A gravity model for global value chains

The gravity model

A typical tool in assessing bilateral trade’s causes and effects may be the gravity model. In a recently available paper (Baldwin and Taglioni 2011), we show that the gravity equation isn’t valid for trade flows where trade in parts and components is important.

The essential point is easy.

  • The typical gravity equation comes from a consumer expenditure equation with the relative price eliminated utilizing a general equilibrium constraint (Anderson 1979, Bergstrand 1985, 1989, 1990).
  • As such the typical formulation and empirical application (Anderson and van Wincoop 2003) is most beneficial adapted to explaining trade in consumer goods.

When consumer trade dominates, the GDP of the destination nation is an effective proxy for consumer demand; the GDP of the foundation nation is an effective proxy of its total supply.

  • When international trade in intermediate goods dominates, the utilization of GDPs for the supply and demand proxies is less appropriate.

Consider, for example, the determinants of Thai imports of auto parts from the Philippines. The typical formulation would use Thai GDP to describe Thailand’s import demand, however, the underlying demand for parts is generated by Thai gross production of autos, not its value-added in autos. Given that the ratio of local to imported content will not change, value added is an acceptable proxy for gross output, therefore the standard regression will probably give reasonable results. However, for regions where production networks are emerging, value added should be expected to become a poor proxy for consumer demand.

We utilize the Krugman and Venables (1996) model to explore the impact of allowing intermediates trade in the gravity model. The main element differences arrive in this is of the economic “mass” variables since purchases are actually driven both by consumer demand (that income may be the demand shifter) and intermediate demand (that total production may be the demand shifter).

This observation generates several testable hypotheses.

  • The estimated coefficient on the GDPs ought to be lower for nations where parts trade is important, and really should fall as the need for parts trade rises.
  • As vertical-specialisation trade is becoming more important recently, the GDP point estimates should now be lower.
  • In those cases where in fact the GDPs of the trade partners lose explanatory power, bilateral trade ought to be increasingly well explained by demand in third countries.

For instance, China’s imports should shift from being explained by China’s GDP to being explained by its exports to, say, the united states and the EU. There are two means of phrasing this hypothesis. First, China’s imports certainly are a function of its exports instead of its GDP. Second, China’s imports certainly are a function folks and EU GDP instead of its, since US and EU GDP are critical determinants of their imports from China.

Gravity when parts-and-components trade is important

To consider these conjectures empirically, we estimate the typical gravity model for different sets of countries and sectors for a panel that spans from 1967 to 2007, enabling yearly interaction terms. The results for Factory Asia countries, displayed in Figure 3, show the GDP coefficients falling as time passes, with two clear breaks in the estimated coefficients, 1985 and 1998. The timing and direction of the structural changes have become much based on the literature on the internationalisation of production.

Figure 3 . GDP coefficients for Factory Asia countries, 1967-2008

Notes : Estimated mass-elasticity coefficients with year interactions and pair fixed effects (as in 10). High and low bars show plus/minus 2 standard errors; Factory Asia countries: Japan, Indonesia, Republic of Korea, Malaysia, Thailand, and Taiwan.

These email address details are highly suggestive. On data that’s referred to as being dominated by parts and components trade, we find the mass-variable coefficient relocating the expected direction. However, on data where this type of production fragmentation isn’t widely seen as having been important, we find that that mass point-estimates are stable as time passes.

What’s more, whenever we are the ratio of intermediates to total trade as a regressor, both alone and – moreover – as an interaction with the economic mass variable, we find importer GDP matters less for countries that import a more substantial share of intermediates).

A seek out mass proxies when intermediates are essential

Theory shows that an ideal solution would require data on total costs to proxy for demand for intermediates imports. If the economy is fairly competitive, gross sales will be a good proxy for the full total costs. Unfortunately, such data aren’t available for an array of nations especially the developing nations where production fragmentation is indeed important. On the mass variable for the foundation nation, theory shows that we use gross output instead of value added. Again such data aren’t widely available.

To locate a proxy, we focus on the destination nation’s mass variable. The full total flow of goods may be the sum of consumer goods, whose demand is dependent upon the importing nation’s GDP and intermediate goods whose demand is dependent upon the full total costs of the sector purchasing the relevant intermediates. This suggests an initial measure that adds imports of intermediates to GDP .

To proxy for supply inthe origin nation, we want to capture gross output. Our proposed measure for output size adds purchases of intermediate inputs from all sources (except from itself because of too little data) to value added in manufacturing.

Using these proxies we’re able to fit the info more precisely that with standard gravity equations… The R-squares, which gauge the share of the info which can be explained by the model, increase from … to … etc… etc…

Why do incorrectly-specified mass variables matter?

Numerous gravity studies concentrate on variables that vary across country pairs – say free trade agreements, cultural ties, or immigrant networks. The newest of the studies employ estimators that control for the mass variables with fixed effects. Such studies usually do not have problems with mass-variable mis-specification and are also unaffected by our critique. There are however several recent studies – especially regarding the ‘distance puzzle’ that do proxy for the production and demand variables with GDP. It really is these studies our work speaks to. 1

Since many of these studies are worried with a broad group of nations and commodities, the mis-specification of the mass variable probably includes a minor effect on the results – as the findings of Bergstrand and Egger (2010) showed. More worrying, however, may be the use by authors that concentrate on trade in parts and components such as for example Athukorala and Yamashita (2006), Kimura et al (2007), Yokota and Kazuhiko (2008), and Ando and Kimura (2009). These papers all utilize the consumer good version of the gravity model to spell it out parts and components trade and therefore have mis-specified the mass variable.


We present empirical evidence that the typical gravity model performs poorly by some measures when it’s put on bilateral flows where parts and components trade is important.

Our paper also offers a simple theoretical foundation for a modified gravity equation that’s suitable for explaining trade where international supply chains are essential. Finally we suggest ways that the theoretical model could be implemented empirically.

Our fix is quite a distance from perfect, but we hope it shows other researchers that it might be worth looking for a thing that works better still!


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Kimura, Fukunari, Yuya Takahashi and Kazunobu Hayakawa (2007). "Fragmentation and parts and components trade: Comparison between East Asia and Europe," The UNITED STATES Journal of Economics and Finance, vol. 18(1), pages 23-40.

Krugman Paul and Anthony Venables (1996) “ Intergration, specialisation, and adjustment” European Economic Review 40, pp. 959-967.
Yi, K-M (2003). “Can Vertical Specialization Explain the Growth of World Trade?” The Journal of Political Economy, Vol. 111, No. 1 (Feb.), pp. 52-102.

Yokota, Kazuhiko (2008). “Parts and Components Trade and Production Networks in East Asia -A Panel Gravity Approach”, Chapter 3 in Hiratsuka & Uchida eds., Vertical Specialization and Economic Integration in East Asia, Chosakenkyu-Hokokusho, IDE-JETRO, 2008.

1 For instance, Rauch (1999), Brun et al (2005), Berthelon and Freund (2008), and Jacks et al (2008) use GDP as the mass variable if they decompose the change in the trade flow in to the ramifications of income changes and trade cost changes; Anderson and Van Wincoop (2003) also use GDP as the mass variable in another of their estimation techniques.

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