Low Saving Rates, Not The Debt, Are Burdening Future Generations

Don’t worry, this isn’t another post on the intergenerational non-burden of government debt. I’ve been down that road before with limited success – as Krugman would say, no matter how many times you kill zombie ideas, they keep hanging around because of politics.

Rather, I want to comment on a real intergenerational burden that is rarely discussed, but which is actually more important; namely, the burden that low saving rates can place on future generations.

A simple Solow-Swan growth model, in which technology is exogenous, predicts that countries with high saving rates will reach higher levels of GDP per capita in steady state than will countries with low saving rates. The following picture shows this dynamic for two countries with different saving rates.

The y-axis measures GDP per capita, whereas the x-axis measures time. The top line shows the steady-state growth path for a country with a high saving rate, whereas the bottom line shows the steady-state growth path for a country with a low saving rate.

As the chart shows, saving rates have no influence on the rate of GDP per capita growth in steady state; both lines have the same slope. But the intercepts are quite different, implying that saving rates have an effect on the level of a country’s GDP per capita in steady state. (Everything else equal, higher saving rates lead to higher levels of GDP per capita.) The intuition is that countries with higher saving rates will be foregoing current consumption to build up the capital stock, which will be beneficial in the long run.

Things get a little more interesting if we endogenize technology. Suppose that a Cobb-Douglas-like production function determines GDP per capita for a country with a constant population:

y = (k)^a(A)^(1-a), s.t. 0 < a < 1

where y is GDP per capita, k is the per capita capital stock, and A is the level of technical progress.

Suppose also that k and A are governed by the following simple laws of motion:

dk/dt = sy, s.t. 0 < s < 1

dA/dt = ey, s.t. e > 0

where s is the saving rate and where e is the coefficient of technical progress. The relationship between A and y is usually referred to as the “learning by doing” relationship, which basically states that a higher level of GDP per capita is associated with a faster rate of growth for technical progress. Notice that physical capital does not depreciate in this model.

Now, for simplicity, let’s define the growth rates for k and A in percentage-point terms as:

G(k) = (dk/dt)/k

G(A) = (dA/dt)/A

It can then be shown with some algebra that:

G(k) = s(k/A)^(a-1)

And that:

G(A) = e(k/A)^a

Now, a reasonable assumption in steady state is that capital and technical progress will be growing at the same rate. Hence, G(k) = G(A).

If we solve for per capita, technology-augmented capital in steady state, we then find that:

(k/A) = s/e

which implies that:

G(A) = e(s/e)^a = e^(1-a)s^a

But now we’re done, because we’ve shown that the growth rate of technology in steady state is a function of the saving rate. (A higher saving rate leads to faster growth in steady state, everything else equal.) And, in the long run, technical progress is what determines living standards.

The point is that in a simple model in which technology is endogenous, saving rates affect both the level and the growth rate of GDP per capita in steady state. Many more complicated models arrive at a similar conclusion.

This aspect of neoclassical growth is important. The U.S. economy has been running very low saving rates since the late-1990s, arguably lowering the living standards of future generations. This intergenerational burden is likely to be much more harmful than that imposed by government debt.

To increase saving rates, the U.S. will need to close its trade deficit. (The laws of accounting imply that a large trade deficit will lead to negative domestic saving.) And to close the trade deficit, the dollar will need to fall. There is really no way to get around this story.

Since we are already destined to hand future generations a crappy ecosystem, the least we can do is aim to hand them higher living standards (measured in terms of GDP per capita). Hopefully policymakers will listen and, in turn, will make a concerted to drive down the value of the dollar in the coming years.

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