Picking on Picketty (8) Explanatory Theories

The weakness of Piketty’s analysis is the lack of explanatory theory. The problem with r>g is that it has more descriptive power than explanatory value. He is very effective at describing how things are. However, he is much less effective in explaining why they are as they are. He makes suggestions, but is unable to give the causal links that show why thing are as they are.

His first law of economics is an accounting that does not explain much.

α = r × β

Where

α= share of national income that comes from capital income.
r= rate of return on capital
β=capital/income ratio

If either or both of the rate of return on capital or the capital/income ratio increase, the share of national income going to capital will increase.

The second law of economics is different. Piketty says it only applies in the long-run, under certain assumptions. There will be debate about where and when it applies.

β=s/g

Where

s=savings rate
g=growth rate of the economy

In the long run, the capital/income ratio adjusts to the structural growth of the economy and the savings rate, ie how much is saved out of the increased income.

According to neoclassical economics, an increase in savings does not necessarily lead to an increase production. Growth in production is constrained by population growth and technical innovation. Piketty suggests that this is limited to about 2 percent a year. If savings increases faster, the capital/labour ratio adjusts accordingly.

This formulation allows Piketty to estimate the long run equilibrium capital/income ratio for a given savings rate. This insight is hidden away in the middle of the book, so it has been missed by many who skimmed the book, but it is his most important theoretical contribution.

The law β=s/g apples in all cases, regardless of the exact reasons for a country’s saving rate. This is due to the fact that β=s/g is the only stable capital/income ratio in a country that saves a fraction s of its income, which grows at a rate g.

The argument is elementary. Let me illustrate it with an example. In concrete terms: if a country is saving 12 percent of its income every year., and if its initial capital stock is equal to six years of income, then the capital stock will grow at 2 percent a year, thus at exactly the same rate as national income, so that the capital/income ratio will remain stable.

By contrast, if the capital stock is less than six years of income, then a saving rate of 12 percent will cause the capital stock to grow at a rate greater than 2 percent a year and therefore faster than income, so that the capital/income ratio will increase until it attains its equilibrium level.

Conversely, if the capital stock is greater than six years of annual income, then a saving rate of 12 percent implies that capital is growing at less than 2 percent a year, so that the capital/income ratio cannot be maintained at that level and will therefore decease until it reaches equilibrium.

In each case the capital/income ratio tends over the long run towards its equilibrium level β=s/g... it allows us to understand the potential equilibrium level toward which the capital/income ratio tends in the long run, when the effects of shocks and crises have dissipated (170).

There is a long run equilibrium ratio between wealth and income which remains stable once established. This equilibrium is the basis for Piketty’s claim that the capital/income ratio will increase to about 600 percent in most Western country’s as the growth rate declines to 2 percent or less (assuming the savings rate continues to be about 12 percent.

The equation β=s/g is indeterminate. There are almost limitless values that can satisfy the equation. Piketty constrains them by assuming that the saving rate is determined independently, and remains about 12 percent of national income.

However, changes into the savings rate can make a significant in a slow growth economy (2 percent). If the savings rate rose to 16 percent, the capital/income ratio would be 8. If the saving rate dropped to 8 percent, the capital income ratio would be 4, less than what it is in many Western countries now. This suggest that the savings rate is quite an important variable.

On the other hand, if the saving rate increases dramatically, and the extract capital is channelled into productive activities, the growth rate can increase without a change in the capital/income ratio, ie g=6, s=24 and β=4. This is more like the Chinese situation.