Tom Michl has some comments — insightful as always — on the previous post on functional finance. The key point he raises is that we can’t treat the long-run growth rate as given exogenously. Policy that targets current output will also have effects on the long run trajectory that have to be taken into account. He writes:

I’ve become convinced that the real interest rate belongs in the investment equation, g(r), which means that g-r is not something we can just set greater than zero to solve the problem of fiscal deficits. Also that fiscal policy, e.g. the debt ratio, affects the long run position of the IS curve (assuming interest payments go to rentiers who spend them on consumption), so it affects the r that stabilizes inflation.

The question of exo/endogenous growth is important because a given growth target puts constraints on the feasible fiscal policy, or given fiscal policy, on the ability of a monetary authority to set the inflation-neutral interest rate.

*g*as given. And I agree that there should be some systematic relationship between the liquidity conditions that we summarize as the interest rate and demand conditions, and the long term growth of income. But it doesn’t seem so straightforward to show that this relationship will be a constraint on the fiscal position.

*g*=

*s*/

*c*–

*dk*, where

*g*is the growth rate,

*s*is the average savings rate,

*c*is the incremental capital-output ratio,

*d*is the depreciation rate and

*k*is the average capital-output ratio. This is just accounting. As we know, this accounting relationship is often used to develop the idea of knife-edge instability. But that’s never seemed right to me (and I don’t think it’s what Harrod intended with it.)

*s*is the average savings rate, so in a Keynesian framework it will be a negative function of output. So what this equation is telling us is that if we need to achieve a given growth rate, and the capital-output ratio is fixed, then the output gap will have to adjust so as to get

*s*to satisfy this equation. This is the adjustment that policy is allowing us to avoid. Fiscal policy raises or lowers average

*s*at a given level of income. Monetary policy perhaps raises or lowers

*s*also; more conventionally it is supposed to change the desired capital-output ratio

*c*.

*if*we think that interest rates act through the capital-output ratio, then we need that as an additional degree of freedom if we want to combine full employment, our chosen growth rate, and a stable debt-income ratio. As it happens, Peter Skott and Soon Ryoo presented a paper at the Easterns where the requirement to achieve a target capital-output ratio meant that monetary policy was not available to close the output gap, requiring the use of fiscal policy. The additional degree of freedom is supplied by allowing the debt-GDP ratio to evolve freely. This isn’t a problem in this case. In their model, fiscal policy works through its additions to the stock of assets available to private wealth-owners, not through the flow of demand for currently produced goods and services. So the public-debt GDP ratio will automatically converge to whatever level satisfies the private sector’s demand for net wealth above the capital stock.

*at a given growth rate*. So the model works the same regardless of what you think the growth rate is or should be. If monetary policy works through the capital-output ratio, then we can no longer say that, but in that case the capital-output ratio itself provides an additional degree of freedom. Only if we impose both a given growth rate

*and*a given capital-output ratio do we possibly foreclose the option of setting

*r*at whatever value is consistent with price stability and a constant debt ratio. And even then, I emphasize “possibly,” because it depends on what you think happens to maintain the constraint. It seems to me the most natural answer is that at some point the desired capital-output ratio becomes insensitive to the interest rate, so, assuming that savings are also insensitive, then full employment cannot be reached at our target growth rate through monetary policy alone. In that case, fiscal policy becomes mandatory. This is where Keynes ended up, more or less, and also the implication of Peter’s paper. But this doesn’t give any argument for why interest rates cannot stay arbitrarily low, it just says that even very low interest rates won’t be sufficiently expansionary to get us to full employment at low growth rates and that fiscal policy or some equivalent will be required as well. Which, as they say, is where we came in.