Heijdra Foundations of Modern Macroeconomics (Oxford, 2002)

• he unemployment rate foi- l(' surprises are random, the no tendency for the unem- - ,iition behind this result is )y (8.35)). The unemployed clined to lower wages to get ds after a positive aggregate

U (

Dr empirical and theoretical ovment rates in the UK and utoregressive coefficient in ival to unity. Theoretically,

,,, rs have all the bargaining

Ids, are unable to appoint wage.

i quite easily. Following n and the group of insiders Dr the unemployment rate. process. First, there is the vi models (see Chapter 7). e modest in his/her wage her job. Second, the threat -eaten current employees nployed workers.

swing. Labour demand is

(8.37)

nt, and w is the wage rate ied that wages are set such

- (L /N) — log (L/SI) = n —1,

Equation (8.38) says that the actual wage (w) is a weighted average of the wage insiders would choose (w*) and the reservation wage (wR) (with weight a, representing

the bargaining strength of the insiders), with a correction for the unemployment situation in the labour market. If unemployment U h -1 is very high, insiders are more modest in their wage claims, and the wage is lower. By simple substitutions

the following expression for the unemployment process is obtained:

Since 0 < a < 1 and b 0, (8.39) shows that the unemployment rate displays persistence but no hysteresis. If b is high (strong influence of unemployment on the

bargained wage rate) then there is little persistence. Furthermore, if insider power is high (a close to unity), persistence is high. Hence, this version of the insider-outsider model does indeed deliver more sensible predictions.

8.5 Applications of Trade Union Models

In this section some of the union models discussed in this chapter are used to study two issues. First, we continue our study of the effects of taxation on employment, wages, and unemployment. Second, we study the effects of unions on the rate of

investment by the firm.

8.5.1 The effects of taxation

In order not to unduly test the reader's patience, only one tax experiment is conducted. Suppose that the system of income taxes is progressive, that unemployment

benefits are untaxed, and that the tax function is given by T(w), so that the marginal

tax rate is tM dT dw and the average tax rate is to T/w. It is assumed that the monopoly union model applies, and that the union's utility function is augmented

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(from (8.1)) to include income taxes:

so that the first-order condition for the optimal wage is:

This expression can be simplified by using the result that wdtA/dw = tM - to and using the labour demand elasticity ED (defined below (8.9)):

a progressive tax system, tM > tA, so that s < 1. Recall from Chapter 7 that an increase in progressivity of the tax system is represented by a decrease in s.

For example, assume that the representative union member's indirect utility function is given by U(.) log (.). Then the markup equation (8.42) is simplified to:

From (8.43) we can see that the gross wage w (and thus unemployment U) rises if the unemployment benefit (B) rises, the degree of progressivity falls (s rises), and the average tax rate (tA ) rises. These conclusions are very similar to those that were obtained for the efficiency wage model in Chapter 7.

8.5.2 Unions and investment

Are unions good or bad for investment? Intuitively one would think the latter. The argument might go as follows. When capital is a variable production factor, the demand for labour becomes more elastic. This creates a conflict between what is optimal for the union in the short run and in the long run. Take, for example, the case of the monopoly union discussed in section 1.1. There it was shown that the wage markup bears an inverse relationship with the labour demand elasticity. A short-sighted union will push for high wages and suffer the consequences in the future as firms accumulate capital and labour demand becomes more elastic. Farsighted unions, on the other hand, will demand a lower wage, in the hope that the firm will not invest too much, so that the wage in the future will be comparable. A kind of wage smoothing behaviour may emerge.

This is not the end of the story, however, since there is a credibility problem associated with the wage smoothing union, due to the fact that investment is largely irreversible. The union can announce to the firm that it will follow a smooth (and moderate) wage policy, after which the firm will invest. Once the firm has invested,

however, the firm is shifted easily so the u off a large part of the has this incentive to cl ment of smooth and n the risk and impact of result, discussed for bility issues in Chapt can overcome (son: behaviour. 1 The remainder of ti in a simple two-periol and a firm. This exam (1987b). The firm t

capital stock K1 at equal to:

-= F(1,2, K1 +

where 7rt is real proi is the real wage rate, 4)(.) is the install,: this function capture! an increasing rate) 1 the firm does not in a close at the end of that the capital stoatinvestment levels in which is defined as:

n = Tri + 1+r

F(L i ,Ki) -

where r is the real it

problem are:

an =FL(LI,Ko- aL1

an all

an ( 1\ aL2 1 +

(8.43)

unemployment U) rises if ressivity falls (s rises), and similar to those that were

. - ould think the latter. The ble production factor, the conflict between what is un. Take, for example, the rere it was shown that the )our demand elasticity. A r the consequences in the oecomes more elastic. Far-

. lge, in the hope that the Aire will be comparable. A

Ia credibility problem assothat investment is largely 11 follow a smooth (and nce the firm has invested,

where Trt is real profit in period t (= 1, 2), Lt is employment, It is investment, wt is the real wage rate, is a constant returns to scale production function, and

(I)(.) is the installation function for investment. As we have shown in Chapter 4, this function captures the existence of internal adjustment costs that are rising (at an increasing rate) in the rate of investment, i.e. (1)1 > 0 and (1)ll > 0. Obviously the firm does not invest in the second period because our stylized world comes to a close at the end of that period. Furthermore, we have assumed for convenience that the capital stock does not depreciate. The firm chooses its employment and investment levels in order to maximize the present value of its stream of profits,

which is defined as:

where r is the real interest rate. The first-order conditions for the optimization problem are:

The Foundation of Modern Macroeconomics

In order to keep the model as simple as possible, we work with specific functional forms for the firm's production and adjustment cost functions, and the utility function of the representative union member. The adjustment cost function is quadratic (see (4.2)), i.e. (DO =Ii (1+ b/i ), and the production function is assumed to be CobbDouglas, i.e. Yt = 41g -a , with 0 < a < 1 and Yt representing output. By using these specific functions, (8.47)-(8.49) can be written as:

where ED 1/(1 - a), Lp is the firm's demand for labour in period t, and q is Tobin's q-ratio discussed extensively in Chapter 4. Equations (8.50)-(8.51) show that the elasticity of labour demand is constant. Equation (8.52) shows that investment is increasing in Tobin's q, which itself depends negatively on the exogenously given real rate of interest r and the real wage rate in the second period w2.

The monopoly trade union has the following lifetime utility function:

where p is the pure rate of time preference (see Chapter 6), and V (wt , Lt ) is the instantaneous utility of the union, that is defined as follows:

which indicates that membership of the union is fixed at N, and the unemployment benefit is constant over time. The optimal plan for the union consists of choosing w1 and w2 such that (8.54) is maximized given (8.55) and the labour demand functions (8.50)-(8.51). The necessary conditions for this optimization problem are:

Equation (8.56) has a form identical to the one obtained for the static case (see e.g. (8.8)). A point of tangency is found between a union's indifference curve and the labour demand curve. Assuming that the utility function of the representative

union member is logani, using (8.50) to yield:

1u(w - u(B) =

=

ED W1Uw(W1)

1 log WI = log B + — .

ED

Equation (8.57) is slightly chooses for the second pt., the wage in the second pet pared to the static case v- the second period is more I Specifically, we can easily d

1 U(w2) - UtEn

log w2 = log B + 1

ED - -

where 0 is defined as:

aLy aIiw2

aIi awe

=

Comparing the optimal it is clear that the wage is

wages in the second period The problem with the c, not believe that the union

impossible, the union %N firm when period 2 comL, the light of new informatio when period 2 comes dynamically inconsistent. Th will set the wage at w*, in I did believe the union, and

with w2 substituted (call ti the firm has invested a I, : labour according to (8.51) this demand for labour. and makes its decision ul.

Irk with specific functional mctions, and the utility func-

ent cost function is quadratic iction is assumed to be Cobb-

-n ting output. By using these

(8.50)

(8.51)

(8.52)

(8.53)

in period t, and q is Tobin's (8.50)-(8.51) show that the

!) shows that investment is r• on the exogenously given id period w2.

utility function:

(8.54)

r 6), and V(wt , Lt) is the lows:

(8.55)

, and the unemployment n consists of choosing w1 labour demand functions firm problem are:

(8.56)

(8.57)

Ni for the static case (see is indifference curve and )n of the representative

Chapter 8: Trade Unions and the Labour Market

union member is logarithmic (u(.) = log (.)) equation (8.56) can be rewritten by using (8.50) to yield:

ED

Equation (8.57) is slightly more involved. The union realizes that the wage that it chooses for the second period influences the firm's investment decision: the higher the wage in the second period, the lower the rate of investment by the firm. Compared to the static case with no investment, therefore, the demand for labour in the second period is more elastic, and the wage rate chosen by the union is lower. Specifically, we can easily derive that:

ED +

where is defined as:

Comparing the optimal wage rates in the two periods (as given in (8.58) and (8.59)), it is clear that the wage is lower in the second period, i.e. w*i > w2. By offering low

wages in the second period, the firm is encouraged to invest a lot.

The problem with the optimal union wage profile (WI , W2) is that the firm will not believe that the union will stick to it! Indeed, if a legally binding agreement is impossible, the union will not stick to the wage rate w2 it has announced to the firm when period 2 comes along. The reason is not that it has changed its mind in the light of new information, but rather that it faces a different incentive structure when period 2 comes along. In technical terms, the optimal policy for the union is

The reason why the firm does not believe that the union will set the wage at W2 in period 2 is easy to demonstrate. Suppose that the firm

did believe the union, and decided its investment plans according to (8.52)-(8.53)

with w2 substituted (call this investment level At the beginning of period 2, the firm has invested a lot and has a total capital stock of K1 + I;, and demands

labour according to (8.51) with K1 + Ii substituted. The union, however, observes this demand for labour, knows that the capital stock cannot be shifted any more, and makes its decision on the optimal wage in the second period on the basis of the

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The Foundation of Modern Macroeconomics demand curve:

which is iso-elastic with wage elasticity ED (in absolute terms), so that the union sets the wage in the second period at the same level as in the first period, i.e. i'2 = wl > 14/2. The firms knows this, and hence is not going to believe the union if it announces w2.

So what is the solution to this conundrum? Although a more complete treatment will have to wait until Chapter 10, common sense suggests a solution for our present problem. The firm knows that it is going to get ripped off in the second period "come

hell or high water". Hence, it expects to be charged the wage rate 14/ = WI' in both periods (t = 1, 2), and bases its investment decision on this knowledge. Indeed, this assumption on the part of the firm is consistent with the actual behaviour of the

union. For that reason, the wage profile (14/, wD is called the time-consistent policy of the union. But, since Ma > W2 (and thus 1,6 > wD, and investment depends negatively on the wage rate in the second period, the firm will also invest less under the consistent wage profile (14/ . , wD than under the inconsistent wage profile vq). Hence, the effect of a union that is unable to stick to its promises is to stifle

investment.

8.6 Punchlines

In this chapter the three most important models of trade union behaviour have been studied, namely the monopoly union model, the right-to-manage model, and the efficient bargaining model. The objective function of the union is the expected (or average) utility of the union's members. In most of the discussion we assume that the number of union members is fixed.

In the monopoly union model, the union unilaterally picks a wage rate such that union utility is maximized subject to the proviso that the solution lies on the labour demand curve. The union thus acts as the monopolistic seller of labour exploiting the downward-sloping labour demand curve of the firm. The optimal wage choice of the union can be represented as a simple markup expression involving unemployment benefit and the elasticity of the labour demand function. The union's choice implies that both the wage and the unemployment rate are above their respective competitive levels. Productivity shocks typically lead only to employment changes so that the model is consistent with real wage rigidity. (The proviso must be made because a union which is fully employed is only interested in higher wages so that positive productivity shocks do not translate into employment expansions.)

In the right-to-manage model, the firm is still allowed to decide on employment but the wage is the outcome of a bargaining process between the union and the firm.

Using the concept of gt written in a markup elasticity an addition& bargaining strength of t is that it contains the special (extreme) cases. that it is Pareto int : the bargaining strictly 1

The efficient bargaini the union bargain ON of this bargaining pros When combined wit.. the model predicts a u employment are h profits into jobs. going to labour, is bat moves closer to the c

In the remainder of ious union models. I labour market is that ii ployment rate. We brit as the degree of cent: tant institution. Some either many very small the intermediate case. 1 ment rate but intermec harm, large nation-%% the outcomes of excess do not take into acct. ..

macroeconomy. Another stylized fac

high degree of persist, . membership rule of tr ing hysteresis. If the then strict hysteresis a' ing process, via the r predicts a high degree As a final applicatic union on the invest:

firm investment becau to offer low wages in t not credible to the fir renege on its promise

(8.61)

c terms), so that the union -. the first period, i.e. li/2 = 1g to believe the union if it

a more complete treatment zis a solution for our present the second period "come wage rate 14/' = wl in both his knowledge. Indeed, this c actual behaviour of the

d the time-consistent policy and investment depends e firm will also invest less ie inconsistent wage profile ck to its promises is to stifle

union behaviour have ght-to-manage model, and the union is the expected the discussion we assume

ks a wage rate such that solution lies on the labour

.11er of labour exploiting he optimal wage choice of -)n involving unemploy- - ion. The union's choice are above their respective to employment changes he proviso must be made d in higher wages so that

ent expansions.)

o decide on employment n the union and the firm.

Chapter 8: Trade Unions and the Labour Market

Using the concept of generalized Nash bargaining, the resulting wage can again be written in a markup format. In addition to unemployment benefit and demand elasticity an additional component entering the markup solution is the relative bargaining strength of the union. An attractive feature of the right-to-manage model is that it contains the monopoly union solution and the competitive solution as special (extreme) cases. An unattractive feature of the right-to-manage solution is that it is Pareto inefficient, i.e. it is possible to make one of the parties involved in the bargaining strictly better off without making the other party worse off.

The efficient bargaining model solves this problem by assuming that the firm and the union bargain over both the wage and the employment level. The outcome of this bargaining process is a range of efficient wage-employment combinations. When combined with a "fair share" rule, dividing output over the two parties, the model predicts a unique wage-employment solution. Interestingly, wage and employment are higher than under the competitive solution as the union turns profits into jobs. Wage moderation, consisting of a smaller share of the output going to labour, is bad for employment because the wage-employment solution

moves closer to the competitive solution.

In the remainder of this chapter we show a number of applications of the various union models. In Chapter 7 we saw that one of the stylized facts about the labour market is that institutions may be an important determinant of the unemployment rate. We briefly discuss the hypothesis that corporatism, loosely defined as the degree of centralization of the wage-setting process, may be such an important institution. Some authors have claimed that unemployment is low if there are either many very small or few very large unions but that unemployment is high in the intermediate case. Hence, high or low corporatism both lead to a low unemployment rate but intermediate corporatism does not. Intuitively, small unions do little harm, large nation-wide unions practise wage moderation because they internalize the outcomes of excessive wage claims, but middle-sized unions are both strong yet do not take into account all the adverse consequences of their wage claims on the

macroeconomy.

Another stylized fact that can be explained with the aid of a union model is the high degree of persistence in the unemployment rate (the near-hysteresis effect). The membership rule of the union turns out to form a key model ingredient explaining hysteresis. If the unemployed union insiders become outsiders the next period, then strict hysteresis applies. If the outsiders are allotted a role in the wage bargaining process, via the reservation wage, then the model becomes more realistic and

predicts a high degree of persistence.

As a final application of the union model, we study the effects of a monopoly union on the investment plans of firms. It turns out that unions may be bad for firm investment because of the hold-up problem. The optimal choice of the union is to offer low wages in the future in order to induce the firm to invest a lot. This offer is not credible to the firm, however, because once the firm has invested the union will renege on its promise and demand higher wages. Intuitively, the union "holds up"

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The Foundation of Modern Macroeconomics

(as in a Western movie) the firm's capital stock. The firm will formulate its optimal investment and production plans in the full knowledge that it will be held up in the future and will therefore invest less than it would otherwise have done. This is the famous underinvestment result. The scenario sketched is an example of the dynamic inconsistency which arises is many different settings in macroeconomics. In Chapter 10 we return to this important issue.

Further Reading

On the interaction between union wage setting and firm investment, see Grout (1984), van der Ploeg (1987b), Anderson and Devereux (1988), and Devereux and Lockwood (1991). Gottfries and Horn (1987) present a union-based model of unemployment persistence. Lindbeck and Snower (1988) is a good reference to the insider-outsider literature. Manning (1987) embeds the union model in a sequential bargaining framework. Koskela and Vilmunen (1996) study the effects of income taxes in a union model. For good surveys of the union literature, see Oswald (1982, 1985), Farber (1986), Pencavel (1991), and Booth (1995). See Cross (1988) for an interesting collection of articles on hysteresis.

Search in

The purpose of this chap

1.How can we expla,, of search in the lab

2.How does taxatioi,

the equilibrium un

3.How can the sea unemployment r.

9.1Search in the

The labour market in rr ers leaving a job and er US the flow of workers (Blanchard and Diamon mous flows, due to the s are bound to cause prof versa. At a macroecona labour market is relat.. Chapter 7, US unempk theory of search beha\ this matching process 1 cally different from the notion of an aggregate explains, rather than as! and jobs are brought tt process which stochasti in a pair-wise fashion. 1

m will formulate its optimal dge that it will be held up in

'1 otherwise have done. This iketched is an example of the settings in macroeconomics.

Grout (1984), and Devereux and Lockwood model of unemployment

D the insider-outsider literature. bargaining framework. Koskela union model. For good surveys z Pencavel (1991), and Booth

es on hysteresis.

Search in the Labour Market

The purpose of this chapter is to discuss the following issues:

1.How can we explain the duration of unemployment? We introduce a simple model of search in the labour market.

2.How does taxation affect the equilibrium unemployment rate? How can we reduce the equilibrium unemployment rate?

3.How can the search-theoretic approach explain observed persistence in the unemployment rate?

9.1Search in the Labour Market

The labour market in many countries is characterized by huge gross flows of workers leaving a job and entering unemployment and vice versa. For example, for the US the flow of workers entering or leaving a job amounts to 7 million per month (Blanchard and Diamond, 1989, p. 1)! It would be tempting to argue that these enormous flows, due to the simultaneous occurrence of job creation and job destruction, are bound to cause problems. There are a lot of workers looking for jobs, and vice versa. At a macroeconomic level, however, it appears that (at least in the US) the labour market is relatively efficient at matching jobs and workers. As we saw in Chapter 7, US unemployment seems to be relatively low and stable. The modern theory of search behaviour in the labour market is specifically aimed at describing this matching process that takes place in the labour market. This theory is radically different from the previous labour market theories discussed so far in that the notion of an aggregate labour market is abandoned. As Diamond (1982, p. 217) explains, rather than assuming that the market is the mechanism by which workers and jobs are brought together, the modern approach assumes that there is a search process which stochastically brings together unemployed workers and vacant jobs in a pair-wise fashion. This search process takes time and consequently causes loss

The Foundation of Modern Macroeconomics

of output. When a worker and a job meet each other, negotiations take place to determine the wage.

9.1.1 A simple models

The modern theory of search makes use of the so-called This is a hypothetical concept, not unlike the production function, which turns out to be very convenient analytically. A matching function determines the number of jobs that are created ("matches") each instant, as a function of the number of unemployed job-seeking workers and the number of vacancies that exist (plus exogenous variables). Firms have jobs that are either filled or vacant. It is assumed that only vacant jobs are on offer. The firm is not searching for workers to replace existing (but unsatisfactory) workers. Workers either have a job or are unemployed, and only the unemployed engage in search. There is no on-the-job search in the model discussed in this section. By making these assumptions, the two activities of production of goods and trade in labour are strictly separate activities.

Firms and workers know the job-matching technology, and know that there is an exogenously given job separation process. 2 At each moment in time, a proportion of the existing filled jobs are destroyed, say because of firm-specific shocks making previously lucrative jobs unprofitable. In equilibrium, there is thus a constant inflow into unemployment, and the model predicts an that is strictly greater than zero.

It is assumed that there are many firms and many workers, and that every agent behaves as a perfect competitor. The fixed labour force consists of N workers, and each worker who has a job supplies one unit of labour. (There is no decision on hours of work by the worker, and effort of each worker is constant.) The unemployment rate is defined as the fraction of the labour force without a job, and is denoted by U. The vacancy rate is the number of vacancies expressed as a proportion of the labour force, and is denoted by V. Hence, at each moment in time, there are UN unemployed workers and VN vacant jobs "trying to find each other".

The number of successful matches each instant in time depends on according to the matching function:

XN = G(UN , VN), (9.1)

where XN is the total number of matches, so that X is the matching rate, and G(., .) is a linearly homogeneous function, with Gu > 0, Gv > 0, Guu < 0, Gvv < 0, and Guu Gvv –GUS > 0. The intuitive idea behind (9.1) is that at each instant XN

1 The exposition given in this section closely follows Pissarides (1990, ch. 1).

2 Mortensen and Pissarides (1994) and Pissarides (2000, ch. 2) develop a matching model with an endogenous job destruction rate.

a

meetings occur bets% Which particular w, Consider a small matches and VN vacan dt equals (XN/ VN,.,:.

write q as:

q = G(UN, VN) VN

where 8 V /U is the v analysis. Obviously, sh

filled in the time in to7 of a vacancy being fille these results are deriN

In view of the assun function can be demon

dq Gu d0 = 02 <

and

dq G, 77(0) 0 — =

q dO 6q

where ri(0) is the absol Unemployed workers instantaneous probabi' number of vacancies ex This instantaneous prob

G(UN, VN)

UN

The f (8) function has th

df r

f(e) do = q(a) e‘"

Since f (0) represents t, ing a job, the expected di intuitive, since unemi _ a shorter duration of un vacancies. The defini

3 The trick is to write (9.1)

(q0) =- 1 — Gv lq, whichisl