1The scientific work of Jean Paelinck is a perfect illustration how to succeed in integrating three different but highly connected research fields : spatial theory, regional modelling (including both theoretical and applied, i.e. econometrical aspects) and regional policies. His scientific carrier seems to have been mainly devoted to these three interrelated aspects, from the very beginnings at the end of the fifties, up to the end of the nineties, nowadays.
2We intend to show here that such a research program led to numerous advances and decisive contributions in at least three linked fields : measurement on regions (1) and research on causality (2) and evolutionism (3) in regional modelling.
3Whatever the concept of region we must face (natural, homogeneous or polarised ; administrative, operational or policy-oriented regions) the problem soon rises how to define, to cut out, to mark off, to aggregate and reassemble the elementary spaces into what we finally call regions -even if we are not quite sure of the consistency of our cutouts and clusters-.
4In a book we may consider as a first synthesis on regional economics, Jean Paelinck (1975) devoted an entire chapter (more than eighty pages) to the problem of measurement on regions (pp. 169-251), dealing with various aspects : numerical taxonomy, factor analysis (principal components methods, contiguity analysis, spatial auto-correlation methods, cluster analysis) and spatial diffusion techniques. The methods reviewed are complete and the relative advantages of selecting a technique rather than another are well explained. The French literature is known and quoted.
5However, it seems now, two decades later, that those efforts are less necessary. Because the problem of defining optimal regions (i.e. regional entities which are as neutral as possible towards evoluting phenomena such as densities, migrations, production and accumulation within the regions) became an obsolete problem, or more exactly, a problem mainly depending on available data on an adequate spatial basis. In the case of France and of other European countries, we know that we rarely dispose of infraregional data, for instance at the "departmental", infra-departmental, local or "communal" level, and that regional cut off is of the "putty-clay" type.
6Thus, the regions to be analysed and compared, will long remain the administrative regions, even if we dream of homogeneous, neutral or optimal regions or sub-regions in a changing pattern. Except in less developed countries where statistical data are not yet consistent, or in semi-industrialized countries where the regional boundaries are not quite rigid (such as in Poland or in Portugal in Europe), the problem of regional partition is partly behind us.
7Thus, it is not surprising to note a shift from problems of optimal regional delimitation to the selection of the best indexes, in order to appreciate, to measure and sometimes to correct interregional discrepancies. It is more than a pure statistical or technical problem and a lot of searchers, especially Atkinson, Champernowne and Theil, paid attention to it during the two last decades. Indeed, the indexes of inequality or discrepancy between the regions are numerous. Every index throws light on a specific point. For instance, some indexes are more sensitive to the extreme parts of the distribution of inequalities, either in the higher or in the lower part of the distribution. Others are more sensitive to the median part. Rare are the indexes which are equally sensitive to changes in every part of the distribution. Thus the choice of a "good" index is not only a technical but also partly a political problem from the moment when we intend to correct regional disparities by adequate policies.
8In a recent paper, A.Valeyre (1993), after other French searchers, such as Bourguignon (1979) or Gouriéroux (1981), reviewed the different forms and properties of about twenty different indexes such as Atkinson, Champernowne, Gini, Hellinger or Theil indexes, together with more classical indexes such as coefficients of localisation or specialization (Isard, Florence, Duncan). Measuring interregional inequalities is indeed improving more and more. With respect to those indexes, the evolution of peripherical regions in Europe since their belonging to the E.U., especially in the case of Greece and Portugal, seems to converge towards reduction of inequalities among regions, due to specific grants, various subsidies and also increasing rates of growth of intraeuropean exports.
9Classification in regional growth modelling is not easy. Harry Richardson (1973) classifies the existing models in six types : export-oriented models, neo-classical, econometric, input-output, policy-oriented models and Kaldorian models. Most frequently, in terms of causality, exogenous models are opposed to endogenous ones which have been developed more recently, according to suggestions by Barro, Lucas and Romer. Another cleavage opposes them according to whether they may induce converging or diverging processes between regions regarding the level of income, wages, productivities ..., which is of most interest in terms of regional policies. We explore briefly the problem of causality inside three types of models : the two first are exogeneous, the last one is endogeneous.
10A very simple model of that first type is the following :
i = Axia (or i = ai) /1/ 11where
i = regional income in region i (or i= rate of growth of regional income in i)i = total exports from region i to all other regions j ≠ i (or i = exports rate of growth in region i)12a = elasticity or regional income with respect to exports (generally close to 1).
13Of course, such a very simple model can be improved, if we introduce the net income coming from other regions, and the production process among regions through adequate production functions, with capital, labour and technical progress, neutral or not.
14The explanatory power of such models is rather poor, except if we consider that the exports of one region may be viewed as the aggregated demand for imports from all other regions, that leads to interregional growth modelling, i.e. input-output interregional models.
15These models suppose that regional growth depends on relative shares of the two regional factors : labour and capital, their respective rates of growth and the annual shift of technical progress, as follows :
i = ai+ (1-a) i + ti /2/16where
i, i = labour (l) and capital (k) rates of growth in region i,17ti = annual shift of technical progress in i,
18a, (1-a) = relative shares of the production factors in a Cobb-Douglas production function with constant return to scale.
19If we suppose also complete and free mobility of the two factors according to the productivity or wages discrepancies among regions, we get a slight more complex formula -see Smith, 1975- :
i = f(i, Mi, i, ri) /3/20with
21ni = rate of growth of population in region i,
22Mi = immigration ration in i,
23ki = rate of growth of capital in region i,
24ri = mean productivity of capital in i,
25f is an homogeneous function of degree 1.
i is negative in and M, and positive in r and . Another important result is that discrepancies in regional rates of growth induce converging processes regarding wages among regions. In other words, according to those neo-classical models, interregional discrepancies tend to correct themselves.
26A good example is the Dixon-Thirlwall model (1975), which is very close to an endogenous model of the Kaldor-Verdoorn type -see also G.Hamard (1995)-.
27In that DT model, regional growth depends on exports growth as in the exogeneous export-based model :
i = gi (g close to 1) /4/28Exports growth is linked to variations in domestic and foreign prices and to changes in the foreign demand :
i = ai + bf + cf /5/29(a < 0 ; b and c > 0)
30with
i,f = rate of growth of domestic prices in region i and of foreign prices in other regions,f = rate of growth of foreign demand.31Changes in domestic prices in region i are explained by changes in wages w , the mean productivity of labour r and t, the margin on labour costs (which can be kept constant). In relative terms, we have :
i = i - ri + ti /6/a :i = di + (d > 0) /7/32Replacing /5/ to /7/ into /4/, we finally obtain :
i = /8/.and t, and positively on a, f and f.33Is there any converging or diverging evolution among regional rates of growth ? To know it, we introduce a time lag into equation /5/ such as :
/9/.34Thus, the condition for divergence -see Dixon and Thirlwall (1975)- is : -adg < 1.
35Taken that a is always negative, that d is rarely more than 0,5 and that we may suppose g 1, the condition is rarely satisfied and we may assert, except under very particular initial conditions that the model is most probably converging, thus reducing discrepancies among respective regional rates of growth.
36Using models of the Kaldor-Verdoorn or of the Dixon-Thirlwall type, several authors -see for instance Sakashita and Kamoike (1973) and also Paelinck et alii (1983)- have concluded to probable reducing inequalities among regional per capita income. See also Barro and Sala-i-Martin (1991, 1995) for convergence processes across states and regions. The Dixon-Thirlwall model along Kaldorian likes can be extended -for an application to French regions, see P.Ralle (1993) and for a presentation in terms of regional equilibrium, see G.Hamard (1995)-. A recent application of the Barro model to European regions during the period 1970-1990 by H.Capron (1997) shows that most regions in twelve countries are on a slowly convergent path (21 to 51 years, according different specifications of the model). A few regions are very late : they often are former industrialized regions as Nord-Pas de Calais and Lorraine in France, the Belgian regions in Wallonia, the Asturias and Galicia in Spain and the Alentejo in Portugal.
37Evolutionism in regional growth modelling springs out of different main streams : the work of Prigogine and of the "School of Bruxelles", laying on biological models of the Lotka-Volterra type (the so-called prey-predator model), the work of Forrester, applying system analysis to urban dynamics and, sometimes, to regional attractivities and evolutions, and a lot of more recent studies in non linear dynamic systems analysis, including chaos, bifurcation and catastrophe theory, fractales, etc... Jean Paelinck has worked in each of these fields -see for instance Paelinck and alii (1985), especially chapter 5 on multi-regional dynamics (pp. 143-183) or, more recently, Paelinck (1995) on urban dynamics, including Lotka-Volterra generalised models and partial derivative potentiel models-.
38No doubt those efforts are still to be improved, as regional and urban dynamics are "terribly complex" (Paelinck, 1995). In a comprehensive survey on chaos and ecologically based models, Nijkamp and Reggiani (1995) emphasize those difficulties : "Catastrophe theory especially, has become fairly popular in regional science ... A weak element in catastrophe models is that the identification, explanation and estimation of critical turning point is extremely difficult, since their occurrence is too irregular to be captured with sufficient statistical evidence by normal time series. As a consequence, catastrophe theory has often been used for illustrative expositions rather than for predictive purposes, so that its operational basis remained feeble. It was apparently easier to trace ex post the behaviour of an unstable system than to identify ex ante regime switches (pp. 185-186).
- 1 FLEUR : Factors of Localization in EURope. See for instance Ancot and Paelinck, 1983 ; Molle, 1983 (...)
39Probably, the most successful and operational model among all the non linear, dynamic and evolutive models Jean Paelinck has elaborated, is his "FLEUR" Model 1.
40That model is an extension of the well-known shift and share analysis, using location and specialization coefficients "à la Isard". Using simple shift and share techniques, the model explains the evolution of a region (or of a sector) with respect to its relative share in the complete set of regions (or sectors) and to specific time oriented factors (shift). Paelinck's idea is to introduce explicit temporalities through time paths towards equilibrium patterns (time).
41Formally, we define location elasticities for a sector i in a region r as the relative rate of growth of production of sector i in region r to the corresponding rate of growth of production of sector i in the whole set of regions, that we denote (.). Thus we define this location elasticity Eiri. as :
iri. = (dyir/yir) / (dyi./yi.) (with yi. = ) /10/42If we assume that the production of sector i in the region r tends to an equilibrium value yeir, according to a logistic process, such as :
43yeir = (ayi.) / (1+ α yi.-1 e-gir) /11/
44with gir, measuring the benefits of locating the sector i in region r ;
45and a and α= constants.
46We are now able to define an equilibrium location elasticity Eeiri. which is very simple (see Paelinck et alii, 1985, p. 144) :
47Eeiri. = 2 - (yeir/ayi.) = 2 - a-1 seir /12/
48with seir = yeir/yi. = equilibrium share of region r in the total output of sector i in the whole set of regions.
49The advantage of the FLEUR-Model is that, according to different values of the parameters a (which can be taken as a variable), α and gir, and by introducing different speeds of adjustment, we can simulate on demand converging or diverging, cyclical and even bifurcating evolutions (on that last point, see Paelinck and alii, 1985, pp.163ss. and, more recently, Paelinck, 1992). Thence, the FLEUR-Model is opening a broad avenue to various analysis of regional growth dynamics and to equilibrium or disequilibrium models -see Girardi, 1993, with applications to Spanish and Italian regions-.
50What we could name the 3S-model (Shift, Share and Space) may also be viewed as an extension of the FLEUR-model with explicit spatial interactions between regions. Coming back to equation /11/, we can replace gir by a more explicit function of attractivity of region r for the sector i, for instance through a system of distances between regions. It is a first way to conceive spatial regional interactions. Another way is to define for each region a potential variable "à la Isard" which depends both on distances and flows between regions. Following Girardi, 1993, one can also introduce an attractiveness probability function of the sector i within the region r, through a logistic function of time.
51A serious limitation with those models is an adequate measure of the stimulus threshold among regions. The attractive or repulsive forces between spaces are probably not strictly proportional to distances (or to simple functions of distance) but are ruled by significative thresholds. When and where a region or a state is far off enough to have no influence at all on another region or state ? To come back to Jean Paelinck's vocabulary once more, it is a question of "allotopy", and we know it is a complex question. Nethertheless, the FLEUR-model is flexible enough to welcome any refinement one could import from the theory of migrations, from gravity models or from spatial diffusion techniques or analyses.
52How can we appreciate Paelinck's various contributions in regional modelling ? As the FLEUR model clearly shows it, regional modelling is to match with various and contrasted situations : converging or diverging, even cyclical, intermittent or suddenly changing evolutions. We need not only a single complex model but a set of multi-regime nested models. The theory of bifurcation, the models of Fick and anti-Fick diffusion processes, which Jean Paelinck explored recently, seem to be promising. But a lot of phenomena have to be correctly integrated in comprehensive regional modelling, as for instance the rise of networks and of network externalities, the exact role of local endogeneous development and of various proximities, the interweaving of qualitative factors of structural or cultural changes. Regional growth seems to be a kind of complex and subtle alchemy. For the next future, we foresee rather more diversity or divergence than unifying factors at work among regions, except if we anticipate a strong effect of various regional policies in peripheral and poor European regions. No doubt regional growth modelling is still going to improve in the decade to come.