Externalities and Growth

Externalities play a central role in most theories of economic growth. We argue that international externalities, in particular, are essential for explaining a number of empirical regularities about growth and development. Foremost among these is that many countries appear to share a common long run growth rate despite persistently different rates of investment in physical capital, human capital, and research. With this motivation, we construct a hybrid of some prominent growth models that have international knowledge externalities. When calibrated, the hybrid model does a surprisingly good job of generating realistic dispersion of income levels with modest barriers to technology adoption. Human capital and physical capital contribute to income differences both directly (as usual), and indirectly by boosting resources devoted to technology adoption. The model implies that most of income above subsistence is made possible by international diffusion of knowledge.

On the 4D generalized Proca action for an Abelian vector field

We summarize previous results on the most general Proca theory in 4 dimensions containing only first-order derivatives in the vector field (second-order at most in the associated St\"uckelberg scalar) and having only three propagating degrees of freedom with dynamics controlled by second-order equations of motion. Discussing the Hessian condition used in previous works, we conjecture that, as in the scalar galileon case, the most complete action contains only a finite number of terms with second-order derivatives of the St\"uckelberg field describing the longitudinal mode, which is in agreement with the results of JCAP 1405, 015 (2014) and Phys. Lett. B 757, 405 (2016) and complements those of JCAP 1602, 004 (2016). We also correct and complete the parity violating sector, obtaining an extra term on top of the arbitrary function of the field $A_\mu$, the Faraday tensor $F_{\mu \nu}$ and its Hodge dual $\tilde{F}_{\mu \nu}$.Comment: LaTeX file in jcappub style, 11 pages, no figures. v2: Minor changes according to the referee requirements. A new parity-violating term in the Lagrangian has been uncovered and the text has been changed accordingly. The conclusions are, essentially, unchanged. v3: Miscellaneous changes. Version to be published in Journal of Cosmology and Astroparticle Physic