# Some theory on the sustainability of different levels of social protection in a Monetary Union.

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**ABSTRACT:**this paper we shall examine the issue of the downward levelling of social protection in greater depth by answering two questions on how important this problem may become in the context of the EMU: a) To what extent has `benign neglect' of the possibility of a downward levelling of social protection been justified until now, at least in those countries where it is most developed ? b) How great is the problem of social dumping likely to be in terms of deviation from the actual level of social protection with respect to the `optimal'? The first question concerns the influence that the successive phases of European integration have exerted on social protection in the Member States. Can one detect a trend towards convergence in incomes and social protection and, if so, in which direction? We consider that briefly in this paper. The question we focus on is an estimation of the cost incurred through the lack of co-ordination in the monetary union as it is today. The approach we take is to compare the existing levels of protection with the optimal level of protection which a fictitious (European) central planner might aim for. We will not consider employment or wage effects from the transition to economic unification or the trade policy consequences of labour market imperfections as shown by, for example, Brander and Spencer (1988) and Mezzetti and Dinopoulos (1991). Instead, we concentrate on the equilibrium outcomes of the EMU as such (like Abraham, 1993 and 1994, Lejour, 1995 and Lejour and Verbon 1996). We use a standard two-country general equilibrium model of international trade in differentiated goods (e.g. Helpman and Krugman, 1985) without trade barriers but with a common currency, which is extended along three lines. First, in order to take better account of European ...10/2000; - SourceAvailable from: Glenn Rayp
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**ABSTRACT:**We analyze the consequences of product market integration in a simple two-country, two-sector, general-equilibrium model with imperfect competition due to economies of scale. In contrast to the existing literature we take explicit account of the labor-market structures in the integrating economies. It turns out that the specific labor-market structures are very important for how integration affects total production and product market structure in a particular economy. However, integration always gives rise to a welfare gain in both economies. Copyright Kluwer Academic Publishers 1994Open Economies Review 01/1994; 5(1):115-130. · 0.44 Impact Factor

Page 1

Some Theory on the Sustainability of Different Levels of

Social Protection in a Monetary Union

Wim Meeusen and Glenn Rayp

CESIT Discussion paper No 2001/08

November 2001

Centre for the Economic Study

of Innovation and Technologyof Innovation and Technology

S i TS i T S i T S i T

Centre for the Economic Study

Page 2

Some Theory on the Sustainability of

Different Levels of Social Protection

in a Monetary Union

Wim Meeusen and Glenn Rayp1

1. INTRODUCTION

In this chapter we analyse the long-run properties of a two-country

Grossman-Helpman type of ‘expanding product variety’ monopolistic

competition model in which the equations expressing continuous clearing of

the labour market are replaced by equations that impose continuous

equilibrium on the social security budget (compare with Grossman and

Helpman, 1991). We will assume that, although the process of product

innovation is solely under the control of private firms, the accumulation of

knowledge has partly a public character and thereby creates positive

knowledge spillovers for other firms. The model will therefore exhibit

sustainable (endogenous) growth, even if, for reasons of simplicity and

transparency, physical and human capital accumulation is discarded.

At the same time however the economies, even in the long-run, will not

necessarily operate at full employment levels since the labour markets do not

automatically clear: the wage rates are the result of a bargaining process

between unions and employers.

The government levies a uniform tax rate on labour and entrepreneurial

income and finances in this way the payment of allowances to the

unemployed. The basic research question is whether different levels of

innovativity in the two countries, resulting for example from different levels

of R&D-productivity, allow for lasting discrepancies in social protection

under conditions of integrated goods markets.

We present the model in section 2. We examine its long-run properties in

section 3, and the properties of its solution under different assumptions with

Page 3

Convergence Issues in the European Union 2

respect to international knowledge spillovers in section 4. In section 5 we

draw conclusions.

2. THE MODEL

We start from the familiar Dixit-Stiglitz specification of the utility of a

representative consumer under conditions of monopolistic competition (Dixit

and Stiglitz, 1977):

) 1

−

(

) 1

−

(

*

1

= ∑

+

=

s

s

s

s

nn

i

ic

U

. (9.1)

ci represents the consumption of a good i by the representative consumer in

both countries. n and n* are the numbers of differentiated goods produced in

both economies. The demand side of the economies is characterised by a

uniform elasticity of substitution between goods, equal to s > 1.

This utility is maximised under the following budget constraint:

nn

ii

∑

==

11

e is total expenditure by the representative consumer; pi and

prices of the individual goods produced in country 1 and country 2

respectively.

A fundamental result from duality theory is that a price-index P of the

following form is associated with u:

ecpcp

i

in

i

i

≤+∑

+

*

*

.

*

i p are the

()

s

ss

−

+=

∑

=

i

∑

=

i

−−

1

1

*

1

1*

i

1

1

i

nn

ppP

. (9.2)

From the first-order conditions follow the demand function of an

individual consumer for a good of type i :

Page 4

Social Protection in the EU 3

. ,...,1

,...,1

*

*

i

ni

P

e

P

p

c

ni

P

s

e

P

p

c

in

i

i

=

=

=

=

−

+

−

s

(9.3)

We obtain the total demand for good i by aggregating over the individual

demands of all consumers:

ni

P

EE

P

p

P

eNN

P

p

cNNCCx

ii

iiii

,...,1

)(

)(

**

**

=

+

=

+

=+=+=

−−

ss

. ,...,1

)(

)(

*

**

i

**

i

**

n

*

i

ni

P

EE

P

p

P

eNN

P

p

cNNCCx

iniin

=

+

=

+

=+=+=

−

−

+++

s

s

(9.4)

N and N* are the number of individuals,

are the global consumption level of the domestic goods demanded by the

consumers in the own and in the other country, and the goods produced in the

foreign country demanded by domestic and foreign consumers, and E and

E* are total national spending in each economy on goods produced in both

economies.

The demand for a good i , consequently, is negatively dependent on its

relative price and positively linked to total demand. The choice of a

‘numeraire’ ensures complete determination of that expression. For that we

follow Grossman and Helpman (1991) and assume that total nominal

spending is equal to 1, which is another way of saying that the two countries

form a monetary union in which the central bank follows a strict policy of

zero-growth nominal money supply.

It holds in this case that

*

*

+∑∑

==

ii

i C ,

*

i

C , resp.

in

C+ and

*

ni

C+

1

*

1

*

i

1

=+=

EExpxp

n

i

n

ii

. (9.5)

Page 5

Convergence Issues in the European Union 4

Following Sørensen (1994) and others, we keep the supply side of the

economy as simple as possible. The n + n* goods are produced using in each

country one and the same constant returns to scale production function with

only one input, labour (l). Each good is produced by a single firm that enjoys

its (relative) monopoly as a result of propriety rights obtained as innovator.

As an expression of the production of goods we have therefore:

alx

ii

=

a and a* represent labour productivity and are assumed to be uniform over

all production units in each country.

Profits per firm in each country can now be written as

xp

−=

p

.) ,...,1(

) ,...,1(

**

i

**

i

nilax

ni

=

==

(9.6)

.

*

i

*

i

*

i

*

i

*

i

iii

x

ii

lwp

lw

−=

p

i w and

If we assume that entrepreneurs take no account of the effect that a price

change in the individual variety will have on the price index P, then the first-

order condition for maximising profit are the following mark-up equations:

w

p

i

−

s

It is possible to considerably simplify the model if we now first consider

wage formation.

With respect to the determination of the wage rate, we assume that all

workers in the manufacturing sector of both countries are members of a trade

union operating in their sector, exercising monopsony power over the labour

supply, in the sense that it is the trade union that is solely responsible for

wage bargaining. Note that this does not mean that there is no intersectoral

labour mobility. It however does mean that the trade union active in the

sector only cares about the well-being of its own members.

The trade union organisations are not directly concerned with matters of

government finance and therefore do not consider the equilibrium of the

social security system as an external limitation. They behave in a utilitarian

manner, which implies that they endeavour to maximise the global utility of

their members:

*

i w are the sectoral wage rates in each country.

*

*

i

*

i

1

resp.

1

a

w

p

a

i

−

=

=

s

ss

. (9.7)

Page 6

Social Protection in the EU 5

where li are the employed union members, and Mi is the total member

number. The subscripts e and u refer respectively to the utility of working

and unemployed members (cf. Oswald, 1985). After reverting to indirect

utility functions, we can describe the objective of the trade union

organisations thus:

) 1 (

P

w

i

t

uiiei

ulMul

)(

−+

, resp.

uiiei

ulMul

)(

***

−+

.)(

) 1 (

resp.,)(

*

*

i

*

i

**

i

*

i

*

Ui

) 1 (

) 1 (

**

i

−+

−

=

−+

−

=

−

−

P

b

lM

P

w

lO Max

P

b

lM

w

lO Max

w

ii

i

i

Ui

t

t

t

(9.8)

b and b*, the levels of the unemployment benefit (uniform across sectors in

each country), are determined by the government and are therefore

exogenous as far as the union is concerned. t and t* are the uniform tax

rates ( 0 ≤ t,t* < 1 ).

The solution for the optimal gross sectoral wage rate, if the unions do not

care about the effect of their claims on the overall price level, has again a

mark-up form:

b

w

i

=

−−

ts

The net money wages w (1 – t) and w*(1 – t*) are therefore uniform across

sectors and are a fixed mark-up above the social security benefits b and b*.

They are invariant with respect to the level of social security contributions. A

rise in taxes, in other words, is fully recovered on the gross wage and

employment adjusts itself accordingly (see e.g. Holmlund et al., 1989, p. 27).

As a consequence of (9.9), we may now simplify the notation and drop the

subscripts with respect to the variables p, p , l and x:

and

pppp

ii

==

pppp

*

*

*

*

i

) 1 (

) 1

−

(

resp.

)1 () 1(

w

b

−

ww

===

t

s

ss

. (9.9)

.) resp.(, ,...,1 allfor and

andand

,and

,

***

i

**

i

**

i

=

**

nnixxxx

llll

i

i

i

===

=

==

Page 7

Convergence Issues in the European Union 6

It now also holds that

, 1

=

***

+

(

np

xp nnpx

)

(9.10)

)1 /(1

1 *

p

*1

s

ss

−

−−

+=

nP

(9.11)

s

p

s

p

**

*

resp.,

xp px

wlpx

==−=

. (9.12)

If v(t), resp. v*(t), denotes the value of the claim to the supposedly

infinite stream of profits that accrues to the representative firm at time t , we

get

∞

−−

etv

t

()

()

u

s

u

(

u

(

u

s

u

(

u

(

u

(

u

(

d

))

)(

andd

))

)(

**

)()*

)()

=

=

∫

t

∫

∞

−−

xp

etv

xp

tRR

tRR

(9.13)

R(u) represents the cumulative discount factor.

Separate from their productive activity, entrepreneurs are also involved in

R&D and innovation. They finance product development costs by issuing

equity. If there are no knowledge spillovers, and if A, resp. A* are the

(constant) labour intensities of R&D activity, then the rate at which new

products (‘variants’ in the terminology of Grossman and Helpman) are

created is the following:

l

n

resp.dd

=

t

A

l

nt

A

RR

dd

*

*

*=

,

where

vative activity.

If, on the contrary, part of the knowledge created in the innovative firm

cannot be appropriated and spills over to the rest of the economy, then the

above equation should be amended. If we assume that the knowledge stock

KR that becomes available for the ‘other’ firms reduces in a proportionate

way the labour requirements necessary for designing new products, we get

the following expression:

*

R

and

R

ll are the economy-wide amounts of labour devoted to inno-

Page 8

Social Protection in the EU 7

t

KA

l

nt

KA

l

/

n

R

R

/

R

R

dd anddd

**

*

*==

.

We incorporate the phenomenon of international knowledge spillovers in the

model by assuming that KR can be proxied by the number of variants in the

own economy plus a fraction y of the number of variants in the other

economy. This finally yields for the rate of innovation at each moment of

time, under conditions of knowledge spillovers from R&D:

*

and

Ann

Free entry to innovative activity then means that an unlimited amount of

additional workers will be hired for this purpose as long as the marginal

returns of the newly hired researcher ((n+y n*)v/A)dt exceed the marginal

cost wdt . This is of course not compatible with a situation of general

equilibrium as it means that labour demand would be unbounded. In the

opposite case product development would come to a standstill. We must

therefore conclude that the free entry condition takes the following form:

**

≥

+

nnnn

yy

*

*

R

*

*

*

*

*

A

l

n

nn

n

n

&

g

lnnn

&

g

R

yy

+

=≡

+

=≡

. (9.14)

.0 resp.,0 whenever holding equality with

resp.,

*

*

**

>>

≥

+

n

&

n

&

v

Aw

v

wA

(9.15)

The tax rates t and t*, the unemployment benefits b and b* and the

other social security allowances s and s* are set by the government in terms

of their own social preferences, and under the constraint that the social

security budget balances at each moment of time:

n

g nlL

t

y

+

.)()(

and,)()(

**

*

*

********

*

*

****

**

wA

nn

n

+

glnLsbA

nn

n

+

glnL

wA

nn

n

y

gnlsLbA

nn

y

t

y

+=+−−

+

+=+−−

(9.16)

L and L* are the active population. The ‘other’ social security allowances

may refer to pensions in a pay-as-you-go system and to public health

insurance. Its total amount is supposed to be proportional to the active

Page 9

Convergence Issues in the European Union 8

population. It of course holds that 0 ≤ s < b. We will also assume, for

simplicity, that s and s* are given, e.g. by a law voted by the respective

parliaments.

The balanced budget requirement then means that in actual fact the

government disposes of only one free policy parameter. Because b and b*

are instruments expressed in money terms, the optimal value of which may

therefore be assumed to vary over time, and because t and t* are

proportions, it seems to be more natural to concentrate on the latter as policy

variable, and to treat the b’s as being implicitly determined by (9.16), given

t and t*.

Finally, we need an equation explicitly expressing the fact that firms are

valued at their fundamental value and that, as a result of it, there is no

arbitrage on the capital market. This equation is obtained by differentiating

equation (9.13). This yields

and,

p

−=

rvv

&

r is of course the common rate of interest.

***

p

−=

rvv

&

. (9.17)

3. THE LONG-RUN PROPERTIES OF THE MODEL

In order to be able to proceed further in the analysis we now turn to the

properties of the long-run balanced growth equilibrium of the model, hoping

in this way to obtain relatively neat expressions.

We can considerably simplify the model by imposing the obvious long-

run requirement that the current accounts are balanced, i.e. the national

industrial product npx (resp. n*p*x*) is equal to national expenditures on the

goods markets E (resp. E*). This implies that for the profits of the

representative enterprise, and its market value we may now write:

E px

==

s

s

p

ss

p

*

***

*

resp.,

n

Exp

n

==

(9.18)

and, because of (9.13), assuming that the markets shares and the interest rate

remain constant:

E

gr

++

s

)(

and

)(

**

*

*

*

*

grn

E

gr

v

grn

v

+

=

+

===

s

pp

. (9.19)

Page 10

Social Protection in the EU 9

From (9.18) and (9.19) it follows immediately that

n

v

p

*

*

*

*

*

*

*

and

g

n

n

&

v

v

&

g

n

v

&

−=−==−=−==

&&&

p

pp

. (9.20)

Page 11

Convergence Issues in the European Union 10

We shall also assume that, next to (endogenous) product innovation, there

is also process innovation, which takes the form of a constant, but exogenous,

rate of increase of labour productivity in the manufacturing sector of both

countries ( constant/

=

aa &

and constant

=

aa &

We now can derive a number of simple relations between different rates of

change, each time holding in both countries (in order not to burden the text

unnecessarily we drop the equations for the other country).

Let us first consider the free-entry condition (9.15). In the long run it holds

that

w

&

+−

( gr

y

/**

).

v

v

&

nn

w

=

)

*

, (9.20)

from which it follows, since the growth rate of v is a constant and equal to

minus g, that the growth rate of (n + y n*) should be a constant too. From

this it follows in turn, given that the growth rates of the number of variants in

the economy g and g* must be supposed to be constants on the long-run

growth path, that the proportion n/n* of the number of variants in both

economies must be a constant. It therefore holds that

)( gr

=+

w

&

.0

and

**

=

=

w

ggnn

y

(9.21)

From the price and wage mark-up equations (9.7) and (9.9) we can now see

that

b

&

=

.

,0

a

a

&

a

a

&

w

w

&

p

p

&

b

−=−=

(9.22)

Note that, because of the zero-growth monetary rule, the steady rise in

labour productivity is reflected in a negative rate of change of the price-level

and in the steady growth of real wages.

Together with the monetary zero-growth condition (9.10), this implies that

the following relation must hold in the long-run:

x

an

x

a

&

g

n

&&

−=≡

. (9.23)

Page 12

Social Protection in the EU 11

It is obvious that

growth of the economy. From the production point of view, real income can

indeed be defined as

GDP

GDP

==

aa/ &

cannot be anything else than the long-run rate of

.

ng

p

v

nx

p

n

&

v

nx

p

N

R

+=+

2

Balanced growth means that the manufacturing sector and the R&D sector

of the economy must grow at the same rate. From the above results it directly

follows that the rate of growth of the economy (and of both its sectors) must

therefore be equal to

aa/ &

:

.)( gr

)( gr)(gr of growth of rate

a

a

&

g

p

p

&

v

v

&

ng

p

v

x

x

&

g nxGDP GDP

RR

=+−==

+==≡

From the necessary constancy in the long run of the market shares of both

countries in a situation of balanced growth, and the equality of their rates of

innovation it inevitably follows that the rates of process-innovating (Harrod-

neutral) technological change must be identical in both countries, and

therefore also their real rate of growth. From (9.4) it indeed follows that

s

−

=

1**1

pn np

ss

−−

+

p

x

and therefore

s

−

==

−

x

=−

1

*

*

*

11

xp

p

pn

x

EE

np

. (9.24)

If it holds that

0

*

*

==

E

E

&

E

E

&

then, after some transformations and making use

of (9.22) and (9.23), (9.24) and its equivalent for the other country can be

rewritten as follows:

*

*

a

a

The message of (9.25) is obvious: if the rate of Harrod-neutral technological

progress in the own country is higher than abroad, then the constancy of the

)(and) ( )1 (

*

*

*

*

*

a

a

&

a

a

&

x

x

&

x

x

&

a

&

a

&

gg

−=−−−=−

ss

(9.25)

Page 13

Convergence Issues in the European Union 12

market shares would imply that its rate of innovation should be lower. Since

different rates of innovation are incompatible with balanced growth, then –

naturally enough – the rates of increase of labour productivity should be

identical. Any other situation would lead to unbalanced growth and the

elimination from the market of the country with the lowest rate of growth. As

the rates of increase of a and a* are exogenous in the model, the analysis of

the long-run properties of the model under conditions of balanced growth is

therefore only relevant for countries with a comparable level of development,

so that the appeal to the standard neoclassical conclusions with respect to

convergence in growth is warranted.

4. SOLUTION OF THE MODEL

It turns out that relatively few transparent analytical results can be obtained

for the case where 0 < y < 1. One has to revert in this case to simulations on

a calibrated model to obtain solutions for g , b and b* in terms of the policy

variables t and t* and the parameters s , A and A* .

In the following we will therefore concentrate on the special cases y = 0 and

y = 1, but only after having established two significant expressions in the

general case for the unemployment rate u and the real value of the

unemployment benefit.

From the equilibrium condition on the social security budget (9.16) it

indeed immediately follows that the unemployment rate is given by the

following:

n

g nlL

u

1

)1 )(1(

*

−+

−−−

=

+

−−

≡

ts

tsts

y

b

c

L

A

nn

. (9.26)

It obviously holds that

0 and0

>

∂

∂

>

∂

∂

t

u

b

u

.

These partial derivatives should be interpreted with care: the equilibrium

condition on the social security budgets (equations (9.16)) implies b is not a

free parameter but is a function of t and indeed also of t*, which

themselves can be regarded as being a function of the free parameters

s and s*. We have therefore

Page 14

Social Protection in the EU

(

sbb

13

We show elsewhere that in the absence of social security (b, s and t equal

to zero), in the one-country as well as in the two-country case, the model then

reduces to the special case of the labour market clearing model of Grossman

and Helpman (1991, chapters 3 and 9) (see Meeusen and Rayp, 2000b).

From the mark-up equations (9.7) and (9.9) we can deduce the following

expression for the unemployment benefit in domestic purchasing power

terms:

−

= a

p

) )( ),(

**s

tt

=

. (9.27)

) 1 (

1

2

t

s

s

−

b

. (9.28)

4.1. The case y y = 0

This case refers to the situation where knowledge spillovers are confined to

the borders of the respective countries.

After putting y = 0 in equations (9.14)-(9.16), leaving open for the time

being the possibility that g and g* would be different, and defining V = 1/(nv),

i.e. the inverse of the aggregate equity value of all the firms in the

corresponding country, we obtain, after having combined the free-entry

condition, the wage mark-up equation and the ‘monetary union’ equation:

t

s

On the other hand we have that

u nl

−=

) 1 (

where u is given by (9.26).

Combining (9.29) and (9.30), again using the mark-up equations, yields

[

1 (

1

A

−

Together with the no-arbitrage condition on the international capital markets

(9.19), this results in a solution for g in terms of, essentially, domestic

parameters and policy variables like L, A, s and t :

apnl

bA

VE

bA wA

V

t

s

ss

−−

=⇒

−−

==

11111

. (9.29)

gAL

−

, (9.30)

] ])

1

gALu VE

−−=s

s

.

Page 15

Convergence Issues in the European Union 14

1 (

−

−+

−

t

+

−

=

r

A

L

b

s

g

1

1

)

1

s

t

s

s

, (9.31)

although, surely enough, b is not solely domestically determined but also a

function of parameters and decisions taken in the other country. It holds –

under the earlier mentioned caveat with respect to the meaning of the partial

derivatives (see (9.27)) – that

∂

<

∂

A

t

Meeusen and Rayp (2000b) show that this solution for the innovation rate

for the two countries – like the corresponding cases examined by Grossman

and Helpman (1991) – refers to a saddle-point equilibrium resulting from

rational expectations of the respective national investors on the international

capital market.

It is clear that in these conditions g and g* will not necessarily be equal.

The following equation, obtained in the same way as (9.25), will clarify the

analysis:

*

gg

E

E

The first possibility, namely that rates of Harrod-neutral technological

progress differ between the two countries, and therefore the rates of growth

of their economies, is of relatively little interest. The fastest growing

economy will in the limit take over the whole market. Evidently, its policy of

social protection is sustainable.

If, as a second possibility, the growth rates of a and a* would become

equal, by whatever spontaneous process of convergence in growth, without

the rates of innovation becoming equal as well, then, because of (9.33), the

most innovating economy will in the limit drive out the other one. Its social

policy would then of course also be sustainable. (9.31) and (9.32) make clear

through which mechanisms such a superior rate of innovation might be

achieved: a higher productivity of R&D (i.e. lower A), a lower tax rate, or

lower unemployment benefits.

This leads us to the third possibility (discarding the fluke possibility that

both terms in the right-hand side of (9.33) would exactly compensate): both

the Harrod-neutral rate of technological progress and the innovation rate

converge. The market shares then remain constant.

0 and0,0

<

∂

∂

<

∂

∂

b

ggg

. (9.32)

) ( ) 1

−

(

*

*

*

*

a

a

&

a

a

&

E

&

E

&

−+−=−

s

. (9.33)