Conventional measures of openness usually build exclusively on measures of direct trade. Either, the total value of trade is measured by its value added or adequately normalized exports or imports are used to approximate trade costs. And raw exports are often filtered to isolate the value added they contain.1 But in a world of global value chains, focusing exclusively on direct trade gives a distorted view of the exposure to foreign shocks (‘openness’). What matters is not whether a sector is open to trade, but rather whether its customers are down the value chain. We introduce a measure of high order trade, ‘HOT’ for short, that abstracts from direct trade altogether. This presents two advantages: first, we can compute precise exposure to foreign shocks for activities that trade none of their output directly, most prominently services. Second, we can introduce instruments for openness at a level of aggregation and coverage that is unprecedented.

For each sector, HOT computes the fraction of gross output sold to downstream customers located across a border. In general, downstream customers may purchase a sector’s output directly, or indirectly from its (direct or indirect) customers. Our innovation is to consider the domestic/foreign status not only of the direct purchasers of a sector’s output, but also of its indirect purchasers, at second and higher orders. We think of this as an intuitive generalization of the standard approach to measuring openness, and a timely one as high-order linkages increasingly cross borders with the advent of global supply chains.

Computing HOT for all sectors in 43 countries reveals a country ranking that is similar to the one obtained by other measures: small countries like Luxembourg or Ireland are very open, and large ones like Japan or the US are closed.2 Figure 1 depicts the values of HOT for five large economies over time, and confirms that Germany is very open while the US and Japan are closed. The figure also exhibits the dip in world trade experienced immediately after the crisis of 2008. Across sectors, however, the conclusions are very different. According to conventional measures, the distribution of openness across sectors is highly skewed: open sectors are typically the exception, even in open countries. This is illustrated in Figure 2 which plots conventional measures of openness across sectors for each country. As an example, the median ratio of export to value added across sectors is 0.15 in the Netherlands, suggesting that most sectors are in fact closed even though the Netherlands is a very open country. Germany is a case in point, with very few, very open sectors. Hence, according to Figure 2, foreign shocks should affect only a minority of sectors, even in very open economies. The world according to HOT is much more open on average. This is intuitive: while some sectors do not trade directly across the border, supply chains that never cross a border are rare. The distribution of HOT across sectors is more symmetric than the alternatives based on direct trade. Some sectors are open even in countries that are relatively closed on average. Open countries tend to have open sectors across the board, including those that are customarily labelled “non-traded.” Overall, foreign exposure is widespread in the world economy according to HOT. It is, too, according to the violent, and almost universal effects COVID-19 had across the world economy.

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Figure 1  High Order Trade (HOT) values

Notes: High Order Trade (HOT) is depicted over time for five countries and the world. Country values are value added weighted averages of sector level HOT. World HOT is a GDP weighted average of country HOT. Value added is converted in USD at PPP exchange rate.

Source: World Input-Output Data and OECD.

Figure 2 Dispersion of High Order Trade (HOT), exports relative to PPP GDP and trade in value added relative to PPP GDP across sectors for each country in 2014.

Note: The mid-point is the median, the thick segment is the interquartile range, and the whiskers are extreme values.

Source: World Input-Output Data and OECD.

A measure of openness for the service sector

Trade in services is hard to measure. One approach is to compute service trade using intermediate trade as reported in input-output tables.3 Another approach is to compute value added trade for services, but that can be difficult when direct trade is close to zero.4 Figure 3 plots for each sector the distribution of HOT across countries. On average, services rank at the middle of the distribution of sectors: less open than most manufacturing, but much more open than many others, like construction, real estate or food. Services are consistently more open according to HOT than measures based on direct trade. In fact, some services are among the most open sectors in some countries – e.g. IT in India. This is intuitive and plausible in a globalized world where services are often sold to domestic exporters.

Figure 3 Dispersion of High Order Trade (HOT) across countries for each sector in 2014.

Note: The mid-point is the median, the thick segment is the interquartile range, and the whiskers are extreme values.

Source: World Input-Output Data and OECD.

The consequences of openness

Clearly, there are large differences between HOT and its predecessors, especially across sectors. The question is whether HOT does a better job than other measures at capturing the propagation of shocks across borders, which we know to happen via the supply chain (see Acemoglu et al. 2015). To answer this question, we implement three estimations that are commonly used in firm-level data and in country panels (Imbs and Pauwels 2020). We first ask whether a sector’s openness correlates systematically with its productivity.5 Second, we study whether openness correlates with growth.6 Third and finally, we introduce a bilateral version of HOT and ask whether it correlates with the synchronization of business cycles at sector level. Once again, that question is rampant in the aggregate and at the firm level.7

We document systematic positive and significant correlations between HOT, labor productivity, growth, and synchronization at sector level, which is evidence for shocks propagating via the global value chain. Running the same estimation with conventional measures of openness leads to unstable coefficients exhibiting the wrong sign. Thus, correlates of openness at sector level are consistent with firm-level (and some aggregate) evidence when openness is measured by HOT, but not when it is measured by any of its predecessors.

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However, as trade does not happen in a vacuum and as exporters tend to operate in high productivity, high growth environments, this could also explain the correlation between productivity and growth, and HOT. But in this case, causality would run from growth and productivity to openness. Of course, establishing the putative consequences of openness to trade is an important area of research. To do so, we introduce an instrument for HOT at the sector level, over time, and for any country with input-output data. This is another important improvement of our HOT measure over existing measures of openness, as those are usually virtually impossible to instrument at such a level of generality.

Our instrument uses the network structure of HOT: for each sector, we separate the first- from the higher-order links, as first-order links are clearly endogenous to the circumstances of the considered sector. There is little question that a sector’s first-order, direct openness can be caused by its productivity: a sector trades more across the border if it is has more high-performing firms. But the fact that downstream sectors themselves are more open is less likely to be caused by upstream productivity: downstream openness is mostly caused by downstream productivity.8

Using these instruments, we establish a significant effect of HOT on productivity and synchronization. But there is no significant effect of HOT on growth, consistent with a Ricardian view of trade where openness triggers reallocation, with level effects but no permanent growth consequences.

Our results show that we need a new measure of foreign exposure that is consistent with the emergence of global value chains and our recent experience with the propagation of COVID-19 shocks. HOT provides such a measure.


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1 See Alcalá and Ciccone (2004), Baldwin et al. (2003), Head and Mayer (2004), Johnson and Noguera (2012).

2 The computations are performed using the 2016 release of the World Input Output Tables. The country coverage represents about 85 percent of world GDP. For details about WIOT, see Dietzenbacher et al. (2013).

3 See for instance Eaton and Kortum (2018).

4 See for example Johnson (2014).

5 See among many others the seminal studies of Bernard and Jensen (1995, 1999, 2004) at firm level, or productivity enhancing reallocation effects in Amiti and Konings (2007), Topalova and Khandelwal (2011), Bernard et al. (2018), or DeLoecker and Van Biesebroeck (2018).

6 See for instance the survey by Baldwin et al. (2003) across countries, or Amiti and Konings (2007), Halpern et al. (2015) or Bøler et al. (2015) at firm level.

7 See Frankel and Rose (1998), or Kalemli-Özcan et al. (2013). At firm level, see di Giovanni et al. (2017, 2018).

8 In many-to-many matching environments, firms with many buyers tend to sell on average to buyers with few connections, i.e. to relatively low productivity firms. See Bernard et al. (2019) for evidence on Japan and Bernard et al. (2018) on Norway. In a one-to-one matching environment, Dragusanu et al. (2014) shows that positive assortative matching is non-existent for intermediate trade.