China, the Renminbi, and Global Imbalances: A Quantitative View

President Obama’s trip to China has returned to scrutiny the role of China’s currency and macroeconomic policies in perpetuating global imbalances. [0] [1] [2]



china01.gif

Figure 1: Log real value of RMB (blue, left axis), and Chinese trade balance in billions USD at annual rates (red, right axis) from Chinese statistical sources, and twelve month trailing moving average (maroon). Source: IMF, International Financial Statistics, ADB, NBER and author’s calculations.

Various observers have continued to ascribe a central role to real RMB appreciation to effect global rebalancing. I think it’s useful to remember that, given a Chinese trade balance in excess of 260 billion USD, appreciation can only have a certain impact. From Cheung, Chinn and Fujii (forthcoming):

…using a single equation error correction model, allowing for coefficient shifts with Chinese accession to WTO, leads to a statistically insignificant estimate of the price elasticity. In the 2000-06 period, the implied price elasticity is zero. Using this point estimate, then a 10% appreciation would actually lead to a shrinkage of the trade balance from 400.9 billion to 355.2 billion. This estimate of 45.7 billion (2000$) is somewhat less than the $88.6 billion current dollars reported in Marquez and Schindler (forthcoming) [working paper version].

The export equations take the form:


Δ exp t = θ 0 + ρ exp t-1 + θ 1 y* t-1 + θ 2 r t-1 + θ 3 k t-1 +
σ 1 Δ exp t-1 + 2 lags of first differenced right hand side variables + quarterly dummies + WTO dummy + v t

Where exp is log exports, y* is log RoW GDP, r is the real exchange rate, and k is the Chinese capital stock. The import equations take the form:


Δ imp t = β 0 + φ imp t-1 + β 1 y t-1 + β 2 r t-1 + γ1 Δ imp t-1 + 1 lag of first differenced right hand side variables + quarterly dummies + WTO dummy + u t

Where imp is log imports, y is log GDP.

Separate regressions are run for ordinary and processing trade, over the 1993Q4-07Q1 period. The adjusted R2‘s range from 0.77 to 0.92.


If we take the Goldstein-Lardy misalignment estimates of 20% to heart, then a 20% appreciation would lead to an approximately 91.4 billion (2000$) reduction in the Chinese trade balance. As best as I can tell, the export prices from China, and to China (as proxied by unit value indices for Hong Kong) have probably stayed constant relative to 2000; hence the nominal impact is around 90 billion USD (with considerable uncertainty surrounding this point estimate).


This leaves a large Chinese trade surplus in place, around 170 billion even before the rebound in the Chinese surplus anticipated as the world aggregate demand recovers. Now, to the extent that Chinese reserve accumulation is due to a current account surplus and capital inflows, one could hope that a revaluation would have an additional knock-on effect by deterring capital inflows (the argument would be revaluation would eliminate expectations of appreciation that would provide capital gains on holding RMB). That is, recall the balance of payments identity:


CA + KA + ORT ≡ 0


Where CA is the current account, KA is private capital account, and ORT is official reserves transactions.


Figure 2, drawn from Prasad and Sorkin (2009) shows that net inflows were not a major factor, at least in 2008.


china02.gif

Figure 2 from Eswar Prasad and Isaac Sorkin, “Sky’s the Limit? National and Global Implications of China’s Reserve Accumulation,” mimeo (July 2009).

This suggests to me that rebalancing requires as much or more Chinese fiscal stimulus and a concerted effort to encourage private consumption via enhancing the social safety net, in addition to RMB revaluation. (This can be seen in a Mundell Fleming framework, as applied to China [3]). And it also requires determined action from the US side as well (see here). If only we’d conducted a sane fiscal policy in 2001-08 [4], our range of action would now be wider in this respect.

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31 thoughts on “China, the Renminbi, and Global Imbalances: A Quantitative View

  1. DOR

    By the way, what was the impact of the LAST 20% appreciation?
    Oh, that’s right. The trade balance shot up, didn’t it?

  2. ppcm

    A strong axiom is embedded in the demonstration, that is national incomes and private incomes are inelastic to the volume of RMB import or remain constant.

  3. Tom

    You’re right that yuan appreciation would not nearly solve the entire US-China trade deficit.
    China restricts imports in numerous other ways besides exchange-rate manipulation.
    I think the US needs to intelligently use retributive tariffs to promote free trade, by attaching them to objective and clear tests that if passed would lead automatically to their repeal. Such as linking tariff levels to currency intervention levels.
    Allowing the yuan to appreciate would give a big boost to the development of a consumer economy in China, and not just to imported consumer goods. China’s manipulation of its exchange rate is part of a larger scheme, in which the government essentially confiscates some earnings from exporters and redirects that capital to public projects, which are predominantly export-oriented.
    China’s current stimulus is also part of this same scheme. The government forces exporters to exchange their hard-currency revenues for freshly created yuan, which become part of the pool of capital from which the government borrows to fund its stimulus, which is predominantly being spent on developing China’s export potential. Theoretically China could change its stimulus to be more consumer-oriented, but that is unlikely to happen given their government culture, and it would be much less effective than simply allowing private entities to direct the capital they earn from exports to consumer-oriented projects, as is working very effectively in other Asian countries, eastern Europe, Turkey and Latin America.

  4. spencer

    From 2004 to 2008 the yuan appreciated about 21%.
    the net result was about a 3% increase in the average price of US import from China.
    What we have learned over the years is that firms, businesses are very adept a offsetting the impact of currency changes.

  5. Tom

    Spencer: You’re right about yuan appreciation not much affecting the price of China’s exports, but that is not how yuan manipulation affects trade balances. Yuan manipulation restricts imports by making hard currency more expensive within China.

  6. steve

    Fixing the $/Yuan relationship is not about goods flows, but about the impact of capital flows on u.s. interest rates. A revaluing yuan raises real interest rates here and, as such, creates a u.s. growth profile more balanced between saving and investment. the problem in the last cycle is that the fed, believing we lived in a free foreign exchange market world, allowed u.s. rates to be too low as chinese capital flowed in and with credit too cheap well we know the rest. u.s. rates must allow for saving/investment to rebalance and that starts with a free floating $ against our trading partners with whom we have huge trade deficits and a stable currency relationship

  7. RicardoZ

    I am sure that Paul Krugman is hopping mad. China Central Television lists their “Top ten international experts in China” with Nobel Laureate Robert Mundell, a founder of supply side economics, as the only economist mentioned from the Western Hemisphere.
    http://english.cctv.com/20091116/104027.shtml
    Mundell has been advising China on monetary issue for many years. Yesterday he spoke in Beijing at the Business Week CEO Forum.
    I find it interesting that one of the authors of the Mundell-Fleming model is actually advising the Chinese to continue their monetary policy: a loose peg to the dollar with an eye toward the euro and toward gold. We see the US dollar in constant decline because of all the Keynesian/monetarist demand-siders stealing our money and then giving 25% back saying it will “stimulate” us back to health. All the while China continues its economic growth. Apparently it is not the Chinese who need to correct monetary policy but the US.
    Why is it that Americans come up with the greatest economic methodology for building world prosperity then throw it out the window in less than 10 years in favor of an old, mercantile-based theory that has failed over and over? I do understand that the mercantilist demand-side model gives “intellectual” support to big government central planning, but the rest of the world is discovering our wisdom even as we throw away our prosperity. Hmmmm!

  8. Tom

    Steve: The $/yuan relationship has to do very much with both capital and goods flows.
    Your analysis of how the capital flows work is a popular one but misses the very important fact that the capital is not really Chinese, but mostly US capital cycling through China and back to the US.
    Very roughly, instead of a free trade, market-exchange-rate situation in which two countries exchange goods, the US buys Chinese goods but China buys a lesser value of US goods and the difference in US Treasuries. The main differences for the US are less manufacturing jobs, more public jobs (including, arguably, in foreign wars), and an increasing portion of future tax revenues pledged to the Chinese government.
    Your analysis would be correct to the extent China redirects its trade surpluses with other partners such as the EU and Japan into US capital markets. I’m sure that has happened but I don’t think it’s happening much now.

  9. Norman

    Someone please explain the effect on China of its taking in $500B per year in foreign reserves but essentially buying it with yuan/RMB which is at least 40% undervalued so that they are losing $200B in buying dollars at too high of a price. To put it simply they are paying $10 to buy $6 worth of currency.

  10. Tom

    Norman:
    First, a Chinese exporter gets that $6 by producing and exporting stuff.
    Second, the Chinese exporter is forced to exchange that $6 for yuan at a fixed rate.
    There are two possible buyers: the central bank, or an importer.
    The central bank brings to the market lots of freshly created yuan. It uses its dominant position on the market to bid up the price of dollars.
    This makes dollars more expensive for the importer, and thus makes imports more expensive for Chinese people and companies.
    So yes, the importers are overpaying.
    But the central bank is not overpaying, it is confiscating dollars and giving out freshly created yuan as partial compensation.

  11. Get Rid of the Fed

    I think you have the wrong imbalance. It is not macroeconomics. It is micro, specifically the labor market. Try at least tripling wages in china and let’s see what happens (and if capital in search of cheap labor moves somewhere else, raise wages there too).

  12. Juan

    Se ha debido el incremento exponencial del superavit exterior de China a una cuestion exclusiva de precios?. De hecho, el yuan se ha revaluado en terminos reales un 60% entre enero de 1994 y diciembre de 2008, un 26% desde enero 2005. Podriamos ver una repeticion de la conocida como paradoja de Kaldor, segun la cual, los incrementos en las exportaciones alemanas y japonesas tras la II Guerra Mundial se produjeron en paralelo a una apreciacion de sus respectivas monedas. Es la competitividad no basada en el precio . Por otro lado, una hipotetica apreciacion del nominal yuan no implica necesariamente que se reduzca el valor de las exportaciones chinas: por un lado, su ventaja en precios puede ser tal que, aun encareciendose en dolares, no sean sustituidos por otros productos. De esta forma, aumentaria el deterioro de la cuenta corriente de EE.UU. Por otro, porque con una apreciacion del yuan resultarian mas baratos los productos importados por China (no olvidemos que es un gran importador de materias primas y, cada vez mas, de productos intermedios) que, trasladados a los precios finales en la exportacion, reduciria el impacto sobre las ventas al exterior. Es mas, cabria la posibilidad de que los productos chinos, mas caros en dolares tras una revaluacion del yuan, sean sustituidos por productos provenientes de otros paises, no por productos norteamericanos, dejando invariante la posicion exterior de EE.UU. Por no mencionar que la diferencia de costes salariales es tan favorable a China, que la revaluacion del yuan tendria que ser muy importante para que se dejara notar con claridad en las balanzas comerciales. En definitiva, es posible que las autoridades norteamericanas estan sobrevalorando el papel de China en la resolucion de los desequilibrios de su cuenta corriente.

  13. GK

    Am I correct to conclude that when China’s exchange rate with the dollar inevitably rises to PPP parity by 2017 :
    1) US trade deficit will close, due to fewer imports FROM and more exports TO China.
    2) All the remaining countries poorer than China (India, VietNam, Indonesia) will see upward pressure on their currencies, since too much of the World’s GDP is at high value, and too few poor countries remain.
    3) China’s nominal GDP will be more than the US, making it the largest economy in the world, despite having a per-capita GDP still just one-fourth of the US.
    Are the first two correct? I know the third is correct.

  14. Steven Kopits

    - If I recall correctly, half the trade deficit comes from oil. If we want to reduce the gap, oil would be a good place to start.
    - if we take the Blame-it-on-Beijing approach, the primary risk of an under-valued yuan is too much liquidity and interest rates too low.

  15. Get Rid of the Fed

    GK said: “1) US trade deficit will close, due to fewer imports FROM and more exports TO China.”

    We might import less, but other than food, I don’t see what products we are going to export to china.

  16. Cedric Regula

    Tom has described how the Chinese pseudo peg works the way I have heard it works, but I’ll add a little to the story. If the PBoC really was intervening the traditional way in FX, it would “cost” the central bank a lot of money. But doing it their way, it is almost free. Almost, because they must issue sterilization bonds to counter the inflationary impact of all the RMB printing they do. But this policy does stimulate exports and discourages imports, not to mention new business creation which will localize what were once imports (read…semis, aircraft…watch out Silicon Valley, Japan, Taiwan, Boeing and Airbus). On top of that they have export subsidies and nearly closed financial markets so that capital flows can’t disrupt the Party’s game plan for the RMB that much.
    My understanding of Obama’s discussion on the RMB concluded with the Chinese saying they like what they are doing now and don’t wish to change it…and by the way can you keep your currency from falling.
    Also, I’m not convinced that the USG sincerely wants to change the status quo, since doing so implies losing a large treasury bond customer and some upward pressure on interest rates.
    But maybe they will prove me wrong. I’ll even steal a page from EMs that have introduced a really cool way(from their perspective) of discouraging currency appreciation and suggest this solution to our government. Tax foreign investment in Treasuries. Include the Japanese and any other foreigners that think the USG is a great big piggy bank. Maybe this would help re balance US consumption vs US savings as well.
    But I’m sure someone will point out that this would be bad for the economy. so I’m not holding my breath.

  17. Get Rid of the Fed

    Cedric Regula said: “Also, I’m not convinced that the USG sincerely wants to change the status quo, since doing so implies losing a large treasury bond customer and some upward pressure on interest rates.”

    How about the really rich in both countries like that they are both getting richer and more powerful from this arrangement?

  18. Robustus

    I manage a small, profitable, branded product manufacturing business. Presently, the Chinese, Vietnamese, Indians, and other asian tigers don’t produce in our segment. If and when they do, their US landed cost would be half of ours, as in other US segments where they have elected to compete.
    While our branded consumer shield would forestall penetration temporarily, we ultimately would be forced by our customers to buy offshore to remain competitive, or sell out to a lower cost offshore producer. Realistic exchange rate adjustments would unlikely to affect the adverse cost differential, or the outcome for our company and its 200 dependents.
    I rarely see economists address the implications of such overwhelming production cost differentials across the global economy in detail.
    So, I ask if any economist present has analyzed differential competitive cost factors, and how it is integrated into their assessment of trade balances and exchange rate policy?

  19. kaoo

    Posted by: Tom at November 20, 2009 05:43 AM
    You’re right that yuan appreciation would not nearly solve the entire US-China trade deficit.
    China restricts imports in numerous other ways besides exchange-rate manipulation.
    ———————————–
    You are completely wrong. It’s not China restricts imports, but the U.S. restricts exports. OK?
    You should figure out one thing, according to the comparative advantages, we don’t need the American shoes and clothing, or even cars. We hope to buy high-tech products, which the U.S. government is unwilling to sell to China.

  20. Tom

    GK: Roughly speaking, “PPP” is a way of adjusting GDP to show how it would look in non-US countries if their wage levels were similar to the US. IE, why is a potato more expensive in Switzerland than in India? Because wage levels are higher in Switzerland, which feeds into costs in various ways including taxes and property values.
    I think Chinese wage levels will increase much more slowly than you seem to believe, unless there is some very unexpected democratic revolution.
    Kaoo: I don’t see this as a Chinese vs American issue. Yes, our government restricts some exports to China, because there are obvious limits to how much an undemocratic government can be trusted. Undoubtedly your government sharply restricts imports and not just from the US. When you talk about what China “needs” or “doesn’t need”, you yourself sound protectionist, because the advantages of trade are not in importing only what you can’t produce yourself, but in specializing in what you are best at.
    That said, you’re right that China also has many great advantages, which go beyond cheap labor, and the US has let itself fall behind in many kinds of manufacturing.

  21. Cedric Regula

    Robustus
    You have raised a very valid issue about whether exchange rate policy can make enough of a difference. I’m not an economist, but I’ve had some experience with the subject. I started my career in manufacturing just in time for the Japanese Invasion. At that time Japanese labor was $5 and US labor was about $15. Mitsubishi was the biggy in my industry and was selling competitive product at half our price. I quit and got a job in the defense industry before the company went under. A few years later we finally got the Plaza Accord. But over time, Japanese wages moved towards parity with the US (with the glaring exception of senior management compensation).
    The wage & benefit gap with the Chinese is now something like $3 vs $30-$35 for non-union, and up to $70 if you are union with a stockholder, bondholder and taxpayer subsidy.
    Economists like the currency adjustment method because they say wages are “sticky” and it is easier to give the entire country what amounts to a cut in pay to improve competitiveness. And if you think about it a little bit, it probably isn’t possible to cut pay significantly with out driving everyone into bankruptcy, destroying the tax revenue base and making the consumer, corporations and government unable to service debt. This is the definition of debt deflation, the greatest horror economists have ever known.
    But the math doesn’t work unless the dollar/RMB changes by a huge amount. Or Chines wages go up by a huge amount. But that is not how the Party wants to do it. They say about a third of the country(400 Million) are unemployed or under employed and in extreme poverty. They want to grow GDP and distribute it in $3 pieces to the entire country.
    All well and good, except the export model is still the preferred way of growing GDP. Ergo, a big problem for the ROW.

  22. Anonymous

    Tom wrote:
    The central bank brings to the market lots of freshly created yuan. It uses its dominant position on the market to bid up the price of dollars.
    This makes dollars more expensive for the importer, and thus makes imports more expensive for Chinese people and companies.
    So yes, the importers are overpaying.
    Tom,
    You are right on the mechanics but misleading in your wording.
    China does not “bid up the price of the dollar.” The US debases the dollar. China simply keeps parity with the dollar.
    This does make imports of dollar denominated good more expensive for the Chinese people but they do not just import dollar goods. The dollar has fallen by about 1/3 againt the euro so euro imports are not nearly as expensive as dollar imports. Similar situation with the yen. Chinese imports will shift to euro imports and yen imports while dollar imports will slip.
    So I agree that importers of dollar goods are overpaying, but this is a problem for dollar-world not the Chinese importer or euro-world or yen-world. The longer it takes for the US to wake up to this the more US imports and exports will take a hit.

  23. Norman

    Let me know if there is anything wrong with this reasoning:
    For easy mathematics let us assume that the RMB is 50% undervalued. That means for every dollar that China adds to their foreign reserves they are paying $2 in their own currency. China will be adding $500B to their foreign reserves this year which means they have a $250B loss which equates to about 6% of their GDP. Therefore China’s GDP isn’t growing at 8.5% but rather a paltry 2.5%.

  24. Cedric Regula

    Norman,
    That’s not the way it works. The PBoC has a “dollar surrender law” (if I remember what it’s called correctly. Plus it would be in Chinese anyway).
    This means Chinese companies accept dollars in payment, but cannot legally go to FX and exchange them for Euros, or RMB at a market rate because the PBoC only allows a tiny amount to trade in FX (in case someone wants to go to the Olympics) and Chinese companies must deposit the dollars in a local bank and accept whatever the dollar/RMB exchange rate is that quoted by the PBoC. The PBoC prints up the necessary RMB to make the exchange. That costs nothing but paper and ink. But printing all that RMB would tend to cause domestic inflation(tho probably not now, it would probably fight deflation in the current environment) and in normal times they would sell “sterilization bonds” to mop up excess liquidity. They pay interest on these so that is the only cost the central bank has. The PBoC then buys Treasuries with the dollars and tries to make enough interest to cover their cost of operations. The loop is now closed and they never used an open market mechanism at an open market exchange rate.

  25. HZ

    Tom,
    What do you suppose the West would export to China if Yuan/USD is raised? If there is demand for those goods why aren’t the multinationals already manufacturing them in China to satisfy Chinese needs even without yuan appreciation? Chinese demands are very much in commodities. Yes raising the Yuan would make them more affordable as imports. But they will be also more expensive for the US (for example, oil) and on the balance will not solve US problem. In the end US has excessive demand — put a tax on imports or all consumptions if you like.

  26. Cedric Regula

    HZ
    The West, and Japan multinationals have been localizing production in China. The two largest automakers in China are GM and Volkswagon. Intel is building some sort of semi plant there, but they claim its not a leading edge technology plant. Westinghouse licensed their 3rd gen nuclear reactor design and all the components will be built in China. That’s just a few. Japan has been moving low cost consumer product production there for decades.
    The only thing slowing the exodus to China is they actually have a shortage of skilled workers. The government also demands 51% ownership in the foreign subsidiary, which gives some companies second thoughts. But China does have a free enterprise zone where they are allowing foreign companies to operate 100% owned subsidiaries. And there is no reason that what they make in China stays in China either.

  27. RicardoZ

    If you compare the GDP of countries you will notice that the US is about 3 times that of second place Japan, but China is in third place. There are many who say don’t worry, because it will be a long time before the Chinese economy is as large as the US economy.
    In 1980 China was the 11th largest economy with the US economy about 15 times that of China and China remained there until the 1990s. By 2000 China had climbed to number 6 with the US economy down to about 9 times the Chinese economy. In 2008 China had moved to third only behind Japan with the US economy now only about 3 times the Chinese economy almost the same as Japan. It is interesting to note that other economies have remained about the same relative to the US economy while the Chinese economy has shot up like a rocket.
    If the Chinese economy continues to grow relative to the US as it has in the recent past, it will be as large as the US economy in less than 10 years. I would venture to say that with the current US government destroying growth that the Chinese economy will be as large as the US economy in five years.

  28. don

    Norman and Cedric -
    Norman is essentailly right, in a static sense. The return to China for its exports is its imports plus the value of its dollar loans. To keep it simple, let’s suppose for the moment that the value of the loans does not fade (e.g., they will buy the same amount of corn in future as they would today, plus a premium to compensate for delayed consumption). Then, the cost of the undervalued yuan is the amount received in exchange for the amount exported. If the yuan is 50% undervalued (and assuming full employment in the counterfactual state – a crucial assumption)the value of the receipts will be 50% less than without the undervaluation. That would be the cost of China’s currency policy.
    Now, let’s add some dynamics. Without the export subsidy, China’s exports would be smaller, but so would its entire output. Unemployment is labor completely wasted, as unused labor cannot be stored. Recall Keynes’ insight that the economy can realize an economic gain from hiring men to dig holes and then refill them, owing to the ‘multiplier’ effect. So, the question is, does the gain in output compensate for the cost of China’s export subsidy? In my opinion, it is not even close, and that is why China is so reluctant to surrender the policy.

  29. don

    Menzie -
    The amount of undervaluation seems like a poor place to start. I would ask “what would happen to China’s capital flows if it gave up its currency interventions?” Its current account balance would then become equal to the net private capital outflows. One view (which I agree with) is that, without the export subsidy, you would find much less enthusiasm for investment in China. That would be the dominant source of the offsetting private capital outflow (unless the government took to actively encouraging its residents and companies to invest abroad). Thus, the adverse effect on the CA would be somewhat smaller than the current reserve accumulation. But I doubt if the net private capital outflows would replace even half of the drop (to zero) in official outflows. After all, FDI in China was only $92 billion in 2008. Even pushing this to zero would still result in a current account surplus drop of almost $200 billion. The only question is, with no imminent yuan appreciation, what would happen to so called ‘hot money’ flowing to China. From your graph, though, it does not look like there is much room for that to fall, either, as the difference between the official outflows and the CA surplus is not very big.

  30. Tom

    Anoymous wrote: China does not “bid up the price of the dollar.” The US debases the dollar. China simply keeps parity with the dollar.
    The two aren’t contradictory. The Chinese central bank bids up the price of the dollar in yuan terms on the Chinese domestic exchange market (to the extent that there is a market). That’s the mechanism by which China keeps parity with the dollar as the US debases it.
    HZ: As for what China would import, look at other Asian countries, or other emerging market countries, which have freer trade and see what they are importing. Look at what privileged Chinese classes are buying and imagine if middle-class Chinese could afford the same things. Let me clarify: with free trade and an unmanaged, convertible currency, China’s trade surplus with the rest of the world would come down quickly to zero. The US would not be the sole or even biggest beneficiary (the EU and Japan would be), but the US would get a share of the increased imports market, probably about equal to its share of current imports. Yes believe it or not the Chinese would even buy some US cars! The new money types particularly love our big blingy gas-hog jeeps and trucks. I guess the US has to specialize in something.

  31. James

    I think you people have some misconceptions about how China’s export economy operates. I am an Expat who owns a WFOE inside China. I will explain this to you:
    1. When I export goods to America, I am paid in dollars and these dollars are exchanged for RMB at the bank. The exchange rate is fixed. It is around 6.8RMB per 1USD.
    2. VAT Rebate: (Value Added Tax)This varies by industry. But let’s take Solar parts for example. The VAT Rebate is 17%. The Government will then pay back about 17% of everything that I export (Example $1.00 = $1.17In addition, as WFOE who is investing money inside China I enjoy all kinds of tax exemptions for 3 to 5 years. + Not taxed on materials I import into the country for export.
    3. As a result, this system keeps the price of goods in China artificially low. It benefits foreign buyers.
    4. Couple this with China’s red hot real estate market, 9% growth and red hot real estate market and you have a recipe for economic disaster brewing.
    China cannot adjust it’s currency anymore against the USD.

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