This Project is inserted in the Theory of Endogenous Growth. We want to increase scientific knowledge about different models of endogenous growth with physical capital, human capital, and R&D applied to the world economy and to small open economies. In the first class, of closed world economy models, the frontier knowledge is defined by a generation of endogenous growth models that include physical and human capital accumulation, vertical and horizontal R&D, in which literature has made an attempt to quantify the different externalities due to market failures in the R&D process (e.g. Strulik, 2007). Thus, the main lines to be pursued include introducing new cumulative assets in this class of models, such as social capital and natural capital, and new sectors, namely a sector of basic research. Social capital and natural capital are essential factors to define the wealth of Nations (World Bank, 2006), so their consideration in this type of models is crucial. Besides that, the consideration of a basic research sector is new in models with human capital accumulation. However, its inclusion and the interaction it may have with the other sectors (final good, differentiated goods, R&D, Human Capital) may introduce great differences in the equilibrium features, namely in stability properties and in convergence paths. Furthermore, there are externalities associated with social and natural capital and with the nature of basic research as a pure public good that have never been considered in this framework. We want to find these features, to calculate transition paths and to quantify the different types of externalities through the implementation of calibration exercises.

These findings would be useful to identify, quantify and optimally time policy adoption. Concerning endogenous growth in open economies we will use two different approaches, modeling small open economies and modeling trade between two large blocks, North and South. Regarding small open economies, we will identify the knife-edge conditions present in models with two R&D sectors for such economies, following the results of Turnovsky (2002). We expect to find very strong conditions for models with accumulation of human capital. We may have to pursue an alternative way of opening the economy, through foreign direct investment in varieties, an idea presented in Reis (2001). We will characterize these models, in terms of steady-state properties and convergence.

The North-South growth and trade literature based on the role of human capital and R&D is focused on the connection between economic growth, convergence, and trade patterns, studying such topics as transfer of knowledge, directed technical change, the role of intellectual property rights, wage inequality, among others. The inclusion of R&D in these models is done using horizontal innovation (expanding varieties models) or vertical innovation (quality-ladders growth models). Traditionally, quality-ladder type models predict that once a new and better technology is installed the old one is immediately replaced and stops being produced. If we take a closer look at what happens in real economies, we see that improved technologies sometimes coexist with old technologies in different countries. To introduce this type of effects in the model we will build a model where expanding varieties are made in the (more developed) North and quality improvements – or adaptation to specific markets - are made in the (less developed) South. This inclusion of both vertical and horizontal innovations in the same model was introduced by Young (1998) for the closed economy case. Since we are assuming that the South is less developed we are also interested in studying possible development stages for this region. This is similar to the work of Chui et al. (2001) for the horizontal innovation case. Externalities, changes in equilibriums, and in transition paths of these types of models are also of relevance to the literature and are not much explored. It is also important to study the role of basic research in a context of North-South type models of economic trade and growth, since the existence of a strong basic research sector in an open setting model can bring along international externalities that are not explored in the literature.

The question of natural capital in an open economy that trades is also very significant and hasn’t been fully analyzed. In particular, the work to be developed will explicitly take into account that some natural capital is local, in the sense that its effects are felt only inside the country, and some is global, with external spillovers that require international coordination, for example through voluntary agreements. The goal is to study the implications for growth of typical natural capital problems in a North-South framework, as well as to compare the effects of different policies (for example, in climate control).  

The methodologies involved in the project are: model building, identifying equations that describe transition and equilibrium paths, calibrating the models with empirical and past theoretical literature, and whenever possible solving for the equilibrium paths following the method of backward integration (Brunner and Strulik, 2002).

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