CHINA’S official statisticians attract plenty of criticism from baffled outsiders. In recent months, however, they have also endured attacks from party colleagues. On August 26th China’s corruption watchdog, the Central Commission for Discipline Inspection, charged Wang Baoan, head of the National Bureau of Statistics (NBS) from April 2015 to January 2016, with a variety of sins, including moral decay and “superstitious activities”. Earlier this year, the commission also paid a visit to Liaoning province in China’s industrial north-east, where it urged local officials to stamp out widespread data fraud.

These exhortations may be having some effect. The recent collapse in Liaoning’s economic indicators (fixed-asset investment fell by 58% in the first half of the year, compared with a year earlier) may partly reflect efforts to wring the “water” out of fraud-soaked figures, according to Liu Liu and Hong Liang of China International Capital Corp, an investment bank.

Many flaws in China’s data are well documented. Provincial GDP figures do not add up to the national total. Quarterly and annual growth do not always mesh. Of the three ways to measure GDP (by counting output, expenditure and income), production figures are reported miraculously quickly, even as the counterpart numbers for spending and earnings appear agonisingly slowly.

Recent numbers have raised fresh questions. Fixed-asset investment by private enterprises fell by 1.2% in July, compared with a year earlier. Meanwhile the equivalent figure for state-owned enterprises surged. Services have been strong, even as industry has struggled. Growth has not dipped below 6.7%, even as prices slipped into deflation in late 2015.

These doubts and discrepancies have motivated an understandable search for alternatives. As far back as 2000, scholars turned to indicators like electricity consumption as a statistical refuge from what one called the “wind of falsification and embellishment” rustling the official data. But electricity is a less reliable guide as an economy evolves away from power-hungry industry towards low-wattage services. In a post-industrial economy like America, for example, GDP can grow even as electricity consumption shrinks (as it did in 2015).

Ker-ching momento
Liaoning itself inspired a somewhat broader alternative. When he was the province’s party chief, Li Keqiang, now China’s premier, said he relied on rail freight, electricity and bank lending to keep track of the local economy, preferring them to the GDP figures, which, he noted, were “man-made”.

His comments inspired this newspaper in 2010 to combine all three indicators into a simple gauge of the national economy, the “Li Keqiang index”.

The most sophisticated version of this index was created in mid-2013 by John Fernald, Israel Malkin and Mark Spiegel of the Federal Reserve Bank of San Francisco. They fitted their version of the index to the official GDP figures from late 2000 to late 2009, then examined whether the fit remained snug in subsequent quarters. Surprisingly, it did. An index born out of frustration with the official numbers seemed to enjoy a stable, consistent relationship with them—up to the end of 2012 at least.

This snug relationship has since broken down, however, according to our update of their work.

Whereas the NBS reported growth slowing gradually to 6.7% in recent quarters, the Li Keqiang index shows it dropping below 5% (see chart). This gap may reveal flaws in the official data. But it may equally reflect shortcomings in the index, which would not have picked up the boom in financial services that boosted China’s GDP over this period.

In relying on just three alternative indicators, Mr Li was relatively parsimonious. Other critics have been less picky. Some have passed a dragnet through China’s databases, which are teeming with raw statistics on the physical output of individual products: tonnes of steel, metres of silk, litres of beer, even kilowatts of solar cells.

In a recent blog post for the Financial Times, Chris Balding of Peking University’s HSBC Business School in Shenzhen collected data on 69 “major industrial products” listed by Wind, a data provider.

A simple average of these products shows industrial growth (year on year) of about 0% in the second quarter, compared with the official figure of about 6%. Goldman Sachs has gone even further, combining 89 products. Their measure shows industrial output actually shrinking in mid-2015, followed by a modest recovery since.

The appeal of these output data is that they are less “man-made” than the headline figures. It is more straightforward to count tonnes of cement, square metres of glass or kilowatt-hours of electricity than it is to calculate the value added by a business. But without some measure of monetary value, it is impossible to know how much weight to give one product compared with another. “Tractors”, for example, appear four times in various guises in Wind’s data list. That gives them an outsized 5.8% weight in Mr Balding’s simple average of 69 products. (Goldman Sachs instead weights its products by revenues.)

Counting tonnage is also, in some ways, a step backwards. China was once obsessed with measuring the sheer quantity of industrial goods, so as to fulfil the requirements of ambitious central plans. Back then, it was foreign critics who pointed out the shortcomings of such measures, which cannot capture quality, variety and efficiency. Growth often stems from reducing inputs or introducing novelty, not expanding volumes. For example, the NBS recently added smartphones, industrial robots and new-energy vehicles to its list of major industrial projects.

Other alternatives to official data are futuristic, rather than anachronistic. Some data-sceptics have turned to space, using satellite images of China’s city lights to estimate its GDP. Others, such as the boffins at the Big Data Lab of Baidu, China’s biggest online-search company, are relying on smartphones. Through the mobile devices in people’s pockets, they can track online searches for—and physical visits to—shops, cinemas, industrial parks and other places of consumption and employment.

They say their work can successfully predict fluctuations in Apple’s Greater China revenues and expose possible data fraud. Some cinemas, for example, reported much higher box-office takings than you would expect given the number of people who searched Baidu’s maps for the cinemas’ location.

These high-tech alternatives are still in their infancy and may never provide more than a timely cross-check of official statistics. Fortunately, technology can also improve those official numbers. The NBS, for example, now receives direct data reports from almost 1m firms through an online system, initiated about four years ago. It has also expanded its central survey teams, making it less reliant on local help.

As a result of these and other reforms, the official figures may be improving. In a second paper Messrs Fernald and Spiegel, together with Eric Hsu of the University of California, Berkeley, pit GDP against ten of its rivals. They test its ability to explain fluctuations in exports to China, as reported by America, the European Union and Japan, a gauge of China’s economic fortunes that neatly sidesteps the country’s statistical system. They find that China’s GDP does a much better job after 2008 than it did before. Indeed, the official figure tallied better with their trade-based benchmark tan any other single indicator, except rail freight. (Some combinations of indicators did, however, outperform GDP, especially a combination of rail, electricity, retail sales and a measure of the availability of raw-material supplies.)

Investors may disdain China’s official data but they cannot disregard them. The figures can still move markets, which is why unscrupulous traders sometimes try to get hold of them in advance. Leaks used to be commonplace. But investigations and arrests over the past few years seem to have made the bureau more watertight. Mr Wang may now be in disgrace. But his alleged superstitions probably date back to his long career at the finance ministry, rather than his short stint at the statistics bureau. Beijing presumably thinks the bureau’s reputation can withstand the bad publicity, or it would not have charged him so publicly. The accusations may be a paradoxical sign of confidence in the NBS. Some indicators move contrarily.