Regional Science and Urban Economics 20 (1990) 359-376. North-Holland

KNOWLEDGE AND COMMUNICATIONS INFRASTRUCTURE AND REGIONAL ECONOMIC CHANGE

Ake E. ANDERSSON

Department of Economics, University of Ume4, 901 87 lime+. Sweden

Christer ANDERSTIG and Bjiirn HARSMAN

Oflice of Regional Planning and Urban Transportation, 102 29 Stockholm, Sweden

Received March 1988, final version received May 1989

This study is concerned with an analysis of the relations between infrastructure and productivity. It is based on a production function approach, permitting variable returns to scale with respect to the quantity and quality of labor. The infrastructural capacity of a region is represented by a geometric aggregate of air, road, rail, building capital and R&D capacities. A non-linear econometric procedure is used to estimate the influence of infrastructure upon gross productivity of regions.

1. Introduction

The transition from an industrial society to a service and knowledge society seems to be a characteristic trait of most industrialized countries in the western world. According to Andersson (1986) ‘it is very probable that we have now arrived at a period of an emerging fourth logistical revolution, associated with the growth of information processing and communication capacity as well as the growth of the knowledge base. This development goes hand in hand with a successive improvement of the transportation system, especially the structure and operation of the air transportation system’.

Accepting this approach to the emerging economic transformation, its implications for economic peformance in different regions is an issue of great interest. As for the regional development in Sweden it has been shown, e.g. by Anderstig and Harsman (1986a), that knowledge intensive activities are of growing importance in the Swedish economy, and that these activities tend to grow faster in regions with good accessibility by roads and air, and with universities.

This paper aims at looking further into the regional consequences of the logistical revolution, by discussing how the regional production pattern is affected by differences in terms of factors of production and elements of infrastructure. The discussion is empirically oriented which means that we

01660462/90/$03.50 0 199GElsevier Science Publishers B.V. (North-Holland)

360 A.E. Andersson et ml., lnfrastructuru and regional economic change

present quantitative estimates of the relationship between regional produc- tion and various types infrastructure.

During the last decades a large number of empirical studies have similarly been concentrated on the relation between infrastructure and regional economic development, e.g. Mera (1973), Blum (1982), Wigren (1984), Lakshmanan (1986), Carlino and Mills (1987).

In the definition of infrastructure we take the publicness (in time and space) of capital as the basic dimension. All capital that influences conditions of production beyond the spatial and dynamic limits of the decision-making firm is regarded as infrastructural capital. Thus a building that stands for many decades as well as networks connecting firms are infrastructural objects. Likewise, research outputs as well as the teaching of cognitive skills often have the dynamic and spatial extension to warrant inclusion in infrastructure.

In numerous studies it has been recognized that production technologies may differ between regions, see e.g. Aberg (1973), Lande (1978) Garofalo and Malholtra (1984), Uno (1986), Luger and Evans (1988). In our opinion, enlarging the usual kind of factors represented in the production models, by including infrastructure elements as well, may be an interesting approach in this field of research.

In this paper, however, the issue of differing technologies will not be addressed. The analysis is of an aggregative kind, where regions are treated as macroeconomic entities and where only a limited set of infrastructure elements are included. Some elements, representing the transportation and education system, are related to hypotheses put forward in Andersson (1986). Firstly, the business principle of ‘Just in Time’ is useful only if the truck and air transportation system is of sufftciently high quality. Secondly, the expanding sectors in the economy are generally knowledge oriented, and their location thus tends to be sensitive to locations in regions where labor at high levels of education are relatively abundant, e.g. in regions with colleges or universities.

2. Production and infrastructure

In standard theory of production, inputs and outputs are related to each other by activity analytic input-output relations or by production functions. The general production function is very similar to the input-output descrip- tion of technology in one respect. All inputs and outputs under the control of the decision maker are included. Assuming a general production function description we have a situation, in which a vector v of inputs is transformed into a vector x of outputs within a specified period of time. The mapping of u into x can be described by

A.E. Anderson et al., Infrastructure and regional economic change

xsf(v)zO for ~10.

361

In econometric analysis simplifications are often needed. Unfortunately, these simplifications are often ritualized. to scarcity of data is transformed One example is the CES-function

q=A(a,CP+a,LP)“P,

where three assumptions are made:

What was originally a simplilication due via a convention into a law-like model.

(1)

value added (q) is strictly proportional to the constant proportions input vector (u), when capital (C) and labour (L) are excluded,

value added (q) is a constant fraction of total output (x),

only one commodity or a fixed ‘commodity basket’ is produced.

All these three assumptions are disputable, especially in periods of structural transformation of an economy. In reality, these simplifications are not compatible with proper analysis of location, because transportation of goods are oriented to the inputs of intermediary commodities, excluded from analysis in any value added representation of production.

The exclusion of transportation means that all networks are assumed implicit. This implies that infrastructure must be represented by the four parameters (A, ccr, cz2, p). Mostly regional variations have all been represented by an index Ai in a production function

qi=Ai(cr,Cp+c(,Lf)“P (2)

with A, being regressed against infrastructural characteristics of the regions i (i= 1,. . ,a), while assuming c(~,c(~,P equal for all regions.

In the case of p+O and Ai= nk Oft, with D,=infrastructure of type k, the analysis of the relation between production, ordinary inputs and infrastruc- ture then further reduces to

(3)

According to Frisch production processes are in general subject to ‘the regular ultra passum law’ (RUPL), meaning that along any monotonically rising (linear) path in input space the ‘passus coefficient” declines mono-

‘For a scalar output function x=f‘(v) the passus coellicient is detined to be

E&$.?, x

which is greater than 1 for increasing returns to scale and vice versa.

362 A.E. Andersson PI al., Infrastructure and rqionul economic chanp

tonically, so that there is a region of increasing as well as a region of decreasing returns to scale and an infinitesimally small range of constant returns to scale.

It is thus obvious that the many suggested econometric production functions of the Cobb-Douglas, CES and other constant scale elasticity functions are not compatible with RUPL and thus are rather of an ‘ad hoc’ nature compared to the more general Frischian RUPL-functions. The transformed CES function’

xsAexp(-y/z),

is, however, although simple compatible with RUPL. Such a function is also compatible with an endogenous determination of the scale of production of all firms at a general equilibrium of the economy.

We assume that infrastructure of different types are always needed for production to take place in a region. This means that different types of infrastructure form a decomposable set of preconditions for the production activities: Land without ir$xstructure is useless. This is not neccessarily true for the different inputs used by the firm. However, the production function should be specified so as to allow for RUPL.

We have thus chosen to combine RUPL in the use of inputs, variable for the short-term decision makers of the regions, with multiplicative represen- tation of infrastructure items, not variable for the short-term regional decision makers3 We have, however, been forced to the simplification of the value added approach, rather than the total production and input vector approach. The production functions used is written

qi = n D$ exp ( - y/‘zi),

with

zi=n I$;, (7) m

L,,=labor input of type m.

As the estimations are based on aggregate regional product data we have not deemed it reasonable to follow the practice of deriving reduced factor demand and other dual approaches to the estimation problem.

Econometric analyses of production and input allocation between regions

*Suggested in a slightly simpler form by Puu (1974). “Econometric analyses based on such a transformed Cobb-Douglas production function

without infrastructure elements are found in Ringstad (1967).

kE. Anderson et al., Infrastructure and regional economic change 363

are often performed without proper discussion of the equilibrium problems connected with infrastructural stocks and investments. According to the mathematical physicist Haken (1983a) the use of lags is inferior to a proper analysis of the qualitative difference of time scale of different subsystems of a dynamic system. The basic theorem shows that if the time scales are sufficiently different, then one is generically permitted to disregard the dynamics of the slower process equations (infrastructure equations) in the equilibration of the fast process equations.

Thus - most of the time - it is mathematically correct to analyse the economic production equilibrium as if the infrastructure is in equilibrium. For an economic application to dynamic economics of Haken’s theorem, see Andersson and Zhang (1989). Empirically, this implies that firms can be assumed to allocate production and labor onto an infrastructural ‘stage’, where the ordinary market equilibrating mechanisms work in an environ- ment assumed practically invariant.

Thus all the infrastructure is representable as slowly changing environmen- tal variables, not being influenced by the fast economic variables of the markets. This does not mean that there are no interactions between markets and infrastructure. It only implies that these market and infrastructural mutual interactions must be observed at the short periods of structural instability when the economic system traverses between one equilibrium production and price structure to another.

Haken has further shown that such a short period of strong interaction can generically be captured by the ‘cusp phenomenon’. When applied to infrastructure-production interaction this can easily lead to long infrastructure-production cycles of the relaxation-oscillation type, well- known in physics. These theoretically and empirically important roles of time scale variations were partly conjectured by Samuelson (1947) but the implications were not fully realized until Haken (1983b).

Accordingly, we assume that Haken’s approximation principle can be applied in the analysis of the influence of infrastructure upon regional production. Thus, we avoid the use of ad hoc lag structures, which are only applicable in periods of very rapid transition when economic disequilibrium is a proper assumption.

Implicitly, we assume in the following that the Swedish economic system can be analyzed as an equilibrium system both in 1970 and in 1980, which are the years of an econometric analysis of the relation between infrastruc- ture and economic performance of the regions. It is fairly clear that 1970 was a year of structural stability and that thus estimates for that period are methodologically completely valid. Some indicators of industrial change in the 1980s are such that it is possible that the Swedish economy was in a state of disequilibrium in 1980 and thus that the econometric study based on the equilibrium assumption is invalid.

364 A.E. Andersson et ul., Infrastructure and regional economic change

3. Infrastructure indicators and other data

The properties of the production function presented Above makes it possible to separate the output elasticities of ‘input potentials’, e.g. slow infrastructural elements, from those of quickly ‘attractable factors’, e.g. labor inputs. Following Blum (1982), who makes this distinction between inputs, an input potential is defined as an input factor which, for a medium- to long- term period, is characterized by spatial immobility, whereas an attractable factor is spatially mobile in the short run. This distinction is in line with Leven et al. (1970), who argue that capital, as a stock variable, should be separated from the flow character of other inputs.

The ‘input potentials’ included in the present study can be classified in six groups, and are measured as follows:

Ideal variables Available nroxies

I. Private regional capital

2. Transportation network capacity (a) Roads

(b) Airport

(c) Railroads

3. Distance to major export/import region

4. Interregional accessibility

5. Research and cognitive education

6. Land

Assessed value of building capital, 1000 SEK

Length of long-distance highways and other main roads (measured as tenths of kilometers) Number of passengers in scheduled air traffic (measured in thousands of passengers) Length of main lines (measured as tenths of kilometers)

Travel time in minutes by car to nearest metropolitan region (Stockholm. Gothen- burg or Malmii)

Weighted average interregional travel time, index

Number of professorial chairs (hundreds)

Developed land area in square kilo- meters

The 70 regions concerned are labor market regions, defined as aggregates of municipalities connected by labor force commuting.

Private regional capital is measured by the total assessed building value (land value excluded) of apartment house units and industrial and develop- ment units, where, according to the Tax Assessment Act, the assessment value is to be set at an amount corresponding to 75 percent of the assessed unit’s market value. The measurement of capital is indeed a complex issue, but the measure chosen is, however, the only available proxy for aggregate private capital.

A.E. Anderson et al., Infrastructure and regional economic change 365

Also with respect to the infrastructure capital elements the measures are not quite satisfactory. In the case of airport capacity the observed variable is actually indicating capacity utilization, although measured by the maximum yearly number of passengers during the last five-year period. The reason why this measure has been chosen is mainly that any single physical capacity measure, e.g. feet of runway, is inadequate. The interregional air transpor- tation network capacity is Sweden is in both years, 1970 ands 1980, fairly well represented by the volume capacity at the nodes (airports); the travel time variation is relatively small.

For roads and railroads the capacity has been measured by the total length of long-distance highways and other main roads, and main lines, respectively. As these extensive infrastructural elements, length of roads and railroads, are poor representations of the respective capacity one could use the corresponding density measures, e.g. by normalizing roads and railroads per square kilometer total land area. Such a procedure, used in one specification of the production function (model l), is in accordance with theoretical arguments given by Beckmann and Puu (1985).

Since total land area is economically very heterogeneous normalized variables gives, however, biased capacity measures. In many regions, the northern regions in particular, economic activities are concentrated to a few agglomerations, while the major part of the land area is no part of the economic region. In alternative specifications of the production function land, measured as developed land area, has been explicitly included as an infrastructure element, excluding land used in the primary sector.

Although the inclusion of the latter variable makes it possible to interpret the estimated parameters for roads and railroads fairly well, these physical capacity measures are still inadequate. From a theoretical point of view ‘transportation network capacity’ mainly boils down to intraregional, inter- regional and international accessibility.

The third category listed above reflects ‘international accessibility’. Each metropolitan region has been assigned an international airport (Copenhagen for Malmii). Such an international airport is assumed to be a factor of growing importance for regional economic growth. The fourth category reflects ‘interregional accessibility’. This measure, an index for weighted average interregional travel time, is based on a modal distribution between car, train and airplane, determined by travel time minimization and the distance to the centre in each of the other 69 regions, where travel times (including terminal time) have been weighted by the attraction of the destination.

The fifth category of infrastructure elements, ‘Research and cognitive education’, henceforth named R&D, is measured by the number of professor- ial chairs located in the region. Also in this case an accessibility measure would have been preferable.

366 k.E. Andersson et al., Infrastructure und regional economic change

Table 1

Summary statistics for input variables, 1980.

fnout variable Mean Standard dev. Minimum Maximum

1 Building capital 2.67 x 10h 5.88 X 106

2 Roads 41.26 29.85

3 Airport capacity 0.16 x lo6 0.63 x 10h

4 Railroads 11.63 9.44

5 Professorial chairs 20.23 70.19

6 Travel time to 176.84 164.73 metropolitan region

7 Index for average 206.53 45.82 interregional travel time

8 Developed land area 179.22 111.10

9 Knowledge intensity 0.148 0.029

10 Labor 55.72 x 10” 99.88 x lo3

2.62 x IO6 46.06 x IO’

0.20 182.80

0 5.16 x lo6

0 60.00

0 373.00

29.39 818.90

loo

66.88 823.16

0.104 0.234

10.90 x 103 776.22 x 10’

311

As can be seen from table 1, presenting summary statistics for input variables, some regions lack one or several infrastructural elements. In these cases the corresponding input variables have been given a very small positive value, to make estimations feasible. This ad hoc operation is fairly reason- able, since regions are defined to be labor market commuting regions. Consequently direct interregionul accessibility to airports, universities etc. in most cases is assumed to be very low.

The additional corporate ‘attractable factors’ are measured in two ways: the labor input - measured by the number of employed - and the knowledge intensity of the labor input, measured by the share of knowledge occupations in total employment.

The reason to pay special attention to knowledge occupations (education, R&D, journalism, artistic activity, etc.) has been discussed above. The reason to represent this variable as an intensity has to do with the general difficulty to obtain precise estimates of the separate effects of the variables involved. By the chosen representation the labor input variables do not become severely interrelated. There are, however, strong relationships among several of the variables included. In addition to the variables listed in table 1, a variable representing the interaction effect between airport capacity and R&D capacity is also included. Total regional income is used as the only available indicator of total regional output.

4. Specification of functional forms and empirical results

An earlier study [Anderstig and Harsman (1986b)] has indicated that estimations should at least include the interaction between R&D and airport

A.E. Andersson et al., lnfiastructure ond regional economic change 367

capacity. Obviously variables representing interaction effects cannot be put in the same multiplicative form as for individual infrastructural elements, as represented in eq. (6). Further, the form chosen for the interaction variable should imply that the output elasticities with respect to’the elements included are increasing at a decreasing rate. On this basis, and judging from the statistical performance of alternative formulations, the interaction between R&D (professional chairs) and airport capacity, denoted Di and Dj respec- tively, is represented by D, of eq. (8).

One simple way of representing synergies within a multiplicative form would be by postulating the following exponential component function:

D,=exp(P,,,(Di* Dj)pk).

In order to reduce the number of parameters to be estimated we have chosen to set /I, = /Ik:

D, = exp (jjk( Di * Dj)‘“).

As shown below this assumption does not constrain the output elasticities in any economically unreasonable way.

The output elasticities w.r.t. Di and Dj are written, for Di,

EDt =/Ii + /?,f(Di * Dj)‘*.

Assuming O<flk < 1, the output elasticities have the satisfying properties of positive first derivatives and negative second derivatives.

As for parameter variability over time we have argued that R&D and airport capacity are elements of growing importance. We do not, however, expect any significant increase in /Ik, since large investments have been made in new universities and airports in the period 197&1980, mainly as part of regional policy, and this new capacity is not fully utilized at the end of the period. Roads and railroads are, on the other hand, infrastructural elements where the capacity, given the measures, is almost unchanged in the period 1970-1980. In this case we should expect an increase in the parameter of roads and a decrease in the parameter of railroads, reflecting the changing observed relative weights of fast and slow transportation modes.

Turning to the ‘attractable’ factors, denoting total labour input L, and the knowledge intensity L,, we should expect parameter variability indicating an increase in output elasticity with respect to knowledge intensity. Reformulat- ing (6) into

q=A.exp-z, (10)

368 A.E. Andersson et al., Infrastructure and regionui economic change

where

z = L, a, * ,q a’,

and differentiating with respect to c(,,

c7q (7q (;lz

?a, sz c?z,

gives

37

(11)

.- ~~=-L,“~*L~at*lnL,>O,

&Y, ,

(12)

(13)

since

O<L,<l, lnL,<O.

?q/?z= -A*exp-z<O (14)

and thus

?q/hi, < 0. (15)

A declining knowledge intensity parameter (a,) thus implies rising produc- tivity due to knowledge,

As to the parameter of total labor input we expect a positive sign but a decrease over time reflecting a successively decreasing importance of the purely quantitative aspects of labor input.

In the sequel the empirical results are presented, with reference to four different specifications of the production function, model l-model 4. All estimates are obtained with the Marquardt algorithm in SAS NLIN pro- cedure. Asymptotic standard errors of the estimates are reported in paren- theses, and an estimate is denoted significant, by an asterisk (*), according to an asymptotic 95 percent confidence interval for the parameter.

At first the results of model 1 are presented, where output and applicable input variables are normalized by land area. Some preliminary conclusions can be made on the basis of these results. First, labor should not be treated as a homogeneous production factor; both knowledge intensity and total labor input have significant parameters for 1970 as well as for 1980. It should also be noted that the parameters for knowledge intensity and labor change the way expected, implying increasing importance for quality and decreasing importance for quantity.

The estimated parameters for building capital and distance to metropolitan region (the proxy for international accessibility) are also significant both years, and have the signs expected. Railroad capacity has significant influence

A.E. Anderson et al., Infrastructure and regional economic change 369

on regional productivity for 1970 but not for 1980. The parameter for road capacity changes in the reverse direction indicating that fast and flexible transportation grows in importance.

Production 1970=exp(5.419)* 1 Building capita1°.391*

(0.686) (0.065)

. Distance to metro-0.207* .Airport capacityO,OOO

(0.043) (0.004)

. R&D capacity-0,05a*. exp(0.309*.(Airport*R&D)“.309’

(0.023) (0.035) (0.035)

. Main roads -0.010 . RaiIroadsO.074’

(0.033) (0.028)

.exp-(Knowledge intensity0,375’ . Labor”.372*)m l

(0.064) (0.048) ’

Production 1980 = exp(5.899)*. Building capita1°.462’

(0.732) (0.07 1)

. Distance to metro-0.203*. Airport capacity’.“’

(0.043) (0.004)

. R&D capacity-0.045 . exp(0.266* .(Airport*R&D)0.266’)

(0.025) (0.037) (0.037)

. Main roads0,“j3 . Railroads0,03z

(0.033) (0.029)

exp -(Knowledge intensity0.z63* . Labor0.302*) - ’

(0.128) (0.063)

The interaction between R&D and airport capacity is clearly significant both years. The parameter has the expected sign and in fact captures the

370 A.E. Andrrsson et ul., Infrastructure and regional economic change

whole influence of these factors. Hence R&D capacity and airport capacity have measureable effects on regional productivity only when combined. It should, however, be noted that there is a very strong correlation between airport capacity and building capital.

To conclude, in all essentials the results agree with stated expectations and prior notions. This, however, does not necessarily imply correctness. One problem attached to the specification above concerns the normalizing procedure. To the extent that this means normalizing by idle land, the corresponding capacity measure will be underestimated. On the other hand, by normalizing the output variable as well, this measure is correspondingly underestimated. No matter what statistical consequences that follow from the normalizing procedure, alternative formulations of the model are called for, to find out the sensitivity of results to normalization and to the specification in other respects.

In table 2 the estimation results of three alternative models (2, 3 and 4) are presented. In these models the variables are not normalized, but all models include one variable representing developed land area. Another additional variable is the one representing interregional accessibility. Model 2 and model 3 differ in the way R&D and airport capacities are represented. The results presented above raise the question of the main effects, and for that reason the interaction variable is excluded in model 2, whereas the main variables are excluded in model 3. Model 4 follows the notion that ‘accessibility’ is an adequate representation of ‘transportation network capa- city’, and so the variables representing road, railroad and airport capacity are excluded.

The residual error sum of squares (SSE) corresponding to each specifi- cation is reported, although no formal tests are carried out to discriminate between the alternative model specifications. The functional form is the same as in model 1, presented in eqs. (6)-(15).

In all essentials the results presented in table 2 are in agreement with those of model 1: The interaction between R&D and airport capacity is clearly significant (model 3) and outweighs the main effects, of which only R&D is significant (model 2). The proxy for international accessibility, distance to metropolitan region, is significant irrespective of model specification. The proxy for interregional accessibility, the index of interregional travel time, has also a parameter estimate with expected sign, but the standard error is relatively large.

Also according to these alternative model specifications the effect of main roads is of growing importance; the parameter estimate is significant for 1980 but not for 1970. Since this partial effect is present at the same time as international and interregional accessibility are represented by separate variables, the parameter of road capacity may reflect the increasing effect of intraregional accessibility. As for railroad capacity it is reasonable to assume

A..?. Andersson et al.. Infrastructure and regional economic change 371

Table 2

Estimates of aggregate production functions, according to three model specifications. Total regional output in 70 A-regions in 1970 and 1980 (asymptotic standard errors).

Model 2 Model 3 Model 4

1970 1980 1970 1980 1970 1980

Constant 0.141 ~ 0.57 1 0.864 0.155 0.072 PO.528 (0.876) ( 1.046) (0.866) (1.004) (0.786) ( 1.032)

Building capital 0.235* 0.293” 0.180” 0.250 0.238” 0.269” (0.049) (0.05 I) (0.050) (0.049) (0.046) (0.050)

Main roads -0.006 0.045” 0.001 0.041” (0.023) (0.022) (0.022) (0.020)

Railroads 0.010 0.010 0.030 0.031 (0.029) (0.027) (0.028) (0.025)

Airport capacity 0.002 0.005 (0.003) (0.003)

R&D 0.056” 0.046” 0.057” 0.047 (0.014) (0.011) (0.013) (0.012)

Auport *R&D 0.156” 0.150” (0.011) (0.010)

Distance to metro -0.071” -0.075” -0.079” -0.081” -0.064” PO.067 (0.029) (0.026) (0.027) (0.024) (0.024) (0.023)

Interregional travel -0.126 PO.126 -0.135 -0.143 -0.128 -0.055 time, index (0.087) (0.083) (0.085) (0.076) (0.081) (0.083)

Developed land area 0.08 1 0.135” 0.049 0.085 0.08 I 0.181’ (0.054) (0.048) (0.053) (0.046) (0.052) (0.047)

Knowledge intensity - 0.022 - 0.080 0.018 -0.051 -0.029 ~ 0.050 (0.046) (0.062) (0.039) (0.052) (0.043) (0.054)

Labor 0.283’ 0.263” 0.273” 0.258” 0.287” 0.269” (0.017) (0.020) (0.014) (0.018) (0.015) (0.018)

SSE 0.801 0.685 0.762 0.603 0.807 0.781

“Parameter is significantly different from zero, according to an asymptotic 95 percent confidence interval.

that the influence on regional productivity, if any, is exclusively captured by the variable measuring interregional accessibility.

At a comparison of all three models, the specification used in model 3 gives the lowest value of SSE, due to the variable representing interaction between R&D and airport capacity.

The estimated parameter for building capital has the expected sign and is significant in all model specifications. As for the estimated parameter for developed land area, it has the sign expected but the partial effect is not generally significant.

Total labor input has significant parameter estimates in all model specifi- cations, where the parameter, as expected, decreases over time. The know- ledge intensity, however, has no separate effect on regional productivity, in

312 k.E. Andersson et al., Infrastructure and regional economic chunp

contrast to the result in model 1. Alternative ways of distinguishing between various types of labor input have been tested. Replacing knowledge intensity. in terms of occupations, with a corresponding intensity measure in terms of level of education makes no difference to the estimation results of the respective model specification. An alternative formulation, where the labor input variables are represented by the number of employed in different occupation/education categories makes it even more difficult to get precise estimates of the separate effects of the variables involved.

Turning to the special issue of spatial effects, discussed in e.g. Anselin and Griffith (1988) it should be admitted that this kind of problems has not been properly dealt with in this study. Among potential problems heteroskedasti- city appears, however, to be negligible.

In addition to the model specifications presented above, some other ideas have been tested but rejected for various reasons. For example, a proxy for port capacity did not prove to be of any influence, nor did a dummy variable representing social overhead capital, measured by presence of seat of the county government.

To sum up, the empirical results from the alternative model specifications (l-4) show that it is only the effect of the knowledge intensity that is sensitive to the use of normalized variables, whereas the effects of the various infrastructural elements are relatively unaffected.

Let us end by illustrating how the results obtained can give further policy relevant information. First, a comprehensive illustration of the regional equipment of infrastructure elements is provided by estimating the regional scale-elasticity, the ‘passus coefftcient’.

From eqs. ( 10) and (11) we have

(16)

and the scale-elasticity, with respect to the labor inputs, is given by

tz(L,,L,)= c?q L,+c:q ,L,

CL, q ?L, q

=(xc+cc,)(L,l“L, “‘), (17)

which may also be written:

The scale-elasticity in (18) is written as a function of the supremal output capacity A and the actual output q, where A represents the regional

A.E. Anderson et al., Infrastructure and regional economic change 373

2.25

1.25

025

0.00 10 20 30 40 50 60 70

Order of regtonal output

Fig. 1. The scale elasticity’s variation with regional output, 1970 and 1980.

equipment of infrastructure elements. Estimating the production function (16) thus gives an estimate of the scale-elasticity.

As a simple illustration we have used the estimated parameters according to model 1 above, and the estimated scale-elasticity’s variation over regions is presented in fig. 1. The regions are put in order of estimated output ij, from lowest = 1 to highest =70.

Fig. 1 shows a tendency of decreasing scale-elasticity with order of estimated output. It can be seen, however, that there is no continuous

decrease in scale-elasticity with increasing order. For example, in 1970 the scale-elasticity for Uppsala, order 67, is greater than that of several regions with lower output.

According to fig. 1 the scale-elasticity is decreasing over the period 1970- 1980. Further, the variation of the scale-elasticity is decreasing over the period, which indicates that the output capacity, with respect to infrastruc- ture elements, is more equally utilized in 1980. Yet, in 50 regions the estimated output corresponds to less than 50 percent of estimated infrastruc- ture capacity. This rate of utilization is close to 75 percent in the three metropolitan regions (order 6X&70), indicating that a general bottleneck problem is at hand.

Another approach to extract policy relevant information, of more specific kind, follows lines suggested by Blum (1982), assuming that regional variations in marginal rates of substitution (MRS) can be used to indicate bottlenecks or excess capacity in the regional equipment of infrastructure elements. Let us very briefly touch on two examples. Firstly, for each region, the MRS of highways for building capital is compared with the national average. The result indicates excess capacity, as regards highways, in almost all regions in the northern part of Sweden, and bottlenecks in metropolitan regions. Secondly, the bottleneck analysis shows that there are severe imbalances in the supply of university capacity in Swedish regions, indicating that close to ten regions have substantial benefit-cost ratios associated with creation of new university capacity.

Though a discussion in terms of bottlenecks and excess capacity has a lot of merits from a pedagogical and policy point of view, a closer discussion of underlying assumptions and infrastructure definitions is called for.

Finally, the estimated production function can be used as a set of 70 regional constraints within a non-linear optimization procedure. In such a NLP-model, e.g. regional development policy costs can be minimized within the framework of infrastructural investment policies needed to achieve regional development targets. The results of such a study are reported in Anderstig and Mattsson (1989).

5. Summary and conclusions

This study is oriented to the relation between infrastructure and economic performance of industries in different regions. The approach is to use cross- sectional data for the 70 Swedish A-regions within the theoretical framework of production functions. We have chosen to use production functions which can accommodate the ‘Regular Ultra Passum Law’ in which infrastructure is aggregated into a multiplicative factor, while the factors of production variable to the firm in the short term are subjected to variable returns to scale.

A.E. Andersson et al., Infrastructure and regional economic change 375

We have abstained from explicit consideration of dynamics. This approach is based on the assumption that an adiabatic approximation procedure can be used. This implies that the time of adaption of infrastructure is much longer than of the variable factors of production so that equilibrium assumptions can be made in the econometric cross-section study.

The variable inputs under the direct control of the firms are only qualified and other labor inputs. The econometric tests are made on a set of A- regions, which are the commuting regions of Sweden, also used in the subdivisions of Swedish labor market policy.

The study shows that there are clear relations between the supply of infrastructure and the productivity of the regions as a macroeconomic entity. The most important infrastructural factors are related to research and development capacity and to transportation and communication possibilities. Total production is statistically primarily influenced by road, airport and R&D capacity.

The econometric study further shows that while railroads had a significant effect upon regional productivity in 1970 this effect does not appear in the results for 1980. Fast and flexible transportation modes are obviously of growing importance. Earlier studies have indicated that airline transportation and research and development capacity interact synergetically. With reference to these studies we have also inserted such a synergistic factor, which turns out to be highly significant and important for regional productivity.

The study also reports on some analysis of infrastructural bottlenecks. The results indicate that there are severe bottleneck problems in the Swedish road system, implying that road investments should be concentrated to certain regions, primarily the metropolitan regions and their vicinities, if maximal national development should be achieved.

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