# IIE's Bergsten, Bad Math, & PRC Yuan Intervention

♠ Posted by Emmanuel in , at 5/16/2009 12:42:00 PM
I was very puzzled after reading this statement in a letter to the Economist from Fred Bergsten, director of the Peterson Institute of International Economics. In response to a recent article on China's currency practices, he had this to say:
The punchline to your article on China’s foreign-exchange reserves is that “China cannot sour on the dollar without letting its own currency rise” (Economics focus, April 25th). This is not correct. China can continue to hold down the yuan’s exchange rate by buying dollars but then convert those dollars into euros or other hard currencies. The exchange rate between the dollar and the euro would change but the yuan would remain substantially undervalued.
Sorry, Mr. Bergsten, but it is you who are incorrect. Let's go back to Foreign Exchange 101. All the world's exchange rates are expressed with reference to the US dollar, also known as the "buck" or the "greenback." Now, there are only two possible ways of expressing these exchange rates. You can state how many local currency units are equivalent to \$1. For instance, Japan's currency, the yen, is expressed like so: \$1/¥95. Or, exchange rates are expressed in terms of dollars needed to acquire one unit of the local currency, such as that of the Eurozone: €1/\$1.35.

Whatever it is, the numerator currency always has a value of 1; it is only the denominator currency whose value changes in an exchange rate quotation. That's why the abbreviations here are USD/JPY and EUR/USD, respectively. Now, a "cross rate" is an exchange rate expressed without reference to the dollar. For example, let's consider EUR/JPY. To get this cross rate, we must multiply EUR/USD with USD/JPY so that USD cancels out: (1/1.35)x(1/95) = 128.25 yen for every euro. As you can see, EUR/JPY cannot be computed without reference to the US dollar. Hence, Bergsten is incorrect in stating "China can continue to hold down the yuan’s exchange rate by buying dollars but then convert those dollars into euros or other hard currencies." This is tantamount to saying the yuan cannot possibly revalue in relation to the dollar if official EUR/CNY purchases increase. Of course not: the dollar already is and will always be involved in cross rate transactions.

Further, Bergsten has trouble distinguishing between stocks and flows. What counts more is the latter. As he points out, the US dollar is readily traded. However, nobody cites China using the dollar in international transactions--something virtually everybody does, though China is proposing alternatives--as the basis for currency manipulation. Rather, it is the unparalleled accumulation of dollar-denominated assets like Treasuries (Brad Setser says they're worth \$1.5 trillion and rising) that matters. Using the USD as a vehicle currency has little bearing on its value--this is as true now as when the euro commanded \$1.60. Hence, it is a "flow" concept that local currencies must be exchanged for dollars to transact internationally. What matters more is how proceeds from international transactions are stored--this is a "stock" concept. If the Chinese stop adding to their stock of dollar assets, then dwindling demand for dollars will lower its price.

Finally, remember that China is not the sole entity in currency markets, hard as it is to believe sometimes. So far, its continued patronage of Treasuries and other dollar-denominated assets despite cheap talk to the contrary has, to a significant extent, assuaged others' concerns about holding dollars. It's the PRC as backstop and lender of last resort to the US buoying others' confidence in the greenback. Now suppose this understanding changes. Will the expectations of other dollar holders regarding the future value of these assets remain the same? Of course not. Being a particularly flighty sort, FX traders will start dumping dollars instantly. Go ask Tim Geithner. Hence, we don't need a dramatic sell-off of existing dollar assets by China to get the ball rolling, but only a firm sign of diversification into other currencies.

Here's the bottom line: the Economist could have been more specific in saying "China cannot sour on the dollar without letting its own currency rise...in relation to the US dollar." Bergsten failing to appreciate the nature of foreign exchange only worsened matters. Of course, falling demand in dollar-denominated assets will cause the renminbi to rise in relation to the dollar. It's strange world we live in: a Nobel Prize winner doesn't know how GDP is computed, while a director for an institute of international economics doesn't know what a cross rate is or what the difference is between stocks and flows. These sorts of mistakes you'd expect from undergrads, but from Important Economic Authorities, they are quite unacceptable.

Sorry, Fred Bergsten, but your letter to the Economist merits an "F"!