Does importing more inputs raise exports? Firm-level evidence from France

Abstract

Does an increase in imported inputs raise exports? We provide empirical evidence on the direct and indirect channels via which importing more varieties of intermediate inputs increases export scope: (1) imported inputs may enhance productivity and thereby help the firm to overcome export fixed costs (the indirect productivity channel); (2) low-priced imported inputs may boost expected export revenue (the direct-cost channel); and (3) importing intermediate inputs may reduce export fixed costs by providing the quality/technology required in demanding export markets (the quality/technology channel). We use firm-level data on imports at the product (HS6) level provided by French Customs for the 1996–2005 period, and distinguish the origin of imported inputs (developing vs. developed countries) in order to disentangle the different productivity channels above. Regarding the indirect effect, imported inputs raise productivity, and thereby exports, both through greater complementarity of inputs and technology/quality transfer. Controlling for productivity, imports of intermediate inputs from developed and developing countries also have a direct impact on the number of exported varieties. Both quality/technology and price channels are at play. These findings are robust to specifications that explicitly deal with potential reverse causality between imported inputs and export scope.

Appendices

Appendix 1: A simple model

In this Appendix, we present a simple partial equilibrium model which sheds light on the mechanisms via which imported inputs affect firm TFP and export scope. There is a continuum of domestic firms in the economy that supply differentiated final goods under monopolistic competition. Firms differ in their initial productivity draws ($\varphi$) which are introduced as in Melitz (2003). In order to produce a variety of final good y, the firm combines three factors of production: labor (L), capital (K) and a range of differentiated intermediate goods (M _ij ) produced by industry i, that can be purchased in the domestic or foreign markets. If the firm sources its inputs internationally, it may import intermediate goods from two different sets of countries distinguished by their levels of development. As is traditionally assumed, countries in the North have higher GDP per capita than those in the South. The technology is represented by a Cobb–Douglas production function with factor shares $\eta +\beta+\sum\nolimits_{i=1}^{I}\alpha_{i}=1$ (for simplicity, we omit the firm subscript):

$$ y=\varphi L^{\eta }K^{\beta }\prod\limits_{j\in \{D,N,S\}}\prod\limits_{i=1}^{I}\left( M_{ij}\right)^{\alpha_{i}} $$

(1)

where $M_{ij}=\left(\sum_{v\in I_{ij}}\chi_{ij}m_{iv}^{\frac{\sigma_{i}-1}{\sigma_{i}}}\right) ^{^{\frac{\sigma_{i}}{\sigma_{i}-1}}}$.

The range of domestic and imported varieties of intermediate goods in industry i are aggregated by CES functions M _ij , where i is the industry, j the country region (i.e., domestic, North or South), $I_{j}=\{1,\ldots.,M_{j}\}$ and σ _i  > 1 is the elasticity of substitution across the varieties in industry i. The technology/quality parameter, χ _ij , captures the fact that imported inputs may enhance firm efficiency differently depending on their origin. We assume that χ _ij is greater than one for inputs sourced from the most developed countries, i.e., j = N, and equal to one otherwise. In this set up, each foreign country may produce one variety of inputs per industry, we thus match our empirical framework where a variety is defined as a product-country pair.

As is common in the literature (e.g., Ethier 1982 and Markusen 1989), we consider that intermediate inputs are symetrically produced at a level $\overline{m}$. This yields $M_{iD}=N_{iD}^{\frac{\sigma_{i}}{\sigma_{i}-1}}\overline{m}_{D},\quad M_{iS}=N_{iS}^{\frac{\sigma_{i}}{\sigma_{i}-1}}\overline{m}_{S}\hbox{ and }M_{iN}=\left(N_{iN}\chi_{i}\right)^{\frac{\sigma_{i}}{\sigma_{i}-1}}\overline{m}_{N}$, where N _iD , N _iS and N _iN are the number of domestic and imported (from the South or the North) varieties of intermediate goods. The production function for a variety of final good, equation (1), can thus be rewriten as:

$$ y=\varphi L^{\eta }K^{\beta }\prod\limits\limits_{j\in \{D,N,S\}}\prod\limits_{i=1}^{I}\overline{M}_{ij}^{\alpha_{i}} \left(N_{ij}\chi_{ij}\right)^{\frac{\alpha_{i}}{\sigma_{i}-1}} $$

(2)

where $\overline{M}_{ij}=N_{ij}\overline{m_{j}}$. Following Kasahara and Rodrigue (2008), we make the simplifying assumption that firms either source their inputs domestically or internationally (from both the North and the South). Intermediate goods imported from the North have a higher technological content whereas inputs sourced from the South have a lower price, as input prices reflect the assumed relatively lower cost of factors of production in the South. As is standard, the first-order condition is such that prices reflect a constant mark-up, $\rho =\frac{\phi -1}{\phi }$, over marginal costs, $p=\frac{MC}{\rho }$, where the marginal cost of production is determined by MC _D if the firm sources its inputs domestically and MC _F if it does so on foreign markets. ²⁸

$$ MC_{D}=\frac{p_{k}^{\beta}w^{\eta}{\overset{I}{\prod}}_{i=1}p_{iD}^{\alpha_{i}}} {\varphi{\overset{I}{\prod}}_{i=1}N_{iD}^{\frac{\alpha_{i}}{\sigma_{i}-1}}} $$

(3)

$$ MC_{F}=\frac{p_{k}^{\beta}w^{\eta}\prod_{j\in \{N,S\}}{\overset{I}{\prod}}_{i=1} p_{ij}^{\alpha_{i}}}{\varphi {\overset{I}{\prod}}_{i=1} \left(N_{iN}\chi_{iN}\right)^{\frac{\alpha_{i}}{\sigma_{i}-1}} \left(N_{iS}\right)^{\frac{\alpha_{i}}{\sigma_{i}-1}}} $$

(4)

where w is the wage, p _k is the price of capital goods and p _ij is the price of inputs from industry i and region j. ²⁹ Combining the demand faced by each firm, $q_{j}(\varphi)=\left(\frac{P}{p_{j}(\varphi)}\right)^{\phi}C$—where P is the aggregate final goods price index and C is aggregate expenditure on varieties of final goods—and the price function, $p_{j}(\varphi)=\frac{MC_{j}}{\rho}$, revenues are given by $r_{j}(\varphi)=q_{j}(\varphi)p_{j}(\varphi): r_{j}(\varphi)=\left(\frac{P}{p_{j}}\right)^{\phi-1}R$, where R = PC is the aggregate revenue of the industry, which is considered exogenous to the firm. Firm domestic profits thus simplify to $\pi_{j}=\frac{r_{j}}{\phi}-F$, where F is the fixed production cost. Firms that import, also incur a fixed import cost, F _m . Firm export profits are given by $\pi_{x}=\frac{r_{x}}{\phi}-F_{x}$, where F _x includes the production fixed costs (which include the import fixed cost for importing firms), F, as well as the export fixed costs which, as explained below, fall in the technology/quality parameter, i.e., $F_{x}=g\left(F, \frac{f_{x}}{\chi_{ij}}\right)$.

Using the price and revenue functions defined in the previous section, we derive the following expression for firms’ export revenues: ³⁰

$$ r_{x}=\Uppsi\left(\frac{\varphi {\overset{I}{\prod}}_{i=1}\, \left(N_{iN}\chi_{iN}\right)^{\frac{\alpha_{i}}{\sigma_{i}-1}} \left(N_{iS}\right)^{\frac{\alpha_{i}}{\sigma_{i}-1}}}{\prod\nolimits_{j\in \{N,S\}}\prod\nolimits_{i=1} p_{ij}^{\alpha_{i}}}\right)^{\phi-1} $$

(5)

where $\Uppsi=P^{\phi-1}R\left(\rho^{-1}\left(1+\tau\right) p_{k}^{\beta}w^{\eta}\right)_{,}^{1-\phi }$ with τ being the variable export cost, P the aggregate price index of final goods and R aggregate industry revenue, all of which are exogenous to the firm. The corresponding profit can thus be written as

$$ \pi_{x}=\frac{\Uppsi}{\phi}\left(\frac{A}{\prod\nolimits_{j\in \{N,S\}}\prod\nolimits_{i=1}\,p_{ij }^{\alpha_{i}}}\right)^{\phi -1}-F_{x} $$

(6)

The tradebility condition for export is given by: $\pi_{x}\left(\varphi_{x}^{\ast}\right)=0$, where $\varphi_{x}^{\ast }$ is the Melitz (2003) productivity draw of the marginal firm serving the export market.

Appendix 2: Empirical results

(See Tables 10, 11, 12, 13, 14 and 15)

Table 10 Intermediate inputs

Table 11 Distribution of imported inputs by sector

Table 12 First stage of the IV estimations of Tables 6 and 7

Table 13 Alternative productivity measure

Table 14 Export status and imported inputs

Table 15 Intensive margin and destination of export and imported inputs