Introduction

1. External information Interindustry linkages and firm size: does it make a difference? An empirical illustration for Spain Esteban Fernández Vázquez(1) and Isidoro Romero Luna(2) Estimation methodology Introduction An IO table that distinguishes between small, medium and big enterprises Backward linkages of service activities and firm size: some findings for Spain The p and w unknown probability distributions will be estimated by applying the Cross Entropy (CE) technique. We will minimize the Kulback divergence with respect to two a priori probability distributions (q1 is the a priori distribution for pand q2 for w) subject to a set of constraints: Subejct to: If no a priori information is available, the distributions q1 and q2 are assumed as uniform distributions and the CE estimation is transformed into a Maximum Entropy (ME) problem Some previous studies in the literature have focused on the relationship between firm size and the productive linkages. On earlier works some attention has been paid to this issue using an input-output approach, but the information contained in a national or regional input-output table does not allow for the study of interindustry relations distinguishing the size of the firms. Our objective is to estimate an input-output table for Spain where the information of some sectors is split up depending on the firm size. For this purpose we use Cross-Entropy techniques that allow the use of some additional indirect information. Our hypothesis is that the intersectoral linkages can present significant differences depending on the firm size. This initial guess is tested from our estimated input-output table that differentiates among large, medium and small firms in several industries. The normalized backward linkages are shown in the following figure for the 10 services branches studied: The industries on the previous table will be spilt up on three different types depending on the size of the enterprise. An example with only one industry j: The interindustry flows from and to j are going to be divided distinguishing the size of the firms that form this industry. Some additional information (external to the IO table) is required in order to make this division. Specifically, we need some information about the intermediate input and output of the small (s), medium (m) and big (b) firms of industry j: The interindustry flows concerning industry j on the previous matrix can be spilt like this: Although the row and column sum can be known values, the interindustry flows of the matrix are still unknown and should be estimated somehow. For this estimation we assume that every zij unknown value can be written as a proportion of the original flows of the non-divided matrix. Generally speaking, the backward linkages of the small and medium companies are generally bigger than those of big firms. The only exception is on the Research and Development services, where the big companies present larger linkages than smaller enterprises. These results seem to confirm the idea that, at least for the case of Spanish service activities, SMEs present stronger connections with their providers than the companies with larger size. The estimated probabilities must fit the column and row sums included as additional information The basic problem: relating linkages and firm size In a traditional symmetric input-output table there is no information about the size of the companies in each industry: From such an input-output table, the linkages between the industries of this economy can be analyzed by applying well-known techniques in the input-output field (Rasmussen´s multipliers, hypothetical extraction, etc.). But an important issue concerning interindustry linkages is the size of the firms. Actually, the most common hypothesis is that Small and Medium Enterprises (SMEs) present larger linkages, given their usually higher level of territorial integration and maintain stronger linkages with suppliers and clients (Florio, 1996; Crone and Watts, 2000; Görg and Ruane, 2001). Moreover, it is commonly believed that large enterprises frequently have more intense linkages with productive units located outside the economy than with firms operating in the same area. The objective of this research is to incorporate the discussion on the implications of the firm size into the study of input-output interindustry linkages. Some references An empirical study: commercial services in Spain (2000) Crone M. and Watts H. D. (2000): MNE supply linkages and the local SME sector: evidence from Yorkshire and Humberside, Local Economy 15, 325–337. Florio M. (1996): Large firms, entrepreneurship and regional development policy: ‘growth poles’ in the Mezzogiorno over 40 years, Entrepreneurship and Regional Development 3, 263–295. Golan A. and Judge G. (1996): Recovering information in the case of underdetermined problems and incomplete economic data, Journal of Statistical Planning and Inference, 49, 127-136. Golan A., Judge G. and Miller D. (1996): Maximum Entropy econometrics: robust estimation with limited data, John Wiley & Sons, New York. Görg H. and Ruane F. (2001): Multinational companies and linkages: panel-data evidence for the Irish electronics sector, International Journal of Economics and Business 8, 1–18. Romero I. and Santos F.J. (2007): Firm size and regional linkages: a typology of manufacturing establishments in Southern Spain, Regional Studies, 41 (5), 571-584. As empirical illustration we will split 10 service activities that are present in the Spanish IO table of 2000 applying the estimation methodology described above. We have considered as “small” all the companies with a number of workers smaller than 20; the firms of “medium” size will have more than 20 but less than 100 employees; finally the firms with 100 workers or more will be considered as “big”. The following additional information has been obtained from the Annual Services Survey elaborated by the Spanish Statistical Institute (INE): This information has been used to estimate the cells of the intermediate flow matrix. An equivalent approach has been applied to obtain the vectors of final demand and total output. This allows obtaining the Leontief inverse matrix including the services branches that have been divided according their size. From this model, we will measure the backward linkages of these 10 industries obtaining the Rasmussen’s multipliers and we will check if there are significant differences depending on the firm size. Contact information IO Table Probabilities to be estimated