Lowy Institute

Debate: US-China: Measuring decline and rise

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Dr Ken Henry and his team are busy preparing the Government's White Paper on 'Australia in the Asian Century', due to be released in the middle of this year.

In Australian academic, business and media circles there is breathless excitement about the rise of China (and the US decline they assume as its inevitable corollary). But one of the points I would make to the White Paper team is that it would be a major error to write out the US (as the White Paper's title seems to imply), and that we may yet prove to be living in the Asia Pacific century, or indeed the Indo-Pacific century.

Following President Obama's November visit and his historic address to the Australian parliament, a number of influential academic, business and political figures expressed concern about moves (supported by both the major parties) to strengthen further the Australia-US alliance.

In essence, their concern was that stationing a relatively small number of US Marines in Australia's north for half the year might feed the concerns of our largest trading partner that we are part of a US-led strategy to 'contain' it.

To the extent that anyone thinks current US policy really resembles Cold War containment, this reflects woeful ignorance of US strategy during the Cold War and now. But their argument also rests on an assumption that America has had its day and that China's burgeoning gross domestic product will translate directly into predominant power which Australia has to start heeding, now.

I have argued elsewhere that, far from becoming a liability, Australia's strategic relationship with the US is becoming more important. That conviction is made stronger by an important new article by Michael Beckley in the journal International Security.

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Beckley notes the widespread view that the US is declining relative to China and that this owes largely to the leveling effects of globalisation. He analyses a broad set of economic, technological and military indicators to reach a conclusion which, if true, is as profoundly important as it is unfashionable; far from declining in relative terms, America is now wealthier, more innovative and more militarily powerful compared to China than it was in 1991. Here are some of Beckley's main points:

  • Estimates of China's power tend to be exaggerated (and estimates of America's power tend to undershoot) because: GDP correlates poorly with national power (per capita wealth providing a better indicator of surplus wealth available for broader national purposes); conclusions are often based on static single-year snapshots rather than trends over time; and China is often compared with itself (at an earlier time), rather than with America (which is itself not standing still).
  • The US is not like Britain and other eclipsed hegemons but holds a unique geopolitical position owing to an unprecedented combination of material advantages; as a result it exercises 'structural power' – an ability going beyond the use of force or coercion to set global agendas and shape the range of choices open to other countries.
  • America has its problems, including public debt and a fractious polity, but suggestions of imperial overstretch and decline are premature. Past hegemons succumbed after fighting wars against major powers on multiple fronts and spending anything between 10% and 200% of GDP on defence to do it; by contrast, the US spends a relatively modest 4% on defence and confines itself to knocking off the odd rogue regime or occasional humanitarian interventions.
  • Rather than operating neutrally to close the gap, globalisation – and particularly globally networked production – may be an active political process shaped by the US to serve its interests (yes, that's right – the conspiracy theories may be true!).
  • Wealth, innovation and (conventional) military capabilities are the most vital elements of power in the contemporary international system.
  • Yet, for all China's double-digit economic growth, massive investments in education and research and rapid military modernisation, today the US is wealthier compared to China than it was in 1991, China continues to lag behind America in innovation, and (despite some asymmetric advantages) the US-China military gap is growing, not shrinking.

Not everyone will agree with Beckley's methodology or with all of his conclusions. The relative contributions of wealth, innovation and military capability to national power, for example, are debatable. Nor is it to suggest Australia or the region should be complacent. Even if Beckley is right, misperceptions of the balance of power in Asia – on either side – can be dangerous.

Nonetheless, he has done us a considerable favour by questioning some of the glib assumptions that underpin much of the Australian debate – in particular by cautioning against the idea that raw economic power necessarily translates directly into global clout and by highlighting significant shortfalls in China's ability to innovate (some of which Fareed Zakaria has also documented).

At least one of Beckley's conclusions could almost have been written with Australia's White Paper in mind:

The best that can be done is to make plans for the future on the basis of long-term trends; and the trends suggest that the United States’ economic, technological and military lead over China will be an enduring feature of international relations, not a passing moment in time, but a deeply embedded condition that will persist well into this century.

'Whose century?' indeed.

Photo by Flickr user Jennikokodesu.


Andrew Shearer's recent post on US-China comparisons prompted me to take a look at the paper by Michael Beckley he recommended. While I don't have anything useful to contribute on the specific subject of the US military/security edge over China, a couple of things did strike me.

First, I would summarise many of Beckley's points regarding the clear superiority of the US in measures of innovative capacity such as R&D spending and patent citations as reflecting the big difference in GDP per capita between the two countries. Given the close correlation between the level of a country's development and many of these variables, these results are exactly what we should expect when comparing a developed and developing economy. 

Or, to put it another way, countries at the economic frontier are likely to grow more through innovation while countries involved in catch-up growth will rely on a different growth model. 

This difference is one of the factors that lie behind concerns about so-called 'middle-income traps': the policies and institutions you need to deliver the growth that get you from low- to middle-income status may not map all that well onto those that get you from middle-income to high-income status. So while it's quite possible that the gap with the US on these innovation-style indicators will narrow as China develops and its GDP per head rises, it's not a foregone conclusion.

Second, I was surprised by the claim – at least with regard to economic variables – that the US lead over China has grown since 1991. That's certainly not what I would take away from the data. Of course, there are lots of potential variables to consider, and there are probably some data points that would support this story. 

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But there's a great virtue in parsimony, and given that the simplest measure of wealth we have is GDP, I'm going to claim that comparing GDP and GDP per capita over time should do a pretty good job of capturing much of what's going on in the relative economic positions of the two economies. After all, most of the other potential variables we might consider can be thought of as inputs or contributors to GDP. And as I've noted before, although GDP has a lot of well-known shortcomings, a general dearth of alternatives tends to mean that we end up using it anyway.

That still leaves us with the problem of how best to measure it. Long-standing Interpreter readers will be familiar with the ongoing debate over whether PPP or US dollar GDP is the best choice. Arvind Subramanian discusses this issue in his recent book on China's rise, and goes for the interesting option of weighting the GDP variable in his 'index of economic dominance' half on a PPP basis and half on a US dollar one. 

Below, I try to side-step this issue by charting both the US dollar and the PPP series for GDP and GDP per capita, expressed as a ratio of the Chinese to the US value (all data taken from the latest IMF WEO database, including the latest Fund forecasts out to 2016):

Looking at these two charts, even on the measure that's least favourable to China – GDP per capita measured on a US dollar basis – it's pretty hard to argue that China has gone backwards relative to the US since 1991. On a PPP basis, the degree of catch-up is actually rather impressive. Moreover, it's possible that this still understates China's progress.

Finally, having just made the case for GDP as the appropriate metric for economic comparisons, I'm going to back away from that claim a bit. One recent  approach to measuring national wealth has been pursued by the World Bank, where analysts have constructed an alternative estimate comprising the sum of produced capital (machinery, structures and equipment), natural capital (agricultural land, forests, minerals, energy) and intangible capital (calculated as a residual, but intended to capture human, social and institutional capital including hard-to-measure factors like the rule of law and the quality of governance). 

The idea of this measure is that, unlike GDP, which only captures the value of production, it takes into account both environmental factors and intangibles. The Bank has produced estimates for national wealth for three years (1995, 2000 and 2005), and again I've plotted the ratio of Chinese to US wealth on both a total and a per capita basis.

I'll finish with two points based on this last comparison.

First, both the overall and the per capita wealth ratios are much lower than the comparable ratios for GDP. While this reflects significant gaps across all three measures of wealth — according to the Bank's estimates, natural wealth per capita in China in 2005 was about 30% of US levels, produced capital was about 6% of US levels, and intangible capital less than 1.5% of US levels – the last of these is the standout item for me. This brings us nicely back to my opening point: that there are significant differences between developed and developing/emerging economies. One of those differences is the relative size and quality of the kind of things that make up intangible capital.

Second, even on these measures, China has still made some modest progress in terms of catch-up. This slower progress also suggests (not surprisingly) that closing the gap in human, social and institutional capital is likely to be tougher for emerging markets than closing the gap in machines and factories.

Photo by Flickr user kk+.


Michael Beckley is an International Security Program Research Fellow at Harvard Kennedy School's Belfer Center.

Is the US in relative economic decline to China? In a recent article in International Security, I say 'no'. In a post on this blog, Mark Thirlwell says 'yes'. Who's right? 

The answer is: we both are, but only by our own definitions of decline. I define decline as a narrowing of the wealth gap between the US and China. Thirlwell defines decline in terms of economic growth rates. Thirlwell and I come to opposing conclusions because the US is growing at a slower rate than China while simultaneously becoming wealthier. 

How can this be? Normally, growth rates dovetail with changes in wealth gaps. But these measures often diverge when comparing a rich country like the US to a poor one like China. 

Since 1991, China's per capita income rose 11% annually while America's rose 3.5% annually. But 11% of US$900 (China's per capita income in 1991) is less than 3.5% of US$24,000, the US's per capita income for that year. As a result, the average Chinese citizen is US$17,000 poorer compared with the average American today than he was in 1991. 

The figure below illustrates this phenomenon. The blue line denotes the absolute difference between US per capita income and that of China. The red line shows China's per capita income as a fraction of America's. 

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Source:  International Monetary Fund World Economic Outlook Database, September 2011. 

The best way to deal with this situation is simply to report both figures: the US is growing more slowly but becoming richer than China. Yet most analyses of US decline, including Thirlwell's, only report growth rates. 

It's not hard to see how defining decline in terms of growth rates produces nonsensical results. Over the past twenty years, more than half the countries in the world grew faster than the US, including such titans as Bangladesh, Pakistan, Uzbekistan, and Rwanda. Moreover, by Thirlwell's definition, the US has been in decline to China since 1968, during the Cultural Revolution and over a decade before Reform and Opening. 

The problem with growth rates is that they compare countries to their former selves. China's growth rates are high in large part because its starting point was low. For this reason, Harvard political scientists Sheena Chestnut and Alistair Iain Johnston contend, 'it strains the concept...to characterize any state with a faster growth rate than the United States as a rising power. This does not fit with a commonsensical notion of rising power.' 

One can argue that comparing growth rates helps account for potential diminishing returns of wealth. For example, Georgetown political scientist Erik Voeten recently asserted 'it is much easier for a country with a GDP per capita of 30K to bully a country with a GDP per capita of 1K than it is for a country with a GDP per capita of 50K to bully a country with a GDP per capita of 15K.'

Perhaps. But one can also imagine the opposite being true. Highly developed countries may get more bang for the buck than less developed countries – that is, every dollar they spend on innovation, military capabilities, international influence, etc. produces greater returns. This idea of increasing returns to wealth fits with the standard conception of economic development as efficiency of production and is supported by studies showing that more developed countries are better able to translate their basic resources, or 'latent power', into actual capabilities (for examples, see here, here, here and here).

Obviously, growth rates should not be ignored. They provide an important data point and allow us to make educated guesses about the future. But neither should they be conflated with total growth nor used to define loaded terms like 'decline' or 'catch-up'.

One last point. China is growing faster but falling behind the US across most indicators. But in terms of GDP, China is growing faster and closing the gap – by most projections, China's GDP will overtake America's sometime in the next decade or two. Most analysts view this impending GDP transition as a looming power transition. And Thirlwell places a great deal of emphasis on GDP in his post.   

To be sure, GDP figures serve a vital function in defining the set of potential major powers – Luxembourg is extremely wealthy in per capita terms, but its small population precludes it from raising an army, let alone entering the ranks of the great powers. But beyond this basic function, GDP figures can mislead more than they illuminate, at least in certain cases. China is one of these cases.

It is often forgotten that China had the largest GDP for the first half of its 'century of humiliation' (1839-1945) when it was torn apart by Western powers and Japan. The UK, on the other hand, ruled a quarter of the globe during the 19th century, but was never, even at its peak, the largest economy in the world. The figures below show GDP and GDP per capita figures for 1870. The data on GDP per capita matches much better with our understanding of which countries were powerful in 1870.


Source:  Maddison, Statistics on World GDP. 

China is obviously not as weak today as it was in 1870. But much of the case for the rise of China and the decline of the US rests on GDP figures, so it's important to recognise that GDP has never been a good proxy for national power or aggregate wealth. GDP is largely a function of population, and people are both assets and a liabilities because they both produce and consume resources. China's 1.3 billion people produce much output, but they also consume most of it immediately, leaving little wealth for national purposes. 

GDP figures help define the potential major powers. But when you're comparing two big contenders like the US and China, GDP per capita becomes a much more important measure because it represents how developed each country's economy is and how much surplus wealth is available for national purposes. By that measure, along with more specific measures of innovative and military capacity, the US is rising relative to China, at least for now.

Photo by Flickr user papalars


As Michael Beckley acknowledges in his reply to Mark Thirlwell, it is hard to say definitively whether America is declining economically relative to China, because it depends what you measure. On some measures it is, and on others it's not. So the next question is: which measures should we pay attention to? And that depends on why we are interested.

In the present debate, flowing from Michael's excellent essay in International Security, we are interested in what the economic trends mean for America's strategic and political power, particularly in relation to China. And we are interested in that primarily because of the implications of shifts in relative power for America's management of its relationship with China. 

So we have three questions to answer before we can draw strategic policy conclusions from the economic data. First, which economic measures are most relevant to judgments about relative strategic and political power? Second, how far are these measures actually moving? And third, how far do the relevant measures have to move to make a difference to the way America frames its policies towards China?

Let's look at them briefly in turn.

Which measure? 

If I read him right, the core of the Michael's argument is that the wealth of a country's citizens, measured as average per capita income, is more useful than the overall size of its economy, measured as GDP, as an index of the country's strategic power.

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Obviously, this is only right within limits. As Michael says, Luxembourg hardly ranks as a global power despite high per capita incomes, so overall size counts for something. Intuitively, the primary economic factor determining national power is the total resources that can be applied by the state for national purposes, and that would seem to depend much more on the size of the overall economy than the wealth of individual citizens.

Michael's response to this, again if I understand him correctly, is that per capita income is nonetheless a better index of national power because it correlates with two other factors which counterbalance the effects of sheer GDP size. First, higher per capita income countries have more advanced economies and can harness more advanced technology, therefore using their resources more efficiently, so they get more power for each dollar. But is this true? I'm not sure it is, at least in the military field with which I am most familiar. History suggests that large numbers of simple weapons can often beat smaller numbers of more expensive ones. Quantity has a quality all its own.

Second, I think Michael argues that high per capita income countries have an advantage in power because they can devote a higher share of their overall wealth to national purposes, since a lower proportion is needed for bare necessities. 

Again, it is not clear how far this is true. The proportion of national wealth available for national purposes depends on many other factors apart from per capita income – including how much of the economy the government controls directly, and how willing the people are to surrender what they control to the government. It is not at all clear, for example, that the US Government commands a bigger share of America's wealth than the Chinese Government does of China's. 

So while I agree that GDP is a very imperfect measure of the economic foundations of national power, I think it remains the best we've got.

How big a shift?

As Michael suggests, many people both exaggerate the scale of China's rise, and wrongly believe that America is declining. There are interesting questions about the long-term trajectory of the US economy, but it is simply wrong to say that the shift in relative size of GDP between the US and China is even partly the result of US decline. It is all down to China's growth.

Remarkable as that growth is, I agree with Michael that it is often exaggerated. China is unlikely to 'rule the world'. It has little chance to achieve the preponderant share of global GDP that America has previously enjoyed, partly because of inherent limits to its own trajectory – especially demographic – and partly because there are just too many other big players in the world with (actually or potentially) the combination of big population and high productivity required to generate a huge economy. China may be the biggest for a while, but it will be one of a crowd at the top.   

Nonetheless, China is much bigger economically relative to the US than it was ten or twenty years ago, and much bigger relative to the US than any country has been for over a century. This is a very big shift. And if size of GDP is a correlate of power, it is a very big shift in relative power. 

What does this mean?

Is this shift big enough to make a difference to the way America manages its relationship with China? To be more specific, does it mean that the US should rethink the widespread assumption that continued American strategic primacy is the only acceptable basis for the future relationship? To be even more specific, does it make sense for the US to try to impose its primacy in China, as China's power grows? Well that's a big question, but here are two quick points.

First, this question is not entirely answered by deciding who is stronger. What matters in framing the relationship between the US and China is not just how much power each has, but what they need to do with it. 

There are three key asymmetries in the US-China relationship which all break China's way. China's objectives are focused in Asia, while America's are globally dispersed. The theatre of competition is on China's doorstep, but an ocean away from the US. And in the military sphere, to maintain primacy in Asia, America must maintain sea control, while to prevent that China need only achieve sea denial. Together these asymmetries mean that China does not have to become as strong as America for the balance of costs and risks of sustaining primacy in Asia to grow sharply for America.

Second, the answer does not just depend on what America can do, but on what it wants to do. We might argue about how far China's power has grown, but we cannot doubt that it has grown a great deal. It will therefore cost America a lot more to sustain primacy in future than it has in the past, against China's clear opposition. The big question for America is whether the costs are worth it. That of course depends on what the alternative is. If the only alternative is Chinese hegemony in Asia, maybe they are. But that is not the only alternative.

Photo by Flickr user Silly Little Man.


This passage in Hugh's latest post sparked two questions in my mind:

There are three key asymmetries in the US-China relationship which all break China's way. China's objectives are focused in Asia, while America's are globally dispersed.

  1. Isn't it the case that one asymmetry in the US-China relationship that has long broken in favour of the US is America's system of alliances and security partners in Asia, which helps support its primacy? If China is a 'lonely superpower', the US is a very popular one in Asia and growing more popular.
  2. Aren't China's strategic objectives growing more dispersed geographically as its power, energy imports, etc expand? If so, could this asymmetry also be breaking the way of the US?

Photo by Flickr user Beverly & Pack.


Robert Ayson is Director of Centre for Strategic Studies at Victoria University, Wellington. 

The recent Interpreter debate over the relative power of China and the US is important in its ambition but questionable in some of its method. The problem is the assumption that we can decide whether the US really is in relative decline on the basis of an economic comparison with a growing China, and on then finding some way of determining how that material power makes for influence.

Even if we were to agree on the same metric for measuring that economic power, we would still have a variable where each unit of power is equal. But power is about relationships (what I can do to you?; what do you think I can do to you?; what do others think I can do to you and to them?). It is not about comparisons (am I bigger than you?; do you think I am bigger than you?; do others think I am bigger than you?). We are doing too much of the latter sort of analysis.

Because it is about social relationships, power is as much about perception as it is about concrete capacity: I don't perceive you as powerful simply on the basis of your size or other material factors (compare Japan and Israel for a moment). And because it is about perception, power is lumpy rather than smooth (as Thomas Schelling might say). Some units of power are much more equal than others. Changes in power status do not simply appear gradually and cumulatively. Large symbols of change, which shock and otherwise alter our perceptions, are often more important than a collection of small concrete ones.

Let us take as an example Britain's decline in Asia. Unlike today's debate over what China's rise means for America's influence, this example of decline is incontestable.

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Britain's economic exhaustion after the second of two world wars in the first half of the century was part of a relative economic decline that was both systemic and perceptible. But, at least looking backwards, people are less inclined to remember the 1967 sterling crisis than the physical withdrawal of British forces east of Suez. Like the failure of Britain's Singapore strategy a generation before, this was a huge, lumpy, change which affected others. It was symbolic of that wider systemic weakness, but that weakness was not enough on its own to guarantee it. It took a political decision: an act of will.

So much of the current debate is about the search for signs of those underlying and slow-moving systemic trends (as if we really can detect them properly) rather than the critical dimension of real decline: the political inability or unwillingness to sustain influence.

Of course, this can happen when material power has run out: the sheer will to use power is not enough if there is not going to be anything to wield. But it can also be caused by a reluctance to influence others even when there is material power there to utilise. And this seems to me to be the big question: not how the US and China measure up materially, but how they measure up politically and psychologically.

This leaves open the possibility of a shock even if our economy-watching is as good as it gets. I think its an open secret that both the US and China will have massive and globally important economies in a generation's time and more. But that only gets us so far. And if it is unwise to extrapolate China's recent growth rates it may be even more hazardous to apply a similar linear logic to Mr Obama's pivot in Asia.


Malcolm Cook responds to my argument that US-China strategic competition is weighted China's way with two counter-examples. First, doesn't the US have a big advantage in its network of allies in Asia? And second, doesn't China now have global interests just as America does, so it too must spread its strategic efforts globally, rather than reap the advantage of being able to concentrate them in Asia, as I had suggested? Both goods points, but alas, I do not think either make much difference.

First, whether its allies are an asset or a liability for the US against China depends on how closely US objectives align with their allies' objectives. I think the alignment is much weaker than it often appears. 

The US wants to perpetuate American primacy in Asia, even at the expense of an adversarial relationship with China. Its Asian allies want to prevent China getting primacy, but that's not the same thing. In fact, they will not support the US sustaining primacy if the cost is US-China hostility. Most still hope they can avoid both Chinese hegemony and US-China hostility. 

So US allies do not share US objectives as they are now defined, and if push comes to shove, they will not help the US achieve them. The allies, then, are not an asset for the US – in fact they are probably a liability, though that's another argument.

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Second, yes, China today has growing interests around the world beyond Asia. But are they strategic interests – by which I mean, are they interests that China values so highly that it would defend them with armed force? I don't think they are. America claims strategic interest in Europe, the Middle East and elsewhere that require it to be able to deploy decisive military power globally, whereas China, like most other countries, does not seek to defend its wider interests with armed force in the same way.

What about energy shipping lanes from the Middle East, you ask? I know this goes against conventional wisdom, but I don't think China has the need or the capacity to defend these, and I see little evidence it is wasting money trying. 

The bottom line is that China does not try to project significant strategic power beyond the Western Pacific, so it can focus its efforts in the Western Pacific. America is trying to maintain a global posture. As many US commentators have said, all the talk of the pivot to Asia overlooks the fact the America still asserts a big role in a lot of other places that haven't gone away.

Photo by Flickr user Luke Redmond.


Rob Ayson's characteristically wise and subtle post makes the very important point that what matters about power is not what you've got, but what you choose to do with it; human choices like that are subjective things, and hence hard to plot on graphs, let alone predict. 

As Rob hints, choices about power are especially hard to plot or predict because power is, to use a word he taught me to apply in this context, transactional: your choices about the exercise of power towards me profoundly influence my choices about the exercise of power towards you, and vice-versa. Absolutely right.

So, two modest points in response, the first just by way of elaboration. A key element of Rob's argument is that one of the biggest subjectivities in strategic choices is in perceptions about respective power. What will drive the strategic choices about one another in Beijing and Washington over the next few years is not the reality of their relative power – whatever that might turn out to be — but the perceptions of it in each place.

That recalls Geoffrey Blainey's argument in his excellent The Causes of War written back in the 1980s. Blainey argued that the main causes of wars are differences of perception between countries about their relative power, which they end up going to war to resolve. 

That is why perceptions of power are so important, and differences in perceptions are so dangerous. If the US and China end up going to war in Asia over the next decade or two, it will be in large measure because each believes they are strong enough to dominate Asia against the wishes of the other. My bet is that both are wrong, but that won't stop them fighting to find out.

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The second point is by way of defence of the efforts of those trying to assess the balance of relative power in some kind of objective terms despite its inherently subjective nature. I think Rob might be gently hinting that we should save our breath, and wait and see what the great powers choose. From an analytic perspective that's right, but of course we don't just want to understand the world but to influence it. The 'lumps' in power transitions that Schelling talks about are very disruptive indeed, so we ought to try to smooth them out as much as possible.

If Blainey is right, then one of the best ways for us to help manage power transitions and smooth the lumps is to do all we can to understand, and convey to both sides, how power is shifting, thereby minimising the difference of perceptions of power between them. 

Or, to put that more specifically, the US and China are more likely to avoid war if America does not persist in believing it can perpetuate its primacy in Asia over the next few decades in the face of China's power, and if China does not entertain the illusion that it will be able to displace the US from Asia completely. Which is why I think it is a good idea to keep talking about these issues.  

Photo by Flickr user The White House.


I'm sympathetic to the distinction Michael Beckley raises between GDP and GDP per capita in his post on defining decline; it's a point I also focused on in my original post. Each gives us different readings about national capabilities.

But the other question I raised concerned comparisons over time. Specifically, I was surprised by Beckley's contention that the economic gap between the US and China had grown since 1991, and I plotted some GDP and GDP per capita data to suggest that the gap looked like it had shrunk. Beckley disagrees and the source of this difference is that, while I focus on ratios, including the ratio of GDP per capita, Beckley looks at the absolute difference in GDP per capita between the two economies.

It certainly makes sense to look at the absolute difference when comparing the two economies at a given point in time. But absolute differences do not do a good job of capturing changes over time. That's why we should normalise the data when making these kinds of comparisons – for example by constructing ratios or indices.

To see why, take the following (deliberately simplistic and extreme) example. Suppose that, at the start of our comparison period, GDP per capita in the US was $1000 while GDP per capita in China was just $1. Then assume that by the end of our comparison period US GDP per capita had risen to $1.001 million while Chinese GDP per capita had risen to $1 million. So China has grown much faster than the US over this period, but the US remains the wealthier economy: 

By the end of this simplistic example, has China shown signs of catching up with the US or not?

If we look at absolute values, we would have to say 'no'. In fact, the gap between the two countries has increased, rising from $999 at the start to $1000 at the end. And yet the message that China has gone backwards relative to the US is incredibly counter-intuitive.

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So instead, let's look at the ratios. On this metric, while Chinese GDP per capita was just 0.1% of US levels at the start, it has climbed to 99.9% of US levels by the end. This is an extreme (and unlikely) example of catch-up growth that is nevertheless consistent with the US remaining wealthier, and with the absolute gap between the two measures of GDP per capita having increased.

But doesn't using ratios give an exaggerated picture of China's catch-up? (Beckley said in his post that, by my definition, 'the US has been in decline to China since 1968...') Well, not really. The chart below still suggests that the catch-up story only gets going after the start of the reform period*:

I suspect part of the difference in emphasis here is due to conflating the ideas of catch-up and decline. 

From my perspective, the former need not imply the latter. In other words, the Chinese economy can converge on the US economy without the latter declining, since the catch-up growth story is perfectly compatible with a world in which both economies can keep growing and in which the US can also keep getting richer in absolute terms (see my simplistic example above). Note that my original post does not mention US decline once.

The security debate sometimes seems to treat Chinese catch-up as necessarily equivalent to US decline. Perhaps this reflects an important difference between positive-sum-style economic thinking and zero-sum-style strategic thinking, a difference in approach I have highlighted elsewhere.

* In order to graph both series back to 1950, I have used data constructed by the economic historian Angus Maddison. In my original post I used data from the IMF's World Economic Outlook database, so I have included that too, for comparison. I discussed the big difference between the Maddison and IMF data on GDP per capita (and GDP) as measured using PPP rates in this post.