Tag Archive for 'Solow Growth Model'

The short-long-run, the medium-long-run and the long-long-run

EC102 has once again finished for the year.  It occurs to me that my students (quite understandably) got a little confused about the timeframes over which various elements of macroeconomics occur.  I think the reason is that we use overlapping ideas of medium- and long-run timeframes.

In essense, there are four models that we use at an undergraduate level for thinking about aggregate demand and supply.  In increasing order of time-spans involved, they are:  Investment & Savings vs. Liquidity & Money (IS-LM),  Aggregate Supply – Aggregate Demand (AS-AD), Factor accumulation (Solow growth), and Endogenous Growth Theory.

It’s usually taught that following an exogenous shock, the IS-LM model reaches a new equilibrium very quickly (which means that the AD curve shifts very quickly), the goods market in the AS-AD world clears quite quickly and the economy returns to full-employment in “the long-run” once all firms have a chance to update their prices.

But when thinking about the Solow growth model of factor (i.e. capital) accumulation, we often refer to deviations from the steady-state being in the medium-run and that we reach the steady state in the long-run.  This is not the same “long-run” as in the AS-AD model.  The Solow growth model is a classical model, which among other things means that it assumes full employment all the time.  In other words, the medium-run in the world of Solow is longer than the long-run of AS-AD.  The Solow growth model is about shifting the steady-state of the AS-AD model.

Endogenous growth theory then does the same thing to the Solow growth model: endogenous growth is the shifting of the steady-state in a Solow framework.

What we end up with are three different ideas of the “long-run”:  one at business-cycle frequencies, one for catching up to industrialised nations and one for low-frequency stuff in the industrialised countries, or as I like to call them: the short-long-run, the medium-long-run and the long-long-run.

Endogenous Growth Theory

Following on from yesterday, I thought I’d give a one-paragraph summary of how economics tends to think about long-term, or steady-state, growth.  I say long-term because the Solow growth model does a remarkable job of explaining medium-term growth through the accumulation of factor inputs like capital.  Just ask Alwyn Young.

In the long run, economic growth is about innovation.  Think of ideas as intermediate goods. All intermediate goods get combined to produce the final good. Innovation can be the invention of a new intermediate good or the improvement in the quality of an existing one. Profits to the innovator come from a monopoly in producing their intermediate good. The monopoly might be permanent, for a fixed and known period or for a stochastic period of time. Intellectual property laws are assumed to be costless and perfect in their enforcement. The cost of innovation is a function of the number of existing intermediate goods (i.e. the number of existing ideas). Dynamic equilibrium comes when the expected present discounted value of holding the monopoly equals the cost of innovation: if the E[PDV] is higher than the cost of innovation, money flows into innovation and visa versa. Continual steady-state growth ensues.

It’s by no means a perfect story.  Here are four of my currently favourite short-comings:

  • The models have no real clue on how to represent the cost of innovation. It’s commonly believed that the cost of innovation must increase, even in real terms, the more we innovate – a sort of “fishing out” effect – but we lack anything more finessed than that.
  • I’m not aware of anything that tries to model the emergence of ground-breaking discoveries that change the way that the economy works (flight, computers) rather than simply new types of product (iPhone) or improved versions of existing products (iPhone 3G).  In essence, it seems important to me that a model of growth include the concept of infrastructure.
  • I’m also not aware of anything that looks seriously at network effects in either the innovation process (Berkley + Stanford + Silicon Valley = innovation) or in the adoption of new stuff.   The idea of increasing returns to scale and economic geography has been explored extensively by the latest recipient of the Nobel prize for economics (the key paper is here), but I’m not sure that it has been incorporated into formal models of growth.
  • Finally, I again don’t know of anything that looks at how the institutional framework affects the innovation process itself (except by determining the length of the monopoly).  For example, I am unaware of any work emphasising the trade-off between promoting innovation through intellectual property rights and hampering innovation through the tragedy of the anticommons.