Internationalization and performance: Degree, duration, and scale of operations

Abstract

We assess the theoretical underpinnings and associated empirical findings of the three-stage sigmoid–curve relationship between degree of internationalization (DOI) and performance by re-examining the results reported in one of the prominent studies in the literature. We further conduct our own analyses of 23,474 observations of 2,620 US manufacturing firms over the period 1976–2008 and account for self-selection of firms into different degrees of internationalization by using a generalized propensity score estimator. Both sets of results show that the relationship between DOI and performance conforms to a mostly negative sigmoid curve and does not support the three-stage theorization. Further examination reveals that two major conceptual and empirical shortcomings underlie the disparity between the theoretical predictions of the three-stage model and these empirical findings. First, whereas theory relies overwhelmingly on enhanced scale of operations as a causal mechanism through which internationalization contributes to performance, empirical studies preclude proper identification of scale-related benefits. Second, theory and empirics tend to confuse temporary difficulties experienced upon entry into international markets with examining the benefits realizable at different levels of DOI, regardless of the firm’s short-term difficulties in realizing those benefits. Our empirical results show that correcting for each of these shortcomings contributes to diminishing the theory–empirics gap.

Résumé

Nous évaluons les fondements théoriques et les résultats empiriques associés de la relation sigmoïde en trois étapes, entre le degré d'internationalisation (DDI) et la performance, en réexaminant les résultats présentés dans l'une des études les plus marquantes de la littérature. Nous menons en parallèle nos propres analyses sur 23.474 observations de 2.620 entreprises manufacturières américaines au cours de la période 1976-2008 et expliquons l'auto-sélection des firmes par rapport aux différents degrés d'internationalisation en utilisant un estimateur généralisé du coefficient de propension. Les deux séries de résultats montrent que la relation entre le DDI et la performance est conforme à une courbe sigmoïde principalement négative et ne confirme pas la théorisation en trois étapes. Une étude plus approfondie révèle que deux insuffisances conceptuelles et empiriques majeures sous-tendent la disparité entre les prédictions théoriques du modèle à trois étapes et ces résultats empiriques. Tout d'abord, alors que la théorie repose en grande partie sur l'augmentation de l'échelle des opérations en tant que mécanisme causal par lequel l'internationalisation contribue au rendement, les études empiriques excluent une identification adéquate des avantages liés à l'échelle. Deuxièmement, la théorie et les données empiriques tendent à confondre les difficultés temporaires rencontrées lors de l'entrée sur les marchés internationaux avec l'examen des avantages réalisables à différents niveaux du DDI, indépendamment des difficultés à court terme de la firme pour obtenir ces avantages. Nos résultats empiriques montrent que la correction de chacune de ces insuffisances contribue à diminuer l'écart entre la théorie et les données empiriques.

Resumen

Evaluamos los fundamentos teóricos y los hallazgos empíricos asociados a la relación de la curva sigmoidea entre el grado de internacionalización (DOI) y el rendimiento, mediante el re-escrutinio de los resultados reportados en uno de los más prominentes estudios en la literatura. Además, realizamos nuestro propio análisis de 23.474 observaciones de 2.620 empresas manufactureras de los Estados Unidos en el periodo 1976-2008 y explicamos la autoselección de las empresas en diferentes grados de internacionalización mediante el uso de un estimador de puntaje de propensión generalizado. Ambos conjuntos de resultados muestran que la relación entre el grado de internacionalización y el rendimiento se ajustan a una curva sigmoidea negativa y no apoya la teorización de tres etapas. Un examen más detallado muestra que dos importantes deficiencias conceptuales y empíricas subyacen a la disparidad entre las predicciones teóricas de este modelo de tres etapas y estos hallazgos empíricos. Primero, mientras que la teoría se basa abrumadoramente en una escala de operaciones mejoradas como un mecanismo causal mediante el cual la internacionalización contribuye al rendimiento, los estudios científicos impiden una identificación adecuada de los beneficios relacionados con la escala. Segundo, la teoría y los empíricos tienden a confundir dificultades temporales experimentadas al ingresar a los mercados internacionales con el escrutinio de los beneficios alcanzables en diferentes niveles del grado de internacionalización, sin importar las dificultados de corto plazo de la empresa en darse cuenta de esos beneficios. Nuestros resultados empiricos muestran que la corrección de cad una de estas deficiencias contribuye a disminuir la brecha la teoría y lo empírico.

Resumo

Avaliamos os fundamentos teóricos e os achados empíricos associados da relação curvilínea sigmoidal de três estágios entre o grau de internacionalização (DOI) e desempenho, reexaminando os resultados relatados em um dos proeminentes estudos da literatura. Nós ainda conduzimos nossas próprias análises de 23.474 observações de 2.620 empresas de manufatura dos EUA no período 1976-2008 e consideramos a auto-seleção de empresas em diferentes graus de internacionalização usando um estimador generalizado de propensity score. Ambos os conjuntos de resultados mostram que a relação entre DOI e desempenho está em conformidade com uma curva sigmoidal primordialmente negativa e não suporta a teoria de três estágios. Um exame mais aprofundado revela que duas principais deficiências conceituais e empíricas subjazem a disparidade entre as previsões teóricas do modelo de três estágios e esses achados empíricos. Em primeiro lugar, enquanto a teoria depende sobremaneira de operações em escala aprimoradas como um mecanismo causal através do qual a internacionalização contribui para o desempenho, estudos empíricos impedem a identificação adequada de benefícios relacionados à escala. Em segundo lugar, a teoria e o empirismo tendem a confundir as dificuldades temporárias experimentadas após a entrada em mercados internacionais, com a análise dos benefícios realizados em diferentes níveis de DOI, independentemente das dificuldades de curto prazo da empresa na realização desses benefícios. Nossos resultados empíricos mostram que a correção de cada uma dessas falhas contribui para diminuir a lacuna teórico-empírica.

概要

我们通过重新研究文献中的一项著名研究里所报告的结果来评估国际化程度(DOI)与绩效之间的三段式S型曲线关系的理论基础和相关实证研究结果。我们用广义倾向评分估测进而对在1976 - 2008年间2620家美国制造业公司的23474个观察进行分析,并解释处于不同程度国际化的公司的自我选择。两组结果都显示,DOI和绩效之间的关系符合大多是消极的S形曲线,并不支持三段式理论化。进一步研究发现,理论和实证的两个主要的不足揭示了三段式模型的理论预测与这些实证研究结果之间的差距。首先,虽然理论压倒多数地依赖于作为因果机制的业务规模的提升,通过该机制,国际化对业绩做出了贡献,但实证研究排除了与规模有关收益的适当识别。其次,理论和实证研究往往将进入国际市场所经历的暂时困难与在不同的DOI层面实现收益的调查相混淆,不管该公司实现该收益的短期困难如何。我们的实证研究结果表明,对这些缺点每一个都进行修正有助于缩小理论与实证的差距。

Appendices

Appendix 1

S-Shape Curves and the Three-stage Model

The literature regarding the three-stage relationship has extensively considered the “S-shape curve” and the “three-stage relationship” as synonymous (e.g., Contractor, 2007; Lu & Beamish, 2004). Consequently, the negative coefficients for linear and cubic terms of DOI accompanied by a positive coefficient for the quadratic term (which inevitably generate an S-shape curve) have been considered as support for the applicability of the “three-stage theorization” in associated empirical studies. However, as our empirical study and re-examination of L&B results demonstrated, it is important to note that not all S-shape curves conform to the image depicted by the three-stage model (i.e., the one demonstrated in Figure 1a). As exhibited in Figure 1, the resultant S-curve may take three generic forms, of which only “form a” conforms to the predictions of three-stage theorization. The aforementioned pattern of coefficients is merely a necessary (rather than sufficient) condition for the support of the three-stage model. One must take two additional precautions in inferring the three-stage theorization from this pattern of coefficients.

For a cubic polynomial, $Performance_{DOI} = \alpha DOI^{3} + \beta DOI^{2} + \gamma DOI,\;\left( {\alpha ,\;\gamma < {0\;{\text{and}}\;\beta } > 0} \right)$, to generate a curve similar to Figure 1a (i.e., the one theorized by the three-stage model), it must have one local minimum and one local maximum. Therefore, the derivative of the polynomial $\left( {{\text{i}}.{\text{e}}.,\;\frac{\partial Performance}{\partial DOI} = 3\alpha \;DOI^{2} + 2\beta \,DOI + \gamma } \right)$ must have two distinctive roots. The expression $3\alpha \;DOI^{2} + 2\beta \;DOI + \gamma$ possesses two distinctive roots if and only if $\Delta = \left( {\left( {2\beta } \right)^{2} - 4\left( {3\alpha } \right)\left( \gamma \right)} \right)$ is strictly greater than zero. If ∆ ≤ 0, the derivative of the equation has less than two roots, and a generic form similar to Figure 1c will be produced (with the maximum of the polynomial occurring at DOI = 0 and $Performance_{DOI} = 0$). Therefore, $\Delta = \left( {\left( {2\beta } \right)^{2} - 4\left( {3\alpha } \right)\left( \gamma \right)} \right) = 4\beta^{2} - 12\alpha \gamma > 0$ (hereinafter, condition #1) is a necessary condition for the coefficients to generate a curve concordant with the three-stage theory (i.e., the one depicted in Figure 1a).

Whereas condition #1 ascertains the presence of positive-slope stage in the relationship between the independent and dependent variables, the presence of a positive stage of relationship does not necessarily support the three-stage model. For the three-stage theorization to hold, there must be some DOIs at which an internationalized firm outperforms its non-internationalized counterpart (i.e., there must be some DOI “at which the benefits of internationalization are realized”). Put differently, there must be at least one non-zero DOI (according to three-stage theory, a considerable range of DOI) at which the performance is higher than the performance at DOI = 0. Moreover, this non-zero DOI should fall within the acceptable range of DOI, e.g., in our case, given the foreign-sales ratio as the measure of internationalization DOI ≤ 1. Otherwise, the net of the benefits/costs accrued from internationalization would remain negative at all DOIs, and the three-stage theory’s prediction that internationalization is beneficial to the firm for most of the DOI range would be contradicted. More formally, provided that the larger root of the derivative is within the DOI range²³, the maximum of the curve must occur there rather than at DOI = 0.

As discussed above, the derivative of the DOI–performance relationship can be calculated as $\frac{\partial Performance}{\partial DOI} = 3\alpha \;DOI^{2} + 2\beta \,DOI + \gamma$ (where α, β, and γ, respectively, represent the coefficients of cubic, quadratic, and linear terms of the DOI). Because α, γ < 0, and β > 0, the larger root of the derivative can be calculated as $DOI_{\hbox{max} } = {{\left( { - 2\beta - \Delta } \right)} \mathord{\left/ {\vphantom {{\left( { - 2\beta - \Delta } \right)}}} \right. \kern-0pt} {6\alpha }}$. This condition (hereinafter, condition #2) can be stated as follows: $Performance\; \left( {at\; DOI = \left[ {\left( {{{ - 2\beta - \sqrt {4\beta^{2} - 12 \alpha \gamma } } \mathord{\left/ {\vphantom {{ - 2\beta - \sqrt {4\beta^{2} - 12 \alpha \gamma } }}} \right. \kern-0pt} {6\alpha }}} \right) } \right]} \right) > Performance \left( {DOI = 0} \right).$

Substituting the $DOI_{\hbox{max} }$ for the DOI in the DOI–Performance polynomial, this simplifies to

$\alpha \left[ {\frac{{ - \left( {2\beta } \right) - \sqrt {4\beta^{2} - 12 \alpha \gamma } }}{6\alpha }} \right]^{3} + \beta \left[ {\frac{{ - \left( {2\beta } \right) - \sqrt {4\beta^{2} - 12 \alpha \gamma } }}{6\alpha }} \right]^{2} + \gamma \frac{{ - \left( {2\beta } \right) - \sqrt {4\beta^{2} - 12 \alpha \gamma } }}{6\alpha }>0$ (Condition #2) (where α, β, and γ, respectively, represent the coefficients of cubic, quadratic, and linear terms of the DOI).

Condition #2 is stronger than condition #1 because it not only ascertains a non-monotonic relationship with a positive stage of relationship (subject to inquiry at condition #1) but also defines some additional requirements for the positive stage of the relationship (it requires the positive stage to be substantive enough to take the performance above its value at DOI = 0, i.e., its value before the decline of low DOIs).

The empirical findings of our study (before modeling the dependency of relationship on duration) and the findings of L&B all fall short of simultaneously satisfying conditions #1 and #2. Empirical findings reported in Table 2 (Models 4–6) of Lu and Beamish (2004) are unable to satisfy condition #1 and therefore yield a monotonically negative relationship between DOI and performance (resembling Figure 1c)²⁴. Before modeling the dependency DOI–performance relationship on duration empirical findings of our study (Models 4 and 5 of Table 2 – Figure 3 – and Model 4I of Table 3 – Figure 3) complies with the weaker condition #1. Even after accounting for the scale-related benefits of internationalization (Model 4I of Table 3 – Figure 3b), our models cannot meet condition 2; thus, the positive-slope stage of the relationship across all these models proves too transitory to even restore the level of profitability attained prior to the performance decline at low DOIs. Thus, although our models (prior to modeling the impact of duration) and those of L&B conform to the S-shape curve, neither support the relationship predicted by the three-stage theory.

Stochastic Nature of Regression Coefficients and Probing Condition #2

Our analysis, thus far, assumed that point estimates from a regression analysis (i.e., $\hat{\alpha },\;\hat{\beta },\;and\;\hat{\gamma }$) can substitute for their corresponding population parameters, α, β, and γ without further intricacies. This overlooks the stochastic nature of the sampling process, which attaches a confidence interval to each regression coefficient (unlike true population parameters, which are deterministic). Verifying the inequality of condition 2 thus must recognize the uncertainty of estimates from a sample of observations, rather than the whole population. Let us refer to the term appearing in the left-hand side of the condition #2 as θ. Since $\hat{\alpha },\;\hat{\beta },\;and\;\hat{\gamma }$ (regression coefficients) are substituting for α, β, and γ in the estimation of θ, the resultant $\hat{\theta }$ will be non-deterministic and should be defined with a confidence interval when probing the statistical significance of the inequality of condition #2. Only when an appropriate confidence interval around $\hat{\theta }$ excludes non-positive values one can conclude that $\hat{\theta }$ is significantly greater than zero, and thus that condition 2 is satisfied.

Please note when $\hat{\theta }$ itself fails to satisfy the inequality of condition #2, any confidence intervals around it will necessarily contain non-positive values (or undefined values when ∆ < 0), and therefore condition #2 can be rejected regardless of the selected level of significance (i.e., $\hat{\theta }$ cannot be significantly greater than zero when it is not greater than zero)²⁵. Thus, no confidence interval needs to be constructed when the point estimate (i.e., $\hat{\theta }$) itself cannot comply with condition #2 (e.g., our re-examination of L&B results and our replication models). When $\hat{\theta }$ is greater than zero, however, to probe the statistical significance of condition #2, confidence intervals around $\hat{\theta }$ can be estimated. If those confidence intervals exclude non-positive values, then it can be concluded that $\hat{\theta }$ is significantly greater than zero (i.e., condition #2 holds in a statistically significant manner). Necessary for defining these confidence intervals is an estimate of the standard error of $\hat{\theta }$. Since $\hat{\theta }$ is not a linear combination of regression coefficients (and given the complexity of the variance–covariance matrix of the regression coefficients), reaching a closed-form solution for the standard errors of $\hat{\theta }$ (based on the standard errors of $\hat{\alpha },\;\hat{\beta },\;{\text{and}}\;\hat{\gamma }$) is infeasible, and approximations based on, say, a Taylor expansion are too imprecise given the number of non-linear terms involved.²⁶

One pragmatic solution is bootstrapping to estimate the standard error of $\hat{\theta }$. Each bootstrap replication fits the DOI–performance regression in a bootstrap resample of size N (formed by sampling with replacement from the pool of observations) and estimates the $\hat{\theta }$ based on the regression coefficients of that fitting. After B-time repetitions of this procedure, bootstrapped estimates of $\hat{\theta }$, i.e., $\hat{\theta }$ … $\hat{\theta }_{B}$ are utilized to estimate the standard error of $\hat{\theta }$ and define a bootstrapped confidence interval around it (Efron & Tibshirani, 1993: 153–158). When applying this in a typical DOI–performance study, a few issues merit elaboration: first, in panel-data samples, bootstrap resampling should occur at the firm level rather than the observation (i.e., firm-year) level to avoid bias (Cameron & Trivedi, 2009: 420–421). Thus, each bootstrap replicate fits the DOI–performance regression in a bootstrap resample – with replacement – of C firms (where C denotes the number of firms in the pool of observation). Second, in some bootstrap replicates, $\hat{\theta }$ may turn out to be undefined (i.e., when ∆ < 0). To enable θ to be consistently estimated (incorporating the replicates in which $\hat{\theta }_{B}$ turns out to be undefined), we make a slight change to the definition of θ. We define θ in the following manner:

$$ \theta = \left\{ {\begin{array}{ll} {\alpha \left[ {\frac{{ - \left( {2\beta } \right) - \sqrt {4\beta^{2} - 12\alpha \gamma } }}{6\alpha }} \right]^{3} + \beta \left[ {\frac{{ - \left( {2\beta } \right) - \sqrt {4\beta^{2} - 12\alpha \gamma } }}{6\alpha }} \right]^{2} + \gamma \frac{{ - \left( {2\beta } \right) - \sqrt {4\beta^{2} - 12\alpha \gamma } }}{6\alpha },\;\;\;\;\;if\;\;\;4\beta^{2} - 12\alpha \gamma \ge 0} \\ {0,\;\;\;\;\;if\;\;\;4\beta^{2} - 12\alpha \gamma < 0} \\ \end{array} } \right. $$

Compliance with condition 2 requires θ to exceed zero. The case of θ ≤ 0 occurs either because $4\beta^{2} - 12 \alpha \gamma \le 0$ (i.e., the derivative has no root, and thus we address Figure 1c²⁷) or since the performance at the second root of the derivative (of DOI–performance polynomial) is less than the performance at DOI = 0 (form b in Figure 1). In either of these cases, the condition 2 is not satisfied. A Stata program can be used to (i) resample B times from the pool of observed firms and (ii) estimate $\hat{\theta }$ based on regression coefficients of each fitting.

A confidence interval around $\hat{\theta }$ can then be constructed based on the results of these fits to probe whether this confidence interval excludes non-positive values. Part A of our Internet supplementary material presents a Stata program to implement this bootstrapping procedure and estimate a 95% confidence interval around $\hat{\theta }$. If the 95% confidence interval produced by this bootstrapping procedure excludes non-positive values, condition 2 is satisfied in a statistically significant manner (as the null hypothesis can be rejected at p < .05). It merits emphasizing that when the point estimate of $\hat{\theta }$ fails to satisfy the inequality of condition #2 – i.e., $\hat{\theta }$ is less than zero or undefined – any confidence interval around $\hat{\theta }$ will contain non-positive values, and therefore condition #2 can be safely rejected without constructing a confidence interval.

Appendix 2: Covariate Balance given the Generalized Propensity Score (GPS)

The impact of adjusting for the generalized propensity score on removing the covariates’ imbalance (and therefore potential bias) is reported in Table AP2 (below). Weighting on generalized propensity score amounts to forming a pseudo-sample in which observations unlikelier to self-select into their current dose of internationalization (i.e., with lower propensity scores) are more represented in the regression analysis than observations naturally inclined to select their current dose of internationalization (by weighting the observations on their inversed propensity score of selecting into current dose of treatment). This pseudo-sample more closely approximates a randomized assignment process in which self-refraining observations are assigned into a particular dose of internationalization as often as self-selecting observations are (thus remedying for the under-representation of the self-refraining observations in observational samples (see Robins et al. 2000)). A comparison of unadjusted and adjusted t-statistics indicates that our propensity score adjustment performs well in removing the covariate imbalance among observations going through each dose of treatment versus the rest of sample. Prior to adjustment for GPS, 27 of 36 covariate-comparison t-statistics were significant at p < .05 (with excessively large mean-difference scores) indicating strong covariate imbalance. After adjusting for the generalized propensity score, only four t-statistics remain significant (at p < .05). Please note that it is natural for a few adjusted statistics to remain significant (e.g., in Hirano and Imbens (2005) where adjustment process commences from a substantially more balanced (pre-adjustment) sample, still two t-statistics remain significant after adjustment for GPS). Also, to deal with imbalance in Sales (partially driven by endogeneity and internationalization-backed sale-enhancements), we employ an instrumental variable approach (see “Accounting for the Scale-related Benefits” in our Results section and Part D of our Internet Supplementary Material).

Table AP2 t-statistics for covariate mean-equality (across the dose of interest vs. the rest of sample) before and after adjusting for the GPS