Does Tobin’s q Matter for a Firm’s Choice of Globalization Mode?

Abstract

For the last two decades, sorting of firms by productivity into different modes of globalization has been well documented both theoretically and empirically in the trade literature. Melitz (2003) presents a model in which the most productive firms export goods to foreign markets, whereas less productive firms supply goods only to their domestic market.

4.1 Introduction

For the last two decades, sorting of firms by productivity into different modes of globalization has been well documented both theoretically and empirically in the trade literature.¹ Melitz (2003) presents a model in which the most productive firms export goods to foreign markets, whereas less productive firms supply goods only to their domestic market. Helpman et al. (2004) extend the framework in Melitz (2003) to incorporate the possibility that firms serve foreign markets through foreign direct investment (FDI). They predict that only the most productive firms find it profitable to serve foreign markets via FDI and that medium-productivity firms serve foreign markets through exports. A large empirical literature confirms these sorting patterns (e.g., Bernard and Jensen 1995, 1999; Head and Ries 2003; Helpman et al. 2004; Kimura and Kiyota 2006; Mayer and Ottaviano 2007). On the other hand, an offshored production may be conducted via FDI or outsourced to a local firm. In such a situation, Antràs and Helpman (2004) predict that relatively more productive firms conduct FDI, whereas relatively less productive firms choose foreign outsourcing (FO). Because of data limitations, only a few studies have reported firm-level evidence on this issue. Using Japanese data, Tomiura (2007) observes that firms engaging only in FO tend to be less productive than those engaging in FDI. Federico (2010) and Kohler and Smolka (2012) find similar patterns for Italian and Spanish firms, respectively. In contrast, Defever and Toubal (2013) report a reverse ordering of firm productivity due to the higher fixed costs of outsourcing for French firms.

In the previous chapter we investigated the effects of the various aspects of firms’ performance on their globalization activities. We measured firm performance by productivity, Tobin’s q, and intangible asset intensity. In this chapter we focus more on Tobin’s q (Tobin 1969). Specifically, we attempt to sort firms into different modes of globalization by Tobin’s q. Our study is motivated by a theoretical analysis by Chen et al. (2012). Combining the property-rights approach (Grossman and Hart 1986; Hart and Moore 1990) and the knowledge-capital model (Horstmann and Markusen 1987; Markusen 1984, 2002), they examine how the relative importance of knowledge capital over physical capital affects a firm’s choice between FDI and FO for the offshored production. They show that firms with a higher physical-capital intensity tend to choose FO, whereas firms with a higher knowledge-capital intensity tend to conduct FDI. An interesting testable hypothesis is obtained from this result: firms with a high Tobin’s q (i.e., the ratio of firm’s market value to the replacement value of book equity) tend to conduct FDI, whereas those with a low Tobin’s q tend to choose FO. Because the firm’s market value reflects both knowledge-based and physical assets, and given that the book value of capital reflects only physical assets, a firm with a higher knowledge-capital intensity will have a higher Tobin’s q. Thus, the above hypothesis follows. Moreover, although the knowledge-capital model predicts that firms with a high Tobin’s q tend to prefer FDI to exports to serve the foreign market, this relationship is not so robust as the imperfect contractibility of knowledge capital and the costly transfer of knowledge capital tend to make FDI less attractive to knowledge-capital intensive firms.

In our empirical study, we employ detailed Japanese firm-level data covering the period 1994–1999. Our dataset includes information on sales, employment, capital, research and development (R&D) expenditure, direct exports, the values of domestic and foreign outsourcing of the companies headquartered in Japan, and the sales of their foreign affiliates. Moreover, corporate balance sheet data are included. Our dataset enables us to identify not only whether a firm engages in a particular globalization activity (i.e., exports, FDI, and FO) but also the extent to which it is involved in that activity. We utilize this feature of our dataset to construct indexes to measure the relative choice of globalization mode by calculating the ratio of the values of FO (i.e., total expenditure on outsourcing to foreign contracting firms) to the total FDI (i.e., total sales of foreign affiliates) and the ratio of the volume of direct exports by the headquarters company to horizontal FDI (i.e., sales of foreign affiliates, excluding exports to Japan). Thereafter, we regress these indexes of globalization activity on Tobin’s q. Our measurement of Tobin’s q is based on the simple approximation proposed by DaDalt et al. (2003). Furthermore, we regress the indexes of globalization activity on the total factor productivity (TFP) of individual firms to demonstrate the manner in which sorting patterns by Tobin’s q differ from those by the firm’s productivity. We employ the method developed by Olley and Pakes (1996) to compute TFP. Our analysis mainly focuses on firms engaging in multiple globalization modes and attempts to reveal whether a difference in Tobin’s q (and TFP) motivates these firms to select more or less FDI relative to FO or exports.² In addition, we verify the robustness of results by including firms choosing a single globalization mode in estimations.

We need to address two important econometric issues in our analysis. First, the globalization indexes in our sample exhibit strong negative skewness and include outliers. As is well known, the presence of outliers may distort the classical least squares estimator (Wooldridge 2010). Thus, we employ several estimation methods to cope with this issue, namely, the median regression (or quantile regression) estimators, Huber M-estimators, and the MM-estimators (Huber 1981; Rousseeuw and Yohai 1984; Verardi and Croux 2009; Wooldridge 2010). The second econometric issue is endogeneity. Endogeneity potentially arises when factors that simultaneously influence the choice of globalization mode and Tobin’s q exist. Except for this the problems of omitted variables may involve endogeneity. To control for possible endogeneity, we employ the endogenous quantile regression (QRIV) techniques proposed by Lee (2007), using two sets of instrumental variables (IVs). We discuss our estimation strategy in detail in Sect. 4.4.

The main findings of this chapter are as follows. First, we find that Tobin’s q is negatively (positively) and significantly correlated with the ratio of FO to the total FDI (the ratio of total FDI to FO), which strongly supports the hypothesis that a higher Tobin’s q is associated with a higher FDI engagement relative to FO by multinational enterprises (MNEs). In contrast, little evidence exists on a definite relationship between Tobin’s q and the ratio of exports to horizontal FDI (or the ratio of horizontal FDI to exports). This result seems to imply that the imperfect contractibility of knowledge capital and a higher technology transfer cost actually matter for knowledge-capital intensive firms to choose between exports and FDI, because these factors weaken the positive relationship between Tobin’s q and the ratio of FDI to exports. These findings are quite robust even when we include firms engaging in a single globalization mode in estimations. Moreover, we find that the relationship between Tobin’s q and the firm’s choice of globalization mode fairly differs from that of TFP. When we regress our globalization indexes on TFP, we find that TFP is negatively (positively) and significantly correlated with the ratio of exports to horizontal FDI (the ratio of horizontal FDI to exports), whereas no significant relationship exists between TFP and the ratio of FO to the total FDI (or the ratio of total FDI to FO). The former result is consistent with the theoretical prediction of Helpman et al. (2004) and a large number of existing empirical studies (Head and Ries 2003; Helpman et al. 2004; Kimura and Kiyota 2006; Mayer and Ottaviano 2007; Yeaple 2009).³ However, the latter result differs from the prediction and findings of Antràs and Helpman (2004) in a limited number of existing studies (Federico 2010; Kohler and Smolka 2012; Tomiura 2007).

This chapter extends the empirical analysis of Jinji et al. (2019b) in three ways. First, we employ different estimation techniques from theirs to examine the impact of Tobin’s q on the firm’s choice between FO and FDI. In this respect, we provide evidence consistent with their findings. Second, we analyze the relationship between Tobin’s q and another choice of globalization mode, namely, the choice between export and FDI. Third, we extend the analysis to the impact of productivity (i.e., TFP) on the firm’s choice of globalization mode. The second and the third issues are not investigated by Jinji et al. (2019b)

The remainder of the chapter proceeds as follows. The next section discusses our empirical hypotheses. Section 4.3 describes the data and variables employed in the analysis. Section 4.4 explains our estimation strategy. Section 4.5 reports the estimation results. Section 4.6 concludes the chapter.

4.2 Theory and Hypotheses

This section briefly discusses our empirical hypotheses and theory behind them. We mainly focus on the relationship between the firm’s value of Tobin’s q and its mode choice for globalization strategy. As a straightforward extension of the q investment theory to the case of FDI (i.e., investment abroad), one may simply expect a positive relationship between Tobin’s q and FDI. In the presence of an alternative mode of globalization, however, we need to consider the relationship between Tobin’s q and a shift of the firm’s activities between FDI and an alternative mode in each of the following two different situations: offshoring of production and the supply of goods to foreign markets. As we argue below, the relationship between Tobin’s q and FDI will differ in these two situations. A key in our argument below is that, besides its role in the investment theory, Tobin’s q indicates a firm’s knowledge-capital intensity (relative to physical capital).

We first consider the situation in which production is offshored to a foreign country. A firm has two options: to produce goods at a foreign subsidiary (i.e., FDI) or to outsource production to a local firm (i.e., FO). In this situation, we expect that Tobin’s q is positively related to the ratio of FDI to FO. Our argument is based on the theoretical analysis by Chen et al. (2012) and Jinji et al. (2019b). Chen et al. (2012) demonstrate that knowledge-capital (relative to physical capital) intensity rather than physical capital (relative to labor) intensity is an important factor for the firm’s choice between FDI and FO. The reason is as follows. The owner of physical capital can relatively easily control the use of the physical capital. In contrast, it is relatively difficult for the owner of knowledge capital to specify and completely control the use of the knowledge capital. This is mainly because knowledge capital is partly non-excludable in nature and hence its use is not fully contractible.

Let us consider the case in which the production in foreign country requires both physical and knowledge capital along with non-contractible effort by a local agent. The local agent is a manager if production occurs at a subsidiary and a licensee if it is outsourced to an independent local firm. An MNE that owns knowledge capital produces a good in two periods. Under FO, the agent who owns the physical capital makes an efficient effort to utilize its capital in period 1. Under FDI, in contrast, as the MNE owns the physical capital, the agent has no incentive to make an effort under the incomplete-contracting environment. On the other hand, under FO, the MNE transfers only an insufficient amount of the knowledge capital to the agent to prevent the agent from using knowledge absorbed in period 1 together with the physical capital for outside uses in period 2. Under FDI, as the agent who does not own the physical capital cannot use the absorbed knowledge for outside uses in period 2, the MNE transfers the full amount of the knowledge capital to the agent in period 1. The more important knowledge capital is in production, the smaller is the loss for the MNE from the agent’s inefficient effort in period 1 under FDI and the larger is the loss for the MNE from an insufficient transfer of the knowledge capital to the agent under FO. Thus, the MNE prefers FDI to FO. If the physical capital is more important, the opposite is true and hence the MNE prefers FO.

We can easily extend the above model by Chen et al. (2012) to the case in which a final good is produced by assembling many intermediate goods. The whole production process is offshored to a foreign country. Intermediate goods vary in their knowledge-capital intensity. An MNE decides whether to outsource production for each intermediate good. Then, as the average knowledge-capital intensity of the MNE is higher, a smaller fraction of intermediate goods is outsourced. As argued in Sect. 4.1, a higher knowledge-capital intensity implies a higher value of Tobin’s q. Given this, the above argument yields our first empirical hypothesis that Tobin’s q is positively related to an FDI engagement relative to FO by MNEs.

We next consider the situation in which a firm supplies its goods to a foreign market. The firm can do so either via exports or horizontal FDI. There are two types of fixed costs: firm-specific fixed costs that mainly reflect knowledge-based assets and plant-specific fixed costs that mainly reflect physical assets. The knowledge-capital models of horizontal FDI (Horstmann and Markusen 1992; Markusen 1984, 2002) reveal that the jointness property of knowledge capital leads to multi-plant economies of scale. Hence, a firm with a higher intensity of knowledge capital tends to prefer FDI to exports. However, this tendency will be weakened as the degree of contractibility of knowledge capital is lower. This is because a wage premium is required when a manager of the foreign subsidiary, who absorbs knowledge capital, moves to a local competing firm (Fosfuri et al. 2001). In addition, the use of knowledge capital in foreign production incurs technology transfer costs that are increasing in technological complexity (Keller and Yeaple 2013). A higher intensity of knowledge capital generally implies higher technology transfer costs. This factor functions against the tendency mentioned above. Overall, whether a higher intensity of knowledge capital is associated with a lower ratio of exports to FDI depends on the relative strengths of the three factors mentioned above. Thus, our second empirical hypothesis is that there is no clear-cut relationship between Tobin’s q and an MNE’s ratio of exports to FDI.

4.3 Data and Variables

4.3.1 Data

We primarily collect data from three datasets of Japanese companies: the Basic Survey of Japanese Business Structure and Activities (BSJBSA) or Kigyo Katsudo Kihon Chosa, the Basic Survey on Overseas Business Activities (BSOBA) or Kaigai Jigyo Katsudo Kihon Chosa, and the Nikkei Economic Electronic Database Systems (NEEDS) Company Financial Reports.

BSJBSA and BSOBA are annual surveys by the Ministry of Economy, Trade, and Industry (METI).⁴ BSJBSA is a mandatory survey for all firms with 50 or more employees and paid-up capital or investment funds exceeding 30 million yen. It covers mining, manufacturing, wholesale/retail trade, and service industries, and approximately 26,000 firms responded to the survey in 1999. On the other hand, BSOBA is an approved-type survey for Japanese corporations which (as of the end of March) own or previously have owned overseas affiliates. BSOBA lists two types of overseas affiliates: (1) those with at least 10% of their capital held by a Japanese parent company; and (2) those with at least 50% of their capital held by a foreign subsidiary that in turn has at least 50% of its capital held by a Japanese parent company. However, BSOBA excludes foreign affiliates in the financial, insurance, and real estate industries. Approximately 2,200 Japanese parent companies and 14,000 overseas affiliates responded to the survey in 1999. The data from BSJBSA and BSOBA include sales, employment, capital, R&D expenditures, headquarters’ direct exports, and their foreign affiliates’ sales. BSJBSA for the period 1994–1999 also includes information on outsourcing, that is, the number of domestic and foreign firms to which a headquarters company has contracted manufacturing and/or processing tasks and the total expenditures on the contracting out of business activities. Unfortunately, detailed data on outsourcing are unavailable after 2000. Because of this data limitation, our sample is restricted to the period of 1994–1999.

The corporate balance sheet data that we use to calculate Tobin’s q and TFP are extracted from NEEDS, which incorporates approximately 4,000 publicly traded firms on the Japanese stock market, and covers the period from 1975 to the present. All publicly traded Japanese firms are identifiable using two codes—a Nikkei company code defined by Nikkei, Inc., and a security code defined by the Japanese Securities Identification Code Committee. Given that firm codes in BSJBSA and BSOBA differ from those in NEEDS, we use the Nikkei company code to link the three datasets. In addition, we identify approximately 1,000 to 1,300 headquarters companies for each year during the period 1994–1999 by matching full names and addresses of companies in the three datasets.⁵ In our sample, each headquarters company engages in at least one globalization activity (exports, FDI, or FO).⁶

4.3.2 Indexes of Globalization Activity

As shown by Table 3.1 in Chap. 3, many firms engage in multiple globalization modes rather than a single mode. For example, more than 550 firms engaged in both exports and FDI in 1999. This is more than double the number of firms engaged only in exports in 1999. This evidence is important when we select our preferred empirical framework.

Moreover, our dataset contains unique information regarding other dimensions of firms’ globalization activities, including sales of foreign affiliates, the value of exports from the headquarters in Japan, and the value of FO. We utilize the information available in our dataset to measure the extent of engagement in each globalization mode by taking the ratio of the size of a particular activity (exports, FDI, or FO) to the domestic sales of headquarters companies. Moreover, we can measure the firm’s relative choice of globalization mode by calculating the ratio of two variables representing its globalization activity. First, we denote domestic sales by headquarters companies in Japan as D, the total sales of foreign affiliates as I, the value of exports from the headquarters companies as X, and the total expenditure on outsourcing to companies abroad as O. Note that we can measure the size of the total FDI by I. Thereafter, we construct an additional measure of FDI denoted as $I^h$ (where the superscript h refers to the horizontal type) by excluding exports to Japan from the sales of foreign affiliates, which measures the size of horizontal FDI. We employ these variables to calculate the ratio of each globalization activity (i.e., X, I, $I^h$, and O) to D, denoted as RXD, RID, $RI^hD$, and ROD, respectively. Moreover, we calculate the ratio of O to I, denoted as ROI, to capture the relative choice between FO and FDI, and the ratio of X to $I^h$, denoted as $RXI^h$, to capture the relative choice between exports and horizontal FDI. In the index for the relative choice of exports over FDI, we use $I^h$ as the measure of FDI because, as Helpman et al. (2004) reveal, horizontal FDI matters to firms when choosing between export and FDI. Conversely, ROI measures the relative choice of FO over FDI. In this index, we consider that the total sales of foreign affiliates, including exports to the source country, are an appropriate measure of FDI. Note that by specifying the total sales of foreign affiliates as a measure of FDI, our analysis is consistent with that of Chen et al. (2012), who consider only the case where production occurs in the foreign country and a domestic firm chooses either FDI or outsourcing. In their model, FDI can be horizontal or vertical.

Table 4.1 summarizes the definition of variables that measure the firm’s globalization activities.

Table 4.1 Definition of variables

4.3.3 Tobin’s q and TFP

We measure Tobin’s q (Tobin 1969) using the ratio of the firm’s market value to its tangible assets. We follow DaDalt et al. (2003) and specify the following simple approximation of Tobin’s q ⁷:

$$\text {Tobin's } q=\frac{MVE+PS+LTDEBT+CL+BVINV-NCA}{TA},$$

where MVE denotes the year-end value of a common stock, PS denotes the liquidation value of a preferred stock, and LTDEBT, CL, BVINV, CA, and TA denote the book values of long-term debt, current liabilities, inventory, current assets, and total assets, respectively. We exclude PS in our measure of Tobin’s q because the requisite data are unavailable.

We estimate TFP following Olley and Pakes (1996) and Keller and Yeaple (2009). We first define value-added and capital stock. The value-added of firm i at time t $Y_{it}$ is measured as follows:

$$Y_{it}=SA_{it}-COGS_{it}-SGA_{it}+OR_{it}+PE_{it}+DE_{it}+ST_{it},$$

where SA, COGS, SGA, OR, PE, DE, and ST denote total sales, cost of goods sold, selling, general and administrative expenses, office rents, payroll expenses, depreciation expenses, and sundry taxes of firm i at time t, respectively. All values are converted into real measures using the GDP deflator released by METI.

The capital stock $K_{it}$ is estimated by the perpetual inventory method:

$$\begin{aligned} K_{it}=I_{it}+(1-\delta )K_{it-1}, \end{aligned}$$

(4.1)

where $K_{it}$ is the stock of equipment of firm i at the end of period t, $I_{it}$ is the real investment of equipment of firm i during period t, and $\delta$ is the depreciation rate. Real investment $I_{it}$ includes three types of investment involved in firm production: buildings and structures, machinery, and transportation machinery and tools. Following Hayashi and Inoue (1991), we apply depreciation rates of 5.2%, 9.5%, and 8.8% to buildings and structures, machinery, and transportation machinery and tools, respectively. We estimate each type of investment using Eq. (4.1) first and then aggregate them into $K_{it}$.

Then, let $y_{it}$ be the logarithm of the value added of firm i at time t, and $k_{it}$ and $l_{it}$ be the logarithm of the firm’s capital and labor, respectively. We consider the following production function:

$$\begin{aligned} y_{it}=\beta _0+\beta _kk_{it}+\beta _ll_{it}+\omega _{it}+\eta _{it}, \end{aligned}$$

(4.2)

where $y_{it}$ is the logarithm of value-added $\ln Y$ in firm i at time t, $k_{it}$ is the logarithm of the capital input $\ln K$, $l_{it}$ is the logarithm of the number of full-time employees $\ln L$, $\omega _{it}$ is productivity, and $\eta _{it}$ is either the measurement error or a shock to production. Both $\omega$ and $\eta$ are not observed. Olley and Pakes (1996) argue that the endogeneity of input demand and self-selection induced by the exit behavior bias the OLS estimates of Eq. (4.2). In general, endogeneity arises because input choices are determined by the firm’s beliefs regarding $\omega _{it}$ when these inputs are used.

Following Olley and Pakes (1996), we assume that labor l is the only variable factor whose choice can be affected by the current value of $\omega$ and that capital k is a fixed factor only affected by the distribution of $\omega _{it}$, conditional on the information available at time $t-1$ and past values of $\omega$. The investment demand function is then given by $i_{it}=i(\omega _{it},k_{it})$. Provided $i_{it}>0$, the equation is strictly increasing in $\omega$ for any k, so that the investment demand function can be inverted to yield $\omega _{it}=h(i_{it},k_{it})$. Substituting this result into Eq. (4.2) gives

$$\begin{aligned} y_{it}=\beta _ll_{it}+\phi (i_{it},k_{it})+\eta _{it}, \end{aligned}$$

(4.3)

where $\phi (i_{it},k_{it})=\beta _0+\beta _kk_{it}+h(i_{it},k_{it})$. Because $\phi (\cdot )$ contains the productivity term $\omega$, which is the source of the simultaneity bias, we can estimate Eq. (4.3) to obtain consistent estimates for $\beta _l$.⁸ We use a fourth-order polynomial with interaction terms in investment and capital to identify the unknown function $\phi (\cdot )$. As the investment demand function (and hence $\phi (\cdot )$) should differ across industries, we estimate different polynomials for each of 10 main sectors: (i) food, textiles/apparel, and wood/paper products; (ii) chemicals, pharmaceuticals, and refined petroleum products; (iii) non-metallic products, basic metals, and fabricated metal products; (iv) machinery and precision instruments; (v) electrical and electronic equipment; (vi) transportation equipment; (vii) construction; (viii) trading; (ix) wholesale trade; and (x) other service activities.

A firm maximizes its expected value of both current and future profits and evolves according to an exogenous Markov process. In every period, the firm decides whether to continue an operation along with decisions on its labor input l and investment i, conditional on staying in the market. With consistent estimates of $\beta _l$, we use estimates of the survival probabilities to identify $\beta _k$. The survival probabilities $Pr_{it}$ are obtained using a probit regression on a fourth-order polynomial with the interaction terms for capital and investment with a one-period lag. The final step to estimate $\beta _k$ is as follows:

$$\begin{aligned} y_{it}-\hat{\beta }_ll_{it}=\beta _kk_{it}+g(\hat{\phi }_{it-1}-\beta _kk_{it-1}, \widehat{Pr}_{it})+\eta _{it}, \end{aligned}$$

(4.4)

where variables with a hat ($\hat{\ }$) indicate estimators of these variables. In Eq. (4.4), we also estimate the unknown function $g(\cdot )$ using a fourth-order polynomial with interaction terms for $\hat{\phi }_{it-1}-\beta _kk_{it-1}$ and $\widehat{Pr}_{it}$ with non-linear regression on $\beta _k$. Using consistent estimates of $\beta _l$ and $\beta _k$, we estimate TFP as

$$TFP_{it}=y_{it}-\hat{\beta }_l l_{it}-\hat{\beta }_k k_{it}.$$

Table 4.2 provides descriptive statistics for variables in our analysis. As shown, the percentiles and means suggest that the distributions of these indexes are extremely negatively skewed.

Table 4.2 Descriptive statistics

Table 4.3 reports the correlations of the variables. In our data, it turns out that the correlation between Tobin’s q and TFP is positive but weak. The correlation coefficient is 0.013.⁹

Table 4.3 Correlations of variables

4.4 Estimation Strategy

In this section, we explain our empirical strategy. First, when we estimate the relationship of Tobin’s q or TFP to our globalization indexes RXD, RID, $RI^hD$, and ROD, we need to address the censoring problem in the data because only a small proportion of the sampled firms engage in all three globalization activities. Thus, we implement Tobit regression, in addition to the ordinary least squares (OLS) estimation.

Second, as discussed in the previous section, the relative globalization indexes (i.e., ROI and $RXI^h$) in our sample have a strong negatively skewed distribution, indicating that heterogeneity across firms may be substantial, and outliers may exist in the dataset. As is well known, the presence of outliers can strongly distort the OLS estimator, leading to unreliable results. Thus, in addition to the OLS method, we employ several robust regression methods to cope with these issues, as robust OLS estimator, median regression estimator, Huber M-estimator, and MM-estimator. The robust OLS (ROLS) is an OLS regression with robust variance estimates (Huber 1981). The median regression estimator, or quantile regression (QR) estimator, deals with the heterogeneity across firms and the presence of outliers (Wooldridge 2010). Although the QR estimators are resistant to the existence of vertical outliers (i.e., outliers in the y dimension without outlying in the x dimension), they behave poorly in the presence of bad leverage points (i.e., points associated with outlying values in the x dimension that locate far away from the true regression line) (Verardi and Croux 2009). In addition, their efficiency is low at a normal distribution (Huber 1981). The Huber M-estimator generalizes the QR estimators by considering a loss function other than the absolute values of the residuals, which increases the efficiency, keeping robustness with respect to vertical outliers (Verardi and Croux 2009). However, the M-estimators are not robust with respect to bad leverage points (Rousseeuw and Yohai 1984). Finally, the MM-estimator introduced by Yohai (1987) performs well in both high efficiency and a high breakdown point. A breakdown point is the smallest fraction of contamination (i.e., very bad outliers) in the sample that can cause an estimator to take on values arbitrarily far from the true values (Rousseeuw and Leroy 1987). Thus, a higher breakdown point means that the estimator is more resistant to outliers.¹⁰

In addition to the issue of outliers, endogeneity is another important issue to be addressed in our estimation. Endogeneity potentially arises because factors that simultaneously influence the choice of globalization mode and Tobin’s q may exist. The problem of omitted variables may also involve endogeneity. For example, previous studies in the investment literature have shown that the presence of adjustment costs or financial frictions causes Tobin’s q to diverge from the marginal value of installed capital, or “marginal q” (Abel and Eberly 1994; Hennessy 2004). More recently, Abel and Eberly (2011) have demonstrated that investment is positively related to both Tobin’s q and cash flow even in the absence of adjustment costs or financial frictions. Moreover, Gala and Julio (2012) suggest that, in addition to Tobin’s q and cash flow, firm size may play an important role in explaining investment. Therefore, our regression of the globalization indexes on Tobin’s q may suffer from omitted variable bias if these variables are not controlled for.

We employ the QRIV technique proposed by Lee (2007) to control for possible endogeneity with the potential presence of outliers. The estimation procedure comprises two steps: the first step is to estimate the residuals of the reduced-form equation for the endogenous explanatory variable (i.e., Tobin’s q); and the second step is to use the reduced-form residual as an additional explanatory variable to estimate the primary equation, which describes the relationship between the choice of globalization mode and Tobin’s q.

In our QRIV estimations, we employ IVs that are assumed to be related to the omitted variable problem in measuring firm performance, which are suggested in the literature (Abel and Eberly 2011; Gala and Julio 2012). Among others, we employ two sets of IVs to verify the robustness of our estimation results. The first set includes the cash flow $CF_{i t-1}$ and the years in business $T^B_{it}$ for the headquarters company i, where $CF_{i t-1}$ stands for the beginning-of-year cash flow for the headquarters company i in year $t-1$.¹¹ We denote the QRIV with the first set of IVs as QRIV(1). The second set of IVs comprises $CF_{i t-1}/K_{i t-1}$, $LnK_{i t-1}$, and $LnT^B_{it}$, which denote the ratio of cash flow to capital stock, the natural logarithm of capital stock, and the natural logarithm of years in business for the headquarters company, respectively. Now $K_{i t-1}$ is the beginning-of-year capital stock for the headquarters company i in year $t-1$. We use LnK as a measurement of firm size, as suggested by Gala and Julio (2012). We denote the QRIV with the second set of IVs as QRIV(2). We assume that if changes in these IVs are not controlled, they will be part of the error, accounting for inconsistent estimates as long as they are correlated with the performance of the headquarters companies, such as Tobin’s q.¹²

4.5 Empirical Results

4.5.1 The Relationships of Tobin’s q and TFP to the Degree of the Firm’s Engagement in Globalization Modes

We first analyze the relationship between Tobin’s q or TFP and the degree of the firm’s engagement in a particular globalization mode by regressing each of RXD, RID, $RI^hD$, and ROD on Tobin’s q or TFP. Results are reported in Table 4.4.

Table 4.4 OLS and Tobit estimates

The upper panel of Table 4.4 shows the results of OLS and Tobit regression of the globalization indexes (i.e., RXD, RID, $RI^hD$, and ROD) on the logarithm of Tobin’s q, denoted as LnQ. The estimation results for TFP are summarized in the lower panel of Table 4.4. The OLS and Tobit estimates of LnQ are both statistically significant and positive except for the case of $RI^hD$. In contrast, the OLS estimates of TFP fail against the null hypothesis for all of the globalization indexes. After we control for censoring problems by adopting Tobit regression censored at zero, the estimates of TFP are positively significant for RXD, $RI^hD$, and ROD.

Our results indicate the positive relationship between Tobin’s q and the globalization indexes. In addition, the results for TFP are consistent with Tomiura (2007) for the most part. That is, highly productive firms tend to engage in more globalization activity (FDI, exporting, or FO). However, the results for RID suggest that higher-productivity firms do not necessarily have a higher ratio of foreign affiliate sales to domestic sales of the headquarters company. This may be because FDI in RID includes both the horizontal and vertical types of FDI, and vertical FDI may not be implemented by high-productivity firms.

4.5.2 Tobin’s q and the Relative Choice of Globalization Modes

We next regress the indexes of the relative choice of globalization modes on Tobin’s q. As we calculate the ratios of the two globalization modes and their multiplicative inverses (i.e., FO to the total FDI for ROI, exports to horizontal FDI for $RXI^h$, and their multiplicative inverses, RIO and $RI^hX$), we exclude the observations that have zero values for at least one of the two modes.¹³ We check the robustness of our estimation results by including the observations with zero values in Sect. 4.5.3.

Table 4.5 Estimation results (explanatory variable: LnQ)

Table 4.5 summarizes the results of regressing the four globalization indexes on the logarithm of Tobin’s q, denoted as LnQ. We first estimate the model by the OLS. As shown in row (1) of Table 4.5, the OLS estimates of the coefficients of LnQ are all insignificant, and the magnitude of the estimated coefficients is relatively large, suggesting that the presence of outliers seriously affects the regression coefficients. Thereafter, we run the ROLS with robust variance estimates.¹⁴ As reported in row (2), the magnitude of the estimated coefficients becomes modest by employing ROLS, and the coefficient of ROI is negative at the 5% significance level.

We next run the robust regression with QR, Huber M-estimators, and MM-estimators.¹⁵ Estimated results are reported in rows (3), (4), and (5) in Table 4.5, respectively. As shown in the table, the three types of estimates are all significant and negative for ROI and positive for RIO, indicating that Tobin’s q is positively correlated with a motive of a firm toward more FDI and away from FO. Unlike ROI and RIO, the estimates of $RXI^h$ and $RI^hX$ are statistically insignificant, except for the MM-estimate of $RXI^h$, which is negative at the 10% significance level. Thus, we cannot find any evident relationship of Tobin’s q to the choice of globalization mode between horizontal FDI and exports.

Furthermore, we employ a QRIV technique using two sets of IVs, as explained in the previous section, to account for the possible endogeneity.¹⁶ Table 4.6 reports the estimated results from the QRIV median estimates. It indicates that the results are quite consistent between the two sets of IVs. That is, the estimated coefficient of LnQ is negative and statistically significant for ROI and positive for RIO, whereas the estimated coefficients are all insignificant for $RXI^h$ and $RI^hX$. These results suggest that our findings reported in Table 4.5 can be supported even after controlling for possible endogeneity in our estimations.

Table 4.6 Endogenous  quantile regression (explanatory variable: LnQ)

As the globalization indexes in our sample have a strong negatively skewed distribution, the relationships between the globalization indexes and firm characteristics may substantially differ at different points in the conditional distribution of the globalization indexes. We estimate the coefficients of LnQ for ROI and $RXI^h$ at various quantiles between 10% and 90% using QRIV(2) to check heterogeneity between globalization indexes and firm characteristics. We report the results in Fig. 4.1. In this figure, we plot point and interval estimates from QRIV(2) for LnQ. In each panel in Fig. 4.1, the horizontal axis measures the quantile, and the vertical axis measures the value of estimates. Moreover, the thick black lines depict the point estimates at various quantiles, and dashed lines indicate the lower and upper bounds of a 95% confidence interval.

Panel (1) shows that the confidence interval for the estimated coefficient of LnQ in the regression of ROI lies below zero at all quantiles between 10% and 90%. In contrast, panel (2) shows that the 95% confidence interval in the regression of $RXI^h$ includes zero at all quantiles. As a result, Fig. 4.1 suggests that the estimated results reported in Table 4.6 hold at all quantiles between 10% and 90%.

Fig. 4.1

Estimates and confidence intervals for LnQ by QRIV(2)

4.5.3 Robustness of the Results

In the analysis in the previous subsection, we focused on firms engaging in multiple globalization modes. However, firms may choose a single mode rather than multiple modes, as suggested by theoretical models such as that in Chen et al. (2012). Thus, we check whether our results in the previous subsection are robust even when we include firms that engage only in a single mode in our estimation.

The globalization indexes we used in the previous subsection are ROI and RIO for the choice between FO and FDI, and $RXI^h$ and $RI^hX$ for the choice between exports and horizontal FDI. Here, we include observations with zero values for the numerator of each index. For example, in the case of RIO, all firms in the sample for estimation engage in FO but some of them do not conduct FDI.

Besides the estimation techniques we employed in the previous subsection, we estimate the model using a censored quantile regression (CQR) technique to address the censoring problem in the data.¹⁷ As shown in Table 3.2, the value of ROI is zero even at the 0.70 quantile because only a small fraction of firms that conduct FDI also engage in FO. Consequently, we cannot obtain technically sound quantile estimates, such as a median estimate, for ROI. Therefore, we omit the estimated results for ROI.

Table 4.7 Robustness check by including single-mode firms (explanatory variable: LnQ)

The estimated results with zero values in the numerator of the globalization index are reported in Table 4.7. The Huber M-estimator, QR, and CQR provide positive and statistically significant estimates of the coefficient of LnQ in the regression of RIO. In contrast, in the regression of $RXI^h$, statistically insignificant estimates are obtained for LnQ, except for the Huber M-estimator. Similarly, for $RI^hX$, insignificant estimates of LnQ are provided, except for the MM-estimator. These findings are quite consistent with those in the previous subsection.

Thus, from the analysis in this subsection we conclude that our findings in Sect. 4.5.2 are quite robust even when we include firms engaging in a single mode in the estimation.

4.5.4 TFP and the Relative Choice of Globalization Modes

We next regress the indexes of globalization modes on TFP using the same estimation methods as those employed in Sect. 4.5.2 to investigate any possible differences between Tobin’s q and productivity in the firm’s choice of globalization mode. Table 4.8 reports the estimated results.

Table 4.8 Estimation results (explanatory variable: TFP)

As shown in the table, the estimates of ROI and RIO are insignificant for all estimators. We cannot find any significant relationship of TFP to the choice of globalization mode between FDI and FO.¹⁸ On the other hand, as for its relationship with the choice between horizontal FDI and exports, the results indicate that the estimates of $RI^hX$ are positive and statistically significant, except for OLS, and that the estimates of $RXI^h$ are negative and significant by QR and Huber M-estimators. This suggests a positive relationship between TFP and a motive of a firm toward a greater horizontal FDI and less export, which is consistent with the findings in the large empirical literature.

It is then apparent from a comparison between Tables 4.5 and 4.8 that the relationships of Tobin’s q with the relative choice of globalization modes clearly differ from those of TFP.

4.6 Conclusion

Using Japanese firm-level data, we empirically investigated the manner in which the firm’s choice of globalization mode differs according to the value of Tobin’s q. Our empirical results indicated that Tobin’s q is negatively related to the ratio of FO to FDI by Japanese MNEs. This finding implies that the knowledge-capital intensity plays an important role in the choice between FDI and FO, as Chen et al. (2012) demonstrate. This finding is consistent with that of Jinji et al. (2019b). In contrast, we could not find a definite relationship between Tobin’s q and the ratio of exports to horizontal FDI. This may be explained by the dominance of a higher technology transfer cost for knowledge capital and/or the imperfect contractibility of knowledge capital over multi-plant economies of scale of knowledge capital. Moreover, we found that the relationship between Tobin’s q and an MNE’s mode choice for globalized activity fairly differs from the relationship between productivity and an MNE’s choice of the mode for globalized activity. Our estimated results revealed that TFP is negatively correlated with the ratio of exports to horizontal FDI but has only an insignificant relationship with the outsourcing decision. The former evidence supports the prediction by Helpman et al. (2004) and is consistent with the findings of existing empirical studies.