The Scarce Support Inside a Multinational
The Japanese parent–affiliate evidence shows a peculiar combination: foreign affiliates expanded, parent-side support employment and wages rose, yet total employment at the Japanese parent stayed broadly flat and domestic fixed assets declined. This chapter asks what internal constraint can produce those movements together. The answer is a model of parent-side support—a productive capability shared between domestic operations and foreign affiliates—and it gives the reader a precise way to understand why more valuable overseas activity need not create a domestic production boom.
Support is a shared production input, not just headquarters overhead
When people imagine a factory moving abroad, they often picture only machines and production workers. A multinational also depends on less visible work: coordinating suppliers, organizing logistics, managing sales channels, handling procurement, adapting products, solving operational problems, and connecting an affiliate to the parent’s systems and knowledge. These functions may be performed in a head office, a commercial branch, a sales establishment, an office, or another business unit. They are not the same thing as manufacturing labor, but they can determine how much production an operation can manage.
The Japanese parent survey captures part of this capability as non-production support employment. The category includes commercial and business establishments outside the head office, and it can cover work for domestic operations, foreign affiliates, or both. The survey does not reveal each worker’s destination or task. That limitation matters: the category is evidence of an organizational margin, not a direct census of labor devoted to overseas subsidiaries.
The affiliate survey provides a second, narrower window. Workers dispatched from a Japanese parent to a foreign affiliate are recorded separately. When such workers increase, the data show that at least some labor supplied by the parent is being used abroad. The paper finds that the increase in dispatched workers is particularly strong for sales- and services-oriented affiliates, the types of operations where coordination, commercial support, and cross-border business functions are especially relevant. This does not mean that every dispatched worker performs the same task. It does show why a multinational’s foreign expansion can require parent-side work even when the physical production itself remains overseas.
The model turns these observations into a simple resource problem. Let domestic production use production labor and a quantity of parent support called “S sub d.” Let the foreign affiliate use local production labor and support from the parent called “S sub a.” The parent’s total support capacity is “N,” and the key constraint is:
N = S sub d + S sub a.
The notation says something more important than the algebra. Support sent to the affiliate is not free from the parent’s point of view. The same pool of coordination and commercial capability could instead be used to improve domestic operations. A parent can increase the pool by hiring more support workers, but it cannot instantly create unlimited experienced managers, procurement knowledge, customer relationships, or logistical coordination. The cost of expanding the pool rises at the margin.
This is why support is different from a simple budget that can be divided without consequence. If a parent has ten effective units of support capacity, directing more of them abroad leaves fewer for domestic operations unless the firm also expands capacity. If it hires additional support, the new workers may be costly to find, train, and coordinate. The firm therefore faces both an allocation margin—where existing capability is used—and a scale margin—how much total capability to create.
The shared constraint does not claim that domestic and foreign operations use identical people in identical ways. It represents an opportunity cost inside the parent: attention, coordination, commercial expertise, and organizational capacity can be directed toward one operation or another. The model’s abstraction is useful precisely because the survey cannot observe every internal assignment. It connects the observed categories to a firm-level choice without pretending that a support-employment count is a complete map of the firm’s organization.
Why a weaker yen changes the allocation decision
The parent chooses support by comparing the value created in domestic operations with the value created in the foreign affiliate. Let the domestic operation’s optimized value be V(S sub d), and let the affiliate’s value be V*(S sub a), measured in foreign currency. The Japanese parent internalizes an effective fraction of the affiliate’s value, represented by ξ. If E is the number of yen per unit of foreign currency, the affiliate’s value to the parent is expressed in yen as EξV*(S sub a). Total support labor costs C(N), with a marginal cost that rises as the parent expands support employment.
The parent’s simplified problem is therefore to choose S sub d and S sub a to maximize:
V(S sub d) + EξV(S sub a) − C(S sub d + S sub a).*
The symbols can be read as a comparison of marginal returns. At an interior allocation, the last unit of support used domestically must be worth the same as the last unit used at the affiliate after converting the affiliate’s return into yen. In the paper’s notation, the central condition is:
V′(S sub d) = EξV′(S sub a).*
A prime means the additional value created by one more unit of support. The equation does not say that the parent is calculating a literal accounting charge for every hour of management time. It says that the firm balances the marginal contribution of support across its two operations.
Now let the yen depreciate. E rises: one unit of foreign-currency affiliate value translates into more yen. Before the firm changes anything, the right-hand side of the allocation condition becomes larger. Support devoted to the affiliate has a higher home-currency return than it had before. The parent therefore has an incentive to move support toward the affiliate, increasing S sub a and reducing S sub d.
The firm need not choose between pure reallocation and pure expansion. Because support labor becomes more valuable overall, the parent may hire more of it. But the rising marginal cost of support means that expansion is not limitless. The model’s local prediction is consequently fourfold: support allocated to the affiliate rises, support allocated to domestic operations falls, total support employment rises, and the support wage rises.
That prediction helps explain the parent-side data. A stronger affiliate opportunity can increase demand for people who coordinate, sell, purchase, and manage cross-border operations. Wages in the support margin may rise because the firm is competing for a scarce capability. At the same time, total employment need not rise much: support employment can increase while other parent employment declines. The empirical pattern—higher average wages, more non-production support employment, lower other employment, and approximately flat total parent employment—is consistent with a firm reallocating and selectively expanding its organizational capacity rather than hiring broadly for domestic production.
The model also connects support to production labor. Suppose more parent support makes it more profitable for the affiliate to hire local production workers. Then the rise in S sub a increases affiliate production labor and affiliate output. If domestic production also benefits from support, the fall in S sub d puts downward pressure on domestic production labor and domestic output. This is the mechanism’s answer to the apparent contradiction: the foreign operation can expand precisely because the parent has shifted a scarce complementary input toward it.
The word “pressure” is important. In the firm-level or partial-equilibrium model, domestic multinational production can fall as support is redirected. But that is not a prediction that Japan’s aggregate output must fall after every depreciation. Domestic demand may increase, foreign demand may change, and the conventional expenditure-switching channel may support production at home. Other firms without the same affiliate exposure may also respond differently. The model isolates one internal crowding force; it does not replace the whole economy.
Translation is not the same as expansion
The support mechanism matters because a foreign-income increase can otherwise be misread. Suppose an affiliate earns the same foreign-currency operating surplus before and after a depreciation. Converting that unchanged surplus into yen produces a larger number. That is a real change in the parent’s measured home-currency income, but it is a valuation effect. It does not require more affiliate workers, more output, more dispatched employees, or more support at the Japanese parent.
The parent-support model adds a second margin. The higher yen value of the affiliate’s activity changes the return to support used there. If the parent responds by increasing S sub a, the affiliate can produce more and earn a larger operating surplus. The yen value of affiliate income then rises for two reasons: the existing foreign surplus is worth more in yen, and the foreign operation itself has expanded.
This distinction aligns with the evidence. Affiliate profits and payments to parents rise in the yen-denominated data, but those outcomes could contain translation. Affiliate employment and parent-dispatched workers also rise, which is evidence that at least part of the response is real activity. At Japanese parents, support employment and wages rise while total employment remains broadly flat. The joint pattern is difficult to describe as passive translation alone, because translation by itself does not create a reason to hire or reassign support workers.
Nor does the model require every yen of higher affiliate profit to be paid immediately to Japan. The parameter ξ is an effective pass-through of affiliate operating value into the parent’s income and allocation decision. It is not the same as a legal ownership share or a statutory dividend rate. The data’s affiliate-to-parent payment ratio helps discipline the strength of the financial linkage, but the model abstracts from the detailed distinction between distributed earnings, reinvested earnings, and intercompany interest.
This also clarifies what the model does not claim about the parent workforce. If support employment rises, the model says that the firm values more support capacity, not that every support employee is physically sent abroad. Some workers may serve domestic and foreign operations simultaneously. Some may be in commercial establishments rather than formal headquarters. The model’s “support” is broader than a job title and narrower than total parent employment: it is the productive organizational input that the two operations compete to use.
Several alternative explanations remain possible. A financial windfall could relax constraints and allow a parent to expand domestic activity. A readily scalable support function could let the affiliate grow without crowding out domestic operations. A vertical input channel could make affiliates that buy from Japan more competitive. The paper’s additional tests find no stronger parent response among initially more leveraged firms and no positive interaction between the revenue-side shock and Japan-input intensity. Those findings weaken the financial-relaxation and vertical-input stories for this episode, while the observed affiliate-workforce heterogeneity supports the organizational interpretation. They do not prove that all other channels are absent.
The model itself is deliberately spare. It leaves out vertical input sourcing, transfer pricing, endogenous affiliate location or ownership, and capital accumulation. It assumes that parent support is an internal input rather than a separately priced service sold to the affiliate. These omissions make the mechanism easier to isolate, but they also define its boundary. The model explains why an existing multinational network can redirect activity after a depreciation; it does not decide whether a firm should build a new factory in Japan over a longer horizon.
The resulting judgment is precise. A yen depreciation changes the relative value of the parent’s existing operations. When support is scarce, an affiliate gain can pull organizational resources toward production abroad. Total support and wages may rise, but domestic multinational production can receive less support. The mechanism does not say that Japan receives no benefit. It says that benefits to Japanese parents and residents can arrive through foreign production and organizational income rather than through a broad expansion of production located in Japan.
That firm-level conclusion now needs to be connected to national accounts. The next question is how the same allocation looks when an economy can serve foreign customers either by exporting from home or by producing through affiliates abroad—and why those choices produce different movements in GDP, GNI, trade, and direct-investment income.