The ladder of internationalization modes: evidence from European firms

Abstract

How do firms enter international markets? To answer this question, this paper uses a unique multi-country firm-level dataset which, besides direct exporting and FDI, provides explicit information on a number of internationalization modes: indirect exporting, outsourced manufacturing and service FDI. We present a theoretical framework in which modes requiring higher and higher commitment have progressively higher fixed and lower marginal costs. By estimating multinomial and ordered logit models, we present evidence in line with such a sorting framework with respect to TFP and innovativeness. We identify three ’clusters’ of modes: indirect exporters are similar to non-exporters, direct exporters and outsourced manufacturers constitute a second cluster while service and manufacturing FDI are the most demanding internationalization modes.

Appendices

Appendix A: Theoretical framework

In this section we describe a theoretical framework for our empirical analysis of many internationalization modes when firms are heterogeneous both in terms of their productivity and the quality of their products. In order to do this, we build on the model of Aw and Lee (2014), who, in turn use the Crozet et al. (2013) framework. We generalize this model to many internationalization modes. An advantage of this framework is that it directly generates an empirically relevant ordered logit specification in which both productivity and quality has a positive association with choosing modes requiring stronger commitment in terms of fixed costs.

However, we somewhat modify the model to provide a better fit for our data. First, as not all internationalization modes are available at the firm-country level, we will study how the firm serves foreign markets in general. Second, differences in production costs between home and foreign will be included in the fixed costs of the different internationalization modes rather than displayed explicitly.

1.1 The cost structure of internationalization modes

Let us consider the decision of firm i which is based in the home country and considers serving consumers in the foreign country. The firm can choose between N internationalization modes. For example, in our empirical exercise the firm can choose from among five modes: indirect exporting, direct exporting, outsourcing, service FDI and manufacturing FDI.

In a very simple fashion, we will characterise the cost structure of each internationalization mode with two parameters: the fixed cost of entering the foreign market, $F^n\ge 0$, and an iceberg-type per-unit transportation cost, $\tau ^n \ge 1$. We interpret these two parameters very broadly. The fixed cost includes every type of one-time expense like the cost of finding business partners, the cost of buildings and machinery or the administrative costs of setting up foreign operations. $\tau ^n$, besides transportation costs, includes less tangible elements such as the markup charged by intermediaries, the hold-up costs resulting from contractual frictions and the wage differences between countries. In what follows, we will call the vector of these two variables, $\{F^n; \tau ^n\}$, the cost structure of mode n.

Our key assumption is that internationalization modes can be ranked in a way that serving the foreign market with a more ‘demanding’ internationalization mode requires larger fixed costs but allows the firm to transport the product with a smaller variable cost. Hence, we assume that:

$$\begin{aligned} F^n<F^{n+1}, \, \forall n \,\,\,\,\, \text {and} \,\,\,\,\, \tau ^n>\tau ^{n+1}, \, \forall n \end{aligned}$$

(8)

Furthermore, we assume that for each mode:

$$\begin{aligned} \ln \frac{ \left( F^{n+1}-F^{n}\right) \left( \left( \tau ^{n+1}\right) ^{1-\sigma }-\left( \tau ^{n}\right) ^{1-\sigma } \right) }{ \left( F^n-F^{n-1}\right) \left( \left( \tau ^{n}\right) ^{1-\sigma }-\left( \tau ^{n-1}\right) ^{1-\sigma } \right) }>0, \forall n \end{aligned}$$

(9)

where $\sigma >1$ is the elasticity of demand.

1.2 Demand and technology

Consumers have a constant elasticity of substitution utility function:

$$\begin{aligned} U=\left( \sum \limits _{i=1}^n\left[ a(i)^\lambda q(i)\right] ^{\frac{\sigma -1}{\sigma }}\right) ^{\frac{\sigma }{\sigma -1}}, \end{aligned}$$

where a(i) shows the consumer’s taste for variety i. We will interpret this demand shifter as the ’quality’ of the product, though it can also include brand recognition and other factors that are attractive to consumers. $\lambda \ge 1$ shows the importance of quality in consumer preferences relative to prices.

The demand function in the foreign market for variety i is:

$$\begin{aligned} q(i)=\frac{E}{P}a_i^{\lambda (\sigma -1)}p(i)^{-\sigma } \,\, \hbox {where} \,\, P=\sum \limits _{j=1}^n a(j)^{\lambda (\sigma -1)}p(j)^{1-\sigma }, \end{aligned}$$

where E is the total expenditure and P is the price index in the foreign market.

Firms are heterogeneous in two dimensions: productivity and quality. We assume that both parameters are unknown before the firm enters, and that they are exogenous and cannot be modified after entry. $\omega (i)$ shows the physical productivity of firm i, while a(i) denotes the quality of the product. Firms producing more innovative goods will have a higher unit cost. Without a loss of generality, we will assume that the wage level in the home country is 1 (and wage differences between the two countries are included in the fixed costs of different internationalization modes). The constant unit cost of production is:

$$\begin{aligned} c(i)=a(i)^\gamma / \omega (i), \end{aligned}$$

where $\gamma \ge 1$ determines the marginal cost of producing more innovative goods. We assume that $\lambda >\gamma$, i.e. consumers appreciate quality more than its cost.

Under CES demand and monopolistic competition, firms set prices using constant markups. When the internationalization mode n is chosen, the price, revenue and profit are:

$$\begin{aligned} &p^n(i) = {} \frac{\sigma }{\sigma -1}\tau _nc(i) \\ &r^n(i) = {} \frac{E}{P}\left( \frac{\sigma }{\sigma -1}\right) ^{1-\sigma }a(i)^{\lambda (\sigma -1)} \left[ \left( \tau ^n \right) ^{1-\sigma } \omega (i)^{\sigma -1}a(i)^{\gamma (1-\sigma )}\right] \\ &\varPi ^n(i) = {} \frac{1}{\sigma }r^n(i)-F^n \end{aligned}$$

1.3 Internationalization mode choice

The assumptions about the cost structure suggest that firms enter the foreign market whenever it is profitable for them to choose internationalization mode 1, $\varPi ^1(i)>0$. The condition for this is:

$$\begin{aligned} \frac{E}{P}\left( \frac{\sigma ^{-\sigma }}{(\sigma -1)^{1-\sigma }}\right) a(i)^{(\lambda -\gamma )(\sigma -1)} \left( \tau ^1 \right) ^{1-\sigma } \omega (i)^{\sigma -1}- F^1\ge 0 \end{aligned}$$

One can express the threshold productivity level with the quality level of the firm and the model parameters. We will denote this threshold productivity function as $\bar{\omega }^1(a)$:

$$\begin{aligned} \bar{\omega }^1(a) \equiv \left( F^1\right) ^{\frac{1}{\sigma -1}} \left( \frac{E}{P}\right) ^{\frac{1}{1-\sigma }} \left( \frac{\sigma -1}{\sigma ^{\frac{\sigma }{1-\sigma }}}\right) \left( \tau ^1\right) ^{-1} a(i)^{\gamma -\lambda } \end{aligned}$$

Given our assumption that $\lambda >\gamma$, this locus is a hyperbola in the a-$\omega$ plane: if a firm can produce higher quality goods, its threshold productivity is smaller. The shape of the hyperbola depends both on the consumers’ valuation of quality ($\lambda$) and the cost of producing it ($\gamma$). In particular, the hyperbola becomes steeper if $\lambda -\gamma$ increases; i.e. quality becomes more important for consumers relative to its cost. Other parameters, including the fixed cost, the elasticity of demand and market size do not affect the slope of this curve but they can shift it in and out. A smaller market size, for example, shifts the curve out, making it harder to enter the export market.

Figure 5 shows such a function. Firms with a-$\omega$ combinations above the curve enter the foreign market, while firms below it will only produce for the domestic market (or exit).

The thresholds for choosing other internationalization modes can be derived similarly. Let us denote the curve when firms are indifferent between choosing trade mode $n-1$ and n with $\bar{\omega }^n(a)$. This curve is defined as $\varPi ^{n-1}(i)=\varPi ^{n}(i)$:

$$\begin{aligned} \bar{\omega }^n(a) \equiv \left( F^n-F^{n-1}\right) ^{\frac{1}{\sigma -1}} \left( \frac{E}{P}\right) ^{\frac{1}{1-\sigma }} \left( \frac{\sigma -1}{\sigma ^{\frac{\sigma }{1-\sigma }}}\right) \left( \left( \tau ^{n}\right) ^{1-\sigma }-\left( \tau ^{n-1}\right) ^{1-\sigma } \right) ^{\frac{1}{1-\sigma }} a(i)^{\gamma -\lambda } \end{aligned}$$

(10)

Again, the shapes of these hyperbolae depend only on $\gamma -\lambda$; the cost structure of internationalization modes only shifts them out from the origo. Also, the assumption on the relative cost structure guarantees that the distance of these curves from the origo is increasing in n.

Figure 6 shows that the model implies a two dimensional sorting. Firms will choose internationalization mode n if their $\omega -a$ combination is between the loci $\bar{\omega }^n(a)$ and $\bar{\omega }^{n+1}(a)$.

Fig. 5

Foreign entry

Fig. 6

Different entry modes

Appendix B: Additional tables

See Fig. 7 and Tables 5, 6, 7, 8, 9, 10, 11 and 12.

Fig. 7

Average semi-elasticities, separate logits and mlogit. This figure shows the average marginal effects (semi-elasticities) of TFP and Innovativeness on the probability of choosing the different modes estimated from separate logit models for each mode (left panel). The right panel shows the semi-elasticities estimated from the core multinomial logit model as a comparison

Table 5 TFP and standardized TFP by modes

Table 6 Components of the Innovativeness measure by top-coded modes

Table 7 Vertical and horizontal FDI and outsourcing

Table 8 Manufacturing FDI categories

Table 9 Outsourced manufacturing categories

Table 10 No distinction between horizontal and vertical motives—multinomial logit

Table 11 TFP and innovativeness: robustness of ordered logit results

Table 12 Number of firms by country and top-coded mode

Appendix C: Online appendix

This Online Appendix consists of three parts. “Further descriptive tables” section includes additional descriptive evidence on sorting across modes by presenting how TFP and innovativeness differs across modes within countries. “Additional robustness checks” presents some of our regression results in detail and includes a number of robustness checks. “Production function estimation” describes our production function estimation procedure.

1.1 Further descriptive tables

See Tables 13 and 14.

Table 13 Average TFP by country and top-coded mode

Table 14 Average innovativeness by country and top-coded mode

1.2 Additional robustness checks

See Tables 15, 16, 17 and 18.

Table 15 Multinomial logit coefficients when controlling for foreign sourcing variables

Table 16 Multinomial logit coefficients when controlling for foreign sourcing and management variables

Table 17 Multinomial logit results with a different top-coding

Table 18 Generalized ordered logit

1.3 Production function estimation

We perform the production function estimation on the value added with capital and labor inputs following Wooldridge (2009). Wooldridge (2009) shows that the two-step production function estimation procedures developed by Olley and Pakes (1996), Levinsohn and Petrin (2003) and Ackerberg et al. (2015) can be implemented in a one-step generalized method of moments (GMM) framework.

The production function estimating equation with all variables in logs is

$$\begin{aligned} y_{it} = \beta _l l_{it} + \beta _k k_{it} + g\left( k_{i,t-1},m_{i,t-1}\right) +\delta _t+ \epsilon _{it}. \end{aligned}$$

(11)

Value added output of firm i in year t ($y_{it}$) is a function of the current labor ($l_{it}$) and capital ($k_{it}$) use and a function g(.) of lagged capital and material use, which proxies for the expected (in $t-1$) component of the current total factor productivity, while the $\delta _t$ are year intercepts. As it is customary in the literature, we specify function g(.) as a third-degree polynomial with interaction terms.¹⁹ The error term $\epsilon _{it}$ also incorporates the (unexpected) productivity shock.

The parameters of interest, $\beta _l$ and $\beta _k$, measure the output elasticity of labor and capital, respectively. In order to obtain unbiased estimates, however, one has to account for the possible correlation between the current variable input ($l_{it}$) and the productivity shock in the error term. This is achieved by a generalized method of moments instrumental variable estimation, where $l_{it}$ is instrumented with $l_{i,t-1}$, while all other right-hand side variables are instruments for themselves.

We measure value added output as sales minus material costs, labor input by the number of employees, capital input by fixed assets and material use by material costs of the firm. We deflate sales and material costs with industry- and country-specific producer prices and fixed assets with country-specific prices for capital goods.²⁰

We estimate (Eq. 11) on an unbalanced panel of the broadest possible set of French, German, Italian and Spanish firms in the Amadeus database over years 2004–2013. We perform the estimation separately by country and three-digit NACE industry.²¹ Figure 8 presents the histogram of the estimated output elasticities of labor for our baseline estimation sample. The estimated industry-country elasticities fall in a reasonable range with a sample mean of 0.66.

Fig. 8

Histograms of $\hat{\beta }_l$ by country

Based on the estimated output elasticities we can calculate the total factor productivity (in log) of firm i in year t as

$$\begin{aligned} \ln \text {TFP}_{it} = y_{it} - \hat{\beta }^{(cj)}_l l_{it} - \hat{\beta }^{(cj)}_k k_{it}, \end{aligned}$$

where $\hat{\beta }^{(cj)}_k$ is the estimated output elasticity for capital, specific to country-industry cj. Figure 9 presents histograms of the estimated firm-level productivities by country.

Fig. 9

Histograms of TFP by country