The NPF makes sense in a simple context. Suppose you are an entrepreneur with a fruit orchard. You can pay to have fruit trees planted. That is your capital. After a while the fruit trees mature, and you hire workers to pick and sell the fruit. That is your labor. The function Y = f(K,L), which says that output is a function of capital and labor, is a reasonable model that can help to predict your decisions and the share of income that goes to your workers.

Economists from Ricardo to Piketty have wanted to describe the relationship between economic growth and income distribution in terms of simple laws. For the past fifty years or so, the NPF has been the go-to tool for economists trying to do this. Mathematically, it is very elegant for that purpose.

But thinking of the economy in terms of an aggregate NPF has many problems, including the following:

1. Capital aggregation. There is a huge, huge literature on this (see “Cambridge capital controversies”). The result was that the economists who claimed that you cannot construct a meaningful aggregate out of different types of capital equipment won the theoretical battle but lost the practical war. That is, those who use capital aggregation admit that it is bogus, but they go ahead and do it anyway. It’s a matter of “I need the eggs.”

2. Solow residual. The NPF can account for only a small fraction of changes in economic growth over time or differences in productivity across countries. The unexplained differences are known as the Solow residual. Again, there is a huge literature devoted to this issue.

3. Labor heterogeneity. In the NPF, there is one wage rate, which is what is needed to induce you to give up an hour of leisure. In the real world, there are many different salaries paid to different people.

4. Capital proliferation. Over the past fifty years, economists have conceptualized many types of capital. We now have human capital, social capital, organizational capital, institutional capital, environmental capital, network capital, consumer capital, cultural capital, knowledge capital, innovation capital, and so on. Some forms of capital help with understanding labor heterogeneity. Other types help with the Solow residual. But these multiple forms of capital mess with the simple NPF and with the correspondence between theoretical concepts and real world data.

5. Knightian uncertainty. Unlike our theoretical orchard-owner, real-world entrepreneurs must cope with the fact that the return on a particular investment is unknown ex ante. The distribution of income among capitalists is affected by differences in ex post returns. Moreover, since so much of “labor” income is an accrual to human capital, all of us are capitalists, and hence most “labor” income is subject to differences in ex post returns.

So, should we use the NPF to guide economic policy to try to achieve the best balance among growth and the distribution of income? Some possibilities:

(1) The criticisms of the aggregate NPF are not important, so that policy conclusions are still sound.

(2) Some of the criticisms are devastating, but we need some tool to guide policy, and until something better comes along our best choice is the aggregate NPF.

(3) Some criticisms are devastating, and as a result we should be very cautious and humble about making policy pronouncements based on our understanding of the NPF.

To me, (3) makes the most sense. But that is not a popular position at the moment.