( ) ⎪ ⎨ ⎧ − = ) , , , , , ( l l o g l o g l o g d i s t Y S S H K R H K f T T T T D og m h j = d , d δ δ
As mentioned output growth is a function of (exogenous) labor (L) and capital (K) accumulation as a well as of endogenous accumulation of technology (T) and services both domestic and imported (Sh, Sm). The introduction of services in the production function (eq. 1), can be interpreted as the result of the decomposition of TFP in presence of spillovers generated by the interaction among sectors in the economy. This effect can be connected to the Information Technology (IT) sector as shown in Mun and Nadiri (2002), where the TFP decomposition is obtained from the correspondence between the cost function, the production function, and the inclusion among explanatory variables of the services-sector spillover-effects. Services can be treated as a production factor in the same way as intermediate goods. It follows that the model (1)- (3) can be seen as a way to endogenize the components of TFP and to take into account the feed back effects of output growth on the TFP components themselves. Moreover, since in the Penn World Tables capital is accumulated and depreciated spending on producer durables, which does not include IT and other service spending, we explicitly consider this component that in most studies is included in the TFP residual.
Services, both domestic and imported (eq. 2), grow with output and with technology reflecting the idea that they represent an important intermediate input and that the share of “advanced” services in the economy increases with technology accumulation.5 The relevance of technology in the production of services has been widely considered in literature (see e.g. Zagler, 2002). Our innovation is that the link between services and technology is modeled and tested simultaneously with the relationship between technology and services. Moreover, in our model, the production and import of producer services depend on both the level and the composition of output. In this respect we follow the idea that producer services coordinate the specialized production members of a complex production process into a unified operation (Francois, 1990). Therefore the importance of producer services depends on the scale of production and on the degree of complexity in production. Different sectors make different use of producer services according to the complexity of their production activity (see Guerrieri and Meliciani, 2004), therefore in eq. 2 producer services are also expressed as a function of the structure of the economy (STR) according to how the manufacturing sector is oriented towards the use of services in production. To this purpose we use the index developed in Guerrieri and Meliciani. (2004).6 Finally producer services depend positively on the exogenous expenditure in information technology (ICT), due to its key role in their innovation process that we have already discussed, and negatively on higher levels of regulation (REG) as discussed in Nicoletti and Scarpetta (2003).
5 Francois and Reinert (1996) find that income levels are strongly linked to demand by firms for intermediate or producer services.
For a precise definition of the indicator see Section III.A.