The case for a populist Central Banker

*Corresponding author. Tel.: 212 998-8907; fax: 212 995-3932.E-mail address: [email protected] (A. Velasco)

European Economic Review 43 (1999) 1317}1344

The case for a populist Central Banker

Vincenzo Guzzo!, AndreH s Velasco!,",*!Department of Economics, New York University, 269 Mercer Street, New York, NY 10003, USA

"NBER, Cambridge, MA 02138, USA

Abstract

We present a general equilibrium optimizing model in which we study the joint e!ectsof centralization of wage setting and central bank conservatism on economic perfor-mance. Several striking conclusions emerge. In relatively centralized labor marketsemployment and output are decreasing, and in#ation is intially increasing and thendecreasing, in the degree of central bank conservatism. A radical-populist central bankerwho cares not at all about in#ation (alternatively, who is not conservative) maximizessocial welfare. Economic performance is not U-shaped in the degree of centralization ofthe labor market, in contrast to conventional wisdom. ( 1999 Elsevier Science B.V. Allrights reserved.

JEL classixcation: E5; J5

Keywords: Central bank conservatism; Centralization of wage setting; Credibility; In#ation; Unem-ployment

1. Introduction

Two conjectures have become part of the conventional wisdom.The "rst is that greater central bank conservatism (CBC, de"ned as a greater

weight placed by the Central Bank on an in#ation as opposed to an employmentobjective) reduces average in#ation rates while leaving average real activity

0014-2921/99/$ } see front matter ( 1999 Elsevier Science B.V. All rights reserved.PII: S 0 0 1 4 - 2 9 2 1 ( 9 8 ) 0 0 1 2 7 - 5

1Notice that this de"nition of CBC makes it operationally equivalent to having a conservativebut non-precommiting central banker, as suggested by Rogo! (1985b).

2Part of the issue is what is being measured (Bruno}Sachs focus on &corporatism' in the labormarket, while Calmfors}Dri$ll focus on &centralization'), and how to measure it.

una!ected.1 In particular, greater CBC enables countries to overcome thein#ation bias "rst stressed by Kydland and Prescott (1977) and Barro andGordon (1983). Relevant work is also provided by Schaling (1995). Evidence forthe e!ect of CBC on in#ation is presented by Grilli et al. (1991), among others.Alesina and Summers (1993) provide some evidence that CBC has no impact onreal activity; Hall and Franzese (1996) are less certain. The issue awaits moredetailed statistical analysis.

The second bit of conventional wisdom is that economic performanceis U-shaped in the degree of centralization of wage setting (CWS, de"ned asthe number of independent units that participate in wage bargaining or wagesetting). This notion is derived from the work of Bruno and Sachs (1985)and Calmfors and Dri$ll (1988), who argued that in highly decentralizedlabor markets unions have no monopoly power, while in highly centralizedmarkets monopoly unions internalize the e!ects of their actions and hencemoderate their wage claims; with an intermediate number of unions neither ofthese bene"cial e!ects takes place, and economic performance is presumably atits worst. Both Bruno and Sachs (1985) and Calmfors and Dri$ll (1988) marshalsome evidence but again, the issue is not fully settled empirically.2

This paper o!ers a general equilibrium model, largely built up from micro-foundations, in which neither of these tenets of conventional wisdom holds true.The key insights come from studying the e!ects of CBC and CWS jointly.Indeed, we "nd that once one takes into account the interaction between centralbank conservatism and labor market centralization, many of the standardresults concerning the e!ects on economic performance of CBC and CWSconsidered separately no longer hold.

CBC and CWS are seldom discussed together, although conceptually theynaturally should be. The e!ects of CBC depend on the extent of an in#ation biasunder discretion, which in turn must depend (among other things) on thestructure of the labor market and the distortions present there. Conversely, thee!ects of monopoly power in the labor market on nominal and real variablesmust necessarily depend on the rules governing monetary policy } in particular,how accommodating the central bank is. Empirically, this suggests that whentrying to measure the e!ects of CBC one should control for the degree of CWS,and vice versa.

For a #avor of the basic arguments (more detailed results follow), considera standard monetary policy game in the spirit of Barro and Gordon (1983), butwith two twists:

V. Guzzo, A. Velasco / European Economic Review 43 (1999) 1317}13441318

3For simplicity assume that each union's brand of labor is an imperfect substitute for the labor ofothers, and that unions are symmetric in that they are of the same size and their labor supply enterssymmetrically in the production function of the representative "rm. Notice that, while we willassume imperfect substitutability among labor types, this is not a monopolistic competition model.In such a model unions are small in that they neglect the e!ect of their actions on aggregateoutcomes. Here, by contrast, we will assume a situation where the number of unions is small enoughthat they internalize, at least partially, the aggregate e!ects of their individual actions.

4One might think that low CBC lead to strong indexation mechanisms and hence to high wages.This channel is not active here because the unions care about in#ation and internalize theconsequences of higher claims. But alternative formulations could endogenize the degree of indexa-tion and give it a role.

(a) Wage setters are not atomistic; instead, they are organized in unions.These unions set nominal wages on behalf of their membership.3

(b) Unions dislike in#ation, unlike the standard story in which they care onlyabout the expected real wage.

In this context, and for an exogenously "xed price level, it should be clear thatthe outcome of the game among the unions should be Pareto ine$cient, witha real wage that is too high and employment and output that are too low relativeto the "rst best.

Introduce now a central bank that controls the price level (or the rate ofin#ation, it does not matter which) and that moves after unions have set theirnominal wages for the relevant time period. Such a central bank will be temptedto act opportunistically and de#ate the real value of set wages to the extent thatit cares about employment and output. In the standard model, wage settersanticipate this temptation, so that in equilibrium you get positive in#ation withno change in the ine$ciently low employment level.

So far nothing is new. But consider now the e!ects of having non-atomisticwage setters. When deciding upon its desired wage markup, each union willunderstand that, the higher the average markup and the lower the level ofemployment, the greater the in#ationary temptation faced by the central bank,and the higher the equilibrium in#ation rate. Hence, this concern for theresulting in#ation may lead unions (which move before the central bank, and aretherefore Stackelberg leaders vis-a-vis the monetary authority) to moderatetheir real wage claims. And notice: The less conservative (more populist) thecentral bank is, the greater the in#ationary cost of high wage markups, andhence the lower the markups may be in equilibrium.4

From the theoretical point of view, this last result follows from the fact thatthere are two games being played simultaneously: One among the unions andone between the unions as a whole and the central bank. Even if the central bankprecommits in its own game (which is what having greater CBC is equivalent toin this setting } see below), the outcome is not necessarily improved since

V. Guzzo, A. Velasco / European Economic Review 43 (1999) 1317}1344 1319

opportunistic behavior can still occur in the other game. This is also thereasoning behind Rogo!'s (1985a) result that international monetary coordina-tion can be counterproductive. The result can also be viewed as an example ofthe theory of the second best. Introducing a second distortion (opportunisticcentral bank behavior) into an economy already distorted by monopolisticbehavior in the labor market can be welfare improving.

More speci"cally, the model below has the following implications for therelationship among CBC, CWS and macroeconomic performance.

1. The conventional wisdom that discretionary policymaking yields an in#a-tion bias while leaving employment and output at suboptimal levels, relies ontwo special assumptions:

(a) unions are myopic (they do not internalize the consequences of theiractions);

(b) unions su!er no costs from in#ation.If either of those is adopted, our model yields precisely the standard

results.2. For a "xed number of unions, a radical-populist central banker, who

cares not at all about the costs of in#ation, maximizes the welfare of thepopulation by delivering zero in#ation and optimal employment and outputlevels.

3. For a "xed number of unions, employment and output fall as CBCincreases. This occurs because each union realizes that the in#ationary conse-quences of raising its wage fall as CBC rises, and hence engage in moreaggressive wage-setting in equilibrium.

4. For a "xed number of unions, in#ation is inverted-U-shaped in the degreeof CBC. This is because higher CBC enlarges the in#ation bias (as we saw in (3)above), but also the central bank's determination to "ght this bias.

5. For a "xed and su$ciently large number of unions, a moderately con-servative central bank delivers the lowest welfare levels. This follows directlyfrom (3) and (4) above: A little bit of CBC increases in#ation while reducingemployment; it takes a lot of CBC for in#ation to fall, and hence for welfare toincrease.

6. For a given level of CBC, if the elasticity of substitution among di!erenttypes of labor is su$ciently small, then economic performance and welfare areuniformly decreasing in the number of unions. For larger values of this elasticity,economic performance and welfare are hump-shaped in the number of unions(which we take as a proxy for the degree of decentralization of wage setting), andthere is an intermediate degree of decentralization that maximizes economicperformance and welfare.

Some discussion of the previous theoretical literature, and how our workdi!ers from it, is warranted. The links among CBC, the structure of the labormarket and economic performance have been analyzed formally before. Thepaper by al Nowaihi and Levine (1994) was the "rst to study the behavior of


a single union that does care about in#ation, but did not tackle the issuesstudied here. Cubitt (1995) considers a monetary policy game between a centralbank and a single union; thus, he cannot explore the implications of varyingdegrees of CWS. Bleaney (1996) does incorporate a variable number of unions,but they are assumed not to care about in#ation. In none of these models can theconnection among di!erent degrees of CBC, labor market centralization andeconomic performance be properly studied. Finally, Gruner and Hefeker (1999)study the e!ects of EMU in a setup with many countries, each of which containsone union which cares about in#ation; the model in that paper could potentiallyyield results similar to ours concerning the role of CBC, but the focus there isentirely di!erent.

The closest paper in the literature is the recent one by Cukierman and Lippi(1999), which was written simultaneously with this one. They also considera monetary policy game with many unions, and study the interactionamong labor market centralization, and economic performance. The maindi!erence is that they use the demand for labor facing the individual unionas a primitive building block of the model with the crucial assumption thatthe elasticity of substitution among the labor supplied by di!erent unions isalways increasing in the number of unions, and goes to in"nity as the numberof unions goes to in"nity. By contrast, we use the production function asthe primitive and work with a fully micro-founded model which yields verydi!erent implications for the relationship between the number of unions andthe elasticity of labor demand. These modelling di!erences matter a great dealin terms of results. For a su$ciently high level of unions' in#ationaversion, Cukierman and Lippi (1999) reproduce the conventional wisdomthat economic performance is U-shaped in the number of unions, andtherefore an intermediate degree labor market centralization is worst. Forlow levels of in#ation aversion they "nd that economic performance andcentralization are monotonically and negatively related. We "nd that,depending on parameter values, the opposite results obtain: Economic perfor-mance is either always increasing or U-shaped in degree of centralization;in the latter case, an intermediate degree labor market centralization isbest.

Empirically, there is some preliminary evidence for some of the interactionsamong CBC, CWS and economic performance that we predict here. Forinstance, Hall and Franzese (1996) "nd that in economies with a highly decen-tralized labor market higher CBC increases unemployment. Bleaney (1996) "ndshigher that average in#ation is (weakly) associated with higher CWS, even aftercontrolling for CBC.

The paper is organized as follows. Section 2 presents the basic model, andSection 3 computes the equilibrium of the relevant game. Section 4 examines theimplications of the equilibrium for government policy and the optimal structureof the labor market, while Section 5 concludes.


5Alternatively, we may assume the technology to be Cobb}Douglas in aggregate labor andcapital, with the labor share equal to a and capital constant and normalized to one.

2. The underlying economy

The economy is populated by a single representative "rm that produces thesingle consumption good, and a continuum of symmetric workers (indexed byi and arranged in the unit interval) who supply labor, receive dividends from the"rm, and consume. Workers are organized in n52 unions (indexed by j ), eachof which has a set of members of measure n~1 on whose behalf it sets wages.There is also a government, which sets the rate of in#ation and hence a!ects realwages.

2.1. The xrm

The representative "rm produces output using labor from the di!erentworkers. The "rm behaves competitively, taking wages as given. Its technologyis given by

>"AP1

0

¸(p~1)@pi

diBap@(p~1)

, 04a41, p'1, (2.1)

where > is the representative "rm's output and ¸iis labor input from worker

i. The number of unions n is going to have an e!ect on production throughits e!ect on the distribution of real wages. The parameter p is the elasticityof substitution among the di!erent types of labor supplied by workers, and ais a returns to scale parameter.5 Notice that if all ¸

iare the same, then

>"¸ai.

The "rm maximizes pro"ts

D">!P1

0

=i¸

idi (2.2)

subject to (2.1), taking wages as given. The solution of this problem consists "rstof a demand function for each labor type

¸i

¸

"A=

i=B

~p(2.3)

where

="AP1

0

=1~pi

diB1@(1~p)

(2.4)


6 In#ation aversion is introduced directly, but it would not be hard to derive it from primitives ifmoney entered the utility function or were held for shopping-technology purposes. In those casesindividual welfare would always be decreasing in expected in#ation. It would also be decreasing inrealized in#ation if in#ation tax revenues were not rebated.

7Notice that L;i/L¸

i"!c log¸

i/¸

i(0 if ¸

i'1, and L2;

i/L¸2

i"!c(1!log ¸

i)(0 if ¸

i(e.

Hence, the function has the standard shape if 1(¸i(e. This is true in all equilibria below as long

as c'a.

and

¸,

:10¸i=

idi

=. (2.5)

Notice from (2.4) that if all =iare the same, then="=

i. Expression (2.3) in

that case implies ¸"¸i, which is perfectly intuitive.

The second rule for the "rm is the supply function

>"A=

a B~a@(1~a)

(2.6)

so that output is naturally decreasing in the aggregate real wage.Finally, the "rm distributes pro"ts evenly among its owners (all of the

workers). Hence, if Di

are the dividends paid by the "rm to worker i, inequilibrium we have

Di"D. (2.7)

2.2. The workers

Each of the workers has the utility function

;i"log C

i!

c2

(log ¸i)2!

b12

n2, c'0, b150, (2.8)

where Ciis consumption by worker i, and c and b

1are preference parameters.6

For technical convenience we shall assume c'a.7 Note that since there are onlyworkers in this economy, then (2.8) is the social welfare function, which can beused to evaluate the desirability of alternative policies and of alternative monet-ary arrangements.

The representative worker's budget constraint is

Ci"=

i¸i#D

i. (2.9)


8By contrast, when we introduce a government below, it will internalize the e!ect of Dion the

welfare of union i. The di!erence, of course, is that a government takes account of all economy-wideinteractions. This di!erence will give rise to a strategic interaction between government and unionseven in that case in which the government aims to maximize the union's welfare.

9We can do this without loss of generality because the level of inherited real wages, whether at theindividual or aggregate level, in no way a!ects the equilibrium. This is because changing nominalwages is costless, so for any given previous real wage and expected in#ation, unions always attaintheir target real wage.

Throughout, each worker (and the union that represents her, no matter howlarge) takes D

ias given. Aside from monopoly power, this will be the other key

distortion present in the model.8

2.3. The unions

Each union j is assumed to represent the workers that lie contiguously in theinterval ( j!n~1, j ). The representative union is benevolent, in that it maximizesthe utility of its members:

<j"nP

j

j~n~1

;idi. (2.10)

The union targets the same real wage=ifor each of its members in order to

maximize this objective function (since members' preferences, the way theirlabor enters into the "rm's technology, and the weight the union places on theirwelfare are all symmetric, it is optimal for the wage to be the same for allmembers). To try to achieve the desired real wage, the union sets the rate ofincrease of the nominal wages of its members at the start of every period, andcannot alter it later when the rate of increase of the price level becomes known.The real wage for worker i is given by

=i"

1#ui

1#n(2.11)

where n and uiare the percent increases in the price level and the nominal wage

of the union to which worker i belongs and where we have normalized theinherited real wage of worker i to unity.9

Since it enjoys some monopoly power, the union must take into account thedependence of labor demand on this wage. In doing so, it takes the nominalwages set by other unions as given. That is to say, we will compute theequilibrium to a game of Bertrand competition among the n unions, all of whichinteract strategically with the government.


Key in the solution of the unions' problem is the elasticity of demand for thelabor of each worker i as perceived by the union. The appendix shows thiselasticity is

L¸i

L=i

=i

¸i

"!p#Cp (1!a)!1

(1!a) DAL=L=

i

=i=B

"!p#Cp (1!a)!1

(1!a) D n~1A=

i=B

1~p. (2.12)

If we impose symmetry so that all=iare the same, we see from (2.4) that this

implies=i/="1. Hence, in symmetric equilibrium the elasticity is

L¸i

L=i

=i

¸i

"!t, t,p#C1!p(1!a)

(1!a)n D . (2.13)

Notice that the number n of unions enters when considering the e!ect changesin an individual wage have on the aggregate wage level=. A key feature of ourmodel is that each union takes into account the e!ect that its actions have onaggregates, and the larger the union the stronger is this e!ect. If nPR, tPp,which is intuitive: If there are in"nitely many unions, the weight of each isarbitrarily small and the impact of the actions of each is negligible, and we areback in the case of standard monopolistic competition in which each uniontakes the aggregates as given.

One can think of t as an indicator of the degree of competitiveness in thelabor market: The larger t, the more elastic the demand for each union's labor,and the smaller its monopoly power. It is often asserted (Calmfors and Dri$ll,1988) that competition in the labor market is increasing in the number of unions.In this context that may or may not be the case. The source of this ambiguitybecomes clear from rewriting (2.3) (see details of how to do this in theappendix) as

¸i"a1@(1~a)=~p

i=(p(1~a)~1)@(1~a) . (2.14)

The e!ect of the aggregate wage rate = on the individual labor demand isambiguous, and depends on the sign of the expression (p (1!a)!1)/(1!a).Increasing=, ceteris paribus, reduces the relative wage=

i/=, which increases

labor demand for type i, but also increases aggregate real wages, reducesaggregate output and labor demand, and hence reduces demand for labor oftype i. If the expression (p (1!a)!1)/(1!a) is positive (that is, if p (1!a)'1),then the relative wage e!ect dominates, and demand for labor of type i isincreasing in=. In that case, competitiveness in the labor market is enhancedby a larger number of unions, so that each has a limited in#uence on theaggregate wage and cannot attempt freely to manipulate it in order to increasedemand for its own labor. Henceforth we label the e!ect of n on t the


10Notice, however, that p (1!a)'1 is also the case where t(p, so that permitting unions tointernalize the aggregate consequences of their actions actually leads them to seek higher wages thanthey would in the standard monopolistic competition case.

11Once again, this can be done without loss of generality, for reasons explained above.

&competition e!ect.' If p (1!a)'1, so that Lt/Ln'0, then a higher number ofunions enhances competition, and vice versa.10

2.4. The government

The objective function of the government is

J"P1

0Clog C

i!

c2

(log ¸i)2D di!

b'

2n2. (2.15)

Notice that the government is benevolent } in that it maximizes that portion ofthe workers welfare function that is unrelated to in#ation } but its weight onin#ation may di!er from that of the workers. Of course, the case in which thegovernment is fully benevolent, so that b

'"b

1, is just a special case of our

analysis.The government maximizes (2.15) by setting the rate of price in#ation every

period. In doing so, it a!ects the level of the aggregate real wage, whose timepath is given by

="(1#u)/(1#n) (2.16)

where n and u are again the percent increases in the price level and the nominalwage and where we have normalized the inherited real wage to unity.11

3. Solving the game

We are now in a position to compute the equilibrium to the game among then unions and the government. The timing of moves is as follows. Unions move"rst, setting the rate of nominal wage growth u

ifor each worker i in each union

j. The government moves next, setting the rate of price increase n. Given thesetwo moves and the inherited prior individual real wages and aggregate realwage, (2.11) and (2.16) give the contemporary real wages=

iand=. Finally, the

"rm sets employment and output by moving along its labor demand curve.Notice that this timing leaves the government free to move after the unions,

with no precommitment of any kind. Hence, in the jargon of monetarypolicy games, we are computing an equilibrium in which policy is set in a&discretionary' fashion.


We solve the stage game backwards. Since the government moves last,consider its problem "rst. It maximizes (2.15) subject to the technology (2.1), the"rm's optimality conditions (2.3) and (2.6), the dividend rule (2.7), and the wagelaws of motion (2.11) and (2.16). The appendix shows the resulting policy rule is

n"a!c:1

0log ¸

idi

(1!a)b'

(3.1)

so that the government trades o! at the margin the costs and bene"ts ofemployment and in#ation.

Turn now to the problem faced by the representative union, which movesbefore the government. The representative union takes into account the just-computed solution to the government's problem. It maximizes (2.10) withrespect to u

i, subject to (2.9), (2.12), (2.11), and (3.1), taking the actions of the

remaining unions as given. The appendix shows that the solution of thisproblem implies the "rst-order condition (C.5), which in symmetric equilibriumbecomes the policy rule

n"CaA1!t

tc B#log ¸D Cn(1!a)b

'b1

D (3.2)

where the condition ¸"¸iholds. The union also trades o! bene"ts and costs,

including those of in#ation.Finally, in symmetric equilibrium the government policy rule (3.1) becomes

n"a!clog ¸

i(1!a)b

'

(3.3)

where again we have ¸"¸i. Combining the rules of government (3.3) and union

(3.2) we obtain the equilibrium level of employment for the representative unionand for the economy as a whole:

log ¸"AacB/ (3.4)

where

0(/,

(t!1)n (1!a)2b2'#tb

1c

tn (1!a)2b2'#tb

1c

41.

In turn, (3.4) implies

log>"Aa2c B/ (3.5)

and

n"Aa

1!aBA1!/

b'B . (3.6)


12On the contrary, if b1PR (in#ation is very costly for the union), / converges to one, the

employment and output levels converge on the "rst best, while in#ation goes to zero in equilibrium.

It is straightforward to compute that the welfare level under discretion is

;i"A

1

2BAa2c BC/(2!/)!

b1c(1!/)2

(1!a)2b2'D (3.7)

which, and for a given b1

and b', is maximized at /"1. That is to say,

parameter settings for which /(1 yield sub-optimal welfare levels.

4. Implications for Central Bank policy and labor market centralization

The discretionary equilibrium just computed has several striking implica-tions. We explore them in this section.

4.1. Standard results as a special case

The model embeds the standard results in the Kydland and Prescott (1977)and Barro and Gordon (1983) tradition as a special case. This happens in one oftwo parameter limits. First, if b

1P0 (agents and the unions that represent them

are indi!erent to in#ation, as in the original Kydland}Prescott}Barro}Gordonformulation), /P((t!1)/t)(1, and employment and output are equal tosuboptimal levels. In#ation is positive and equal to

n"Aa

1!aBA1

tb'B'0,

which indicates an in#ation bias. This is the standard result in the literature onthe time inconsistency of monetary policies.12

Second, if nPR, so that the actions of each union have negligible e!ects onaggregates, then /P((p!1)/p), and employment and output go to their stan-dard monopolistic competition levels. We again have an in#ation bias, given by

n"Aa

1!aBA1

pb'B'0.

We therefore have

Result 1. The conventional wisdom that discretionary policymaking by the CentralBank yields an inyation bias, while leaving employment and output at suboptimallevels, relies on two special assumptions.


(a) Unions are small and therefore do not internalize the aggregate consequencesof their actions.

(b) Agents and the unions that represent them suwer no costs from inyation.If either of those is adopted, our model yields precisely the standard results.

Without either of these assumptions, on the other hand, the features of theequilibrium are very di!erent from the conventional wisdom, as we see next.

4.2. Making the Central Bank more conservative

The parameter b'is the weight that the Central Bank places on in#ation. If

b'is large, then the central banker is, in Rogo! 's (1985b) terminology, conserva-

tive (it is more conservative than the population when b''b

1, of course).

Alternatively, the size of b'could be interpreted as an indicator of Central Bank

independence, with more independent monetary authorities having a larger b'.

In the limit as b'PR, the Central Banker cares only about in#ation. Since we

know that in this case no time inconsistency issues can arise (technically, theprecommitment and discretion solutions coincide), then the case of b

'PR can

be thought of as capturing the case of perfect Central Bank precommitment andtherefore perfect independence. We will stick to the interpretation of b

'as an

index of Central Bank conservatism, but the reader should keep in mind that (atleast in the limit) it also captures the degree of Central Bank independence.

How do employment, output and in#ation levels depend on how conservativeor populist the Central Bank is? We explore these questions holding the numbern of unions constant.

Notice "rst that if b'is zero (in#ation is not costly for the government), /P1

and the employment and output levels converge on the "rst best, namelylog ¸"a/c and log >"a2/c. The reason is that in this case the government willimplement any rate of in#ation necessary to take output to its "rst best level,regardless of what nominal wage increases unions have obtained. Understand-ing this, unions realize that nominal wage gains provide no bene"t, and simplyplace the nominal wage at a level such that the "rst best aggregate real wage canbe attained with no in#ationary costs. Hence, in equilibrium, in#ation is zero.Finally, it is easy to check that if b

'is zero we have ;

i"a2/2c, which is its "rst

best level. We therefore have:

Result 2. For a xxed number n of unions, a radical-populist Central Banker, whocares not at all about the costs of inyation, maximizes the welfare of the populationby delivering zero inyation and optimal employment and output levels.

As b'rises, output and employment fall, since they are both increasing in /,

and L//Lb'(0 unambiguously. The intuition, as before, is that unions under-

stand that a Central Bank that is concerned about in#ation will not necessarily


erode their wage gains, and hence have an incentive to seek higher wages. Inequilibrium their conjecture turns out to be true, real wages are higher, andemployment and output are lower. Hence,

Result 3. For a xxed number n of unions, employment and output fall as the CentralBank becomes more conservative.

The behavior of equilibrium in#ation as b'rises is very interesting. As we just

saw, output falls with b', and this creates an incentive for the Central Bank to try

to raise it via higher in#ation (algebraically, this is re#ected in the numerator of(3.6), which is decreasing in /, and hence increasing in b

'). At the same time,

a higher b'

makes in#ation costlier for the authorities, which pushes in#ationdown (this is re#ected in the denominator of (3.6), which is increasing in b

').

Hence, the relationship between b'and equilibrium in#ation is non-monotonic.

In#ation rises as b'increases from a low level (while holding b

1constant), but

falls eventually. The appendix proves that:

Result 4. For a xxed number n of unions, inyation is hump-shaped in the degree ofCentral Bank conservatism, and a moderate Central Banker (one that is neitherstrongly conservative nor strongly populist), with preferences given by

bH'"S

cb1

(n!1)(1!a)2,

maximizes the rate of inyation.

The following example reveals that non-monotonicity. Let p"8, a"3/4,n"10, and c"b

1"1. We then have Fig. 1.

If b'PR, /P((t!1)/t) and the employment and output become sub-

optimal. In#ation, as Fig. 1 suggests, goes to zero. The intuition should be clear.If the Central Bank will under no circumstance erode real wages via in#ation,then unions are free to set their preferred real wage (more precisely, theequilibrium real wage that emerges from their non-cooperative interaction) bypicking the corresponding nominal wage level.

Notice that the standard result that a more conservative Central Bank alwaysleads to lower in#ation holds as a special case of our model. From the expression

bH'"S

cb1

(n!1)(1!a)2

we see that if nPR (and the actions of each union have negligible e!ect onaggregates) or b

1"0 (agents and unions do not su!er costs of in#ation), then

bH'"0. Since we know that bH

'is a maximum, and that therefore utility is always


Fig. 1. CBC and in#ation.

decreasing if b''bH

', it follows that in these special cases the farther above zero

is b', the lower is in#ation.

Finally, welfare levels are also non-monotonic in b'. The appendix proves the

following result:

Result 5. For a xxed number n of unions, welfare is U-shaped in CBC, anda moderate Central Banker (one that is neither strongly conservative nor stronglypopulist), with preferences given by

bHH'

"Scb

1(n!2) (1!a)2

,

minimizes welfare.

The intuition for the non-monotonicity result is simple. A bit of conservatismincreases in#ation while lowering output, and hence welfare falls as CentralBank conservatism rises from an initially low level. A larger doses of conserva-tism is necessary for the bene"ts of lower in#ation to outweigh those of loweroutput, and hence raise welfare.

Again a standard result } that a more conservative Central Bank isalways good for welfare } holds as a special case of our model. From theexpression

bHH'

"Scb

1(n!2) (1!a)2

we see that if nPR or b1"0, then bHH

'"0. Since we know that bHH

'is a minimum, and that therefore utility is always increasing if b

''bHH

',


Fig. 2. CBC and welfare.

13Notice also that if n is exactly equal to 2, then bHH'

PR. It follows that for welfare to benon-monotonic in CB conservatism, n has to be strictly larger than 2.

it follows that in these special cases the farther above zero is b', the higher

is utility.13Notice that the Central Banker with welfare-minimizing preferences may be

more or less conservative than the population at large. From the de"nition ofbHH'

it is easy to see that

bHH'

'b1

if b1(c (n!1)~1(1!a)~2 ,

bHH'

"b1

if b1"c (n!1)~1(1!a)~2 ,

bHH'

(b1

if b1'c (n!1)~1(1!a)~2 .

An example, with the same parameter values as before is revealing. We haveFig. 2.

4.3. Increasing the number of unions

What is the e!ect of the number of unions on employment, output, in#ationand welfare? Here we tackle these questions holding constant the degree ofcentral bank conservatism.

Note, "rst, from Eqs. (3.4)} (3.7), that all the variables of interest depend onn exclusively via the coe$cient /. When this coe$cient is equal to one, employ-ment and output are at their "rst-best levels, in#ation is zero, and welfare ismaximized. Since, for "nite b

1and b

', / is always below its optimal level of one,

employment, output, and welfare increase with /, and in#ation decreases with /.


14 In other words, p(1!a)'1 is a necessary but not su$cient condition for / to be non-monotonic in n. The su$cient condition is p'p6 or, equivalently,

p(1!a)'A2#k1#kB'1.

The key relationship, then, is that between the number n of unions and thecoe$cient /. The former a!ects the latter in two ways:

(a) First, holding ((t!1)/t) constant, / is decreasing in n. Intuitively,the larger the number of unions, the less each internalizes the in#ationaryconsequences of its actions. Henceforth we term this the &internalizatione!ect.'

(b) Second, and as we saw earlier, / is increasing in ((t!1)/t), and in turnthe elasticity of labor demand t depends on n. Above we termed this the&competition e!ect.' Recall that this e!ect has an ambiguous sign, whichdepends on parameter values. If p (1!a)(1, so that Lt/Ln(0, then alarger number of unions reduces competition; the partial e!ect of this is toreduce /.

Hence, if p (1!a)(1, both the internalization and the competition e!ectwork in the same direction, and a larger n reduces / (and employment, outputand welfare, while increasing in#ation). On the other hand, if p (1!a)'1, theinternalization and the competition e!ects work in opposite directions; hence,/ may increase or decrease with n. Some tedious algebra reveals that / is indeedhump-shaped in n if p'p6 , where14

p6 ,(1!a)~1A2#k1#kB

and

k,(1!a)2b2

'cb

6

'0.

This discussion can be summarized in:

Result 6. For a given level of CBC,(a) If the elasticity of substitution among diwerent types of labor is suzciently

small (p4p6 ), then economic performance and welfare are uniformly decreasing inthe number of unions.

(b) Otherwise, economic performance and welfare are hump-shaped in thenumber of unions, and there is an intermediate degree of centralization thatmaximizes economic performance and welfare.


Fig. 3. (a) / and n for a large p. (b) / and n for a small p.

15Recall that we are assuming 1!a"0.25.16Cukierman and Lippi (1999) also obtain that result.

Two examples of this result follow. The "rst involves the same parameters asin Figs. 1 and 2, plus a now "xed b

'"3.5 and a very large p"20, so that

p(1!a)"5.15 We then have Fig. 3(a).By contrast, if we choose a small p"2, so that p(1!a)"1/2, we then have

a monotonic relationship given in Fig. 3(b).Result 5 is in stark contrast with the conventional wisdom and with the

arguments of Calmfors and Dri$ll (1988), who conjecture that the relationshipbetween economic performance and the degree of centralization of wage settingshould be U-shaped.16 That conjecture is predicated upon three assumptions:

(a) Internalization of aggregate e!ects by each union is always decreasingin n.


17Recall that it yields (b) if and only if p(1!a)'1.

(b) Competition in the labor market is always increasing in n.(c) The internalization e!ect dominates for small n, while the competition

e!ect dominates for large n.By contrast, our model yields results that are compatible with (a), but need

not yield (b) and never yields (c).17 The reason for these di!erences are simple,and chie#y have to do with the way the number of unions a!ects the competitivestructure of the labor market. As we have argued before, we can think of theelasticity of demand for union j@s labor with respect to its relative wage as anindex of the competitiveness of the labor market: the less elastic demand, themore monopoly power. In our setup, this elasticity may be increasing ordecreasing in n.

And as n becomes very large, labor demand does not become in"nitely elastic;rather, its elasticity converges to the technological parameter p. Hence, evenwith in"nitely many unions each retains some monopoly power, and thereforethe fact that each does not internalize the consequences of its actions (preciselybecause n is large) is detrimental to welfare.

Calmfors and Dri$ll (1988) seem to assume that as the number of unionsbecomes very large the relevant elasticity also becomes very large and themonopoly power of each union disappears; Cukierman and Lippi (1999) assumethis explicitly. In that case, whether or not each internalizes the e!ects of itsactions in that case becomes irrelevant. Those papers conclude that havingmany unions is good for welfare, while we conclude that it is bad. The di!erenceresults from di!erent underlying models of how labor enters the productionfunction and of competition in labor markets.

4.4. Interactions between the number of unions and the degree of Central Bankconservatism

We can now consider the joint interaction of the number of unions and thedegree of Central Bank conservatism. For the sake of brevity, we focus on thee!ect on only three variables: The level of employment (and, indirectly, output,which is monotonically related to the level of employment), in#ation, andwelfare. Moreover, we rely only on simulations, since algebraic expressionsbecome quite unmanageable.

Consider two examples put together using the same parameter values as inthe previous section. In Fig. 4(a) we take up the case of a large p, so thatp (1!a)'1 and therefore Lt/Ln'0. We see there that, for any level of CBC,the logarithm of employment is hump-shaped in the number of unions, as weshowed before. Nonetheless, this non-monotonicity is very sharp for high levels


Fig. 4. (a) Employment, CBC and n for large p. (b) Employment, CBC and n for small p.

of CBC, and much less so for low levels of CBC. In the limit, as b'goes to zero (so

that the Central Bank is indi!erent to in#ation), we know that the level of employ-ment is equal to the "rst best regardless of the number of unions, so that thenon-monotonicity naturally disappears. In this case greater Central Bank conser-vatism is particularly costly when there are either very few or very many unions.

On the other hand, the decrease in employment that results from greatermonetary conservatism is smaller the larger is the number of unions (the gridbecomes #at for large n). This "ts our earlier results, for we saw above that asnPR we are back in the standard model in which real economic performanceis independent of the degree of central bank conservatism.

In Fig. 4(b), by contrast, p is small, so that p (1!a)(1 and thereforeLt/Ln(0. This means that, for any given level of CBC, employment is alwaysdecreasing in the number of unions as long as b

'is above zero. In the limit, as

b'goes to zero, we have the same phenomenon as in Fig. 5(a): Employment is

independent of the number of unions. In this case, greater Central Bankconservatism is particularly costly in the case of very decentralized wage setting(large n). And, as in Fig. 5(a), the decrease in employment that results fromgreater monetary conservatism is larger the larger is n.


Fig. 5. (a) In#ation, CBC and n for large p. (b) In#ation, CBC and n for small p.

Next we consider the joint e!ects of the number of unions and CBI on the rateof in#ation. The relevant simulations (still using the same parameter values) arecontained in Fig. 5(a) and (b).

In both cases in#ation is hump-shaped in the degree of CBC. And in bothcases the e!ect (whether positive or negative) of a marginal change in thenumber of unions on in#ation seems to be largest at intermediate levels ofCentral Bank independence. This result "ts well with our earlier observationthat, in the limits as b

'P0 and b

'PR, in#ation goes to zero independently of

the number of unions.The only di!erence between the two cases is that in#ation is monotonically

increasing in the number of n of unions if substitutability among labor types islimited (p is low), and U-shaped if substitutability among labor types is substan-tial (p is high). This means that the e!ect (whether positive or negative) ofCentral Bank independence on in#ation seems to be largest at either very highor very low n if p is high, and at high n if p is low.

Finally, consider the joint e!ect of the number of unions and CBC onindividual welfare. The simulations (still using the same parameter values) are inFig. 6(a) and (b).

In both cases welfare is U-shaped in CBC, but we see clearly now that thenon-monotonicity is sharpest for large numbers of unions and a high degree oflabor market decentralization; as the number of unions gets smaller and we


Fig. 6. (a) Welfare, CBC and n for large p. (b) Welfare, CBC and n for small p.

approach n"2, the relationship tends toward monotonicity. This correspondto our earlier analysis. Recall that the welfare-minimizing degree of CBC isgiven by

bHH'

"Scb

1(n!2) (1!a)2

,

so that bHH'

PR as nP2. In the limit case of n"2, welfare is minimized whenb'becomes in"nitely large.The main di!erence between the cases depicted in Fig. 6(a) and (b) has

to do with the behavior of welfare as the number of unions changes. Forlarge p welfare is hump-shaped in n, while for small p welfare is mono-tonically decreasing in n. This follows from the earlier result that the coe$cient/ is hump-shaped in n for large p, and monotonically decreasing in n forsmall p.


5. Conclusions

According to the traditional view in the literature, a high degree ofCentral Bank conservatism reduces average in#ation rates, with little or nocost to the performance of the real economy. In this paper we argue that suchlinks cannot be analyzed independently from the degree of labor corporatism} and that once one does, some of the conventional wisdom is over-turned.

We build up a general equilibrium model, fully developed from microfounda-tions, that investigates in a systematic way the interactions among CentralBank conservatism, centralization of wage setting and economic performance.The model yields several striking results. For a given level of CWS, highCBC can be costly in terms of employment and output (this e!ect is particularlystrong if the labor market is highly centralized). Furthermore, in#ation isnot monotonic in the degree of CBC, but follows an hump shape. Takentogether, these two results imply that a moderately conservative Central Bankerachieves the lowest possible welfare level. On the other hand, a populist CentralBanker maximizes welfare by providing zero in#ation and the optimal level ofemployment.

Conventional wisdom on the e!ects of labor market centralization also turnsout to be misleading. We show that, depending on parameter values, economicperformance may be monotonically decreasing or hump-shaped in the numberof unions. More generally, the model suggests that the relationship betweenlabor market centralization, on the one hand, and variables such as employ-ment, output and in#ation, on the other, are likely to be dependent on modelspeci"cs. In particular, the speci"cation of technology, and the implied relation-ship between the elasticity of labor demand and the number of unions is likely tobe key. Further research using other speci"cations of how labor enters theproduction function, and what determines substitutability among labor types,should shed light on these issues.

Acknowledgements

Generous "nancial support from the C.V. Starr Center for Applied Econ-omics at NYU is gratefully acknowledged. Comments by Je!rey Frieden,Hans-Peter Gruner, Torsten Persson, Guido Tabellini, Harald Uhlig and CarlWalsh were extremely useful in re"ning our arguments.


Appendix A. The 5rm's problem

A.1. Firm's cost minimization

The "rm minimizes total cost :10¸i=

idi subject to (2.1), taking the level of

output > as given. The solution is

¸i"A=

i=B

~p>1@a (A.1)

and

P1

0

¸i=

idi"=>1@a (A.2)

where= is de"ned in (2.4) in the text. Using the de"nition of ¸ in (2.5) also in thetext, and combining it with (A.1) and (A.2), we obtain the demand function (2.3)in the text.

A.2. Firm's proxt maximization

The representative "rm is competitive, so that it takes the aggregate wage= as given. The "rm sets the level of output> by maximizing per-period pro"ts(2.2) subject to the cost function (A.2). The solution is the supply function (2.6) inthe text.

Appendix B. The government's problem

The government maximizes (2.15) subject to the technology (2.1), the "rm'soptimality conditions (2.3) and (2.6), the dividend rule (2.7), and to the aggregatereal wage law of motion (2.16), which can be expressed as

log=+u!n. (B.1)

It turns out to be easier to re-write this problem somewhat, expressing allvariables in the objective function (2.15) in terms of wages only. Recall that (2.14)in the text gives demand for each individual labor type as a function ofindividual and aggregate wages. It can be rewritten as

¸i"a1@(1~a)A

=i=B

~p=~1@(1~a) . (B.2)

Multiplying both sides by =iwe have

¸i=

i"a1@(1~a)A

=i=B

1~p=~a@(1~a) . (B.3)


Similarly, using (2.6) in (2.7) we can write individual union dividend #ows as

Di"(1!a)

>

n"(1!a)aa@(1~a)=~a@(1~a) . (B.4)

Hence, combining (2.9), (B.3) and (B.4) consumption per union is

Ci"a1@(1~a)A

=i=B

1~p=~a@(1~a)#(1!a)aa@(1~a)=~a@(1~a) . (B.5)

The government's problem can now be reformulated as maximizing (2.15)with respect to n subject to (B.2), (B.5) and (B.1). The "rst-order condition is

P1

0GA

a1!aB!A

c1!aB log ¸

iH di"b'n . (B.6)

Rearranging we have (3.1) in the text.

Appendix C. The unions' problem

The representative union j maximizes (2.10) with respect to uifor all i in the

interval ( j!n~1, j ), subject to (2.9), (2.12), (3.3), (B.1), and to the individual realwage law of motion (2.11), which can be expressed as:

log=i+u

i!n. (C.1)

The "rst-order condition for each wage in the interval is

=i¸

iC

iA1#

L¸i

L=i

=i

¸iB!A

L¸i

L=i

=i

¸iB c log ¸

i"b

1n A

LnL=

iB=i

. (C.2)

To compute the term (Ln/L=i)=

idi!erentiate (B.6) to obtain

LnL=

i

"!Cc

(1!a)b'D P

j

j~n~1A

L¸i

L=i

1

¸iB di. (C.3)

Because all workers in the interval ( j!n~1, j ) are symmetric, we can integrateacross them. Multiplying both sides of the resulting equation by=

iwe have

ALnL=

iB=i

"

!cAL¸

iL=

i

=i

¸iB

(1!a)b'n

. (C.4)

Substituting (C.4) into (C.2), the representative union's policy rule becomes

=i¸i

CiA1#

L¸i

L=i

=i

¸iB!A

L¸i

L=i

=i

¸iB c log ¸

i"!cb

1nA

L¸i

L=i

=i

¸iB

(1!a)b'n

. (C.5)


C.1. Deriving the elasticity of labor demand

In the above expressions the elasticity ((L¸i/L=

i) (=

i/¸

i)) is key. We now

proceed to compute this elasticity. Combining (A.1) and (2.6) we have

¸i"A=

i=B

~pA

a=B

1@(1~a)(C.6)

as it appears in (2.14). Taking derivatives in this expression we can calculate theelasticity

L¸i

L=i

=i

¸i

"!p#C(1!a)p!1

1!a DL=L=

i

=i=

. (C.7)

We can compute

L=L=

i

=i=

in the following way. Recall "rst that all wages set by the union have to be thesame and that it takes the wages set by other unions as given. Then, from thede"nition (2.4), moving all the wages inside the interval ( j!n~1, j ) together,and holding all the wages outside this interval constant, we obtain

L=L=

i

=i=

"n~1A=

i=B

1~p. (C.8)

Used in (C.7), this yields (2.12) in the text.

Appendix D. General equilibrium

Combining (2.2) and (2.6) we have that D"(1!a)>. In a symmetric equilib-rium in which all D

iare the same, pro"t per union is

Di"(1!a)>"(1!a)C

i. (D.1)

Given budget constraint (2.9), which speci"es that consumption per union mustbe equal to =

i¸iplus pro"t per union, (D.1) reveals that

Ci"=

i¸

i#(1!a)C

i(D.2)

so that aCi"=

i¸i.

At the same time, in symmetric equilibrium

=i=

"1,L¸

iL=

i

=i

¸i

"!t.

Making these substitutions in (C.5) we have (3.2) in the text.


Appendix E. Proof of Result 4

From (3.6) and the de"nition of / is we can calculate

LnLb

'

"

n (1!a)2b2'

cb1

C1!n (1!a)2b2

'cb

1D

t C1#n (1!a)2b2

'cb

1D

2. (E.1)

Setting Ln/Lb'"0 and rearranging we obtain

bH'"S

cb6

(n!1) (1!a)2.

It is easy to check that L2n/Lb2'(0, so that bH

'is a maximum.

Appendix F. Proof of Result 5

Total utility can be written as ;i";[/(b

')] where the function ;[/] is

found using the de"nition of / and can be written as

;i"A

1

2BAa2c BC/(2!/)!n (1!/)A/!

t!1

t BD . (F.1)

The "rst derivative of this expression with respect to / is

L;i

L/"A

1

2BAa2c BC2!2/!nA1!2/#

t!1

t BD . (F.2)

so that;ihas a unique extremum at /HH"(2(n!1)t!n)/2(n!1)t. It is easy

to check that the second derivative of (F.1) is always positive, so that /HH consti-tutes a minimum. Notice that /HH(1 always, and that /HH5(t!1)/t, sincewe assumed from the start n52.

Since

t!1

t4/(b

')41,

/HH can be attained by manipulating b'. Given L//Lb

'(0 everywhere, we can

identify a value of b'

which ensures that /"/HH. This is the value of b'

thatminimizes utility. Call it bHH

'. Using the de"nition of / it is straightforward to

compute

bHH'

"Scb

6(n!2) (1!a)2

.


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