There’s a new paper out of China, claiming that more than a third of investment spending since 2008 was wasted. It’s a claim that resonates, given what we know about corruption, ghost cities, and all that. But as SR of The Economist points out, the paper itself doesn’t actually do what it claims. It doesn’t at all show that there has been a lot of waste — in fact, the data it cites are perfectly consistent with no waste at all.

Why do we care? Well, for one thing economics should be done right regardless. But the waste claims will also, of course, be used as a club to beat Keynesian fiscal policy. So you should know that anyone citing this estimate is actually revealing that he either doesn’t understand growth economics or doesn’t care.

What the paper does is look at the ratio of capital added to economic growth — the so-called incremental capital output ratio. It finds that the ICOR has been lower in recent years than it was in the past, and attributes all of the shortfall to waste.

But what if there were no waste at all? What if China were simply engaged in capital deepening? What would we expect to see in that case? The answer is, exactly what we do see. The ICOR data say nothing at all about waste.

Think about a standard production function (Figure 1), and imagine that the Chinese economy is moving up and to the right on that curve, from A to B to C, as it accumulates capital.

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In that case the economy does face diminishing returns, but that’s what is supposed to happen.

What the “$6.8 trillion in waste” paper does, however, is in effect to insist that the accumulation of capital in moving from B to C should yield the same increase in output per unit of capital as the accumulation from A to B. Graphically (Figure 2), it’s drawing a line from A to B and extrapolating it, then claiming that any shortfall from that extrapolation represents waste:

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Once you think about it that way, you see that it’s obviously silly. Diminishing returns are not the same as waste.

Now, I’m not claiming that there’s no waste in China; I’m sure there’s plenty. And at that point we need to get into the question of what would have happened to those resources otherwise; if they would have been unemployed, wasteful spending is better than no spending. But that’s all a different discussion, to which the $6.8 trillion estimate makes no contribution.