HAS CHINA really blown $6.8 trillion on worthless investments over the past five years? This is the startling claim made by two Chinese government researchers that has, understandably, caused quitea stir. If true, it would mean that fully 37% of Chinese investment since 2009 was wasted on building bridges to nowhere and homes with no one in them. There is, without question, plenty of worrying evidence that Chinese investment has become less efficient in recent years. But a closer look at how the researchers produced the $6.8 trillion figure badly damages their claim. Calling it a back-of-the-envelope estimate would be undeserved praise.

The $6.8 trillion calculation was made by Xu Ce of the National Development and Reform Commission, an economic planning agency, and Wang Yuan of the Academy of Macroeconomic Research, a think-tank under the commission. Their analysis was published last week as an opinion piece in the Shanghai Securities Journal, a government-run newspaper. In their article, they estimate that worthless investment totalled 7.9 trillion yuan in 2009; 5.4 trillion yuan in 2010; 4.7 trillion yuan in 2011; 10.6 trillion yuan in 2012; and 13.2 trillion yuan last year. That amounts to 41.8 trillion yuan over the past five years, or $6.8 trillion at the current exchange rate.

These are remarkably precise figures for wasted investment, something that, by its nature, is extremely hard to pin down. There are practical difficulties – for example, we know that some government investment funds have been skimmed off by corrupt officials, but it takes careful forensics to track the ill-gotten gains of one rotten official, let alone thousands of them. Even greater are the theoretical challenges. China has clearly built too many homes, too quickly, but if some of those that stand empty today are eventually bought then what once seemed a wasted investment could yet turn into a productive one.

So how exactly do Mr Xu and Ms Wang arrive at their numbers? Their method is to compare China’s capital efficiency in the 1980s and 1990s with the past decade; they treat any decline in efficiency as evidence of wasted investment. Although they don’t publish their calculations in full, their conclusions have the virtue of being very easy to replicate from official data. (Be warned that this is slightly wonky.)

Mr Xu and Ms Wang base their analysis entirely on the concept of incremental capital output ratio, or ICOR. ICOR is a measure of how much investment it takes to produce each additional unit of growth in an economy, with investment the numerator and additional GDP the denominator. The higher a country’s ICOR, the less efficient it is – that is, it takes more investment to produce a smaller amount of economic output. Mr Xu and Ms Wang begin by calculating that China’s average ICOR from 1979 to 1996 was 2.6. To do so they tot up each year’s ICOR and calculate a simple average. Here is a table of all of China's ICORs from 1979 to 1996, yielding the same average that they calculate:

Investment Added GDP ICOR bn yuan bn yuan 1996 2878 1095 2.63 1995 2547 1300 1.96 1994 2034 1328 1.53 1993 1572 937 1.68 1992 1009 499 2.02 1991 787 323 2.44 1990 675 204 3.31 1989 633 192 3.29 1988 570 311 1.83 1987 446 177 2.52 1986 394 143 2.75 1985 346 171 2.02 1984 252 115 2.19 1983 204 63 3.26 1982 178 58 3.07 1981 163 42 3.92 1980 160 50 3.20 1979 148 49 3.04 1979-1996 average 2.59 (Sources: National Bureau of Statistics; The Economist)

For the next step, they calculate the ICORs from 1997 to 2013. Here is the table for that. As in Mr Xu and Ms Wang’s article, the average ICOR is 4.

Investment Added GDP ICOR bn yuan bn yuan 2013 28036 5727 4.90 2012 25277 5678 4.45 2011 22834 6980 3.27 2010 19360 5404 3.58 2009 16446 3280 5.01 2008 13833 4938 2.80 2007 11094 4389 2.53 2006 9295 3529 2.63 2005 7786 2647 2.94 2004 6917 2434 2.84 2003 5596 1614 3.47 2002 4557 1145 3.98 2001 3977 1028 3.87 2000 3484 762 4.57 1999 3295 459 7.17 1998 3131 487 6.43 1997 2997 749 4.00 1997-2013 average 4.03 (Sources: National Bureau of Statistics; The Economist)

These numbers are fine for what they are – estimates of the efficiency of Chinese investment – but it is at this point that the two researchers make several unreasonable leaps of logic. First, they use the 1979-96 ICOR average of 2.6 as their baseline estimate of what China’s ICOR ought to be were its investments all efficient. Next, they calculate the difference in China’s investment efficiency from 2009-13. For example, in 2009, the ICOR was 5, which is 48% less efficient than the baseline ICOR of 2.6. Therefore, they conclude, 48% of all Chinese investment in 2009 – 7.9 trillion yuan – was worthless. Similar calculations for each year up until 2013 yields the eye-popping result that 41.8 trillion yuan has been wasted.

There are two major, indeed fatal, flaws in this. First, why have they chosen 1979-96 as their baseline for ICOR efficiency in China? A quick glance at the tables above reveals that there was a big jump in ICOR (that is, a big decline in efficiency) from 1997-2000, followed by an improvement. The 1979-96 selection leads to a sharp downward bias in their baseline estimate. If we break the ICOR into decades, and break out the past five years separately, the results are very different, as this table shows.

ICOR 1980-89 2.8 1990-99 3.3 2000-08* 3.3 2009-13 4.2 (Sources: National Bureau of Statistics; The Economist) * stopping pre-stimulus

Using Mr Xu and Ms Wang’s method for calculating efficiency differences, we now can compare the ICOR of 4.2 over the past five years with 3.3, the average for both of the previous two decades. This is a much more relevant yardstick than the pre-1997 era. On this revised basis, China’s investments after the global financial were 21% less efficient than in the 1990-2008 period. Sticking to Mr Xu and Ms Wang’s approach, this would mean that 21% of all investment over the past five years – 22.6 trillion yuan ($3.7 trillion) – had been wasted. That is still a lot of money to burn through, but it is almost half their headline-grabbing estimate.

That leads to the second and even bigger flaw – namely, this is a lousy method for calculating wasted investment. ICOR serves as a rough guide to the efficiency of investment. It does not, however, show how much money was been wasted, only that it is generating smaller or bigger growth returns compared with previous years. For example, say that an investment of $1000 boosts GDP by $500 this year, but only by $400 next year. In this case, ICOR will have risen from 2 to 2.5. Using Mr Xu and Ms Wang’s framework, because investment is 20% less efficient in the second year than it was in the first year (ICOR of 2.5 vs 2), this is tantamount to 20% of investment, or $200, being worthless. But that is completely absurd. All we can conclude is that the return on investment has fallen, not that $200 has been wasted. Moreover, it is inevitable that in years when investment soars – which was, after all, the point of China’s stimulus package – investment returns will appear to suffer. The real question is whether those investments deliver returns over time, hence the point in looking at average ICORs over a longer period.

None of this is to give the Chinese economy a clean bill of health. As we have written, debt has increased too quickly, and declines in both productivity and investment efficiency are worrisome. But $6.8 trillion down the drain in just five years? This at least is one thing that will not keep us up at night.