The Arthurian — Growth Modeling: The Asymptotic Decline of Output

Let's take this model that captures the pure impact that "savings = investment" has on the long run standard of living, let's take it and tweak it a tad. Let's NOT suppose there are no financial markets…. 

The assumption that financial markets exist has two effects on the Solow Growth Model: It makes growth slower and costs higher. The rate of growth is reduced, because productive investment is reduced. And productive sector costs increase, because income accrues to savings.
Growth is slower and costs are higher, because financial markets exist. Sounds like a stagflation problem, don't you think?. Lucky for us, this is only a model.

The New Arthurian Economics
Growth Modeling: The Asymptotic Decline of Output
The Arthurian

Alex Tabarrok — Piketty v. Solow

Alex Tabarrok agrees with Krusell and Smith

I’ve already suggested one reason why Piketty’s saving assumption seems too strong–Piketty’s assumption amounts to a very strong belief that we will always replace depreciating capital first. Another way to see this is to ask where does the extra capital come from in the Piketty model compared to Solow? Well the flip side is that Solow predicts more consumption than Piketty does. In fact, as g falls in the Piketty model so does the consumption to output ratio. In short, to get Piketty’s behavior in the Solow model we would need the Solow savings rate to increase as growth falls.

Krusell and Smith take this analysis a few steps further by showing that Piketty’s assumptions about s are not consistent with standard maximizing behavior (i.e. in a model in which s is allowed to vary to maximize utility) nor do they appear consistent with US data over the last 50 years. Neither test is definitive but both indicate that to accept the Piketty model you have to abandon Solow and place some pretty big bets on a non-standard assumption about savings behavior.

Marginal Revolution
Piketty v. Solow
Alex Tabarrok | Bartley J. Madden Chair in Economics at the Mercatus Center and am an associate professor of economics at George Mason University