Empirical identification of key sectors: some further evidence

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1 Environment and Planning A,, volume, pages - Empirical identification of key sectors: some further evidence W B Beyers Department of Geography, University of Washington, Seattle, Washington, USA Received April, in revised form November Abstract. Techniques for the identification of key sectors have been developed in recent years. This paper proposes improvements in these methods of calculation and provides an illustration of these techniques. Introduction He wings () has recently investigated the usefulness of techniques for the identification of key sectors. He has focused on measures developed by Hazari (0), which are similar to those in the studies by Rasmussen (), Chenery and Watanabe (), Hirschmann (), and Perroux (). Although Hewings' work goes a long way towards identifying areas for further research and sets in perspective the values of these methods, there are several additional matters which need clarification. The purpose of this paper is twofold. First, there is an improvement that can be made in the method of calculating forward-linkage measures. Second, by defining the inputoutput model in an inter framework, we can obtain multilevel measurements for key sectors. This type of decomposition is of relevance to national planners concerned with the multi impact of -development strategies (Goreux and Manne, ). In this paper only a few of the measures used by Hazari and Hewings will be used to illustrate these computational procedures. Forward-linkage measurements Hazari and Hewings define their measurements of forward linkages on the row elements of a Leontief inverse matrix for a national economy. Column or input coefficients were used in the calculation of their inverse matrices. In effect they have calculated measures of forward linkages based on the strength of backward linkages. These measures are not comparable with Rasmussen's power of dispersion, and other similar measures that were developed using input coefficients, where the strength and distribution of backward linkages were used to calculate the values of Uj (power of dispersion) and Vj (value added). The obvious solution to the problem created by their methodology would be to utilize measures based on forward linkages or sales coefficients. It should be noted that Rasmussen (, pages 0- ) did not utilize measurements of forward linkages in his definition of key industries. Chenery and Watanabe (, page ) used direct purchases and direct-sales coefficients to measure the strength of backward and forward linkages. Perroux () and Hirschmann () refer to propulsive or key industries as having strong forward and backward linkages, although they do not provide techniques of measurement for these relationships. There is an alternative formulation of the Leontief () input-output model which may be developed on the columns of the model, instead of the usual form which uses the rows. Proceeding from the basic accounting identity for purchases, we have X, = %X t,+ V, + M,, ()

2 W B Beyers where Xj are the total purchases of the /th sector, Xij are the interindustry transactions between sectors / and /, Vj is the value added in the /th sector, and Mj are imports to the region for the /th sector. Let us define a sales coefficient, by, as follows: bit = f; () Then by substituting equation () into equation (), we obtain X f = Y,b if Xi+Jj + M f. () In matrix notation this system may be expressed as X = XB + V+M. () On solving for X we obtain X= (V + MXI-B)-. () This formulation defines the level of output in any sector as a function of the supply of imports and value added, as well as the structure of forward linkages. Each element in the matrix (I-B)" defines the output supplied to the /th (column) sector per unit of final supply, (V + M), in the /th (row) sector. By reading across a row in this inverse matrix, we can define the direct and indirect supply to all sectors as a result of a change in final supply in the /th (row) sector. Supply multipliers are defined by summing rows in this matrix, which is in contrast to demand multipliers that are defined on the column in the traditional Leontief inverse matrix based on purchases coefficients (Augustinovics, 0). By using the inverse matrix based on sales coefficients, we can develop more comprehensive and meaningful measures of forward linkages than are possible with Hewings' and Hazari's formulation. Such measurements would be more compatible with the frameworks developed by Chenery and Watanabe, Hirschmann, and Perroux. Thus, for backward linkages, it is proposed that the power-of-dispersion measures, as-developed by Rasmussen [based on the (I A) - matrix], should be utilized to help in the identification of key sectors. In the calculation of measures for forward linkages, such as Rasmussen's sensitivity of dispersion, it is proposed that the inverse matrix, based upon sales coefficients [(I-B)" matrix], should be employed. Multilevel measurements In recent years the concept of key sectors has become quite important in the development literature. Programmes to help lagging or distressed regions in developed national economies have proliferated (Hansen, ; Kuklinski, ). Contemporary models of growth poles and growth centers characterize key sectors in a more complex fashion than by just having relatively strong forward and backward linkages (see Erickson,, for example). These key sectors should also be rapidly growing, be relatively efficient, and be leading sources of innovations. However, measurement of the strength of their linkages is only one characteristic of a key or 'lead' sector within the framework of growth-pole or growth-center theory (Erickson, ; Thomas and Le Heron, ; Pred, ). From the standpoint, a sector which is classified as 'key' at the national level may have weak connections. Alternatively, sectors with strong degrees of connection, and which may be classified ly as key sectors, may

3 Empirical identification of key sectors: some further evidence not be considered key industries at the national level. In order to focus on these geographical differences in linkage strength it is proposed that an inter inputoutput formulation be utilized. For example, in a two-region model we might focus upon an area which is the subject of development interest, and the second region could be the rest of the national economy. Other izations could be used, depending upon the purposes of the study. An empirical example For the purposes of illustration some inter input-output data have been developed for two divisions of the United States. One region is an urban area, the Puget Sound region. The second region is defined as the rest of the United States. Table presents estimates of the power of dispersion and the sensitivity of dispersion for these data. [The reader is referred to Hazari (0), Hewings (), or Rasmussen () for an explanation of the computational aspects of these measures.] In calculating the power of dispersion measures, the coefficients of (I-A)" were used, whereas the coefficients of (I-B)" were used to calculate the sensitivity of dispersion measures. Key sectors were defined by Hazari as having a greater than average degree of connectivity with the economy; that is, those sectors whose values of the power of dispersion (C/ ; ) and sensitivity of dispersion (U t ) were greater than unity. In table, and inter values for these two measures are provided at a twenty-two sector level of detail. Table. Regional and inter power of dispersion and sensitivity to dispersion. Sector number 0 Name Agriculture Mines Food products Textiles Wood products Furniture Paper products Printing Chemicals Petroleum Stone-clay-glass Ferrous metals Nonferrous metals Fabricated metals Motive machinery Machine shops Industrial machinery Electrical machinery Aerospace Other transport equipment Ut * - 0-0* ^ *00 0* U t a (rar ik) 0 0 Uf (rank) Other manufacturing Services/construction a r = 0-; rank orderings not independent. b r = 0*; rank orderings independent. 0 inter inter inter inter 0

4 W B Beyers It can be seen in the two-way classification schemes, shown in tables and, that only one (wood products) of the twenty-two sectors satisfies Hazari's (0) keysector definition both at the and inter level, whereas a number of other sectors satisfy the definition at one level only. These data imply that key sectors defined at one scale may not be classified this way at another scale. In order to test for the overall degree of variation in linkage strength, rank correlations of the ordering of the U t and U f measures of the sectors were calculated. These tests indicated a nonindependent ordering of the forward-linkage ranks, but an independent ordering of the ranks of the backward linkages. Similar statistical results were found for the measures of variance (Vi and V f ) proposed by Hazari (0), although the ranks are not reproduced here.. Because of the openness of an economy the size of the Puget Sound region, it is not surprising to find interindustry connections in particular sectors much weaker than or stronger than the connections of the same sector at the national scale. For example, the aerospace sector has the lowest value of the power of dispersion ( /,-) ly, but at the national scale this sector is ranked fifth highest in terms of the power of dispersion. As a contrast, the services-construction sector has a high power of dispersion locally, but a rank of only nineteenth in the index at the national scale. As a partial explanation, in the case of the aerospace sector, it can be said that purchases were very modest, but the degree of intermediate sectoral dependence at the Table. Regional two-way classification power of dispersion and sensitivity of dispersion. C/r > i o Of < -0 Sector number Final demand (%) Sector number Final demand (%) a The entries for final demand show the percentage of the sector's total sales made to final demand (local and national consumption, investment, government, and foreign exports). Table. Inter two-way classification power of dispersion and sensitivity of dispersion. Sector number Sector number 0

5 Empirical identification of key sectors: some further evidence national scale was quite significant. In the case of the services-construction sector, the majority of the sector's backward linkages are, so that the values of the direct purchases and inverse coefficients did not increase much relative to all sectors. Given the significant variations in the inter measures of the power of dispersion, / ; -, the lack of variation in the forward linkages is at first puzzling. Two explanations seem possible: () forward-linkage patterns are proportionally more consistent at the and inter levels than backward linkages, or () there are peculiarities inherent in the measurement technique, or the economy studied, which lead to these results. It has been observed elsewhere that industries in the Puget Sound region have a strong degree of connection with and national final demand that is, with consumption, investment, government, and export sectors (Beyers, ). Not only is the services-construction complex focused strongly on local consumption and investment, but the region's manufacturing industry is also strongly specialized in the production of capital goods, especially aircraft, aerospace goods, ships, other transportation equipment, and electrical and nonelectrical machinery. Connections to these final-demand sectors lie outside the matrix of interindustry relations, and are thus excluded from calculation of the sensitivity-of-dispersion index. Table shows that there is a tendency for sectors defined as key sectors to have weak relations with final demand, whereas those with strong final-demand links are ranked very low in terms of their sensitivity of dispersion. Although the input-output model could be closed with respect to more elements of final demand, such calculations have not been undertaken here. At the scale the output-multiplier impacts associated with the 'lateral-induced' system (which includes local components of final demand and value-added) may be relatively strong (Beyers, ). These relationships should possibly be endogenized when making calculations to identify key sectors. At present, however, we know so little about the interindustry structures of metropolitan regions that it is very difficult to assess whether the pattern of forward linkages of sectors in the Puget Sound region, identified in this paper, is in any way typical. We should also note that these linkages show a considerable variation in and inter measures of key sectors. This result seems at odds with Hewings' (, pages -) finding of stability in the and inter measurements. The reason for this divergence lies in the differences in the computational method used by Hewings and that used in this paper. Figure helps to illustrate this issue. Both Hewings and the author of this paper employed an inter inputoutput formation to calculate the values of U i U f, and the other measures related to key-sector identification. Figure shows the general organization of the two- systems used by both authors. In figure, A RR and A ss are the intra interindustry matrices for regions R and S, whereas A RS and A SR are the inter interindustry direct-requirements matrices between the two regions. In calculating and inter linkage measurements, Hewings used the relevant coefficients within the intra coefficient (A RR ) block. In this paper the key-sector measures were estimated by using the A RR block, whereas the inter measures were calculated by using the A RR and A SR blocks for column ARR A RS A SR A ss Figure. A two-region interindustry model.

6 W B Beyers measures, and the A RR and A RS blocks for row measures. The 'inter' measures of He wings were more limited in scope than those presented in this paper. The reason why Hewings found such stability in his and inter calculations was because there was so little feedback in the component of his inter interindustry model that it increased the magnitude of the coefficients over the model only slightly, and hence did not change the general magnitudes of the key-sector identification measures. Conclusions In this paper an improved method for the calculation of the sensitivity of dispersion has been defined by using an alternative formulation of the Leontief () inputoutput model. It has also been shown that the region chosen for analysis may greatly influence the definition of key sectors. Although not all of the measurements utilized by Hazari and Hewings in their analyses were repeated here, it is suggested that the inverse matrix, based on sales coefficients, together with other policy-analysis measures, should be used when examining forward-linkage patterns, and that explicit attention should be given to the multi impacts of development programmes. These methodological comments and multi measurements complement the results of Hewings' work which showed the ambiguity of Hazari's proposed measures of key-sector identification. It should now be clear that simple measures of key sectors, based on interindustry data, need to be scrutinized from a variety of additional perspectives before development programmes are articulated. Acknowledgements. The support of the National Science Foundation for this research is gratefully acknowledged. The author would also like to thank Morgan D Thomas and Geoffrey J D Hewings for their helpful comments on this paper. References Augustinovics M, 0 "Methods of international and intertemporal comparison of structure" in Contributions to Input-Output Analysis Eds A P Carter, A Brody (North-Holland, Amsterdam) pp - Beyers W B, "On geographical properties of growth center linkage systems" Economic Geography 0 - Chenery H, Watanabe T, "International comparison of the structure of production" Econometrica - Erickson R A, "The 'lead' firm concept: an analysis of theoretical elements" Tijdschrift voor Economique en Social Geografie November-December, pp - Goreux L M, Manne A S (Eds), Multi-level Planning: Case Studies in Mexico (North-Holland, Amsterdam) Hansen N M (Ed.), Growth Centers in Regional Development (Praeger, New York) Hazari B R, 0 "Empirical identification of key sectors in the Indian economy" Review of Economics and Statistics 0-0 Hewings G J D, "The effect of aggregation on the empirical identification of key sectors in a economy: a partial evaluation of alternative techniques" Environment and Planning A - Hirschmann A O, Strategy of Economic Development (Yale University Press, New Haven, Conn.) Kuklinski A (Ed.), Growth Poles and Growth Centers in Regional Planning (Mouton, The Hague) Leontief W W, "Quantitative input-output relations in the economic system of the United States" Review of Economics and Statistics 0- Perroux F, "Note sur la notion de Pole de Croissance" Economie Appliquee (-) 0- Pred A R, Major Job-providing Organizations and Systems of Cities Commission on College Geography Resource Paper Number (Association of American Geographers, Washington, DC) Rasmussen P, Studies in Inter sectoral Relations (North-Holland, Amsterdam) Thomas M D, Le Heron R B, "Perspectives on technological change and the process of diffusion in the manufacturing sector" Economic Geography - p a Pion publication printed in Great Britain