CHINA'S top-to-bottom audit of its local-government debt was keenly awaited. But it seems it wasn’t very closely read.

Most commentary on the National Audit Office's report concluded that China's local red ink amounted to 17.9 trillion yuan in mid-2013 (equivalent to $2.9 trillion or about a third of China's GDP). That was 67% higher than the 10.7 trillion counted at the end of 2010, a dramatic and disturbing "surge".*

But if you take the NAO's own methods seriously, you can reach a different interpretation: China's local-government liabilities rose from 18.4% of GDP in 2010 to about 22% in mid-2013.** That is still a big increase. But it's more of a swell than a surge.

What accounts for the difference in these two interpretations? How do you turn a debt surge into a swell? For one thing, you can compare China's growing debts to its growing economy. China's nominal GDP was 33.9% bigger in the year to mid-2013 than it was in 2010. Less obviously, you can also read the NAO's footnotes.

The 17.9 trillion figure lumps together three different types of liability. It includes 10.9 trillion yuan that local governments themselves owe to their creditors. To that figure, it adds 2.7 trillion yuan of debt guarantees: money, owed by other entities, that local governments have explicitly promised to repay if the original borrower can't. Third, it includes a further 4.3 trillion that local governments have implicitly guaranteed. This is money owed by other entities that local governments would probably feel compelled to repay, if push came to shove, even though they have not explicitly promised to do so.

The 2.7 trillion and 4.3 trillion represent "contingent" liabilities. They are obligations that will fall into the government’s lap only if something bad happens. If the original borrowers fail to repay, the government will be on the hook. But how big is that if? The weight of a contingent liability depends on the odds that the contingency will in fact arise.

Most commentators implicitly assumed the odds were 100%. They added these liabilities together to reach the 17.9 trillion total. But that figure does not appear anywhere in the NAO's report. In fact, in its first footnote, the NAO cautions against simply adding these different liabilities together.***

How then should these contingencies be booked, according to the NAO? Later in the report, it claims that the government has, in the past, had to repay no more than 19.13% of its explicitly guaranteed debt and 14.64% of its implicitly guaranteed debt. Using those two percentages, it can calculate the expected size of China's contingent liabilities. Putting it all together, it concludes that China's local and central liabilities, contingent and otherwise, amounted to 39.43% of GDP in 2012.

The NAO itself stops there. But you can apply the same method to China's local government liabilities alone. If you do so, they amounted to 22% of GDP in mid-2013 and 18% in 2010.*** (To repeat, these figures include local governments' own debts and also their "expected" exposure to the debts of other, allied entities.)

You can certainly quibble with the NAO's approach. Perhaps the 19.13% and 14.64% pay-out ratios are too low. Perhaps its definition of government is too narrow, and the other, allied entities whose obligations the government has guaranteed are, in practice, clearly part of the government themselves. Fiscal authorities around the world vary a lot in how they account for contingent liabilities. But it seems odd to wait this long for the NAO's report and then simply ignore its own interpretation of its findings.

Footnotes to the auditors' footnotes:

* The figures for mid-2013 include the debts of over 30,000 “townships” (the lowest level of China’s government, each responsible for about 10,000 people or so). The old audit did not. Comparing the two totals will then exaggerate the strength of the surge. But, as it turns out, township debts do not make much difference. Without them, the 17.9 trillion falls to 17.5 trillion, which still implies that local-government debts grew by 63.5% in two-and-a-half years.

** To derive a GDP figure for the year to mid-2013, I added together China's quarterly GDP from 2012Q3 to 2013Q2 inclusive. It comes to about 53.94 trillion yuan.

*** In its audit for 2010, the NAO did simply add these three types of liabilities together, thereby providing the 10.7 trillion yuan total that everyone then reported and cited. It's interesting that it avoided doing so this time around.