A Rough Estimate of $F_{damage}$ and the Expected "Should-Be Exchange Rate" of RMB

So, when I mentioned the concept of $F_{damage}$ to my AI assistant, it asked me, "How much do you think China's 'domestic prices' are suppressed?" I replied, "Let's assume a suppression of 1/3 for now, meaning we estimate with $F_{damage}=33\%$."

1. Exchange Rate Verification: The Truth of Structural Undervaluation

1.1 The Paradox and Correction of Purchasing Power Parity (PPP)

Foreign media often argue that the RMB is undervalued based on purchasing power parity (PPP). Their line of reasoning is as follows:

• China unit price ($P_{CN}$): approx. 25.00 RMB (actual price).
• US unit price ($P_{US}$): approx. 5.95 USD.
• Nominal PPP exchange rate: $25 \div 5.95 \approx \mathbf{4.20}$.

This calculation ignores the structural loss factor $F_{damage}$. Within China, the price we observe (the annual price of a basket of representative goods) is the "actual price" after loss. If we want to derive the "should-be exchange rate" of the RMB, we must use the domestic "should-be price" of the RMB, which we refer to as the "ought-to-be price." The observed or statistically recorded domestic price is, of course, the "actual price."

Restoration Formula:

$$\text{应然价格} = \frac{\text{国内价格}}{(1 - F_{damage})}$$

1.2 Ought-To-Be Exchange Rate Calculation

Taking into account $F_{damage} = 0.33$ (a loss multiplier of approximately 1.49), the true equilibrium anchor is:

• Ought-to-be price: $25 / (1 - 0.33) \approx \mathbf{37.31 \text{ 元}}$.
• Ought-to-be exchange rate: $37.31 / 5.95 \approx \mathbf{6.27}$.

Comparison of Conclusions:

• 4.20 (PPP Line): A bloated illusion based on "damaged prices", which extremely exaggerates the strength of the RMB.
• 6.27 (Ought-To-Be Line): The true purchasing power equilibrium point after $F_{damage}$ correction, which is a level of exchange rate relatively close to reality.
• 7.20 (Nominal Line): The price further depressed by the central bank on the basis of the ought-to-be line through regulation mechanisms, in order to hedge against internal loss.

2. Supporting Evidence

This reminds me of a study on the RMB exchange rate that I read a long time ago, conducted by a team led by Lu Zhengwei, an economist at Industrial Bank.

They mentioned distinguishing a "basket of representative goods" into "tradable goods" and "non-tradable goods", especially labor. Then, they proposed a "non-trade-weighted" RMB exchange rate. I recall that in a printed copy of their paper, a rate of 6.2 RMB / 1 USD was mentioned. However, I cannot find that paper for the time being. Fortunately, I managed to find an article he published on the "China Chief Economist Forum" titled The Big Mac Index Lacks Professionalism, and the Undervaluation of the RMB is a Fallacy.

Below I quote a few paragraphs that I deem relatively important:

"Principles of economics tell us that for something to be subject to the 'law of one price', it must not only satisfy the condition of being of uniform quality in both countries, but more importantly, it must be a 'tradable good'. Otherwise, if it is a 'non-tradable good', simply applying the 'law of one price' will lead to misleading conclusions. The degree of tradability of a good or service is related both to its physical properties (those not easily transported across borders have low tradability; conversely, high tradability) and is closely related to the legal regulations of each economy."

Of course, as a veteran who has been working in study abroad services for ten years (by the time I read this article in 2015), I think the following sentence is the real point!

"Many things, although physically easy to transport across borders, can also become non-tradable goods under conditions where the legal regulations of various economies set up many constraints, such as labor and rent."

However, I think Myanmar's Myawaddy and Cambodia in the last two years might not agree, since it is simply too easy for them to recruit labor holding Chinese passports.

"According to research conducted by Parsely & Wei based on data from thirty-four economies from 1990 to 2002, in the cost structure of a Big Mac hamburger, the 'non-tradable' portion, such as labor, rent, and electricity costs, accounts for 55%; the 'tradable' portion, such as raw material costs for beef, cheese, and bread, accounts for only 31%. Among these, labor costs account for 46% of the entire Big Mac hamburger price, making it the single largest source of Big Mac costs, while beef accounts for only 9% and bread for 14%."

"By comparing the aforementioned difference in labor costs between China and the US with the degree of RMB undervaluation, it is found that the trends of the two are basically consistent, and the difference in weighted labor costs is even higher than the degree of RMB undervaluation measured by the Big Mac Index (see Figure 2). Thus, the difference in labor costs between China and the US constitutes the main source of the difference in the retail price of Big Mac hamburgers, and the degree of RMB undervaluation calculated by the Big Mac Index decreases as the difference in labor costs between China and the US narrows.

If the 'non-tradable' portion contained in the Big Mac is excluded, and only the 'tradable' portion that theoretically fits the 'law of one price' is compared, the conclusion reached is completely opposite to that derived from the Big Mac Index: the RMB is not only not undervalued against the US dollar, but is actually overvalued to some extent."

"In fact, considering that labor is the main 'non-tradable' component, the Big Mac Index, by violating economic principles to simply apply the 'law of one price' to the entire hamburger price, in effect rigidly assumes that the per capita income of residents in any economy should be consistent with the US per capita income in USD. Only through such calculation can the obtained exchange rate be reasonable; otherwise, it must be that the lower the income of an economy, the more its calculated exchange rate is undervalued."

All in all, I recall that they actually had a paper calculating that the "non-trade-weighted" exchange rate of the RMB should be 6.2 RMB/USD, meaning the degree of undervaluation compared to the exchange rate back then was not significant.

But what interests me more is what he pointed out: the lower the income of an economy, the more its calculated out exchange rate is undervalued, as well as their proposed "weighted labor costs."

So, this is at least consistent with my intuition: the "damage" in labor prices leads to a lower "$P_{CN}$", which in turn leads to the overestimation of the RMB exchange rate calculated using the so-called Big Mac Index or PPP (purchasing power parity).

Of course, there are far more factors that cause our domestic prices to be suppressed in reality, not just the single item of "weighted labor costs." In fact, if we expand this "weighted labor cost" to the income, welfare, and various rights of labor as a whole, we will deeply understand that the "low human rights advantage" is the recipe for success of the so-called "China Model." It is also the reason why China, through 30 years of reform and opening up—especially after joining the WTO—rapidly developed into the so-called "world factory."

3. Conclusion: China's Export Advantage Does Not Lie in the Exchange Rate

I would like to conclude with a brief "letter to the editor"—China's Export Advantage Does Not Lie in the Exchange Rate—which I published in FTChinese on February 21, 2010:

"Having read the article Who is Footing the Bill for the RMB?, I feel that the core of China's export advantage in tradable goods does not actually lie in the exchange rate. Back when the exchange rate was even lower, Chinese exports were not as booming as they became later after the RMB was allowed to appreciate.

The core of China's export advantage in tradable goods lies in cheap labor. Furthermore, due to China's relatively good primary, secondary, and vocational education, there is a larger pool of qualified labor compared to other developing countries, which is why output is so high. Once labor costs are significantly raised, China's products will no longer be as competitive."

Therefore, to answer everyone in a single, simple sentence at the end: the main reason why foreigners perceive China's exchange rate as overvalued, or feel that the Chinese government has deliberately suppressed the RMB exchange rate, is the cheap domestic prices they observe. And the primary factor causing these cheap domestic prices is the "comprehensive low level of human rights," even though Lu Zhengwei used the term "low weighted labor costs" to mask this social phenomenon of a "low level of human rights."

And what we should understand here is that with the so-called price loss $F_{damage}$, the ones who suffer the most are the people and groups with the least bargaining power in the economy.

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4. International Valuation Space: Measuring $F_{damage}$ via Exchange Rate Differences

From an international perspective, $F_{damage}$ can also be estimated using the difference between the PPP exchange rate and the actual nominal exchange rate:

$$F_{damage}^{国际} = 1 - \frac{E_{PPP}}{E_{nominal}}$$

Taking the RMB as an example:

• PPP exchange rate $E_{PPP} \approx 4.20$
• Actual nominal exchange rate $E_{nominal} \approx 7.20$
• $F_{damage}^{国际} = 1 - 4.20/7.20 \approx 0.417$

This is highly consistent with the $0.33 \sim 0.50$ range we estimated from domestic micro-data.

The "valuation space" between the PPP exchange rate and the actual exchange rate is not a "market deviation," but rather a quantitative expression of the differences in $F_{damage}$ across countries. The lower the income of an economy, the higher its domestic $F_{damage}$ is, and the greater the deviation between the PPP exchange rate and the actual exchange rate will be.