Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

7rFE

Chapter 8: Trade Unions and the Labour Market

FE	w

R and an indifference n attains a utility level Put point C is efficient.

ns, especially in the two parties bargainItly smart to eliminate Adel. For that reason,

and Solow (1981).

ion and the firm bar- e bargaining problem up. Now the negotia- - e wage-employment

(8.17)

(8.18)

(8.19)

wEB

LC

LEB

N L

Figure 8.5. Wages and employment under efficient bargaining

By combining (8.18)-(8.19), the so-called contract curve is obtained:

1 X	Vw		(	= L	(8.20)
Jr —	—
	— (V — ) 7rw	=	V — )7TL	Vw n-w

In words, the contract curve (CD in Figure 8.5) represents the locus of (w, L) combinations for which efficient bargaining solutions are obtained. For any point on the contract curve, there is no (w, L) combination that makes one party better off without simultaneously harming the other party. In graphical terms, the contract curve represents all tangency points between iso-profit curves and union indifference curves.

One immediate implication of the efficient bargaining model is that the real wage exceeds the marginal product of labour. Indeed, (8.20) says that rci, = VLTrw / Vw < 0 (since V', > 0, Vw > 0, and 7rw < 0). Hence:

L AFL (L, k) — w < 0 <#. w > AFL (L, R).

(8.21)

Hence, with the exception of the competitive solution, efficient contracts are not on the labour demand curve. Of course, we have already discussed three points on the contract curve, namely points C, ER and EM in Figure 8.4.

In Figure 8.5, the entire contract curve is drawn as the dashed line connecting points C and D. We assume that full employment is possible in principle. This means that the profit level associated with the full employment level on the contract curve (point D) exceeds the fall-back profit level of the firm (i.e. > In that case, the entire line segment CD constitutes the contract curve. As it stands, the model is not yet fully specified because it does not yield a prediction about any particular wage-employment outcome—all (w, L) combinations along the line CD are efficient.

195

Lc).

The Foundation of Modern Macroeconomics

McDonald and Solow (1981, p. 903) suggest closing the model by postulating a socalled "fair share" rule. After repeated interactions in the past, the union and the firm have somehow settled on a "fair" division of the spoils. In terms of the model, the equity locus (EE) can be written as follows:

wL = kY = kAF(L, K), 0 < k

(8.22)

where k is the share of the spoils going to the union (the firm gets 1 — k of output in the form of profits). The slope of the equity locus can be determined in the usual fashion:

Ldw + wdL kAFLdL (di = kAFL — w < 0, (8.23) dL EE

where the sign follows from the fact that 71-1, AFL — w < 0 (solution lies to the right of the labour demand function) so that a fortiori w > kAFL. The equity locus is downward sloping and shifts up and to the right if labour's share of the pie (k) is increased.

By combining the equity locus EE and the contract curve CD, the equilibrium wage-employment combination is obtained at Eo . A very surprising conclusion is reached. Compared to the competitive solution (point C), employment is higher (and unemployment is lower) under the efficient bargaining model (LEB > The layman's sentiment, mentioned in the introduction to this chapter, is only partially correct. Wages are higher than in the competitive solution (wEB > B) but employment is also higher than in the competitive solution. The intuition behind this result is that the union prevents the firm from grabbing the maximum profit level (at point C), and instead turns some of this profit into jobs for union members.

In that sense the next conclusion that can be drawn on the basis of the efficient bargaining model is perhaps less paradoxical than it may appear at first sight. Wage moderation, as modelled by a smaller share of the pie for labour (dk < 0), turns out to be bad for employment! Graphically, a lower k shifts the EE locus down and to the left, shifting the equilibrium from E0 to E 1 . The power of the firm is de facto increased, and the wage-employment combination is forced closer to the competitive solution.

Hence, the efficient wage bargaining model yields some surprising conclusions. The problem with the model appears to be its tenuous empirical relevance. Although simultaneous bargaining over wages and employment is efficient, it is hardly ever observed in practice. It therefore appears that the RTM model (which includes the monopoly model as a special case) has a closer affinity to reality than the efficient bargaining model. In other words, in the real world the relevant case appears to be that firms and unions negotiate over the wage rate, but that the firm can unilaterally determine the employment level.

8.1.4 Trade un

Before turning to behaviour in a 1, unions may have is homogeneous, called the primary has a competitive to N. EmploymL .4 workers, so that in the primary _ and LY (w2), respei in Figure 8.6. In ti for a union inch.. , is wivr and employ of labour betwe, clearing competi ti 4. , respectively. I all workers that c the secondary sec?

1.:;1 = N — L . He employment of labs and secondary

WM

01

Figure 8.6.

196

by postulating a st, the union and tht

terms of the mode

(8.27

n gets 1 - k of ou` termined in the usu,..

(8.2 -

(solution lies to the (FL. The equity loafs share of the pie (k)

CD, the equilibriurprising conclusion mployment is higher g model (LEB > this chapter, is only Aution (WEB > B) but The intuition behind the maximum profit s for union members. basis of the efficient

at first sight. Wage bour (dk < 0), turns the EE locus down power of the firm is forced closer to the

rising conclusions. relevance. Although -1t, it is hardly ever ( which includes the than the efficient nt case appears to be firm can unilaterally

Chapter 8: Trade Unions and the Labour Market

'3.1.4 Trade unions in a two-sector model

Before turning to the next issue, it is instructive to study the effects of trade union behaviour in a two-sector setting. This allows us to study the spillover effects that unions may have on the non-unionized sector of the economy. Suppose that labour is homogeneous, but that there are two sectors in the economy. The first sector, coled the primary sector, is unionized, and the second, called the secondary sector, has a competitive system of wage determination. The labour force is fixed, and equal to N. Employment in sector i is denoted by L1 , and U is the number of unemployed workers, so that N = L1 + L2 + U. We assume that a monopoly union sets the wage in the primary sector. The demand for labour in the two sectors is given by L if (wi) and LY(w2), respectively, where w i is the wage in sector i. These schedules are drawn in Figure 8.6. In the primary sector, the monopoly union selects the tangency point for a union indifference curve and the demand for labour (point M). The wage rate is wM and employment is L. In the absence of a union, and with perfect mobility of labour between the two sectors, the common wage rate would be at the market clearing competitive level w c, and employment in the two sectors would be Ll and 4, respectively. If the union sets the wage in the primary sector at 4, however, all workers that cannot find a job in that sector supply their labour inelastically to the secondary sector, so that the wage rate in that sector is w2 and employment is

= N - L. Hence, with a monopoly union in the primary sector, there is full employment of labour at the aggregate level, but wage disparity between the primary and secondary sectors. Workers in the secondary sector would rather work in the

W1	LiD(Wi)	W2
		LY(W2)

A4

We

B B

w M

2

02

Ly Ly

Figure 8.6. Unemployment in a two-sector model

/

The Foundation of Modern Macroeconomics

primary sector (because wages are higher there), but are prevented from getting work there because of the union's wage-setting power.

Suppose now, however, that unemployment benefits equal B, and that B exceeds the wage for which full employment would prevail in the economy, i.e. B > w . In such a case, employment in the two sectors would equal IT and g, respectively, and unemployment would be equal to UB .

8.2 Corporatism

Our fifth stylized fact in Chapter 7 suggests that there are large differences in the unemployment rates of countries of the developed world. We saw that (at least up until the early 1990s) countries such as the US, Japan, Austria, Sweden, Norway, and Finland are characterized by low unemployment, whilst countries such as Belgium and the Netherlands have high unemployment. Calmfors and Driffill (1988) suggest that the unemployment rate may have something to do with the degree of corporatism that exists in the economy, and that the relationship is parabolic, as is drawn in Figure 8.7. Although the concept of corporatism is hard to define precisely, Calmfors and Driffill intend it to mean the degree of centralization of the wage-setting process. In terms of Figure 8.7, a low degree of corporatism is found in countries such as Japan, Switzerland, Canada, and the US, since these countries are characterized by relatively competitive labour markets. A very high degree

U	Belgium
w	The Netherlands

of corporatism is Finland. An

Belgium, and Austri The reason w1-1 ;tidy be that highl) -caller unions w

:e to a higher pri,, wage-price spiral int an both higher

-.ages (via the inde

nt. To the exte:

• rates, union n1,, 3kgain, large unions :ions. Third, it

Anen there are sma ects will be absc al., 1991, p. 30). The reason why

- .employment frc

power and are henc do not internalize 4 L4cmselves are smut Unemployment )ugh to cause tiriployment level ,

ntioned above. 1 by an interm,,

extreme cases.

Japan	Sweden
/United States	Austria
Canada
competitive labour	centralized wage
market	bargaining
	degree of corporatism

Figure 8.7. Unemployment, real wages, and corporatism

198

8.3 Fiscal Incr

nn a recent article, ti - e character'. ,?ubtic sector. Their, 14 *.h a rise in the

pay for its, .; . - 1

3 located on the di r on the fact th

The basic model. There is pelf

ree of

are prevented from getti-

equal B, and that B exceerl e economy, i.e. B>w- f. In

.al Li' and LB, respective!

are large differences in the d. We saw that (at least up :ria, Sweden, Norway, and t countries such as Belgium r-Nrs and Driffill (1988) sug- g to do with the degree of elationship is parabolic, as

sm is hard to define precentralization of the

• of corporatism is found the US, since these coun- lrkets. A very high degree

Sweden

Austria

1centralized wage bargaining

ratism

Chapter 8: Trade Unions and the Labour Market

of corporatism is found in countries such as Austria, Norway, Sweden, Denmark, and Finland. An intermediate degree of corporatism is found in the Netherlands, Belgium, and Australia.

The reason why highly corporatist countries have a good unemployment record may be that highly centralized unions tend to internalize external effects that smaller unions would cause. First, higher wages at the microeconomic level translate to a higher price level at the macroeconomic level. Small unions do not take this wage-price spiral into account, but large national unions may. Second, higher wages mean both higher unemployment, and in most countries, higher civil servants' wages (via the indexing clauses), thus raising the government's revenue requirement. To the extent that the additional revenue must be raised by means of higher tax rates, union members may not experience an increase in their after-tax wages. Again, large unions are more likely to internalize this external effect than small unions. Third, it is possible that leapfrogging effects (see Chapter 7) are important when there are small unions. With a high degree of centralization, however, these effects will be absent. A national union cannot overbid its own wage claim (Layard et al., 1991, p. 30).

The reason why countries with a low degree of centralization fare well on the unemployment front is that unions, if they exist at all, are very small, have very little power and are hence rather harmless. As a result, the fact that these small unions do not internalize externalities does not matter much, because the externalities themselves are small in that case.

Unemployment is at its worst for intermediate cases. There, unions are large enough to cause some damage (in the form of higher wage claims and lower employment levels), but too small to feel inclined to internalize the external effects mentioned above. By being neither one nor the other, the countries characterized by an intermediate degree of centralization inherit the bad features of both extreme cases.

8.3 Fiscal Increasing Returns

In a recent article, Blanchard and Summers (1987a) argue that the countries in the EC are characterized by so-called fiscal increasing returns due to the existence of a large public sector. Their idea is very simple: an increase in employment can be associated with a rise in the after-tax real wage rate. Put in more colloquial terms, a tax cut can pay for itself. Their argument is not based on the assumption that the economy is located on the downward-sloping part of the Laffer curve (see Chapter 1), but rather on the fact that high employment means low expenditure on unemployment benefits. The basic mechanism can be demonstrated with the aid of a very simple model. There is perfect competition on the goods market and output Y is produced

199

INN .

The Foundation of Modern Macroeconomics

with the following constant returns to scale production function:

Y = F(L, k), FL > 0 > FLL, (8.24)

where L is employment and K is the fixed capital stock. Assume that the government keeps its budget deficit constant if unemployment is diminished. The government budget restriction is:

G + Ow(1 - t) [N - Id] = tY, (8.25)

where G is exogenous government spending on goods and services, t is the tax rate (so that tY is tax revenue), N is the given labour force (so that N - L is the number of unemployed members of the labour force), wN w(1 - t) is the after-tax real wage rate, and 0 is the constant replacement ratio (0 < < 1). It is assumed that the unemployment benefit is linked to the after-tax real wage. The tax rate t ensures that the government budget is balanced.

With perfect competition in the goods market, the demand for labour is implicitly defined by the marginal productivity condition:

FL(L, K) = w. (8.26)

Equations (8.24)-(8.26) contain four endogenous variables (Y, L, w, and t), so that a macroeconomic relationship between after-tax real wages wN and employment L can be deduced:

	wN w(1 - = FL(L, K)[	F (L, K) - G - Ow(1 - t)(N - L)	(8.27)
		F(L, K)

Equation (8.27) has a hump-shaped form, as has been illustrated in Figure 8.8. If employment is very low, the effect of diminishing returns to labour is dominated by the decrease in the tax rate which is made possible by the larger tax base. As a result, net wages can rise. When employment is high, on the other hand, the reverse happens: the tax rate effect is dominated by the decreasing returns to labour, and the net wage falls as employment expands.

More formally, the slope of (8.25) can be calculated as follows (see the Intermezzo below):

	dwN _ owN)	— + + t (oLl	(8.28)
	dL (1 - coG)L	1 - t

where coG is the share of government spending in output, 04, is the share of labour income in output, t is the initial tax rate, and a is the substitution elasticity between capital and labour in the production function (see Chapter 4).

Blanchard and Summers (1987a, p. 548) close the model by assuming that the after-tax real wage rate is fixed at some exogenous level, say w N in Figure 8.8. This could be either because of extensive indexing or due to the influence of trade unions.

Figure 8.8. Fil

At that level of net wage acterized by low emplo:. is high. It is likely that ( s equilibrium. If this is indi A rise in the union's wa, librium shifts from E' to Furthermore, there is s. unions. By keeping the a reduction in the tax rw to the good equilibrium. Blanchard and Sumrn

is unstable. To demo' adjustment rule for the t

t = y [G + ,8w(1

where the gross real w::

after-tax real wage at/at > 0: unless the ek.4 this equilibrium is self - E"', on the other hand, 1 the extent that WN is trul a bad equilibrium. Eithe equilibrium, or there is accompanied by ever getting the EC countriLz

200

0, which

at/at >

n function:

(8.24►

,u me that the government iminished. The government

(8.25)

Ind services, t is the tax rate so that N — L is the number

—t) is the after-tax real

<1). It is assumed that the age. The tax rate t ensures

nand for labour is implicitly

(8.26)

tiles (Y, L, w, and t), so that _es wN and employment L

— L )]

(8.27)

illustrated in Figure 8.8. If is to labour is dominated by the larger tax base. As a the other hand, the reverse :ig returns to labour, and

slows (see the Intermezzo

it. wL is the share of labour stitution elasticity between

2r 4).

odel by assuming that the

•say WN in Figure 8.8. This nfluence of trade unions.

Chapter 8: Trade Unions and the Labour Market

WN

	E"
E'	E"'

WN

L

Figure 8.8. Fiscal increasing returns

At that level of net wages, there are two equilibria; a "bad" equilibrium at E' characterized by low employment, and a "good" equilibrium at E"', where employment is high. It is likely that (some of) the EC countries may find themselves in the bad equilibrium. If this is indeed the case, a rather perverse policy conclusion is reached. A rise in the union's wage claim turns out to be good for employment! The bad equilibrium shifts from F! to E"'. Conversely, wage moderation is bad for employment. Furthermore, there is scope for a wage-tax deal between the government and the unions. By keeping the after-tax real wage rate unchanged (at CvN), a simultaneous reduction in the tax rate and gross real wages can shift the economy from the bad

to the good equilibrium.

Blanchard and Summers (1987a) suggest, however, that the bad equilibrium is unstable. To demonstrate this instability, we postulate the following ad hoc adjustment rule for the tax rate:

t = y [G /3w(1 — t)[N — L] — tF(L, k)] , y > 0, (8.29)

where the gross real wage is given by (8.26) and we retain the assumption of a fixed after-tax real wage CvN. As is shown in the Intermezzo, around point E', we have that 0: unless the economy is exactly at point E', a small deviation away from

this equilibrium is self-perpetuating, so that the equilibrium is unstable. For point E"', on the other hand, we have that atiat < implies stability. Hence, to the extent that 141N is truly fixed, there are two possibilities if a country finds itself in a bad equilibrium. Either there is automatic adjustment from the bad to the good equilibrium, or there is a gradual deterioration of the employment performance accompanied by ever increasing tax rates. Of course, a wage-tax deal would help in getting the EC countries from the bad to the good equilibrium.

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The Foundation of Modern Macroeconomics

Intermezzo

Stability in the Blanchard-Summers model. The relationship between wps, and the employment level L, implied by equations (8.24)-(8.26) can be deduced as follows. First, we loglinearize these equations:

Y = on,L,					(a)
(t	coG)iN - fi( 1 - t)(orL		+ (I t)t,		(b)
	( 1 - coL				(c)
where Y	L	wN dwAT		dt-1(1-t),-4,	G/Y,
and (Di, wL1Y . In view of the definition of wN, we also have that:

(d)

By substituting (a)-(c) into (d) and simplifying, the following expression is obtained.

	=( 1	(,6	t	(e)
	coGJ		1 - t

Since L dL11, and ii/N dwN/wN we can rewrite (e) to obtain (8.28). Stability of the equilibria E" and E" can be investigated as follows. The

adjustment mechanism (8.29) is linearized as follows:
di -y Y [f3(1			+ — .
By using (a) and (c), and recognizing that wN = 0
from (a):
y Y	1 a),			(# t
dt = ' a	)[	-)			t	]dt.	(g)
1 —

Hence, by (e), dt I dt < 0 if wN depends negatively on L and dt 1 dt > 0 in the opposite case. Hence, point E' is unstable and point E"' is stable.

8.4 Hysteresis and the Persistence of Unemployment

The second and fourth stylized facts from Chapter 7 demonstrate that there is a high degree of persistence in the European unemployment rate. How can models

based on trade union) in the membership nil typical union has a ti ti is possible, however, t, worse, are kicked out. the simple model by BI Suppose that the supply (an index of a b„ the general price index

= (m - /3) - a( Pi

where all variables are r p, is the price charged to returns to scale, and function is yi =

market implies that prii demand for labour is

= (m - w) - a(t4,

where w is an aggregaz, Each firm has a give workers are taken into these workers are refers the firm, is the firm al insiders has sufficient t it is assumed that the v.

number of insiders:

Eli = n7,

where E is the expec

Eli = Em - Ew - a(wi - the same size, so that tri choose the same nomi:

wi = w = Ew.

It follows that n7 = the final expression for

1, =m-w -a(w;-

1= (m - Em) + n',

where the firm index i

(8.34) shows that okuy

202

lationship between wN and 1 -48.26) can be deduced as

(a)

(b)

(c)

— t), dw/w, coG G/ Y, llso have that:

(d)

, e following expression is

L. (e)

obtain (8.28).

tigated as follows. The

(f)

Cn that Cy = t, we obtain

(g)

L and dt/dt > 0 in the is stable.

'employment

4. 'monstrate that there is a nen t rate. How can models

Chapter 8: Trade Unions and the Labour Market

based on trade unions explain this phenomenon? The key to the solution is found in the membership rule of the union. Up to this point we have assumed that the typical union has a fixed number of members (say N members, as in section 2). It is possible, however, that unemployed union members either quit the union, or worse, are kicked out. What may happen in such a case is illustrated with the aid of the simple model by Blanchard and Summers (1986, 1987b).

Suppose that the demand for each firm's product depends on the real money supply (an index of aggregate demand) and the relative price of the product vis-a-vis the general price index:

yi = (m — p) — a(pi — p), a > 1, (8.30)

where all variables are measured in logarithms, yi is output, m is the money supply, pi is the price charged by firm i, and p is the aggregate price index. There are constant returns to scale, and only labour is used in the production process. The production

function is yi = /i, where li is employment in firm i. Perfect competition in the goods market implies that price is set equal to marginal cost, so that pi = wi. Hence, the

demand for labour is given by:

li = (m — w) — a(wi — w), (8.31)

where w is an aggregate index of nominal wages.

Each firm has a given number n7 of attached workers. Only the interests of these workers are taken into account in the wage bargaining process, for which reason these workers are referred to as the insiders. Only if all insiders are employed by the firm, is the firm allowed to hire any outsiders. We assume that the group of insiders has sufficient bargaining power to set the wage unilaterally. Furthermore, it is assumed that the wage is set such that the expected employment is equal to the number of insiders:

Eli = n7, (8.32)

where E is the expectations operator. By using (8.31)—(8.32), we derive that Eli = Em — Ew — a(wi — Ew) = n7. All firms are identical and all insider groups have the same size, so that the equilibrium is symmetric. Consequently, all insider groups choose the same nominal wage, so that:

wi = w = Ew. (8.33)

It follows that n7 = Em — w. By substituting this expression into (8.31) we obtain the final expression for employment (per firm):

li = m — w — a(wi — w) = m — Em + n7

1 = (m — Em)± n*, (8.34)

where the firm index i can be dropped in the final step due to symmetry. Equation (8.34) shows that only the unexpected shock in aggregate demand has any effect on

203

The Foundation of Modern Macroeconomics

employment (per firm). Suppose that the membership rule of the group of insiders is as follows: n7 = li ( — 1), i.e. only insiders that were employed in the previous period will belong to the group of insiders in the current period. By substituting this membership rule into (8.34), the hysteresis effect is obtained:

1 = (m — Em) + 1( — 1), (8.35)

which, for a given labour force 14, can be rewritten in terms of the unemployment rate U as:3

U = —(m — Em) + U( — 1). (8.36)

Equation (8.36) yields the very strong conclusion that the unemployment rate follows a random walk. To the extent that aggregate demand surprises are random, the change in unemployment, A U is random also. There is no tendency for the unemployment rate to converge to any particular level. The intuition behind this result is straightforward. After a bad shock, employment falls (by (8.35)). The unemployed become outsiders, and the remaining insiders are not inclined to lower wages to get their former comrades back into a job. The opposite holds after a positive aggregate demand shock.

Of course, the hysteresis result is far too strong, both for empirical and theoretical reasons. Empirically, as we saw in Chapter 7, the unemployment rates in the UK and US display a lot of persistence but no hysteresis. The autoregressive coefficient in the unemployment process (see (7.3)) is high but not equal to unity. Theoretically, an unsatisfying assumption made so far is that the insiders have all the bargaining power and can set the wage unilaterally. Firms, in other words, are unable to appoint the unemployed who may be willing to work at a lower wage.

It turns out, however, that the model can be salvaged quite easily. Following Blanchard (1991), the bargaining process between the firm and the group of insiders is made more interesting by recognizing an explicit role for the unemployment rate. Unemployment has two distinct effects in the bargaining process. First, there is the fear effect that we also encountered in the efficiency wage models (see Chapter 7). If unemployment is high, a typical insider is a bit more modest in his/her wage claims. If unemployed, it may not be so easy to find another job. Second, the threat effect exists. If unemployment is high, employers can threaten current employees (the insiders) that they will be replaced by (hungry) unemployed workers.

A simple model that includes both aspects is the following. Labour demand is very simple:

/=—w+E, (8.37)

where E is a stochastic shock (with EE = 0), 1 is employment, and w is the wage rate (all in logarithms). Just as in the previous model, it is assumed that wages are set such

3 In levels, the unemployment rate is given by U (N — L)/N = 1 — (L/N) — log (L/SI) = Fz — I, where the approximation is valid for small unemployment rates.

that the insiders (of wL i.e. w* = —/( — 1). An un

the utility value of leisur the reservation or unen;t .

employment would be correct indicator for lab

the actual wage w is a.

w = aw* + (1 —

1

Equation (8.38) says th...

ers would choose (le) ai the bargaining stren,:h situation in the labour fr more modest in their the following expressit.i.4

I

U = aU( — 1 1 + b

Since 0 < a < 1 and b persistence but no hystei bargained wage rate) th high (a close to unity), ix model does indeed deliv

8.5 Applications (

In this section some of tt two issues. First, we c( • wages, and unemployi, investment by the firm.

8.5.1 The effects of

In order not to undu.► t ducted. Suppose that the benefits are untaxed, and tax rate is tM dT I dw a monopoly union mode

204