Regional policy from a supra-regional perspective

TL;DR: In this article, a simple short-run two-country four-region model is introduced to study the trade-off (differentiating for different regional productivity and different strengths of agglomeration economies), which are innovatively modelled on the demand side.

Abstract: The issue of the interplay between the two objectives of equity and efficiency for national policy-makers in charge of regional policy is becoming topical once again in regional economics. This paper first reviews this issue theoretically and looks at recent literature contributions to show that, although many advances have been made, little attention has been paid to the effects of regional structural differences on the trade-off between the two objectives. Then, to demonstrate that differences between the regions of which a country is composed may influence the results of the models, a new simple short-run two-country four-region model is introduced to study the trade-off (differentiating for different regional productivity and different strengths of agglomeration economies—which are innovatively modelled on the demand side). In this short-term model, the national policy-maker can affect entrepreneurship through the set-up costs of firms. Similarly to the traditional literature, for countries composed of identical regions, spatially dispersed allocations of public support to production are more efficient with low agglomeration economies whereas spatially concentrated allocations are more efficient with high agglomeration economies. As the regions become different, however, unbalanced allocations of public support to the most advanced region become more efficient even in the case of relatively weak agglomeration economies, until, when regions are sufficiently different, the most efficient allocation of public support to production is always concentrated in the most advanced territories. If some sort of compensating mechanisms were available, in the short-run the policy-makers could decide to support the competitiveness of the already more-productive regions and transfer income to the lagging ones. All these issues are studied with reference to southern Italy (“Mezzogiorno”) and eastern Germany (former DDR) in order to show not only the similarities with the model’s predictions but also the many differences, resulting from the far greater complexity of actual development processes.

Summary

1 Introduction

• A large number of economic models have been developed in the past 15 years in order to explore endogenous regional growth and the location of economic activities, with the consequent differentials of development among territories.
• These developments appear, however, to have taken place without paying enough attention to the effects entailed by regional policies from an aggregate point of view.
• The relative failure of many regional policy attempts, which weren’t able to induce growth and convergence, and the introduction of increasing returns in economic models, have then shown the possibility of a trade-off.
• For some time, this issue hadn’t been at the core of the researchers’ attention, but is returning to the theoretical limelight.
• If this is the case the authors face a trade off between equality and growth”, (Maystadt, 2000, p.4).

2 Desired properties of regional policies

• It must be noticed that the quadrants II and IV are not comparable from a Paretian point of view, and this poses another problem to the policy maker, who, even when having the instruments allowing her to chose one of the two stable equilibria, may be facing a trade-off between two desirable objectives.
• By securing a more balanced spread of economic activity across the Union, regional policy helps to reduce the pressures of over-concentration, congestion and bottlenecks” (Commission, 2004, p. xxvi-xxvii).
• Unfortunately, the political decision-makers are not always aware of the possible drawbacks of the policies they are going to implement.

3 Regional policy in growth, agglomeration and

• The spatial impossibility theorem (Starrett, 1978) affirms that when transport is costly and space is homogenous, then no equilibrium exists which involves the movement of goods.
• This is further proof that adding the spatial dimension to economic models leads to important complications and, even more importantly, to results that are highly dependent on the hypotheses.
• Finally, policies can be very effective when they act as a selection mechanism able to lead the economic system towards the desirable equilibrium, if the starting point is not a stable equilibrium.

4 Regional policy in a two countries four regions

• In Section 2, a framework has been developed to classify the effects of regional policies on the two axes of equity and efficiency (Table 2).
• This model does not use agglomeration and assumes that some structural differences among regions may exogenously exist; in this sense, if the possibility of structural rearrangement is implied in the long-run, this is a short-run model.
• In order to address the question, an economy consisting of two countries and four regions (two regions per country) is modelled.
• This may be modelled on the supply side, for example by making more productive the firms of regions where more firms are present, but for their purposes, it is equivalent and easier to model agglomeration economies on the demand side.
• The publicly provided production factor is assumed to decrease the requirement of investment of the firms of the region, i.e. their total set-up costs, in the same measure for all firms: PUBi is therefore non excludable within each region.

4.1 Simplified model

• Let’s now study the supply side and firm behavior, starting with the limit case δ = 1 (complete rivalry) because it offers the possibility to obtain analytical solutions.
• Remembering that the behavior of all firms in each region is symmetric, the cost equation is now given by: C(xi) = ( Fi − PUBi Ni ) wi + aiwixi (5) Each firm maximizes its profit by setting its price , once the demand function is known (Eq. 4).
• In fact, there exists a mass effect, due to the assumed agglomeration economies, and a congestion effect, due to the rivalry in the use of the publicly provided factor.
• The income of both domestic regions, calculated in terms of the numeraire (and foreign) region also depend on the structural parameters of the latter.
• The analysis of the derivatives in this simplified model shows therefore that the behavior of the model is complex and depends, in addition to the market and demand parameters, on the parameters of the regions, i.e. on their specific structure.

4.2 General model

• This section works out the more general case in which there is some degree of rivalry in PUBi (δ < 1).
• The demand side of the model is unaffected, the supply side, instead, changes as implied by Equation.
• The labour demand of each firm, together with the fixed labour endowment of the region (Li), gives the number of firms present in each region.
• Since the GDP of the two region country is still Liwi +.
• Obviously this general framework encompasses the limit case of Section 4.1.

5 Equity, efficiency and regional policy

• In the simplified case, although the most efficient β (hereafter β∗) could be any value between 0 and 1 depending on the structural differences of the regions, the curvature of the graph were always concave.
• When agglomeration economies are low , as far as regional productivities become increasingly different, β∗ moves from 0.5 towards an unbalanced value, until the authors reach a situation in which the maximum efficiency is to give all public support to the larger region.
• This figure has on the horizontal axis the (exogenously given) differences between the regions, and on the vertical axis the values of β.
• If the differences are therefore above D∗s , there are policies able to combine equity and efficiency only if the starting allocation of PUB is extremely unbalanced towards the weaker region.
• As Lombardini (1992) points out, in Italy, an efficient industrial policy has never been set up, instead all the policies have been developed in an assistantial manner, indeed the southern regions have developed only as a big market for the north’s products.

6 Conclusions

• This paper has addressed the issue of the compatibility of the two possibly separated objectives of national economic efficiency and interregional equity within a framework of regional policy.
• If the regions composing a country are identical, the model behaves as the bulk of the literature predicts: for strong agglomeration economies, the most efficient policy is to support entrepreneurship in just one region, when agglomeration economies are lower it is efficient to divide the public productive support equally among the two regions.
• If transfers of income are not available, the most equitable policy is always to give the same to both.
• When the regions are differently productive, though, the most intuitive and diffused result is controverted.
• The model leaves open the possibility that policies concentrating the productive support in the already stronger region, with some income compensation for the poorer, could, despite being efficient in the short-run, be detrimental to long-run growth.

Figures

Table 2: Classification of the possible effects of regional policies.

Figure 4: The relationship between regional exogenous characteristics, β∗ and βeq in case of strong agglomeration economies (left) and weak agglomeration economies (right): regions differing in size (Li, top), fixed set-up costs (Fi, center) or flexible costs (ai, bottom). On the horizontal axis the percentage difference between the regions, with a positive value indicating an advantage.

Figure 1: Relationship between γ and δ: in the upper part of the squares the relationship between β and total GDP is concave. (γ on the horizontal axis; graphics for σ = 1.5; 2.0; 4.0).

Figure 2: The relationship between β and national GDP in case of strong agglomeration economies: results with identical regions (top) with slightly different regions (middle) and with more different regions (bottom).

Figure 5: The relationship between β∗ and βeq in case of strong agglomeration economies (top) and weak agglomeration economies (bottom).

Figure 3: The relationship between β and national GDP in the extreme case of complete rivalry or in case of weak agglomeration economies: results with identical regions (top) with slightly different regions (middle) and with more different regions (bottom).

Table 1: Classification model equilibria.

Full text

Regional Policy from a Supra-Regional Perspective
Ugo Fratesi
∗
24th November 2005
JEL Codes:
R13, R58, H79 E61
Keywords: Regional Policy, Agglomeration Economies, National Effi-
ciency, Interregional Equity.
∗
Politecnico di Milano, Piazza Leonardo da Vinci, 32, 20133 Milan, Italy.
Telephone:+39-(0)2-2399-3966. Fax: +39-(0)2-2399-2710. E-mail: ugo.fratesi@polimi.it.
1

2
Abstract
This paper introduces a new 2-country 4-region model in order to study
the possible trade-offs arising between national efficiency and interregional
equity, differentiating for different strengths of agglomeration economies and
different regional productivities. In this static model the national policy
maker can affect entrepreneurship through the set-up costs of firms.
It is evidenced that, for countries composed of identical regions, spatially
dispersed allocations of public productive expenditure are more efficient with
low agglomeration economies whereas spatially concentrated allocations are
more efficient with high agglomeration economies. As the regions become
different, however, unbalanced allocations of public productive expenditure
towards the most advanced region become more efficient also in case of rela-
tively weak agglomeration economies, until, for regions sufficiently different,
the most efficient allocation of public productive expenditure is always to
concentrate it in the most advanced territories.
For this reason, if some sort of lump-sum compensating mechanisms
are available, short-sighted national policy makers, not taking into account
long-run growth and factor mobility, can rationally decide to support the
competitiveness of the already more-productive regions and transfer income
to the lagging ones, a behaviour which is shown to have significant similar-
ities with two real cases.

1 Introduction
A large number of economic models have been developed in the past 15
years in order to explore endogenous regional growth and the location of
economic activities, with the consequent differentials of development among
territories. These developments appear, however, to have taken place with-
out paying enough attention to the effects entailed by regional policies from
an aggregate point of view. National policies designed to reduce regional
inequalities may in fact turn-out to be sub-optimal from a country-wide
perspective. Unfortunately, it is too often unclear under which values of pa-
rameters regional policies are also able to increase the aggregate economic
performance of nations (or over-national communities) and which policies
are, instead, to be simply considered as a means to increase the equality of
income across space.
In the past, the issue of the compatibility of national economic efficiency
with a flatter spatial pattern within the country used to be a very impor-
tant one. The most diffused belief was that interregional equity and national
efficiency would normally be achieved at the same time due to decreasing re-
turns. The relative failure of many regional policy attempts, which weren’t
able to induce growth and convergence, and the introduction of increasing
returns in economic models, have then shown the possibility of a trade-off.
For some time, this issue hadn’t been at the core of the researchers’
attention, but is returning to the theoretical limelight. The scarcity of avail-
able resources - due to tighter financial constraints - is making the analysis
of the effects of regional policies on the overall efficiency of the economic
system more important, since it has now become crucial to know wether
truly new resources have become available (as in the traditional approach
that used to see regional policies as pure development policies) or if there is
a price in terms of efficiency, or aggregate income, to be paid in favour of an
increased equity between regions. To say it with the words of the chairman
of the Board of Directors of the EIB:
“In the past, the consensus was that regional policy could support growth,
and that convergence would come about by poorer regions catching up with
richer ones. Increased equality and growth could go hand in hand. Recent
experience has led a number of commentators to question this. They argue
that there are strong economic forces that lead to divergence between regions.
Regional policy cannot do much to overcome these forces. This means that
regional spending is simply a transfer of income from rich to the poor - with
little effect on productivity gap in poor regions. Indeed, this may led to lower
overall prosperity if it drains resources from those wealthy innovative regions
that are the main engines of economic growth. If this is the case we face a
trade off between equality and growth”, (Maystadt, 2000, p.4).
This paper investigates when the trade-off arises within a static context,
using a new model which is able to represent different levels of economies
3

of agglomeration and multi-regional countries. The purpose of the analysis
is to assess the effects of regional productivity differentials on the optimal
choices of policy makers.
Most economic literature still regards regional policy in terms of infras-
tructural policy, or even more specifically, in terms of mere transport infras-
tructure, which used to constitute the bulk of many interventions until the
early 90s. However, this type of intervention already had a large number of
exceptions, for example the policies inspired by the Perroux’s Growth Poles
theory (Darwent, 1969). The focus on infrastructure is mainly due to the
difficulty of modelling complex territorial aspects, especially the relational
ones, but, in some cases, one could also conjecture a simplified understand-
ing of regional policies. Most economists, however, are now aware of the
large amount of work that remains to be done in that direction, for example
Baldwin et al. (2003).
Different from most of the literature, regional policy is here modelled
innovatively: the model represents in fact territorial policy affecting en-
trepreneurship, in particular allowing the nation state to act on the set-up
costs of firms.
The paper is organized as follows: Section 2 introduces the desired prop-
erties of regional policies, with a simple taxonomy that allows to compare
them; Section 3 surveys the recent relevant contributions - it has to be stated
in advance that most of these contributions involve agglomeration, whereas,
for the purposes of this paper, only agglomeration economies are needed
and modelled; Section 4 introduces a two-country, four-region model able
to analyse the issue, especially what happens to equity and efficiency if the
regions are different from each other. Section 5 uses the model in order to
investigate equity and efficiency according to the theoretical framework of
Section 2 and mentions two empirical cases that bear strong similarities to
the predictions of the model. Section 6 concludes the study.
2 Desired properties of regional policies
With the introduction of models with imperfect competition (Dixit and
Stiglitz, 1977) and consequent agglomeration (Krugman, 1991a,b, Ottaviano
and Puga, 1998, Fujita et al., 1999, Neary, 2001, Fujita and Thisse, 2002)
questioned first was the linearity of the relationship between transport costs
and regional development, then, partly as a consequence, the linearity of
regional development, since increased attention has been devoted to issues
such as history, the lock-in and expectations (Ottaviano, 1999, 2001, Bald-
win, 2001). It is interesting to remember that, in models with multiple
equilibria, a force that pulls the economy out of an unstable equilibrium
cannot normally be counterbalanced by a successive and opposite force of
the same size; this is because of cumulative effects that move the system
4

Regional Disparities
EQUILIBRIA
OF MODELS
High Low
High
II I (Best
situation)
Growth /
Income
Low
III (Worst
situation)
IV
Table 1: Classification model equilibria.
towards the stable equilibrium (or one of the stable equilibria when more
than one exists).
We can represent the possible equilibria of multi-regional models of lo-
cation/agglomeration in a four-quadrants graph (Table 1). We will have on
the vertical axis growth or income (depending if the model is dynamic or
static), measured for the whole country; the horizontal axis represents the
extent of regional disparities. Both axes should actually be depicted on a
continuous scale, but in the discreet form the meaning and implications are
more evident.
When decreasing returns are present, like in exogenous growth models (Solow,
1956) or in traditional location models, the maximum income is achieved in
a dispersed equilibrium, the same one that we indicated in quadrant I as
“best situation”, since it is optimal from a Paretian point of view.
When increasing returns are present, on the contrary, a number of models,
especially of the New Economic Geography (NEG, the most relevant for our
purposes of those will be mentioned in the next section) have outlined that
the equilibrium is more likely to be one with high income/growth and high
agglomeration at the same time, even if for some values of the parameters
it is generally possible to have situations of high income/growth and low
agglomeration, or (and this is the worst case) situations in which regional
disparities are high despite of a low income/growth. For example, Otta-
viano and Thisse (2002) have identified a case of market failure in which,
for intermediate transport costs, the market outcome is agglomeration, even
if a dispersed allocation would be desirable on both equity and efficiency
grounds.
The theoretical developments of the last 15 years, therefore, have some-
5

Frequently asked questions

Q1. What are the contributions mentioned in the paper "Regional policy from a supra-regional perspective" ?

This paper introduces a new 2-country 4-region model in order to study the possible trade-offs arising between national efficiency and interregional equity, differentiating for different strengths of agglomeration economies and different regional productivities. 

Q2. What are the future works in "Regional policy from a supra-regional perspective" ?

The model proves to be very easy to use to study what may be the trade-offs between equity and efficiency if the country is composed of different regions. The model leaves open the possibility that policies concentrating the productive support in the already stronger region, with some income compensation for the poorer, could, despite being efficient in the short-run, be detrimental to long-run growth. 

Q3. What is the reason for the compatibility of objectives?

In the literature, often cited as a reason for the compatibility of objectives, is the inflationary consequences of agglomeration, so that countries with lower concentration of economic activities will tend to have a lower Phillips curve (Higgins, 1988). 

Q4. What is the problem with the spatial impossibility theorem?

The spatial impossibility theorem (Starrett, 1978) affirms that when transport is costly and space is homogenous, then no equilibrium exists which involves the movement of goods. 

Q5. What is the purpose of the analysis?

The purpose of the analysis is to assess the effects of regional productivity differentials on the optimal choices of policy makers. 

Q6. What are the main effects of temporary policies?

On the other hand, due to the existence of lock-in, temporary policies can have permanent effects due to locational hysteresis and self-reinforcing mechanisms. 

Q7. What is the way to compensate the lagging regions with income transfers?

And in the short-run, as this paper has shown, when countries are composed of sufficiently differ-ent regions, there always exists a trade-off between interregional equity and national efficiency, unless transfers are available, in which case the best national policy is to concentrate the support to entrepreneurship in the most advanced regions and compensate the lagging ones with income transfers. 

Q8. What is the way to measure the relationship between agglomeration economies?

When agglomeration economies are low (Figure 3), as far as regional productivities become increasingly different, β∗ moves from 0.5 towards an unbalanced value, until the authors reach a situation in which the maximum efficiency is to give all public support to the larger region. 

Q9. What is the case with identical regions?

The case with identical regions is not surprising, and the authors can also represent the space of the other parameters in which the relationship is concave: given any value of love for variety (σ) and any value of rivalry in the use of the public production factor (δ), it is possible to know how large agglomeration economies have to be in order to have a concave relationship between β and aggregate GDP. 

Q10. What is the main reason why the cost of moving is so high?

Attanasio and Padoa Schioppa (1991) found five separate and additional causes that increase the cost of moving: the fact that women are now in the labour market in large numbers makes it more difficult for men to relocate because of the need to find two jobs instead of one; the differences in the prices of basic facilities, especially housing; labour laws that make firing and hiring very difficult; the aggregate unemployment rate that may affect the gains from migration; and, finally, even the fact that after some years of low migration mobility itself is more difficult, possibly because of the loosening of ties deemed useful to relocate. 

Q11. What is the efficient policy choice for agglomeration economies?

When regions are identical but agglomeration economies are low, on the contrary, the most efficient policy is to implement a balanced policy between the regions, even when, as in this case, the only target is aggregate GDP. 

Q12. What factors are used to classify the effects of regional policies?

These effects may depend on a number of factors, including the strength of agglomeration economies, the dynamic or static framework and the characteristics of the regions of which a country is composed. 

Q13. What is the main feature of the actual functions?

The interplay of the objectives of equity and efficiency, consistent with the framework of Table 2 and with the results of the model of section 4, can be summarized by a stylized figure (5) that depicts the main features of the actual functions. 

Q14. What is the reason why a national government could be induced to not pursue real development policies?

For this reason, a national government facing structural imbalances among the regions of the country, especially if short-sighted, could be induced not to pursue real development policies in the lagging regions, especially if some compensating mechanisms allowing the equity objective to be achieved differently, are available.