Measuring Dependence with Aggregate Trade Statistics

Many studies construct measures of dependence using aggregate trade statistics. Typically, scholars follow Oneal and Russet (Reference Oneal and Russet1997) (OR) who use the sum of bilateral imports and exports divided by GDP. The intuition is straightforward. As bilateral trade increases (the numerator), there is more at stake in a particular trade relationship and therefore more harm in cutting off trade flows. As GDP (the denominator) increases, trade is a lower fraction of the country’s overall economic activity, and therefore less harm is done. Additionally, a larger GDP could indicate a greater ability to mitigate harm by increasing domestic production.

Alternative approaches within this category are generally different permutations of aggregate GDP and trade measures combined with bilateral trade flows (Gartzke and Li Reference Gartzke and Li2003). For example, Barbieri (Reference Barbieri1996) and much subsequent work emphasize trade shares. Country i’s dependence on country j equals the value of trade for the dyad $ ij $ divided by i’s overall trade across all dyads. OR and Barbieri also use extensions of these measures to capture symmetry in a dyad.Footnote ⁴

With some partial exceptions described below, these approaches share an implicit assumption that every dollar of lost trade is equally harmful for welfare. There are three major ways that this assumption is violated.

First, trade flows vary in the availability of a substitute supplier of that good. Some trade flows are more easily replaced by production from another trading partner (Gray and Potter Reference Gray and Potter2012; Kim, Liao, and Imai Reference Kim, Liao and Imai2020). The Philippines imports $ 47\% $ and $ 19\% $ of its steel from China and Russia, respectively. None of the remaining sources make up more than $ 8\% $ of their imports. Malaysia, on the other hand, imports $ 26\% $ and $ 19\% $ from its two largest partners, China and Japan. Two other countries make up $ 12\% $ of their imports, and a third makes up $ 8\% $ . Malaysian steel imports are more evenly spread across different producers, compared to the concentrated import origins for the Philippines. Replacing a trade flow that represents a greater percentage of total imports is harder than replacing a flow that is one among many. Mansfield and Pollins (Reference Mansfield and Pollins2001) and Barbieri (Reference Barbieri1996) recognized that the ease of replacing a lost trade flow with an alternative partner affected dependence. Barbieri’s trade share measure $ \left(\frac{{\mathrm{trade}}_{ij}}{{\mathrm{trade}}_i}\right) $ was intended to capture this.Footnote ⁵

Second, flows vary in the availability of a substitute good. Not all goods have readily available substitutes. It is less disruptive to substitute brown rice for white rice, compared to finding a substitute for a specialized pharmaceutical. $ $ 10 $ M of rice imports and $ $ 10 $ M imports of chemotherapy drugs will both have the same impact on measures based on aggregate trade statistics, even though substitutability means they have very different implications for welfare. Some studies of dependence have incorporated the ease with which you can find substitutes (Crescenzi Reference Crescenzi2003; Gowa Reference Gowa1995; Liu and Yang Reference Liu and Yang2025; Polachek Reference Polachek1997). They generally use static measures of import demand elasticity at the industry level.

Third, some trade flows are in final consumption goods but others are in intermediate products. Intermediates are goods that are inputs (or inputs into inputs $ \dots $ ) of other goods. Increased fragmentation of production along global value chains was a huge driver of intermediates trade (Hummels, Ishii, and Yi Reference Hummels, Ishii and Yi2001). Intermediates trade has comprised a substantial portion of global trade over the last three decades (Miroudot, Lanz, and Ragoussis Reference Miroudot, Lanz and Ragoussis2009). Osgood (Reference Osgood2018) calls the ability to source intermediates inputs one of the “primary drivers of producer preferences” over liberalization.

The welfare effect of interrupting trade in final goods is direct and localized. The welfare effects of interrupting intermediates trade are more complicated, since those disruptions ripple down the value chain. The degree to which imported intermediates affect downstream production varies across countries and time, but also across industries and firms within industries (Osgood Reference Osgood2017). If imports of integrated circuits (chips) were interrupted, this has implications for firms that use chips as inputs to circuit boards, which are inputs into electronic devices, which are inputs into the production of myriad downstream goods. Again, interruptions to final goods and intermediates have identical effects on measures based on aggregate trade statistics, but the full implications of those interruptions differ drastically.

Though some extensions of aggregate trade measures account for one of the three considerations above, none account for them all. Most applications still default to the baseline OR or Barbieri measure.

Measuring Dependence with Significant Products

The second existing approach studies trade in a small number of products which are known to be very difficult to substitute. Many of the products chosen, such as oil and semiconductors, are intuitively critical to the global economy. The underlying assumption is that a country’s dependence on an entire trade relationship is correlated with its dependence on the chosen products. Scholars studying resource competition analyzed the relationship between oil and conflict. States which depend on oil imports might use military means to secure their supply (Klare Reference Klare2007; Westing Reference Westing1986). Zeng (Reference Zeng2024) incorporates a list of significant goods into a measure of the externalities of trade. Global value chain disruption during the COVID-19 pandemic made policymakers concerned about access to semiconductors, an extremely widely used intermediate product (Chen and Evers Reference Chen and Evers2023; Farrell and Newman Reference Farrell and Newman2020).

Unlike aggregate trade statistics measures, this approach can differentiate between types of trade flows. However, this approach also falls short of a full accounting of dependence. First, the modern global economy includes trade in many products. The strategic goods approach misses cases where a state’s political leverage does not derive from a limited number of products. Small amounts of dependence in a large number of products add up. This approach also uses a binary classification of flows as strategic or not, but provides no method of weighting the importance of different strategic products. Second, the modern global economy is dynamic. The relevance of any case study of a particular product might quickly become irrelevant. Some products may become significant in unanticipated ways. For example, COVID-19 laid bare the importance of seemingly unimportant items like masks.

Estimating Dependence in the Modern Economy

The ideal measurement of dependence requires a full accounting of how an interruption in trade affects a country’s welfare. This measurement should account for three major features of modern international trade: substitutability, intermediates trade, and the availability of alternative trading partners. It should do so for all trade flows, not just a small subset of significant ones. Ideally, it should be microfounded in trade theory. Creating an estimate of dependence with all of these features is daunting. In principle, such an estimation could be undertaken using a structural model of bilateral trade flows. Historically, the main obstacle to such an exercise was the proliferation of models of international trade, each presumably having different implications for the gains from trade. The main tool for understanding comparative advantage trade, the Ricardian model, was not amenable to studying the gains from trade between more than two partners (Helpman Reference Helpman2014). Multi-country generalizations of the Heckscher–Ohlin model did not enjoy robust empirical support, making it difficult to use them as the basis for calculating the gains from trade (Bowen, Leamer, and Sveikauskas Reference Bowen, Leamer and Sveikauskas1987; Trefler Reference Trefler1995). Empirical models based on a gravity-like equation were good at predicting observed trade flows, but they were not initially derived from a theoretical model of trade. The challenge was not necessarily finding a model of trade which could describe dependence, but rather choosing the right model from among the many options available.

Major developments have gradually made it possible to construct a direct estimation of trade dependence. First, Eaton and Kortum (Reference Eaton and Kortum2002) developed a quantifiable multi-country generalization of the Ricardian model. This generalization was a member of the class of gravity models. Suddenly, by virtue of its newfound connection to Ricardian trade and its previously established robust empirical support, the gravity model approach took pole position in the race for the leading model of trade theory. But there was a litany of seemingly equally valid possible variations on the gravity model.

In a major paper, Arkolakis, Costinot, and Rodriguez-Clare (Reference Arkolakis, Costinot and Rodriguez-Clare2012) (hereafter ACR) showed that all variations within a very wide class of trade models generate exactly the same gains from trade, tied to a gravity equation. Moreover, the gains from trade in this class depend entirely on a small number of parameters that can be estimated from standard trade data. Crucially, these parameters have natural mappings to features of the global economy that are not captured by existing measurements. The simplicity of the estimation procedure and its wide applicability greatly reduce the complexity of estimating dependence and strengthens the connection between the theory of trade and the concept of dependence.

ACR derive an expression for the welfare effect of an interruption to trade, that is, a trade shock, as a ratio $ {\hat{W}}_j={W}_j^{\prime }/{W}_j $ , where $ {W}_j $ is the economic welfare of country j in the no-shock scenario and $ {W}_j^{\prime } $ is its welfare in the scenario with the shock. This is ideal for studying dependence because the $ {\hat{W}}_j $ formulation of welfare explicitly models the counterfactual nature of dependence—it compares two scenarios, one with a shock and one without. We express welfare changes as

(1) $$ \begin{array}{rl}{\hat{W}}_j={\Pi}_s{({\widehat{\lambda}}_j^s)}^{\eta_j^s/{\beta}_j^s{\varepsilon}^s},& \end{array} $$

where $ {\beta}_j^s $ is the share of intermediate products in production in sector s and country j, $ {\varepsilon}^s $ is a trade elasticity for sector s, $ {\eta}_j^s $ is the pre-shock consumption share of sector, and $ {\widehat{\lambda}}_j^s={({\lambda}_j^s)}^{\prime }/{\lambda}_j^s $ is a ratio of the share of domestic expenditure across the scenarios. Remarkably, the quantity $ {\hat{W}}_j $ is expressible in terms of four parameters, three of which (intermediates share $ {\beta}_j^s $ , the trade elasticity $ {\varepsilon}^s $ , and the share of domestic expenditure before the shock $ {\lambda}_j^s $ ) can be directly observed or estimated from data. For ease of reading, we suppress notation for years, indexed by t. Footnote ⁶

Two of those parameters immediately incorporate things we highlighted above: product substitutability and intermediate inputs. The interpretation of $ \varepsilon $ depends on the particular underlying model of trade, but the canonical interpretation suffices to build intuition here. A smaller (less negative) elasticity means that an import flow is less sensitive to trade costs. A smaller elasticity reflects how a particular trade flow is persistent even as trade costs rise, indicating its greater importance. The welfare expression places greater weight on flows in sectors with smaller elasticities.

For an affected country and a sector, $ {\beta}_j^s $ describes the (inverse) intermediate input shares. A higher value means the sector relies less on intermediate input shares. A sector that relies more on intermediate inputs is one in which there will be greater amplification of input/output feedback in any trade disruption. As input shares increase ( $ {\beta}_j^s $ decreases), a sector is more damaged by disruptions in its inputs from intermediate goods. The expression places greater weight on such a sector.

The share of domestic expenditure without a trade shock, $ {\lambda}_j^s $ , is observable from data. The share of domestic expenditure in the scenario with the shock $ {({\lambda}_j^s)}^{\prime } $ is the one remaining parameter which is unobserved and therefore cannot be estimated from data. ACR note that this quantity is known with certainty under autarky: the share of domestic value added must be $ 100\% $ . ACR calculate the total welfare gains from trade relative to autarky by plugging in $ {({\lambda}_j^s)}^{\prime }=1 $ . There is no way to know with certainty what the domestic share of value added will be in other scenarios. There are two margins of adjustment that could impact the share $ {({\lambda}_j^s)}^{\prime } $ in the event of an interruption in trade with one partner. First, the domestic economy could adjust to the new prices by increasing production of some goods and decreasing production of others. Second, the alternative trading partners could adjust their exports in response to the new prices. Both adjustments could blunt the negative welfare effects from interrupting trade. Our compensation measure, described below, incorporates the second margin of adjustment.

Upper Bound Dependence and Compensation Dependence

Our first new measure estimates dependence using the above formula. Consider the effect on the welfare of the target state j if sender state i were to cease exporting to j. Footnote ⁷ To reduce the costs of this trade stoppage, the state might adjust its production or its imports from alternative partners. Any adjustment is for the purpose of increasing welfare. Therefore, the maximum reduction in welfare that state j could experience when state i severs its trade relationship occurs when domestic production in j and the exports from alternative trade partners are unchanged. Therefore, the welfare expression—assuming zero imports from country i and holding all other exports and domestic production constant—represents an upper bound on the opportunity cost of interrupted trade.

This value, which we call upper bound dependence, is our first major new measure of dependence. It is a direct measure of the highest possible amount of dependence in a given bilateral trade relationship. Unlike measures based on aggregate statistics, upper bound dependence can be interpreted directly. Its value represents the fraction of country j’s initial welfare remaining after country i ceases to export all goods to j holding all other production values and exports constant. In other words, it is the lowest possible fraction of country j’s welfare remaining if country i ceases exports. An alternative interpretation of upper bound dependence is that it is a short run measure of dependence before enough time has passed for the new equilibrium to be reached.Footnote ⁸

Recall that the ACR approach clearly incorporated two of the three major changes to the world economy, substitutability and intermediates trade, but it did not directly incorporate the ability of alternative trade partners to compensate for lost trade. Similarly, while useful, upper bound dependence also does not directly incorporate this. Without further strong assumptions about the cross price elasticities for all possible goods and suppliers, it is not possible to directly estimate how well alternative trade partners could replace the lost trade.

However, a single assumption can enable meaningful progress toward incorporating the availability of alternative trade partners. Assuming that the composition of the export mix from unaffected partners remains constant, we can ask: how much would unaffected trade need to increase to fully replace the lost welfare if country i ceased exporting to country j? In other words, how much would unaffected trade need to be “scaled up,” either by intensifying existing trade flows or forging new ones, in order to make the target “whole” again? We call this value compensation dependence. It captures the idea that the existing trade network can buttress against any one state’s dependence on another.Footnote ⁹

Figure 1 depicts both measures graphically. The top panel shows the status quo ex ante, with B trading various amounts in various industries with three partners (A, C, and D). The thickness of each arrow shows the value of each trade flow. The dark middle bar shows B’s welfare in each scenario. Suppose A cuts off exports to B, as in the bottom left. B’s welfare decreases to some fraction of its original value. This drop is the upper bound measure. Now, suppose that C and D increase their exports to B enough to raise B’s welfare back to its original level.Footnote ¹⁰ The compensation measure describes how much thicker each of those export flow arrows need to become to make B’s welfare “whole” again.

Figure 1.

Upper Bound and Compensation Dependence

Note: Four countries are depicted in each panel of the figure by circles. Trade volumes are depicted as directed edges, where the thickness of the edge is proportional to the value of country B’s imports. The top inset of the figure depicts an initial scenario where country B imports three goods $ s=\{1,2,3\} $ from three countries A, C, and D. The small rectangular bar placed inside the circle of country B depicts their welfare in the initial scenario; the bar is filled completely indicating their welfare starts at $ 100\% $ . The lower left inset shows a scenario in which country A has ceased to export to country B. The rectangle is only partially filled indicating that country B’s welfare has suffered. The magnitude of the decrease in welfare is the upper bound measure. Note that in this scenario the exports from countries C and D are unchanged. The lower right inset shows the compensation measure. The rectangle is now fully filled once again because the exports from countries C and D have been increased to compensate for the welfare losses caused by A’s cessation of exports. The export mix, depicted by the relative thicknesses of the edges, remains unchanged in all scenarios.

Figure 1. Long description

The diagram consists of three panels showing directed trade edges between circular nodes A, B, C, and D.

* Top Panel: Initial Scenario. Node B is at the center, receiving three directed edges from each of the other nodes. Edges are labeled s = 1, s = 2, and s = 3. The thickness of the edges varies, with s = 2 from node A being the thickest. Inside node B, a horizontal rectangular bar is completely filled black, representing 100% welfare.

* Bottom-Left Panel: Upper Bound Dependence. Node A is separated from the network by a vertical dashed line. All trade edges from A to B have been removed. The welfare bar inside node B is now only half-filled, indicating a decrease in welfare. A text box explains that this represents the maximum damage A can inflict on B by withdrawing trade.

* Bottom-Right Panel: Compensation Dependence. Node A remains separated by the dashed line. Trade edges from nodes C and D to node B have increased in thickness compared to the initial scenario, while maintaining their relative product mix. The welfare bar inside node B is once again completely filled black. A text box explains that this represents the percentage increase in trade from other partners required to compensate B for the loss of trade from A.

For a tangible example, consider the Western export restrictions targeting Russia following its invasion of Ukraine. Upper bound dependence describes the harm to Russian welfare from lost access to Western goods, based on the degree to which they are intermediate inputs and the availability of substitute goods. Compensation dependence describes the degree to which Russia can find substitute suppliers, like China, for things that previously originated from sanctioning countries.Footnote ¹¹

To reiterate, the main advantages of the upper bound and compensation measures are that they directly estimate the opportunity cost of an interruption in trade across the entire economy and they take into account key features of the modern global economy. The upper bound measure indicates a ceiling on the total possible dependence in a bilateral relationship. It up-weights flows in sectors that are harder to substitute $ (\varepsilon ) $ and flows in sectors that are intermediate inputs into downstream production $ (\beta ) $ . The compensation measure accounts for the third feature of the modern economy by incorporating how easily a state’s trade network could compensate for an interruption from a particular partner. These two measures are directly interpretable as statements about welfare and they depend on weaker assumptions than existing measures that rely on aggregate statistics. The two measures have relative strengths. The compensation measure captures longer-term adjustments that states can make by using alternative suppliers, but it also entails additional assumptions that the upper bound measure does not require. The compensation measure may therefore be more appropriate for analyses of interactions taking place over longer timeframes. Upper bound may be appropriate for shorter-term interactions that are resolved before states can adjust with compensation, such as episodic sanctions threats.

There are some margins of adjustment that may affect welfare which are not captured in our approach. For example, we cannot account for variation across countries or time in their ability to finance consumption by borrowing. We also cannot account for variation in the ability of countries to adapt using technological advances. We can partially account for variation in countries’ ability to increase domestic production. If a country already has a large domestic value added in a particular sector, then our approach downweights that sector. We would note that some of these adjustments likely take a long time. For example, a country cannot rapidly advance technology to compensate for welfare losses. Ramping up domestic production also takes time and there is no guarantee that a country will reach the efficiency level of its original trade partners.

There may be unobserved factors which impede the ability of a state to “scale up” its trade with particular alternate partners in response to an interruption in trade. The compensation measure already partially accounts for these factors. Many factors which would impede scaling of a trade flow already impede trade ex ante—before a sender interrupts trade. Relatively low initial trade would imply a relatively large scaling factor, and therefore a relatively large compensation value. Thus, our measure already accounts for initial factors which do not change when the sender chooses to interrupt trade.

Our measure also describes welfare in terms of aggregate national utility, or equivalently, the utility accrued to a representative consumer from consumption. We do not model ways in which a national leader might care more or less about specific subnational groups. For example, a democratic leader might care more about the welfare of citizens in their party or an authoritarian might have less concern for aggregate welfare.

Some related literature studies dependence and geopolitics under the heading of “geoeconomics.”Footnote ¹² Thoenig (Reference Thoenig2024) uses a structural gravity approach to estimate the opportunity costs of war from forgone trade and the destruction of production capacity. Ding (Reference Ding2025) incorporates the consequences from lost capital services. Clayton, Maggiori, and Schreger (Reference Clayton, Maggiori and Schreger2026a) model a hegemon who can coerce others by threatening to disrupt particular flows in global commerce. Clayton, Maggiori, and Schreger (Reference Clayton, Maggiori and Schreger2026b) derive a hegemon’s power over a target country from a similar underlying economic model to ACR and incorporate manipulation of finance as a coercive lever. Another related literature describes “weaponized interdependence” (Drezner, Farrell, and Newman Reference Drezner, Farrell and Newman2021; Farrell and Newman Reference Farrell and Newman2019). This literature emphasizes the coercive leverage that the United States enjoys because of its central position in finance and information networks. Like us, they disagree with conventional wisdom about complex interdependence, but they de-emphasize trade flows as a key source of dependence. We find patterns contradicting conventional wisdom even in dyadic trade relations.

Trade Elasticities

Trade elasticities describe the degree to which imports into country j from country i change as iceberg costs between the two countries, $ {\tau}_{ij} $ , change. Caliendo and Parro (Reference Caliendo and Parro2015) show that we can recover an estimate of these elasticities from any model that results in a gravity equation for trade, including the broad class of models from ACR. The procedure uses two inputs—trade flows and tariffs—to estimate $ \varepsilon $ . This procedure expresses trade flows between three countries as an odds ratio “triplet.” This is especially useful because it simplifies an expression of $ \varepsilon $ as a function of trade flows between the three countries, i, j, k, and a directed-dyad-specific trade cost: tariffs ( $ \tau $ ).Footnote ¹⁴

With trade flow and tariff data, the triplets can be constructed and $ \varepsilon $ can be estimated using OLS.Footnote ¹⁵ Theoretically, elasticities must be negative. An increase in iceberg costs should decrease trade. In practice, with OLS, estimates are sometimes positive. We use a Bayesian regression to ensure that estimated elasticities are negative. We set the prior distribution for the regression coefficients to be normal, with a mean of $ -4.5 $ and a standard deviation of $ 1 $ .Footnote ¹⁶ We constrain the posteriors to have a maximum of $ -0.25 $ and an unbounded minimum. This constraint ensures that we get theoretically sensible elasticity estimates that still have meaningful variation across time and industry.

Our estimates of $ \varepsilon $ are industry-specific. Elasticity estimates are global; they are not importer or exporter or dyad-specific. They vary by year and show substantial variation across time.Footnote ¹⁷ The trade flow and tariff data both come from the UNCTAD Trade Analysis and Information System (UNCTAD 2026).

Consumption Shares, Import Penetration, and Intermediate Products

The variable $ {\lambda}_j^{st} $ describes the share of domestic expenditure in sector s in year t. It is one minus the import penetration ratio, where the import penetration ratio is the share of total expenditures in an industry that are from imports. We calculate $ {\lambda}_j^{st} $ as follows (again dropping industry and year subscripts): $ 1-\frac{\mathrm{Imports}}{\mathrm{Production}\ \hbox{-}\ \mathrm{Exports} + \mathrm{Imports}} $ . The import/export values are totals, across all partners.

Recall that $ {\lambda}_j^{s{t}^{\prime }} $ refers to a possible counterfactual where one of j’s partners, i, cuts off exports of a certain product to country j, with a corresponding value of $ {x}_{ij} $ . For our upper bound measure, $ {\lambda}_j^{\prime } $ equals $ 1-\frac{\mathrm{Imports}-{x}_{ij}}{\mathrm{Production}-\mathrm{Exports}+\mathrm{Imports}-{x}_{ij}} $ . Data for domestic production and bilateral imports and exports come from the OECD’s TiVA dataset. The consumption shares ( $ {\eta}_j^s $ ) are calculated from the same data and defined as $ \frac{\mathrm{Production}-\mathrm{Exports}+\mathrm{Imports}}{\mathrm{Total}\ \mathrm{Production}-\mathrm{Total}\ \mathrm{Exports}+\mathrm{Total}\ \mathrm{Imports}} $ where the term “Total” aggregates across all sectors and trade partners by state–year.

The share of domestic value-added production, $ {\beta}_j^s $ , is measured at the country–year–industry level. The value of $ {\beta}_j^s $ reflects the importance of intermediate products in that sector. These measures also come from the TiVA dataset.Footnote ¹⁸

Dependence over Time

Has dependence increased over time? Using our compensation measure, we can show that the answer is: yes, very quickly, and overwhelmingly driven by China. With aggregate statistics, the story is less clear. To describe global dependence, we again look at the maximum value of the compensation measure for each country–year observation across its partners. The maximum value asks: “how dependent is your most dependent relationship?” It is a good way to summarize dependence because the maximum dependency represents a kind of worst case scenario for that state. It describes the height of potential economic coercion targeting that state, since no other trade partner can do more damage. The maximum dependency is also arguably more relevant than, for example, the mean dependence across all of a state’s trading partners. A small decline in dependence on a dozen trading partners might be more than canceled out by a large increase in dependence on a single large partner. Looking at the distribution of maximum dependencies is also theoretically grounded. Ikenberry (Reference Ikenberry2001) and Keohane (Reference Keohane1984) argued that hegemonic power profoundly shapes the logic of international cooperation. Studying maximum dependencies describes the international structure of states’ dependence on hegemonic power(s).

Figure 3 plots trends in the maximum values of the compensation measure on the left side and in the maximum value of the OR measure on the right side.Footnote ²³ Since there are many observations per year, we plot the average of the metric across countries for each year and include a third degree polynomial line.Footnote ²⁴ We take logarithms due to the high skewness in the measures from a few states being highly dependent. Then, measures are normalized to the unit interval to equalize their support.Footnote ²⁵

Figure 3.

Bin Scatter of the Maximum Values of the Compensation and OR Dependence Measures, Logged and Normalized to the Unit Interval to Equalize Their Support and Facilitate Comparison

Figure 3. Long description

The image consists of two side-by-side scatter plots with binned data points and fitted trend lines. Both panels share an x-axis representing years from 1995 to 2020.

Left Panel:

- The y-axis is labeled Compensation Measure, ranging from minus 1.9 to minus 1.6.

- The data points show a slight initial decline from 1995 to 2002, followed by a sharp, non-linear increase through 2020.

- A solid black trend line follows a U-shaped curve that transitions into a steep upward slope after 2010.

Right Panel:

- The y-axis is labeled Aggregate Statistics Measure O R, ranging from minus 1.75 to minus 1.60.

- The data points are more widely dispersed than in the left panel.

- A solid black trend line shows an inverted U-shape, peaking around the year 2010 before beginning a downward trend toward 2020.

The largest values of the compensation dependence measure have generally increased over time. OR dependence has also increased, but not to the same degree. The OR measure is more sensitive to years in which a global crisis caused a temporary decrease in trade as a share of world GDP. The OR measure dips more sharply in 2008/2009 because of the financial crisis and again in 2020 as COVID decreased trade. However, lower levels of trade may indicate lower levels of dependence according to the OR measure, they do not necessarily mean lower levels of dependence according to our measures. Suppose a shock, like COVID interrupted nearly all trading relationships. In some ways, dependence has gone down since a country now trades less with each partner and overall. But at the same time, dependence on the remaining relationships has increased substantially, even if aggregate trade flows are lower.

Furthermore, there is immense heterogeneity across countries in how compensation dependence has changed over time. Figure 4 shows results from a clustering algorithm designed to detect how changes over time differ across groups of countries.Footnote ²⁶ We found two types of trends: countries whose compensation dependence generally increased and others who decreased. Both trends have a common cause: increased dependence on China.

Figure 4.

Clustering Countries by Their Trends in Maximum Values of Compensation Dependence

Figure 4. Long description

The top panel is a line graph with an x-axis representing years from 1995 to 2020 and a y-axis ranging from minus 2.00 to minus 1.25. Two data series are shown. The Decreasers series, marked by pink dots and a downward-sloping pink curve, starts near minus 1.6 in 1995 and gradually declines to minus 2.0 by 2020. The Increasers series, marked by grey triangles and an upward-sloping blue curve, starts near minus 2.1 in 1995 and rises to minus 1.25 by 2020. The curves intersect around the year 2010 at a value of minus 1.85.

The bottom panel is a world map where countries are shaded based on the two clusters.

* Decreasers, shaded pink, are concentrated in North America including Canada and Mexico, parts of Northern and Eastern Europe, Russia, China, and parts of North Africa.

* Increasers, shaded blue, are concentrated in the United States, South America including Brazil and Argentina, Western Europe, India, Southeast Asia, and Australia.

* Countries in grey are not categorized in either cluster.

Figure 5 illustrates the role of China in explaining these patterns. The vertical axis measures each state’s dependence on China while the horizontal axis measures its greatest dependence on any partner other than China. Often, this is the United States, but not always. The first column shows each country’s starting point in 1995. Points above the 45 degree line are most dependent on China while points below the line are most dependent on some other state. The middle and right columns show how each country’s dependence on China and the other partner has changed in that time period. Countries are grouped into the same groups as in Figure 4. This helps show why the trends differ for each cluster of countries.

Figure 5.

Vectors Indicating Change over Time in a Country’s Dependence on China (Vertical Axis) and Its Maximum Dependence on Any Other (Non-China) Partner

Note: Lines connect the initial values for each state in 1995 to their values in the year shown. The diagonal black line is a 45 degree line. Points above the line are most dependent on China. Dependence is plotted after normalization to the unit interval and after taking the natural log.

Figure 5. Long description

The grid consists of two rows and three columns. The vertical y-axis is labeled Dependence on C H N and the horizontal x-axis is labeled Dependence on other partner. Both axes use a natural log scale from minus 6 to 0. A diagonal 45-degree line bisects each plot from the bottom-left to the top-right.

* Top Row: Decreasers.

- 1995: Black dots are clustered in the bottom-right quadrant, well below the diagonal line, indicating low dependence on C H N relative to other partners.

- 2005: Gray circles represent 1995 positions with arrows pointing to black dots representing 2005 positions. Most arrows move upward and slightly left, showing an increase in C H N dependence.

- 2015: Arrows are longer and more vertical. Many points approach the diagonal line, indicating C H N dependence is nearing parity with the maximum other partner.

* Bottom Row: Increasers.

- 1995: Similar to the top row, dots are concentrated in the bottom-right quadrant.

- 2005: Arrows show a significant upward shift. A few points cross above the diagonal line, meaning C H N has become the primary trade partner.

- 2015: A dense cluster of points and arrows is located near the top of the plot. A significant portion of the points now sits above the diagonal line, indicating C H N is the dominant partner for these states.

Consider first the group, with decreasing dependence over time. These states (especially European states, Canada, and Mexico) have historically been dependent on traditional powers other than China. Their dots tend to cluster in the lower right portion during the earlier years. Yet, over time, their dependence on China increases. Dependence on their original traditional partners has fallen as China has become a more productive alternative trade partner. As indicated by the vectors in the middle and right columns, these states approach, but generally do not cross, the 45 degree line from below. Consider next the group with increasing dependence over time. States whose dependence is increasing tend to have always had relatively strong economic connections with China. Countries in this cluster cross the 45 degree line relatively early and continue moving toward the northwest corner. They, too, became more dependent on China during its economic rise.

The story of global dependence between 1995 and 2020 is the story of competition between the United States and China. Dependence on China grew dramatically over time. Figure 6 shows how the measure used gives very different answers for when this change occurred. The OR measure shows a weak, slow decline in dependence on the United States. Since trade with most countries increases with the United States over this time, the OR measure (because of how it is constructed) can only explain this by saying that trade with the United States has not risen as quickly as GDP growth in its partner countries. The compensation measure tells a different story. The decline in dependence on the United States is earlier and somewhat steeper. This means that the additional changes that our measure accounts for—trade in intermediates, sector level trade elasticities, and alternative trade partners—combined to undercut other countries’ dependence on the United States. The decline is not simply explained by other countries’ GDP growth.

Figure 6.

Global Dependence on USA and CHN over Time

Figure 6. Long description

The two panels share a vertical Y axis labeled Dependence ranging from minus 5 to minus 2 and a horizontal X axis representing years from 1995 to 2020. A legend at the bottom identifies blue circles as C H N and pink triangles as U S A.

* Left Panel titled Compensation. The C H N data shows a strong linear increase starting near minus 5 in 1995 and rising steadily to approximately minus 2 by 2020. The U S A data shows a gradual linear decrease starting near minus 3 in 1995 and ending near minus 3.5 in 2020. The lines intersect around the year 2006.

* Right Panel titled Oneal and Russett. The C H N data follows an asymptotic curve, rising sharply from minus 4.6 in 1995 and leveling off toward minus 2.2 by 2020. The U S A data shows a very slight downward linear trend, starting just below minus 2 in 1995 and ending near minus 2.4 in 2020. The lines intersect later in this model, around the year 2017.

Interdependence over Time

How has interdependence changed over time? Using our measures, it has not increased. Dependencies have gotten more asymmetric over time—contrary to trends when using aggregate statistics. Figure 7 illustrates the entire dyadic dataset by averaging compensation dependence across years for each pair of states.Footnote ²⁷ The horizontal axis shows “sender” states and the vertical axis shows “targets.” The color of each cell represents the compensation dependence of the target state on the vertical axis on the sender state on the horizontal axis. Darker, redder squares mean that the target is more dependent on the sender. We order states by their average dependence as a sender, from left to right.

Figure 7.

Network of Directed-Dyad Dependencies

Figure 7 Long description

A square heatmap grid with the Y-axis labeled Target and the X-axis labeled Sender. Both axes list three-letter country codes. A diagonal line of white squares runs from the bottom-left (D E U, D E U) to the top-right (L A O, L A O), representing self-referential data points.

Below the grid, a color scale bar titled Compensation (mean, log, normalized) ranges from -5 (dark blue) to -1 (dark red).

Data distribution patterns:

* The highest concentration of non-blue cells (indicating higher compensation values in yellow, orange, and red) is clustered on the far left of the chart, particularly for Senders like D E U, U S A, C H N, F R A, and I T A.

* Vertical bands of lighter blue and yellow appear for major global economies acting as Senders.

* The right half of the chart, representing Senders like M L T, B R N, and L A O, is almost entirely dark blue, indicating lower compensation values.

* Specific high-value outliers (red cells) are visible, such as the intersection of Target I S R and Sender U S A, and Target C A N and Sender U S A.

* The grid contains approximately 60 countries on each axis.

The plot highlights the extent to which dependence is dominated by a small number of great power sender states. If dependence was symmetric and interdependent, then the matrix would also be symmetric. Clearly, it is not—there are many brighter colors above the diagonal than below. Most states are highly dependent on China, the United States, or Germany. In turn, these great powers depend on relatively few other partners. States of the former Soviet Union tend to be particularly dependent on Russia. The largest dependencies in the entire dataset are in South Asia—Japan and Cambodia are highly dependent on China. These findings are not necessarily at odds with the standard narrative about interdependence. After all, in a hegemonic world, we would expect some degree of concentrated economic power. What matters more to the standard theory is whether the global economy is becoming more interdependent over time.

Over time, dyads have not trended toward greater parity in their dependencies. The top two panels of Figure 8 show trends in interdependence across all dyads, using the compensation measure and the OR measure. For each dyad, we calculate the difference in i’s dependence on j and j’s dependence on i. We then take the absolute value of this difference, for each measure. Smaller values reflect more interdependence. As before, both measures are normalized to the unit interval and log-transformed before taking differences.

Figure 8.

Interdependence over Time

Note: Points show differences in directed dyadic dependence over time, averaged across dyads. The top panel shows this difference for all dyads. The bottom panel shows this for maximally dependent dyads.

Figure 8. Long description

The figure consists of four scatter plots with trend lines arranged in a two-by-two grid. All plots share an x-axis representing years from 1995 to 2020 and a y-axis labeled Difference in Dependence.

Top row: Interdependence by All Dyads.

* Left panel (Compensation): Shows a slight linear decrease. Data points fluctuate between 0.8 and 0.7.

* Right panel (Oneal and Russett): Shows a steep, steady linear decline from approximately 2.1 in 1995 to 1.8 in 2020.

Bottom row: Interdependence by Max Measure.

* Left panel (Compensation): Displays a U-shaped curve. Values remain stable around 2.8 until 2010, then show a sharp non-linear increase reaching approximately 3.4 by 2020.

* Right panel (Oneal and Russett): Displays a downward curve that flattens out. Values drop from 3.5 in 1995 to a low of approximately 2.9 around 2010, followed by a slight plateau or minor increase to 3.1 by 2020.

For the OR measure, the difference in dependencies for a dyad is steeply decreasing over time, indicating that interdependence is rising quickly. The “average” dyad has trended toward greater parity. This is not the case for compensation dependence. Differences in compensation dependence are very weakly decreasing over time.

The relationship of each state to the hegemon and other great powers is distinctly important for international relations. Thus, we also investigate whether interdependence is increasing according to the maximum degree of dependency for a country. The difference in trends between compensation and OR dependence is even more stark if we focus on maximum values of each measure. The bottom two panels of Figure 8 make the same calculations for differences in dependencies, but using only the maximum value for a country. As above, we take each country and find the partner on whom they are most dependent. Then we take the difference in the dependency measure for that dyad. This asks: “Who are you most dependent on, and how dependent are they on you?” It therefore describes trends in parity within a dyad, when looking only at a country’s most dependent relationship.

Compensation dependence tells a very different story from the aggregate statistics. Once again, the OR series declines over time, showing that interdependence is rising even among highly dependent partners. But the compensation measure actually shows the world becoming less interdependent among maximally dependent relationships. Countries’ maximum values of compensation dependence are increasing, and those partners that they greatly depend on are not becoming corresponding more dependent on them.

One interpretation of these two results is that symmetry in compensation interdependence among all dyads is rising because compensation interdependence has become greatly imbalanced when looking at maximum dependencies. Higher dependence on states like China, in general, increases the symmetry of dependence between states, by comparison. For example, consider two states, A and B. In 1995, an interruption in trade between the two might have caused more economic pain in State A than in State B according to compensation dependence. However, by 2015, both states trade extensively with China. Although they are both now more dependent on China than they ever depended on any other state, an interruption between States A and B is now a relatively minor problem that can be solved by increasing imports from China by a small percentage. It looks like A and B are closer to parity in their mutual dependence, only because they both became tremendously dependent on another partner. Figure 9 shows that this describes the experience of Japan, Korea, and the United States as potential targets. This figure shows compensation dependence on China and each country’s highest non-China dependencies from 1995. In each panel, dependence on non-China states is displaced by dependence on China, and the dependence on China hits a higher peak than with any other state.

Figure 9.

Dependence on China versus Primary Non-China Partners Dependencies for Japan, Korea, and the United States

Note: For each country, the gray lines show the countries they depended on most in 1995. These examples show how interdependence can fall among all dyads even while it rises when looking at maximum levels of dependence.

Figure 9. Long description

A multi-panel figure with three vertical line graphs labeled J P N, K O R, and U S A. The Y-axis represents Compensation Dependence on a logarithmic scale from -4 to -1. The X-axis represents years from 1995 to 2020.

In all three panels, a thick dark blue line representing China shows a consistent upward trend, indicating increasing dependence.

* In the J P N panel, the blue line starts at -3 in 1995 and rises to -1 by 2015. Gray lines for the U S A and K O R show a downward trend, with the U S A line dropping from -1.8 to -2.8 and K O R dropping from -3.2 to -4.0.

* In the K O R panel, the blue line starts at -3.4 and rises sharply to -1.1. Gray lines for the U S A and J P N both decline from around -2.0 to approximately -3.0.

* In the U S A panel, the blue line starts at -3.7 and rises to -1.4 by 2017 before a slight dip. Gray lines for C A N and J P N show a steady decline from -2.0 and -2.5 respectively down toward -3.0 and -3.5.

A legend at the bottom indicates the thick blue line is Dependence on China and the thinner gray lines are Other primary partners.

Effect on Compensation Dependence

We first use the compensation dependence of country i on China in year t as the outcome variable. The treatment variable is a binary indicator that equals 1 in the first year in which China gave the recipient $ 1 $ million or more in ODA-like funding according to the AidData project (Custer et al. Reference Custer, Dreher, Elston, Escobar, Fedorochko, Fuchs and Ghose2023; Dreher et al. Reference Dreher, Fuchs, Parks, Strange and Tierney2018; Reference Dreher, Fuchs, Parks, Strange and Tierney2022). We focus on actual disbursement of money rather than announced participation in BRI, since the former describes when economic transactions actually begin.

Our empirical approach needs to distinguish the effect of increased Chinese assistance from the effects of China’s general rise in the world economy. A simple correlation of Chinese assistance with dependence on China could mean that programs like BRI have increased dependence, but it could also be an artifact of how most states increased their dependence on China regardless of whether they receive any Chinese assistance. To better isolate the effects of Chinese assistance on dependence, we leverage China’s staggered assistance and investment around the world in a difference-in-differences framework. Our objective is to estimate the dependence of states having received Chinese assistance under the counterfactual where they received none. The difference-in-differences framework relies on an identification assumption: the observed trajectory of dependence for states that did not receive assistance is an estimate of what would have happened in states that did receive it. Due to the staggered nature of assistance, we use the Callaway and Sant’Anna (Reference Callaway and Sant’Anna2021) estimator to properly weight cohorts of states that received assistance at different times. This estimator has the additional advantage of producing average treatment effects of the treated for each cohort and calendar year. We include the recipient’s GDP, trade with China, and level of democracy (measured by VDEM) as controls.

Figure 10 shows the results.Footnote ³⁰ The top panel shows our estimated treatment effects on the vertical axis, with the years since entry into treatment on the horizontal axis. Treatment has a relatively quick, large, and durable positive effect on compensation dependence. The treatment effect is statistically distinguishable from zero starting a few years after treatment. It remains positive and generally grows in magnitude in subsequent years. The estimates are substantively meaningful. After five years, a country receiving assistance would need to scale up imports from non-Chinese sources by $ 19\% $ to compensate for lost trade with China, compared to $ 13\% $ for a country that did not receive assistance.

Figure 10.

Effect of Chinese Assistance on Recipient’s Dependence on China

Note: The compensation dependence measure is the outcome variable.

Figure 10. Long description

The line graph uses a grid background with a horizontal dashed line at 0.0 on the Y axis. The Y axis is labeled A T T (Comp. Depend. of recipient on C H N) with a scale from -0.1 to 0.4. The X axis is labeled Years Since Receiving $1M Assistance with a scale from -5 to 15.

Data points are represented by dots with vertical error bars.

* Pre-assistance period (Years -5 to -1): Five pink dots are clustered near the 0.0 baseline with small error bars, showing no significant trend.

* Post-assistance period (Years 0 to 15): Sixteen blue dots show a positive linear increase.

* At Year 0, the value is approximately 0.0.

* By Year 5, the value rises to approximately 0.06.

* By Year 10, the value reaches approximately 0.14.

* By Year 15, the value peaks at approximately 0.22.

The vertical error bars widen significantly as time progresses from Year 0 to Year 15, indicating increased variance in the long-term effect. A legend at the bottom identifies pink as Pre and blue as Post.

This positive finding is very robust.Footnote ³¹ We show results adding one covariate at a time to demonstrate that the results are not sensitive to the inclusion of control variables. We also include a specification where the control group includes only “not yet treated” units. We produce a two-way fixed-effects specification to show that our results do not depend on the use of the Callaway and Sant’Anna estimator or on binary treatment cutoffs. We also include specifications for different definitions of treatment. The statistical and substantive significance of the results is unchanged whether we define treatment as the first year in which a state received greater than zero, $ 0.5 $ million, $ 1 $ million, or $ 5 $ million in financing from China. Across all specifications, the coefficients on treatment are always between $ 0.08 $ and $ 0.13 $ . Furthermore, we use the Goodman-Bacon decomposition to ascertain whether our results are driven by a small group of treated units (Goodman-Bacon Reference Goodman-Bacon2021). If the effects are driven by an event in a single year—for example, if the results were a consequence of confounding due to China’s entry into the WTO in 2001—this decomposition would identify an outlier treatment cohort. The results indicate that units treated in 2000 receive a weight of $ 0.2 $ in the estimate, more than twice that of the next highest cohort of treated units. Yet, excluding these units does not substantially change the estimate. We also exclude years from the analysis on a rolling basis and demonstrate a high degree of robustness. We also show how results are similar using a broader definition of foreign assistance.

Figure 11 shows identical analysis using China’s dependence on the recipient as the outcome measure. The treatment effects are all near zero. This suggests that Chinese assistance facilitated dependence on China but did not increase interdependence. We do not see evidence of a corresponding increase in China’s dependence on the recipient.

Figure 11.

Effect of Chinese Assistance on China’s Dependence on the Recipient

Note: The compensation dependence measure is the outcome variable.

Figure 11. Long description

A coefficient plot with a horizontal dashed line at zero.

* The Y-axis is labeled A T T (Comp. Dep. of C H N on recipient) with a scale from negative 0.02 to 0.02.

* The X-axis is labeled Years Since Receiving $1M Assistance, ranging from negative 5 to 15.

* Data points are shown as dots with vertical error bars representing confidence intervals.

* Pre-treatment phase (Years negative 5 to negative 1): Five light red data points are clustered tightly around the zero line with small error bars, indicating no significant prior trend.

* Post-treatment phase (Years 0 to 15): Sixteen dark blue data points. Starting at year 0, the coefficients generally remain near or slightly above zero.

* Trend: As time progresses from year 0 to year 15, the vertical error bars significantly widen, indicating increased variance. While most point estimates remain positive, particularly peaking around year 13, they frequently overlap with the zero line, suggesting statistically insignificant effects in the long term.

Figure 12 shows results from an identical estimation, except using the OR measure of dependence as the outcome measure. The results are very different. The effects of aid on the OR measure are generally negative and indistinguishable from zero. Using this measure, we would reach the opposite conclusion of the above analysis—that Chinese aid has, if anything, decreased recipients’ dependence on China.Footnote ³² We contend that the former analysis is more accurate, since it captures the myriad ways that trade patterns could subtly change. Those changes could affect bilateral dependence, even if they had minimal (or even positive or negative) effects on aggregate trade statistics.

Figure 12.

Effect of Chinese Assistance on Recipient’s Dependence on China

Note: The OR aggregate statistic dependence measure is the outcome variable.

Figure 12. Long description

A line graph with a horizontal X axis labeled Years Since Receiving $1M Assistance, ranging from negative 5 to 15. The vertical Y axis is labeled A T T (O R Dep. of recipient on C H N), with values from negative 3e-04 to 2e-04. A dashed horizontal line represents the zero baseline.

Data points are plotted with vertical error bars representing confidence intervals.

* The Pre phase (years negative 5 to negative 1) is shown in pink. These points hover closely around the zero line with small error bars, indicating no significant trend prior to assistance.

* The Post phase (years 0 to 15) is shown in dark blue. Starting at year 0, the coefficients show a downward trend, reaching a trough around years 6 and 7 at approximately negative 1e-04.

* From year 8 to 15, the coefficients gradually rise back toward the zero baseline.

* The error bars in the Post phase are significantly larger than in the Pre phase, widening progressively as the years since assistance increase.