+w,(t)E,(t)+D,(t)-z(t)Cw,(t)E,(t) +w,(t)E,(r)

+w,(t)E,(t)+max(O,(l-a(t))F(t)}l,

(10)

where w,(t) indicates the state wage rate, w,(t) the dole rate, E,(t) the number of unemployed, and o(t) the fraction of F(t) reserved for investment. For 6(t), see (15).13 The state wage rate and the dole rate are taken to be proportionally related to the private wage rate:r4 w,(r)=4w,(t),

w”(r)=r&(r)?

The tax rate is bounded from consumption basket xi- (>O).” The be violated as the state does not have of the period, when s(t) is determined z’(t)=

1 -p(t)x;-/w,(t).

C#I>*>o,

$
(11)

above by a statutory (subsistence) maximum tax rate r+(t) - which may all the relevant information at the start - equals: (12)

The following relations are more particularly assumed to hold for the state and do not necessarily hold when the tildes are deleted (except for equilibria - see section 3). The state is supposed to aim at a balanced budget; the budget consists of expected tax revenues on the one hand, and expected r3Note that only distributed profits are taxed. r4As wages in the state sector typically seem to follow wages in the private sector [in The Netherlands, e.g., the wage rate for state employees has officially been tied to the private wage rate for about 20 years now; for the United States, see Quinn (1979)], and unemployment benefits are often legally tied to the wage rate in social security systems [see, for the European Communities, Commissie van de Europese Gemeenschappen (1976)], it seems acceptable at this stage of the analysis to take their relationship as a political fact for bureaucrats and politicians. A more refined model would have to consider these payments as outcomes of politico-economic processes. r5A statutory, absolute minimum income level exists, e.g., in Germany, Belgium, and Luxembourg; see Kapteyn and Halberstadt (1978).

F. van Winden and B. van Praag, The state and the private sector

expenditures

and state debt redemptions

61

on the other:

The state is assumed to expect no problems in hiring private labour demand is related to expected product stocks, and labour productivity:

workers; demand,

expected available

E&)=Ef(t), I?,(t)=min(i?~(t),Er-E:(t)}, i$(t)=max

(14)

(0, [-r?d,(t)-S(t)]/L$(t)}.

Note that E”,(t)=E,-am-El,(t). p”(t)=p(t--1),

Furthermore, a,(t)=w,(t-l),

it is assumed oi,(t)=a,(t-l),

while p(t)[Xf(t)-Xc(t)]

xz(t)=Xb(t-1),

that C(t)=o(t-1).

in (8) is neglected.

(15) Clearly, more sophisticated expectation patterns ~ involving different lag structures or least squares adjustments, for example ~ could be employed.16 From the foregoing equations it can be checked that the tax rate can be written as a function of state demand for labour, to be denoted by z(t)

=G:@)l. Tax rate and state demand for labour. Whenever the state finds it impossible to meet its budget constraint (13) - through normal taxation ~ it is supposed to levy the maximum tax rate and to curtail state expenditure as much as possible; in that case: Ei(t)=E; and z(t)=t+ (t). Apart from such a situation of state ‘bankruptcy’ the state behaves as if it solves the following programme, using eqs. (1) through (15) (with tildes added where demanded):

max P,Cz(t),Ef@)l, WI, &I) s.t.

E,

&(t)zE,,

t(t)Szf

(16)

(t).

16The expectations satisfy the desirable condition that equilibrium (i.e. a stationary situation; see. the next section).

they

are all realized

in case

of an

wanWinden and B. van Praag, The state and the private sector

As it is impossible, in general, to find an explicit analytical solution to this the optimal values for Et(t) and r(t) are in the numerical programme, experiments, reported in section 4, determined by a search-procedure. 2.2. Labour

and labour market

A large number of suppliers of labour is assumed. We exclude the formation of coalitions inside and outside the market.” Except for job preferences, workers are assumed to be identical. One part of the labour force (y, O
{Ez(t),E;(t)}

and

E,(t)=min

{Ef(t),E:(t)}:

where

E~(t)=max

{yE,,E,-E:(t)}

Ei(t)=ma::

{(1 -y)E,,E,-E:(t)}.

(17)

and

The wage rate should depend on the relative bargaining strength of worker and firm. It is assumed that the relative change in the wage rate is a continuous monotonically increasing function g of the relative excess-demand for labour if no constraints are effective. In that case the wage rate is given by Ed,@-l)+E;(t-l)-Ef

Et g(.)> However,

it stands

to reason

that

-1,

g(0)=0.18

the wage rate is bounded

from above

(18) by

“Because of the ‘free rider’ problem, a large group of actors should not be expected to organize itself just because of a common interest in activities for the acquisition of a collective good [see Olson (1973)]. 18Assuming that w,(O)>O, it follows from eq. (18) that w,(t)>O.

F. van Winden and B. van Praag, The state and the private sector

63

value of labour productivity. This upper bound is denoted by w,‘(t) [ =p(t)a,(t)]. Moreover, the minimum income assumption [see the discussion preceding relation (12)] demands that [l -z(t)]w,(t)5fi(t)x;should hold. The corresponding wage rate is denoted by w,(t). In view of the numerical experiments in section 4, let p(t)=p(t - 1). For the special case that w;(t) > w,’ (t) it is assumed that the law is overridden by the law of the market; in that case w,(t) = w,’ (t). Thus, we have w,(t)=min

{max [w; (t), w:(t)],

w,’ (t)},19

(19)

where

w;(t)=p(t)cr,(t).20 2.3. Product

market

Nominal demand for consumption is supposed to equal the total amount of money, Z(t), that households dispose of. It consists of disposable wage related income, disposable dividend income (from the previous period) and forced savings, if any, due to supply shortages in previous periods.” In real terms :

T3Q=$)

i

Cl -~(t)lCw,(t)E,(t)+w,(t)E,(t)+w,(t)E,(t)]

+max{O,[l-s(t-l)][l-c7(t-l)]F(t-1))

,

+p(t-l)[XZd(t-l)-X;t(t-l)] I where the superscript c stands for consumption. Investment demand X:(t) is given by eq. (25). Total

demand

equals:

(21) “Assuming that X,(O)>O, it follows from eqs. (26), (27), and (33) that Ed,(t)>O. 200nly the tirms know what price they are going to charge for their products; see subsection 2.4. “It is implicitly assumed that, apart from wage-related income for which loans can be contracted with the bank (but which have to be paid off as soon as possible), some money is available on a long term base in the economy, so that there can be positive transfers between periods of dividend income and/or investment funds even though D,(t)=D,(t)=O.

64

F. van Winden and B. van Praag, The state and the private sector

Total supply X;(t) is given also eq. (6) - it is assumed based on orders:”

by eq. (5). With respect that investment demand

to transactions ~ see is handled first as it is

X~(t)=min{X~(t),X;(t)},

(22)

XGt(t)=min

(23)

2.4. The behaviour

(Xid(t),Xb(t)-X:(t)}.

of the firms

The following is assumed. A homogeneous good, that can be used for consumption as well as investment, is produced by a large and constant number of identical small firms. Firms do not expect to have any influence on the state; coalitions inside or outside the market are excluded. Within the boundaries of their relatively small production capacity, firms expect to sell whatever they supply at the expected market clearing price. Investment orders and demand for labour are expected to be met. Investment is totally self-financed. Investment orders are to be executed in the next period, otherwise they are reconsidered [see the last term of (S)]. Loans, free of interest, can be contracted with the bank for the advance payment of wages, but have to be paid off as soon as possible. Buyers are evenly distributed over the firms. Under the given conditions, our object of study may as well be the industry, or business, rather than the individual firm. In the sequel, aggregate variables will, therefore, be used. Interests. It is postulated that the firms act as if they maximize a time preference discounted expected flow of dividends, indicated by P”,,; moreover, a three period planning horizon is assumed (see below):

B,(t)=

i: p,ln{[l-0(t,t+n)]F”(t+n)}, n=O P,ZO,

where F is defined by (8). 23 Double ZZIn the numerical

experiments

reported

C&-l, ”

time indices in section

OSa(t,t+n)Zl,

(24)

that will only be used for

4, investment

demand

never exceeded

total

supply. 23The expected dividend contributions of periods t + 1 and t + 2 may be supposed to indicate the contribution of periods further extending into the future. If preferred, the weights p. can be transformed into ‘normal’ discount rates, and the time horizon can be extended to include more than 3 periods. If n=O,. _,T (T>2) and o(t,t+n)=O for n >O, so that only the effect of investment in period t is considered, the same solution for o(t) is obtained as in (36), with p = p,/(p, + pZ + + pT). Using dynamic programming techniques to determine cr(t,t + n), future investments can be allowed for as well.

F. van Winden and B. van Praag,

The state and the private sector

65

instrument variables such as C.J~ are employed to distinguish between the period that a decision on the value of an instrument variable is made (denoted by the first index), and the period for which it is made (denoted by the second index). If the value of the second index exceeds that of the first, this is to indicate, moreover, that the instrument value under consideration may be revised in subsequent periods, until the final decision is made. Instruments. Three instruments are available to the firms: demand for labour, product price, and the investment ratio 0. Constraints. In addition to the aforementioned assumptions, and the relations (4) through (9), the following relations are used. As in case of the state, we start again with some objective relationships, where tildes should be thought added for future periods. Investment orders are tied up with the reservation of funds after the determination of the new product price (see below) at the end of the previous period : x;(t)=o(t-l)F(t-1)/p(t).

(25)

Newly acquired capital goods cannot the period following transactions:

be used for production

sooner

0<6<1,

K,(t)=(l-6)K,(t-l)+X~(t-l),

where 6 stands for the depreciation rate of private capital; for X;(t), Production is restricted by the following production function:

X,(t)=a,(t)E,(t)=P~,(t),

than

in

(26) see (22).

(27)

where p denotes a constant output-capital ratio, and K,(t) stands for utilized private capital. 24 Labour productivity is supposed to be related to the stock of state capital (accumulated state production) K,(t), in the following way:

q~)=vK,(~)q,

v>o,

K,(t)=(l-i)K,(t-l)+X,(t-l),

r/20,

(28) O<&l,

(29)

where 5 denotes the rate of depreciation of state capital; for E,(t+n), see (31). The parameter ;r? indicates the elasticity of labour productivity with regard to state capital. If q=O, we have a fixed coefficients technology with cc,(t) = V,V t. State capital K, and state output X, can be considered as ‘public ‘%ince the impact of technological development on the capital-output ratio is less clear, p is assumed to be constant [see Anderson (1961), Arrow (1962, p. 159),‘Bacon and Eltis (1978, p. 109)].

66

F. van It’inden and B. uan Praag,

The state and the private

sector

intermediate goods’ as the whole amount supplied enters the production function of each firm. 25 As q>=O we m a y sp eak of public goods rather than public bads. The folloying relations, (30) and (31), do not necessarily hold when the tildes are deleted. From the assumptions it*follows that

E&+n)=Ed,(t+n),

qt+n)=r?f(t+n),

Z;(t+n)=P,(t+n),

n=1,2.

(30)

Let, furthermore, _E,(t+n)=w,(t),

Q(t+n)=a,(t),

n=1,2.

(31)

Product price, demand for labour, investment ratio. A plausible assumption for a firm operating under conditions of atomistic competition seems to be that it sets its product price in accordance with what it believes to be the market clearing price, using the excess demand for its product over the past period as an indication qf the situation on the market.26 The rate of price change is taken to be a continuous monotonically increasing function h of the excess demand. Thus,

p(t+l)=p(t)

l+h [

xd,w-X;(t)

(

x;(t)

' II(.)> )I -1,

h(0)=0.2’

(32)

As 8d,(t+l)=gi(t+l), given p(t+l), it follows that p(t,t+2)=p(t+l). Given the ‘fixed’ coefficients technology [see eqs. (27) and (31)] and the condition that loans have to be paid off as soon as possible, it is readily seen that whenever the expected value of labour productivity exceeds the expected demand will be wage costs, i.e. p(t, t + n)di,(t + n) > G,(t + n), labour determined by the size of the capital stock. It is supposed that this will also be the case if an equality holds. Thus,

‘%ee McMill& (1978). In McMillan (1978), and also in Aarrestad (1978), optimal control models are developed, focussing upon the maximization of a social welfare function, in which a similar non-negative relationship appears between productivity and (the stock of) a public intermediate good. z6Cf. Fisher (1972). *‘Recall that the decisions on p(t + 1) and o(t) are made at the end of period t. Assuming that X,(O)>O, it follows from (5), (17), (19), (26), and (33) that X;(t)>O. Assuming that p(O)>O, it then follows from (32) that p(t)>O. If p(t)>O, w,(t)>O, and Ed(t)>O, it follows from (19X (20) and (21) that Xd,(t)>O.

F. van Winden and B. van Praag, The state and the private sector

if

p(t,t+n)d,(t+n)2GP(t+n),

n=O, 1,2.

67

(33)

As p(t)a,(t)2w,(t) see (19) eq. (33) at least holds for period t.28 Workers that have been contracted by a firm will always be fully employed. However, as labour supply may fall short of labour demand [see (17)], capital need not be fully utilized. Because of the time lag for the completion of investment projects [see eqs. (25) and (26)], a firm’s inuestment bdecision in period t is relevant only for the production capacity from period t +2 on, and not for that of period t+ 1. It follows that the expected excess funds contribution of period t+ 1, F(t+ l), is independent of the investment decision of period t. For F(t+2), it is obtained that

(34) where the first two factors indicate the expected rate of return on capital, and the third the expected size of the capital stock. Because of the investment lag and the three period time horizon, only a(t) [ = a(t, t)] need be considered. Assuming that p0 + pZ >O, let P =

PO/h

Then s(t), defined

+

(35)

P2).

by (36)

gives the value of a(t) that is obtained from the first-order condition for a constrained maximum of (24) if, for rather obvious reasons, F(t) >O, p(t + l)a,(t)>w,(t) [see (30), (31), (32), (34)], and P>O.~~ Now, clearly, a(t)=0 when either F(t)50 or p(t+ l)~(,(t)zw~(t) holds, and u(r)= 1 when p=O. It follows that

o(t)

=o

if F(t)50 and/or

=max{O,s(t)},.

otherwise.30

p(t+l)a,(t)sw,(t), (37)

*‘Later periods are only of interest insofar as investments are considered, and in that case p(t, t + n)oi,(t + n)> Gp(t + n) should hold (see the ensuing text). “Due to the strict concavity of P,(t) a global maximum is obtained. It is easily shown that ?;(t+l)>O if P(t+2)>0, so that (24) is well defined in this case. 301t is easily shown that the same behaviour results when real or disposable (after-tax) dividends are considered.

68

F. van Winden and B. van Praag, The state and the private sector

3. Equilibrium analysis An equilibrium is defined by the constancy of all variables over time.3’ The necessary and sufficient conditions for an equilibrium are enumerated in the Appendix. From these conditions, a number of equilibrium characteristics can be derived that will be presented below. Proofs are straightforward and will be given in footnotes, if necessary. In indicating equilibrium values of variables, the time index will be omitted whenever it is self-evident. 1. An equilibrium need not exist; an equilibrium need not be unique. The first part is ultimately due to the minimum consumption level xi-, which may be too high. Important in this respect are the time discount parameter of capitalists (see 3) and the type of state (see 8).32 The latter part is due to the wage rate inequality condition (A4), and the fact that corner solutions may be obtained for programming problem (16) which means that different equilibria may be sustained by the same type of state (see below). As the numerical experiments will show, equilibria do exist. 2. Expectations are realized; capital stock is fully employed, but labour may be underemployed; private labour productivity. It is easily checked from eqs. (14), (15), (30) and (31) that all expectations are fulfilled in equilibrium. Product supply equals product demand, and labour demand is realized, but it may be less than labour supply [see (A4)]. The full capacity utilization of capital follows from the realization of labour demand. For private labour productivity [see (A2)] it is obtained that:

the stock of state capital state, labour productivity,

is K, = (a,/<)E,. The relationship and labour demand is illustrated

3. Investment ratio; rate of return on capital; the firms. Because of (A3) and (A7), o=(l-p)/[l+p(l--)/6].

between in fig. 1.

time preference

type of

condition

for

(39)

31Due to the fixed size of the labour force the model cannot generate non-zero steady state growth. Moreover, it can be shown that an equilibrium marked by stationarity for quantity variables (excluding the stock of money) and a constant rate of change for price level and wage rate can only exist if that rate of change is equal for both of them and D,(t)#O [as a(t)>0 D,(t)=O, see (9) and (37)]. However, an should hold because of replacement investments, equilibrium concept that allows for D,(t)#O is hard to accept, given the assumption that priority is given to a balanced budget, Also note that the assumptions exclude an equilibrium with no production at all (see footnote 27; in addition, recall that x;- >O). 321t is clear from eqs. (27) and (38) that X, is bounded from above, by Xc say. Suppose xiand (A4): pX;‘> (1 -r)t,bw,E,~p~‘,~E,>pX~, which obviously >X,f/E,. Then, using X;‘=XF, cannot hold.

F. van Winden and B. van Praag, The state and the private sector

69

type of state -E 4.-----S z‘ 15 i X, = BKp

LEn

Fig. 1. Type of state, labour

productivity,

and labour

demand.

If p =O, i.e. capitalists only care about future dividends, then g= 1. If 6+1, in which case capital becomes fully circulating, then a+1 -p. The rate of return on capital r is defined as: r=F/(pK,). Using (A3) and (39) it is obtained that r=6/0=6+p/(l-p).

(40)

The first equality is not surprising; the second equality shows, however, that the equilibrium rate of return only depends on the depreciation rate 6 and the time discount parameter of the firm p, which are exogenously determined, which implies that r is invariant in case of multiple equilibria. As r < p should hold, it is demanded, using (40), that

P
+P-4.

4. Wage rate and rate of return letting WP=wP/p, one obtains that

(41) on capital.

Using

(A2) and

(A3), and

bGp= (1 - r//l&

This expression resembles the ‘wage-profit curve’ or ‘wage-interest frontier’, which plays an important role in the theory of capital [see, e.g., Harcourt (1974)]. Note, however, that as r is exogenously determined in our model (see 3) there is no trade-off relationship between the real wage rate and the rate of return in equilibrium. In this respect, the real wage rate appears as a residual [see Dobb (1973, pp. 267 seq.)].33 ‘The real wage rate also depends, however, on labour productivity, which is positively related to state employment if q>O [see (38)]. Now, although different equilibrium levels of state employment do not necessarily require different types of states, it will be shown below [see (43)] that if one does not “This is not to say that nothing can be done about it. The crucial question becomes how p is determined. Class struggle may be one of its determinants. Observe, though, that the consequences could be different from what might be expected. As it seems plausible that an inverse relationship exists between the strength of the position of capitalists and p, it is likely that capitalists demand a’high rate of return when in a weak position, which leaves a low equilibrium value for the real wage rate. The conclusion may be that an equilibrium tendency is not very likely in that case. See, in this context, Sraffa (1960, p. 33). JPE

D

F. van Winden and B. van Praag, The state and the private sector

70

want to rely - for a particular equilibrium level of state-employment - on the particular path that the economic process may take towards an equilibrium (assuming that an equilibrium directed path is followed) then the type of state does matter, which is of course important from a political point of view. 5. Income distribution. Dividing both sides of (42) by cl*, one obtains the share of the before-tax real private wage sum in private output; it equals (1 -r//3) and is invariant in case of multiple equilibria (its complement is the before-tax profit share). The share of total real disposable wage-related income (including unemployment benefits and wages for state workers) in private output, however, is only invariant and equal to the aforementioned private wage sum share - if O= 1, in which case the tax burden is fully borne by workers and unemployed.34 If B-C 1, this share is positively related to the equilibrium level of state employment; in that case part of the extra taxes are paid by the capitalists, due to the uniform tax rate. As regards the distribution of income between labour and capitalists, it clearly matters then what type of state governs. With respect to the ‘size of the cake’, it follows that private output should be maximized in order to maximize the before-tax private wage sum as well as total disposable wage-related income when C= 1. There will be trade-off between the latter and the amount of private output when o < 1 (see 16). 6. An unemployment equilibrium requires that z =T~ (see (A4)). This follows from the way that the wage rate is determined (for another reason see 7). In case of unemployment the wage rate falls until the minimum income level is reached. An equilibrium of this type is not very likely, though, whenever the difference between w, and w, is small. In that case, the state has not much room, financially, to manoeuvre. Slight perturbations may force it to trim the state apparatus in order to meet its financial constraints (see subsection 2.1). 7. Equilibria E

with z =CT+ demand that >

mc+

s[

(1

-PL)(f

28K+(1-K-)

--K)

1

E,.35

34This share equals: (l-r/p)+s(l-a)r/fi. Using (39) and (40), it can be written as l-[(l -r)p+6(1 --p)]/[p(l -p)]. Denoting the ratio in this expression (the profit share) by I/-‘, it can be shown that: pX,=MK where M stands for the money stock that is permanently present in the economy (see (A6)). j51t can be checked from eqs. (l), (3t(6), (14) and (15) that any type of state, apart from (K =0, p= l), is interested in stepping up state employment as long as E,(t - l)iE, -&d,(t). Thus, E,(t - l)=E,-pP(t), and, therefore, E,=Ef-E, should hold when T
F. van Winden and B. van Praag, The state and the @Date sector

71

Equilibria with z < z+ are full employment equilibria. This is not only due to the way that the wage rate is determined, as referred to in 6. It can be shown that any type of state, apart from (K=O, CL= 1) for which ES=_& should hold, is interested in stepping up state employment whenever unemployment would be expected otherwise and no financial bottlenecks are present (recall that expectations are realized). Note that (43) only establishes a lower bound for E,. This suggests that as far as the political part of the politico-economic system (the type of state) is concerned no unique equilibrium need exist (see below). Notice, moreover, that this lower bound is positively related to K (indicating the strength with which the interests of bureaucrats are represented) for p>O, and inversely related to p (which indicates the weight attached to private production by politicians) for K < 1. 8. There exists a (non-empty) class of states for which in equilibrium z=z+ necessarily holds.36 Where it all comes to is that, on the one hand, a certain private employment level is required for the production of the minimum consumption basket xi- >O for which the necessary income level is guaranteed by the state, while, on the other hand, types of states exist that would try to further encroach upon private sector employment when not financially constrained [see (43)]. Note that the types of states for which in the case q > 0 ~ the lower bound of E, given by the right hand side of (43) is too small are, nevertheless, compatible with an equilibrium since any type of state sustains an equilibrium with E, larger than that lower bound [excepting (rc=O, p= l), for which E; should be large enough; see 73. The crucial equilibrium condition here is that zzrf should hold. This condition demands that E, - (A,E: + A,)E, +A, 50, where A,, A,, and A, are exogenously determined, and A,, A, >O, A, ~0 [see (A8)]. The relationship between 7 -T’ and E,, for E, +E,=E,, is sketched in fig. 2. It has at most two real roots. The downward sloping part of the curve should be neglected for q =O. Changes in v cause changes in the size of the class of states of which the activities are curbed by the ta:; rate constraint; the larger is q, the smaller its size will be [see (A8)]. In this context it may be noted that the carrying capacity of the economy regarding the size of the state sector ~ defined by the maximum feasible state-size as measured by E, or w,E, - is determined by the largest possible

then follows from the first-order condition for program (16), taking E,(t)=E,-e(t). If ti=O and p = 1 then E, =E, -E, = ES- should hold as there would be an indeterminacy when E, - pP(t) >E-. The inequality sign is then due to the fact that ES- >O. 36For T
F. van Winden and B. van Praag,

72

The state and the private sector

,E, = Ef - E,

I \

Fig 2. The relationship

between

r-r+

and E,.

value of E, that still satisfies (A8) [recall that wS=4wpr and see (38), (40), (42); it is easily seen from (A8) that E,=E,-E, should hold in that case]. This value is indicated by A in fig. 2. The carrying capacity is fully utilized in case of an equilibrium involving a type of state for which r =r+ necessarily holds. Note, furthermore, that the class of states for which the right hand side of (43) equals this largest possible value of E, performs a pivotal role in the political space spanned by K and p in the sense that it divides that space into a set of states for which s(t)=z+ (t) necessarily holds in equilibrium, and another set of states for which this equality does not necessarily hold (assuming that there exists an equilibrium with t < 7’). 9. If for an arbitrary then it is an equilibrium 10. Zf for

(K,P) an equilibrium exists for which z= Z+ holds, for all (K, ,u), except possibly for (K =O, n= 1).37

an arbitrary

(rc,p)

a full

employment

equilibrium

exists

with

z

CT+, then there exists for all (K, ,u) E { (tc, u) 1K > 0 or u < 1) a full employment equilibrium with z =z+ and an unemployment equilibrium. For (rc=O, n= 1) only the latter

may hold.38

11. If an equilibrium equilibrium 12. If for exists

for

exists

all (rc,n), except

an arbitrary

a full employment

for

an arbitrary

possibly

for

(rc,n) an unemployment equilibrium

(rc, p),

then

there

exists

an

(rc=O, p= 1) (see 6, 9, 10). equilibrium

exists,

then there

as we11.39

37This follows immediately from the behaviour of the state as described under 7, and the fact that T is positively related to E,. It is an equilibrium for (K=O, n= 1) as well, if E, =E, happens to hold. 3sThe first part is easily checked from the equilibrium conditions, given characteristic 9, by changing E, and E,. For the second part, suppose that E, =E; for the equilibrium with r < 5’. 39Neglecting (Al) for the moment, it can be checked from (A2)-(A7) that a new equilibrium can be obtained with E,=E,-E, by choosing a sufftciently higher level of E, [in which case r +, see (A8)]. As regards (Al), observe that there always exist types of states for which (43) is sztrisfied, as E,zE,: >O [in addition note that E, is bounded away from zero if n >O; see (A8)].

F. van Winden and B. van Praag, The state and the private sector

13

13. More than one (tc,,u) can be associated with an equilibrium.40 It means that, from a comparative static point of view, changes in the polity do not necessarily demand changes in the economy. 14. More than one equilibrium may exist for a type of state (see 10 and 12). It means that, from a comparative static point of view, changes in the economy do not necessarily require changes in the polity. Definition. A unique equilibrium is defined by: (a) the existence one equilibrium per type of state, and (b) the identity of equilibria of states.

of at most over types

15. If there exists only one equilibrium for an arbitrary (tc, u) E { (tc, ,u) 1K > 0 or u < l} then: (1) it is a full employment equilibrium with t=z’; (2) it is a unique equilibrium for all (K,~)E { (K,,u) 1ti>O or u < l}; (3) it is a unique equilibrium ,for all (~,p) if E,=E, happens to hold (see 10 and 12 for (l), 9 and 10 for (2) the footnote attached to eq. (43) for (3)). In case of a unique equilibrium, there is a maximum of structural coercion on the activities of the state; all equilibrium compatible types of states behave in exactly the same way. 16. The necessary and sufficient conditions for an equilibrium with maximum private output are given by: (Al)-(A7), E,+E,=E, and E, =max {EL, [y/(1 +q)] .E,). If q >O, private output does not only depend on the employment of capital and labour but also on the employment of labour by the state. Obviously, E, +E, =E, should hold for a maximum of X,. Using (4), (38), and E, 1 EL, it then follows from the first order condition for a maximum of X, that E, = max {EC, [y/( 1 + v)] .E,} ; a minimum state size, E, = E;, only results when q/( 1 + q) 5 EL/E,. It may be interesting to note that a unique equilibrium need not imply maximum private output. The differential between the state wage rate and the private wage rate, and the investment ratio are important in this respect.41 Suppose that 4 = 0 = 1, in which case there is no wage differential between state and private sector, and tax revenues from dividend income are absent, it then follows that maximum private output is implied by a unique equilibrium, as in that case the before-tax real private wage sum should 40This follows from 9 for equilibria with T = 5+, and from the latter part of the proof of 12 for equilibria with r CT+. “For r) = I, it is obtained from (A8) that, in case of a unique equilibrium, E,=ma:: {ES-, CO.54 -(I +A,)/(2A,)]} should hold, where l+A,=-{l~~+(l-a)[(l-r/~)-‘-l]}/(~-~). Maximum feasible private output demands that: E,=max {E;,O.SE,}. Thus, if q= 1, a unique equilibrium implies maximum private output only if max {E;, 0.5E,} =max {E;, [0.5E, - (1

f.4,)/&4,)1.

14

F. van Winden and B. t;an Praag,

The State and the private sector

obtain its maximal value, for, otherwise, it would be possible to shift labour from one of the sectors to the other, thereby increasing the wage sum beyond what is necessary for minimum consumption (recall from 5 that the equilibrium share of the before-tax real private wage sum in private output is constant).42 As regards the types of states that are compatible with a maximum private output equilibrium, note from characteristic 9 that such an equilibrium, for an arbitrary type of state, would be sustained by any (rc,~) E {(Ic,~) 1K>O or p Cl} if r=s+; if 7<7+ then, because of (43) it is only sustained by the class of states for which I* -

[2oK/( 1 - K) + I]/( 1+ y) 2 0 or

p - [2&c/(1 - K) + l]

(E, -E;

)/E, 2 0.

(44)

4. Dynamics In this section we present the results of a number of numerical experiments with the model. For notational convenience, the time index will again be deleted whenever it is self-evident. Parameter values and initial conditions will be given first. With respect to the wage equation (18) and the price equation (32) it is, respectively, assumed that g=[Et(t-l)+Ed,(t-1) -E,]/E,, and h=[Xd,(t1)-Xi(tl)]/X;(tl), which means that relative changes in product price and wage-rate are supposed to equal the relative excess-demand for product and labour, respectively. Parameter a, = 1 fl=O.5 y=O.l

6=0.1 [=O.l r/=1

6,= 0.05 v=O.29 p=O.l

values 4=0.9 *=o.s =5 XcP

E, = 1 E,= 100

Note that the elasticity of private labour productivity with respect to state capital is assumed to be positive (q = 1). The only parameter values that remain to be specified are K, which indicates the relative strength with which the interests of bureaucrats and politicians are represented by the state, and p, which represents the weight attached by politicians to private versus state production. As K and /1 are both defined on the [O,l]-interval, types of states, indicated by (IC,~),are 42A unique equilibrium with 4 = 1 and o = 1 demands that (1 - T)I(Iw~(E, + EP) =px;- (E, +E,) =px;-E, (since 5 =T+ and E,+E,=E,), while (1 -z)w,E,=zw,E, (balanced budget); it follows that W&,=X~~ E,/$ should hold. Using (AE), it is straightforwardly shown that a unique equilibrium with 4 = o = 1 implies that E, = max {ES-, [q/(1 + a)] ‘E,}.

F. van Winden and B. van Praag, The state and the private sector

represented fig. 3).

by points

on the unit

square

Fig. 3. The political

spanned

15

by these parameters

(see

space

, In general, the value of K may, for example, be supposed to depend on the size of the state, and, in case of government changes, on the frequency of these changes; both factors will typically shape the power of the bureaucrats in so far as that is based on information. The value of p may be assumed to be dependent on the interests/ideology and seat distribution of the politicians. In this simple model, K and p are exogenously determined [changes in types of states are made endogenous in Van Winden (1979a, 1981)]. Our main concern are the consequences of interest representation by the agents that make up the state organization, and the impact of structural coercion on these consequences (see section 1).

Initial D,(l)= E,(O)=10

0

conditions

2(0)=0.09

E,(O)=

D,(O)=0

K,(l)

85 =4500

S(O)=0 p(0)

= 1

p(l)=

1

w,(O)=20

These initial conditions are sufficient to determine the initial values of all the remaining variables. Four patterns of motion were generated by the types of states that were considered: (1) equilibria, (2) regular cycles, (3) cycles marked by a periodic ‘bankruptcy’ of the state, forcing it to put z =z+ and ES= EL, and (4) shrinking private production accompanied by an accelerating inflation due to a chronic financial breakdown of the state. Figs. 4, 5 and 6 show the time-paths of some of the variables for three types of states, generating the first three patterns of motion. Fig. 4. Private output biased state (K=O, ,u=O.99). This type of state consists of a government that is only marginally interested in state production whenever this is expected to interfere with private production, and an obedient, powerless, bureaucracy. It is not interested in higher levels

F. van Winden and B. mm Praag,

16

The state and the private sector

of employment than what makes up the difference between total labour force and the expected private demand for labour. In short, the state adjusts itself to the behaviour of business on the labour market.43

-IE, 0.8 -

a-* -.-,-I-

a-,- I_,_,_,_,_.

--1-.-,_,_a_

,_._,.

*_...-s

+ E, l/E,

-Es/E,

, ,_

----lyi2.10~) x x x K&t2.104) -_obklO3)

-T -wI *-

E, /Y

u+D,/Y Y=w,E,+pXp

-._----~_

---

_ ____ -0 -

IPX~-W,E~)I(PX,)

_lXdp-xlpuxlp I

-0.31

0

30

60

90

Fig. 4. Private

Expecting an excess supply for labour; E,

120

output

biased

of labour

150

--w&(+2.1021

180 *t

state (K=O, ~=0.99).

at t = 0 the state steps up its demand

1 - (w,/p)/c~,].~~ The investment ratio CJ increases, followed, with a lag, by an increase in K,. The latter effect gradually dominates the rise of clP and causes private demand for labour to grow. An excess demand for labour results. State employment is forced back 431n case that K=O and p
solution

to (16) that

e(t)

F. van Winden and B. van Praag,

The state and the priuage

sector

77

(y =O.l) and clp declines. In the meantime wp/p rises due to the excess demand for labour and a decrease in p induced by an excess supply on the product market (stocks reflect the budget surplus of the state and the time lag in the spending of disposable business funds). Profit margin and investment ratio, consequently, fall. The contraction, however, does not terminate into a depression. After some time an equilibrium results. Fig. 5. Bureaucratic state (K= 1, 0 I_ p 5 1). This type of state is characterized by a powerless government. The figure shows a regular cycle. The growth target of the bureaucrats stands in the way of a rapid expansion of E, like the private output biased state effectuated.45 Labour productivity

-_(Ep

+ E,liEf

-E,/Et ----Kp(+2.104)

0.6 .-

” I I RPlc2.104) --rrp(ilO”l

0.0

-T -w,E,/Y mD,IY Y = wrE, + pXP

0.5

-0

0.3

-(PX~-WPEPMPXP) ,(X;-X;)/X; --w,/P(+2.102)

0.1 0.0 -0.1 -0.31

0



30

60

90

Fig. 5. Bureaucratic

and, consequently, E, again

the capital-labor

120

150

180

-t

state (K = 1, 0 5 p 5 1).

ratio scarcely

increase.

The expansion

e(t)=Ef(t - l)e’.

of

78

F. van Winden and B. van Praag, The state and the private sector

the other hand, the tax rate and excess supply and demand on the product market. The share of state production in total production X as estimated in the national accounts [i.e. wsE,/(w,E,+pX,)], more or less follows the development of E,. Note, finally, that contrary to what might be expected this state does not even realize the level of state employment that the private output biased state established. Fig. 6. State goods biased state (k-=0.5, p=O.Ol). In this case we have a government that is only marginally interested in private production, and an influential bureaucracy, say because of the dependence of politicians on the bureaucratic apparatus that goes with a strong emphasis on state production. The drawings show some interesting profiles. The very fast expansion of E, is brought about by a sharp decline of private demand for labour. This decline results from an increased capital-labour ratio ~ due to the expansion of E,

-w,E,/Y r++D,/Y Y = w,E,

+ pXp

-*

--w,/p(+2.10~1

Fig. 6. State goods

biased state (~=0.5,

p=O.Ol).

F. van Winden

and B. van Pruug,

The state

and the priuate

sector

79

- and a diminishing investment level following a strong increase of the real wage rate. A persistent rise of the product price, however, accompanying a shrinking private production level ultimately brings the real wage rate down (t = 60). The upper bound on the tax rate falls and, given a rate of 96 “/,, it does not take long before it becomes active. When t =69 the state is forced to trim its organization and to keep the tax rate at its maximum, because it cannot meet its financial constraints. After a while, the state recuperates, added by a recovery of the private sector, and the process starts again.46

Sensitivity All in all 25 types of states were considered, based on the following values for p and K: p=O, 0.01, 0.5, 0.99, 1; K=O, 0.25, 0.5, 0.75, 1. Table 2 gives an overview of the results that were obtained; the cell numbers correspond with the aforementioned patterns of motion.47 Table 2 Types of states and patterns

of motion.

K

I(

0

0.25

0.5

0.75

1

0 0.01 0.5 0.99 1

3 4 1 1 4

3 3 1 2 2

3 3 1 2 2

4 3

2 2 2 2 2

I 2 2

It appears that equilibria occur when state production is mildly favoured, if it is pushed too hard then cycles marked by financial problems for the state show up, if it is too much restricted then regular cycles such as shown by the bureaucratic state occur. We have tried to describe the underlying processes in the text accompanying the figs. 4, 5 and 6. The fourth motion pattern, marked by a chronic financial breakdown of the state and an accelerating inflation, shows up in case of such rather extreme types of states as (K =O, p=O.Ol) and (K=O, p= 1); in the first case the state is almost exclusively interested in state production, which leads to an enormous expansion of the state at first, but the state is in short time 46An influential bureaucracy with a modest state employment growth target may have a mitigating impact on the demand for labour by such a government for some time. For example, ifp=Oand K>O, then J$‘(t)=E,(t-l)exp[s+(l-K)/(~K)]. 471t may be interesting to note that for the 15 types of states composed from the same values for K, but from the middle three only for p, the same patterns of motion were obtained with a model in which an ‘auctioneer’ operated in the product market to balance supply and demand per period, except that the numbers for (K = 0, p = 0.01) and (K = 0.75, p = 0.01) changed places.

80

F. van Winden and B. van Praag, The state and the private sector

financially forced to put z =z+ and Es=_& ; in the second case the state is exclusively interested in private production which also leads to a minimal state size.48 In all these cases, the chronic financial difficulties of the state are due to a persistent negative maximum tax rate, compelling the state to subsidize. This may be caused by a low wage rate (due to unemployment) and/or a high price level (due to a large money supply and a low private production level). State debts accumulate, state employment is kept at a minimum, private output decreases as labour productivity declines, the price level increases, and still larger subsidies are called for. Using the parameter values and equilibrium condition (A8), it is easily computed that the feasible range for E, in equilibrium is at any rate restricted to: 3.8=
F. van Winden and B. van Praag,

The state and the private sector

81

particularly important for the occurrence of regular cycles. The value of y determines the level of state demand for labour that is protected against competition from private demand for labour in case of an excess demand in the labour market. An even development of E, is assured, up to &‘(t)=yE,, which is important given the lower bound on the equilibrium value of E, (see (43)). This even development of E, will be reflected in the development of private labour productivity, which is important for the firms’ behaviour; moreover, a higher level of labour productivity reduces, by enhancing the labour intensity of production, the pressure under the wage rate in case of an expansion of private production.” Note, furthermore, that the state’s expectation that private demand for labour will - on average - equal the previous period level of E, (see (14) and (15)), may easily lead to an unintentional crowding-out phenomenon in the labour market - which is the only market in the model where such a phenomenon may occur ~ when y is high. As long as Ei (t) 5 yE,, the firms cannot encroach upon E,. The time path of E, is clearly important in this respect.

5. Concluding remarks The research outcomes to which our simple other things, the following.

model has led suggest,

among

-States may practise a Keynesian type of policy (in the sense that state production and employment are increased in case of an expected excess supply of labour) not because of the fact that politicians are preoccupied with stabilization, or worried about the unemployment level, but because they are, inter alia, interested in state goods as such, and therefore, in employing resources that would otherwise be idle. As a consequence, even outspoken pro private sector governments may come to sustain a large sized state sector. -Bureaucrats (when powerful) may have a restraining influence on governments that are strongly interested in expanding or contracting the state sector, because they are presumably interested in a gradual expansion of the state. However, insofar as bureaucrats are also interested in a continuous expansion of the state, bureaucratic types of states are bound to be confronted with problems in the long term, given the restricted size of the labour force and some minimum consumption level in terms of private product. “Using 0.9 instead of 0.1 for y, the motion of table 2 changed into equilibria, except for which pattern number 4 was obtained. Using in the labour market (instead of (17)) for the the pattern number for the bureaucratic state

pattern for all types of states in the last two rows (K = 1, ~=0.99), (K = 1, F= l), and (K =0, p= l), for a proportional rationing scheme based on demand states represented by the figs. 4, 5, and 6, changed from 2 into 4.

82

-A

F. van Winden

and B. van Praag,

The State and the private

sector

particular feature of the model is that labour productivity in the private sector may be dependent on accumulated state production. If so, an interesting consequence of this, in the context of our model with a linear technology, is that the equilibrium real wage rate does not only depend on the rate of return on capital and the capitalloutput ratio, but also on the type of state, while the rate of return on capital does not (the latter appears to depend on the depreciation rate of private capital goods and the - exogenously determined - time preference of the firms). Moreover, although the share of the equilibrium before-tax real private wage sum in private output is, given for any type of state, the share of total real disposable wage-related income (including unemployment benefits and the state wage sum) is positively related to the state employment level, and, thus, to the type of state, unless all profits are ploughed back for investment so that no taxes can be obtained from dividend income. The political relevance of such results is clear, and they point at one possible source of conflict between wage earners and shareholders as regards preferred types of states. As was already noticed in an earlier publication [see Van Winden (1980)], some types of states may have a pivotal position in the political space in the sense that they break down that space into sets of states that show different kinds of behaviour. This is due to the activation of constraints by these states. In this model a pivotal class of states is encountered which divides the political space into a set of states for which in equilibrium the tax rate necessarily attains its maximal value, and another set of states for which this does not necessarily hold. As it is argued that an equilibrium path with a maximum tax rate may be difficult to arrive at and hard to follow, the former types of states seem to be prone to generate economic cycles for this reason. Further research into the location of pivot states seems to be worthwhile. For example, if one considers to incorporate state behaviour as an endogenous variable in an econometric model, the presence of pivot states may violate the smoothness assumptions that are typical for such models.

-The type of state may be an important factor for the occurrence of economic cycles. Once one agrees that politicians and bureaucrats try to promote their own interests this is not at all surprising, of course. Cycles may deliberately be created [cf. Kalecki (1971) and the studies on the ‘political business cycle’, such as Nordhaus (1975), MacRae (1977)], or accidentally occur as a side-effect. In our model they are generated, inadvertently, by, on the one hand, types of states that have a strong interest in state goods, and, consequently, push state production too hard, which leads to financial problems (this type of cycle may have some relevance for a number of present-day capitalist economies), and on the other hand, by types of states that restrict state production too much. In

83

F. van Winden and B. oan Praag, The state and the private sector

the second case, the positive relationship between state production and labour productivity, and the structure of the labour market appears to play an important role. Especially now that an increasing number of people seek the solution to many problems in modern capitalist economies in a smaller state sector, the potential negative aspects of such a contraction will deserve more of our attention. -Although the type of state generally matters, there may be circumstances in which the degree of structural coercion exerted by the private sector on the behaviour of the state (as determined by a minimum consumption level, for example) is such that all (non-revolutionary) types of states will show the same sort of behaviour. Only for those circumstances does the plea, with which we will end, for the (empirical) study of the character of the state - that is, of the interests and relative power of its agents seem to be without much use.

Appendix: Necessary The necessary (Al)-(A7):

and sufficient conditions for an equilibrium

and

sufficient

E, = e = solution E; sE,sE,,

conditions

of programme

and zlr+ -

1

“F >o, c-

[

1

>o,

where a,, = v[(a,/[)EJ,

&

wp= [

at any rate if Ef + E”,
(1 -o)F

w,C($-$)E,+$&-EJI 7=*+=1-

c [ *%

1

are given

by

that

(AlI

where F = (pap - wp)E, > 0,

[ 6P fi

implying

(16)

2

E, = E”, = (B/a, Kp > 0,

wp2

for an equilibrium

iff wP=wp,

C-

642) (A3)

1

=wp

-1 II

(A4)



(A9

84

F. van Winden and B. van Praag,

The state and the private sector

(1 -z)(l -o)F+oF =M, where M is the stock of money permanently present in the economy,

o=l-p[l+(l-G)pK,/F]>O.

that is (A6)

(A7)

Condition (Al) follows from eqs. (16)-(19) and F ~0 (see (A3)); the first part of (A2) is obtained from (17)-(19), (33) and F >O, the second part from (3) (28), and (29); the first part of (A3) follows from (22), (25) (26), and (32), the second part from (5)-(9), (22), (32), and F >O; (A4) follows from (19), and F >O; the first part of (A5) is obtained from (13), the second part from (12) and (A4); (A6) is derived from (5)-(7), (20) (21) (25) and (32); (A7) follows from (36), (37) and (A3). The following relations are useful in checking whether the conditions (A2)(A7) are satisfied: eqs. (39))(42) and, because of (A4) and (A5),

E,-(A,E:+A,)E,+A,~o,

(‘48)

where

U-o)CU -rlP)F’

Al =IC/(l-rlP)v(dW{l+

-

ll>/C(4 - $).ql

-*1>0; A, = ICI-G/(4 Clearly, condition (given E,).

>Q

for c and r, see (39) and (40).

(A8) is not satisfied

if ES+0

(given E,; if v]>O), or Ep+O

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85

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