New Growth Theory models

What causes economic growth has been one of the central concerns of economists since time immemorial. The classical growth theories held that mere accumulation of capital contributed to growth. Economists led by Joseph Schumpeter claimed that entreprenuership generated "creative destruction" which transferred resources from inefficient to more efficient systems of production, thereby expanding wealth.

The neo-classical growth theory (Solow-Swan growth model) introduced exogenous technological change to explain growth when the diminishing returns to scale sets in. New growth theorists led by Paul Romer and Robert Lucas, endogenized technological change by introducing the concept of human capital, which unlike physical capital is subjected to increasing returns to scale. Economies can ensure sustained economic growth by investing more in human capital, so as to offset the diminishing returns on physical capital.

Robert E Lucas has new NBER working papers here and here where he unveils new variants of the new economic growth theories. These models are bulit on the premise that all knowledge resides in the head of some individual person, so that the knowledge of a firm, or economy, or any group of people is simply a list of the knowledge of its members (technology frontier). Under this model, each person gains from the knowledge of the people around him and his ideas in turn stimulate others.

The different agents/individuals in an economy have varying knowledge levels, and a description of the state of knowledge of this economy requires the entire distribution of knowledge over individual agents. This distribution is called the technology frontier of the economy. Taking the example of an economy with a single good and a labour only production technology, Prof Lucas models how the technology frontier can be expanded and economic growth achieved.

An individual producer is characterized by his current cost level, which is a random variable drawn from the technology frontier distribution. He is also subject to a stochastic flow of new ideas, which in turn corresponds to new cost levels. When he receives a production idea that is better than the one he is now producing with, he adopts it and this new cost becomes his new equilibrium cost state. If he receives a higher production cost idea, or no idea at all, his cost state remains unchanged. The technology frontier evolves endogenously in this manner.

Update 1
Here is an interview of Paul Romer.