Theoretical Model

To motivate the empirical analysis, we set up an industry-equilibrium model in which Eastern firms can use two channels to export their products to the West, and vice versa.⁵ Via one channel, they can produce their goods at home and directly export them to the other region. Via the other channel, they can indirectly export to the other region by using low-cost PRC as a final assembly platform. As we shall see below, the model will provide a theoretical explanation for the negative correlation between the average distance traveled by the PRC's processing imports and the average distance traveled by its processing exports. In addition, it will allow us to identify two testable hypotheses related to the PRC's processing trade patterns.

Consider an industry-equilibrium model encompassing three economies.⁶ There are two advanced economies (East and West) that are fully symmetric with high wages and large markets for the industry's output. In addition, there is a third economy (PRC) that has low wages, no market for the industry's output, and that is geographically located closer to East than to West. In this model, the only role that the PRC plays is thus that it is a potential lowcost location in the vicinity of East for processing final goods. The assumption that the PRC does not have a market for the industry's output is harmless because, by the very nature of the processing trade regime, processed goods are not allowed to be sold in the PRC market.

A continuum of firms in East and West has the know-how to produce a single differentiated product. These are the only active firms in the industry because we assume that the knowledge is nontransferable to domestic firms in the PRC. Each advanced-economy firm needs to produce its intermediate good at home, but can process its final good in any of the three economies.

All consumption of the differentiated products takes place in the East and West. Specifically, in each advanced economy i∈[Ε,W] a representative consumer allocates an amount of expenditure Yi to the industry. Within the industry, the consumer has a utility function that exhibits constant elasticity of substitution e = 1/(1 - α). Maximizing the utility function subject to the consumer's expenditure generates the demand function that a firm faces in advanced economy i:

where the demand level Aⁱ is exogenous from the point of view of the individual firm.⁷ In this case, the monopolistically competitive firm charges the following price for its product:

where c denotes the firm's marginal unit production cost and 1 / α represents the markup factor.

We distinguish the economies in several ways. First, wage rates are higher in the advanced economies than in the PRC; in particular, W^E = W^W = 1 > W^c = W. Second, the PRC is located closer to East than to West, while West is equidistant to both East and PRC. Denote τ^ij as the melting-iceberg trade cost of shipping goods from economy i to economy j, where τⁱⁱ = 1 and τ^ij = τ^ji > 1 for i ≠ j. We assume that trade costs increase linearly with distance so that τ^EC = t < τ^WC = τ^WE = τ (see Figure 2 [ PDF 80.3KB | 1 page ]).⁸ These locational assumptions reflect the notion that the PRC acts as the low-cost processing platform in the vicinity of East. To see this, note the differential impact that an increase in trade costs t and τ play in our model. A rise in t increases trade costs only between East and PRC, thus making it less attractive to indirectly export through the PRC. Conversely, a rise in t increases the trade costs between West and PRC as well as West and East, thus reducing the incentives for both direct and indirect exports.

The production of a final good variety involves two distinct stages: intermediate good production and final good processing. Intermediate goods need to be produced in the firm's home economy j at cost aw^ƒ = a where a equals the firm's labor-per-unit-output coefficient. The final good can be processed in any economy l ∈ {E, W, C} at an extra ad valorem cost w^l. The combination of production costs and melting-iceberg trade costs then implies that the unit cost of producing an intermediate good in economy j, processing it into a final good in economy l, and delivering the final goods to economy i equals:

To interpret this unit cost function, suppose that a firm with labor-per-unit-output coefficient a conducts both production stages in East and sells its output domestically.⁹ From equation (3), its unit cost then amounts to a. If it conducts both production stages in East and then exports the final goods to West, the unit cost equals aτ. If the firm produces its intermediate goods in East, processes its final goods in the PRC, and delivers them to West, the unit cost amounts to atwt. Because w < 1 and t,τ > 1, it is clear that the attractiveness of conducting processing activities in the PRC depends on the tradeoff between lower wages and higher trade costs.

Our model features intra-industry firm heterogeneity as developed by Melitz (2003). To set up its headquarters in advanced economy i, a firm needs to bear a fixed cost of entry F_e, measured in labor units. With this fee, the entrant acquires the design for a differentiated product and draws a labor-per-unit-output coefficient of a from a cumulative Pareto distribution G(a) with shape parameter z. Upon observing this draw, the firm decides either to exit the industry or to start producing. If it decides to produce, it bears an additional fixed cost f_D of initiating production operations. There are no other fixed costs when the firm sells only in the domestic market. If the firm chooses to export to the foreign market, however, it bears an additional fixed cost f_X of forming a distribution and servicing network in the foreign economy. Finally, if it sets up a processing plant abroad, it bears one additional fixed cost f_P.

We take on the following simplifying assumption:

Assumption 1: (t²w) ^ε−1 > 1 > (tw) ^ε−1 > f_x/(f_p + f_x).

Assumption 1 ensures that (i) at least one firm from advanced economy i processes its final goods in the PRC for export to advanced economy j ≠ i;¹⁰ and (ii) no firm from advanced economy i sets up a processing plant in the PRC to export back to its own market in economy i.¹¹ Assumption 1 and the unit cost function in equation (2) ensure that, despite the PRC’s relative proximity to East, the analyses for economies East and West are completely symmetric. Below, we conduct the analysis for advanced economy i. We call firms from economy i “domestic” firms and firms from the other advanced economy j “foreign” firms.

In advanced economy i, there are three types of firms that sell their final goods: type-D domestic firms that conduct both production stages in economy i and sell their output domestically; type-X foreign firms that produce both stages in the advanced economy j and export their final goods to economy i; and type-P foreign firms that produce their components in advanced economy j, process their final goods in the PRC, and then export to economy i. Using equations (1) to (3), we can derive the operating profits that the three types of firms face:

where Bⁱ = (1 − α)Ai/α^1−ε.

We depict these profit functions in Figure 3 [ PDF 71.8KB | 1 page ]. In this figure, a^1-ε is represented on the horizontal axis. Because ε > 1, this variable increases monotonically with labor productivity 1/a, and can be used as a productivity index.¹² All three profit functions are increasing with this productivity index: more productive firms are more profitable in all three activities. For a given productivity level, type-D firm profits are always higher than the other two firm-types because type-D firms invoke both a lower fixed cost and a lower marginal cost (due to assumption 1). Type-X firms face a lower fixed cost but a higher marginal cost than type-P firms. These profit functions imply that domestic firms with a productivity level below (aⁱ_D)^1-ε expect negative operating profits and exit the industry, while firms with productivity levels above this cutoff become type-D firms. Foreign firms with productivity levels below (aⁱ_X)^1-ε do not sell their products in advanced economy i; foreign firms with productivity between (aⁱ_X)^1-ε and (aⁱ_P)^1-ε become type-X firms; while those with a higher productivity become type-P firms. Using equations (4) to (6), the cutoff coefficients (aⁱ_D)^1-ε, (aⁱ_X)^1-ε, and (aⁱ_P)^1-ε are determined by:

Free entry ensures equality between the expected operating profits of a potential entrant and the entry cost F_e. The free entry condition together with equations (7) to (9) provide implicit solutions for the cutoff coefficients aⁱ_D, aⁱ_X, and aⁱ_P, and the demand levels Bⁱ in every economy.

If we take into account the PRC's bilateral trade patterns for Eastern and Western firms, and the locational assumptions shown in Figure 2, our theoretical model fits the stylized facts of the PRC's processing trade well. In line with Figure 1, our theoretical model predicts a negative correlation between the distance from which the PRC's inputs are imported (import distance) and the distance to which the PRC's final goods are exported (export distance). The inputs that the PRC imports from the nearby East are processed into final goods and exported to the far-away West. Conversely, the inputs that the PRC imports from the faraway West are processed into final goods and exported to the nearby East (Figure 4 [ PDF 83.7KB | 1 page ]).

Furthermore, we can use our model to derive a number of testable hypotheses related to the PRC's processing trade. In Appendix 1 [ PDF 121.4KB | 2 page ], we demonstrate that the bilateral export value of the PRC to advanced economy i can be expressed as:

where Ω¹_p denotes the total industry sales of type-P firms in economy i, σX,P captures the relative market share of type-X firms to type-P firms in economy i; and σD,P captures the relative market share of type-D firms to type-P firms in economy i. Equation (10) provides the intuitive result that, all else equal, an increase in the relative market share of type-D firms to type-P firms in advanced economy i reduces the PRC’s exports to i. Similarly, an increase in the relative market share of type-X firms to type-P firms in advanced economy i reduces the PRC’s exports to i.

It is straightforward to calculate from equations (11) and (12) that:

Equation (13) suggests that a rise in t increases the relative market share of type-X firms to type-P firms, σX,P, while a rise in τ leaves σX,P unaffected. The differential impact of t and τ is related to our notion that the PRC is the low-cost processing platform in the vicinity of East. On the one hand, an increase in t only raises the trade costs related to using the PRC as an export platform. As a result, it reduces the attractiveness of indirect exports through the PRC, thus inducing some foreign firms to substitute indirect exports for direct exports. This leads to an increase in the relative market share of type-X firms to type-P firms. On the other hand, an increase in τ raises the trade costs for both direct and indirect exports. In our model, it therefore leaves the relative market share of type-X firms to type-P firms unchanged. Similarly, equation (14) indicates that a rise in both t and τ increases the relative market share of type-D domestic firms to type-P foreign firms, σD,P, but that the effect of an increase in t is larger. Combined with equation (10), these results suggest that an increase in both t and in τ has a negative impact on the PRC's exports to economy i, , but that the effect of an increase in t is larger.

Note that t and τ play a different role in the PRC's processing exports to East and West. When exporting to West, t reflects the trade costs related to import distance and τ reflects the trade costs related to export distance. Conversely, when exporting to East, t reflects the trade costs related to export distance and τ reflects the trade costs related to import distance. This leads to two hypotheses relating import and export distance to the PRC's processing exports:

Hypothesis 1: Ceteris paribus, PRC's processing exports are negatively affected by both an increase in import distance and an increase in export distance.

Hypothesis 2: Ceteris paribus, PRC's processing exports to East are (i) more sensitive to export distance and (ii) less sensitive to import distance than its processing exports to West.

In the two sections that follow, we present the data and methods that we use to test these hypotheses.

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