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The World Bank released the latest purchasing power parity (PPP) estimates of GDP on April 30. These estimates are published once every 5 to 6 years, based on the elaborate survey of prices across the world conducted by the International Comparison of Prices (ICP) project. The latest estimates pertain to the year 2011, while the previous estimates were for 2005. The new data affords an opportunity to revisit that hardy perennial of global policy questions: To what extent is the Chinese currency undervalued?
And our surprising answer is: perhaps not at all. We can say with some confidence that the renminbi is now fairly valued, which is a striking change from even 2005, when the currency was undervalued by nearly 30 percent. This change possibly heralds the end of nearly two decades of China's mercantilist development strategy based on boosting exports by keeping the currency artificially low.
The methodology for estimating currency undervaluation and overvaluation using PPP estimates, as well as the contrast between the PPPbased and other macroeconomybased approaches by Cline (2013) and Gagnon (2012), are discussed in greater detail in Subramanian (2010). Here we only present the results derived from the PPPbased approach.
The basic idea underlying the PPPapproach is that there is a positive relationship between prices and income per capita known as the BalassaSamuelson effect: Poorer countries usually have lower prices in the nontradable goods and services sector and hence a lower general price level, which allows resources to flow to tradable sectors: A low price level thus reflects a depreciated exchange rate. This relationship is stable enough to provide a benchmark: For a given level of income, we can infer what the level of prices and hence the equilibrium exchange rate should be. Prices below this level indicate undervaluation, and above this level, overvaluation.
The BalassaSamuelson Relationship
Note: A country below (above) either line has an under (over)valued exchange rate.
For the purpose of this post, we use two different ways to determine this benchmark: a linear regression, where the price level is simply a linear function of GDP per capita, and a quadratic function, where we take into account the fact that this relationship is weak for poor countries (and hence the downward sloping part of the curve) and robust for emerging markets (the upward sloping part).^{1} The figure illustrates the two models.
We estimate the relationship for two different samples, and given our agnosticism on the choice of the "right" sample or model, we express our main result as an average of those four estimates (2 models times 2 samples). ^{2} Given the error margins intrinsic in such estimations, broad trends rather than precise numbers should be the important takeaways from our analysis.
For China, we find that the renminbi was only slightly undervalued in 2011—by around 1.7 percent, and even possibly overvalued (see table) if we are to believe the quadratic model.
Benchmark years  GDP per capita (in PPP dollars)  Linear model  Quadratic model  Average undervaluation (percent)  



Sample 1 (percent)  Sample 2 (percent)  Sample 1 (percent)  Sample 2 (percent)  


2005  4,802  34.5  35.0  23.9  19.4  28.2  
2011  10,057  9.7  9.8  2.7  10.0  1.7  


For 2005, using the same methodology, the average currency undervaluation was about 28 percent. In other words, the correction of China's current account surplus—which rose from 6 percent of GDP in 2005, peaking at 10.1 percent in 2007, before falling to 1.9 percent in 2011—was indeed accompanied by a real appreciation by 27 points relative to the benchmark.^{3}
The ICP data relate to 2011. However, we can use the estimates for 2011 and project the equilibrium valuation for 2014. Between 2011 and endMarch 2014, China's per capita GDP grew about 13 percentage points faster than the United States, which should translate into an appreciation of around 3.2 percent.^{4} The actual real appreciation of the renminbi between end2011 and March 2014 was about 7 percent according to the Bank for International Settlements. This suggests that the average undervaluation until 2011 of about 1.7 percent has been effectively eliminated since then by the renminbi's appreciation (over and above the level required by China's GDP growth). The renminbi in 2014 is thus fairly valued.
This estimate is of potential historic significance. Provided China does not reverse its exchange rate policy, by lapsing back into largescale intervention and engineering renminbi depreciations as it is doing now, it will have put behind the pillar of its development strategy, which has involved maintaining a cheap currency to boost exports. The significance of our estimates, based on the most recent data released, is this: Not only are broad macroeconomic aggregates (for example, the current account deficit) moving in the right direction, but underlying relative price movements (and signals) seem to have shifted in a way to stop the flow of resources into export sectors, which now allows China to proceed with its rebalancing strategy. Put differently, there is room for cautious optimism that imbalances will not reemerge because underlying fundamentals are being addressed.
The end of Chinese mercantilism—and relief for the rest of the world—may be in sight.
Notes
1. Technically, the linear model is expressed as: ln (Pi) = α + β ln (Yi) + εi, where P and Y are the price and income per capita levels for each country, and the quadratic model is ln (Pi) = α + β ln (Yi) + γ (ln (Yi))^2 + εi. To be consistent between the 2005 and 2011 estimations, we normalize the price level to that of the United States.
2. Sample 1 excludes oil exporters and sample 2 additionally excludes small countries (population below one million inhabitants) and those which were not part of the benchmark in the 2005 round (all of which can potentially have problematic price level data). We also ran the regressions for a sample including all countries and the results remain broadly similar. The chart corresponds to sample 2.
3. It is true that in 2011 China intervened heavily in foreign exchange markets, to the tune of about $450 billion, but any impact from this action on underlying prices—which is captured in a PPPbased approach—would have taken some time.
4. The linear model yields a slope of 0.246—so the expected appreciation is 0.246*.13=3.2 percent. Other models point to a slightly lower value.