The Relationship between Product Complexity and Exchange Rate Elasticities: Evidence from the People's Republic of China's Manufacturing Industries

More complex products are less substitutable in international trade and may therefore have lower price elasticities. We investigate this issue using 960 types of Chinese manufactured exports to 190 partner countries disaggregated at the Harmonized System 4-digit level. We measure complexity using Hidalgo and Hausmann’s (2009) product complexity index. We find that price elasticities are lower for more complex goods. These results imply that the People’s Republic of China can reduce its exporters’ exposure to tariffs, trade wars, and exchange rate volatility by upgrading its export basket.


Introduction
The People's Republic of China (henceforth PRC) faces tariffs, trade wars, volatile exchange rates, and other challenges. How can Chinese firms sustain their exports in the face of these shocks? Abiad et al. (2018) and Asian Development Bank (2018) noted that products with lower demand elasticities will be less affected by impediments to trade. They also observed that goods that are complex (in the sense of Hidalgo and Hausmann, 2009) are difficult to produce. Thus purchasers need time and effort to find substitutes for these goods. Since finding substitutes is difficult, microeconomic theory indicates that complex goods should have lower price elasticities. Simple goods, on the other hand, are like commodities and are more substitutable. Theory thus implies that they should have larger elasticities.
Only a few studies have examined the relationship between Hidalgo and Hausmann's product complexity index (PCI) and elasticities. Arbatli and Hong (2016) investigated whether more complex exports from Singapore have lower exchange rate elasticities.
Employing a Mean Group estimator and annual data at the Harmonized System (HS) 4-digit level from 1989 to 2013, they reported that products with higher PCIs do have lower elasticities. Thorbecke (2018)  period. He reported that Chinese exports that are more complex according to Hidalgo and Hausmann's measure have lower exchange rate elasticities.
We investigate elasticities not only for the PRC's exports to the U.S. but for its exports to the world. Examining trade elasticities for the PRC's exports to the world obviates misspecification issues that can arise when examining elasticities for the PRC's exports to a single country (see, Ahmed, 2009). We estimate elasticities for the PRC's exports of 960 manufactured goods to 190 countries over the 1995-2018 period. We then investigate whether there is a relationship between products' exchange rate elasticities and their PCIs.
For all goods, we report an export elasticities of -0.67, implying that a 10 percent renminbi appreciation will reduce exports by 6.7 percent. We also find lower elasticities for more complex goods.
In previous work Cheung, Chinn, and Qian (2012) used DOLS to estimate elasticities for the PRC's exports to the world over the 1994Q3-2010Q4 period. Employing the IMF's CPI-deflated real effective exchange rate, they reported that a 10 percent renminbi appreciation would reduce total exports by between 9 and 16 percent, manufacturing exports by between 9 and 15 percent, and primary exports by between 7 and 12 percent. Kato (2015) used panel DOLS and annual data on Chinese exports to 26 countries over the 1995-2011 period to estimate elasticities. He examined Chinese exports of high skill & technology intensive manufacturing products and medium skill & technology intensive manufacturing products. He culled data on exports by skill level from the United Nations Conference on Trade and Development. He found that a renminbi appreciation reduced exports of high skill & technology intensive exports but not of medium skill & technology intensive exports. Xing (2018) investigated how renminbi appreciations and rising wages affect the PRC's comparative advantage in labor-intensive assembly operations. He focused on processed exports, goods that are produced using imported parts and components. He examined two types of processed exports: pure assembly exports (PAE) and mixed assembly exports (MAE). PAE is dependent on low wage labor. According to Xing, PAE is the lowest value added segment of global value chains. Examining the PRC's exports to more than 100 countries over the 1993-2013 period, he found that a 10 percent appreciation of the nominal U.S. dollar/renminbi exchange rate would reduce PAE's share in the PRC's export basket by 24 percentage points and MAE's share by 15 percentage points. He also reported that a 10 percent wage increase in the PRC would reduce PAE's share by 16 percentage points and MAE's share by 11 percentage points. Thus exchange rate appreciations and wage increases would reduce exports more in the PRC's lower value-added regime. Cheung, Chinn, and Qian (2015) examined the PRC's processed and ordinary exports to the U.S. over the 1994Q1 to 2012Q4 period. They employed the Pesaran, Shin, and Smith (2001) bounds testing approach that allows variables to have different orders of integration.
Their exchange rate measures include both the CPI-deflated real exchange rate and the CPIdeflated real exchange rate corrected for feedback from the PRC's trade surplus. For both measures they reported larger price elasticities for ordinary exports than for processed exports. They noted that this could be because ordinary exports are more dependent on local factors of production than processed exports are. Baiardi, Bianchi, and Lorenzini (2015) focused on one particular low-technology export, clothing. They disaggregated clothing exports into individual 4-digit Standard Industrial Trade Classification categories over the 1992-2011 period. They measured relative prices as the ratio of the PRC's export unit value for each 4-digit clothing category at time t to the average export unit value for other key exporters of the same good at time t.
Using system Generalized Method of Moment estimation, they reported that a 10 percent increase in relative prices would reduce the PRC's clothing exports by between 8 and 9 percent.
It is not clear from these and other studies whether the PRC's exports of more complex products have lower elasticities. Our contribution is to investigate this issue systematically using data on the PRC's exports of 960 manufactured goods to 190 trading partners and Hidalgo and Hausmann's (2009) complexity measure.
The next section presents our data and methodology. Section 3 presents the results.

Data and Methodology
The theoretical model informing this investigation is the imperfect substitutes model (see Chinn, 2004Chinn, , 2005. In this framework imported goods are imperfect substitutes for domestic goods. Import demand is a decreasing function of the price of imports (in the importing country's currency) relative to the price of domestic goods. Export supply is an increasing function of the price of exports (in the exporting country's currency) relative to the price of goods in the exporting country. Equating import demand with export supply and using the real exchange rate to relate prices in the two currencies yields the following export function: where Xt represents exports, RERt represents the real exchange rate (importing country's currency per unit of export country's currency), and Yt represents importing country GDP.
The parameter β1 should be negative and larger in absolute value the more elastic import demand is to the relative price of imports and the parameter β2 should be positive.
We follow Abiad et al. (2018) and Asian Development Bank (2018) in positing that purchasers require more time and effort to find substitutes for goods that are difficult to produce and thus that these goods should have lower import price elasticities. If import price elasticities are lower, then the imperfect substitutes model implies that exchange rate elasticities in equation (1)  The approach of Hidalgo and Hausmann (2009) involved employing copious export data to infer a country's capabilities. Building on the Scrabble analogy, they examined not the number of letters that the player has but the complexity of the words they create. To do this, they employed the method of reflections to measure the complexities of economies and products. For an economy, they measured complexity by its diversification. They defined diversification as the number of products that a country exports with revealed comparative advantage (RCA) greater than one. For a product, they measured complexity by its ubiquity.
They defined ubiquity as the number of countries that export the product with RCA greater than one. Intuitively, an economy that exports more products with RCA greater than one is more diversified and a product that fewer countries export with RCA greater than one is less ubiquitous. Higher diversification implies that an economy has more capabilities and lower ubiquity implies that a product requires more capabilities to produce. Formally, diversification and ubiquity can be represented by: where e represents an economy, p represents a product, Mep equals one if an economy e exports product p with RCA greater than one and Mep equals zero otherwise. The method of reflections involves first calculating diversification and ubiquity from equations (2) and (3) and then solving equations (4) and (5) below iteratively: 2 Contributors to this literature include Lewis (1955), Rostow (1959), Kuznets (1966), Kaldor (1967), and Chenery and Taylor (1968). k e,n = 1/k e,0 � M ep p k p,n−1 (4) We use the PCI derived from this approach to measure complexity.  Ilzetzki, Reinhart, and Rogoff (2020) argued that, while the exchange rates of the Chinese renminbi, the U.S dollar, the Japanese yen, and the euro have been eerily stable, volatility could reemerge. If this were to happen, exports of products with lower exchange rate elasticities would remain more stable relative to exports of products with higher elasticities. Stable export flows would allow producers to focus on upgrading their technology and satisfying consumer preferences rather than coping with volatile sales.
Further, protectionist pressures in the U.S. have exploded and led to tariffs on Chinese exports. In standard models, tariffs and exchange rates exert identical effects on export volumes (see, e.g., Krugman, 1979, andEaton andKortum, 2002 We can only estimate equation (7) with fixed effects along three dimensions (j, p, t) instead of four dimensions(i, j, p, t) because the PRC is the only exporting country. As Benassy-Queré et al. did, we also include the importing country's real GDP ( ) as an additional control variable. We cannot include the PRC's real GDP since it is collinear with the time fixed effect ( ). We thus focus on the export equation: We employ interaction terms to investigate whether exchange rate elasticities are different for the PRC's exports disaggregated into the five levels of sophistication: where D1 is a dummy variable equaling 1 if the export category p ranks in the most complex 20 percent (highly sophisticated) and 0 otherwise, D2 is a dummy variable equaling 1 if the export category p ranks between the 60 th and 80 th percentile in the complexity rankings (medium highly sophisticated) and 0 otherwise, D3 is a dummy variable equaling 1 if the export category p ranks between the 40 th and 60 th percentile in complexity ratings (medium sophisticated) and 0 otherwise, and D4 is a dummy variable equaling 1 if the export category p ranks between the 20 th and 40 th percentile in complexity ratings (medium low sophisticated) and 0 otherwise. We also use an equation similar to (9)  We obtain bilateral FOB export data from the PRC to 190 countries at the HS 4-digit level for 960 manufactured goods between 1995 and 2018 from the Atlas of Economic Complexity.
The Atlas in turn collected these data from the UN Comtrade database.
We obtain data on the bilateral real exchange rate between the PRC and each importing countries from the CEPII-CHELEM database 6 . The exchange rate is defined so that an increase represents an appreciation of the Chinese renminbi. We obtain data on real GDP in the importing countries from the CEPII gravity database. 7 Table 1 provides descriptive statistics for the variables in equation (9).

Results
Table 2 presents the results from estimating equation (9). Column (2)  implying that the exchange rate elasticities differ across complexity levels.
In column (2)  Taking averages of the elasticities across columns (2) through (5), the results indicate that a 10 percent renminbi appreciation is associated with a drop in exports of 2.5 percent for the most sophisticated exports, 4.5 percent for medium high sophisticated exports, 6.8 percent for medium sophisticated exports, 8.5 percent for medium low sophisticated exports, and 12.4 percent for the least sophisticated exports. Thus these findings indicate that sophisticated exports such as lubricants, zirconium, and titanium are less sensitive to exchange rates than unsophisticated exports such as natural rubber, sulphur,and prepared fish. The coefficient on PCIRanking is negative and highly statistically significant. This implies that exports of more complex products are less responsive to exchange rate changes.
There is a problem interpreting the coefficient in equation (10) because the regressand is a cardinal measure and the regressor is an ordinal measure. To circumvent this we use PCI values as the right-hand-side variable. We also use a log-log specification so that we can interpret the coefficient as an elasticity. 8 The results are: log(βBRER,i ) = 0.775*** + 0.269** log(PCIValue,i) (11) (0.189) (0.120) No. of observations = 960, Heteroscedasticity and autocorrelation consistent standard errors in parentheses. *** (**) = significant at 1% (5%) level. Adjusted R-squared = 0.133. Standard error of regression = 0.244. Durbin-Watson statistic = 2.12. Dummy variables included for each harmonized system 2-digit category.
The coefficient on PCIValue is positive and statistically significant. This implies that exports of more complex products are less responsive to exchange rate changes. The coefficient indicates that a 10 percent increase in PCI values is associated with a 2.69 percent increase in the exchange rate elasticity.
As a sensitivity check we run a regression analogous to equation (11)  The coefficient on PCIValue is positive and statistically significant. This implies again that exports of more complex products are less responsive to exchange rate changes. The coefficient indicates that a 10 percent increase in PCI values is associated with a 1.27 percent increase in the exchange rate elasticity. The GDP elasticities in Table 2 Table 3 indicate that the income elasticities are typically greater than unity for the two most sophisticated export categories.
One important implication of the findings in this section is that more sophisticated exports from the PRC are less sensitive to exchange rates. This indicates that technological upgrading can help to maintain stability in the volume of the PRC's exports in the face of exchange rate fluctuations.
China's complexity rating based on the approach of Hidalgo and Hausmann (2009) rose from 46 th place in 1995 to 18 th place in 2018. As China's exports are becoming more sophisticated, the results in this paper imply that its exchange rate elasticity will fall. Taking average elasticities across columns (2) through (5) of Table 2 indicates that elasticities for the two most complex categories are -0.45 and -0.25. Assuming that import elasticities are also small, then it seems likely that the Marshall-Lerner conditions will only just hold or not hold at all for China in the future. Thus, depreciations in the real exchange rate will have very limited impact in improving China's trade balance going forward.

Conclusion
Researchers at the International Monetary Fund, the Asian Development Bank, and other institutions have noted that complex products (in the sense of Hidalgo and Hausmann, 2009) have fewer substitutes (see, e.g., Arbatli and Hong, 2016, Abiad et al., 2018, and Asian Development Bank, 2018. For this reason complex goods should have lower price elasticities. Albatli and Hong (2016) is one of the few studies that presents empirical evidence that products with higher product complexity indices have lower exchange rate elasticities.
They found that more complex exports from Singapore decrease less when the exchange rate appreciates than less complex exports do.
We investigate this issue for the PRC's exports over the 1995-2018 period. We employ bilateral data on its exports of 960 products disaggregated to the HS 4-digit level to 190 partner economies. We find that a 10 percent appreciation of the Chinese yuan reduces total exports by 6.7%. We also find that more sophisticated exports as measured by their PCIs are less exposed to exchange rate appreciations.
There should be a relationship between how exchange rates affect exports and how tariffs affect them. In theory, exchange rates and tariffs exert identical effects on export volumes. The results in this paper thus imply that more complex products will be less exposed not only to exchange rates but also to tariffs and other factors affecting the PRC's export prices.
The PRC's manufacturers are buffeted by volatile exchange rates, tariffs, trade wars, and other factors. Producing more sophisticated products can help to stabilize the flow of manufacturing exports in the face of these shocks. The Chinese government has employed trade and industrial policies to upgrade its industries (Huang, Salike and Zhong, 2017).
These policies helped the PRC's economic complexity ranking, as measured using the method of Hidalgo and Hausmann (2009), to increase from 46 th in the world in 1995 to 18 th in the world in 2018. To maintain stability, the PRC should continue upgrading its industrial structure and advancing towards the technology frontier.    (3)), MIT Observatory of Economic Complexity rankings (column (4)), MIT Observatory of Economic Complexity values (column (5)). The regressions include the PRC's manufacturing exports (960 goods) disaggregated at the HS 4-digit level to 190 countries over the 1995-2018 period. These exports are divided into five complexity levels using the four methods listed above. The real exchange rate is interacted with dummy variables for four complexity levels.
The regressions also include time and importer-product fixed effects. All variables are measured in natural logarithms. *** denotes significance at the 1% level using clustered standard error at importing country level.  (3)), MIT Observatory of Economic Complexity rankings (column (4)), MIT Observatory of Economic Complexity values (column (5)). The regressions include the PRC's manufacturing exports (960 goods) disaggregated at the HS 4-digit level to 190 countries over the 1995-2018 period. These exports are divided into five complexity levels using the four methods listed above. Real GDP is interacted with dummy variables for four complexity levels. The regressions also include time and importer-product fixed effects. All variables are measured in natural logarithms. *** denotes significance at the 1% level using clustered standard error at importing country level.