For years, various policy analysts and policy makers have asserted that the Chinese currency, the Renminbi (RMB), is substantially undervalued (Goldstein 2007). The observers in this camp generally point to the large and – until recently expanding – Chinese trade surplus as prima facie evidence in favour of this argument [1]. The burgeoning foreign exchange reserves have only reinforced this view.

In Cheung, Chinn and Fujii (2007), we make the uncontroversial point that currency misalignment can only be evaluated formally within the context of some sort of economic model. The controversy arises when determining which model to use. Policymakers facing political, diplomatic, and operational pressures often appeal to models in the Mundell-Fleming framework, where trade balances and reserve accumulation play a central role. Alternatively, one can appeal to long run models, such as purchasing power parity (PPP) or its variants, which might incorporate non-tradable goods, wealth effects, and productivity trends. The dispute over which model is most useful depends in part on the time horizons that policy makers are interested in.

Consequently, we cannot argue that there is a correct model to use. However, we do feel that we can use a relatively uncontroversial model to highlight two major insights that are relevant to economists in both the policy and academic realms:

- It’s important to account for statistical uncertainty when considering point estimates.

- Data uncertainty complicates analysis in subtle ways.

We suspect that many readers will find either the first point or the second point unsurprising, but seldom both. In our experience, policymakers are more acutely aware of the latter, while academics the former.

In order to highlight these two points, we exploit a well-known relationship between deviations from absolute purchasing power parity and real per capita income using panel regression methods. By placing the RMB in the context of this well-known empirical relationship exhibited by a large number of developing and developed countries, over a long time horizon, this approach addresses the question of where China’s real exchange rate stands relative to the “equilibrium” level.

# Statistical uncertainty

As previously noted, it is common to calculate the numerical magnitude of the degree of misalignment, perhaps noting a range of estimates. In Cheung, Chinn, Fujii (2007), we estimated the degree of misalignment using the per capita income/price level relationship, but in addition measured the degree of statistical uncertainty. In this respect, we extended the standard practice of considering both economic and statistical significance in coefficient estimates to the prediction dimension. The estimated relationship is:

r = 0.13 + 0.30y

where *r* is the “price level”, relative to the US level, and *y* is per capita income in PPP terms also relative to the US. Both the intercept and the slope coefficient are statistically significantly different from zero.

# China’s currency is not statistically significantly misaligned

In Figure 1, we show the bivariate relationship between the price level and real per capita income (both in PPP terms), obtained using the 2006 vintage of the World Development Indicators. The solid line is the regression line. The long dashed line is the one standard error interval, while the short dashed line is the two standard error interval.

**Figure 1**. Price level and real per capita income

It is clear that there is a statistically significant relationship. The red line shows the trajectory of the Chinese currency, insofar as information available in 2006 indicated. Despite the fact that the extent of misalignment is substantial – on the order of 50% – it is also clear that China’s currency is not statistically significantly misaligned.

Notice that the deviations from the conditional mean are persistent; that is, deviations from the real exchange rate-income relationship identified by the regression exhibit serial correlation. Jeffrey Frankel [2] (2006) makes a similar observation, noting that half of the deviation of the RMB from the 1990 conditional mean persists in 2000.

This finding has an important implication for interpreting the degree of uncertainty surrounding these measures of misalignment. We estimate the autoregressive coefficient in our sample at approximately 0.95 on an annual basis. A simple, ad hoc adjustment based upon the latter estimate suggests that the standard error of the regression should be adjusted upward by a factor equal to 2. Consequently, one would conclude that the Chinese currency is not misaligned, even using a 50% significance level that some policymakers have suggested as a more appropriate cut-off.

We further assess the robustness of the results in the presence of several conditioning variables. These additional factors include demographic variables, measures of trade openness, policy factors such as the extent of capital controls, and institutional factors. While these conditioning variables exert significant effects, their inclusion does not change the basic message: The RMB does not appear to be undervalued by this criterion.

There is of course another way to view these results; namely that we could not reject the null hypothesis that the RMB is undervalued by 20%. The message we took from these findings is that a certain degree of circumspection was necessary when making declarations, one way or the other, regarding misalignment.

# Data uncertainty: The impact of the World Bank’s GDP revision

In a recent paper (Cheung, Chinn, Fujii 2008) we repeated our basic analysis, using the 2008 vintage of data. This revised version of the data incorporated updated estimates of China’s GDP and price level. The new benchmark data from 2005 resulted in a 40% reduction in China’s estimated GDP per capita and a corresponding increase in the estimated price level. As a consequence, using the earlier vintage of data, and our previously estimated regression line, the RMB misalignment is eliminated. However, taking proper account of this measurement issue involves a slightly more involved approach, because data for many countries were substantially revised as well. This means that we need to re-estimate the regression.

Re-estimating the price level–income relationship, we find a smaller impact of income on relative prices than obtained using the earlier data. The coefficient drops from 0.3 to 0.2; however, the estimated coefficients remain statistically significant. The estimated relationship is shown in Figure 2, along with the corresponding confidence bands.

**Figure 2**. Price level and real per capita income, revised

Given the change in the sample period and the change in the estimated coefficients, one would not be too surprised to find the estimated misalignments change. However, the magnitude of the change is surprising. Essentially, as of 2006, there is no significant misalignment, in either the economic or statistical sense. The undervaluation is on the order of 10% in log terms, and the maximum estimated undervaluation is in 1993.

These results speak for themselves. When the data themselves are subject to substantial measurement error, one needs to be particularly circumspect in making policy conclusions. We have not considered how to formally integrate the two types of uncertainty, but it is clear that both types are important.

# References

Cheung, Yin-Wong, Menzie Chinn, and Eiji Fujii, 2007, “The Overvaluation of Renminbi Undervaluation [3],” *Journal of International Money and Finance *26(5) (September 2007): 762-785. Also NBER Working Paper No. 12850 [4].

Cheung, Yin-Wong, Menzie Chinn, and Eiji Fujii, 2008, “Pitfalls in Measuring Exchange Rate Misalignment: The Yuan and Other Currencies [5],” NBER Working Paper No. 14168.

Frankel, Jeffrey, 2006, “On the Yuan: The Choice between Adjustment under a Fixed Exchange Rate and Adjustment under a Flexible Rate [6]”, CESifo Economic Studies 52 (2), 246-75.

Goldstein, Morris, 2007, “A (Lack of) Progress Report on China's Exchange Rate Policies [7]”, Working Paper 07-5 (Peterson Institute for International Economics).

Wang, Tao, 2004, “Exchange rate dynamics [8],” in Prasad, Eswar (Ed.), China’s Growth and Integration into the World Economy. Occasional Paper No. 232. IMF, Washington, D.C., pp. 21-28.