Last week Derek Scissors, a think tank analysts at the American Enterprise Institute, published an article in which he referred to an October, 2014, study by Credit Suisse that attempts to measure total household wealth by region and by country. Scissors argues that in the interminable debate about whether or not China will overtake the US as the world’s largest economy, it is widely assumed that there is only one correct way to decide the answer, and that is by comparing the GDP’s of the two countries. Some people argue that nominal GDP at the current exchange rate is the appropriate measure, whereas others prefer the to use PPP-adjusted GDP, but there is no reason, Scissors points out, that either of these in fact are the appropriate comparisons:

There is a debate over which country has the world’s largest economy. One side cites gross domestic product adjusted for purchasing power parity and puts China on top, while various other indicators show the United States ahead. The claims are used to gauge China’s importance, highlight Sino-American competition, and sometimes identify China as a threat.

What is almost never in dispute is that China is rising economically relative to the United States. If China is not ahead yet, it is said, the day is coming when it will be. However, at least one vital indicator casts doubt on that thesis: national wealth. From the beginning of 2008 through the middle of 2014, China may have lost ground to the United States in total wealth.

As Scissors points out, “Credit Suisse put net private American wealth at $42.9 trillion, compared to $4.7 trillion for China: a ratio of more than 9:1”, meaning that the US is 9.1 times wealthier than China. However their GDP rations are very different. A quick check lists that at the end of 2014 China reported GDP of $9.18 trillion, whereas the US reported $16.77 trillion, so that US GDP is 1.8 times China’s GDP.

This might at first seem strange. A country’s GDP is supposed to measure the amount of wealth created during the period measured, and is often thought of as analogous to the earnings generated by a business. I am not sure exactly what the Credit Suisse estimates of total household wealth represent, but if we think of them as being equal, or at least proportional to, the total market value of each economy’s assets and of their ability, combined with the labor of American or Chinese people, to produce goods and services, it seems that every dollar of American income is 5.0 times as valuable as every dollar of Chinese income. To put it in stock market terms, the US P/E multiple is five times the Chinese P/E multiple.

Is that plausible? Yes it is, although I make no claim about the accuracy of the ration. Although I don’t find the debate about whether the Chinese economy will overtake that of the US, and if so, when, especially interesting or even intelligent, I do think the question about the relative economic value of the two countries is interesting because it illuminates quite a lot about both the Chinese economy and about how we should be thinking about economic growth.

But before I explain why a higher US “multiple” can easily be justified, let me turn back to the question of GDP. A country’s gross domestic product, or GDP, is the sum of the value of all the goods and services produced during the GDP period. The OECD defines it, perhaps not as elegnatly, as “an aggregate measure of production equal to the sum of the gross values added of all resident, institutional units engaged in production (plus any taxes, and minus any subsidies, on products not included in the value of their outputs).”

What good is GDP?

GDP, as we all know, is intended to measure economic wealth creation during a particular period. But, as we also all know, it doesn’t do this very accurately. Simon Kuznets, the person who is generally credited with having “invented” GDP, in a 1934 report to the US Congress, knew this and was fairly consistent in warning about its weaknesses. The problem with GDP is that there are many things included in GDP calculations – some people propose that these include military expenditures, or brokerage fees – that don’t reflect any real change in the ability of the economy to produce goods and services, whereas other things that do, are often not part of GDP. The most typical examples are things we call positive or negative externalities. For example while there may well be positive economic value in creating chemicals and dumping the effluvium in a nearby river, if we ignore the economic costs associated with polluting a river, which may include lower future returns on farming and fishing, and higher future health care costs, and less “pleasure” for future hikers, boaters, and nature lovers, then the “real” economic value of producing the chemicals is likely to be lower than its contribution to GDP.

What’s more, for something to be part of GDP it has to be part of the recorded cash economy. Prostitutes certainly provide a highly valued service, and an argument can be made that drug dealers do too, at least in a way analogous to bartenders, but they are rarely included in GDP figures. Babysitting provided by an agency is part of GDP, but if a neighbor or relatives do it, it is not part of GDP. I also want to mention something that is rarely given enough credit as adding to household consumption, certainly to my consumption, but this is the enormous value I get out of Google’s search function, which I am sure vastly exceeds whatever contribution Google adds to GDP. Maybe not everyone is as ecstatic as I am about the fact that I can sit in my office and easily access vast amounts of information, references, and data, but if this were taken away from me it would impoverish me far more than losing a car, or most of my wardrobe.

There is no question that GDP, in other words, does not measure what we usually think it measures, but this doesn’t make GDP a useless number. There are two reasons why it makes sense to invest the time and effort into calculating GDP. First, as long as we constantly remind ourselves of the errors implicit in calculating GDP, and try to correct for them, GDP can give us a rough proxy for total value creation. The second reason is, in my mind, much more important. GDP can be a very useful tool for making comparisons between economies, or between time periods.

In fact this is one of the main uses of GDP, and it can be very accurate, but its usefulness depends crucially on a condition that is very easy to specify, and yet is so poorly understood and so often violated by economists, that it is frankly a little shocking. There can be failures in the ability of the GDP calculation to capture real value creation, but as long as the failures are consistent, and biased in the same direction, the comparisons are still useful and can be extremely precise and accurate. For example the errors in the calculation of US GDP in 2013 are probably consistent with the errors in the calculation of US GDP in 2014, so that the ratio of 2014’s GDP to 2013’s GDP, which we call the GDP growth rate, is probably extremely close to the real growth in the value of the US economy.

Similarly the GDPs of Canada and the UK are probably constructed incorrectly in ways fairly consistent with that of the US. When I say that at the end of 2014 the US economy was 9.1 times the size of the Canadian economy and 7.4 times the size of the British economy, according to their reported GDPs, we can be reasonably confident that the truth is not too far from that number.

What can you measure with a broken scale?

There is one way that GDP between countries can be distorted, and that is because GDP comparisons are made according to current exchange rates, and of course these vary constantly in real terms. It may turn out that once you adjust for cost, the standard of living in the US may actually imply that the US economy is more, or less, than 9.1 tikes the Canadian economy or 7,4 times the British economy. There is a way to correct for this, and that is to adjust the British and Canadian GDP numbers on a purchasing power parity (PPP) basis, so that price difference caused by fluctuations in the real value of the currencies of the three countries are eliminated. This isn’t necessarily easy unless Canadians, English and American households divide their purchases among various goods and service in exactly the same proportions, but it is possible to do a reasonable approximation.

It may now sound like I am belaboring the point unnecessarily with my next metaphor, but there is a reason for this, so please bear with me. I want to make an extremely important point, one which I have made before, and while engineers, mathematicians and bond traders find it annoying that I would even bother making such an obvious again, economists have so much trouble understanding it, and through them journalists, that I am going to try again to explain.

We often hear that the real way to compare two economies is not on the basis of reported GDP but rather on the basis of the PPP-adjusted GDP. I the article I cited above, for example, Derek Scissors notes that in the debate over whether China or the US is the world’s biggest economy, “one side cites gross domestic product adjusted for purchasing power parity and puts China on top.” In another article he explains why he dismisses the PPP-adjusted GDP calculation, and while his reasons are correct, I think he misses the main and most obvious point.

Let’s assume I had a broken scale at home that caused the recorded weight of anyone who used it to be consistently higher than his real weight. This would be annoying, but the scale would still be good for two things. First, and most obviously, if I weigh myself every day, I will get a fairly accurate record of the percentage change in my weight on a daily basis, and although I might not know what I really weigh, if all I care about is how well I am managing my weight, the broken scale is as good as an accurate one. This is the equivalent of comparing a country’s GDP growth from one period to the next.

The second thing I can do is compare my weight with that of my friend, who also uses my inaccurate scale, which perhaps we do every New year’s day and publish on my blog. This allows our friends to compare our progress and make jokes at our expense. This progress, or lack of progress, is real. If we do it one New Year’s day, for example, and he turns out to weigh 10% more than I do on my inaccurate scale, it’s a pretty safe bet that he also weighed 10% more than I did in reality, and our friends can make fun of him for weighing more than me. This, of course, is analogous to comparing US GDP with that of the UK or Canada. The real numbers may be inaccurate, but the comparisons are valid.