# Back of the Envelope Estimates of Chinese Trade Elasticities

And pitfalls in partial equilibrium analyses

Following up on my previous post, I want to examine what would happen if the Chinese yuan appreciated in real terms, either because of nominal appreciation, or because of more rapid inflation in China versus its trade partners. Here are some back of the envelope estimates.

Figure 1: Chinese trade balance (blue), and China-US trade balance (red), in billions of USD, at annual rates, not seasonally adjusted. NBER defined recession dates shaded gray. Source: For Chinese trade balance, IMF, International Financial Statistics, and ADB, Asia Regional Integration Center; for China-US trade balance, BEA/Census via St. Louis FRED II; NBER, and author’s calculations.

The Macroeconomically Uninteresting US-China Balance

First, consider what would happen to imports to the US originating from China. Assume, as in a standard elasticities approach augmented with a supply factor [0], that exports are a function of partner country income, the real exchange rate, and cumulated foreign direct investment. Then the implied error correction specification is:

Δ exp t = β 0 + φ exp t-1 + β 1 y t-1US + β 2 q t-1 + β 3 z t-1 + γ 2 Δ y USt-1 + γ 3 Δ y USt-2 + γ 4 Δ q t-1 + γ 5 Δ q t-2 + γ 6 Δ z t-1 + γ 7 Δ z t-2 + u t

Where exp is log US real imports from China, yUS is log real US GDP, q is the log CPI deflated bilateral exchange rate, and z is cumulative FDI. Exports have been converted into real terms by deflating by the core PPI. Seasonal dummies are included (very important!).

Estimating this over specification over the 2000Q1-2009Q4 period yields an adjusted R2 of 0.94, SER=0.034, and passes a LM test for serial correlation of order 2, at the 10% msl. The implied long run price elasticity is 1.02 (and is statistically significant). The rate of reversion is 0.3 per quarter, implying a half-life of a deviation is 2 quarters. (By the way, the selection of the sample period is almost completely arbitrary; the data could be extended backward to about the mid-1990′s. However, I wanted to focus on recent behavior, spanning mostly China’s participation in the WTO.)

In terms of US exports to China, a comparable error correction specification, incorporating one lag of first difference terms, leads to an estimated long run coefficient of 1.7 (with standard errors of 0.2, estimated via nonlinear least squares).

In words, this means a 10% appreciation of the bilateral yuan, holding constant other currencies, leads to a 10% reduction in US imports of Chinese goods in the long run, and a 16% increase in US exports of goods to China. To get an impression of the dollar magnitudes (keeping in mind the elasticities pertain to real quantities), US imports of Chinese goods from 2009Q3-10Q2 was \$323.6 billion, and US exports of goods to China over that same period was \$80.3 billion. Mechanically applying these long run elasticities to these values implies something like a \$45 billion change. Of course, an exchange rate change itself should change the price of US imports from China (this is called exchange rate pass through), which would mean the dollar price of US imports from China would rise; if pass through was 25%, then, 0.25×0.10x(323.6-32.4) = \$7.3 billion (a similar calculation can be undertaken for US exports to China, but this would be a smaller dollar amount, given the smaller amount of US exports to China). In other words, by this calculation, the impact on the US-China nominal bilateral trade balance would in this case be less than \$45 billion.

However, the ceteris paribus assumption is unlikely to hold . It is likely that even if the US-China trade balance were to be affected (which it would be in real terms), the overall US trade balance would likely be little affected, since that is driven by domestic saving-investment balances (as in the macroeconomic balance approach), and the value of the US dollar relative to a broad basket of currencies.

Chinese Total Exports

The preceding argument explains why macroeconomists tend to focus on overall trade balances. What about overall Chinese trade flows? Turning first to the Chinese exports, note that once one detrends real Chinese exports, one can see the negative relationship between exports and the value of the real value of the CNY.

Figure 2: Detrended log real Chinese exports (blue), and log real trade weighted value of CNY (red). Detrending: log real exports – 6.06xlog rest-of-world GDP – 0.51xlog cumulative FDI, coefficients estimated over the 2000Q1-10Q2 period, quarterly dummies and constant included. Source: For Chinese trade balance and trade weighted value of CNY, IMF, International Financial Statistics, and ADB, Asia Regional Integration Center; and author’s calculations.

In order to more formally investigate the relationship between these variables, once again use an error correction specification, where now exp is now total Chinese goods exports, and y* is rest-of-world log GDP, and q is the log trade weighted exchange rate for the China (CPI deflated, from the IMF).

Δ exp t = β 0 + φ exp t-1 + β 1 y t-1* + β 2 q t-1 + β 3 z t-1 + γ 0 Δ exp t-1 + γ 2 Δ y *t-1 + γ 3 Δ y USt-2 + γ 4 Δ q t-1 + γ 5 Δ q t-2 + u t

Estimating this over specification over the 2000Q1-2009Q4 period yields an adjusted-R2 of 0.94, SER=0.032, and passes a LM test for serial correlation of order 2, at the 10% msl. The implied long run price elasticity is 0.75 (and is statistically significant). The rate of reversion is 0.46 per quarter, implying a half-life of a deviation is a little over 1 quarter.

This 0.75 long run elasticity is higher than the Cheung et al. (2010) estimate of between 0.34 to 0.64, estimated over the 1993-2006 period, but lower than the Ahmed (2009) quasi-long run elasticity of 1.8, estimated over a sample ending in 2009 (Ahmed’s figure is for growth rates on growth rates, since he uses a first differences specification).

I was unable to obtain a reasonable estimate of a price elasticity for Chinese imports. This result might be in part due to inappropriate aggregation of ordinary and processing imports, but I think that is only part of the story, since in Cheung et al. (2010), we are unable to obtain sensible price elasticities even after disaggregation.

In words, holding all else constant, a 10% appreciation of the trade weighted real value of the yuan will induce a 7.5% reduction in Chinese exports. To get a feeling for the quantities involved, Chinese nominal exports in the 2009Q3-10Q4 period were \$1.385 trillion. A 7.5% reduction of this amount is \$104 billion; but a change in the value of the yuan should induce a partially offsetting \$32 billion increase in total nominal value of exports (assuming 25% pass through, and 10% appreciation). The net dollar impact would then be only about \$72 billion. This is not an unsubstantial impact, given 2009Q3-10Q2 trade balance was \$155.6 billion (or the \$200 billion forecast by China Economic Quarterly, or \$212 billion in the IMF’s Article IV review of China). On the other hand, it is substantially less than the \$170 billion impact on the Chinese current account for a 10% real appreciation estimated by Cline (2010). This divergence is consistent with the differences in implied elasticities; the implied export elasticity in Cline’s study is 1.3 (versus 0.75 here). Note that Cline assumes a unitary price elasticity of Chinese imports, while "http://www.federalreserve.gov/pubs/ifdp/2006/861/default.htm">Marquez and Schindler, Cheung et al. (2010), and I (in this analysis) have not been able to obtain a correctly signed coefficient for Chinese imports, let alone a unit elasticity.

Caveats

This is a weblog post, so I have cut many corners in this analysis — mostly because I don’t have ready access to all the relevant data. In the interest of full disclosure, here are the things I would fix before ascribing more to these results.

• Imports and exports are aggregated in terms of ordinary versus processing goods; one would want to disaggregate and examine the components’ behavior.
• The results could be further tested for robustness against changes in sample periods, and in lag specifications.
• The bilateral trade results (US-China) use only US data, and do not cross-check the results against the use of Chinese data (see Schindler and Beckett (2005) for discussion).
• The bilateral trade results (US-China) do not include third country effects, in particular those associated with exchange rates (in Cheung et al. (2010), the third country exchange rate index coefficient is not statistically significant, but is economically large in certain instances).
• The results are not checked against the use of an alternative deflator (the US core PPI is used; in Cheung et al., we use a variety of deflators for robustness checks).
• The trade weighted value of the CNY are divisia indices (see discussion here); if one used actual levels and trade weights, as suggested by Thomas, Marquez and Fahle (2008), one might obtain different results. In addition, using a unit labor deflator would likely lead to yet a different result (see the IMF’s Article IV report, p.19, for a graph.)
• I have used simple seasonal dummies to account for the seasonality in Chinese data; however, it is not clear that these quarterly dummies are sufficient to fully address the issue.
• In terms of the calculations of nominal magnitudes, much hinges on the pass through coefficient. CBO (2008) places the pass through in the 0.35 to 0.55 range, while my simple correlation in 2008 placed the pass through coefficient at about 0.25 [1].

Concluding Thoughts

The above estimates are clearly not definitive (after all, they’re not peer reviewed, and as serious economists, we want to give greater weight to peer reviewed analysis). Rather, I wanted to show how these results were obtained, and how disagreements arise over the specific impacts. In my view, the main disagreements are not over the point estimates (although those are nontrivial). Rather, the disagreements are driven mostly by the (usually unstated) ceteris paribus assumptions.

In the case of the China-US balance, much hinges on (i) what happens in the rest of the US economy, and (ii) what happens to the other bilateral exchange rates in addition to the USD/CNY rate. Item (ii) clearly is important. Estimates in Cheung et al. suggest that the impact of a CNY revaluation on the US-China trade deficit will be larger if the other currencies remain fixed — but only because some of the US-China bilateral deficit will be reallocated to these other competing countries.

In the case of the Chinese overall balance, we see that the impact of a CNY appreciation is, while nontrivial, not sufficient alone to eliminate the Chinese trade balance, especially over time. Moreover, a reduction in the Chinese trade surplus does not necessarily match up necessarily with a reduction in the US trade deficit. In fact, if other East Asian currencies revalue as the CNY revalues, then the implied reduction in Chinese exports is less, but the implied reduction in the US trade deficit is greater (since the trade weighted dollar would fall more). In other words, in discussing the impacts these exchange rate changes, the differences in conclusions are sometimes as much driven by these auxiliary assumptions as by the elasticities of primary focus.

Previous posts on Chinese trade balance and revaluation: [2], [3], [4], [5], [6], [7], [8], [9]. See also Aziz and Li (2007), also couched in cointegration framework. My argument that currency revaluation is a necessary adjunct to other macro policies is contained in this paper.

## 11 thoughts on “Back of the Envelope Estimates of Chinese Trade Elasticities”

1. MarkS

Thanks Menzie for the thumbnail ratios for import/export effects of CNY appreciation. Thanks also for restating the obvious, that the US dollar has to devalue against most currencies (its overall trade weighting), rather than against the Renmembi alone.

2. 2slugbaits

Menzie: You said that deterministic seasonal dummies were very important. And you emphasized this point. Since the model is nonstationary in levels form, would it have made a difference if you had assumed seasonal first differences? In other words, do we know that seasonality effects are stationary as is implied with using deterministic dummies? I can’t think of any obvious intuitive reason why deterministic seasonal dummies would not be adequate, but when you get very high R-squares in an ECM you have to worry about some hidden spurious correlations.

3. Menzie Chinn

2slugbaits: Good question. In other instances, I have tried to deal with seasonality in a variety of manners. I’m not sure the issue is integration of the seasonal component. If one looks at the data, it looks like the seasonal shrinks in importance over time. (See this post for discussion of use of X-12, on monthly data), so it’s a different sort of nonstationarity.

Dropping the seasonal dummies in, for instance the Chinese exports ECM, reduces the adjusted R-squared from 0.94 to 0.74. The error correction term coefficient is still negative and statistically significant, so I suspect the results are not being driven by spurious correlation in the Engle-Granger sense.

4. don

“the overall US trade balance would likely be little affected, since that is driven by domestic saving-investment balances”
What Krugman said about “immaculate transfers (and his criticism of Joe Stiglitz, when he made that mistake (“Oh, my…”)
Agree, though, that the issue is more profitably expressed in terms of capital flows. Currency interventions conducted by a country with strict capital controls and a nonconvertible currency result in a large corresponding increase in its net capital outflows. Thus, for example, a reduction in Chinese official purchases of \$300 billion per year would result in a comparable change in its net current account. To argue that this net change would find no sizable counterpart in the China – U.S. trade balance, despite the importance of U.S. trade in the overall Chinese total, seems unlikely to me.

5. Menzie Chinn

don: You truncated the quote in a misleading fashion. Let me more accurately quote myself: “…since that is driven by domestic saving-investment balances (as in the macroeconomic balance approach), and the value of the US dollar relative to a broad basket of currencies.” That statement should make it clear that I believe relative prices are important, as I have stated on numerous occasions.

My point is that changing the US-China relative price (aka the bilateral real exchange rate) will have some impact on the overall US trade balance, but to have a big impact, the change must be noticeable in the US effective exchange rate. In technical terms, one needs to make a guess on the reaction function of other East Asian countries with respect to their currencies. If China as first mover provides cover for the other countries, then we will get a substantive impact. I don’t think that’s a controversial point, but it is one that is often obscured in popular debates.

On the net capital outflow issue, why does it have to manifest itself in dollars, even if the trade surplus is with the US?

6. rayllove

I’m just glad that Menzie ‘did’ “cut many corners in this analysis — mostly because I don’t have ready access to all the relevant data.”
Because… this conversation is causing my brain to swell. I suppose a person’s brain becomes conditioned to this strenuous sort of activity over a long period of time but my brain has had enough for now.
In short, I think this all means that the US is trying to put as much blame on the Chinese as possible for the recent AAA fraud fiasco so as to clear the way for a debt shift via inflation in an effort to create jobs while making the non-investment class in the US more competitive with foreign labor without diminishing the needed hegemony to gain global market share for the investment-class in the US and the other developed nations but like I said, my brain is swollen so I could be missing something here. But I think that is what this means: “Δ exp t = β 0 + φ exp t-1 + β 1 y t-1US + β 2 q t-1 + β 3 z t-1 + γ 2 Δ y USt-1 + γ 3 Δ y USt-2 + γ 4 Δ q t-1 + γ 5 Δ q t-2 + γ 6 Δ z t-1 + γ 7 Δ z t-2 + u t”
But it could mean anything?

7. ReformerRay

Simple minded me would raise the prior question: “Does it make sense to talk about trade elasticies?” I am stuck on the view that elasticies refer to a change in the quantity taken as a result of change in price”. S-I is not a measure of quantity taken or of price. Ditto for current account balance.
It is easy to accept the causation assummption that price controls quantity taken. We have no prior intuition as to the direction of causation when CAP = S – I. A discussion of the direction of causation should precede a discussion of elasticities.
Change in the quantity taken has some influence on price but so many other factors influence price of goods that we have no interest in calculating the effect of quantity taken on price (an inelastic supply of a good provides an exception).
Causation must be established before elasticities calulations make sense.

8. Ekim

Long story short, if Chinese citizens have more purchasing power, they will be able to buy more.
Their purchasing power is low because their central bank extracts a lot via the printing press. State run companies also don’t send the profits to shareholders to spend (a big part of Chinese savings), or pay their workers very much. Chinese citizens also save more, because they have to provide for their own old age.
Convincing the Chinese central bank to extract a bit less purchasing power (stop pegging the renminbi to the dollar) addresses one of the factors. The Chinese are trying to address domestic printing by encouraging their citizens to buy more gold, but this only puts Chinese gold miners to work.

9. don

Menzie: Didn’t mean to misrepresent – jumped to an unwarranted conclusion, probably caused by so often hearing the argument from pundits (such as Roach).
“On the net capital outflow issue, why does it have to manifest itself in dollars, even if the trade surplus is with the US?”
I don’t think it does, but I think that a nontrivial part of the reduction in China’s net capital ouflow (or the other side of the coin, the net reduction in China’s current acount surplus) would be reflected in a corresponding change in U.S. net capital and trade flows. I doubt that the change would be matched by completely offsetting changes in net saving in other Asian countries, with no effect on U.S. trade (as commonly asserted by pundits). I think a neutral guess would be that China’s trade partners would share the drop in its overall surplus more or less in line with their trade shares. If China’s official interventions take the form mostly of dollar asset purchases, it would be reasonable to expect the effect on U.S. to be larger than this neutral share, because currencies are not perfect substitutes for each other.
Some time ago, I posited why China did not buy yen, and indeed, Japan reacted exactly as I predicted. But I think the move was a masterstroke on China’s part – I didn’t foresee that Japan might be pushed back into direct official intervention, which complicates the strategy of branding currency manipulators.
Ekim: “The Chinese are trying to address domestic printing by encouraging their citizens to buy more gold, but this only puts Chinese gold miners to work.”
Commodity purchases can do the same for the international competitiveness of China’s manufacturing sector as purchases of foreign exchange. So can direct foreign investments by its sovereign wealth funds. And the way central banks seem intent on debasing their currencies, these may be a better investment strategies. We might expect to see more such actions if China is sufficiently pressured to ease up on currency purchases.
As Krugman has said, China is behaving badly, and needs to be seriously dissuaded from its current path. Too bad Ben is undertaking a substantively like strategy.

10. rayllove

Don,
Perhaps in the future the three little pig story will be modernized to include a little pig who lives in a ‘glass house’.
Too many short-view policies have left the US in a weak position in relation to the Chinese.