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This paper develops a multi-sector endogenous innovation model that is able to take changing productive relations among sectors into account. It is shown that while productivity and demand shocks do not induce any changes in productive relations and linkage effects, shocks in the productivity of R&D increase both backward and forward linkages. Key sectors are characterized as having high forward and backward linkages, which are consistent with the definition of key sectors in the existing empirical studies. However, vertical specialization generates not only sectors with high backward and low forward linkages, but also sectors with low backward and high forward linkages. As a consequence of this vertical specialization, the latter sectors become key sectors, in the sense that they have significant effects on business fluctuations. This implies that general-purpose technology sectors emerge, and sector-specific policies for these sectors play a critical role in economic development and growth.
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Tsutomu Harada (2015) studied this question.
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