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May 19, 2015

The Math of China GDP Growth

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 ratios are very different. A quick check shows 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 this particular ratio. While the US should certainly trade at a higher “multiple” than China, whether it should five times higher, or more, or less, is impossible to prove. 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 supposed ideally to be the aggregate value of all the goods and services produced during the GDP period, including any improvement or deterioration of that country’s capital stock. The OECD defines it, perhaps not very elegantly, 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 a country’s (or region’s) 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, understood its weaknesses, and he fairly consistent warned about the ways in which GDP can be mis-used. The problem with GDP is that there are many things included in the standard GDP calculations – some people propose for example 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 reflect such changes are often not part of the GDP calculation. The most typical examples of the latter are things we call positive or negative externalities. For example while there may well be positive economic value in the activities of a factory that produces chemicals while dumping the effluvium in a nearby river, if we ignore the economic costs associated with polluting the river, which may include lower future returns on farming and fishing,  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 reported 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 consumer service, and an argument can be made that drug dealers do too, at least in a way analogous to bartenders, but their activity is rarely included in GDP figures (although in some countries economists are starting to do so). Babysitting provided by an agency is part of GDP, but if a neighbour or relative baby-sits for free 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, which nonetheless I think has enormous value as a consumer service. My life has been transformed, and this is not an exaggeration, by Google’s search function, and I am certain that its contribution to my welfare, and that of the rest of the world, vastly exceeds whatever contribution it is calculated to add to global GDP. Maybe not everyone is as ecstatic as I am about the fact that from my office, home, or even while sitting in a taxi, I can easily access vast amounts of information, references, and data, and so put together in hours something once would have taken me weeks, but if internet searching 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, if only informally, GDP can give us a rough proxy for total value creation. The second reason is, probably much more important, is that GDP can be very useful in allowing us to make comparisons between economies, or between different 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. The GDP calculation might not capture real value creation with great accuracy, and sometimes this failure to capture real economic value creation can be substantial, but as long as these “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, while also embedding incorrect measures of value creation, probably do so in ways that are fairly consistent with the incorrect measures embedded in the calculation of the US GDP. 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, I can be reasonably confident that the truth is not too far from that number. With other countries, however, I should be much less confident about how usefully the ratio of reported GDPs represents the ratio of the real value of one country’s creation of goods and services to the other’s.
Let me add that while some people might immediately and intuitively understand why it must be the case that comparing reported GDPs with one set of countries provides a more accurate description of the relative size of the US economy than another set of countries, I know of at least one economist, as I will show later, not every economist understand why this must be the case. The problem is not mainly that in calculating GDP different countries classify economic activity in different ways, although this certainly is the case. The real reason is that economies are systems, as Hyman Minsky so richly and usefully explained, consisting of interlocking balance sheets, and economic activity is mediated through the connections between the various balance sheets which themselves reflect very different institutional structures.
One of Albert Hirschman’s great insights, whose implications I think are still not fully appreciated by many economists, is that all economic activity, especially rapid growth, creates imbalances within the system, and these imbalances always eventually reverse themselves. The ways in which they do so, however, can vary greatly and are necessarily constrained by the institutions that characterize each economy. In some cases — obvious examples include economies with a very powerful state sector, or economies heavily dependent on the production of one or a few commodities, or economies dominated by other highly concentrated sectors (the alarming increase in banking concentration in the US, perhaps), or economies in which a very large, underemployed rural population is streaming into urban centers, or economies in which business activity is extremely corrupt or heavily bureaucratized, and so on — these institutions can distort the rebalancing process or hamper it long enough for the country to develop deep imbalances.
These deep imbalances can introduce equally deep systemic biases in the calculation of GDP that undermine the implicit assumption behind all GDP comparisons: although GDP calculations necessarily fail to capture accurately the aggregate value of all the goods and services produced during the GDP period, including improvement or deterioration in capital stock, as long as these “failures” are broadly consistent, and biased in the same direction, comparing GDPs can be a meaningful exercize. But economies with very different institutional structures are likely to have very different sets of biases, and I am not sure why economists who understand easily the concept of the “agency problem” — their different incentive structures lead managers to make decisions that might not be in the best interest of the shareholder — have trouble understanding that different institutions can create different sets of biases in the way economic activity correlates to wealth creation, and this undermines the usefulness of GDP as a tool for comparing economies. The agency problem itself, after is, is an example of one such institution, and can cause significant value distortions especially in an economy dominated by the state sector. Economic agents in countries with artificially high interest rates, to take another example, will treat capital very differently than will economic agents in countries with artificially low interest rates, and so the true economic value of activity involving capital will be reported in very different ways when GDP is calculated.
What can you measure with a broken scale?
Fortunately not all factors that undermine GDP comparisons are quite as intractable. 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 times the Canadian economy or 7.4 times the British economy. There is however 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 seem to 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. This is not true. PPP adjustments are useful in certain contexts, not in most others, but this essay is not the appropriate place to explain why. At any rate in the article I cited above 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 Scissors explains why he dismisses the PPP-adjusted GDP calculation, and while his reasons are correct, I think he misses the main reason to reject the usefulness of China’s PPP adjustment.
To explain why, we will switch gears altogether, and assume that 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 it wouldn’t make the scale useless. It would still serve two useful purposes. 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 actual numbers might not be accurate, but the percent change is.
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 January 1, and publish on my blog. This allows our friends to compare our progress and to make jokes at our expense. The progress, or lack of progress, indicated by the broken scale is real, even if the recorded weight isn’t. If we do it January 1 on any given year, 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.
But what happens if we always weigh ourselves in the morning after getting out of bed, whereas this year my friend was away from hone, and by the time he was able to come to my home to weigh himself it was evening and he had already eaten dinner, when he was likely to be heavier than he would have been in the morning. In that case the comparison between us will have been distorted, in my favor.
There is however a way to fix the problem. I can ask him to weigh himself every morning and evening over several days, and to average the difference, and then I can use this average to adjust the weight he recorded this past January 1. This adjustment won’t be perfect, but we can all agree that it is a useful adjustment because it gives us a  more accurate measure of our weight difference on January 1. This adjustment, of course, is analogous to the PPP adjustment – it isn’t perfect, but it certainly improves the accuracy of the comparison.
But let’s say, for some weird reason, I have a second friend with whom I engage in the same ritual. The problem is that this second friend has his own scale, which is also inaccurate, but it is not inaccurate in the same way mine is. Because we live so far apart, we have never been able to figure out what the difference is, but we just know that the two scales are inaccurate in totally inconsistent ways.
Obviously while this second friend can use his scale to measure how well he is managing his weight, any comparison between his recorded weight and mine is pretty much a useless exercise. We know how he is doing on a year-to-year basis, and we know how I am doing, but if we wanted to find out which year it was that we both weighed exactly the same, we wouldn’t be able to tell.
My second friend, however, isn’t terrible smart. If on January 1, he also weighed himself in the evening, and then went through the same adjustment process as my first friend, it would be absurd if he then published the adjusted number and said that this adjustment made the comparison between us much more accurate. Why? Because the adjustment would be functionally random. If his scale recorded higher weights than mine, and the difference was greater than the adjustment, then he would be right to say that the adjustment improved accuracy, but this would just be a result of chance. If his scale record lower numbers than mine, or if it records numbers that are higher by less than half of the adjustment, his adjustment would actually make the comparison between us less accurate.
Damned PPP again
If everyone understood that the weight comparisons between me and my second friend are inaccurate, and my second friend went through the adjustment process as a joke, and everyone understood that it was a joke, it wouldn’t matter much. If when they heard about the adjustment, however, they took the comparisons seriously because they believed that this adjustment represented a real improvement in describing accurately the differences in our respective weights, I would probably find the whole thing either annoying or even funnier.
So what am I talking about – is there really anything analogous to such an absurd story? Unfortunately there is. It is the comparison between the US GDP and China’s GDP on a PPP-adjusted basis. When the World Bank announced China’s PPP-adjusted GDP, it turned out that the PPP adjustment was much larger than expected, and it implied that on a PPP basis, China would overtake the US economically much earlier than expected. I posted a blog entry explaining what I though was quite obvious, that because China’s GDP was constructed differently than that of the US, direct comparisons between the two were not terribly useful. Worse than useless, however, it was downright foolish to make PPP adjustments and imply that what was in effect a  random change in comparability somehow improved the quality of the comparison.
Some people interpreted this to mean that I was arguing that China was using a different set of rules to compile its GDP, but this is not at all what I meant. My point was only that because these two economies were so different, not least because of the enormous roles the two governments played, especially in the financial system, and most especially in the widespread perception of moral hazard within China, it was inevitable that the many ways in which US GDP was miscalculated would differ significantly from the many ways in which China’s GDP was miscalculated, so that the differences would involve a  very different biases between reported GDP and the “real” value of goods and services produced. In that case any kind of “adjustment” that did not specifically eliminate all the differences in bias, especially a PPP adjustment, would as likely make comparability worse as it would make it better.
I assumed that it was obvious how institutional difference were so great between the two that their inconsistent biases would render GDP numbers incomparable, but just in case, I mentioned the most glaringly obvious such difference, which was the very different ways in which the two countries recorded the impact of loans made to projects that did not generate increases in productivity that were large enough to justify the investment. Because these were far more likely to be written down in the US than in China, and because most economists agree that the difference is very large in GDP terms, the failure to recognize bad loans in China is by itself more than enough to invalidate any PPP adjustment.
But it turned out to be less obvious than I thought. A few months later a friend of mine sent me a Bloomberg article with the title “Bad Math Makes China’s GDP No. 1”, and I discovered that I was the perpetrator of this bad math. I was a little worried at first, because I am enough of a math geek that I think launching into a discussion about the sheer beauty of probability theory during a dinner with friends makes me a charming conversationalist, and usually when I try to do economics, and smart people around me patiently point out my mistakes, math is usually not the part that I get wrong. Logically speaking, it seemed that there were only two ways the author of the article, Noah Smith, might prove me to be mistaken. One way was to prove that GDP calculations are actually always very accurate measures of real value creation, and the second way was to prove that the conditions of moral hazard within which much Chinese lending occurs nonetheless makes Chinese banks as likely as US banks to write down loans they have made into projects whose economic value is less than their cost.
Is an obsession with accuracy unhealthy for the economics establishment?
It turned out that I was being rebuked for a very different way of committing my bad math that I had expected. Smith’s spanking, if I understand it correctly, was because he thought I was trying to get economists to stop accounting for GDP in a consistent way. Actually I wasn’t doing any such thing. All I did in my PPP essay, or at least what I thought I did, was to point out that accounting models are attempts to approximate reality according to a consistent set of rules, and sometimes, even usually, they do so reasonably well, but there are times when they distort the picture of reality enough that we should be recognize that the model is largely useless, and so we should ignore its implications.
Smith seemed to think I was doing something far more subversive. I may be a little confused about his objections, in part because I assume that my explanation for why we should ignore the whole PPP excercise for China are pretty unremarkable. At any rate he writes:
There are plenty of doubts surrounding the Chinese figures, of course. The latest price survey might be just as inaccurate as the earlier ones. Chinese provincial gross domestic product figures are notoriously overstated by job-seeking officials. And the calculation the IMF uses to adjust for price differences, called purchasing power parity, contains a lot of assumptions — using market exchange rates, the U.S. still has the biggest economy.
So when I clicked on a Quartz article entitled “Nope, China’s economy hasn’t yet surpassed America’s,” I expected to see these concerns highlighted. Instead, what I found was that the usually reliable and perspicacious China-watcher Gwynn Guilford had bought into a dodgy theory being promulgated by the renowned Beijing University professor Michael Pettis.
Pettis’s theory, in a nutshell, is that bad investments shouldn’t be counted in GDP… What Pettis is suggesting is that we change the whole way we measure GDP. He wants us to use the discounted present value of assets — in other words, a guess about the far future — as our GDP measure. In other words, he thinks true GDP ought to be a measure of wealth creation rather than a measure of current production.
…We must resist that urge. If economists start trying to subtract perceived malinvestment from GDP, then estimates of GDP will vary wildly from economists to economist, based on how big each one thinks the bubble is. For example, suppose it’s 2007 and I think most of the houses that are being built will eventually be occupied, but you believe that most of them will stand empty and eventually be demolished. If we do what Pettis recommends and subtract our subjective estimates of the percentage of future unused housing from GDP, then you and I will come up with two different GDP numbers!
The friend who emailed me the article is a mathematician who became interested in economics through finance, and he was a little too delighted with the article because he knows how frustrated I get by the way economists regularly combine clunky mathematical intuition with a reverence for mathematically formulated statements that often exceeds their worth. He also knows that in class I am particularly insistent that every model has implicit underlying assumptions, and we should not use the model until we have worked them out and find them consistent with the rest of our assumptions (he had taken my arbitrage class many years ago at the Columbia Business School). Because he  understood that I called the PPP adjustment for China useless not because I wanted to tear down the edifice of economics but rather because an implicit assumption fundamental to the PPP model is that if the adjustment is supposed to improve the quality of the comparison, any biases in the reported GDP numbers must be broadly consistent with the biases in the reported US GDP numbers. Here is what my friend said in the email:
This guy says you’re wrong, not because your sacred implicit assumption remained intact [i.e. the assumption that biases must be broadly consistent for GDP to be comparable], and not even because Chinese banks didn’t make bad loans (that’s what I expected him to say). You are wrong because China followed the accounting rules in calculating GDP, and if you start questioning the rules you’ll make it impossible to do economics.  
He’s right, you know. If you start running around sacrificing precision just because of an unhealthy obsession with accuracy, no one is going to be able to get their work published. Maybe if China wrote down its bad debt, its GDP number would be totally different. Well great, and if they did, you could have a whole different set of GDP numbers to play with, and everyone would be happy. But they didn’t. So deal with it.
Very funny, but actually I don’t think Smith understood that I wasn’t saying anything quite so heretical as he thinks. I wasn’t arguing that because GDP is “wrong”, it is therefore always useless and should be jettisoned altogether. I was only making what should have been an obvious mathematical point, which is that without dismantling the whole structure of economics we can still recognize when certain numbers are useless, and we should understand that the PPP adjustment for China is useless. Smith accepts that are many reasons to question the PPP adjustment, some of which he notes in the first paragraph.
He thinks these are legitimate reasons, and they certainly are, but they are also either minor or debatable. The most important discrepancy in our ability to compare the reported GDPs of China and the US, however, forces us to treat the PPP adjustment as a useless exercise, and it is neither minor nor, I would have thought, debatable. Mathematicians, engineers, and bond traders usually roll their eyes at the obviousness of my explanation, and I suspect that some of the regular readers of my blog will comment with eye-rolling avatars, if they exist(or do I mean icons?), but this is why I put together the little story about inaccurate scales, which is not a story about why we should throw all our scales away but rather a story about how they can sometimes be useful and how sometimes they can’t. It may seem silly, but so are the constant references to the implications of China’s PPP adjustment, so one way or the other we’re stuck with silliness.
National P/E ratios
But I started this essay out by saying I wanted to discuss a number of reasons that might explain why the US economy would be valued at a higher “multiple” than the Chinese, and while the US should indeed have a higher multiple, for reasons I explain below, I am not trying to suggest here that the higher multiple implied by the numbers to which Scissors refers is in fact the right one. There are, of course, two parts to the higher multiple and these correspond to “price” and to “earnings” in the P/E ratio. Of course if the “earnings” part of the P/E multiple is calculated in a different ways, as GDPs for China and the US clearly are, that is obviously part of the explanation, but there are a few other points I thought worth mentioning.
1. The difference in the discount rate obviously matters tremendously. In financial terms, the fact that the US economy is more diversified and less volatile means pretty automatically that its income should be discounted at a lower rate. Every unit of annual American wealth creation should be more valuable than the same unit of annual Chinese wealth creation. One big problem here might be in determining expected volatility. Historical volatility is probably a useful proxy for expected volatility in the US case, but not in China for at least three important reasons.
2. First, many analysts dispute the veracity of Chinese GDP data and also claim that reported GDP tends to smooth out fluctuations. While the former claim hasn’t been proven conclusively to be true over the long term, at least as far I can tell, the latter is almost certainly true. I have seen many studies that try to provide alternative measures of GDP, and while they disagree on whether or not GDP is overstated over the long term, they all agree on the smoothing of data. There also seems to be a consensus, which is consistent with both claims, that growth in the past two quarters has been overstated.
3. Second, a country’s balance sheet structure can systematically exacerbate or dissipate volatility, and I showed in my 2001 book, The Volatility Machine, that developing countries tend to design highly inverted balance sheets for a number of reasons (Hausmann's 'original sin' being among the more obvious). This creates high levels of pro-cyclicality that boost reported growth above the natural growth rate during the expansion phase, but of course the same reflexive mechanisms do the opposite during the adjustment phase.
Economists don't often seem to understand this mechanism unless they are also finance specialists, or historians (or read a lot of Hyman Minsky) and in most previous cases, when growth turned out to be largely based on excess leverage and the reflexive relationship between the two, while they were often at first surprised by the unexpectedly strong growth, they nearly always eventually attributed it to unique but sustainable circumstances. Over time, it seems that economists simply adjusted upwards their estimates of potential growth in order to provide a consistent explanation for the higher growth numbers. It is probably worth noting that in nearly every case, the unique but sustainable circumstance that most economists believed explained the surprisingly high growth turned out to be the implementation of either a new kind of growth model, or, and the two were usually intertwined, a new, superior way of economic thinking that had developed among a highly sophisticated policymaking elite (usually belonging to that most flexible of schools, non-Western economics). It is surprising how consistently this pattern repeats, and, although perhaps less surprising, how quickly the consensus eventually spreads within the policy-making elite (although you can nearly always find grumpy internal resistance to the superiority school).
Investors have usually done a better job of recognizing the reflexive relationship between growth and credit, although in the end the this-time-is-different story ends up enchanting investors anyway, whether the reason for thinking that this time is different is a new economic growth model that creates a growth miracle, or new technology that promises to cause a productivity surge enough to justify any stock market price, or a new kind of financial organization that is expected all but to eliminate financial risk or to control it more rigorously. Most bubbles seem to be set off in one of these three forms, and I think it was Charles Kindelberger who pointed out that the story explaining the bubble is always plausible and nearly always justified during the early stages, sometimes powerfully so, and this makes subsequent skepticism all the harder.
If you believe this model applies to China's case, you might argue that the combination of destruction brought on by the Japanese and civil wars, followed by three decades of experimental policy-making, left the country seriously underinvested both in manufacturing capacity and in infrastructure relative to it institutional ability to absorb investment productively. For that reason Deng&#8217s reforms in the 1980s, and the subsequent early stages of the implementation of the investment-driven growth model (to which I have often referred as the Gershenkronmodel) were probably periods of such spectacular real growth, and of real increases in wealth, that it seemed even easier than in previous cases to reject any explanation which pointed to deteriorating imbalances and unsustainable increases in debt as an important source of continued growth.
4. And third, of course, is that the discount rate must include a premium for gapping risk, by which I mean the risk of an unexpected and sharp drop. If investors believe that a developing country like China is more prone to downward shocks than an advanced country like the US, or if investors believe that China&#8217s autocratic political system is more likely to break down than US democracy, or if investors think a more centralized economic system with a few very large players that excercise disproportionate control, like in China, is more vulnerable to systems breakdown then the more decentralized US economy (and there are many other kinds of gapping that can occur), than even if none of these have happened in the past, investors must raise their discount rates anyway. Investors might interpret the significant capital flight from China, and perhaps more importantly the growing flow of wealthy and educated Chinese households from China to the US, as  indications that well-informed Chinese households assume that gapping risk is much higher in China than in the US, and may be rising.
As an aside I worry that in the last of my three examples, China may not be at as big a relative disadvantage as we think. The increasing concentration of financial power in the US to a limited number of institutions cannot help but increase gapping risk in the US economy. As long as investors believe there is a greater chance of gapping in China, the impact on the discount rate can be very high, but Americans should recognize that when any important sector of the economy is heavily concentrated, especially one of such centrality as the financial sector, which intermediates the relationships between most other sectors of the economy, while there may be efficiency gains (although I suspect that these are vastly overestimated), this concentration necessarily creates much stronger institutional constraints that can prevent the economy from natural tendency automatically to adjust as it eliminates imbalances.
These powerful institutional constraints allow imbalances to deepen while creating the illusion of greater stability, which is made all the more dangerous because the deeper the imbalance, the greater the risk ultimately of a disruptive adjustment – which is a form of gapping risk. One of the greatest long-term strengths of the US economy (and of highly institutionalized democracies in general) has been its ability to adjust quickly, if at times brutally. We tend I think vastly to under-appreciate Albert Hirschman&#8217s insight that the long-term success of an economy depends far more on the institutional flexibility that permits it to manage a successful adjustment, following an earlier period of rapid growth or economic disruption, than it does on how successfully it manages the period of rapid growth, which often is enhanced by institutional rigidities. If Hirschman is right, and I think he is beyond any doubt, the concentration of power within the US financial system may represent a vulnerability far greater than those typically discussed in the press and among academics.
All of this suggests that the rate at which we discount US GDP is likely to be much lower than the Chinese discount rate, but we cannot forget that because China is expected to grow more quickly, this too should be factored into the discount rate, to China&#8217s benefit (i.e. it reduces the Chinese discount rate). Of course both US and Chinese GDP growth rates are uncertain, let alone the expected difference between them, and there is too great a dispute among analysts about expected Chinese growth rates even to begin to address it, but if we are trying to explain valuation differences, this has to be part of the explanation.
5. Finally I would argue that all of the above implicitly assumes that GDP is a good proxy for wealth creation. Of course it isn&#8217t. As I discussed above, there is far too much economic activity included in the GDP calculation, or excluded from it, whose real impact on wealth creation is not the same as its impact on GDP growth, for it to be an accurate measure of wealth creation. But GDP might be a reasonable enough proxy as long as we recognize the implicit assumptions in any GDP model, in which case the real value of GDP to economists is not the reported number itself but rather its usefulness in making comparisons.
For the reasons I discussed above, I don&#8217t think we can place much confidence in the quality of the information we can extract from comparisons between the GDPs of the US and China. I would propose that there are at least two very different biases that might explain part of the higher valuation of US wealth. The first has to do with externalities that are not included in GDP calculations. If the US has higher positive or lower negative externalities, this should show up in the form of a higher wealth valuation. It is easy to come up with lists of externalities in favor of one or the other, but I would argue that among higher positive externalities in the US, there are at least tow important ones. First, the value of education, especially at the elite level, which is structured not so much as a distribution of knowledge but rather as a way to process knowledge under changing circumstances. Second, the US has evolved an institutional framework that encourages a level of business, technological and cultural creativity that, certainly from the outside, seems almost astonishing. This framework seems fairly robust but it is partially vulnerable to the extent that attitudes towards immigration and the chaotic and highly diverse financial sector are important components within the framework. I have more broadly referred to the latter as “social capital”, and have discussed several times what I mean by it, perhaps most extensively in a June 10, 2013 essay.
Some analysts might argue that the latter is already included in the US GDP numbers, but if investors believe that the US is more likely to benefit from the unexpected creation of an important productivity-enhancing technology, this is the equivalent of embedding a kind of option in the total value of US wealth, and these options can be quite valuable. On the flip side I would argue that among higher negative externalities in China it is hard not to think immediately of environmental degradation, which leaves China poorer in a way not measured in GDP. I should also mention China&#8217s huge water problem, which is widely recognized and, by implying significant future costs, their properly discounted value should reduce China&#8217s wealth without showing up in today&#8217s GDP numbers. Of course water is becoming a problem not just for China, and I understand that in California it is starting to become a severe constraint on the agriculture sector, but I think the sheer extent of China’s water problem may be unprecedented.
6. And finally, the second of the obvious and large GDP biases that makes it nearly pointless to compare the two GDP numbers &#8212 in spite of all the excitement generated by these comparisons, especially the most foolish of them all, the PPP-adjusted comparison &#8212 is the treatment of debt. I have already discussed why this is such an important issue to invalidate GDP comparisons at face value, but to summarize, if investors believe that the US financial system is far more likely than that of China to write down loans that have funded projects whose returns do not justify their costs, then they also must believe that real economic losses, which would have reduced the amount of GDP calculated for the US, did not reduce the amount of GDP calculated for China, even though the real economic impact would have been identical. If this is the case, US GDP is relatively understated by the amount of the bad loans that are unrecognized in China but that would have been recognized in the US. Some estimates of this number are extremely high, amounting to 30% of GDP or more.
Multiples and growth differentials
There is a lot more to say, but the much greater disparity in US and Chinese wealth than the disparity in their GDP growth numbers might not be hard to justify. I have ignored reasons that might justify lower discount rates or higher GDP adjustments for China mainly because the purpose of this essay is to explain why the US multiple is so much higher than China’s, and of course these reasons exist, but I think whatever the correct ratio should be, there is no question that advanced economies always justify higher multiples than developing economies because they tend to be economically more diversified and politically more stable, and they usually have institutions, including clearer legal and regulatory frameworks, more sophisticated capital allocation processes, less rigid financial systems, and smaller state sectors (which make smooth adjustment, one of the most valuable and undervalued components of long-term growth, more likely).
At the risk of repetition (a risk from which, according to some regular readers, I do not often shirk) in the case of China and the US, I would summarize very broadly by making two points. First, although it should be clear that neither GDP is correct as a true measure of wealth creation, I think there are good reasons to argue that the difference in real wealth creation might be greater than the difference in GDP – in other words that US wealth creation is higher relative to US GDP than China’s wealth creation is relative to China’s GDP – and it is this adjusted GDP, representing real wealth creation, whose value must be discounted to determine the economic wealth of each country. However, depending on how much faster China's adjusted GDP grows than US adjusted GDP grows, this difference must show up in China's favor in the discount rate.
In fact the growth differential must be among the most important factors in determining the relative “multiples”, and it is nominal growth, not real, that matters. There is, of course, a great deal of skepticism about the 7% real GDP growth rate that China has reported, but we should remember that in the first quarter, nominal GDP growth was much lower, 5.8%. What is more, in the past two days there have been a number of announcements that suggest that Beijing is worried enough about the growth slowdown that it may unleash a new wave of infrastructure-based spending. If this is true, it should cause GDP growth to pick up, and so should widen the growth differential between China and the US, but unfortunately this does not mean that there should be a corresponding drop in the rate at which we discount Chinese growth. The decision about how to adjust the discount rate depends on whether investors believe that additional infrastructure spending will increase the country’s potential growth rate, or instead that it will simply increase economic activity at the expense of higher debt. If we assume that Beijing has been reluctant to do this in the past, and is only doing so in response to weaker expected growth numbers, it would suggest the latter explanation, which implies a higher, not a lower, discount rate, and so a lower multiple for the Chinese economy.
Second, ignoring the factor that represents the growth differential, there is absolutely no way to justify similar discount rates for the two economies. Every dollar in the adjusted US GDP must be more valuable than every dollar in China's adjusted GDP, because US wealth creation almost certainly must be discounted at a lower rate. But how much lower? However you measure it, it seems to me that the appropriate US discount rate should be substantially lower, but the two most important adjustments, one of which I discuss above as consisting of the difference in respective growth rates, are likely to be among the most controversial. The other is the impact of balance sheet inversion on the discount rate.
If investors believe that a very large component of China's GDP growth is explained by the pro-cyclicality of balance sheet distortions, or if they accept the validity of CAPM in valuing higher expected growth based  on higher leverage, then they will have to raise the Chinese discount rate to eliminate altogether the value of this additional growth.
I plan to write about this balance sheet issue a lot more elsewhere, including in an upcoming review of Nick Lardy excellent recent book, Markets over Mao: The Rise of Private Business in China. I believe the review will be published in the July 2014 issue ofAsia Policy, the journal of the The National Bureau of Asian Research, and will feature short review essays by five to six experts, followed by a response from Lardy. The point of my review will be to explain why what seems like a paradox is in fact not a paradox.
I don’t think anyone has an understanding of the fundamental nature of China’s economy, its political economy institutional structure, and the evolution of its economy since the beginning of the reforms, better than Lardy. He is also very careful in his work and not prone to excess. His book explains the evolution of China’s transformation from a state dominated economy to one in which the private sector has become the engine of employment and productivity growth. This explanation leads him inexorably to the conclusion that China will continue to grow rapidly during the rest of President Xi’s administration, which is expected to end in 2023. He forecasts average growth rates as high as 8%.
I have read his book and agree with nearly all of it, or at least I am not smart enough or knowledgeable enough to show why he is wrong. And yet just as inexorably I conclude from his book that the risks are substantial, and that if China is able to grow on average at half that rate, Xi will deserve to be widely acknowledged as having pulled off an extraordinary feat.
Whatever the topic, I always see balance sheets
How can the same set of facts lead to such widely differing forecasts? The reasons, I will argue, have to do with how we evaluate the impact of the two sides of an economic entity’s balance sheet on its growth. Lardy, I will argue, and like the majority of economists, thinks of growth largely as a function of how productively the asset side of the balance sheet is managed, and this is true of all economic entities, ranging from businesses to countries to the global economy. The liability structure is not irrelevant, according to this view, but it matters mainly because too much debt creates the risk of a debt crisis, or can undermine confidence. Otherwise it is functionally irrelevant.
For me, and this view is not unanimous but much more widely held among finance specialists, this “asset side” view of growth is only true under specific conditions. Once debt levels are high enough, or the liability structure is sufficiently distorted in ways that can be specified fairly accurately, debt moves increasingly towards functional centrality. It does so in two important ways. First – and although there have been scattered references throughout the literature about this process, there has been no attempt, as far as I know, to describe it systematically – distorted liability structures, or what I call “inverted balance sheets in my book, The Volatility Machine, can create highly pro-cyclical and self-reinforcing mechanisms, especially through the financial sector, that systematically exacerbate expansion and contraction phases in the economy. These can be so powerful that, especially in developing economies, they can turn rapid growth into growth “miracles”, but they also can cause the subsequent adjustment to become a surprisingly difficult period of stagnation.
The second important way debt can become functionally central to growth emerges from the well-known and much studied process that in finance theory is referred to as financial distress. As regular readers of my blog know, I  think of the trigger not as the rising probability of default, which is the standard corporate finance explanation, but rather rising uncertainty about how debt will be resolved. This of course necessarily includes but is not limited to the rising probability of default. I have redefined it in this way because while financial distress is almost always assumed to be something to which only businesses are vulnerable, in fact the theory is applicable to the full range of economic entities, for which in some cases default is irrelevant.
There is a lot more to say, and I hope to develop these ideas more fully in the next few years, but for now I think the discussion Scissors triggered with his essay can be a useful way to think about the Chinese economy – not so much because we need a way to decide which economy is the world’s largest, but rather because the value we place on current and future growth tells us a lot about the quality of that growth. It also has important policy implications that can be very useful to leaders in Washington and Beijing. Thinking about the reform process, especially in China, can be helpfully refined by understanding the value of different kinds of growth.
But its now 4 a.m., a little late even for me. Please pardon the many typos there are bound to be.
About The Author: Michael Pettis is a Senior Associate at the Carnegie Endowment for International Peace and a finance professor at Peking University. He received an MBA in Finance, and an MIA in Development Economics, both from Columbia University.  Michael is also the author of The Volatility Machine, and The Great Rebalancing. He  writes at china financial markets(EconMatters author archive here)    
The views and opinions expressed herein are the author's own, and do not necessarily reflect those of EconMatters. © EconMatters All Rights Reserved | Facebook | Twitter | Free Email | Kindle
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