Erkin Diyarbakirlioglu
email: ediyarbakirlioglu@gsu.edu.tr

The Determinants of International Equity Holdings: Information vs. Culture

Keywords: information distance, cultural distance, gravity model, home bias JEL classification: F36, G14, G15

, and a new measure of the information distance, I analyze a panel dataset showing 24 source countries' bilateral equity holdings in various destinations as of the end-2006. Regressions suggest that the effect of the geography on international portfolio investments is likely to be a phenomenon linked to information asymmetries rather than one reflecting the impact of the cultural proximity between countries.

Introduction

Recent literature on home bias and international portfolio diversification suggests the following results regarding the geographical patterns of aggregate and bilateral asset holdings: 1) Despite the potential gains from global portfolio diversification and the easier access to financial markets worldwide [START_REF] Baele | Time-varying integration and international diversification strategies[END_REF][START_REF] Chiou | Benefits of international diversification with investment constraints: An over-time perspective[END_REF], home bias remains still high across investors [START_REF] Sorensen | Home bias and international risk sharing: Twin puzzles separated at birth[END_REF][START_REF] Baele | Model uncertainty, financial market integration and the home bias puzzle[END_REF][START_REF] Stulz | The limits of financial globalization[END_REF].

2) The propensity to invest cross-border declines with the home country's economic mass, implying that the domestic bias is particularly stronger among emerging-market countries although they are likely to benefit more from global portfolio diversification [START_REF] Campbell | Revisiting the home bias puzzle: Downside equity risk[END_REF][START_REF] Driessen | International portfolio diversification benefits: Cross-country evidence from a local perspective[END_REF].

3) Investors concentrate their already trivial cross-border assets in a handful of destinations [START_REF] Hau | Home bias at the fund level[END_REF] which generally tend to be mature and developed countries, and the huge volumes of cross-border capital flows mainly turn around the industrialized world in contrast to the predictions of the benchmark neoclassical model with frictionless markets [START_REF] Papaioannou | What drives international financial flows? Politics, institutions and other determinants[END_REF][START_REF] Prasad | Foreign capital and economic growth[END_REF].

4) The geography of bilateral portfolio holdings shows evidence of a preference toward physically proximate alternatives, so that distance and stock market correlations reveal out to be significantly positive correlates of the bilateral holdings [START_REF] Lane | International investment patterns[END_REF][START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF][START_REF] Portes | The determinants of cross-border equity flows[END_REF].

These observations make it hard to justify an investor portrait whose objective is simply to maximize the expected risk-adjusted-return on his investments. Pioneering studies in the field such as [START_REF] Adler | International portfolio choice and corporation finance: A synthesis[END_REF] and [START_REF] Solnik | An equilibrium model of international capital market[END_REF], propose that agents should be better off investing into an identical risky portfolio partly hedged against the exchange rate risk (under the assumption of deviations from the purchasing power parity), in which every asset is represented in proportion to its relative weight in the world-market portfolio. However, these models along the lines of rational decision-making and market efficiency paradigms, commonly fail to replicate the size and the asymmetries of the domestic portfolio bias as well as the geographical underpinnings of bilateral asset holdings. For example, using a sample of 25 countries, [START_REF] Baele | Model uncertainty, financial market integration and the home bias puzzle[END_REF] report that local investors exhibit an average home bias between 70% and 80%. [START_REF] Sorensen | Home bias and international risk sharing: Twin puzzles separated at birth[END_REF] show that the average home bias across OECD countries is about 67% as of the end-2003. Moreover, their estimates are far from being homogenous in that emerging countries exhibit substantially higher home bias than developed countries. 1 Studies on the reasons as to why investors overweight the home country in their portfolio allocations mainly fall into two broad categories [START_REF] French | Investor diversification and international equity markets[END_REF]. Among the so-called institutional explanations, a number of attempts tackled the issue in terms of direct barriers to international investments such as capital controls [START_REF] Errunza | International asset-pricing under mild segmentation: theory and test[END_REF][START_REF] Stulz | On the effects of barriers to international investment[END_REF][START_REF] Black | International capital market equilibrium with investment barriers[END_REF] or other forms of market imperfections such as transaction costs [START_REF] Rowland | Transaction costs and international portfolio diversification[END_REF]. However, both the gradual liberalization of capital markets starting from the mid-1980 and the relatively higher volumes of cross-border trading as revealed by high turnover rates in international transactions rule out these explanations [START_REF] Warnock | Home bias and high turnover reconsidered[END_REF][START_REF] Tesar | Home bias and high turnover[END_REF]. A second group of studies highlight investors' hedging motives against domestic price uncertainty due to i) deviations from purchasing power parity [START_REF] Adler | International portfolio choice and corporation finance: A synthesis[END_REF], ii) non-traded consumption goods [START_REF] Stockman | International portfolio nondiversification and exchange rate variability[END_REF][START_REF] Cooper | Home bias in equity portfolios, inflation hedging, and international capital market equilibrium[END_REF], or iii) non-tradable factors such as human capital [START_REF] Baxter | The international diversification puzzle is worse than you think[END_REF]. 2 Finally, the home bias can also be due to information asymmetries between local and foreign investors. [START_REF] Brennan | International portfolio investment flows[END_REF] and [START_REF] Gehrig | An information based explanation of the domestic bias in international equity investment[END_REF] provide theoretical models where home bias arises from an informational advantage possessed by local investors on their home market over foreign investors. Recently, [START_REF] Barron | Endogenous asymmetric information and international equity home bias: The effects of portfolio size and information costs[END_REF] and [START_REF] Ni | The effects of portfolio size on international equity home bias puzzle[END_REF] add up to this literature by showing that, in addition to asymmetric information, portfolio size also contributes to the likelihood of investors to be home biased. Although it provides a simple and intuitive explanation of the puzzle, empirical evidence 1 For example, the average home bias across four emerging markets studied by [START_REF] Baele | Model uncertainty, financial market integration and the home bias puzzle[END_REF] is about 96%.

2 [START_REF] Cooper | Home bias in equity portfolios, inflation hedging, and international capital market equilibrium[END_REF] note that inflation hedging is an unlikely reason of home bias for reasonable degrees of investors' risk aversion. [START_REF] Baxter | The international diversification puzzle is worse than you think[END_REF] show that investors should even sell short their own market to hedge human capital risk because of the strong correlation prevailing between returns on physical capital and human capital. More recently, using Swedish household portfolio data, [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF] show that investors do not engage in hedging nonfinancial and financial income, but instead they tilt their portfolio toward stocks geographically and professionally close to them.

regarding the impact of the asymmetric information on home bias is so far inconclusive. 3Other studies account for the effect of investor psychology on the portfolio selection problem.

Mainly inspired from theories and concepts drawn from the behavioral finance school of thought, the central premise is that individuals are only quasi-rational in their decision-making process (Ricciardi, 2008a) and act mainly according to the principles of [START_REF] Kahneman | Prospect theory: An analysis of decision under risk[END_REF] prospect theory. The main insight is to reject the fully rational model of individual decisionmaking by introducing a series of cognitive and affective aspects likely to influence an investors' risk perception in uncertain or risky decision-making contexts. 4 In applied work related to domestic or international asset allocation, the literature has addressed a number of concepts like the familiarity bias [START_REF] Chan | What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide[END_REF][START_REF] Huberman | Familiarity breeds investment[END_REF][START_REF] Grinblatt | How distance, language, and culture influence stockholdings and trades?[END_REF], narrow framing [START_REF] Magi | Portfolio choice, behavioral preferences and equity home bias[END_REF][START_REF] Nocetti | Markowitz meets Kahneman: Portfolio selection under divided attention[END_REF], or investors' relative optimism and perceived competence about domestic stocks [START_REF] Suh | Home bias among institutional investors: A study of the Economist Quarterly Portfolio Poll[END_REF][START_REF] Strong | Understanding the equity home bias: Evidence from survey data[END_REF]. In short, although it is acknowledged that direct barriers to international investments are nowadays an unlikely reason to explain the home bias, the literature still lacks a fully convincing explanation and the ongoing debate mainly contrasts the informational vs. behavioral explanations of the home bias puzzle.

A common feature of these studies is that they all investigate the extent of the aggregate, i.e. the country level home bias [START_REF] Hau | Home bias at the fund level[END_REF][START_REF] Karlsson | Home sweet home: Home bias and international diversification among individual investors[END_REF], i.e. items number 1 and 2 stated above. In this study, following [START_REF] Lane | International investment patterns[END_REF] and [START_REF] Portes | The determinants of cross-border equity flows[END_REF], I consider the aggregate home bias as given and focus on the determinants of bilateral holdings instead. Specifically, I examine the geography of cross-border equity investments to shed light on the distance puzzle [START_REF] Portes | The determinants of cross-border equity flows[END_REF][START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF], mentioned in items 3 and 4. The underlying theoretical assumption is that, in a fully integrated global economy with frictionless goods and asset markets, i) investors should hold identical portfolios [START_REF] Lane | International investment patterns[END_REF] and ii) capital flows from rich to poor countries where marginal returns are higher (Papaionnaou, 2009;[START_REF] Lucas | Why doesn't capital flow from rich to poor countries?[END_REF]). Yet, to the extent that investors concentrate their foreign portfolio holdings within a handful of proximate and highly correlated destinations, it is unlikely to justify any risk-sharing motive within the existing bilateral portfolio holdings.

I argue that the preference revealed by investors toward geographically proximate alternatives would undergo two different, but somewhat complementary viewpoints. On the empirical side, geography is documented as a key determinant of the investment decisions either domestically [START_REF] Huberman | Familiarity breeds investment[END_REF][START_REF] Coval | Home bias at home: Local equity preference in domestic portfolios[END_REF] or internationally [START_REF] Lane | International investment patterns[END_REF][START_REF] Chan | What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide[END_REF][START_REF] Sarkissian | The overseas listing decision: New evidence of proximity preference[END_REF]. Intuitively, however, distance should not capture the costs of trading in securities since, unlike physical goods, assets are weightless. Distant stocks (or countries) could even be thought of as being better hedge instruments against local or regional risks prevailing among countries geographically closer to each other due to stronger political, economic, and trade linkages they typically share. So, why this is not the case and where does this obvious effect of the distance comes from? According to [START_REF] Portes | The determinants of cross-border equity flows[END_REF], the most natural explanation is that informational frictions are positively correlated with distance, which is a barrier to interaction among economic agents and […] to cultural exchange. From this perspective, distance is mostly related to an asymmetric information framework, implying that "investors buy […] securities about which they have enough information" (Merton, 1987) so that they prefer closer geographies in forming their portfolios.

Besides, the distance puzzle could also be related to some kind of familiarity bias underlying the investor behavior. Ricciardi (2008a) defines the familiarity bias simply as an inclination that alters individuals' risk perception (p. 101). The concept conjectures that individuals feel more comfortable with risks they feel familiar with, so that they use heuristic simplifications in their decision-making process [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF]. Hence, geography would help to capture such mental shortcuts in the context of portfolio selection where investors typically prefer to allocate across nearby stocks or markets. Although it is by now a well-known fact that investors prefer familiar stocks [START_REF] Huberman | Familiarity breeds investment[END_REF] or markets located nearby [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF][START_REF] Grinblatt | How distance, language, and culture influence stockholdings and trades?[END_REF], whether the puzzling effect of the geography goes through the asymmetric information or the familiarity-bias framework, remains unclear. According to [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF], familiarity-driven investment is a rational response to information constraints as opposed to a behavioral heuristic (p. 634). Contrasting the information-driven with the behavioral hypotheses, the authors conclude that i) familiarity mostly affects less informed investors and ii) the more sophisticated the investor is, the weaker is the effect of behavioral familiarity on decision-making. [START_REF] Grinblatt | How distance, language, and culture influence stockholdings and trades?[END_REF] also provide a similar result noting that the influence of distance and culture on stockholdings and trades is smaller […] for more sophisticated household investors (p. 1054). Thus, prior studies show that distance is frequently used in empirical work on home bias and the patterns of international investments, and evidence suggest that distance comes up remarkably strongly with the predicted (negative) sign [START_REF] Portes | Information and capital flows: The determinants of transactions in financial assets[END_REF]. However, it is so far unclear whether the intriguing effect of the distance on international portfolio selection undergoes a behavioral or asymmetric informationrelated channel. Thus, distinguishing purely behavioral familiarity effects from those due to informational asymmetries remains a challenge to the existing literature [START_REF] Portes | The determinants of cross-border equity flows[END_REF].

I propose to contribute to this body of research by analyzing the determinants of bilateral equity holdings within a micro-founded model of international capital market equilibrium.

Setting the bilateral stock of equity holdings as the dependent variable, I estimate a gravity model for international portfolio assets using not only the physical distance but also the informational and cultural distances. Specifically, I construct two artificial variables likely to proxy for informational and cultural frictions across countries, and also likely to underlie the puzzling effect of the physical distance. Namely, I propose a measure of the information distance between two countries A and B by plugging data on bilateral phone call traffic into a simple distance formula developed by [START_REF] Cilibrasi | The Google similarity distance[END_REF]. 5 In turn, I define the cultural distance between A and B using a formula originally proposed by [START_REF] Kogut | The effect of national culture on the choice of entry mode[END_REF] and numerical scores on four country-specific cultural dimensions identified by Hofstede's work on 7 cultural affinities. 6 The main motivation to include these two measures essentially follows [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF] and [START_REF] Portes | The determinants of cross-border equity flows[END_REF] inquiries on the competing hypotheses of behavioral-based vs. information-based familiarity channel of the geography. While investigating the relative effects of physical, cultural and information distance measures on bilateral equity investments, I also control for a number of other gravity-type variables mainly motivated from the previous literature. Namely, I expand the scope of the analysis by including an array of additional variables classified into the following categories: i) Economic Development, ii) Openness, iii) Familiarity, iv) Transparency, and v) Portfolio Diversification.

Data limitations regarding the estimation of bilateral or aggregate investments have usually meant important concerns to academics, 7 restricting the scope of the analyses into single countries (for instance, Sweden in [START_REF] Karlsson | Home sweet home: Home bias and international diversification among individual investors[END_REF]; Japan in [START_REF] Kang | Why is there a home bias? An analysis of foreign equity ownership in Japan[END_REF] Australia in [START_REF] Mishra | Where do Australians invest?[END_REF] or the United States in [START_REF] Ahearne | Information costs and home bias: an analysis of US holdings of foreign equities[END_REF][START_REF] Dahlquist | Corporate governance and the home bias[END_REF]. Other studies have directly focused on the patterns of foreign direct investment [START_REF] Stein | Longitude matters: Time zones and the location of FDI[END_REF][START_REF] Wei | How taxing is corruption on international investors?[END_REF] or those of the international banking assets [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF], for which comparable data on investment positions is readily available. 8 In this study, I use survey data as of the end-2006 from the IMF to analyze the bilateral portfolio allocations of a sample of 24 countries. Since the first time it was published in 1997, the IMF releases the Coordinated Portfolio Investment Survey (CPIS) is being released on an annual basis from 2001 onwards. The CPIS has the main advantage of directly providing holdings data on equities, as well as short and long-term bonds. Although more than 70 reporting countries had participated to the 2006 survey, the sum of the total foreign equity assets held by this 24countries sample is quite representative and covers about 72% of the total assets reported by the 6 See [START_REF] Hofstede | National cultures in four dimensions[END_REF]. Details regarding the calculations of these two distance measures are provided below. 7 Among studies taking into account a broader perspective, cross-border holdings were commonly estimated using flow data from balance of payments statistics [START_REF] Baele | Model uncertainty, financial market integration and the home bias puzzle[END_REF][START_REF] Portes | The determinants of cross-border equity flows[END_REF][START_REF] Bekaert | Foreign speculators and emerging equity markets[END_REF]. However, as warned by [START_REF] Cleaver | Financial centers and the geography of capital flows[END_REF], the use of flows can be misleading to obtain stock positions due to high turnover rates observed in international capital flows and the very nature of the balance of payments methodology. For example, [START_REF] Warnock | Home bias and high turnover reconsidered[END_REF] points out that flow data does not allow concluding on the true origin of foreign investment since the host country and the intermediary country from which the operation is held are not necessarily the same.

8 See also [START_REF] Chan | What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide[END_REF] and [START_REF] Gelos | Transparency and international portfolio holdings[END_REF] who employ data on mutual fund's cross-border equity allocations. For example, [START_REF] Gelos | Transparency and international portfolio holdings[END_REF] use data on 137 equity funds' country-level portfolio allocation (managing a total by US$ 44 billion of assets in emerging markets), while [START_REF] Chan | What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide[END_REF] use of mutual fund equity holdings from 26 developed and developing countries with a breakdown across 48 destinations.

In line with previous work such as [START_REF] Lane | International investment patterns[END_REF] or [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF], I use a gravity model as the basis of the empirical investigations. In its well-known original setup in physics, the model postulates an equilibrium relationship between two distinct objects' masses and the physical distance between them. Since the pioneering work by [START_REF] Tinbergen | Shaping the World Economy: Suggestions for an International Economic Policy[END_REF], the gravity model constitutes an important toolbox to trade economists, while its implementation into the financial globe is relatively recent. Using capital flow data, studies such as [START_REF] Papaioannou | What drives international financial flows? Politics, institutions and other determinants[END_REF] or [START_REF] Portes | The determinants of cross-border equity flows[END_REF] have shown that the gravity model can also explain the patterns of international trade in securities as good as it does in physical goods. Being well supported on the empirical ground, a theoretical support is provided by [START_REF] Martin | Financial super-markets: Size matters for asset trade[END_REF], who develop a two-country equilibrium model from which a gravity-style relationship emerges naturally. In short, the gravity model postulates that the volume of bilateral transactions (or holdings) between two countries is an increasing function of their respective economic masses and a decreasing function of the trading cost among them. In applied work, countries' respective GDPs and the physical distance generally substitute the economic size and the trading cost, respectively.

The paper is organized as follows. The next section reviews the theoretical framework proposed by [START_REF] Martin | Financial super-markets: Size matters for asset trade[END_REF], which also serves as the basis of the subsequent econometric analysis. The third section introduces the methodology and the data set. The fourth section discusses the results of the estimations. The last section concludes.

A Model of International Asset Holdings

In this section, I provide a review of the benchmark theory upon which I base the econometric specification of the gravity equation used for the empirical analysis. The framework follows the general equilibrium model under incomplete markets introduced in a two-country setting by [START_REF] Martin | Financial super-markets: Size matters for asset trade[END_REF], and also studied by [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF], and Faruqee et al. (2004). 10 Let us assume an international capital market where countries are indexed by 𝑖 or 𝑗. Each country is populated by 𝑛 agents with intertemporal, concave and strictly decreasing utility functions.11 At time 𝑡 each agent (i.e. investor) ℎ ∈ {1, … , 𝑛 } is endowed 𝑦 units of tradable good (i.e. the numéraire) which he can either consume or invest in a set of risky projects. 12 The total number of the risky projects developed by an agent is 𝑧 and the cost of developing a new project is a differentiable function 𝑓(𝑧 ) with 𝑓′(𝑧 ) > 0 and 𝑓′′(𝑧 ) > 0. Thus, not only the cost of developing a new project is an increasing function of 𝑧 but the associated marginal cost is also increasing with the number of projects already developed.

The next period 𝑡 + 1 comprises 𝑆 different states of the world, each with equal probability 𝑃𝑟(𝑖 = 𝑆) = 1 𝑆 ⁄ . Following this setup, each risky project can be considered as an Arrow-Debreu style security because its payoff next period is either equal to 𝑑 if state 𝑖 ∈ {1, … , 𝑆} occurs, and 0 otherwise. There are no intermediary income streams such as labor income, so that the dividends 𝑑, are the unique source of consumption next period. Different securities serve as hedge instruments against different sources of risk; consequently, each security is an imperfect substitute of another one. This feature of the model simply implies that diversification across securities is beneficial. Nevertheless, the number of the states of the world is bigger than the total number of Arrow-Debreu securities, implying that 1) the market is incomplete, and 2) at the limit, diversification cannot eliminate all the risk an agent bears.

Risky securities developed by agents in different countries are traded on a frictional international capital market. The residents of the country 𝑖 pay a transaction cost 𝜏 > 0 when they trade overseas or earn a dividend gain in a foreign country 𝑗 ≠ 𝑖. Letting 𝑝 be the price of a share of the project developed by agent ℎ and 𝑠 be the demand of ℎ ≠ ℎ for an asset traded in country 𝑗, the amount paid by ℎ to purchase one share of such an asset is given by 𝑝 𝑠 1 + 𝜏 if the asset pays a dividend next period, and the agent ℎ i.e. the holder of the asset, receives 𝑑 1 -𝜏 per share of project he purchased. Assuming that the transaction costs apply to the buyer of the asset, the budget constraint of the representative agent in country 𝑖 can be expressed as follows,

(1)

𝑦 + 𝛼 𝑝 ∈{ ,…, } = 𝑐 , + 𝑓(𝑧 ) + 𝑝 𝑠 ∈{ ,…, } + 𝑝 𝑠 1 + 𝜏 ∈ ,…,
On the left-hand side of the equation, beside the initial endowment 𝑦 , the investor sells a portion 𝛼 of the securities he developed himself. Put another way, the coefficient alpha represents the investor's diversification level, and by construction, the term 1 -𝛼 corresponds to the share of projects developed by ℎ but which does not float on the market. On the right-hand side, we observe the agent's consumption in the first period, 𝑐 , , the cost he bears to develop new projects, 𝑓(𝑧 ), and his demand for assets developed by agents other than himself in country 𝑖 and in country 𝑗 on which a transaction cost 1 + 𝜏 already applies.

Following the standard rational expectations model of portfolio choice13 , each agent maximizes a time-additive utility of the form,

(2)

𝐸[𝑈 ] = 𝑐 , + 𝛿 • 𝐸 𝑐 , ( ⁄ ) 1 -1 𝜎 ⁄
where 𝛿 is the subjective discount rate of the next period utility from consumption and corresponds to the inverse of investor's coefficient of risk aversion. Obviously, the latter one is different from zero, which also captures the feature that all agents are risk-averse. According to the payoff structure imposed to Arrow-Debreu securities and the hypothesis that all states of the world next period have equal probability, we can explicitly write the expected utility as,

(3)

𝐸[𝑈 ] = 𝑐 , + 𝛿 • 𝐸 ⎣ ⎢ ⎢ ⎢ ⎡ 1 𝑆 1 1 - 1 𝜎 ⎝ ⎜ ⎛ 1 -𝛼 𝑑 ∈ + 𝑑𝑠 ∈ + 1 -𝜏 𝑠 ∈ ⎠ ⎟ ⎞ ⎦ ⎥ ⎥ ⎥ ⎤
Taking the expectation on the right-hand side and rearranging, we obtain, (4)

𝐸[𝑈 ] = 𝑐 , + 𝛿 𝑆 𝑑 1 - 1 𝜎 ⎝ ⎜ ⎛ 1 -𝛼 ∈ + 𝑠 ∈ + 1 -𝜏 𝑠 ∈ ⎠ ⎟ ⎞
under the budget constraint given above. We observe that there are three elements making up the expected consumption in the second period. The first term in the parenthesis on the righthand side of the equation is the expected utility from consumption due to payoffs of the projects developed by the agent himself and which does not float on the market. The second term corresponds to the utility from consumption the representative agent would obtain by dividendpaying projects developed by other agents in the local market. Finally, the third element corresponds to the expected utility from consumption backed by the dividend yields of the projects purchased abroad. Choosing the consumption in the first period, the number of risky projects to develop, the demand for domestic and foreign assets developed by other agents and the number of projects to keep in the second period, the representative maximizes the utility (4) subject to the budget constraint (1). From the first-order conditions, we obtain the following individual asset demands for projects traded in home and foreign countries respectively,

( [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF], the key point is to determine the transaction costs that characterize the international capital market with frictions. Empirical studies typically employ the bilateral distance between the source and the destination countries as an accurate proxy of the transaction costs. However, as discussed in the introduction, whether the impact of the geography undergoes an informational or a behavioral channel remains an unanswered yet relevant question for existing studies.

3 Methodology and Data

Econometric Specification

In light of the theoretical detour above, I propose as the basis of the econometric analysis the following log-linear model for portfolio assets held by investors in country 𝑖 in the destination country 𝑗, (8) log 𝑌 = 𝑐 + 𝛼 log 𝑀 𝑀 + 𝛽 log 𝜃 + 𝛾 log 𝑟 with 𝛼 > 0 and 𝛽 < 0. The product 𝑀 𝑀 stands for the size effect where 𝑀 and 𝑀 denote the respective economic masses of the source and destination countries. The parameter 𝜃 stands for the cost of trading in international capital markets. In this basic form, the equation represents a log-linearized structure of the original gravity model that had been frequently used to explain patters of international trade in goods. As emphasized previously, recent studies such as [START_REF] Portes | The determinants of cross-border equity flows[END_REF] or [START_REF] Portes | Information and capital flows: The determinants of transactions in financial assets[END_REF] have shown that the model performs equally well when we consider trade in financial securities too. The log-log specification implies that parameter estimates are in terms of elasticities, i.e. the ratios of percentage changes in the corresponding variables. Due to the signs imposed to coefficients, the model considers the bilateral trade in securities between a pair of source and destination countries as an increasing function of their respective economic masses and a decreasing function of the trading cost between them.

When going to data, I substitute 𝑌 by 𝐴𝑆𝑆𝐸𝑇𝑆 , i.e. the stock of equity assets held by country 𝑖 (i.e. the source) in country 𝑗 (i.e. destination), and the terms 𝑀 and 𝑀 by the countries respective GDPs. The term 𝑟 captures the return-chasing component as shown in equation ( 7). I substitute it by the average return on the country 𝑗's broad stock market index over the period 2002:01-2006:12 (see below for further details). In equation ( 8), the key parameter of interest is 𝛽 through which I capture the effect of international market frictions, 𝜃 . The first proxy is the geographical distance between the source and host countries. I also control for two alternative distance concepts as mentioned in the introduction. Namely, I add the information and cultural distance measures subsequently into the regressions so as to disentangle the impact of the geographical distance on international asset holdings into an information-based and a cultural component.

While the set of host countries is initially the same for all source countries, not every source country holds a positive amount of foreign equity in a given host. In other terms, while a source country A might have invested in destinations C and D, it might also be the case that another source country B holds foreign assets only in country C and completely neglect country D. A possible way to deal with such zero observations across different pair of subjects is to specify the dependent variable as log 1 + 𝐴𝑆𝑆𝐸𝑇𝑆 . Doing so, whenever there is a missing observation between a given pair of source & host, one obtains zeros, which would then be included into regressions. However, there is a large gap between the number of available observations for the dependent variable and the number of observations for different explanatory variables and filling up with zeros the cases for which there are no bilateral assets holdings would significantly alter the distributional properties of the underlying model. To avoid such biases, I drop zero observations from the raw dataset for the corresponding set of exogenous and endogenous variables when working with a linear model specification.14 I also exclude all bilateral equity holdings involving a destination classified as an offshore financial center (OFC). Although the amounts invested in the OFCs represent non-negligible portions of reporting countries' total foreign equity assets, the background motivation follows Lane and Milesi-Ferretti's statement (2008) who note that these destinations act as pure intermediaries, and are neither true sources nor final destinations of investment (p. 543-544). 15The empirical analysis consists of estimating the empirical counterpart of the theoretical relationship given in equation ( 8) and a number of its variants such as ( 9)

log 𝐴𝑆𝑆𝐸𝑇𝑆 = 𝑐 + 𝛼 log 𝑆𝐼𝑍𝐸 + 𝛽 log 𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸 + 𝛾 log 𝑅𝐸𝑇 + 𝛿 𝒁 + 𝜀
where 𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸 is the distance between the source and destination countries, 𝑅𝐸𝑇 is the host country's market return, 𝑆𝐼𝑍𝐸 is the product of source and host countries' GDPs, and 𝒁 an array of additional control variables that will be introduced later. To gauge for the impact of countries' economic masses, I use nominal GDP data from the World Economic Outlook database.

Given the panel feature of the data set, the model specification depends on the structure imposed to the residuals. As a first alternative, I start by estimating the model with random effects on both sides as given in (9). Second, to control for unobservable source country-specific factors, I add fixed-effects and estimate the following equation ( 10) log 𝐴𝑆𝑆𝐸𝑇𝑆 = 𝑐 + 𝛼 log 𝑆𝐼𝑍𝐸 + 𝛽 log 𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸 + 𝛾 log 𝑅𝐸𝑇 + 𝛿 𝒁 + 𝜀 Data for bilateral equity holdings comes from the IMF's CPIS database available at the IMF's web site. Originally, the CPIS data is a multidimensional array representing the reporting countries' bilateral foreign holdings (organized in columns) across the same set of 237 destinations (organized in rows). 16 From the original data matrix, I consider a subset consisting of the bilateral equity investments reported by 24 developed and emerging-market source countries in various destinations. 17 Nevertheless, the sample is representative enough so that the sum of the foreign assets held by this subset of countries corresponds to 72% of the 74 reporting countries' total foreign assets as provided in the CPIS 2006 data files.

To proxy for the international market frictions, I first employ 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , defined as the flight distance in kilometers between the source and host countries' capital cities. Prior studies suggest that the geographical distance stands as a good proxy of the bilateral frictions in international goods and asset markets. Concerning physical goods, the impact of the geographical distance is easy to understand: Distance can substitute, for example, transportation costs across boundaries. However, assets are weightless and trading in assets should not be affected by the physical proximity. In many empirical studies, however, the coefficient estimates on the geographical distance is found to be statistically significant, suggesting that distance plays a key role to explain the international capital flows or asset holdings. The key argument of this study is that the puzzling effect of the physical distance on cross-border asset trade and holdings can be decomposed into two components, i.e. the information distance and the cultural distance, which account respectively for information-and familiarity-based aspects of investors' preference towards geographical proximity. The following sections briefly discuss these two alternative distance measures and describe the methodologies employed.

Cultural Distance & Information Distance

Cultural Distance

The first measure proposed to substitute the geographical distance is the cultural distance.

Prior studies have provided valuable insights into the economic outcomes of individuals' or societies' cultural characteristics using various dimensions to control for such effects. For example, religion is an important aspect likely to shape out societies' and corporations' culture. [START_REF] Guiso | People's opium? Religion and economic attitudes[END_REF] use the World Values Survey to identify the relationship between intensity of religious beliefs and economic attitudes. They find that religious beliefs are associated to good economic attitudes that are more favorable to higher per capita income and growth. Using data on Finnish investors' share-ownership and equity trades, [START_REF] Grinblatt | How distance, language, and culture influence stockholdings and trades?[END_REF] point out to the importance of language. They state that investors whose native tongue is Finnish prefer to hold and trade in Finnish companies that publish their annual reports in Finnish to Finnish companies that publish their reports in Swedish and vice versa (p. 1054). [START_REF] Stulz | Culture, openness, and finance[END_REF] note that if, as argued by the practitioners of behavioral finance, individuals have psychological biases that matter for finance, it would be surprising that individuals' view of the world as determined by their culture does not matter for how they view and act in financial markets (p. 347). Thus, culture provides a suitable framework to control for various behavioral biases advocated by the practitioners of behavioral finance, which would ultimately shape out the observed geography of international portfolio holdings.

To develop a quantitative measure of market imperfections due to culture, I make use of Geert availability for the fifth one, which is the long-term orientation. Specifically, 1) the Power Distance Index (PDI) represents the extent to which the less powerful members of organizations and institutions accept and expect that power be distributed unequally. This index suggests that the followers as much as the leaders endorse a society's level of inequality. 2) Individualism (IDV)

represents the degree to which individuals are integrated into groups. On the individualist side, we find societies in which the ties between individuals are loose. On the collectivist side, we find societies in which people from birth onwards are integrated into strong, cohesive in-groups. 3) Masculinity (MAS), the opposite being femininity, refers to the distribution of roles between genders. In countries where masculinity is strong, people are keener to seek competitive outcomes; managers tend to make decisions on their own (De [START_REF] Jong | Cross-country differences in stock market development: A cultural view[END_REF]. 4) where 𝑋 denotes the score of the 𝑐th cultural dimension for country 𝑖 and 𝑉 denotes the variance of the 𝑐th cultural dimension. This formula for cultural distance is due to [START_REF] Kogut | The effect of national culture on the choice of entry mode[END_REF], and has been frequently used in applied work (see, among others, [START_REF] Beugelsdijk | A cultural explanation of the foreign bias in international asset allocation[END_REF][START_REF] Lucey | Does cultural distance matter in international stock market comovements? Evidence from emerging economies around the world[END_REF][START_REF] Reus | The double-edged sword of cultural distance in international acquisitions[END_REF][START_REF] Shenkar | Cultural distance, investment flow, and control in crossborder cooperation[END_REF].

Information Distance

The second measure proposed to substitute the geographical distance is the information distance. In contrast to cultural distance, existing studies have not come up with such a direct quantitative measure of the information distance even if imperfections linked to informational asymmetries are widely recognized as a key determinant of the geographical patterns of crossborder portfolio holdings. In related empirical work, researchers have proposed, beside the physical distance, several other proxies to control for information-based frictions. [START_REF] Coval | Home bias at home: Local equity preference in domestic portfolios[END_REF] suggest that airfares or phone rates can be good substitutes to gauge for the economic distance between countries. [START_REF] Ahearne | Information costs and home bias: an analysis of US holdings of foreign equities[END_REF] point out to the information content inherent in the U.S. investor protection regulations, i.e. accounting standards, disclosure requirements and regulatory environment, as an important factor to explain the home bias. [START_REF] Sarkissian | The overseas listing decision: New evidence of proximity preference[END_REF] note that economic distance can help to explain overseas listing decisions of firms, and that cross-listing is more frequent across countries geographically and industrially close to each other. According to [START_REF] Bekaert | Market integration and investment barriers in emerging equity markets[END_REF], inefficient settlement systems and poor accounting standards can be at the root of informational barriers against equity flows into emerging markets. [START_REF] Portes | The determinants of cross-border equity flows[END_REF] capture the informational dimension of cross-border portfolio flows by using bilateral telephone calls, the number of bank branch subsidiaries, and the degree of overlap in trading hours across countries.

To develop a quantitative measure of the information distance between two countries, I employ an indirect theoretical framework developed by [START_REF] Cilibrasi | The Google similarity distance[END_REF]. Omitting the technical details, which would overcome the scope of this study, the authors develop a theory of semantic distance between a pair of objects and propose the following formula of the Normalized Information Distance between two objects 𝑥 and 𝑦, where 𝐾(𝑥) is the Kolmogorov complexity of the string 𝑥, which refers to the length of the shortest computer program of the fixed reference computing system that produces 𝑥 as the output.

However, the expression above is incomputable since Kolmogorov complexity 𝐾(𝑥) is incomputable. [START_REF] Cilibrasi | The Google similarity distance[END_REF] apply this theory to propose a formula that extracts a measure of distance between different objects from the World Wide Web, which is undoubtedly the largest database ever created. 18 Namely, they define the following Normalized Google Distance between two strings 𝑥 and 𝑦,

(13) 𝑁𝐺𝐷 = max{log 𝑓(𝑥), log 𝑓(𝑦)} -log 𝑓(𝑥, 𝑦) log 𝑁 -min{log 𝑓(𝑥), log 𝑓(𝑦)}
where 𝑓(𝑥) denotes the number of web pages containing the string 𝑥, and 𝑓(𝑥, 𝑦) denotes the number of web pages containing both 𝑥 and 𝑦 simultaneously, as reported from searches performed using Google. Finally, 𝑁 corresponds to the cardinal of a universal set including all web pages listed within Google. Note further that the results are insensitive to 𝑁 that can be arbitrarily chosen with the unique condition of being sufficiently larger than max{𝑓(•)}.

In this paper, I employ the previous formulation of the Normalized Google Distance to derive a quantitative measure of the information flow between countries. To obtain the necessary inputs for calculations, I use data on bilateral telephone traffic as a proxy for the overall information flow between two countries. [START_REF] Portes | The determinants of cross-border equity flows[END_REF] also use telephone traffic data as a direct measure of the information exchange between countries. They normalize the volume of total phone calls from country 𝑖 to country 𝑗 by the square root of the product of their respective GDPs.

Unlike [START_REF] Portes | The determinants of cross-border equity flows[END_REF], however, I implement a different approach to control for the information distance, which is analogous to the one proposed by [START_REF] Cilibrasi | The Google similarity distance[END_REF].

Namely, I define the information distance between two countries 𝑖 and 𝑗 as follows:

( where 𝑓(𝑖) and 𝑓(𝑗) denotes country 𝑖 and 𝑗's total phone traffic (incoming and outgoing calls) over a given time period, 𝑓(𝑖, 𝑗) denotes the bilateral phone traffic between countries 𝑖 and 𝑗, all these terms being normalized by 𝑖 and 𝑗's respective populations, 𝑝 and 𝑝 . Finally, I substitute 𝑁 by the total telephone traffic over the full dataset, yielding to a number sufficiently larger than any conceivable 𝑓(•). Implementing the previous formulation instead of directly using the volume of the bilateral telephone traffic between two countries (either in levels or in logs) can be justified given the objective to obtain a distance measure. As underlined by [START_REF] Cilibrasi | The Google similarity distance[END_REF], equations ( 13) and ( 14) have several interesting numerical properties. For example, under this formulation, the information distance between two distinct objects is bounded on the continuous interval [0, ∞) and is always nonnegative. By definition, one obtains 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 0 if 𝑖 = 𝑗, and 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 = 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , i.e. the distance between two objects is symmetric. The measure is also scale invariant in the sense that the set of different outcomes does not depend on the number 𝑁. In fact, as 𝑁 grows, the relative frequencies of different 𝑓(•)

tend toward a fixed fraction of 𝑁. For calculations, I obtain data on international telephone traffic in millions of minutes over the year 2006 and countries' populations in millions as of the end-2006

from "Telegeography". The full dataset comprises a total of 1545 observations for the bilateral telephone communications between a set of 102 source and 206 destination countries. The total international telephone traffic during 2006 is 378,474 millions of minutes, of which about 66,568 millions originate from the traffic between Canada, Mexico and the United States. To avoid measurement biases, I normalize the volume of the international telephone traffic by the countries' population. In fact, examining the data, I observe that the total telephone traffic between France and Italy is about 1,340 millions of minutes while the volume of the telephone traffic between France and Belgium is slightly lower, about 1,310 millions of minutes. However, looking at these numbers we can't deduce that the communication between Italy and France is more intense than the one between Belgium and France since Italy's population is about 6 times than that of Belgium's.

Information and Cultural Distance vs. Geographical Distance

Given the respective definitions of information and cultural distance measures, how one can assess their relationship with the geographical distance? To justify the central hypothesis that the effect of the geography on bilateral portfolio holdings can undergo an informational and/or a cultural component, these two measures should not be strongly correlated with the geographical distance. As a simple response to such concerns, the figure below provides the scatter plots of cultural and information distance measures against the geographical distance.

[Insert Figure 1 here]

The graph in the upper panel shows the scatter between geographical distance (plotted on the horizontal axis) and information distance (plotted on the vertical axis). The graph in the lower panel shows the scatter between geographical distance (plotted on the horizontal axis) and cultural distance (plotted on the vertical axis). For purposes of comparability, I use standardized scores with zero mean and unit variance for each variable. Looking at Figure 1, we observe that these two artificial distance variables can effectively capture distinct aspects of the international capital market frictions by disaggregating the combined effect of the physical distance. The rank correlation between cultural distance and geographical distance is about 8%, while the rank correlation between information distance and geographical distance is a bit higher but still weak, by about 32%. Indeed, countries that are informationally or culturally close (resp. remote) to each other are not necessarily those that are geographically close (resp. remote). For instance, while the United States and Canada rank 59 th when sorted by the physical distance, these two countries rank 33 th and 27 th respectively when sorted by the information and cultural distance, respectively. Another striking example regarding the irregularity between geography and cultural affinities involves the U.S. and Australia who rank 2 nd when sorted by the cultural distance, although these two countries take the 1902 th place in the sample once we consider the flight distance by 16,000 kilometers between Sydney and New York.

Additional Controls

Beside the core variables identified above I also conjecture that the foreign equity holdings would depend on a number of additional gravity-type variables as proposed by previous studies.

Specifically, I hypothesize that foreign openness, economic development, and market transparency can influence investors' decision to allocate their foreign assets into a particular host market. To control for these effects, I estimate augmented forms of the initial gravity model by adding a number of predictor variables described below.

Economic Development

I test whether the level of the destination country's economic development is considered as an asset for investors. As noted by [START_REF] Chan | What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide[END_REF], a country's degree of development and market sophistication should presumably have a positive impact in attracting foreign capital. 19 At an individual investor scale, [START_REF] Grinblatt | How distance, language, and culture influence stockholdings and trades?[END_REF], and [START_REF] Karlsson | Home sweet home: Home bias and international diversification among individual investors[END_REF] argue that home bias is inversely linked to investors' sophistication level. Additionally, as emphasized by La [START_REF] Porta | Legal determinants of external finance[END_REF][START_REF] Porta | Investor protection and corporate governance[END_REF], investors may also feel more comfortable when they purchase stocks from developed markets with healthier legal systems and better investor protection rights.

In line with these studies, the hypothesis maintained is that the level of economic development and market sophistication could lower the costs due to market frictions via better-structured and developed financial markets.

I dispose several proxies to capture the impact of the economic development on bilateral equity positions. First, I propose to introduce the destination country's GDP per capita, 𝐺𝐷𝑃𝑃𝐶 . The second variable assesses the degree of the recipient country's financial market sophistication.

Namely, 𝐹𝑀𝑆𝑂𝑃 is an index variable with scores given out of an upper limit by 7. Higher scores are assigned to superior market sophistication for the country in question. The third variable, i.e.

the investor protection index 𝐼𝑁𝑉𝑃𝑅𝑂 , is an aggregate measure combining a country's i) degree of transparency in transactions, ii) the liability of self-dealing, and iii) the shareholders' ability to sue officers and directors for misconduct. 20 For countries with better investor protection standards, the index assigns higher values. Given their definitions, I expect all these control variables to be positively correlated with the size of bilateral portfolios.

Foreign Openness

Examining the impact of countries' cultural backgrounds on cross-sectional differences in investor protection standards, [START_REF] Stulz | Culture, openness, and finance[END_REF] find that finance is more valuable to countries that can benefit more from being open to international trade (p. 338). According to

Familiarity

Ricciardi (2008a) defines the familiarity as an inclination that alters an individuals' perception of risks implying that investors tend to fear less from familiar risks than those that are unfamiliar (p. 101). With respect to international portfolio selection and the home bias literature, the concept of familiarity implies that investors shrink their portfolios to investment alternatives they feel more familiar with. To gauge for this impact, previous studies employed so far different proxies such as geographical proximity, trade linkages or cultural affinities. For example, [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF] argue that investors prefer to invest in countries geographically and professionally closer to their domestic country (p. 634). [START_REF] Coval | Home bias at home: Local equity preference in domestic portfolios[END_REF] note that US fund managers exhibit systematic biases toward nearby firms' stocks, and [START_REF] Huberman | Familiarity breeds investment[END_REF] provides similar evidence on the effect of geographical proximity using a sample US households' stock holdings. By the same token, other studies proposed that cultural affinities such as the existence of a common language [START_REF] Grinblatt | How distance, language, and culture influence stockholdings and trades?[END_REF] 22 , the origin of the legal system (La [START_REF] Porta | Legal determinants of external finance[END_REF][START_REF] Porta | Investor protection and corporate governance[END_REF], the intensity of bilateral trade [START_REF] Chan | What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide[END_REF], the religious connections [START_REF] Stulz | Culture, openness, and finance[END_REF] 23 etc. would also influence portfolio selection.

Following these studies, I use an array of explanatory variables to control for possible familiarity effects in bilateral equity holdings. The first one, 𝐵𝑇𝑅𝐴𝐷𝐸 , is the relative amount of country 𝑖's foreign trade due to transactions with country 𝑗 as the partner. More explicitly, a percentage of, say, 10% between a source country A and a destination country B, means that the bilateral imports and exports transacted with country B corresponds to one tenth of the sum of all imports and exports of the country A over a particular time period. I also add a number of indicator variables relative to other aspects of familiarity. Namely, 𝐿𝐴𝑁𝐺 is a dummy variable equal to 1 if the source and host countries share a common language and 0 otherwise. The second variable, 𝐿𝐸𝐺𝐴𝐿 , is a dummy equal to 1 if the source and host countries' legal systems derive from a common origin. 24 The third variable, 𝑅𝐸𝐺 , is a dummy variable equals to 1 if the source and host countries fall into the same geographical region. I compute this binary variable by distinguishing between four broad geographical regions following the classification proposed by the World Bank, i.e. Africa, America, Asia-Pacific and Europe.

Transparency

This category of controls is motivated from recent evidence set forth by [START_REF] Gelos | Transparency and international portfolio holdings[END_REF] who investigate the effect of a country's transparency on the foreign investment patterns of emerging market funds. The authors find that international funds prefer to hold more assets in more transparent markets and both government and corporate transparency have separate and distinct positive effects on investment flows from international funds into a particular country.

Compiling various sources, they elaborate two groups of indicators, namely government opacity and corporate opacity. In this study, however, I use other proxies directly observable and allowing for larger sample coverage. 25 Implementing Gelos and Wei's analysis to country-level equity positions, I conjecture that more transparency would imply less (perceived) risk and/or weaker information asymmetry and encourage investors to invest more in this market.

The first variable used to assess a country's transparency is the Corruption Perceptions Index, 𝐶𝑃𝐼 . Briefly, a country's CPI score relates to perceptions of the degree of corruption among public officials and politicians as seen by business people and country analysts. Original country scores range from 0 to 10, with higher values assigned to weaker perceived corruption. Second, I include the Judiciary Independence Index, denoted 𝐽𝑈𝐷𝐼𝑁 , which measures the degree of the independence of a country's judiciary system. Raw scores range between 0 and 7. Higher scores are assigned to higher perceived dependence of the judiciary system to political influences of members of government, citizens and firms. The third variable, the Capital Market Controls index, denoted 𝐶𝑀𝐶 , directly measures the intensity of capital market controls within a country.

It indicates the percentage of capital controls not levied as a share of the 13 different types of international capital controls reported by the IMF. Originally, individual country ratings range between 0 and 10, with lower scores assigned to countries with higher restrictions on foreign capital flows. Therefore, while I expect a positive coefficient estimates on 𝐶𝑃𝐼 , the variables 25 The corporate opacity measure used by [START_REF] Gelos | Transparency and international portfolio holdings[END_REF] covers 53 countries. The scope of my analysis, however, requires a larger data collection in that I deal with up to 102 destination countries.

𝐽𝑈𝐷𝐼𝑁 and 𝐶𝑀𝐶 should be inversely related to the dependent variable.

Portfolio Diversification

After all, the basic premise behind diversification is that it should enhance either the expected return given the risk or reduce the risk given the expected return of a portfolio. Thus, the last category of controls checks whether the existing geography of international equity holdings is guided or not by any diversification motive. Doing so, I employ three variables using data from Morgan Stanley Capital International. Using country gross index series (dividends included) in US$ terms over the period 2002:01-2006:12, I construct: 1) 𝑅𝐸𝑇 , the average 5-year return on the country 𝑗's stock market; 2) 𝑆𝐻𝑅𝑃 , the risk-adjusted-return on country's broad market index computed as the ratio of mean excess return to the standard deviation; and 3) 𝐶𝑂𝑅 , the correlation between the country 𝑖 and 𝑗's stock market returns.26

Descriptive Statistics

Table 2 provides summary statistics regarding the variables described above.

[Insert Table 2 here] For each variable, Table 2 shows the total number of observations, the mean, the standard deviation, the minimum and the maximum scores. The first column displays the expected signs of the regression coefficients. The large differences in the number of available observations across variables imply that the regressions are run over an unbalanced panel. Following [START_REF] Papaioannou | What drives international financial flows? Politics, institutions and other determinants[END_REF], I transform raw scores of financial market sophistication, investor protection, foreign trade to GDP, corruption perceptions, judiciary independence and capital market controls variables so as to restrict the scores between 0 and 100. The largest bilateral equity holdings are US investors' asset holdings in the UK. Germany and Switzerland are the two countries closest to each other according to the cultural distance measure. The smallest information distance is between Japan and South Korea. The smallest and the largest geographical distance are between

Finland & Estonia and Spain & New Zealand. In addition, while the physical distance between the U.S. and the U.K. is up to 5,500 kilometers, these two countries are found to be very close to each other according to both the information and cultural distance measures. Looking at different variables groups, we can observe a significant cross-sectional variation. For example, the GDP per capita ranges from a minimum of US$ 122 for Zimbabwe to a maximum of US$ 72,768 for Norway. The U.K. ranks first in the market sophistication while New Zealand gets the highest score on the investor protection index. An interesting observation is related to the bilateral trade between Canada and the U.S. as shown by a maximum score of 69%. This suggests that 69% of Canada's foreign trade volume originates from transactions with the U.S. as the partner. The second highest score concerning bilateral trade is observed between the U.S. and Mexico with a bilateral foreign trade volume of 68%.

For modeling purposes, it is also useful to check for the pairwise correlations between these variables. Overall, correlations between different variables belonging to the same category are not strong enough to raise concerns about multicollinearity. For example, the average correlation between the economic development variables, i.e. GDP per capita, financial market sophistication and investor protection is about 44%; and the average correlation between transparency variables is about 49%. Correlations between the distance measures are also sufficiently weak: The average is 22%, suggesting that each of these proxies may truly serve to account for diverse aspects of the international market frictions within a gravity model framework.

4 Empirical Analysis

The Gravity Model of Bilateral Equity Holdings

Tables 3 to 5 present the estimation results for the gravity model as described in equations ( 9) and (10). The dependent variable is log 𝐴𝑠𝑠𝑒𝑡𝑠 , i.e. logarithm of the bilateral equity assets held by a source country 𝑖 in the host country 𝑗 as of the end-2006. Results for the full sample includes 24 source countries and are reported in panels A of Tables 3 to 5. Besides, I also distinguish two subsamples that include 12 developed-market source countries and 12 emerging-market source countries separately, whose results are reported in panels B and C, respectively.

[Insert Tables 3 to 5 here] In each table, columns (1) to (3) report the regression results with geographical, cultural and information distance measures to highlight their respective effects on bilateral asset holdings.

Alternatively in columns ( 4) to (6), I control for possible spillovers from information and cultural distance to geographical distance using two-stage regressions to check whether geography affects bilateral asset holdings through information or culture. Concerning Table 5 with non-linear regressions, I make the same comparisons by testing the joint effects of the information and cultural distance on the dependent along the geographical distance, since a two-stage procedure is not available for panel Tobit regressions. To guarantee comparability between the coefficients on different distance variables, I standardize raw scores to bring them to the same scale. The log-log specification imposed to both sides of the regressions implies that the coefficients are in terms of elasticities. Because of the large gap in the number of available observations across different variables in the dataset, in particular concerning information and cultural distance measures (475 against 1560), I eliminate the cases where there is no observation for information distance. 27I consider various estimation techniques. In Table 3, regressions are estimated using generalized least squares (GLS) in columns (1) to (3), and generalized two-stage least-squares (G2SLS) in columns (4) to (6). GLS estimations assume a two-way random effect specification for residuals. I check for the adequacy of random effects for GLS estimations via Breusch-Pagan Lagrange multiplier test [START_REF] Breusch | The Lagrange multiplier test and its applications to model specifications in econometrics[END_REF] where the null hypothesis is that variances across entities are zero. Breusch-Pagan LM statistic is asymptotically distributed as a chisquared distribution and the resulting 𝜒 values are all significant at 1% level suggesting that a random effects specification for error terms could be appropriate. I also check the results using emerging and developed countries subsamples and find that they are unchanged. Regarding the G2SLS procedures, first-stage regressions include the geographical distance as the dependent and information and cultural distances as predictors in columns ( 4) to ( 6) where I report the coefficient estimates on the information and cultural distance variables obtained from the firststage regressions. Table 4 assumes a one-way fixed-effect model to estimate the gravity model in which I include dummies to control for unobservable source-country specific effects. As in the case for random effects under the GLS estimations, I also control for the adequacy of fixed-effects using a joint test to see if source country dummies are all equal to zero. As suggested by highly significant F statistics, I find that adding fixed-effects across different entities can also be appropriate to control for unobservable country-specific characteristics. In Table 4, columns (1) to

(3) display the results obtained from panel OLS procedures where geographical, information and cultural distance variables enter the regressions separately. As in Table 3, columns ( 4) to ( 6) allow information and cultural distance measures to influence geographical distance indirectly through instrumental variables estimations.

In Table 5, I opt for a non-linear procedure and estimate the gravity model using panel Tobit regressions. In fact, previous estimations set the dependent variable as the log of the bilateral equity assets, discarding several observations with zero cross-border assets between a given source and host country pair. Alternatively in Table 5, following [START_REF] Lane | International investment patterns[END_REF], I set the dependent as log 𝐴𝑠𝑠𝑒𝑡𝑠 + 𝜀 with 𝜀 being a small number and use the resulting zero observations within a panel Tobit specification with left-censored data. For comparison, while regressions reported in columns (1) of Table 3 and 4 use 383 observations, Tobit regression with the same set of predictors uses 421 observations. For each model specification the same set of destinations is used depending on data availability. In the end, even though the underlying econometric theory and model assumptions differ across estimations, both statistical and economic implications of the estimated coefficients point out to interesting results.

First, consistent with previous studies such as [START_REF] Papaioannou | What drives international financial flows? Politics, institutions and other determinants[END_REF], [START_REF] Lane | International investment patterns[END_REF] or [START_REF] Portes | Information and capital flows: The determinants of transactions in financial assets[END_REF], we observe that a gravity model of international trade in financial assets performs fairly well. Regressions capture a more or less important part of the variation in the data: Looking at panel OLS regressions with source-country fixed effects, the estimated model including return, size and geographical distance as predictors explains 64% of the variation in asset holdings over the full sample. A non-linear specification using left-censored data with the same set of predictors also captures almost half of the variation in the data (the pseudo R-squared close to 0.5). In contrast to results presented in panels C where I include emerging countries into the estimations, the model fit is improved when I restrict the estimations within the developed countries subsample; the adjusted R-squared is above 70% through columns ( 1) to (3) in Table 4. 28Looking at regression coefficients, we observe that size and distance variables are appropriately signed through different samples and specifications. Bilateral asset holdings respond positively to source and host countries' economic mass as suggested by highly significant coefficients.

Geography has a counter-intuitive impact on bilateral asset holdings, which tend to decrease systematically as the physical distance between the source and destination countries increases.

Further, the physical distance influences emerging countries' investors more than developed countries' investors as suggested by the large gap between the estimated coefficients on geographical distance reported in panels B and C: Under the panel OLS specification we observe that when geographical distance is cut by 50%, emerging countries' foreign equity assets is more than doubled. This observation also underlines the importance of the gravity model to understand the patterns of international portfolio investments. From a purely diversification perspective, remote geographies should be preferred by investors who seek to diversify away the risk on their portfolios, implying that foreign holdings should increase with distance. However, investors are unlikely to follow this rule, and they tend to concentrate their investments across a limited set of foreign countries closer to their own home country.

Second, beside the well-documented effect of the physical distance on international equity investments, the information and cultural distance measures also perform quite well in the gravity framework. This suggests that these two alternative distance measures are also able to account for other aspects of international market frictions beside the geographical distance. Using the full sample and developed-market source countries subsample, both information and cultural distance variables enter the regressions with well-determined coefficients. Using the emerging-market source countries, however, both distance measures are no longer statistically significant, and the cultural distance measure is positively signed implying that it is economically insignificant too. Looking at the estimated coefficients on distance proxies however, we can deduce that the effect of the geographical distance on bilateral assets is systematically higher than those of the information and cultural distance since regressions are run using standardized scores. For example, under the GLS specification, we observe that while the geographical distance has a coefficient by -0.88 in panel A, the coefficients on information and cultural distance variables are -0.50 and -0.32, respectively. These coefficients imply that a 10% decrease in information and cultural distance between two countries is expected to increase the bilateral equity holdings by 5.4% and 3.5%, respectively.

Third, evidence suggest that the controversial effect of the geography on international portfolio investments is more likely to undergo an information-based channel rather than reflecting investors' preference towards foreign markets they are culturally closer to their own home market. In fact, inspection of the results obtained from two-stage procedures given in columns ( 4) to ( 6) allows one a direct assessment of the separate and joint impact of the cultural or information distance, first on geographical distance and then on bilateral equity assets. Looking at panel A of Table 3, we observe that while the first-stage coefficients associated to both information and cultural distance measures are separately significant in columns ( 4) and ( 5), we note that cultural distance is no more significant once it is used to predict the geographical distance jointly with the information distance. The same result also holds for the first-stage estimation results under the fixed-effects specification in Table 4: Information distance explains geography more than the cultural distance as suggested by the significant coefficient for the first variable and insignificant for the second. Further, comparing the respective coefficient estimates of the first-stage regressions reported in columns ( 4) and ( 5), we also find systematically higher coefficients associated to information distance than those obtained for cultural distance, an observation that also holds for Tobit regressions displayed in Table 5. Specifically, we note that the impact of the physical distance on the dependent variable is considerably reduced when information distance is included into the regressions. Thus, evidence presented so far support information constraints as opposed to a behavioral heuristic (p. 634). Thus, the home bias puzzle and investors' preference towards physically markets are likely to be part of an information-based story as opposed to psychological biases argued by the practitioners of the behavioral finance.

Regressions with Other Variables

In To estimate (18), I adopt a one-way fixed-effects specification to control for unobservable source country-specific characteristics. As emphasized previously, either Breusch-Pagan LM test for random effects or the F-test for fixed-effects cannot reject the hypotheses that the model specifications proposed in Tables 3 and4 (columns 1 to 3) are appropriate. In fact, this choice is rather motivated by the fact that most of the available controls reflect destination country-specific characteristics such as the financial market sophistication or corruption perceptions, except the familiarity variables like the bilateral trade or common legal origin dummy. Tables 6 to 8 present the results of estimating equation ( 18) by substituting the term 𝐷𝐼𝑆𝑇𝐴𝑁𝐶𝐸 by the geographical, information and cultural distance measures, respectively. In columns (1) through Tables 6 to 8, I present the results using the full set of controls. In columns (2) to ( 6), I present the results obtained by regressing each group of controls separately on the dependent variable, which is specified henceforth as log of the normalized bilateral equity assets.

[Insert Tables 6 to 8 here]

In line with previous results provided by [START_REF] Chan | What determines the domestic bias and foreign bias? Evidence from mutual fund equity allocations worldwide[END_REF] and [START_REF] Portes | Information and capital flows: The determinants of transactions in financial assets[END_REF], the host country's economic development in attracting foreign capital investments inward is well captured, especially via the host country's GDP per capita, which is significant and correctly signed whether it is regressed jointly with geographical, information or cultural distance measures in columns (2). However, unlike [START_REF] Portes | Information and capital flows: The determinants of transactions in financial assets[END_REF] who report a significant positive impact of the market sophistication on cross-border equity flows, the two other proxies for countries' economic development, i.e. financial market sophistication and investor protection, perform rather poorly with statistically insignificant coefficients. As a further check, I also controlled for the effect of market sophistication and investor protection on bilateral equity holdings separately along with the geographical, information and cultural distance measures in other regressions. I found that both variables enter the models with expected signs and significant coefficients except for the case where I use the investor protection index and cultural distance as predictors.

respective effects of familiarity proxies used in Tables 6 to 8 are mainly captured by the bilateral trade variable. Common language, legal origin and geographical region dummies are of no economic consequence as suggested by statistically significant but negative coefficient estimates on the legal origin and geographical region dummies. Indeed, there is no reason to expect the bilateral equity assets to decrease when the source and host countries share a common legal system origin. The lack of significance concerning these dummies is surprising since prior studies find strong links between these variables and the foreign investment patterns. For example, [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF] report significant positive effect of sharing a common legal origin system on bilateral banking claims. [START_REF] Lane | International investment patterns[END_REF] note that speaking a common language is expected to raise bilateral equity holdings by about 50%. A possible explanation would be that the bilateral trade, which enters the regressions with very well-determined coefficients, could soak up their impact. To check for this effect, I have also run the regressions in columns (3) without including the bilateral trade. For example, using the physical distance and dummies for common language, legal origin and geographical region collectively, I find that only the common language dummy (along the geographical distance) is correctly signed with a coefficient significant at 5% level. The same observation also holds for the common language dummy when regressed together with the information distance.

Destination countries' degree of openness to international trade affects bilateral equity holdings mainly through the mergers & acquisitions variable, which measures the monetary sum of a country's total mergers & acquisitions normalized by its GDP. Regardless of the distance measure used in the estimations, the coefficient on mergers & acquisitions is significant both statistically and economically. I have also used this variable excluding the foreign trade, along with the physical, cultural and information distance variables in different regressions and have found statistically highly significant coefficients. In contrast, countries' foreign trade volume to GDP ratio also enters regressions with significant coefficient estimates, but not with the expected sign: Bilateral equity assets between a given pair of source and host countries is expected to respond positively to the host country's level of openness to international trade [START_REF] Stulz | Culture, openness, and finance[END_REF]. Indeed, the extent to which a given market or country ties economic relations abroad, is likely to improve the amount and the quality of information exchange among the partners involved, and consequently, to boost bilateral portfolio investments.

The positive effect of a host country's transparency is well captured in particular by the corruptions perceptions index. Across Tables 6 to 8, the coefficient on the 𝐶𝑃𝐼 is around 0.30 suggesting that a 50% improvement in the host country's degree of corruption could boost foreign equity stocks by about 15%. Thus, evidence broadly support [START_REF] Gelos | Transparency and international portfolio holdings[END_REF] view that improving a country's transparency could lead to an increase in investment flows, implying a weaker home bias by foreign investors against the country of interest. 29 On the contrary, the two other variables, i.e. the judiciary independence and capital market controls, are of no consequence on the dependent variable as shown by insignificant coefficient estimates. As before, I checked for the separate effect of these proxies in other regressions, the results are unaffected either for the judiciary independence or the capital market controls.

Finally, in columns ( 6), I control for whether the observed bilateral equity holdings are driven by investors' diversification motive and add two variables into the baseline model. In fact, from a portfolio diversification viewpoint, a destination market's Sharpe ratio should be positively correlated with foreign investors' bilateral portfolio assets; and negatively correlated with the pairwise correlation between the source and host countries' market returns since the greater the degree with which two markets are synchronized the lower the gains from portfolio diversification. The results are, however, highly inconsistent with these insights: Not only investors are likely to hold fewer assets in destinations with higher risk-adjusted returns, they are also likely to invest more in destinations whose stock markets are highly correlated with their home market. The coefficient on the pairwise correlation between the source and host markets is around 0.63, significant at the 1% level. Previously, [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF] referred to this observation as the correlation puzzle and, therefore, risk diversification appears to be an unlikely determinant of bilateral equity portfolios.

explanatory power. First, the coefficients on the distance variables are greatly diminished and none of them is helpful to explain the bilateral equity holdings. This suggests that other predictors are likely to absorb the respective effects of the physical, cultural and information distance. When I use the geographical and cultural distance variables, I observe that bilateral trade, mergers & acquisitions, capital market controls and Sharpe ratio are both statistically and economically significant. The only exception concerns the capital market controls variable whose coefficient loses its explanatory power when regressed along with the information distance.

Second, the negative coefficient on the Sharpe ratio generally confirms the estimation results presented in columns ( 6), where I control if bilateral equity holdings could be driven by a diversification motive. Besides, the coefficients on pairwise market correlation are also positive but not significant at conventional confidence levels. As a further check of the correlation puzzle, I have also run the same regressions with the complete set of predictors by excluding the Sharpe ratio. In this case, I have found that 𝐶𝑂𝑅 still enters the models with positive and significant coefficient estimates. Third, estimations provided in columns (1) further highlight the positive effect of destination countries' foreign openness, captured by the mergers & acquisitions, which enters the models in all cases whether one uses geographical, information or cultural distance.

Fourth, we observe that bilateral trade is also a major determinant of the bilateral equity holdings. Not only it has a systematic positive effect on the dependent variable when it is regressed jointly with other familiarity dummies, but it also remains the major predictor in the regressions even though I use other proxies to control for the economic development, transparency or foreign openness. To check for the consistency of the effect of bilateral trade, I have run additional estimations for the general model given in equation ( 18) using different combinations of the control variables. Given the unmanageable amount of possible combinations across this set of available variables, I estimated stepwise regressions (both forward and backward) allowing variables to enter the regressions with a significance level equal to or more than 10%. Regardless of the distance proxy used in regressions, I find that bilateral trade is always the first variable to be included into the regressions with well-determined and correctly signed coefficients and that the distance proxies perform rather poorly once bilateral trade makes part of the predictors within the estimated model. 30 Given this systematic effect of bilateral trade on bilateral equity holdings, the relevant question is to ask if the bilateral trade can be considered as a substitute for information or cultural proximity between countries.

4.3 Disentangling the Effect of Bilateral Trade: Information or Culture?

According to [START_REF] Lane | International investment patterns[END_REF], there exists a strong link between trade and equity holdings and they suggest that this observation is particularly consistent with the informational potential of the strength of bilateral trade relations across countries. They report that a simple econometric specification using bilateral trade as predictor of bilateral equity assets is enough to explain as much as 86% of the variance observed in a dataset including OECD countries' foreign equity assets. [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF] conjecture that the strong link between trade and equity holdings would reflect the preference that investors exhibit for professionally closer countries. Examining the complementarity between bilateral trade and bilateral asset holdings within a simultaneous equation framework, [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF] argue that i) distance which substitutes transport costs in goods market, would induce home bias in asset portfolios and ii) part of the effect of geographical distance on bilateral asset holdings could be related to bilateral trade relations between countries. The authors report that a 10% increase in bilateral trade leads to a 3% increase in bilateral banking claims. Moreover, although the direction of causality between trade and assets runs significantly in both ways, they find that the impact of trade on asset holdings is substantial. [START_REF] Portes | The determinants of cross-border equity flows[END_REF] suggest that information flows via trade in goods could enhance bilateral portfolio holdings to the extent that trading partners are more likely to share and exchange information, thereby eroding a good part of the informational asymmetries in the financial markets.

In light of these studies, I propose a simple way to control for whether the effect of bilateral trade on portfolio holdings goes through the information or cultural distance measures since these two alternative variables are found to be good proxies for geographical distance. Indeed, the direction of causality between trade and asset holdings runs significantly in both ways and omitting bilateral trade in goods within a gravity model of bilateral equity holdings could lead to estimation bias problems as underlined by [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF]. Then, it would be conceivable to introduce the variable 𝐴𝑠𝑠𝑒𝑡𝑠 into the basic gravity model given in equation ( 15)

as a plausible predictor of bilateral trade in goods, As shown by the linear fits, the scatters highlight the relative importance of information proximity against the cultural proximity to explain the effect of bilateral goods trade on the geographical patterns of bilateral equity holdings. Computing the correlation between bilateral trade and information distance, I find a coefficient close to minus 0.38, significant at the 1% level.

In contrast, the correlation between cultural distance and trade is fairly weak by minus 0.05 and statistically insignificant. In brief, evidence is mostly consistent with, and provides empirical support to previous studies such as [START_REF] Lane | International investment patterns[END_REF] or [START_REF] Portes | The determinants of cross-border equity flows[END_REF] who also underline the importance of goods trade in explaining the puzzling geography of international portfolio holdings via its potential value as an information variable.

Conclusion

I analyze a panel data set on country-level bilateral equity holdings as of the end-2006 to provide insights into the puzzling geography of international equity holdings using a gravity model.

Following [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF] and [START_REF] Portes | The determinants of cross-border equity flows[END_REF] inquiries on distinguishing behavioral-based familiarity effects from those originated by informational asymmetries, I argue that the preference revealed by investors towards geographical proximity would undergo two distinct channels. Specifically, I consider two quantitative distance measures as alternatives to geographical distance, i.e. information distance and cultural distance, respectively accounting for information-or familiarity-based aspects of investors' preference towards geographically close markets. While a generally recognized formula to provide a measure of the cultural distance between two countries is already available from previous studies, I believe that this paper is the first to propose and test a direct quantitative measure of the information distance between two countries. The results can be summarized as follows.

First and consistent with previous studies such as [START_REF] Papaioannou | What drives international financial flows? Politics, institutions and other determinants[END_REF], [START_REF] Lane | International investment patterns[END_REF] or [START_REF] Portes | Information and capital flows: The determinants of transactions in financial assets[END_REF], regressions show that a gravity model of international trade in financial assets performs fairly well to explain the observed geographical patterns of bilateral equity holdings. This finding is robust to additional estimations including either the information or the cultural distance instead of the geographical distance, while variation in the data is better captured when geographical distance is used to substitute for transaction costs in international financial markets. The baseline model specification is typically suitable for the full sample and the developed-market source countries subsample, while most of the distance coefficients lack of explanatory power for the emerging-market source countries subsample. I also check for the accuracy of the model using different estimation techniques including non-linear panel Tobit regressions. The results remain unchanged. The impact of the physical distance is further pronounced for emerging-market countries subsample: When geographical distance is cut by 50%, emerging countries' foreign equity assets is more than doubled.

Second, beside the systematic effect of the physical distance on bilateral equity holdings, information and cultural distance measures also perform quite well within the baseline gravity model. Given the lack of correlation between these three distance measures, the proposed measures for information and cultural distances are likely to capture other aspects of the international market frictions along with physical distance. In particular, if the information and cultural distance between a pair of source and host countries decrease by 10%, bilateral equity assets held by the source countries' investors in the corresponding host country are expected to increase by about 5.4% and 3.5%, respectively. Hence, evidence suggests that the effect of the geography on international investment patterns is more likely to be a phenomenon linked to information asymmetries rather than reflecting the impact of the cultural proximity. Indeed, standardized coefficient estimates on information distance are systematically higher than those associated with the cultural distance regardless of the sample or the estimation technique used.

When I employ these two distance measures jointly with the geographical distance in 2SLS and IV estimations, the results from first-stage regressions show that information distance enters the models with expected sign and well-determined coefficients while the coefficient on the cultural distance generally lacks of statistical significance. This result is also robust to Tobit regressions.

Moreover, the impact of the geographical distance on the dependent variable is reduced in most cases once the information distance is included into the model. In short, evidence supports [START_REF] Massa | Hedging, familiarity and portfolio choice[END_REF] view that familiarity-driven investment is a response to information constraints as opposed to a behavioral heuristic.

I control for these results using additional gravity-type variables drawn from previous studies.

I augment the baseline specification by adding several proxies to control for the effects of countries' economic development, openness to foreign trade, transparency and the degree of familiarity with the host market on portfolio investments. I also check if bilateral equity assets are driven by any diversification motive. Destination countries' economic development explains part of the dependent variable as suggested by significant estimates on the GDP per capita variable. Financial market sophistication and investor protection enter the regressions only when they are regressed separately from each other. Foreign openness is also helpful to explain the bilateral equity holdings given the significant results concerning the mergers & acquisitions variable. The positive effect of host countries' transparency mainly goes through the corruptions perceptions index variable. This suggests that improving a country's transparency could enhance foreign investment inward and, consequently, erode some part of the home bias that foreign investors exhibit against the host country of interest. Finally, controlling for portfolio diversification, I find no evidence of any risk diversification motive in bilateral portfolios [START_REF] Portes | The determinants of cross-border equity flows[END_REF], since investors' tendency to hold stocks of a given country increases with the bilateral correlation coefficient between the source and host markets' returns [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF] and decrease with the host country's expected risk-adjusted return.

Beside the impact of the information distance, the most striking result concerns the systematic effect of bilateral trade on bilateral equity holdings. Specifically, bilateral goods trade always enters the regressions with positive and very-well determined coefficients regardless of the estimation technique or the sample employed. Previous studies such as [START_REF] Lane | International investment patterns[END_REF] or [START_REF] Aviat | The geography of trade in goods and asset holdings[END_REF] suggested that part of the effect of geographical distance on bilateral asset holdings could be related to bilateral trade relations between countries. In this paper, I check whether the effect of goods trade on portfolio holdings undergoes an information-or culture-based story. Regressions highlight the relative importance of the information proximity against the cultural proximity in explaining the effect of bilateral trade in goods on the observed geography of international equity holdings via its potential value as an information variable.

I consider the empirical work presented here as robust evidence that information asymmetries are central to understand the nature of international market frictions and the existing patterns of cross-border portfolio investments. The analysis also sheds light into the home bias puzzle suggesting that investors prefer to hold stocks in markets that are informationally close to their own home market. Although the puzzling preference for proximate geographies appears to be better explained by the information distance than cultural distance, further work is needed to effectively isolate the respective impacts of culture and information on the geography of international asset portfolios and to investigate the true direction of causality running from culture to information exchange and vice versa. Even if the information and cultural distance measures are weakly correlated each other, it would be also useful to check for the extent to which information and culture are truly separable by means of additional instruments likely to capture other facets of the information exchange and cultural affinities between countries. ; 3) Familiarity variables, including the bilateral trade volume (BTRADE) as percentage of the source country's GDP, common language dummy (LANG), common legal origin dummy (LEG), common geographical region dummy (REG); 4) Transparency variables, including corruption perceptions index (CPI), judiciary system's independence index (JUDIN), and capital market controls index (CMC); and 5) Portfolio diversification variables, including the expected return (RET), Sharpe ratio (SHRP), and return correlations between the source and host countries (COR).

Dependent: log 𝐴𝑠𝑠𝑒𝑡𝑠 (1) GLS

(2) GLS

(3) GLS (4) G2SLS

(5) G2SLS

(6) G2SLS

Panel A.

  Hofstede's seminal work on cultural affinities. Originally, the study consists of an analysis of a large database of employee values scores collected by IBM between 1697 and 1973 in more than 70 countries. Since 2001, Hofstede's work lists cultural dimensions scores across 74 countries and regions partly based on replications and extensions of the initial IBM study. Based upon a model that identifies the primary dimensions to describe a country's cultural patterns, Hofstede distinguishes five different indicators. I include four indicators, however, due to limited data

  , 𝑦) -min 𝐾(𝑥), 𝐾(𝑦) max 𝐾(𝑥), 𝐾(𝑦)

Ahearne

  et al. (2004), although capital controls have been reduced, they can still affect crossborder investment and the authors give the example of US investors who underweight the Chinese market maintaining substantial barriers to foreign investment. Thus, the openness of a country's international trade or capital flows may promote the foreign investment inward, influencing the geographical spread of the destination countries considered by local investors. The degree of openness can also be considered as a proxy for information costs that investors bear whenever they consider investing into a particular foreign market. To control for these effects, I employ two variables. The first one is an artificial variable assessing a country's degree of openness to international trade. Namely, 𝐹𝑇𝑅𝐴𝐷𝐸 corresponds to the volume of foreign trade in goods and services (i.e. the nominal sum of the imports and exports) scaled by the country's nominal GDP for the year-end 2006. The second variable to control for the effect of foreign openness is mergers & acquisitions, 𝑀𝐴 . It represents the monetary sum of a country's crossborder mergers & acquisitions (i.e. purchases plus sales) scaled by the GDP.21 Again, I expect both of these controls to enter the model with a positive sign.

  this subsection, I augment the baseline specification by adding a number of additional variables previously employed in related studies. Namely, I control for possible effects of the economic development, familiarity, foreign openness and transparency on countries' bilateral equity holdings. I also check for any diversification motive in the observed geography of crossborder equity holdings using the destination market's Sharpe ratio and the bilateral correlation between the source and host market returns. For modeling purposes, omitting the return component and with a bit of rewriting, I consider the following specification for the baseline gravity model as proposed by Portes and Rey (2005, p. 275), (15) log 𝑌 = 𝑐 + 𝛼 log 𝑀 𝑀 + 𝛽 log 𝜃 Decomposing the log-product yields to, (16) log 𝑌 = 𝑐 + 𝛼 log(𝑀 ) + 𝛼 log 𝑀 + 𝛽 log 𝜃 As noted by Portes and Rey (2005), theory suggests that 𝛼 + 𝛼 = 1. Denoting by 𝒁 the set of other controls that will be included, the preceding (15) can be rewritten as follows, (17) log = 𝑐 + 𝛽 log 𝜃 + 𝛿 𝒁 + 𝜀 Substituting the terms 𝑌 , 𝑀 𝑀 , 𝜃 and 𝒁 by their data counterparts, the general estimating model is defined as follows, log 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 𝛿 (𝐸𝑐𝑜𝑛𝑜𝑚𝑖𝑐 𝐷𝑒𝑣𝑒𝑙𝑜𝑝𝑚𝑒𝑛𝑡) + 𝛿 (𝐹𝑎𝑚𝑖𝑙𝑖𝑎𝑟𝑖𝑡𝑦) + 𝛿 (𝐹𝑜𝑟𝑒𝑖𝑔𝑛 𝑂𝑝𝑒𝑛𝑛𝑒𝑠𝑠) + 𝛿 (𝑇𝑟𝑎𝑛𝑠𝑝𝑎𝑟𝑒𝑛𝑐𝑦) + 𝛿 (𝑃𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝐷𝑖𝑣𝑒𝑟𝑠𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛) + 𝜀

  = 𝑐 + 𝛽 log 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 𝛾 log 𝐴𝑠𝑠𝑒𝑡𝑠 If bilateral trade in goods is endogenous to the baseline gravity model of asset holdings and if the effect of the physical distance on portfolio assets can effectively be decomposed into two components, one would expect the predicted values of bilateral trade in goods to be correlated with these alternative distance measures. Then, comparing the correlations between the predicted values of the dependent and different distance proxies, one would understand whether the effect of goods trade on the geography of portfolio holdings goes through an informational or cultural channel. I estimate the preceding equation using panel OLS with source country fixedeffects and substitute the terms 𝐷𝑖𝑠𝑡𝑎𝑛𝑐𝑒 by geographical distance between countries 𝑖 and 𝑗, and 𝐴𝑠𝑠𝑒𝑡𝑠 by bilateral equity assets held by source country 𝑖 in the host country 𝑗 scaled by source and host countries' GDPs products. The estimation results are as follows: (20) log 𝐵𝑖𝑙𝑎𝑡𝑒𝑟𝑎𝑙 𝑡𝑟𝑎𝑑𝑒 = 1.87 -0.32 log 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 + 0.50 log 𝐴𝑠𝑠𝑒𝑡𝑠 All coefficients are statistically significant at the 1% level (assuming heteroskedasticityconsistent estimator for the variance) with a satisfactory goodness-of-fit measure of the regression: R² of within estimates is close to 0.31. Further, the F test to check if all fixed-effects are jointly equal to zero can be easily rejected as well. Given these results, the next figure provides the scatter plots of the predicted scores for the bilateral trade in goods against the information distance in panel A and the cultural distance in panel B. [Insert Figure 2 here]

Figure 1 .

 1 Figure 1. Information and cultural distance measures vs. geographical distance

Figure 2 .

 2 Figure 2. The effect of bilateral trade on asset holdings: Information or Cultural distance?

Table 2 .

 2 Descriptive statistics, raw data set The table reports summary statistics computed from raw data. ASSETS are expressed in US$ millions and, GDPPC in US$ terms. Geographical distance is expressed in kilometers while the informational and cultural distances are without unit. The five sets of other explanatory variables are 1) Economic development variables, including the GDP per capita (GDPPC), financial market sophistication (FMSOP), and investor protection (INVPRO); 2) Openness variables, including foreign trade volume (FTRADE) and the mergers & acquisitions (MA) (both of them expressed as percentages of the country's GDP)

	Variable		Obs.	Mean	St. dev.	Min.	Max.
	D e p e n d e n t
	Assets		1042	7000.63	37122.83	0.00	673978.00
	S i z e a n d d i s t a n c e
	Size	( + )	2736	5.60e+11	2.76e+12	6.89e+07	5.78e+13
	Distance, geographical	( -)	1626	7490.04	4674.48	84.00	19857.00
	Distance, information	( -)	475	247.66	28.89	136.38	350.46
	Distance, cultural	( -)	1560	268.42	104.26	28.05	692.68
	E c o n o m i c D e v e l o p m e n t
	GDP per capita	( + )	2708	11331.09	15552.05	122.50	72768.10
	Fin. market sophistication	( + )	2328	47.54	22.23	0.00	98.26
	Investor protection	( + )	2664	48.90	16.46	0.00	100.00
	O p e n n e s s
	Foreign trade	( + )	2688	5.29	9.45	0.00	100.00
	Mergers & Acquisitions	( + )	2160	2.85	3.24	0.00	14.04
	F a m i l i a r i t y
	Bilateral trade	( + )	2700	0.81	2.85	0.00	68.93
	Language	( + )	2856	0.47	0.49	0.00	1.00
	Legal origin	( + )	945	0.32	0.46	0.00	1.00
	Region	( + )	2856	0.26	0.44	0.00	1.00
	T r a n s p a r e n c y
	Corruption perceptions	( + )	2664	31.04	27.91	2.56	100.00
	Judiciary independence	( -)	2280	52.86	24.93	0.00	100.00
	Capital market controls	( -)	2376	52.58	20.84	0.00	93.38
	P o r t f o l i o D i v e r s i f i c a t i o n
	Expected return	( + )	2040	2.02	1.09	-2.27	4.34
	Sharpe ratio	( + )	2040	31.46	14.16	-23.58	64.29
	Correlation	( -)	2040	50.21	22.72	-38.83	100.00
	Notes:

  The table reports GLS and G2SLS regression results for the gravity model of international equity holdings. The dependent variable is log of equity assets held by the source country 𝑖 in the host country 𝑗. 𝑅𝑒𝑡𝑢𝑟𝑛 is lag-5 year average return on country 𝑗's stock market. 𝑆𝑖𝑧𝑒 is log of the source and host countries' GDP products. 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , and 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 are (log of the) the geographical, information and cultural distances between countries 𝑖 and 𝑗. Concerning the G2SLS specification in columns (4) to (6), "a" denotes coefficient estimates from first-stage regressions. Heteroskedasticity consistent t-statistics obtained using the[START_REF] White | A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity[END_REF] method, are provided in parenthesis below the parameter estimates. Statistical significance at 10% (resp. 5 and 1%) is denoted by *** (resp. ** and *). The table reports panel OLS and instrumental variables regression results for the gravity model of international equity holdings. The dependent variable is log of equity assets held by the source country 𝑖 in the host country 𝑗. 𝑅𝑒𝑡𝑢𝑟𝑛 is lag-5 year average return on country 𝑗's stock market. 𝑆𝑖𝑧𝑒 is log of the source and host countries' GDP products. 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 , and 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 are (log of the) the geographical, information and cultural distances between countries 𝑖 and 𝑗. Concerning the IV specification in columns (4) to (6), "a" denotes coefficient estimates from first-stage regressions. F-statistic is designed to jointly test that all individual effects are zero, for which the null hypothesis is rejected at all conventional levels throughout the table. Heteroskedasticity consistent t-statistics obtained using the[START_REF] White | A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity[END_REF] method, are provided in parenthesis below the parameter estimates. Statistical significance at 10% (resp. 5 and 1%) is denoted by *** (resp. ** and *).

	All countries 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝑅𝑒𝑡𝑢𝑟𝑛 𝑆𝑖𝑧𝑒 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 # of obs. R 2 (overall) Wald 𝜒2 Panel B. Developed-market source countries -1.3818*** (-2.32) -1.7605*** (-2.69) 1.2671*** (14.95) 1.1581*** (14.06) -0.8865*** (-9.26) -0.5017*** (-3.26) 383 383 0.4812 0.3882 560.24 423.42 𝑅𝑒𝑡𝑢𝑟𝑛 -1.7540* (-2.34) -2.1585*** (-2.67) 𝑆𝑖𝑧𝑒 1.3683*** (15.86) 1.2720*** (14.13) 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.7039*** (-6.82) 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.5118*** (-3.16) 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 # of obs. 284 284 R 2 (overall) 0.6616 0.6060 Wald 𝜒2 589.21 515.03 Panel C. Emerging-market source countries 𝑅𝑒𝑡𝑢𝑟𝑛 -2.8360* (-1.97) -2.5713 (-1.59) 𝑆𝑖𝑧𝑒 0.7927*** (3.90) 0.5305*** (2.93) 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -1.1792*** (-4.04) 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.2048 (-0.84) 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 # of obs. 99 99 R 2 (overall) 0.1456 0.0795 Wald 𝜒2 49.28 27.11 (1) Panel OLS (2) Panel OLS Panel A. All countries 𝑅𝑒𝑡𝑢𝑟𝑛 -1.4516** (-2.16) -1.8509** (-2.49) 𝑆𝑖𝑧𝑒 1.2704*** (14.26) 1.1662*** (13.08) 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.8641*** (-8.99) 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.5438*** (-4.11) 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 # of obs. 383 383 R 2 (within) 0.6143 0.6025 F-statistic 20.96 27.19 Panel B. Developed-market source countries 𝑅𝑒𝑡𝑢𝑟𝑛 -1.5050** (-2.05) -1.8366** (-2.38) 𝑆𝑖𝑧𝑒 1.4284*** (15.89) 1.3488*** (15.01) 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.6743*** (-6.71) 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.5533*** (-3.70) 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 # of obs. 284 284 R 2 (within) 0.7460 0.7206 F-statistic 12.49 11.72 Panel C. Emerging-market source countries 𝑅𝑒𝑡𝑢𝑟𝑛 -2.6541* (-1.68) -2.3481 (-1.39) 𝑆𝑖𝑧𝑒 0.9018*** (4.33) 0.6459*** (3.30) 𝐺𝑒𝑜𝑔𝑟𝑎𝑝ℎ𝑖𝑐𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -1.2362*** (-3.78) 𝐼𝑛𝑓𝑜𝑟𝑚𝑎𝑡𝑖𝑜𝑛 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 -0.2535 (-1.14) 𝐶𝑢𝑙𝑡𝑢𝑟𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒 # of obs. 99 97 R 2 (within) 0.3837 0.3122 F-statistic 6.58 7.55 Notes: Dependent: log 𝐴𝑠𝑠𝑒𝑡𝑠 Notes:	-1.2727*** (-2.04) 1.1508*** (13.74) -0.3280*** (-4.07) 358 0.3911 408.74 -1.7383** (-2.17) 1.2950*** (12.79) -0.3376*** (-3.63) 261 0.5861 439.06 -1.2621 (-0.79) 0.5831*** (3.32) 0.0863 (0.31) 97 0.0649 29.20 (3) Panel OLS -1.3222* (-1.88) 1.1569*** (12.36) -0.3278*** (-4.40) 358 0.5649 21.60 -1.4938* (-1.92) 1.3707*** (13.55) -0.3158*** (-3.76) 261 0.6947 11.43 -0.8541 (-0.54) 0.7202*** (3.77) 0.0495 (0.21) 97 0.3084 8.33	-1.3637*** (-2.90) 1.3054*** (19.37) -1.1632*** (-5.27) a 0.4610*** (10.47) 383 0.4791 610.19 -1.5894*** (-3.48) 1.4001*** (22.06) -0.8394*** (-4.05) a 0.6336*** (9.21) 284 0.6596 730.79 -2.6418* (-1.69) 0.8087*** (3.21) -1.0300 (-1.25) a 0.2241*** (4.47) 99 0.1394 40.91 (4) IV -1.3746*** (-2.85) 1.3078*** (18.95) -1.1735*** (-5.21) a 0.4634*** (10.22) 383 0.6328 21.42 -1.4146*** (-3.11) 1.4389*** (22.57) -0.8704*** (-4.16) a 0.6356*** (9.16) 284 0.7424 11.24 -2.5639 (-1.61) 0.8653*** (3.44) -1.0781 (-1.33) a 0.2351*** (4.64) 99 0.3823 7.95	-0.5209 (-0.86) 1.4838*** (11.06) -2.1981*** (-3.02) a 0.1491*** (3.22) 358 0.4198 330.03 -0.0471 (-0.0474) 1.5991*** (10.92) -2.8667** (-2.18) a 0.1106* (2.00) 261 0.4152 222.04 -0.9221 (-0.44) 0.4929 (0.81) 0.5688 (0.24) a 0.1282 (1.60) 97 0.0176 27.80 (5) IV -0.6258 (-1.05) 1.4789*** (11.42) -2.1643*** (-3.05) a 0.1514*** (3.20) 358 0.4508 16.29 -0.0442 (-0.04) 1.5996*** (10.74) -2.8662** (-2.12) a 0.1102* (1.95) 261 0.1990 4.23 -0.7269 (-0.36) 0.6411 (1.28) 0.3318 (0.17) a 0.1493* (1.86) 97 0.2541 7.43	-0.9590** (-2.13) 1.3101*** (18.37) -0.9959*** (-4.80) a 0.4613*** (9.46) a 0.0346 (0.81) 358 0.4827 531.90 -1.2728*** (-2.96) 1.4160*** (21.14) a 0.6607*** (8.62) a -0.0203 (-0.39) 261 0.6445 643.52 -1.5147 (-0.96) 0.7881*** (3.02) -0.6220 (-0.80) a 0.2281*** (4.29) a 0.0686 (0.92) 97 0.1157 35.51 (6) IV -0.9751** (-2.13) 1.3146*** (18.11) -1.0137*** (-4.83) a 0.4654*** (9.26) a 0.0345 (0.78) 358 0.6314 24.28 -1.1382*** (-2.65) 1.4547*** (21.55) -0.7604*** (-3.95) a 0.6687*** (8.60) a -0.0301 (-0.58) 261 0.7404 12.33 -1.2991 (-0.82) 0.8863*** (3.57) -0.6850 (-0.95) a 0.2413** (4.63) a 0.0903* (1.24) 97 0.3767 8.86

For example,[START_REF] Dvorak | Do domestic investors have an information advantage? Evidence from Indonesia[END_REF] finds that foreign institutions in Indonesian stock market enjoy better information due to their experience and expertise.[START_REF] Lütje | What drives home bias? Evidence from fund managers' views[END_REF] report survey results that local investors fail to materialize the informational advantage they pretend to possess. On the opposite,[START_REF] Malloy | The geography of equity analysis[END_REF] and[START_REF] Hau | Location matters: An examination of trading profits[END_REF] argue that local analysts and investors outperform foreigners, a finding supporting the link between physical proximity and information quality.

Ricciardi (2008a[START_REF] Ricciardi | Risk: Traditional finance versus behavioral finance[END_REF] provides two extensive surveys of the behavioral finance theory in comparison to the traditional finance perspective. The author presents a formal introduction to theories related to risk perception and other concepts that influence the individual's decision-making process under conditions of risk and uncertainty. For other related discussions, see, among others,[START_REF] Barberis | A survey of behavioral finance[END_REF] or[START_REF] Shleifer | Inefficient Markets: An Introduction to Behavioral Finance[END_REF].

To my knowledge, this paper is the first attempt to propose such a direct quantitative measure of information distance in finance.

For others papers making use of the CPIS data, see, for example,[START_REF] Lane | International investment patterns[END_REF],[START_REF] Mishra | Where do Australians invest?[END_REF] or[START_REF] Faruqee | The determinants of international portfolio holdings and home bias[END_REF].

In an earlier version of their 2008 paper,[START_REF] Lane | International investment patterns[END_REF] distinguish three alternatives for modeling international portfolio holdings. The first approach, due to[START_REF] Obstfeld | The six major puzzles in international macroeconomics: Is there a common cause?[END_REF], is a static model in which frictions in good markets lead to domestically biased portfolios even tough financial markets are complete.[START_REF] Lane | International investment patterns[END_REF] provide an N-country generalization of the Obstfeld-Rogoff study. The second approach byDavis et al. (2000) assumes a dynamic model of portfolio allocation and consumption under incomplete markets. The third approach, which is also the one I adopt, comes from[START_REF] Martin | Financial super-markets: Size matters for asset trade[END_REF] who develop a model of bilateral asset holdings from which a gravity-type model emerges naturally.

 11 The concavity assumption implies also that agents are risk-averse

.12 Intuitively, the term "agents" substitutes investors and "risky projects" substitutes a risky financial instrument, such as equities for example.

See Uppal and Wang (2003), p. 2467.

On the other hand, non-linear Tobit regressions allow one to include zero observations for the dependent variable by censoring data on the left.

I exclude from the original dataset the following OFCs: Andorra, Anguilla, Antigua and Barbuda, Aruba, the Bahamas, Bahrain, Barbados, Belize, Bermuda, British Indian Ocean Territory, Cayman Islands, Cook Islands, Costa Rica, Cyprus, Dominica, Dominican Republic, Falkland Islands, Faroe Islands, Gibraltar, Grenada, Guernsey, Haiti, Hong Kong SAR of China, Ireland, Isle of Man, Jersey, Lebanon, Liechtenstein, Luxembourg, Macao SAR of China, Malta, Marshall Islands, Mauritius, Monaco, Netherlands Antilles, Niue, Panama, Puerto Rico, Reunion, Samoa, Seychelles, Singapore, St. Kitts and Nevis, St. Vincent and Grenadines, Switzerland, Turks and Caicos Islands, United States minor outlying islands, Vanuatu, Virgin Islands (UK) and Virgin Islands (US).

I also exclude three destinations labeled as international organizations, other countries (confidential data), and other countries (unallocated). The data loss due to this elimination is trivial: The sum of the foreign assets held in these destinations does not exceed 15% of the total assets reported for a particular country in the group of developed countries (the maximum observed for Australia), and

17% in the group of emerging countries (the maximum observed for Poland).17 In the group of developed-market source countries I include Australia, Canada, Finland, France, Germany, Italy, Japan, the Netherlands, Spain, Sweden, the UK and the USA; while the group of emerging-market source countries consists of Argentina, Brazil, Czech Republic, Hungary, India, Indonesia, Malaysia, Mexico, Poland, South Africa, South Korea and Turkey.

The authors' insight is as follows: Words acquire their meaning from the way they are used in the society and, for computers the equivalent of society is database, and the equivalent of use is the way to search the database.

While Chan et al. (2005) consider the economic development, the stock market development and the investor protection standards as separate categories of explanations, I believe that they can all be embedded into a single group, capturing various aspects of a particular country's degree of economic development.

In line with the protecting investors dimension of the World Bank's Doing Business Project,[START_REF] Djankov | The effect of corporate taxes on investment and entrepreneurship[END_REF] propose a measure of legal protection of minority shareholders against self-dealing transactions benefiting controlling shareholders.

To my knowledge, this study is also the first to introduce this variable to gauge for a country's foreign openness.

[START_REF] Grinblatt | How distance, language, and culture influence stockholdings and trades?[END_REF] argue that Finnish households are more likely to invest in the stocks of Swedish firms communicating in the investor's native tongue.

[START_REF] Stulz | Culture, openness, and finance[END_REF] identify three channels through which culture can affect finance: First, the values that are predominant in a country depend on its culture. […] Second, culture affects institutions. For instance, the legal system is influenced by cultural values. Third, culture affects how resources are allocated in an economy (p. 316-317).

I distinguish between legal systems from English, French, German and Scandinavian origins.

In case there is lack of a directly observed time series for a particular destination, I substitute it by an appropriate regional index.

Interestingly, after performing this elimination, I am left with fewer observations for the cultural distance than for information distance. Yet, the dataset still has sufficient number of observations to perform the estimations.

Distinguishing the regression results across developed and emerging countries,[START_REF] Lane | International investment patterns[END_REF] also find a similar result.

Specifically, Gelos and Wei (2005) suggest that becoming more transparent can be an effective way for countries to benefit from international financial integration while avoiding excessive volatility during turbulent times (p.

3012).

Concerning stepwise procedures, I have used a linear specification for the panel data with source country fixed-effects and the bilateral trade is the first control to enter the models after different dummies introduced for entities.

ACKNOWLEDGEMENTS

I thank Jonathan Hull from Telegeography, Florian Plank from Euler Hermes and the GREGOR research team from the Sorbonne Business School for their help to access data.

Financial support by the Galatasaray University Research Fund is greatly acknowledged.

Source: The World Bank's "Doing Business Project" database.

2) Openness: 𝐹𝑇𝑅𝐴𝐷𝐸 : The foreign trade volume of country 𝑗's as a percentage of its GDP. Source: Author's own calculations based on trade statistics obtained from the web site www.trademap.org, GDP data is from the IMF's World Economic Outlook database. 𝑀𝐴 : The monetary sum of the country 𝑗's cross-border mergers and acquisitions scaled by its GDP. Source: Author's own calculations based on data covering the international mergers and acquisitions as reported by the World Investment Report (UNCTAD, 2007).

3) Familiarity:

𝐵𝑇𝑅𝐴𝐷𝐸 : The ratio of the country 𝑖's bilateral trade volume with country 𝑗 to the total foreign trade volume of country 𝑖. Source: Author's own calculations based on data from www.trademap.org. 𝐿𝐴𝑁𝐺 : A dummy variable equal to 1 if countries 𝑖 and 𝑗 share a common language, 0 otherwise. Sources: CIA World Factbook. 𝐿𝐸𝐺𝐴𝐿 : A dummy variable equal to 1 if countries 𝑖 and 𝑗's legal systems come from the same origin, and 0 otherwise. Source: La [START_REF] Porta | Legal determinants of external finance[END_REF]. 𝑅𝐸𝐺 : A dummy variable equal to 1 if countries 𝑖 and 𝑗 are in the same geographical region, and 0 otherwise. Source: The World Bank.

4) Transparency:

𝐶𝑃𝐼 :

The corruption perceptions index. Source: Transparency International, www.transparency.org. 𝐽𝑈𝐷𝐼𝑁 : The judiciary system independence index. Source: The Economic Freedom Network, www.freetheworld.com. 𝐶𝑀𝐶 : The capital market controls index. Source: The Economic Freedom Network, www.freetheworld.com.

5) Portfolio diversification:

𝑅𝐸𝑇 : The expected return on the country 𝑗's market index. 𝑆𝐻𝑅𝑃 : The risk-adjusted return on country 𝑗's market index defined as the ratio of mean excess return to the standard deviation (for purpose of computational facility, the international risk-free rate is assumed to be equal to zero).

variables are computed using index data (dividends included) over the 5-year length period running from January 2002 to December 2006. Whenever there is lack of a directly observable MSCI index for a particular country, I substitute it by a regional MSCI index; that is I employ i) Notes: a) estimated values, b) regional estimated values for "Arab World", c) regional estimated values for "East Africa", d) regional estimated values for "West Africa". The second column labeled "C." displays the country's membership score resulting from a four-means cluster using raw data from www.geert-hofstede.com. Notes: The table reports panel OLS regression results for the gravity model of international equity holdings using cultural distance, 𝐷𝐶𝑈𝐿𝑇 . The dependent variable is log of equity assets held by the source country 𝑖 in the host country 𝑗.

Predictor variables are 1) economic development variables including GDP per capita (𝐺𝐷𝑃𝑃𝐶 ), financial market sophistication (𝐹𝑀𝑆𝑂𝑃 ), investor protection (𝐼𝑁𝑉𝑃𝑅𝑂 ); 2) familiarity variables including bilateral trade (𝐵𝑇𝑅𝐴𝐷𝐸 ), common language dummy (𝐿𝐴𝑁𝐺 ), common legal origin dummy (𝐿𝐸𝐺 ), common geographical region dummy (𝑅𝐸𝐺 ); 3) openness variables including foreign trade to GDP ratio (𝐹𝑇𝑅𝐴𝐷𝐸 ), mergers & acquisitions to GDP ratio (𝑀𝐴 ); 4) transparency variables including corruption perceptions (𝐶𝑃𝐼 ), judiciary independence (𝐽𝑈𝐷𝐼𝑁 ), capital market controls (𝐶𝑀𝐶 ); and 5) portfolio diversification variables including Sharpe ratio (𝑆𝐻𝑅𝑃 ), bilateral market correlations (𝐶𝑂𝑅 ). All regressors, except dummies, are specified in log levels. Regressions control for the source country fixed-effects. F-stat is designed to jointly test that all fixed-effects parameters are zero, for which the null hypothesis is rejected at all conventional levels throughout the table. Heteroskedasticity consistent t-statistics obtained using the [START_REF] White | A heteroskedasticity-consistent covariance matrix estimator and a direct test for heteroskedasticity[END_REF] method, are provided in parenthesis below the parameter estimates. Statistical significance at 10% (resp. 5 and 1%) is denoted by *** (resp. ** and *).