Do we understand the math behind the PPP calculations?
Do we understand the math behind the PPP calculations?
A new PPP study complied by the World Bank has generated some pretty excited and, to some, alarming headlines about the new world order. There has been limited reference to this in the Chinese press, for reasons I will discuss later, but here is the Financial Times on the subject:
The US is on the brink of losing its status as the world’s largest economy, and is likely to slip behind China this year, sooner than widely anticipated, according to the world’s leading statistical agencies. The US has been the global leader since overtaking the UK in 1872. Most economists previously thought China would pull ahead in 2019.
…In 2005, the ICP thought China’s economy was less than half the size of the US, accounting for only 43 per cent of America’s total. Because of the new methodology – and the fact that China’s economy has grown much more quickly – the research placed China’s GDP at 87 per cent of the US in 2011. For 2011, the report says: “The US remained the world’s largest economy, but it was closely followed by China when measured using PPPs”.
With the IMF expecting China’s economy to have grown 24 per cent between 2011 and 2014 while the US is expected to expand only 7.6 per cent, China is likely to overtake the US this year. The figures revolutionise the picture of the world’s economic landscape, boosting the importance of large middle-income countries. India becomes the third-largest economy having previously been in tenth place. The size of its economy almost doubled from 19 per cent of the US in 2005 to 37 per cent in 2011.
The article explains the reason for price adjustments in comparing economies, and says: “The estimates of the real cost of living, known as purchasing power parity or PPPs, are recognised as the best way to compare the size of economies rather than using volatile exchange rates, which rarely reflect the true cost of goods and services.”
There is a lot of very interesting information in the World Bank study but this statement is largely incorrect, or at least exaggerates the way PPP is recognized. Adjusting GDP for differences in purchasing power makes a great deal of sense in certain cases, but the way it is done is so filled with problems that it is extremely difficult to find any economist who takes these measures very seriously.
The concept behind PPP is quite simple. You cannot always compare two countries in a meaningful way by comparing their GDPs at current exchange rates. Prices are different in different countries in ways that current exchange rates do not offset. This means that relative living standards are a function of more than just relative incomes.
This doesn’t mean that comparing the GDP of two countries directly at current exchange rates is useless. For example – and this is a fairly obvious mistake made in the FT article, and indeed in nearly every other article I have seen on the topic – if we are interested in the relative weight of two countries in geopolitical terms you would almost certainly want to compare their GDPs on the basis of current exchange rates. Exchange rates may be volatile, as this article notes, but a direct comparison, unadjusted for price differences, better measures the relative importance of each economy for its trade partners.
And contrary to what the article says later, the World Bank findings should not “intensify arguments about control over global international organisations such as the World Bank and IMF, which,” the article correctly notes, “ are increasingly out of line with the balance of global economic power”. While there is no question that countries like China, India and Brazil should see an increase in their representation among international bodies, it is not because the PPP measure tells us much about the relative weight of these countries.
Its usefulness lies elsewhere. The PPP adjustment attempts to measure the relative living standards between the two countries adjusting for the fact that prices are not equal at current exchange rates. A family earning $40,000 in one country, for example, will have the same nominal income but a better standard of living than a family earning $40,000 in another country if both families spend a significant portion of their income on nannies for their children, and if nannies are far cheaper in the first country than in the second.
This is really what the PPP adjustment tells us, but even here there are lots of obvious problems when we try to compare the two countries. One such problem is the assumption that both families have the same consumption baskets, which the PPP adjustment implicitly assumes. It is very unlikely that this is true for all sorts of reasons, not the least being that consumption itself is affected by relative prices. All of us are likely to adjust our consumption baskets in favor of those goods and services that are cheapest in relative terms.
In Beijing, for example, the cost of getting someone to clean your apartment is far, far lower than it is in New York. On the other hand New York has one of the most vibrant theater scenes in the world. No one would be surprised to hear, consequently, that someone currently living in Beijing is likely to have a cleaning lady come to his apartment far more often than he did when he lived in New York, and is less likely to go to the theater in Beijing than he did when he lived in New York. In that case comparing his standard of living in Beijing and New York, even assuming he had the same income in both places, can be pretty difficult.
But these are all obvious problems with the PPP measure, the kinds that are discussed in almost any undergraduate economics class. As long as we keep them in mind we can find the PPP measures to be quite useful in some circumstances, even if in our excitement over the kinds of news stories that generate headlines we interpret PPP to have geopolitical implications that are almost the opposite of reality.
Not all accounting is the same
But there is another problem with the PPP measure that is much greater, so much so that in some cases it completely invalidates PPP as having any kind of informational content. Economists love to use mathematics – perhaps it gives them a sense of legitimacy – but it is not always clear that they understand it very well, especially when it comes to working out the assumptions that are implicitly embedded in the various models that they use. We have seen especially egregious instances of bad analysis backed by lots of very confidence-inspiring data when it comes to analyzing the Chinese economy. The China PPP adjustment is another example.
Remember that the PPP adjustment is an attempt to correct for a significant distortion in direct GDP comparisons. The PPP model has two important assumptions. The first assumption, an explicit one, is that different countries assign different prices to the goods and services consumed domestically in a way that is not fully captured in the exchange rate. The PPP adjustment is an attempt to correct for this by taking the US economy as the standard, comparing prices of a specified basket of goods and services in the US with the second country (China, in this case), and adjusting China’s numbers upwards or downwards to reflect these differences.
But the second assumption, implicit but just as important, is that the US GDP numbers very broadly capture economic activity in the US in the same way that China’s GDP numbers capture economic activity in China. If this weren’t true, adjusting the two for relative prices would be a useless exercise. This isn’t an assumption, by the way, that either country’s GDP is somehow “correct”. It is only an assumption that any mistakes or biases in the US GDP numbers are the same as those in the Chinese GDP numbers, so that except for prices the two are comparable.
Here, of course, is where the PPP calculation can fall apart, and it is why the assumption should be explicitly stated. If you are comparing the US with an economy that construct GDP in a fairly similar way, Canada for example, PPP adjustments can be very illuminating because it allows you to compare like with like. But if GDP is constructed very differently than it is in the US, the second assumption is violated, in which case the PPP adjustment becomes simply another random comparison, which might or might not be better than the non-adjusted GDP numbers.
In China, it turns out, and not surprisingly, the composition of GDP is very different than it is in the US, mainly because the two countries measure debt very differently. It is not because China sets out to record debt differently – on the contrary, most people will tell you China records it in the same way the US and other countries do, and China certainly intends to. The problem is that in China bad debt is rarely recognized, repayment isn’t enforced, and default is almost non-existent. Banks simply roll bad debt over indefinitely. This makes comparisons between the two countries pretty hard. Why? It helps us to understand this if we think about the difference in the way we account for expenditures related to consumption and to investment. Normally, when you spend money on consumption, you create an expense. When you spend money on investment, you create an asset.
Let us assume that two identical companies each spend $50 on the same thing (say scientific research), but in one company the expenditure is recorded as an expense and in the other it is recorded as an asset. What would the financial statements for each company look like? The answer is pretty obvious. In the current recording period the first company would show $50 lower net profits than the second and $50 less assets and equity – remember however that there is absolutely no difference between the two companies, only in the way they record expenditures.
We should understand that this difference in accounting isn’t permanent. Over time, the second company will amortize, explicitly or implicitly, the $50 in additional assets, so that in future periods its net income will be a little lower every year, until at some point, when the expenditure (asset) is fully amortized, the two balance sheets will again look identical.
The important thing here is to recognize that if two companies (and the same is true for two countries) recognize expenditures in different ways, one as an asset and one as an expense, in the short term their financial statements will look very different but over the longer term they will converge. One of the two will report better income and asset numbers in the period during which expenses are being reported as assets, worse income and better assets numbers during the amortization period, and identical numbers thereafter.
Adjusting for debt
It turns out that the difference between the way the US and China implicitly construct GDP shows up in the way bad debts are treated, and by bad debt I mean the excess of the cost of an investment over its value. What happens if you borrow $100 to create an asset that ends up being worth only $80? The best way to treat this would be to create an $80 asset and the equivalent of a $20 expense, with the latter loss showing up as a claim against profits (for a company) or GDP (for a country).
This is effectively what we do when we write down debt in a market-based financial system. If an investor borrows $100 and invests it in an asset that creates only $80 of value, he will either default, and the debt will be liquidated, with the difference between$100 and $80 showing up as an expense (as loan loss provisions in a bank, for example), or he will write down the difference by transferring money from operating earnings or the sale of assets, with the write-down showing up as an expense.
Let’s assume that in China defaults do not happen to the same extent that they do in the US. First of all, is this a reasonable assumption? It clearly is. Except for the occasional insignificantly small one (what the Financial Times calls a “Potemkin default”), defaults are extremely rare in China, partly because much of the lending into what we usually assume are the worst projects are implicitly or explicitly guaranteed by the state or by local governments and partly because it may be politically difficult to record certain loans as problem loans.
At any rate although I don’t have numbers with me I think it is pretty safe to say that the number and value of defaults in China are a small fraction of those in the US. For this there are only two possible explanations. One is that Chinese investors are and have been far, far less likely to make bad investments than US investors (90-95% less likely if there are 10-20 times as many defaults in the US as in China relative to the sizes of their economies).
A few years ago there may have been a few very brave people who still believed this, but not too many do any more. With a comparatively short history of making investments, much more rapid credit growth in recent years, extraordinarily low interest rates compared to nominal GDP growth rates, and seemingly near-infinite amounts of moral hazard, it is implausible that Chinese investors are so far less likely to make bad investments than US investors.
That leaves the only other possible explanation, which is that bad investments are simply not recognized within the banking system to the same extent that they are in the US, and are in fact rolled over. Because even government officials and senior bankers have admitted many times that this is what happens, I think we can assume that it does. The automatic consequence, if this is true, is that a lot of what should be recorded as “expenses”, e.g. loan losses, are actually treated in China’s GDP calculations as “assets”.
This matters when we compare China’s GDP with that of the US. The two countries treat the accumulation of bad debt in very different ways (not because China intends to, but simply because it is politically difficult in China to force repayment when most of the borrowers are politically powerful), and as in the case of the first company relative to the second, this difference means that as long as China is accumulating and rolling over bad debts, China’s GDP and its assets will be significantly overstated relative to those of the US.
A rough proxy for the amount of the overstatement might be the bad debt on Chinese balance sheets net of liquidation – if we were to define “bad debt” in economic, rather than legal, terms (for example by including debt whose repayment might be considered questionable were all explicit or implicit central or local government guarantees credibly withdrawn). One ironic implication of course is that if China were to engage in an orgy of bad investment, it would get poorer (as more and more money goes to what in reality are expenses) while artificially boosting its GDP growth (as more and more expenses are recorded as assets). This seems to have been what happened in 2009-10 and thereafter.
This is almost certainly why Premier Li has insisted again and again that in spite of what must be tremendous domestic pressure China will not attempt to regain growth by another “fiscal stimulus” after the disaster of 2009-10. This will just boost GDP by creating more losses and effectively converting them into “assets”. According to an article in Friday’s Financial Times:
Premier Li Keqiang has said the government will steer clear of short-term stimulus measures to boost the economy. Li (pictured) said in an article published yesterday that pushing through deeper economic reforms was a wiser and more courageous approach than relying on government spending and borrowing to produce growth.
If the premier refuses another major fiscal stimulus in spite of rapidly slowing growth it can only be because he does not believe that all the growth generated by previous fiscal stimulus package was real, and this can only be because they generated large losses that were not recognized as losses but showed up, instead, in the form of “assets”.
This means that on a comparable basis, if you believe that China does not recognize bad debt in the same way that the US does, China’s reported GDP is likely to be overstated by the failure to recognize the difference between the cost of investment and the value created by that investment. Unless you believe that the US fails to recognize losses on investments to anywhere near the same extent, if you really want to compare the two economies more usefully you would have to do at least two adjustments: you would have to adjust China’s GDP upwards for price differentials and also adjust it downwards for unrecorded losses.
By how much would it have to be adjusted downwards? My back of the envelope calculation is that GDP may be overstated relative to US GDP by 20-30%.
Implying false precision
Is this an implausible number? Probably not. It is admittedly very rough, but it is based on what I think are reasonable assumptions about the annual amount of debt-related overstatement that is likely to have occurred in the past one or two decades. There is already substantial evidence that the Chinese banks have a long-established track record of accumulating bad debt.
China’s last banking crisis, for example, was estimated to have cost China roughly 40% of GDP, with some estimates even higher, but remember that these did not show up immediately. They were created in the late 1990s and were effectively recorded over the 2000-10 period in the form of significant transfers from the household sector (I have explained before how financial repression was the form in which the transfer took place), whose growth lagged GDP growth substantially.
Of course household income still grew very rapidly (7-9% of GDP), driven by even higher growth in GDP, but this was because of a massive increase in investment during the amortization period. Unless the ability to invest productively has sharply improved, much of the previous losses will have been amortized effectively by creating a whole new set of losses in the banking system – a large portion, in other words, was simply rolled over.
Since the huge losses generated in the 1990s, total Chinese debt has become a much larger share of GDP, the accumulation of the debt system-wide has arguably occurred in a more opaque manner, credit has grown at a far more rapid pace, and interest rates have been extraordinarily low (for long periods of times 10-15 percentage points below nominal GDP growth rates). On the other hand Chinese banks have gained an extra decade of experience in making loans and there arguably may have been a small decline in moral hazard.
The former set of circumstances should increase the risk and amount of losses in the banking system and the latter should reduce it. Either way the claim that an amount equal to 20-30% of GDP that should have been written off as loan loss expenses were instead accumulated as assets is not nearly as extreme as it might seem.
I should stop here and make a point that I am almost certain is going to be very widely misunderstood by many people who read this blog entry. My argument is not that China’s “real” GDP is 20-30% lower than its stated GDP. The whole issue of measuring GDP is incredibly complex, and it isn’t meaningful at all to say that a country’s real GDP is some quantity more or less than its stated GDP.
My point is a lot smaller and a lot more precise. China and the US compile their GDP data implicitly in very different ways, among the most notable of which is the way Chinese lenders, banks as well as households, treat a substantial portion of the debt as if it were implicitly or explicitly guaranteed by central or local government agencies. This means investment losses don’t show up as losses (expenses) because it is politically difficult to do so, and are instead rolled over and so show up as assets.
Because their economies are implicitly structured in very different ways, which create very different balance sheets, the two economies cannot be directly compared. One difference, and this of course is addressed in the PPP calculations, is that because relative prices of goods and services are different enough if you want to compare living standards you must make adjustments to average income based on differences in purchasing power.
But another difference – and this may be just as important, or even more so, then relative price differentials – is that the two countries’ balance sheets are not comparable, because of debt, and have materially different ways implicitly to recognize the gap between the cost of an investment and the value of that investment. Adjusting for this fact, I would argue, is just as important in any comparison of the two economies as adjusting for price differences.
So what is the point of all of this? Mainly that sometimes simplifying or adjusting our analyses can be useful, but we should be very aware of the assumptions, explicit and implicit, that underlie our analyses. PPP adjustments are useful when we are comparing two economies that are structurally similar and that compile GDP in ways that make them comparable.
But if we are going to compare two very dissimilar economies, France and Sudan, for example, or Brazil and North Korea, or the US and China, we have to be cautious because there are many other equally important adjustments we must make before we can usefully compare their GDPs. The PPP adjustment is an obvious example, but in these cases just adjusting on a PPP basis is a pretty random way of choosing which adjustment we are going to make.
So what? It may be a random adjustment but it is still an adjustment, right? On average, adjusting for PPP probably leaves us no worse off than not adjusting for PPP, so why would we want to oppose doing so?
Only because the adjustment can imply far more certainty than is warranted (a common mathematical mistake among non-mathematicians). We should be wary because of the implication that PPP is not just a random adjustment, and that it actually significantly improves our ability to compare any two economies. In some cases it does, but too often it cannot, and actually makes the comparison worse. While the PPP adjustment should increase our confidence in our ability to say something meaningful about the relative sizes of the US and Canada, it should not increase our confidence in our ability to say something meaningful about the relative sizes of the US and China.
By the way I should add a quick math point here that is often forgotten. If we believe that in order to make it comparable to that of the US we should adjust GDP upward by 25% to reflect the price differentials (the PPP adjustment) and then adjust it downwards by 25% to reflect the different ways of recording debt-related losses, the net is not a wash. China’s GDP is 7% smaller after the two adjustments.
Beijing opposes the PPP calculations
By the way according to a Friday article in the Financial Times Beijing has been opposed to the new World Bank calculations:
China fought for a year to undermine new data showing it is poised to usurp the US as the world’s biggest economy in 2014 based on purchasing power, according to people who helped compile the report.
The report, released this week by the International Comparison Programme under the auspices of the World Bank, included a line stating that the “National Bureau of Statistics of China has expressed reservations about some aspects of the methodology”. Beijing has declined to publish the headline number for China and the report said that the NBS “does not endorse the results as official statistics”.
The FT article says that the reason Beijing was opposed to the study was fear that “ leaders do not want exposure to the international pressure that comes with being the world’s largest economy, according to people familiar with Chinese official views on the matter.” The article then quotes Vinod Thomas, director-general of independent evaluation at the Asian Development Bank as saying: “They certainly don’t want to overstate the size of their economy. They are sensitive about that.”
I think this is probably correct but I think the FT and others may have missed the point. If GDP is indeed “overstated” by the failure to recognize bad debt, remember that this overstatement is not permanent. The difference will necessarily be amortized over the future, and the result will be that today’s overstatement will be matched by tomorrow’s understatement, and for those who receive my newsletter, I explained in the latest issue that the overstatement is only equal to the understatement if there are no financial distress costs associated with the excessive debt burden. If there are, and there almost certainly will be, tomorrow’s understatement will exceed today’s overstatement.
This means that if you look only at PPP adjustments, China runs the risk of becoming the world’s largest economy earlier than expected, only to slip back to second place over the next few years. This, I suspect, would be a political embarrassment, and it is very understandable why the current administration would not want it to happen.
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