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Market transparency and international allocation of capital

  • Udo Broll
  • Bernhard Eckwert
  • Keith K. P. Wong
Article
  • 26 Downloads

Abstract

The paper analyzes the interaction between the domestic and foreign capital allocation of a multinational firm, and market transparency in the foreign country. Foreign capital investment is risky because of uncertainties about the host country’s institutions and market conditions. We model transparency through a publicly observable signal that provides information about the quality of institutions and market conditions in the foreign country. Under higher transparency, the public signal conveys more precise information. It is shown that higher transparency leads to more dispersion of conditionally expected foreign country risks as they become more sensitive to the realization of the public signal. We characterize conditions under which more transparency encourages or discourages foreign investment. Regardless of the volume of capital flows, the ex-ante expected total cash flow of the firm always increases with more transparency .

Keywords

International capital allocation Country risk Public information Transparency 

JEL Classification

D21 D81 R12 R50 

1 Introduction

Multinational firms are important players in global markets. Multinationals are different from purely national firms because, in general, they are flexible and able to move activities between their plants across countries. The ability of firms with foreign direct investment to arbitrage institutional restrictions such as tax systems, financial regulations and remittance forms, creates economic advantanges which can be transformed into higher global profits. In general, direct foreign investment can be seen as an economic process that determines the volume and direction of resources transferred across borders (see, for example, Bevan and Estrin 2004; Navaretti and Venables 2004; Brakman et al. 2006; Wong 2006; Mackinnon and Cumbers 2007; Broll et al. 2010; Vuksic 2014; Hwang and Lee 2015).

International direct capital flows represent a major source of financing of economic activity in less developed countries. Direct investment inflows may bring increased employment, new technologies, more international trade and higher wages in the host country. These effects are especially relevant for countries in transition and for developing economies. This is one reason why countries try to promote inflows for foreign capital.1 On the other hand, it is often argued that country risk, weak instituions and imperfect enforcement mechanisms adversely affect direct capital flows (see, for example Lucas 1990; Janeba 2002; Markusen 2002; Acemoglu et al. 2002). International firms often have only limited legal recourse if the host country government chooses to default on a debt contract or to expropriate a real or financial asset. Therefore, in order to evaluate the global business environment, multinational firms must assess the country’s risk profile by studying the linkage between the country’s economic policy and the degree of economic risk. This is especially important for firms investing in developing economies (see, for example, Hayakawa et al. 2013).

To cope with country risk, international firms organize and plan foreign investment as a sequential process that determines the direction and the volume of resources transferred to other countries. Our study theoretically analyzes the impact of market transparency on resource allocation and profitability of foreign investment. Transparency is modelled as the provision of a noisy signal conveying information about the institutional and market conditions in the foreign country. The notion of transparency used in our study is adopted from the work by Eckwert and Zilcha (2001, 2003). They characterize market transparency using a criterion which is conceptually related to the literature that emerged from the seminal works by Blackwell (1953); Hirshleifer (1971, 1975) and Schlee (2001); Krebs (2005).

The observable signal can be interpreted as being related to the foreign country’s choice of international trade policy, monetary policy, participation in international organizations, an improvement in the index of economic freedom, better quality of country’s institutions or regional trade agreements. The signal thus captures the country’s institutional and market conditions. The foreign country is considered more transparent if the signal conveys more precise information about the country’s economic and political environment. We find that higher transparency may increase or decrease the volume of direct foreign investment. The impact depends on the shape of the total profit function of the multinational firm. However, the total expected firm profits always increase with more transparency.

The rest of this paper is organized as follows. Section 2 delineates the model of a multinational firm under risk. Section 3 introduces the notion of transparency. In Sect. 4, we analyze the link between foreign country transparency and the firm’s international allocation decision.

2 International capital allocation under risk

We consider a multinational firm that operates for two periods, \(t = 0\) and 1. In period \(t=0\), the firm, which is located in the domestic country, is endowed with a fixed capital stock, \(K_0>0\). At that time, the firm has to allocate an amount of capital, \(I\in (0,K_0)\), to be invested in a foreign economy. The investment generates a deterministic cash flow, \(\Pi _f(I)\), in period \(t=1\). The remaining amount of capital, \(K_0 - I\), is invested at home to generate another deterministic cash flow, \(\Pi _d(K_0-I)\), in period \(t=1\). We assume that \(\Pi _d(\cdot )\) and \(\Pi _f(\cdot )\) are both increasing and weakly concave functions.

While the cash flows, \(\Pi _d(K_0-I)\) and \(\Pi _f(I)\), are known, the actual amount of the cash flow that can be collected by the multinational firm from its direct investment is subject to country risk. We model such country risk by a multiplicative shock, \(\tilde{\alpha }\), that denotes the fraction of the cash flow, \(\Pi _f(I)\), to be lost when the country risk occurs in period \(t=1\). The tilde, \((^\sim )\), signifies that \(\tilde{\alpha }\) is a random variable. The multinational firm holds a prior belief that \(\tilde{\alpha }\) is distributed according to a probability density function, \(\pi (\alpha )\), over support \([\underline{ \alpha }, \overline{\alpha }]\), where \(0 \le \underline{\alpha } < \overline{\alpha } \le 1\).

Prior to the multinational firm’s foreign investment decision, there is a signal, \(\tilde{s}\), whose realization is publicly observed. This public signal, \(\tilde{s}\), is a random variable that is correlated with the country risk, \(\tilde{\alpha }\). Specifically, \(\tilde{s}\) contains useful information about the unknown host country’s political and economic system. Let n(s) be the prior probability density function of \(\tilde{s}\) over support \([ \underline{s}, \overline{s}]\), where \(\underline{s} < \overline{s}\). The multinational firm updates its belief about \(\tilde{\alpha }\) in a Bayesian fashion. Let \(\nu (\alpha |s)\) be the posterior probability density function of \(\tilde{\alpha }\) conditional on \(\tilde{s}= s\) over support \([\underline{\alpha }, \overline{\alpha } ]\). Hence, the expected value of \(\tilde{\alpha }\) conditional on the realized value of \(\tilde{s}\) is given by
$$\begin{aligned} \mu (s) = \int _{\underline{\alpha }}^{\overline{\alpha }} \alpha \nu (\alpha |s)\ \mathrm{d}\alpha . \end{aligned}$$
(1)
The firm’s cash flow (or operating profit) in period \(t=1\) is given by
$$\begin{aligned} \tilde{\Pi } = \Pi _d(K_0-I)+(1-\tilde{\alpha } )\Pi _f(I). \end{aligned}$$
(2)
Conditional on the realized public signal, s, the firm’s decision problem in period \(t=0\) is to choose an amount of direct investment, I, so as to maximize its expected cash flow in period \(t=1\):
$$\begin{aligned} \max _{I\in (0,K_0)}\int _{\underline{\alpha }}^{\overline{\alpha }} {[}\Pi _d(K_0-I)+(1-\alpha )\Pi _f(I)]\nu (\alpha |s)\ \mathrm{d}\alpha . \end{aligned}$$
(3)
The first-order condition for program (3) is given by
$$\begin{aligned} \Pi _d'\{K_0-I[\mu (s)]\}=[1-\mu (s)]\Pi _f'\{I[\mu (s)]\}, \end{aligned}$$
(4)
where \(\mu (s)\) is given by Eq. (1), and \(I[\mu (s)]\) is the optimal amount of foreign direct investment given the realized public signal, s.2

3 Foreign country transparency

We now introduce our notion of transparency. We identify the transparency in the foreign country with the informativeness of the signal, \(\tilde{s}\), which depends on the information system within which signals can be interpreted. An information system, denoted by g, specifies a set of conditional probability density functions of \(\tilde{s}\), \(\{g(s|\alpha ):\alpha \in [\underline{\alpha }, \overline{\alpha }]\}\), over support \([\underline{s},\overline{s}]\). This set of conditional probability density functions, according to which signals are generated for a given realization of the country risk, is common knowledge. The multinational firm acts in a Bayesian manner. It revises its expectations and maximizes its expected cash flow in period \(t=1\) on the basis of the updated belief.

Given the information system, g, we can write the prior probability density function of \(\tilde{s}\) as:
$$\begin{aligned} n(s) = \int _{\underline{\alpha }}^{\overline{\alpha }}g(s|\alpha ) \pi (\alpha )\ \mathrm{d}\alpha , \end{aligned}$$
(5)
for all \(s \in [\underline{s}, \overline{s}]\). By Bayes’ rule, we can use Eq. (5) to write the posterior probability density function of \(\tilde{\alpha }\) conditional on \(\tilde{s}= s\) as
$$\begin{aligned} \nu (\alpha |s) = \frac{g(s|\alpha )\pi (\alpha )}{n(s)}, \end{aligned}$$
(6)
for all \(s \in [\underline{s}, \overline{s}]\).

Blackwell (1953) suggested a criterion that ranks different information systems according to their informational contents. Suppose \(g^1\) and \(g^2\) are two information systems with the associated probability density functions, \(n^1(s)\) and \(n^2(s)\), respectively. The following criterion induces an ordering on the set of information systems.

Definition 1

Let \(g^1\) and \(g^2\) be two information systems. \(g^1\) is said to be more informative than \(g^2\) if there exists an integrable function, \(\lambda (s',s): [\underline{s},\overline{s}]\times [\underline{s}, \overline{s}] \rightarrow \mathbb {R}_{+}\), such that
$$\begin{aligned} \int _{\underline{s}}^{\overline{s}} \lambda (s', s)\ \mathrm{d}s' = 1, \end{aligned}$$
(7)
holds for all \(s \in [\underline{s}, \overline{s}]\), and
$$\begin{aligned} g^2(s'|\alpha ) = \int _{\underline{s}}^{\overline{s}} g^1(s|\alpha ) \lambda (s', s)\ \mathrm{d}s, \end{aligned}$$
(8)
holds for all \(\alpha \in [\underline{\alpha }, \overline{\alpha }]\).

According to Definition 1, \(g^1\) is more informative than \(g^2\) if the latter can be obtained from the former through a process of randomization. Equation (7) implies that \(\lambda (s', s)\) can be interpreted as a probability density function of \(\tilde{s}'\) over support \([\underline{s},\overline{s}]\) for a given value of s. Equation (8) describes the course of the randomization process that transforms the original signal, \(\tilde{s}\), into a new signal, \(\tilde{s}'\), via the probability density function, \(\lambda (s', s)\). If the \(s'\)-values are generated in this way, the information system, \(g^2\), can be interpreted as being obtained from the information system, \(g^1\), by adding random noise. Since \(\lambda (s',s)\) does not depend on \(\alpha\), the signals under \(g^2\) contain no new information about the realization of \(\tilde{\alpha }\) that has not been conveyed by the signals under \(g^1\). As a consequence, the conditional country risk under \(g^1\) must be lower than that under \(g^2\).

Our notion of transparency in the foreign country is based on the informational content of the signal. We characterize the foreign country as more transparent if the signal conveys more information about \(\tilde{\alpha }\). Thus, higher foreign country transparency implies that the conditional country risk is reduced through the dissemination of more reliable information, which leads to the following definition.

Definition 2

Let \(g^1\) and \(g^2\) be two information systems for the country risk, \(\tilde{\alpha }\). The foreign country is said to be more transparent under \(g^1\) than under \(g^2\), if \(g^1\) is more informative than \(g^2\).

The following Lemma 1 formulates an alternative transparency criterion that is equivalent to the order in Definition 2. It provides a convenient practical tool for the analysis of our model.

Lemma 1

The foreign country is more transparent under the information system, \(g^1\), than under the information system, \(g^2\), iff
$$\begin{aligned} \int _{\underline{s}}^{\overline{s}} F[\nu ^1(\cdot |s)]n^1(s)\ \mathrm{d} s>\int _{\underline{s}}^{\overline{s}} F[\nu ^2(\cdot |s)]n^2(s) \ \mathrm{d}s, \end{aligned}$$
(9)
for every strictly convex function, \(F(\cdot )\), defined on the set of posterior probability density functions of \(\tilde{\alpha }\) over support \([\underline{\alpha }, \overline{\alpha }]\).

Note that \(\nu ^1(\cdot |s)\) and \(\nu ^2(\cdot |s)\) are the posterior beliefs under the two information systems. Thus, Lemma 1 implies that more transparency raises the expectation of any strictly convex function of posterior beliefs. For strictly concave functions, inequality (9) is reversed. A proof of Lemma 1 can be found in Kihlstrom (1984). It is worthwhile pointing out that the convexity of \(F(\cdot )\) in Lemma 1 is defined with respect to the posterior beliefs and not in terms of signal realization. As such, higher market transparency neither implies nor is implied by second-order stochastic dominance of the signal distribution.

4 Impact of higher transparency

In this section, we analyze the link between foreign country transparency and the multinational firm’s allocation decision.

4.1 Transparency and foreign investment

According to Eq. (4), the optimal amount of foreign direct investment, \(I[\mu (s)]\), depends on the realized value of the public signal, s, through the conditional expected value of \(\tilde{\alpha }\), i.e., \(\mu (s)\). A higher transparency level implies that the multinational firm faces higher uncertainty from an ex-ante point of view, i.e., before the public signal is revealed. This is due to the fact that \(\mu (s)\) reacts more sensitively to changes in the public signal when the signal becomes more informative.

Denoting the expected amount of foreign direct investment by E(I), we get
$$\begin{aligned} E(I)=\int _{\underline{s}}^{\overline{s}}I[\mu (s)] n(s)\ \mathrm{d}s. \end{aligned}$$
(10)
It is evident from Eq. (1) that \(\mu (s)\) is a linear function of the posterior probability density function, \(\nu (\alpha |s)\). Lemma 1 and Eq. (10) then imply that the expected amount of foreign direct investment increases (decreases) with more transparency in the foreign country, if and only if \(I(\mu )\) is strictly convex (concave) in \(\mu\).
Define \(\phi (I)\) as the ratio of the marginal returns on investment at home and abroad, i.e.,
$$\begin{aligned} \phi (I)=\frac{\Pi '_d(K_0 - I)}{\Pi '_f(I)}. \end{aligned}$$
(11)
We refer to \(\phi (I)\) as the ‘home investment incentive’ (HII). A larger HII means that, at the margin, investing at home becomes more profitable as compared to investing abroad. Differentiating Eq.  (11) with respect to I yields
$$\begin{aligned} \phi '(I)=-\phi (I)\bigg [\frac{\Pi _d''(K_0-I)}{\Pi _d'(K_0-I)} +\frac{\Pi _f''(I)}{\Pi _f'(I)}\bigg ]>0, \end{aligned}$$
(12)
since \(\Pi _d''(I)\le 0\) and \(\Pi _f''(I)\le 0\). We say that HII increases weakly (strongly), if \(\phi (I)\) is concave (convex).

Roughly speaking, under weakly increasing HII, marginal profits in the host country decrease at a faster rate than in the domestic country. In this sense, the foreign country is a developing economy relative to the domestic country. Under strongly increasing HII, by contrast, the foreign country can be considered as economically developed relative to the domestic country.

Using (11), we may rewrite Eq. (4) as:
$$\begin{aligned} (1-\mu )=\phi [I(\mu )]. \end{aligned}$$
(13)
Differentiating Eq. (13) twice with respect to \(\mu\) yields
$$\begin{aligned} I''(\mu )=-\frac{\phi ''[I(\mu )]}{\phi '[I(\mu )]^3}. \end{aligned}$$
(14)
Since \(\phi '(I)>0\), Eq. (14) implies that \(I(\mu )\) is convex (concave) in \(\mu\), iff \(\phi (I)\) is concave (convex) in I. Lemma 1 in combination with Eq. (10) then implies

Proposition 1

(Transparency and foreign investment) More transparency in the host country may encourage or decourage foreign investment activities. Under weakly (strongly) increasing HII, more transparency in the foreign country leads to higher (lower) ex-ante expected direct investment, E(I).

With more transparency about the host country’s market conditions, capital investment reacts more sensitively to changes in the public signal, because the signal is more reliable. Under a more transparent information system the distribution of \(\mu (s)\) will become more spread out: \(\mu (s)\) combines the realization of the signal, s, with the prior of \(\tilde{\alpha }\), and it assigns more weight to the signal if the signal is a more reliable. Therefore, a more precise public signal leads to more dispersed \(\mu (s)\) which is more sensitive to the realization of the signal.

We briefly illustrate the economic meaning of HII being, respectively, weakly or strongly increasing. Differentiating HII in Eq. (11) twice with respect to investment I yields
$$\begin{aligned} \phi ''(I)=\phi (I)\bigg \{\frac{\Pi _d'''(K_0-I)}{\Pi _d'(K_0-I)} -\frac{\Pi _f'''(I)}{\Pi _f'(I)} +\frac{2\Pi _f''(I)}{\Pi _f'(I)}\bigg [\frac{\Pi _d''(K_0-I)}{\Pi _d'(K_0-I)} +\frac{\Pi _f''(I)}{\Pi _f'(I)}\bigg ]\bigg \}. \end{aligned}$$
(15)
Suppose for the purpose of illustration that the foreign country is economically less developed than the domestic country, meaning that marginal profits abroad decrease at a faster rate than in the domestic country. Specifically, assume that \(\Pi _d(I)\) is linear in I, i.e., the home investment exhibits constant returns to scale. Moreover, let \(\Pi _f(I)=I^{\gamma }\), where \(\gamma \in (0,1)\), such that the foreign investment exhibits decreasing returns to scale. In this case, Eq. (15) becomes
$$\begin{aligned} \phi ''(I)=-\frac{\gamma (1-\gamma )\phi (I)}{I^2}<0. \end{aligned}$$
(16)
such that HII increases weakly. By Proposition 1, more transparency promotes direct investment in the host country.
Things look very differently if the foreign country is equally (or even better) economically developed than the domestic country. Suppose, for instance, that marginal profits abroad decrease at the same rate as in the domestic country, i.e., \(\Pi '_d(I)=\Pi '_f(I) =\beta e^{-\beta I}\), where \(\beta\) is a positive constant. Under this specification, Eq. (15) becomes
$$\begin{aligned} \phi ''(I)=4\beta ^2\phi (I)>0, \end{aligned}$$
(17)
such that HII increases strongly. By Proposition 1, in that case more transparency reduces foreign direct investment.

4.2 Transparency and profitability

We finally analyze whether the profitability of the multinational firm benefits from more transparency in the foreign country. We use the ex-ante expected total cash flow as a measure of profitability:
$$\begin{aligned} E(\Pi )=\int _{\underline{s}}^{\overline{s}}\bigg \{\Pi _d\{K_0-I[\mu (s)]\} +[1-\mu (s)]\Pi _f\{I[\mu (s)]\}\bigg \} n(s)\ \mathrm{d}s. \end{aligned}$$
(18)
Equation (1) implies that \(\mu (s)\) is a linear function of the posterior probability density function, \(\nu (\alpha |s)\). It then follows from Lemma 1 and Eq. (18) that the ex-ante expected total cash flow increases (decreases) with more transparency in the foreign country, iff \(\Pi (\mu )=\Pi _d[K_0-I(\mu )] +(1-\mu )\Pi _f[I(\mu )]\) is strictly convex (concave) in \(\mu\). Since \(\Pi ''(\mu )=-\Pi _f'[I(\mu )]I'(\mu )>0\), we establish the following proposition.

Proposition 2

(Transparency and profitability) More transparency in the foreign country leads to higher ex-ante expected total cash flow, \(E(\Pi )\).

According to Proposition 2, the ex-ante expected total cash flow of the firm always increases with more transparency in the host country. To understand the intuition of Proposition 2, note that
$$\begin{aligned} \frac{\partial E[\Pi (\mu )]}{\partial \mu } = - \Pi _f[I(\mu )]. \end{aligned}$$
Since the firm invests more (less) when \(\mu\) decreases (increases), this first-order effect on \(\Pi (\mu )\) is stronger for larger \(\mu\) and weaker for lower \(\mu\). As a result, the firm’s total cash flow function is unambiguously convex in \(\mu\). Lemma 1 then implies that the firm’s expected cash flow increases with more transparency.

5 Conclusion

This paper contributes to the theory of international firms and foreign direct investment by placing special emphasis on the role of transparency in the host country. We analyze the implications of higher transparency, i.e., when more precise public information about the host country’s economic and political environment becomes available through the observation of a noisy signal. In practice, the signal may represent the projection of a research institute, policies of the national central bank or the government, or protection of property rights.

As a main result, our analysis has shown that higher host country transparency may increase or decrease the ex ante expected volume of foreign direct investments. Which case applies depends on the curvature of the home investment incentive, HII. A curvature that is consistent with a less developed economy in the host country implies a positive link between transparency and foreign direct investments. By contrast, if the economy in the host country is equally (or better) developed than in the home country, then higher transparency reduces foreign direct investments. However, despite this ambiguity with regard to the investment volume, more transparency always leads to higher ex-ante expected total cash flow of the multinational firm.

Footnotes

  1. 1.

    For a detailed discussion of competition for foreign investment, see Vuksic 2014.

  2. 2.

    The second-order condition for program (3) is satisfied given the fact that \(\Pi _d''(I)\le 0\) and \(\Pi _f''(I)\le 0\).

Notes

Acknowledgments

We would like to thank our referees for very helpfull comments and suggestions.

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Copyright information

© The Japan Section of the Regional Science Association International 2018

Authors and Affiliations

  • Udo Broll
    • 1
  • Bernhard Eckwert
    • 2
  • Keith K. P. Wong
    • 3
  1. 1.Department of Business and Economics, School of International Studies (ZIS)Technische Universität DresdenDresdenGermany
  2. 2.Department of EconomicsBielefeld UniversityBielefeldGermany
  3. 3.Faculty of Business and EconomicsThe University of Hong KongHong KongChina

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