Laurent Granier
email: laurent.granier@univ-montp1.fr

L12 -Monopoly|Monopolization Strategies < L1 -Market Structure, Firm Strategy, and Market Performance < L -Industrial Organization, L41 -Monopolization|Horizontal Anticompetitive Practices < L4 -Antitrust Policy

Keywords: Competition Policy, Cost Heterogeneity, Endogenous Mergers, Monopolization JEL classification: L12; L41 Competition Policy, Cost Heterogeneity, Endogenous Mergers, Monopolization

 give monopolization conditions in static and dynamic acquisition games.

Introducing cost heterogeneity in a n-firm industry, we provide more general monopolization conditions. Indeed, we show that any industry can be monopolized if cost heterogeneity is large enough. This result provides new informations to competition authorities on concentration possibilities and allows them to focus particularly on some industries.

Introduction

The literature on horizontal mergers presents different types of analyses. Williamson (1968) shows that mergers have positive effects on welfare. But, this idea has often been contradicted. In this sense, competition authorities develop a good tool to monitor mergers. Studies suggest, as [START_REF] Charléty | Analyse Economique des Fusions Horizontales[END_REF], that ex-ante competition policy is more efficient and less expensive than ex-post. For this reason, analyses of merger conditions have appeared. For example, [START_REF] Salant | Losses from Horizontal Merger : The Effects of an Exogenous Change in Industry Structure on Cournot-Nash Equilibrium[END_REF] study incentives to participate to mergers, by considering them as exogenous phenomena.

Finally, to take into account decisions of firms' owners in merger processes, other authors (for instance [START_REF] Fridolfsson | Hold-up of Anti-Competitive Mergers[END_REF], Horn and Persson [2001]) have modelled endogenous merger processes. The main interest of these studies is to give informations to competition authorities on concentration possibilities and allows them to focus particularly on some industries.

Using the same framework, we try to answer a related question: what are merger processes conditions? Because merger decisions are endogenous in our model, we simplify the analysis by concentrating on monopolization processes.

In the same way, Kamien andZang (1990, 1993) considered two acquisition games in which symmetric firms compete "à la Cournot" and a single owner is able to purchase firms. They show on the one hand that, in a static game, monopolization is not possible in industries larger than duopolies. On the other hand, they show in a dynamic game that monopolization is not possible in industries larger than triopolies. Our model is based on the Kamien and Zang models (1990 and 1993) and shows that firms' heterogeneity increases the incentives to merge. Following Gowrisankaran and Holmes (2004) we introduce cost heterogeneity between firms and concentrate on the merger incentives of the most efficient firm. Gowrisankaran and Holmes (2004) present a complex model using Markov Perfect Equilibrium concept. This model allows them to take into account investment decisions but it cannot be solved analytically. For this reason, we present a model without investment decisions. We find that monopolization conditions are then less restrictive. Indeed, this paper presents static and dynamic acquisition games in which the owner of the most efficient firm attempts to buy the other firms. We find that monopolization is always possible if cost heterogeneity is large enough. This result supports the "takeover waves" explanation of Fauli-Oller (2000) based on cost asymmetries. But Faulli-Oller (2000) considered a four-firm industry in which two firms are more efficient than the two others. Moreover, he underlines the role of negative shocks of demand on the profitability of takeovers. Assuming a low realization of demand, we propose to focus on a main topic: monopolization of a n-firm industry in which a single firm is more efficient than others.

The rest of the paper is organized as follow. In the second section, we present the static acquisition game. The third section is dedicated to the dynamic game. Finally, we conclude on contributions of the cost heterogeneity assumption. We focus on n-firm industries and we define by {1, 2,., ,.., } N i n = the initial set of firms 3 . A firm must be sold in one part. Note that each firm is initially owned by an individual owner but if an owner bought other firms, he adopts a behaviour corresponding to a single entity. Note

1 n i i Q = = q ∑ with the individual output of firm i. i q
The inverse demand function for the unique good is given by ( ) 1

P Q Q = -.
We note the linear cost function of each firm ( )

i i C q c q i = with i {1, 2,..., } n ∈ .
can take two values: for the most efficient firm and

i c 1 c c for the other symmetric firms. Note that [0, 1] i c ∈ {1, 2,..., } i n ∀ ∈ and 1 c c ≤ .
We consider a three stage game: in the first stage, the owner of the most efficient firm 4 makes bids for the other firms and owners of the other firms give an asking price for their own firm. In the second stage, the dominant firm decides how many firms he wants to operate. In the third one, Cournot competition takes place in the industry.

We must note that this game is a game with perfect information. For We analyze this payoff in order to determine if the dominant firm is able to make bids to buy out all the competitive fringe firms. As a firm unilaterally refusing to be sold potentially earns a duopoly profit, the acquisition cost is, for each firm, the profit earned in competition with the first firm. The behaviour of the firms asking for a duopoly profit can be seen as an hold up mechanism. The opportunity cost is the profit of the first firm if it does not buy any firm.

We note with 1 ( , ) ( 1)²

n i c c π [ ] 1, 2 , i ∈ [2, [ n ∈ +∞ the profit of firm i in a n-
( 1)²

i j i nc c n ≠ - + + j ∑ (1)
We can establish the monopoly profit of the firm 1:

1 1 1 1 (1 )² ( ) 4 c c π - =
We can give the opportunity cost of the firm 1 (the profit realized by this firm if it buys no firm):

F o r P e e r R e v i e w  1 n c 1 , c  1 -nc 1  n -1c² n  1²
Finally, the acquisition cost of an inefficient firm takes the following form:

 2 2 c 1 , c  1 -2c  c 1 ² 9
If firms are initially present in the industry, the monopolization condition is: n

1 2 1 1 2 1 1 1 ( ) ( 1) ( , ) ( , ) n c n c c c c π π π -- ≥ (2)
(2) holds if ( 3) is checked:

1 ( , ) c c n c ≥ (3) with 1 1 1 1 (4 ² 35 13 4 ² 23 ) 1 ( , ) 2 ( 4 ² 1 7 5 ) c n c n c n n c n c n n + + + -- = + - Lemma 1 Let [ ] 1 0, 1 c ∈ and [2, [, n ∈ +∞ then It always exists a [ ] 0, 1 c ∈ verifying 1 1 1 2 ( , ) c c n c c + ≤ ≤
.

Proof To exclude negative profits, sustainable industry conditions must also be checked. One of these conditions is

1 1 2 c c + ≤ . Indeed,
[ ] 0, 1 c ∈ and [ ] 1 0, 1 . c ∈ Thereby, 1 1 2 1 c + ≤ . As, [ ] 1 0, 1 c ∀ ∈ and [2, [, n ∀ ∈ +∞

, ). c c n c ≥

This result is intuitive because monopoly profits are more sensitive to efficiency than profits in any other market structure. Indeed we have shown that monopolization is possible for every size of industry if the cost heterogeneity is large enough.

Note that

1 1, [0, 1], n c ∀ > ∀ ∈ 1 ( , ) 0. c n c n ∂ ∂ >
Subsequently, the larger the industry is, the stronger the cost heterogeneity must be to have monopolization.

In the symmetric case, that is for 1 c c = , we find, like [START_REF] Kamien | The Limits of Monopolization Through Acquisition[END_REF], that industries larger than two firms cannot be monopolized.

The dynamic game:

We We show that a dynamic analysis increases the number of monopolization opportunities even if the discount factor is smaller than 1. This demonstration provides the proof that dynamic modelling makes monopolization easier.

Keeping the same assumptions and taking into account that the number of firms can decrease between two rounds, we extend the three stages of the static game on an infinite horizon. Note that game participants are perfectly informed 6 . We note

1 1 r δ + =
the discount factor, where is the interest rate.

When it is not specified, conditions and propositions are established with r δ and between 0 and 1.

c

In the two next sections, we provide two illustrations of the dynamic game because the n-firm generalization is very complex. First, we study the case of a three-firm industry and second we analyze the case of a four-firm industry.

With a three-firm industry:

We exclude the one round case because it is equivalent to the static monopolization case.

We assume that there are two rounds because it is easy to prove that a path with more than two rounds does not provide an advantage to the first owner 7 .

Thus, one firm is purchased in the first round and another is bought in the next round. Again, we must analyze conditions of these two acquisitions. Hence a backward induction arguing is followed, that is:

Second round:

After the second stage, if the dominant firm monopolized the industry, it earns an infinite monopoly profit flow.

To obtain this payoff, it must pay the acquisition cost of the remaining firm. As this last firm could earn a duopoly profit by deviating from its own sell off, the firm 1 will have to pay this duopoly profit to monopolize the industry.

The dominant firm could earn an infinite flow of duopoly profits by paying no firm. Therefore, when this last one monopolizes the industry, its opportunity cost is this infinite flow of duopoly profit (proof in appendix A):

1 2 2 1 1 2 1 1 1 ( ) ( , ) ( , ) (1 )
(1 ) (1 )

c c c c π π π c δ δ δ - ≥ - - - (4)
(4) holds if ( 5) is checked:

1 11 1 10 10 c c - ≤ (5)

First round:

At the first stage, in order to monopolize the industry in the following stage, the firm 1 has to buy one firm. To buy the other one, it has to pay an infinite and discounted flow of triopoly profit. As the game is dynamic, the dominant firm can spread his takeovers over several rounds. Consequently, the hold up mechanism of the static game disappears. Moreover, when the firm 1 buys a firm, it gives up his infinite and discounted flow of triopoly profit. It is his opportunity cost. Nevertheless, it will earn a duopoly profit instead (proof in appendix B):

3 1 2 3 2 2 1 1 1 1 1 1 1 1 1 ( , ) ( ) ( , ) ( , ) ( , ) (1 ) (1 ) (1 )
(1 )

c c c c c c c c c π π π π π δ δ δ δ ⎡ ⎤ - + - ≥ ⎢ ⎥ - - - - ⎣ ⎦ δ (6)
(6) holds if ( 7) is checked:

1 ( , ) c c c δ * ≥ (7)
with

c * c 1 ,   1 2 13c 1  22c 1  1 -2 10  7 Lemma 2 Let [ ] 1 0, 1 c ∈ and [0, 1],
δ ∈ then it always exists a verifying

[0, 1] c ∈

≤ ≤ ≤

As the first round condition is the most restrictive, we can state the following proposition:

Proposition 2 Let [ ] 0, 1 , c ∈ [ ] 1 0, 1 c ∈ and [0, 1],
δ ∈ then a monopolization path of a three-firm industry exists if and only if symmetric case, that is for 1 c c = , we find, like [START_REF] Kamien | Monopolization by Sequential Acquisition[END_REF], that monopolization of a three-firm industry is possible if

[ ] 1 2 , 1 δ ∈ . Note that 1 [0, 1], [0, 1], c δ ∀ ∈ ∀ ∈ 1 ( , ) 0. c c δ δ * ∂ ∂
≤ This means that, the larger the discount factor is, the larger the monopolization possibilities are. 8 Indeed, future profits are more valued while acquisition payments are spread over the time.

Moreover, as the owner of the dominant firm does not have to monopolize the industry in an only one round, other owners cannot ask the duopoly profit for their firms: this fall of acquisition cost explains the monopolization facilities in a dynamic context.

Note that, if , monopolization is feasible if and only if

1 c c = δ [ ] 1 2 ; 1 ∈ .
Therefore, we find again the result of [START_REF] Kamien | Monopolization by Sequential Acquisition[END_REF].

With a four-firm industry:

In this industry configuration, there are several monopolization paths, but we can prove that monopolization is easier with three rounds.

Thus, we study this path. Let us solve by the same way:

The conditions of the third and second stage are respectively the same than Third round: the first owner buys the last firm:

1 2 2 1 1 2 1 1 1 ( ) ( , ) ( , ) (1 )
(1 ) (1 )

c c c c π π π c δ δ δ - ≥ - - - (8)
(8) holds if ( 9) is checked:

1 11 1 10 10 c c -≤ (9)
Second round: the first owner buys another firm:

3 1 2 3 2 2 1 1 1 1 1 1 1 1 1 ( , ) ( ) ( , ) ( , ) ( , ) (1 ) (1 ) (1 ) (1 )
c c c c c c c c c π π π π π δ δ δ δ ⎡ ⎤ - + - ≥ ⎢ ⎥ - - - - ⎣ ⎦ δ (10)
(10) holds if (11) is checked:

1 1 13 22 1 2 1 2 10 7 c c c δ δ δ + + - ≤ + (11)
First round: the first owner buys one firm:

At the first stage, in order to monopolize the industry in the following stage, the first firm has to buy one firm. To buy the other, it has to pay an infinite and discounted profit flow of a single firm in a four-firm industry.

Indeed, the hold up mechanism of the static game does not exist. Moreover, by purchasing a firm, the firm 1 gives up his infinite and discounted profit flow of single firm in a four-firm industry. Nevertheless, it will earn a triopoly profit instead (proof in the appendix C):

4 3 3 2 2 1 2 1 1 1 1 1 ( , ) ( , ) ( , ) ( , ) (1 )
(1 )

c c c c c c c c π π π δπ δ δ ⎡ ⎤ - + - ⎢ ⎥ - - ⎣ ⎦
c c c c π π π δ c δ δ δ ⎡ ⎤ + - ≥ ⎢ ⎥ - - - ⎣ ⎦ ( , ) (1 ) (1 ) (1 )
(12) holds if (13) is checked:

1 ( , ) c c c δ ≥ % (13)
1 0, 1 c ∀ ∈ and [0, 1], δ ∀ ∈ 11 1 1 10 10 c - 1 1 1 13 22 1 2 1 1 1 2 1 0 7 2 ( , ) , c c c c c δ δ δ δ + + - + + ≤ ≤ % ≤ we can state that it always exists a verifying [0, 1] c ∈ 1 1 1 2 ( , ) c c c c δ + ≤ ≤ % .
As the first round condition is the most restrictive, we can state the following proposition:

Proposition 3 Let [ ] 0, 1 , c ∈ [ ] 1 0, 1 c ∈ and [0, 1],
δ ∈ then a monopolization path of a four-firm industry exists if and only if 1 ( , ).

c c c δ ≥ % Note that 1 [0, 1], [0, 1], c δ ∀ ∈ ∀ ∈ 1 ( , ) 0. c c δ δ ∂ ∂ ≤ %
This implies that, the larger the discount factor is, the larger the monopolization possibilities are. We state the following inequality:

1 ( , ) c c c δ ≥ % (14)
The expression (14) implies that monopolization of a four symmetric firms industry is not possible. We can also say that there are more monopolization

Conclusion:

In this paper, we have shown that firms' heterogeneity increases the incentives to merge. Since the best method to value these incentives is to make endogenous merger decisions, we have built a model in which owners' decisions are taken into account.

To simplify the analysis, we focused on the extreme case where merger leads to monopolization.

Our results differ from Kamien and[START_REF] Kamien | The Limits of Monopolization Through Acquisition[END_REF][START_REF] Kamien | Monopolization by Sequential Acquisition[END_REF]. Indeed, these authors showed that large industries cannot be monopolized. Introducing a large enough cost heterogeneity, we have shown that monopolization is feasible for all industry sizes. Moreover, monopolization is easier if the game is a dynamic one and especially if the discount factor is high. To reach this conclusion, we provided two illustrations, for three and four firm-industry because in dynamic, the n-firm generalization is too complex. This result supports the "takeover waves" explanation of Fauli-Oller (2000) based on cost asymmetries.

Moreover, the following intuition explains it: the monopoly profit is more sensitive to a fall in production cost than oligopoly profit.

Our results are also in contradiction with Gowrisankaran and Holmes (2004). They show that a large competitive industry stays a large competitive We can determinate, concerning the first round, the duopoly profit of the firm 1:

2 1 1 1 (1 2 )² ( , ) 9
c c c c π - + =
We can give the opportunity cost of the firm 1 (the profit realized by the first firm if it buys no firm):

2 3 1 1 1 (1 3 2 ) ( , ) 16
c c c c π - + =
We can establish the acquisition cost of a firm by the firm 1:

3 1 2 1 (1 2 )² ( , ) 16
c c c c π -+ =
Finally, to monopolize the industry, the first firm has to buy the remaining firm at the second stage The monopolization condition of second period has to take into account this future buying (by actualizing infinite flow of profits when it is necessary):

3 1 2 3 2 2 1 1 1 1 1 1 1 1 1 ( , ) ( ) ( , ) ( , ) ( , ) (1 )
(1 )

c c c c c c c c c π π π π π δ δ δ δ ⎡ ⎤ - + - ≥ ⎢ ⎥ - - - - ⎣ ⎦ δ (6)
which is equivalent to: About the opportunity cost of the firm 1 (the profit realized by the first firm if it buys no firm), it is given by: Finally, as to monopolize the industry, the first firm has to buy another firm at the second stage and the remaining one in the third stage, the monopolization condition of third period has to take into account these future buying (by actualizing infinite flow of profits when it's necessary):

4 3 3 2 2 1 2 1 1 1 1 1 ( , ) ( , ) ( , ) ( , ) (1 )
(1 )

c c c c c c c c π π π δπ δ δ ⎡ ⎤ - + - ⎢ ⎥ - - ⎣ ⎦ 1 2 4 2 1 1 1 1 1 1 ( ) ( , ) ( , ) (1 )
(1 ) (1 )

c c c c π π π δ c δ δ δ ⎡ ⎤ + - ≥ ⎢ ⎥ - - - ⎣ ⎦ (12)
which is equivalent to:

  firm industry with the marginal cost of firm 1 and c the marginal cost of the other firms. Profits of the firm 1 are given by 1 Given that every other firm is symmetric, firms profits are given by 2 i = . Given individual marginal costs c i and the linear inverse demand ( ) 1 P Q Q = -, then firms profits in the nfirm problem are given by Letho and Tombak (1998):

  path of a n-firm industry exists if and only if 1 (

  As seen in the previous section, the same sustainable industry conditions must be checked. Therefore, we establish that

c c c δ * ≥,

 * Here, we show that monopolization of a three-firm industry is possible for every provided that the cost heterogeneity is large enough . In the

%

  These remarks are in line with the intuitions mentioned for three-firm industries, with the actualization effect and the dynamic effect.

  the first round, the triopoly profit of the firm 1 is:

  acquisition cost of a firm by the firm 1 is:

  Williamson, O. (1968) "Economics as an Antitrust Defense: The Welfare Trade-offs", American Economic Review, Vol. 58, pp. 18-36.

Consider the three stages of the game:

  There is monopolization if and only if the first owner's monopoly profit minus acquisition costs exceeds his opportunity cost.

	duopoly profit if it unilaterally deviates from its selling. Therefore, it cannot ask output quantity. Owner's outcome is the sum of profits and transaction cash
	for more than this price. Secondly, the first firm earns more by purchasing a flow.
	firm, spending the duopoly profit of this last, rather than by not purchasing this
	firm.
	F o r In the first one, firm 1 makes bids for all other firms. Simultaneously, other owners give an asking price for their own firms. Note the vector of bids announced by the first owner. The 2 ( ,..., ,..., ) R i n B b b b = F o ∈ r
	i b	P bid is the bid for the firm. Note th i P	2 ( ,..., ,..., ) R i n O o o o = ∈ the vector of
	e e r asking prices announced by the owners correspond to the firm asking price. We note 2 th i e e r	to K the number of firms owned . The asking price n i o
	R e v i e w by the first owner after this stage. In the second stage, the first owner decides how many firms he is going to operate among his K firms. As cost functions are linear, he always decides to operate only the most efficient. Therefore, it is not necessary to analyse this stage. The question is to know how many firms remain after the dominant firm buys out competitive fringe firms. In the third R e v i e w
	stage, owners simultaneously decide output levels.
	example, firms are totally informed of consequences of buying another firm, or
		In this game, we characterize monopoly Nash Equilibrium in pure
	conversely, to be purchased. Hence, an inefficient firm cannot earn more than a
	strategies 5 . Strategies are defined, for each owner, by a bid vector and by an

  the conditions of the second and first stage in the appendix B. But there is another stage in which another firm is previously bought (cf. the proof in appendix A and B).

	F o
	r
	P
	e e r
		R e v i e w
	δ ≥	1/ 22.	Therefore, there are more monopolization
	possibilities in dynamic games than in static ones if	δ ≥	1/ 22.

Page 13 of 21 Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

		Submitted Manuscript
	2	1 1 1 ( )	2 1	1 ( , )	4 1	1
	F o
	r
	P
		e e r
				R e v i e w

  industry. No merger appears in this case. On the contrary, our model shows that large industries can be monopolized if the cost heterogeneity is large enough.Nevertheless, extensions of this line of research are necessary to take into account data neglected in our model. These extensions should include several purchasers in these games, take into account decentralized games in which firms are individually managed, and at last, find oligopoly equilibria to these games, especially if collusion is possible. The aim of these studies would be to provide tools to anticipate concentration processes. Another research should be developed in parallel: a welfare analysis restricted to the cases of industry in which concentration processes are possible.

	Appendix B
	As in the appendix A:
	F o F o F o
	r r r
	P e e r P P The final aim of this research is to identify industries in which monopolization is not possible. Thus, authorities could concentrate on the other industries in order to determine the monopolization processes which could be e e r e e r
	R e v i e w detrimental to the global welfare. Moreover, as firms supposed to monopolize the industries are the most efficient, the possibilities of monopolization decreasing welfare are limited. R e v i e w R e v i e w

It's assumed that entries in the industry are not allowed.

We assume that the firm 1 is the only one who makes bids. Even if we can prove that an inefficient firm have the same incentive to monopolize the industry, firm 1 seems closer to realize this monopolization. Indeed, his previous profits are higher because of his low cost. It could always spend more than inefficient firms if these last were allowed to make bids.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

To simplify the analysis and concentrate on the emergence of monopoly, we exclude acquisition path without monopolization. Nevertheless, given that the level of cost heterogeneity, other equilibria than monopoly can be more profitable.

In particular, the remaining firms are informed of the previous buying.

To buy one firm per round is the most advantageous path to reach monopolization (see[START_REF] Kamien | Monopolization by Sequential Acquisition[END_REF]).

Acknowledgements

I wish to thank Rabah Amir, Simon Andesson, Edmond Baranes and Wilfried Sand-Zantman for their helpful comments.

Appendix A

Given the individual marginal costs and the linear inverse demand the firm profits in the n-firm problem are given by Letho and Tombak (1998):

We can give, concerning the second round, the monopoly profit of the first firm:

We can establish the opportunity cost of the firm 1 (profit realized by the first firm if it buys no firm):

The acquisition cost of a firm by the firm 1 is:

Hence, the second stage monopolization condition is (by actualizing infinite flow of profits):

(1 ) (1 )

which is equivalent to:


James Foreman-Peck
email: foreman-peckj@cardiff.ac.uk

Laurian Lungu

R58 -Regional Development Policy < R5 -Regional Government Analysis < R -Urban, Rural, and Regional Economics

Keywords: Fiscal Devolution, Small Open Economy Modelling, Crowding Out Fiscal Devolution, Small Open Economy Modelling, Crowding Out JEL Classification: R15, R58

Public spending devolution in practice is widely seen as more appropriate for addressing varied political aspirations within state boundaries than is tax devolution. A drawback is that devolved public spending may be subject to irresistible upward pressure, as illustrated by 'formula drift' of the United Kingdom devolved administrations. By crowding out the private sector such public spending can exacerbate the problem it was originally intended to alleviate. When taxpayers do not value increases in government output at least as highly as the private goods and services they must forgo to finance them, then the public sector is too large. This paper estimates a three sector Hecksher-Ohlin model of the economy with the greatest relative rise of the public spending ratio in the United Kingdom, Wales. Simulation of the model shows a net gain in employment from a one percent cut in income tax matched by a corresponding reduction in government spending. This result is consistent with the current level of intergovernmental transfers being excessive.

Introduction

Devolution of public spending may permit local governments to provide public services better adapted to local preferences than their central counterparts [START_REF] Tiebout | A Pure Theory of Public Expenditures[END_REF][START_REF] Besley | Centralised Versus Decentralised Provision of Local Public Goods: A Political Economy Analysis[END_REF]. They are closer to their residents and information dissipates with distance. Within a given budget possibly they can alter the composition, or change the method of delivery. A second, not exclusive, justification for devolution can be a local predilection for devolved government quite regardless of whether it is more responsive or generally better at meeting local needs. People may prefer to be governed by those with whom they identify, independently of the quality of governance 1 .

If expenditure is devolved there is an incentive case that at least some portion of taxes should be also [START_REF] Sanguinetti | Intergovernmental Transfers and Fiscal Behaviour: Insurance versus Aggregate Discipline[END_REF]. In practice, while the subnational government share of public spending has increased in a majority of OECD countries, the share in general government revenues (excluding grants) has failed to rise correspondingly and has even declined in several cases [START_REF] Journard | Fiscal Relations Across Government Levels[END_REF]. Some institutional arrangements may encourage this trend more than others. An example is where an expenditure ministry bargains on behalf of regional authorities for finance with a ministry that raises national revenue and provides for national level public goods. In this case a regime in which the spending ministry gets political benefits from the expenditure will generate more spending than one where taxes, as well as spending, are devolved [START_REF] Sato | Intergovernmental Transfers, Governance Structure and Fiscal Decentralization[END_REF]. On the other hand stabilisation and redistribution weaken the case for tax devolution. When taxes are not devolved and a region experiences a negative demand shock, tax receipts fall and unemployment pay outs increase, boosting government spending and partly offsetting the private sector contraction. This is a form of risk sharing between regions subject to different shocks [START_REF] Persson | Intergovernmental Relations and Fiscal Discipline -Between Commons and Soft Budget Constraints[END_REF].

Hughes [START_REF] Hughes Hallett | Political Devolution without Fiscal Devolution[END_REF] undercuts the normative risk sharing argument by showing that fiscal autonomy for UK regions would reduce volatility of output and inflation 2 .

Interpersonal redistribution also may be reflected in inter-regional net subsidies [START_REF] Melitz | Regional Redistribution and Stabilization by the Center in Canada, France, the UK and the US: A reassessment and new tests[END_REF][START_REF] Decressin | Regional Income Redistribution and Risk Sharing: How Does Italy Compare in Europe?[END_REF]. Tax competition from other jurisdictions anyway limits the extent to which taxation can effectively be devolved. The extent of factor mobility between fiscally devolved administrations is the principal constraint [START_REF] Wildasin | Fiscal Competition in Space and Time[END_REF].

Without devolved taxation, income smoothing by the federal or central government spending, rather than by built-in tax stabilisers, can give rise to higher centrally funded state spending long after negative shocks have dispersed, preventing adjustment [START_REF] Obstfeld | Asymmetric Shocks; Regional Non-Adjustment and Fiscal Policy[END_REF]. Stabilisation presupposes some recovery from shocks and redistribution similarly has no reason to be trended. Soft budget constraints and over-spending biases embedded in political institutions exacerbate a tendency towards upwards drift in devolved public expenditure (Pisauro 2001).

The present paper therefore examines the fiscal performance of the devolved administrations of the UK to assess evidence of such dependency. A test is constructed and a tax and government spending model of the most likely candidate administration is simulated. The employment patterns found are inconsistent with long run regional 2 Unless all shocks are on the supply side.

The Devolved Economy

The model of the devolved 'branch plant' economy is developed from [START_REF] Minford | An Econometric Model of Merseyside: Validation and Policy Simulations[END_REF], and Hecksher-Ohlin-Samuleson principles. It consists of two private sectors, producing respectively traded goods (Y T ), all of which are exported, and nontraded goods (Y NT ), and a public sector. The private sectors employ intensively unskilled labour (L T ) in the traded good production and skilled labour (L NT ) in activities that do not trade across the boundaries. Unskilled labour is immobile across borders but possibly mobile between sectors. Skilled labour is mobile across borders, so that the non-traded wage in the devolved administration equals that of the larger economy,

* NT NT W W = .
Labour markets are competitive; employers' real wage costs equal the marginal product of labour in both traded and non-traded sectors:

) ( ) 1 ( ' T T T EMP L F P W T = + and, ) ( ) 1 ( ' NT NT NT EMP L G P W T = +
where F(.) and G(.) are production functions of traded and non-traded goods and services respectively and EMP T is the employment tax rate. The traded product price, T P is determined in the world market with

B Y G G + =
The expenditure consists of purchases of goods and services to produce output (Y G ) of public administration, health and/or education, say, plus transfer payments (B).

Both create a demand for non-traded goods and services, as does traded good production. Y G requires labour for production,

L T = g T (Y G ), L N = g N (Y G )
The government sector can employ workers from either non-traded or traded sectors. The expectation is that mobile labour will be used more intensively than immobile labour.

The demand for nontraded output depends upon traded output and government spending. Employees in exporting or in government service spend money in shops and on local services and send their children to school. In turn this gives rise to other rounds of spending. An income tax effect depends upon the levels of traded output and government spending and their respective nontraded goods multipliers, on the demand side. On the supply side the level of income tax affects labour force participation and therefore private sector output. Government production, by contrast with transfer payments, competes with the private sector for resources. where Y T are exports and M, imports, all tradable consumption. A net subsidy to the economy (NTR) (T<G) allows a current account deficit and a higher level of demand at a given real exchange rate.

Federal or central government income smoothing in the response to a negative shock to exports and thus to employment and income occurs because T falls (by less than X) and G remains unchanged (or may in fact rise). The regional balance of trade deficit widens and tax revenue no longer covers as much of the cost of government output and employment, so there is an expansion of the subsidy. The share of government output and employment in the total rises.

[ insert Figure 1 here ] Figure 1 shows the case of mobility between traded and nontraded sectors, where the real exchange rate is determined by technical efficiency and therefore is exogenous. If net intergovernmental transfers pay for interpersonal transfers such as pensions and invalidity benefit then they simply boost consumption, allowing demand to exceed output by the amount of the transfer. They also permit more (tradable consumption) imports than (tradable production) exports.

Again, when some of the net transfer pays for government production and therefore employs local labour, some of which would have worked in the private sector, the capacity to import is still enhanced by the block grant from the central government, regardless of whether those in the devolved jurisdiction value the output as much as in 7 the first case. However the capacity to export will be reduced insofar as local labour is diverted from the tradable sector. Hence the balance of payments constraint may not be shifted as much as by pure transfers. The willingness of consumers to substitute government output for tradable consumption (imports) determines the level of demand generated by the block grant. Now consider an increment of government spending not paid for by intergovernmental transfers. Assume that the extra government output is judged an inadequate substitute for private goods forgone as a consequence of the extra taxes paid in the devolved administration3 . Extra taxes and government output reduce private sector output (tradable and non-tradable) at a given real exchange rate. Exports are cut by the transfer of labour from the private to the public sector. Private consumption and therefore imports do not fall initially despite the higher taxes because the taxes pay for the workforce transferred to the public sector. These people still wish to consume tradables, so that imports are not reduced. The economy therefore deflates as a consequence of the self-financed increment in government spending, unless more intergovernmental transfers are forthcoming; since the real exchange rate cannot adjust, monetary forces exert downward pressure on income, employment and output to restore balance of payments equilibrium (PCA shifts left in figure 1)4 . Hence government expansion crowds out the private sector and deflates the economy when government output is not valued sufficiently highly by taxpayers.

The solution in such cases is to increase the size of the tradable sector by supply side policies such as tax cuts matched by public spending cuts. The expansion of the This devolved government over-expansion possibility can be tested. In practice government output is measured at cost, and so, in an exercise implicitly to assess the value users place on government output, must be ignored. Employment is a better welfare proxy. If tax cuts boost employment by more than the equivalent government spending reduction then the balance of payments will be improved, demand and output will be higher. The balance of advantage indicates the valuation of incremental government output.

The Devolved Administrations of the United Kingdom

The UK devolved administrations exercise no tax-raising powers but are primarily funded with block grants from the central government that levies taxes. By contrast the English regions lack authority for devolved spending, as well as for levying taxes. Taxes are typically proportional or progressive (in the UK with the exception of the only local tax, the community charge that accounts for a small proportion of total tax payments). They therefore permit contributions to the finance of services such as heath and education to a common standard according to ability to pay by individual and by jurisdictions. These tax arrangements mean that, unlike central government, there are no electoral advantages for administrations in terms of tax restraint from public spending economy. Since 1979 the size of the block grant has supposedly been governed by the Barnett formula, intended virtually to eliminate the spending per head gap with England in the very long term. The grant per head of the devolved population increases in absolute terms with spending per head in England. Since the administrations spend more per head than England, their percentage increases in budgets would be less under the formula. However political bargaining, 'formula bypass' [START_REF] Heald | Territorial Public Expenditure in the United Kingdom[END_REF]2003), ensured that the spending gap is more likely to increase than to diminish5 . A study of Scottish education spending found that using the English Local Authority approach to assessing 'need', Scottish pupils would receive about 3 percent more than the Englishbut actual spending is considerably higher [START_REF] King | An English Assessment of Scotland's Education Spending Needs[END_REF]. With lower regional incomes the same spending gives rise to a higher ratio of public expenditure to GDP; a region with a 20 percent lower than average income per head would exhibit a ratio of 1.25 if this principle were followed. While temporarily higher ratios might be warranted in response to shocks, permanently higher real government spending, taking the ratio above the warranted level would be a symptom of inefficiency, or of 'gold-plating' relative to rest of the economy, unless the spending ratio in other regions has risen similarly. Stabilisation presupposes some recovery from shocks and redistribution similarly has no reason to be trended. Trends in devolved government spending to income ratios could reflect federal or central government decisions rather than increasing or decreasing dependency. Therefore a test of dependency or inefficiency is whether there is a trend rise in the ratio of government spending to GDP in the devolved administrations relative to the ratio in the core, or to the federal average. As Table 1 shows, the ratio of government spending to output (in per capita term) in Wales and Scotland has risen relative to England since 1976. The ratio is highest for Northern Ireland, where it has been fluctuating around 1.8 since 1976, despite the narrowing of the income gap over the period. England's poorest region, the North East with approximately the same income per capita as Wales, showed a slightly higher government spending ratio than Wales in 2001, though lower in earlier years.

Wales exhibits the strongest trend increase in ratio since 1976, albeit from a low level.

Relative to England, the government spending to output ratio has risen from 1.2 in 1976 to 1.54 in 2000. Wales is therefore the most suitable candidate for testing the consequences of rising central government dependency in a devolved administration.

[ insert Table 1 here ]

Model Specification

To operationalise the model of section 3 a CES function is assumed for traded production and Cobb-Douglas technology for the private non-traded sector. There is a perfectly elastic capital supply at the world price, the rental 'r'. It follows that the gross wage or unit labour costs for traded sector must also be fixed-so that traded sector employment is then determined by the supply of labour to this sector. Employment fixes traded sector output and this determines non-traded sector output by creating the demand for it.

Suppressing subscripts the CRS CES manufacturing production function is:

[ ] / 1 ) 1 ( + = T T L K Y (4.1)
with capital and labour having relative factor shares P (0<P<1). The parameter measures the state of technology ( >0) and denotes the efficiency of production. The elasticity of substitution is =1/1+ with -1<R.

( ) ) 1 ( / / + = K Y d P r T T (4.2) ( ) ( ) [ ] [ ] ) 1 ( / / 1 1 / ) 1 ( ) 1 ( ) 1 ( + = + T T T P r L Y (4.3) Output per worker, T T L Y
, is fixed by the production function and the world price of capital. Cost minimisation determines the gross cost of labour must equal the marginal revenue productivity of labour. Then:

( ) ) 1 ( / ) 1 ( / ) 1 ( + = + T T T EMP T L Y P T W (4.4) Substituting for ( ) ) 1 ( / + T T L Y
from equation (4.3) into (4.4), real gross labour costs in the traded sector become:

( ) [ ] T T EMP T P r P T W / 1 ) 1 ( / ) 1 ( ) 1 ( ) 1 ( + = + (4.5)
The lower the elasticity of substitution ( <1) the smaller is the (inverse) change in the traded sector wage caused by a given change in the capital rental. When the elasticity of substitution is greater than unity, a reduction in the rental also reduces the wage, because the substitution effect dominates the output effect. If productivity is lower in the devolved administration's economy than in the core economy then so will be the regional traded good wage. Otherwise, with a similar capital rental and traded good price, it will be the same.

Non-traded sector output NT Y depends upon aggregate demand (DMD) from the traded or export sector (Y T ) plus components financed by government (G) net of taxes.

( ) The representative agent consumes a bundle of traded and non-traded goods for which a price P is paid, taken as a weighted average of the traded and non-traded price indexes. Each agent is endowed with a fixed amount of time, which is spent either on leisure. The labour supply to the traded sector is derived from on household utility maximisation, where the after-tax real wage relative to unemployment benefits determines the trade-off between work and leisure.

Employment in the traded sector is fixed by exogenous gross wage and the supply of labour to the sector. Output is then determined by the marginal productivity of labour. In logs the marginal productivity equation is: Working population depends upon natural increase, net migration and influences upon labour force participation such as administrative regimes for sickness benefit.

( ) [ ] ( ) [ ] ( ) [ ] T P t w Ln Ln L Y Ln / ) 1 1 / 1 )
Only skilled labour migrates across the border in the present model. Net migration is often supposed to depend upon relative wages and or relative unemployment rates (for example [START_REF] Jackman | Regional Migration versus Regional Commuting: The Identification of Housing and Employment Flows[END_REF]. The impact of public sector employment (public administration, health, education) depends on whether the appointments are from the immobile or mobile labour forces. The effect is captured by the coefficient on government employment in the working population equation.

Unemployment is determined by the difference between working population and total employment, both public and private sector. Thus, unemployment is not the gap between labour supply and demand, it is rather the excess of the labour force over the labour supply 7 . Migration may alter the size of the labour force which in turn will affect unemployment.

Model Estimation

The above model, estimated for the economy of Wales from annual data between 1971 and 2001, is set out in Table 2 below. Manufacturing industry is the proxy for the traded goods sector 8 . Appendix 1 presents unit root ADF tests for the 6 This is a mark-up on manufacturing (traded) sector wages since the traded sector wage is exogenous. 7 For a discussion on the implications of the two models of unemployment determination see, for instance, [START_REF] Blanchflower | The Wage Curve[END_REF]. 8 The correspondence with the theoretical sectors is not exact since there is some traded output produced in the non-manufacturing sector (for example mining at the beginning of the period and tourism at the end. Historically coal exports have been of major significance for the Welsh economy. On the one hand relatively little employment and output (11 percent in the Industrial Production index of 1970) was accounted for by mining even at the beginning of the period. On the other, it was more erratic than [ insert Table 2 here ] The estimated productivity equation (A1.2) is derived from the labour marginal productivity equation (4.8). The effect of tax-adjusted wages relative to manufacturing prices on manufacturing output is statistically significant. Also highly significant is the lagged productivity term, the coefficient of which implies a strong persistence of productivity effects. As part-time workers displaced full time workers, manufacturing labour productivity measured simply as a ratio of manufacturing output to the number of employees in manufacturing could be misleading. 10 As in equation A1.1 the spread of manufacturing-employment and output fell earlier (between 1971 and 1974 output declined 40 percent). So there is an overstatement of buoyancy of export sector in the early years. 9 It is well known that the OLS estimation of equations with lagged dependent variables, as some equations in our model are, renders the DW statistics unreliable. 10 Explaining productivity in UK manufacturing as a whole has proved problematic, partly because apparent productivity slowdown in the 1970s stemmed from incorrect measurement of output and from structural change [START_REF] Cameron | Why Did UK Manufacturing Productivity Growth Slow Down in the 1970s and Speed Up in the 1980s?[END_REF]. constructs the Welsh cost of living index as a weighted average between traded and non-traded regional prices. For simplicity the weights were kept constant over the estimating period. To assess the impact of the rise in the government spending ratio over the years 1971-2001, the employment consequences of an income tax reduction compared with an equivalent government spending increase are simulated with the estimated model.

Simulations

The job effects of a one percent cut in employment tax is also considered. Output is less relevant because it includes a substantial government component valued at cost rather than market prices.

As the model of section 2 implies, if on average taxpayers in the devolved economy regard an increment of government services as more than compensation for the private goods foregone, then their demand for imported goods and services will diminish, and the economy will expand. The converse is true if they prefer the private goods. Measuring the size of the economy by employment, the test of the valuation placed on a marginal change of government output is whether the more jobs are created by a tax cut than by an equivalent increase in government expenditure. Another way of putting the matter is that the valuation measure depends on how the 'cost per job' of the employment created by the public spending increase compares with the 'cost per job' of the taxes raised to finance it.

Simulation 1. Income Tax

Table 3 below presents the quantitative effects of a hypothetical cut in Welsh (and UK) tax rates and of a public spending reduction increase corresponding to a one percent or 1p in the pound reduction in income tax, in 2001.

[ insert Table 3 here ] A one penny in the pound cut in income tax induces a 0.5 percent (supply side) increase in manufacturing output and employment (col. 1). The expansion of the manufacturing sector, stemming from a greater labour input, boosts demand for non- traded output by 1.6 percent so that total output rises 0.65 percent, while total employment increases by 0.54 percent, or some 6,700 jobs. Non-manufacturing employment expands by 0.84 percent -or 4,400 jobs. Working population also grows, going up by 0.22 percent because of immigration and increasing labour force participation. Considering the policy as a job creation exercise, a one penny in the pound increase in the after-tax wage in both sectors yields a cost per job of £31,18011 .

Simulation 2 -Employment Tax.

Table 3 (col. 2) shows the effects of a one percent cut in the employment tax rate paid by the firm. Since the gross wage for the traded sector is exogenous, an increase in the employment tax must be accompanied by a corresponding opposite movement of the nominal manufacturing wage rate. Manufacturing employment increases by 0.48 percent -or 1,760 -triggering an expansion of the manufacturing output. Higher activity in the traded sector has a positive impact on non-traded sector output, which rises by 0.92 percent. To produce this output, employment in the non-traded sector goes up by 0.48 percent -or some 2,500 jobs -and unemployment falls by 0.23 percent.

From the point of view of a job creation, the overall cost per extra job is £39,248 in revenue forgone .

Simulation 3 -Government Spending

This simulation is based on an increase in government spending approximately equal to a one percent increase in income tax, namely a 1.24 percent rise in G. For the year 2001 this amounts to £208.9 million. Another direct consequence of the shock is a boost to public sector employment, EMP G . For every one percent increase in Y G, EMP G was assumed to rise according to the historical average, by 0.45 percent. The expansion of government spending has no impact on the Welsh manufacturing sector (Table 3, col. 3). The direct effect of government spending is around 1,570 jobs which, together with the indirect effects, push up the total employment to 4,070 jobs. The cost per job per year in this case is around £51,327 and the cost per private sector job is much larger.

Comparison of Spending and Tax Simulations

Overall the costs per job are very high -for the income tax cut about equal to the average full time gross wage costs-and especially high for the government spending policy. Since the extra jobs generate more tax revenue in all three simulations, there would be some offset not considered here. The impact on the non-traded private sector is quite powerful and ranges between 0.5% in the government spending simulation to 0.9% in the employment tax simulation. A vital difference though is that the tax reductions expand the traded sector whereas greater government spending has no effect on it at all. Unemployment falls when taxes are cut. The unemployment rate also declines with greater public spending but only because of the induced growth of working population (the denominator of the unemployment ratio).

The simulation shows that a one penny in the £ cut in Welsh income tax (with a corresponding reduction in UK tax) matched by an equivalent cut in Welsh government spending raises employment (and leaves apparent output virtually unchanged). But the spillover effects of public spending on the private non-traded sector are relatively weak.

Consequently the greater part of employment creation in the public spending scenario comes from government jobs; the private 'export' sector only expands in a tax cutting The inference is that, because of the substantial size of the government sector allowed by the net transfers from the central to the devolved economy, at the margin Welsh taxpayers do not value an increment of average government spending as highly as the private goods forgone because of the corresponding increase in tax payments. A tax-cutting strategy would expand the devolved economy.

Conclusion

Devolution of public spending is increasingly seen as an appropriate response to heterogeneous political aspirations within current sovereign state boundaries. Tax devolution is less widespread because of limited or inappropriate tax bases, adverse consequences of tax competition and reduced possibilities for regional stabilisation.

But against these considerations must be weighed the efficiency/moral hazard case for devolving taxes. greater than that of the corresponding tax change then the public sector is too large.

Of the three devolved administrations in the United Kingdom, two of them increased their ratios of government spending to GDP relative to the English economy over a quarter of a century. The third maintained a ratio 80 percent higher than the English over the period. The paper has estimated a three sector Hecksher-Ohlin model of the economy with the greatest relative rise of the public spending ratio, Wales. [START_REF] Ljung | On a Measure of Lack of Fit in Time Series Models[END_REF] is motivated by the fact that this test yields superior small sample performance compared to the original Box andPierce (1970) Q-statistics. Following Enders (2003), who suggests that the number of sample autocorrelations and partial autocorrelations should not be higher than T/4, for our 30 dataset sample we set this to 6. The results are presented below. W NT -Non-traded Welsh wage (£, gross, weekly) T Y -Welsh employees' income tax T EMP -Welsh employers' income tax T YUK -UK income tax BEN -Unemployment benefits FWPOP -Welsh ratio of females in working population SIB -Welsh claimants of sickness benefits (thousands) LOW -London-Wales relative house prices SEW -South-East -Wales relative house prices WPOP = Welsh working population (thousands) P M -Manufactures prices (1990=100) P NT -Welsh non-treaded price index (1990=100) RPI -UK Retail Price Index (1990=100) RPI W -Welsh Cost of Living Index (1990=100)

  equilibrium, suggesting an advantage from balanced reductions in taxation matched by government spending.

  from the federal or central government. Tax receipts (J) are paid directly to the central government. They increase with employment, wage levels and tax rates. The region's current account is then: Y T (e) -M(e) = G -T

  more exports, and shifts the PCA balance to the right, permitting more long term output, employment and income. Failure to take into account the monetary forces set in motion by balance of payments adjustment can conceal the asymmetric effects of government expenditure increase and tax cuts on the level of economic activity in devolved administrations and economies.

  the exogenous traded sector wage T W , can be inferred by substituting for capital in the production function with the marginal productivity condition:

  maintained regressions for I(1) included either an intercept and a deterministic trend or an intercept only, as appropriate. The tests show that the unit root hypothesis cannot be rejected at the 5% significance level for all variables. The data series and definitions are described in Appendix 2. All model equations have been estimated by instrumental variables (IV), using various exogenous variables of the model as instruments 9 . Appendix 3 presents the Ljung-Box Q-statistics for the residuals for model equations. Equation (A1.1), the manufacturing labour supply function, should ideally measure labour supply in hours, rather than in persons, the actual specification. In view of the rise in part-time, primarily female employment and the absence of data either on hours worked or on the proportion of part-time workers in Welsh manufacturing, the ratio of female employees in Welsh working population (FWPOP) is included to control for this change. Demographic shifts and other time-dependent factors are approximated by a time trend.

  therefore introduced as a control. The negative coefficient estimated for the ratio of female employees in working population (FWPOP) is consistent with this interpretation.Turning to the non-traded sector, equation (A1.3) explains the demand for output with the two exogenous components of demand, traded output and government spending. The size of the long run coefficient on traded output/manufacturing reflects the declining share of output of this sector over the estimation period. Firms' demand for labour to produce non-traded output is given by a Cobb-Douglas marginal productivity equation (A1.4). The long run equilibrium ensures that this exhibits constant returns to scale. Equation (A1.5) models the real net non-traded wage as a mark-up over real traded wage. The coefficient of government spending is positive but small, consistent with government demand for labour pushing up wages of selected categories of employees. Equation (A1.6) explains working population. House prices determine the migrant component of working population; higher relative house prices elsewhere discourage migration from Wales but encourage migration to Wales. The net effect on migration may well depend on the region, whether it is a net importer or net exporter of people to or from Wales. Those relative house price terms included are proxies for the whole regional pattern of house price change. Adding in other region house prices does not change the overall impact, even though they are often statistically significant.The inclusion of numbers on invalidity and sickness benefits (SIB) in the equation is designed to test whether working population is reduced by the high claimant rate. The coefficient indeed has a negative sign; in view of the relative sizes of the two elasticity of 0.04 implies that, at the end of the period, for every four entering or leaving receipt of invalidity benefit approximately one person entered or left the working population. Current declines in numbers on benefits are therefore explained by moves into retirement; the majority of male claimants are over 55 years of age. Most net new claimants apparently would have not been part of the workforce if they had not claimed invalidity benefit. The public sector and non-traded employment variables in the equation capture similar, but larger, displacement effects. In 2001 public sector employment was 27 percent of working population, which together with the elasticity of 0.258, suggests a one for one relationship; increases in public sector employment have raised the working population equivalently, either by greater labour force participation or by migration (which includes preventing emigration). Private non-traded employment, accounting for 57 percent of working population in 2001 yet with a similar coefficient, exercises a much smaller influence. Every two extra workers boosts working population by just under one person, because some non-traded labour comes from the unemployed, the traded sector or the public sector. The model is closed with the identities (A1.7)-(A1.10). Government spending (Y G ) and government employment (EMP G ) are treated as exogenous. In the unemployment identity 'employment' includes self-employment. Equation (A1.10)

  sector jobs in total are crowded out by balanced tax and spending increases.

  statistics in parentheses) Y -Welsh output (billions £) Y NT -Welsh non-manufacturing output (billions £) Y T -Welsh manufacturing output (billions £) Y G -Welsh government spending (billions £) G -Welsh government spending, including transfer payments (billions £) EMP -Welsh Employment (thousands) EMP T -Welsh manufacturing employment (thousands) EMP NT -Welsh non-manufacturing employment (ths.) EMP G -Welsh public sector employment (thousands) u_UK -UK unemployment rate (%) u_W -Welsh unemployment rate (%) W T -Welsh manufacturing wage (£, weekly, gross) W UK -Average UK wage(£, gross, weekly)

  With mobility between sectors both W T and NT W are exogenous; consequently the real exchange rate is also. More productive local labour appreciates the exchange rate. Labour supplies depend upon the cost of living, an index of the two prices, T P and

	NT P , and on the income tax rate, Y T .
	Without tax autonomy devolved government spending (G) is fixed regardless of
	tax receipts.
	F o r
					P
					e
					e r
					R
					e
					v i e
					w
					* T P P = . Non-traded goods and T
	services prices	) P can diverge from those in other areas but must remain linked to ( NT
	NT W by production technology. Thus, the real exchange rate is:
	e =	P	NT	T P
					5

  If they do not, they will try to import more private sector goods and services than can be financed and thereby create deflationary pressure in the economy, unless more central government transfers are provided. When a balanced expansion (contraction) of government spending and taxation reduces (increases) employment then the size of the public sector is greater than optimal; the valuation of the increment of government output is less than that of the matched tax payments. The test can be represented also in relative 'cost per job' terms. If the implied 'cost per job' of government expansion is

	them.
	F o r
	P
	e
	e r
	R The political economy of increasing government spending, for instance e
	in 'frontier' regions with secessionist challenges, can encourage excessive government spending in devolved economies in the sense that private sector economic activity is v i e
	crowded out and the possibilities for autonomous economic development unsubsidised w
	by central government are reduced. In the case of the United Kingdom's devolved
	administrations, 'formula drift' has prevented reining public spending into line with that
	of the English economy, despite the existence of a rule intended to achieve this end.
	The present paper has developed a test for over-expansion of the public sector in
	devolved economies. It turns on whether taxpayers value increases in government
	output at least as highly as the private goods and services they must forgo to finance
	21

  Unemployment rates, un_W and un_Uk, and the share of female employees in working population, FWPOP are in percentages. All other variables are in logs.The Ljung-Box Q-statistics for the residuals for model equations The choice ofLjung-Box Q-statistics

	Appendix 1 Appendix 3.
	Unit Root Tests
	Variable # EMP T * EMP NT * WPOP *	ADF Value for I (1) -1.730881 -2.890787 -2.751787
	F o r P e e r F o r P e e r Real net manufacturing -2.671702 wage * Y * -2.199194 Y NT * -2.032721 Y G * -2.77875 Y T * -2.653456 FWPOP * -1.273380 EMP G * -2.178411 SIB * -1.371440 u_UK ** -2.096756 u_W ** -1.905140 EMP * -2.256045 G * -1.901133 LOW ** F o r F o r F o r F o r -1.683851 SEW ** -2.010703 Firms Unit Labour Costs * P P P P -3.445898 e e e e Notes: *MacKinnon critical values for rejection of hypothesis of a unit root (intercept and a trend, 2 lags e r e r e r e r
	Simulation of the model showed a net gain in employment from a one percent cut in income tax matched by a corresponding reduction in government spending. The result is consistent with the current level of intergovernmental transfers being excessive. R e v i e R e v i e included). 1% Critical Value* -4.3226 5% Critical Value -3.5796 R R R R 10% Critical Value -3.2239 **MacKinnon critical values for rejection of hypothesis of a unit root (only intercept, 2 lags e e e e included). 1% Critical Value** -3.6852 5% Critical Value -2.9705 10% Critical Value -2.6242 v i e v i e v i e v i e
		w w w w w w

#

Figure 1. Intergovernmental transfers and state employment Table 1. Regional UK public expenditure to GDP as a ratio of England's public expenditure to GDP, 1976-2001

  calculated values of Q in Table4do not exceed the appropiate 5% values in the chi-squared table so the null of no significant autocorrelation cannot be rejected at this level of significance.Source: Public Expenditure Statistical Analysis (PESA) HM Treasury, various issues(PESA 1998-1999 Tables 7.2B, 7.3B, 7.4B, 7.5B and 7.6B; PESA 2002-2003 Tables 8.3B and 8.4B, PESA 2004[START_REF] Hughes Hallett | Political Devolution without Fiscal Devolution[END_REF] Table 8.1). The 1976 figure has been calculated by multiplying the ratio of devolved spending per head (taken from Table 3, HM Treasury, 1979) by the GDP per capita ratio (England relative to region).

					Submitted Manuscript		Page 28 of 30
	A1.7	WPOP	=	The Ljung-Box Q-statistics for the residuals for model equations Eq. A1.1 Eq. A1.2 Eq. A1.3 Eq. A1.4 Eq. A1.5 Eq. A1.6 0.01 2.02 3.16 * 0.05 1.27 0.06 4.94 * 2.13 3.36 1.47 1.27 0.42 4.94 6.10 3.89 1.73 1.27 2.45 5.59 7.27 6.18 2.36 6.22 2.79 7.86 7.50 9.88 * 3.51 11.02 * 3.01 10.27 8.44 11.85 * 3.79 11.02 * 3.12 F o r P r for output e Demand output e Aggregate private sector supply Primary current Real exchange rate =(w/P) k Private sector output HOS equilibrium value =f(MPL)=e** account balance Inter-govt transfers and imports Private sector Private supply when government uses more local labour SEW LOW SIB EMP + + + F o r P e e r R e v i e w	u	UK	+	EMP
						R
						e
				Year 1976	Scotland 1.27	v i e Wales w Northern Ireland 1.20 1.88	North East England n/a
				1992	1.24	1.46	1.83	n/a
				1997	1.27	1.49	1.78	n/a
				2001	1.34	1.51	1.80	1.56

* Significant at 10% level. The Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK

If increments to what the government was doing were useless in utility terms they would still record a contribution to output because of the way output is measured

PCA , primary current account, balance is the series of output and real exchange rate combinations at which exports equal imports. A given output and real exchange rate determines the demand for imports. If the supply of exports contracts then PCA balance shifts left.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

For Scotland,Midwinter (2002 108) points out that the Scottish Executive was able to accommodate free personal care for elderly and teachers' pay increases within Treasury allocated expenditure growth totals, because its share of the UK budget was rising-despite the Barnett 'squeeze'.

The figure reported is for the year 2001. For example, for the manufacturing sector the cost is £418/week*0.01*52 weeks per employee. For both sectors combined the cost per job is £31,180.

Editorial Office, Dept of Economics, Warwick University, Coventry CV4 7AL, UK Submitted Manuscript

Manufacturing wages (WMAN) -£/week. This is "average weekly earnings, full time manual and non-manual male". For the 1986-2001 period the data is from NES. For the 1971-1985 period no such series is available. However, the NES reports separate time series for manual and non-manual male weekly earnings so that we re-constructed the series by assuming a constant share of manual males in total male employment of 0.7.

This ratio was obtained (approximated) for year 1990 from Table 8.2, pg 159 in DWHS.

To get the real wage the series was deflated by the CPI.

CPI -UK consumer price index ONS, (1990=100).

GDP deflator (GDPD) -ONS, (1990=100)

Price of UK manufactures output (PM) -ONS, 1990=100.

Working population (WPOP) -Thousands. Data for 1974-1996 from DWHS, Table 7.2, pg 137.

Manufacturing, total employment (EMPT) -Thousands. Data for 2000 and 2001 was taken from the NAW. For other periods data is from RT.

Total employment (EMP) -RT. Thousands.

Welsh Output (Y) -£ millions, GDP at factor cost, current prices. Data from 1999 to 2001 are estimates and was taken from NAW. Data from 1974-1996 is from DWHS,