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In this section, I discuss the theoretical mechanism of how an increase in imported intermediate inputs affects a firm’s performance.

5.2.1. Total factor productivity

I follow the partial equilibrium model of Kasahara and Rodrigue (2008) and Bas and Strauss-Kahn (2013) who develop a Melitz-type heterogeneous firm’s model with intermediate goods to explain the simultaneous choices related to importing intermediate goods. In the framework, importing inputs may affect the TFP due to the technological and quality factors that are embedded in the imported inputs.

It can be supposed that to produce a total output𝑌𝑌𝑖𝑖𝑖𝑖for each period of 𝑡𝑡, a firm

𝑖𝑖 uses different types of inputs, namely capital𝐾𝐾𝑖𝑖𝑖𝑖, labour𝐿𝐿𝑖𝑖𝑖𝑖, energy 𝑅𝑅𝑖𝑖𝑖𝑖, and a set of

horizontally differentiated intermediate materials 𝑍𝑍(𝑔𝑔) that can be domestically

sourced or imported. 𝑌𝑌𝑖𝑖𝑖𝑖 = 𝑒𝑒𝜔𝜔𝑖𝑖𝑖𝑖𝐾𝐾𝑖𝑖𝑖𝑖𝛽𝛽𝑘𝑘𝐿𝐿𝛽𝛽𝑖𝑖𝑖𝑖𝑙𝑙𝑅𝑅𝑖𝑖𝑖𝑖𝛽𝛽𝑟𝑟�∫ 𝑍𝑍(𝑔𝑔) 𝜃𝜃−1 𝜃𝜃 𝑁𝑁(𝑑𝑑𝑖𝑖𝑖𝑖) 0 𝑑𝑑𝑔𝑔� 𝛽𝛽𝑧𝑧𝜃𝜃 𝜃𝜃−1 (5.1).

The variable, 𝜔𝜔𝑖𝑖𝑖𝑖, represents serially-correlated productivity shocks. The

elasticity of substitution between any two material inputs is given by 𝜃𝜃> 1. The

variable 𝑁𝑁(𝑑𝑑𝑖𝑖𝑖𝑖) denotes the range of intermediate inputs needed in the production

that can be obtained from home country 𝑁𝑁ℎ,𝑖𝑖 or that are available in the world market

𝑁𝑁𝑓𝑓,𝑖𝑖. The decision on intermediate input is a discrete choice function, denoted by

𝑑𝑑𝑖𝑖𝑖𝑖 ∈{0,1}, to import from abroad or not: 𝑁𝑁(𝑑𝑑𝑖𝑖𝑖𝑖) = (1− 𝑑𝑑𝑖𝑖𝑖𝑖)𝑁𝑁ℎ,𝑖𝑖+𝑑𝑑𝑖𝑖𝑖𝑖𝑁𝑁𝑓𝑓,𝑖𝑖. There is a

range of intermediate inputs that are not produced locally but can be imported from other countries. Consider the equilibrium in which all intermediate goods are

symmetrically produced at level 𝑧𝑧̅. Substituting 𝑧𝑧(𝑔𝑔) =𝑧𝑧̅ into Equation 5.1 leads to:

𝑌𝑌𝑖𝑖𝑖𝑖 = 𝑒𝑒𝜔𝜔𝑖𝑖𝑖𝑖𝑁𝑁(𝑑𝑑𝑖𝑖𝑖𝑖)

𝛽𝛽𝑧𝑧

where𝑍𝑍𝑖𝑖𝑖𝑖 =𝑁𝑁(𝑑𝑑𝑖𝑖𝑖𝑖)𝑧𝑧̅. The TFP is defined as𝐴𝐴𝑖𝑖𝑖𝑖 =_𝐾𝐾 𝑌𝑌𝑖𝑖𝑖𝑖

𝑖𝑖𝑖𝑖𝛽𝛽𝑘𝑘𝐿𝐿𝑖𝑖𝑖𝑖𝛽𝛽𝑙𝑙𝑅𝑅𝑖𝑖𝑖𝑖𝛽𝛽𝑟𝑟𝑍𝑍𝑖𝑖𝑖𝑖𝛽𝛽𝑧𝑧

. Then, from equation

(5.2), we get:

ln𝐴𝐴(𝑑𝑑𝑖𝑖𝑖𝑖,𝜔𝜔) =_𝜃𝜃−1𝛽𝛽𝑧𝑧 ln�𝑁𝑁(𝑑𝑑𝑖𝑖𝑖𝑖)�+𝜔𝜔𝑖𝑖𝑖𝑖 (5.3).

Equation 5.3 indicates that productivity is positively related to the range of intermediate inputs utilised in production. Firms importing intermediate inputs from abroad can employ a larger variety of intermediate inputs and hence have higher productivity than those employing domestic intermediate inputs only.

5.2.2. Export performance

This study connects the decision on intermediate inputs with export performance.

Consider the standard profit maximisation problem of firm 𝑖𝑖: max𝜋𝜋𝑖𝑖𝑖𝑖 = 𝑟𝑟(𝑦𝑦)𝑖𝑖𝑖𝑖−

𝑐𝑐(𝑦𝑦)𝑖𝑖𝑖𝑖, where 𝑟𝑟is revenue and 𝑐𝑐is cost. Both depend on the quantity of production

𝑦𝑦𝑖𝑖𝑖𝑖. Noted that firm 𝑖𝑖 might export part of its production in as much as 𝑦𝑦𝑖𝑖𝑖𝑖𝐸𝐸𝐸𝐸; where

𝑦𝑦𝑖𝑖𝑖𝑖 =𝑦𝑦𝑖𝑖𝑖𝑖𝐸𝐸𝐸𝐸+𝑦𝑦𝑖𝑖𝑖𝑖𝐷𝐷𝐷𝐷𝐷𝐷. As explained in Equation 5.1, the quantity of output produced 𝑦𝑦𝑖𝑖𝑖𝑖

depends on the input choices, including intermediate inputs obtained from domestic

producers 𝑁𝑁ℎ,𝑖𝑖 and from import 𝑁𝑁𝑓𝑓,𝑖𝑖. Each intermediate input is selected to maximise

the firm’s export profits, therefore the profit is also a function of intermediate inputs,

𝜋𝜋𝑖𝑖𝑖𝑖 =𝑓𝑓{𝑁𝑁(𝑑𝑑𝑖𝑖𝑖𝑖)}.

Input decisions affect the cost of production, 𝑐𝑐(𝑦𝑦)𝑖𝑖𝑖𝑖 in several ways. When the

firm selects its combined inputs, the fixed and marginal costs of acquiring the inputs determine the optimal input use. As discussed by Kasahara and Lapham (2013) and Damijan, Konings and Polanec (2014), the fixed costs of getting intermediate inputs

could be significant, especially for imported inputs.9 _{The firm might face credit}

constraints that limit the amount of working capital available; thus only more productive firms (or firms that can utilise inputs efficiently) are able to import. This is also explained by Equation 5.3 that correlates the import decision with productivity.

The marginal costs of obtaining inputs depend on the prices of the inputs as well as other variable costs. Given a certain level of quality required, a firm will choose the cheapest from various options of a specific intermediate material either from domestic or foreign markets. Even though an imported input could be cheaper, firms need to consider additional variable costs before deciding to import. These costs may include import tariffs as well as the costs associated with real exchange rates. Any change in these factors may affect the decision to import intermediate inputs. The firm could thus respond to the changes in these variable costs by adjusting its set of imported intermediate inputs or the levels of the imported inputs used in production or both.

The decision on inputs could affect the revenue 𝑟𝑟(𝑦𝑦)𝑖𝑖𝑖𝑖 via prices as well as the

quantities demanded (Fan, Li & Yeaple 2015). As imported inputs potentially have higher quality, the amount (and the variety) of imported intermediate inputs used in the production could improve the firm’s total revenue. The firm’s export revenue could also increase since specific export markets might demand a specific quality of final products. Additionally, the increase in imported intermediate inputs could influence the firm’s output through the production function as noted. The production

9 _{These fixed costs include sunk costs and per-period fixed costs. The former include costs for}

establishing a network with a foreign supplier and for learning about government regulations, while the latter includes fixed costs per shipment that force firms to reduce the frequency of shipments but with a higher volume (Kasahara & Lapham 2013; Kropf & Saure 2014).

technology could become more efficient due to an increased division of labour (Ethier 1982), or due to the superior quality of imported inputs relative to domestic inputs (Halpern, Koren & Szeidl 2015), or the combination of both.

In the globalisation era where trade costs are getting lower, firms no longer have to focus only on domestic markets but now they have the incentive to serve foreign markets as well. In serving these different markets, the skills needed to navigate the abundant choice of intermediate inputs become more crucial. Access to intermediate inputs at free trade prices becomes a key determinant of export success. This is even more so, as firms become involved in production networks. The increasing degree of specialisation at country level and firm level amplifies the need of intermediate inputs. As discussed in many literatures on global value chains (GVCs), as the global trade intensifies, cross-country transactions via both import on intermediate inputs and exports, also increases (Athukorala & Kohpaiboon 2014; Hummels, Ishii & Yi 2001; Johnson & Noguera 2017). At the micro level, the proportion of manufacturing firms engaged in both importing and exporting activities also increases.

Since many firms both import and export, there could be a two-way relation between the import of intermediate inputs and export performance. Aristei, Castellani and Franco (2013) and Kasahara and Lapham (2013) have discussed some possible mechanisms by which these two activities could be complementary and simultaneous—even though the direction is more obvious from import to export than the other way around. Assuming there are sunk costs for import and export, the most productive firms would self-select into two-way trade. Firms that are one-way traders might switch and become two-way traders if they can spread the sunk costs across the two activities. The cost of exporting (importing) can be reduced whenever the firm in

question already carries out importing (exporting) activities. If a firm has been exposed to foreign markets by importing (exporting), its productivity could be further increased due to the learning mechanism which in turn affects its export (import) performance.