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# Regional economics dynamics

Agglomeration dynamics are stable on the short term and instable on medium-long term. In the so-called knowledge intense sectors, when a new sector is born, firms are not linked to a specific territory. However, when increasing returns to scale arise, firms begin to look for specialised services and tend to concentrate in a given location. A locational advantage is created and agglomeration... Vedi di più

Esame di Economia del territorio docente Prof. D. Marino

Anteprima

### ESTRATTO DOCUMENTO

action and then of the next position. Considering a general class of dynamic system, it is possible

to assess the dynamic of the allocation process. One of the possible applications of the allocation

process concerns, for instance, the distribution of firms in K locations at a certain “event time”.

p (x )

The probability that next firm joins category i is where x is the vector of current proportion

i

12

or firm location. That formalization allows us to determine, at least implicitly, p. By taking into

account only two territories (K = 2) is it possible to show in a graphic (Figure 2) all the possible

dynamics of the system. In the graph it is possible to observe that if the quantity of agents

concentrated in the A region is influenced by the number of agents that are already there.

i

Specifically, if the number of agents in A is larger than a given proportion x , the probability that

the next agents will decide to localise himself/herself in the region A will be higher. Therefore the

region A will attract more agents. On the contrary if the number of agents in A is lower than the

i

proportion x , the probability that agents will choice A as their next localisation will decrease

overtime. It is worth noting that in this stochastic distribution of elements it is impossible to use

the Strong Law of Large Number, since past distributions influence the dynamic of the system,

while in the Strong Law increments are independent. In this dynamic process, each choice of the

system is irreversible and the process must converge to one of the point p, of the feasible

allocations.

System at t +1 = System at t + the choice with the highest probability + a random exogenous dynamic

12 “The vector of probabilities p=(p (x), p (x),…, p (x)) is the allocation function that maps the unit simplex

1 2 K

## K

S of proportions into the unit simplex of probabilities” (Arthur, 1988)

12

Without the random exogenous variable the expected value of System at time + 1 will be equal

=

E ( X X ) X

to the actual state at time + 1: ( ), which is the equivalent deterministic solution.

+ +

t 1 t t 1

The formalization assessed above is the pillar of many studies concerning the localization of firm

13

by a spin off process . In these models new firms are added by “spinning off” from parent firms

one at time. Accordingly, firms are added incrementally to regions with probabilities equal to the

proportion of firms in each region at that time. Empirical evidence underpins this process

especially in the high tech/knowledge intensive sectors. Every point of the unit simplex (the total

of regions) may become an attractor point, so the system can converge to any point. In other

words, “chance” dominates completely the dynamic.

B. Path dependence with recontracting processes.

In the allocation process assessed above, choices made by the system are irreversible. But

what does it happen if at every time the system can “change its mind” deciding to re-contract

previous choices? To model this dynamic it is necessary to consider a Markov-transition in which

the concentration of firms in region A influences the location choice of firms in region B that

every time can change their location by a “jump” in the other region. The region that attracts more

firms increases its probability of attracting the “next one” at time t + 1; hence, self-reinforcing

mechanisms are still possible.

To give a formalization let’s imagine a case in which there are only two regions K (K = (A, B)

= 2) and total population is T = 2N, with a state variable m. Accordingly, N + m firms will prefer

region A, and N – m firms prefer region B. Being p (m) the probability that a firm change its

## AB

location from A to B, and p (m) the probability that a firm change its location from B to A (at

## BA

every unit of time), the probability P(m,t) of finding the system at state m at time t will evolves as:

+ = − − + + + + − −

P ( m

, t 1

) P ( m

, t )((

1 p ( m ) p ( m )) P ( m 1

, t ) p ( m 1

) P ( m 1

, t ) p ( m 1

)

## AB BA BA AB

From which can be derived the Master Equation:

dP ( m

, t ) [ ] [ ]

= + + − + − − −

P ( m 1

, t ) p ( m 1

) P ( m

, t ) p ( m ) P ( m 1

, t ) p ( m 1

) P ( m

, t ) p ( m ) (*)

## BA BA AB AB

dt

That normalized to the variable x in the continuous interval (-1, 1),

m

=

x ;

1

ε = ;

## N

P(x, t) = NP (m, t);

13 See Cohen, 1976 or Klepper, 2004. 13

[ ]

p ( m ) p ( m )

= AB BA

R ( x ) ;

## N

[ ]

+

p ( m ) p ( m )

= AB BA

Q ( x ) N

Yields the possibility to rewrite (*) in the form of a one-dimensional Fokker-Plank diffusion

equation ε

∂ ∂ ∂ 2

P ( x , t ) = − +

R ( x ) P ( x , t ) Q ( x ) P ( x , t )

∂ ∂ ∂ 2

t x 2 x

Substituting diffusion functions R and Q to describe some specific transition mechanism, it is

possible to study the evolution of P over time and its distribution. It is noteworthy that in

recontracting process dynamics transitions remain constant overtime, while in the allocation

process formalization transition magnitude was decreasing overtime

To give another example is it possible to show a model that refers to this kind of dynamic in

the labour market (Aoki, 2003). By adopting mathematical instruments as the master equation

(also called Chapman-Kormogorov equation), it is possible to assess a stochastic dynamic in

which heterogeneous agents faces same limitations in their mobility or in their possibility to be

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hired by some sectors of the economy. The presence of a stationary distribution of equilibria

instead of a single stable equilibrium is one of the first goals that this kind of formalization gives.

Another feature of that approach refers the possibility to consider workers with differences in

work experiences, human capital stocks, geographical localization, and off course for the

sector in which they work. The economy has K sectors, and sector i employs a certain number n ,

i

i = 1, …, K of workers. There are two “states” in which a sector could be: the first is the “normal

time”: =

y c n .

i i i

In this situation the sector produces an output that is equal to the demand expressed by the

market for the sector’s commodities. In the second case the demand is higher than the level of

supply, and the sector goes in overtime capacity; with the same number of workers produce a

higher output than before: = +

y c ( n 1

) .

i i i

Demand for good i is given by s Y, with

i K

=

Y y i

=

i 1

14 The model refers to the entire dynamics in the macroeconomic environment but here we refer to the part of

labour market. 14 ∑ =

s 1

and s is a positive share of the total output Y referred to goods produced by sector i with

i i

i

. Every sector has the excess demand defined by:

= −

f s Y y

i i i

with i = 1, 2, …, K.

Sets of sectors with positive and negative excess demand are denoted by

{ } { }

= ≥ = <

I i : f 0 I i : f 0

; .(**)

+ −

i i

Changes in Y due to changes in any one of sectors affect the excess demand of all sectors. The

model uses (**) as proxy to indicate which group of sectors is profitable (and thus it wants to

expand its production), and, conversely, which one is unprofitable (and so it tries to reduce its

production). According to the model, only one sector succeeds in adjusting its production up or

down by one unit at any given time. The sector with the shortest sojourn time will be the one to

jumps first (because of path dependence). And so dynamics are only determined by the transition

rates in continuous-time Markov chains. Distance among different sectors is defined by using

ultrametric distance. Therefore, the economic environment is structured as a tree diagram in

which every sector is a “leave” which is connected to the rest of the tree trough “nodes”.

Transmission of economic shocks in the environment depends on distances among leaves and

branches. The distance is measured between “nodes”.

Ultrametric distance d(i, j) enjoys the following properties:

a. it is positive unless i = j (in which case it is zero);

b. it is symmetric d(i, j) = d(j, i); 15

c. it satisfies d(i, j) max {d(i, k), d(j, k)}

k

Every sector in overtime fills its vacancies (if there were not vacancies the overtime condition

creates them) with workers laid off by itself or by the other sectors of the economy. Obviously,

workers belonging to the hiring sector have a greater possibility to be hired than workers

belonging to more distant sectors. Using the master equation the distribution of the stochastic

probability that a certain worker of a certain sector will be hired by a sector can be assessed.

Ultrametrics can be introduced also as dummies for institutions and other kind of “special agents”

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whose actions can influence the system as a whole. Accordingly, the analysis not only can be

used to forecast the evolution of the system sic rebus stantibus, but also it can show which are the

main attractors in the system.

Another important result of this approach is that it may be helpful to design policies taking into

account other variables characterising contemporary economy such as natural and environmental

resources, human resources, and technology. Furthermore, incorporating these factors in the

model does not increase the complexity of the mathematical instrument. This specific issue is

broadly analysed in the next section.

15 . The role of institutions in regional agglomeration dynamics is assessed below in section 5.

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4. Economic Policies in Spatial Extended Systems: New Paradigms

Description of the evolution of spatialised economies emphasizes the role of new paradigms

rather than of classical ones. New factors seem to have replaced the earth, work and physical

capital. Natural and environmental resources, human resources and technology are beginning to

get the upper hand following the so-called “technological revolution”. Co-operation within

businesses and between businesses and business systems takes place on a vertical and a horizontal

scale in which the local dimension and the territorial variables constitute the catalyst for processes

of development. Technological expertise and social capabilities (Latella - Marino, 1996) are the

basic elements capable of explaining the different levels of development that can be observed in

different territorial contexts. Territorial variables, in other words, are decisive factors in

explaining development differentials, especially when associated with the idea of market

conceived as a social construction requiring rules that will guarantee its smooth running given that

access rights, exchange mechanisms and opportunities for distribution of the wealth generated not

only do not reassemble themselves uniformly and autonomously in time and space (Sen, 1984 and

1985), but almost always require outside intervention to achieve the objectives set for

development policies. Re-equilibrium policies thus appear necessary to guarantee a more

equitable development process. Within the market it is necessary to define collective rules

ensuring that positive dynamics (increasing return) can develop through the interaction of the

agents operating in it. The territorial dimension and the systemic nature of the production process

are elements that are fundamental to the understanding and governing of development processes.

Public intervention in such a scenario cannot simply be thought of as a mechanism for

allocating resources within the economy but must assume the role of guide and director of

processes taking the shape, on the one hand, of a set of actions aimed at defining and guaranteeing

individual access rights and, on the other hand, of interventions aimed at developing the exchange

capacities of markets and business systems (Bianchi, 1995). An explanation may be sought in the

fact that local communities increasingly interact with the rest of the world in a continuous process

of integration and globalization without necessarily responding to stimuli from the central state.

This obliges us to re-examine the composition of the economic policy maker’s “tool box” and, at

the same time, forces us to radically rethink the very meaning of policies government given that

the central public authority is no longer able to guarantee the development of the local community

in the presence of particular actions enforced by the central authorities (Bianchi, 1995).

Traditional economic policies, when enforced in the context of an open market or of a market

characterized by strong interrelations between agents, lose their capacity to produce the expected

results because the mechanism of response to the policy maker’s input has to deal with a system

characterized by high levels of interrelations between individual decisions and which therefore

displays collective response characteristics which are different from individual response

mechanisms. The consolidated logic of public intervention in economics assumes that the

government authority will identify objectives for which the instruments most likely to achieve

results which can be verified and therefore simulated are chosen. Traditional macroeconomic

policies only work if acting on a closed system for which it is possible to order objectives and

priorities with certainty. In this case the policy maker can govern the system of underlying

relations by assuming linear type response mechanisms. If these assumptions are not verified, the

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complexity of the system makes traditional policies pointless, therefore, to govern a complex

system policy-makers must equip themselves with a set of objective instruments and

programming actions able to cope with non-linearity and the consequences of complexity.

4.1 Planning Actions Spatial Extended Systems: Old and New Approach

From the idea that an economy is a “complex evolving system” in which single individuals are

linked to each other by strong relationships, it follows that dynamic characteristics cannot be

represented by individual approaches but rather by collective properties subjected to subsequent

non-reversible scansions (Arthur, 1988). It is thus conceivable that each economic system, in its

evolution, might manifest both a multiplicity of equilibria, each dependent on previous historical

interrelations, and the presence of inefficiencies and lock in which can be selected during the

evolutionary course of the system to the detriment of possible efficient solutions. Government of

an economy thought of as a complex evolving system therefore excludes the possibility that

commands might be expressed with a prescriptive type mechanism in mind, as would happen if

the system being analysed were essentially closed and characterized by low levels of interactions

between agents. To this it must be added the considerable incidence of variables of a territorial

nature. Territory cannot be thought of simply as a physical support for business activities but

must itself become an active factor conditioning the exploitation of local resources and the

capacities of single businesses to cope with international competition. Therefore, the general

objective of regional policy becomes that of structural adjustment with a view to greater economic

and social territorial integration. So new regional policy must firstly contemplate a “transactive”

rather than a “prescriptive” type of approach and the basis for any action must consider not just

“what must be done” but “in what manner, by what procedures and with whom”. This means

making systematic and widespread use at all levels of the principle of subsidiarity which implies

that decisions should be taken as near as possible to the problem and be appropriate to its solution,

and individual responsibilities should also be identified using the same criterion. Thus the main

task of decision-makers in each Spatial Extended System is to aim at reassembling the rules and

re-establishing the access rights which are the basis of any subsequent action designed to re-

appropriate local culture and raise the threshold of contextual knowledge. On these premises it is

possible to imagine the transfer of outside knowledge and the creation of networks which build up

the basis for the realization of a self-sustained model of development.

To achieve these aims the Spatial Extended System (SES) needs to equip itself with

instruments capable of identifying moments of participation and complementarity among all the

actors that make up the local system. To do this opportunities must be created to allow the human

resources to increase the know-how and acquired cognition that will qualify them to introduce

innovative codes and routines within the productive system. If such cognitive improvement

occurs, there will be an increase in flexibility and specialization and a greater capacity to

understand and govern change and innovation and ultimately an improvement in the overall

efficiency of the productive system. The government of a local system which is complex because

of the continuous, strong interrelations between the individuals operating within it cannot be of a

deterministic kind unless part of it is isolated from the rest of the relations.

The government of a complex system demands a series of deliberations over interventions,

which by their intrinsic nature are irreversible, i.e. they produce permanent changes in the state of

the system. To return to the now extensively examined concept of SES, multiplicity of equilibria,

18

co-operation, proximity, resilience and freedom of access can be pointed to as some important

categories in the description and government of a complex system. The conceptual field within

which the local system has to move is, in fact, of a bottom up kind and provides the archetype for

programming actions capable of leading the evolutionary paths of the SES towards states of

greater growth.

Bianchi’s (1995) taxonomy of interventions identifies the following three procedures:

1. programming according to exogenous concepts;

2. programming according to critical situations;

3. programming according to integration contexts.

Programming according to exogenous concepts is nothing more than the traditional concept

of programming, achieved by means of the exogenous definition of objectives by the policy

maker in conjunction with the identification of the instruments necessary to achieve the pre-

established goals. If complexity and environmental turbulence are low, this method of

programming is effective. This type of programming enters a crisis when the system enters those

critical areas characterized by high levels of turbulence or uncertainty. In such circumstances it is

necessary to programme according to critical situations, i.e. to devise programming capable of

self-regulation in the presence of criticality and of varying parameters in order to overcome any

lock-in or bottle-neck situations. As long as the critical areas are small in size, this approach is

sufficient. If, however, levels of turbulence and complexity are so high that criticality can occur

at any moment, then it is necessary to programme according to integration contexts, i.e.

considering the system as a whole as an organism capable of adapting continuously to the outside

environment.

In this case policies have to take into account the changes they induce in the system itself, i.e.

the way the system metabolizes them. The need for programming according to integration

contexts therefore justifies, as fundamental elements for regional policy, forms of structural

adjustment whose objective is to lower the costs of transaction and which concern:

• the social dimension, linked to the quality of life and culture;

• the ecological aspect, closely connected to the urban habitat, the landscape and the

ecosystem;

• public institutions and productive sectors, with special reference to the organizational

aspect and the quest for efficiency.

Public-private co-operation, improved social standards, the construction of R&S networks and

appropriate territorial policies designed to provide the basis for integration are irreplaceable

instruments for governing the economy and for leading it to the highest levels of development.

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5. An Outline of the Transmission Mechanism of Economic Policy in the Presence of

Complexity.

The collective properties of a territorial economic system in relation to the link existing

between productivity growth and information could be represented in terms of response function.

We would like, at this point, to generalize the previous relationship by constructing an

interpretative model which describes the propagation mechanism of economic policy in a situation

of complexity. The description of the transmission mechanism logically completes the previous

observations regarding objectives and instruments. Single economic policy decisions, aimed at

achieving the j-th objective through the use of the i-th instrument, can be represented as an outside

stimulus which superimposes itself on interactions between agents.

Agents in this approach are thought of as being spatially distributed and linked to each other

by local mutual interactions (of a nearest neighbours type). We use H to indicate the effect of the

economic policy. We can thus define an effective Heff stimulus which includes both outside

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stimulus and agent interaction. Obviously, without agent interaction H and Heff are equal. Heff

therefore assumes the form: ∫

Heff = H + dr'c(r-r')δγ(r')

Where c(r-r’) is a function of correlation between agents which can constitute an acceptable

δγ(r’)

means of modelling the concept of proximity, is a variation in the behaviour of agents

induced by the policy applied, the integral can be linked to the concept of resilience. This type of

behaviour arises in the area of a linear response model for systems with collective properties. The

effect of an economic policy on a complex system made up of many agents interacting with each

other can therefore be described in this way and modelled, as seen in the previous chapter, by

means of the response properties of the system itself. Therefore, in the area of linear response

theory we have a cause-effect relationship of the type:

## E (X) = G (X) H (X)

where E (X) represents the generalized effect, G(X) the response function, and H(X) the

generalized cause.

Therefore it is possible to study the generalized transmission mechanism of the economic policy

describing the response function as a sort of susceptivity which comes to depend on the

distribution of agents within the market. Obviously the type of response depends not only on

distribution, but also on the type of interaction between agents.

6 Some conclusive consideration.

The debate in economics between those who maintain that complexity and its causes plays a

decisive role in the construction of models with high levels of realism and those who think that a

complete and exhaustive description of economic phenomena can be achieved using linear and

equilibrium type models regardless of the complexity of the behaviour of agents and markets is

16 . Heff represents the actual output of the implemented policy.

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relatively recent. In this work we analysed the relationship between complexity and economic

policies from the point of view of regional and territorial economics. The economy as a complex

evolving system (Arthur, 1988) therefore implies that:

• individuals are bound to each other by strong relationships;

• dynamic characteristics cannot be represented by means of individual approaches but only

by collective properties;

• evolution manifests itself by means of multiple equilibria;

• each equilibrium depends on previous historical interrelations through possible

inefficiencies and/or lock-in.

From a conceptual point of view, the main characteristics of the effects that emerge in the

dynamic evolution of a system with complex behaviour can be explained by:

• the difficulty prescriptive type regional and territorial policies have in promoting and

sustaining economic development;

• the loss of importance of the national dimension: the local dimension clashes with the

global dimension;

• the faltering view of economic policy and its propagation mechanism as being based on

principles of command and control;

• the inability of a central planner to govern all the underlying relationships between

economic agents at any given time according to linear type response procedures.

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### DESCRIZIONE DISPENSA

Agglomeration dynamics are stable on the short term and instable on medium-long term. In the so-called knowledge intense sectors, when a new sector is born, firms are not linked to a specific territory. However, when increasing returns to scale arise, firms begin to look for specialised services and tend to concentrate in a given location. A locational advantage is created and agglomeration economies are concentrated there. Only a technological shock can open opportunity for other territories to attract firms belonging to that sector. A similar dynamic can be assessed also in traditional sectors whose competitiveness depends on their capacity of enhance their linkages with knowledge intense activities. Given the high level of complexity characterising the system, the response to policies cannot be linear and it changes according to the number of linkages agents developed within the system as well as agents’ characteristics. In such a condition policy makers have to programme their interventions according to integration context procedure, since the response to the policy and the generalised cause will strongly influence the generalised effect of the policy.

DETTAGLI
Corso di laurea: Corso di laurea magistrale in architettura
SSD:
A.A.: 2011-2012

I contenuti di questa pagina costituiscono rielaborazioni personali del Publisher Atreyu di informazioni apprese con la frequenza delle lezioni di Economia del territorio e studio autonomo di eventuali libri di riferimento in preparazione dell'esame finale o della tesi. Non devono intendersi come materiale ufficiale dell'università Mediterranea - Unirc o del prof Marino Domenico.

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