Vertical Outward FDI in Global Value Chains

• Vertical OFDI is defined as a home-country firm investing abroad in upstream or intermediate production to exploit cost differentials.
• The framework applies a partial equilibrium model with firm heterogeneity and threshold effects in input-cost ratios to guide sourcing decisions.
• Empirical evidence from China’s paper industry shows that supply shocks, such as waste import bans, trigger vertical OFDI among high-productivity firms.

Searching arXiv for the specified paper and closely related work to anchor the article in current research. Vertical outward foreign direct investment (OFDI) is the decision of a home-country firm to invest abroad in upstream or intermediate stages of production and then import those intermediate inputs back home. In international economics, it is distinguished from horizontal FDI by its efficiency-seeking rather than market-seeking logic: the firm reorganizes production across borders to exploit relative cost differences in labor, energy, or intermediate inputs. Recent work on China’s paper industry shows that adverse supply-side shocks in domestic input markets can induce such reorganization, and that the response is governed by threshold effects in relative input costs and by firm heterogeneity in productivity (Anwar et al., 29 Aug 2025).

1. Conceptual scope and distinction from other forms of FDI

Vertical OFDI is a form of cross-border value-chain fragmentation. A firm invests abroad in upstream or intermediate stages—for example, by building or acquiring a foreign affiliate that produces an input or processes a raw material—and imports those inputs to support domestic final-goods production. It is “vertical” because it links different stages of the value chain, and “outward” because the investment flows from the home country to a foreign location (Anwar et al., 29 Aug 2025).

This differs from horizontal FDI, which duplicates similar production in multiple countries to serve local consumers. In the terminology used in the literature summarized here, horizontal FDI is market-seeking, whereas vertical FDI is efficiency-seeking. The relevant comparison is therefore not between domestic and foreign final demand, but between domestic and foreign input costs. In global value chains, vertical OFDI reallocates where particular stages are carried out—for example, pulp production abroad and final paper manufacturing at home—and is undertaken only if the savings in unit production costs justify the fixed costs of foreign establishment or acquisition (Anwar et al., 29 Aug 2025).

A common misconception is that OFDI is intrinsically associated with downstream market access. The paper under discussion instead treats vertical OFDI as a cost-saving response to input-market conditions. In that formulation, foreign investment is not an end in itself; it is a mechanism for changing the location of input production when domestic sourcing becomes relatively expensive.

2. Theoretical framework: cost thresholds, fixed costs, and sorting

The model is a partial equilibrium framework with a monopolistically competitive final-goods industry, heterogeneous firms in the Melitz tradition, CES preferences over varieties, and an explicit intermediate input market. Firms differ in productivity $\varphi$, distributed Pareto, and use labor together with an intermediate input. One worker uses $n$ units of the intermediate input to produce $\varphi$ units of output, so higher $n$ implies greater input intensity (Anwar et al., 29 Aug 2025).

The marginal cost of final-goods production is

$$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$

where $X_1=0$ denotes domestic sourcing, $X_1=1$ denotes foreign sourcing through vertical OFDI, $\delta$ is the domestic unit cost of the intermediate input, and $\tilde{\delta}$ is the foreign unit cost inclusive of transport and other import-related costs. Engaging in vertical OFDI requires an additional fixed cost $f_1$ on top of the basic fixed cost $n$0 of operating in the final-goods market (Anwar et al., 29 Aug 2025).

Under CES demand and monopolistic competition, the paper derives closed-form optimal profits under the two sourcing regimes:

$n$1

$n$2

The firm enters only if profits are non-negative and, conditional on entry, chooses vertical OFDI if $n$3. The central sufficient statistic is the relative input-cost ratio $n$4. If $n$5, domestic sourcing is weakly cheaper, and no firm chooses vertical OFDI. If $n$6, foreign sourcing lowers marginal cost, but adoption still depends on whether the firm can cover the extra fixed cost $n$7 (Anwar et al., 29 Aug 2025).

This produces a three-way sorting pattern. Very low-productivity firms do not enter. Intermediate-productivity firms enter and produce domestically without OFDI. High-productivity firms undertake vertical OFDI. The model formalizes this with an entry cutoff $n$8 and a higher switching cutoff $n$9:

$\varphi$0

$\varphi$1

The resulting partition is $\varphi$2 for exit, $\varphi$3 for domestic production without OFDI, and $\varphi$4 for production with vertical OFDI. Proposition 1 states that the decision depends jointly on the input-cost ratio $\varphi$5 and productivity $\varphi$6 (Anwar et al., 29 Aug 2025).

The paper also derives the probability that a randomly drawn firm undertakes vertical OFDI:

$\varphi$7

where $\varphi$8 is the minimum productivity in the Pareto distribution and $\varphi$9 is the Pareto shape parameter. This probability is zero when $n$0 and increasing in $n$1 when $n$2, with stronger responsiveness when input intensity $n$3 is high. The model therefore predicts threshold behavior rather than a smooth response over all cost levels.

3. Supply-side shocks and the 2017 waste paper import ban

The empirical setting is China’s paper product industry, which has a particularly clear input structure. Wood pulp, derived from timber, is used for household paper, coated paper, double offset paper, and ivory board. Waste paper pulp, derived from recycled waste paper, is used almost exclusively for corrugated paper and container board, which are inputs for carton manufacturing (Anwar et al., 29 Aug 2025).

China had imported large quantities of waste materials since the 1980s. By 2016, it imported 4.85 million tons of waste and accounted for 40% of global waste paper trade. Processing imported waste paper generated substantial pollution. In July 2017, the State Council issued the “Implementation Plan for Banning the Entry of Foreign Waste and Promoting the Reform of the Management System of Solid Waste Import (Decree No. 70, 2017),” targeting pollution-intensive waste such as plastics, paper, and textiles, with the intent to ban these imports by the end of 2017 and expand the bans in 2018 (Anwar et al., 29 Aug 2025).

The paper treats this policy as an exogenous supply-side shock because it was motivated by environmental concerns rather than by any intent to alter firms’ FDI behavior. Its effect varied within the industry because exposure depended on product mix. Firms producing corrugated paper and container board relied heavily on waste paper pulp and were therefore directly exposed to the contraction in raw material supply. Firms producing other paper products relied mainly on wood pulp and were less affected (Anwar et al., 29 Aug 2025).

After the ban, domestic waste paper prices rose and domestic supply of waste paper pulp fell from approximately 64 million tons in 2015–2017 to less than 54 million tons in 2018–2020. In the model’s terminology, the policy raised $n$4, the domestic input price. The theoretical significance is direct: once the supply shock pushes $n$5 across the threshold $n$6, foreign sourcing through vertical OFDI becomes cost-minimizing for sufficiently productive firms. Proposition 3 formalizes three regimes: no OFDI if the shock leaves $n$7, a discrete increase in OFDI when the shock moves $n$8 from below to above $n$9, and a further rise in OFDI probability when $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$0 even before the shock (Anwar et al., 29 Aug 2025).

4. Quasi-experimental identification and difference-in-differences design

The empirical design exploits within-industry variation in exposure to the waste paper shock. Treated firms are those whose product mix includes corrugated paper and container board; control firms are paper producers whose products rely mainly on wood pulp. The pre-policy period runs through 2016, and the post-policy period begins in 2017. The analysis uses firm-level panel data from 2000 to 2023 (Anwar et al., 29 Aug 2025).

The core firm-level specification is a linear probability model,

$$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$1

where $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$2 is an indicator equal to 1 if firm $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$3 in group $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$4 has ever undertaken vertical OFDI by year $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$5, $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$6 is the post-policy dummy, $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$7 is the treatment dummy, $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$8 contains controls including relative firm size, profitability (ROA), age, and polynomial terms, and $$c = 1 + n\big[(1 - X_1)\delta + X_1\tilde{\delta}\big],$$9 absorbs firm and group fixed effects through the within transformation. The coefficient of interest is $X_1=0$0, which measures the additional post-policy change among treated firms relative to control firms (Anwar et al., 29 Aug 2025).

The cumulative OFDI definition is important because vertical OFDI is treated as a one-off cost-saving investment. Once a firm undertakes it, the indicator switches from 0 to 1 and remains there. The paper also estimates an aggregate-level DiD by first constructing yearly probabilities of vertical OFDI by group and then running an analogous regression as a semi-parametric robustness check (Anwar et al., 29 Aug 2025).

Causal interpretation rests on several design features. The policy is argued to be exogenous to prior firm internationalization. Treatment and control firms operate in the same industry, and observable characteristics such as size, age, and profitability are described as fairly balanced. Firm fixed effects absorb time-invariant differences, including inherent propensity to invest abroad. Parallel trends are assessed through event-time interactions; pre-2017 coefficients are individually statistically insignificant, and a joint chi-square test is non-significant with statistic 6.08 and $X_1=0$1. Additional robustness exercises progressively add controls and high-order polynomials, and the treatment effect remains stable. The paper also controls for pre-2015/2016 $X_1=0$2 emission levels and changes, interacted with a fourth-order time polynomial, to address possible anticipation or environmental confounding (Anwar et al., 29 Aug 2025).

5. Empirical findings: magnitude, rarity, and firm heterogeneity

The baseline firm-level DiD estimate is $X_1=0$3 with robust standard error approximately 0.0365, significant at the 1% level. Interpreted directly, this is a 16.39 percentage-point increase in the probability that a treated firm has undertaken vertical OFDI in the post-policy period relative to the control group’s change. Because the overall mean OFDI rate is only 2.48%, the paper characterizes the effect as economically meaningful (Anwar et al., 29 Aug 2025).

Across richer specifications, the estimated treatment effect remains in the range of approximately 0.156 to 0.175 and is always significant at 1%. Aggregate-level estimates are slightly smaller but consistent, approximately 0.126 to 0.137. The temporal pattern is also sharp: before 2017, no firm in the sample engaged in vertical OFDI; after 2017, treated firms exhibit a spike in vertical OFDI M&A events, while control firms continue to exhibit no vertical OFDI (Anwar et al., 29 Aug 2025).

These findings align closely with the threshold mechanism in the theory. Vertical OFDI is rare overall, which is consistent with the proposition that firms adopt it only under strong incentives created by sufficiently severe cost differences. The response is concentrated among firms producing corrugated paper and container board, precisely those with high dependence on waste paper pulp and therefore greater exposure to the input-price shock. Firms relying on wood pulp do not exhibit the same response (Anwar et al., 29 Aug 2025).

The model predicts sorting by productivity, but the empirical sample consists mainly of listed firms, which are plausibly drawn from the upper part of the capability distribution. Even within that truncated sample, only a subset undertake OFDI. The paper reports that larger and older firms tend to be more likely to engage in OFDI in some specifications, whereas profitability has a weaker and less robust relationship, often insignificant or only marginally significant. This is consistent with, though not a direct test of, the theoretical claim that only sufficiently productive or well-resourced firms can absorb the fixed costs of foreign M&A (Anwar et al., 29 Aug 2025).

6. Interpretation, policy relevance, and limitations

The combined theoretical and quasi-experimental evidence presents vertical OFDI as a strategic response to supply-side disruptions. The sequence is explicit: a raw material import ban reduces upstream supply, domestic intermediate-input prices rise, the relative cost of domestic sourcing worsens, and firms that can cover the fixed costs of foreign establishment or acquisition relocate the upstream stage abroad while preserving downstream production at home. In the paper-industry application, this means securing access to waste paper and pulp abroad while maintaining domestic paper-product manufacturing (Anwar et al., 29 Aug 2025).

This interpretation clarifies two points often blurred in discussions of internationalization. First, vertical OFDI is not reducible to generic globalization or market expansion; it is a specific response to relative input costs and supply-chain configuration. Second, firms do not respond symmetrically. The paper’s framework emphasizes that severe shocks or high baseline costs are required to induce switching, and that heterogeneity in productivity generates a sorting equilibrium in which some firms invest abroad, some continue domestic sourcing, and some may exit (Anwar et al., 29 Aug 2025).

The policy implications are two-sided. The waste paper import ban generated an environmental gain by reducing pollution from imported waste processing, and previous studies are reported to document improved air quality in areas previously reliant on waste imports. At the same time, the policy unintentionally encouraged firms to move part of the production process abroad. A plausible implication is that environmental regulation and input-market policy can reshape global value chains even when FDI is not the intended policy target. The paper accordingly suggests that governments may wish to pair import bans with support for domestic recycling capacity or alternative raw material sources in order to reduce the incentive for upstream offshoring (Anwar et al., 29 Aug 2025).

Several limitations qualify the scope of the findings. The sample covers 42 mainly listed firms in China’s paper industry, and listed firms may be more prone to internationalization than smaller firms. The analysis focuses on overseas M&A and does not observe greenfield vertical OFDI, although the mechanism may also apply there. Identification is especially clean because the paper industry permits a sharp distinction between waste-paper-based and wood-pulp-based products; industries with more complex input mixes may make treatment classification more difficult. External validity is therefore a matter of mechanism rather than exact magnitude: the pathway from input-cost shocks to vertical OFDI is presented as general, but the size of the response and the relevant thresholds in $X_1=0$4 will vary across sectors and countries (Anwar et al., 29 Aug 2025).