The distribution of international investment, even at the country level, has many zeros and also has fat tails. This makes most linear estimators ill-suited for statistical analysis of international investment. Using unconditional quantile regressions, this column finds evidence of nonlinearities in the drivers of investment at different points in the investment distribution. Considering these non-linear effects, it suggests a pecking order in barriers that helps explain cross-border equity investment. Improvements in governance factors can increase investment when barriers are severe, before additional factors such as firm-specific information or transaction costs become important.
A large literature tries to understand the drivers of cross-border equity investment. Most papers – including some of ours – show little appreciation for the nature of international investment. The amount of cross-border investment between two countries or, for that matter, in individuals’ portfolios, includes lots of zeros. We invest zero in most of the world’s securities, and even at the country-level zeros make up about one quarter of all observations The distribution of international investment also has fat tails. The mass of zeros makes a fat left tail, while overinvestment in some securities or countries – perhaps investment in our own company or in a neighbouring country – produces a fat right tail. And the distribution has substantial positive skewness.
All this suggests that estimators geared toward average effects, like most linear estimators, are ill-suited for statistical analysis of international investment.
We examine the implications of this in our recent paper with Sergei Sarkissian and Michael Schill (Holland et al. 2024). We find that many factors previously shown to impact international investment (on average) only hold at certain parts of the distribution.
What does the distribution of global equity investment look like?
The above description references the dollar amount of international investment, but for empirical analysis the dependent variable must be properly scaled. We use relative weight, i.e. the ratio of a destination country’s weight in a source country’s equity portfolio to the destination market’s weight in the world market. Relative weight has some useful properties: it is a measure of cross-border equity investment that is motivated by theory, free of any size bias, and adjusted for freely floating shares available to global investors. A relative weight of one – meaning that a country’s holdings of a destination market equity equal the weight of the destination market equity in world float – is consistent with an international capital asset pricing model (CAPM) allocation in the absence of any costly barriers. When a country holds no destination market equity, the relative weight is zero. Any relative weight less than one implies that a country is underweighted (relative to the international CAPM allocation) in the destination market, and a relative weight greater than one implies that a country’s portfolio is overweight in the destination market.
Figure 1 shows the distribution of float-adjusted relative investment weights for 39 investor countries and 39 destination countries from 2001 to 2017 using a broad set of data from the IMF Coordinated Portfolio Investment Survey. The distribution of relative weights is very positively skewed and has large tails. The mean value of 0.33 – average bilateral investment at just 33% of the destination’s weight in the world portfolio – delivers an incomplete view of the distribution. Roughly one-third of the observations are ‘outliers’. The most frequent investment is zero (the tall red bar), but some countries (the short green bars) invest much more than the world CAPM benchmark of one, the point at which the proportion of investor country holdings in the investment destination country equals the destination country weight in the world market portfolio.
Figure 1 The distribution of cross-border investment
Figure 2 shows the cumulative frequency of relative weight. The first 27% of all observations, shown by the red circle in Figure 2, are zero-investment pairs such as Mexico-to-Netherlands in 2010, New Zealand-to-Israel in 2002, and Philippines-to-Japan in 2009. The next 23% of observations have relative weight between 0 and 0.0395, shown by the dotted red line. These include such country pairs as Italy-to-Argentina in 2013 and Singapore-to-South Africa in 2001. The solid blue line shows that about 43% of the sample displays moderate amounts of investment with relative weight above 0.0395 but below one and includes country pairs like Italy-to-Canada in 2003 and US-to-Greece in 2014. Almost all investor countries have positive relative weight in Australia, Germany, the Netherlands, Switzerland, the UK, and the US. Even this moderate investment subsample shows wide variation similar to the entire sample. Finally, although most country pairs show very low to moderate investment, the remaining 7% of the sample, shown in the dashed green line, has relative weight greater than one. The cumulative frequency increases quickly, illustrating investment well above the threshold of one to levels that are three, four, or five times the destination weight in the market portfolio, levels that can be characterised as overinvestment relative to a world CAPM benchmark. Rather than clustering just above one, the frequency at which relative weight exceeds one increases steadily. These include country pairs such as Germany–France in 2016, Australia–New Zealand 2016, and Austria–Germany 2013. Most countries in our sample have at least one destination country pair that they overweight on average. The only investor countries that don’t have at least one destination country that maintains holdings above 100% of the benchmark weight are Canada, Egypt, Indonesia, India, Israel, Japan, Korea, Mexico, Pakistan, the Philippines, Turkey, and the US. In a similar vein, most destination countries are overweighted on average with at least one investor country – the exceptions are Canada, Israel, Japan, Pakistan, South Africa, and the US.
Figure 2 The frequency of relative weights
Why does this description of investment matter?
Standard approaches to estimating what drives cross-border equity investment focus on estimating average effects. A linear estimator such as least squares regression yields estimates of the marginal effect of investment determinants at the average investment. But the wide distribution in cross-border investment reveals that very few country-pairs resemble anything close to ‘average’ and so estimates from linear models cannot capture important drivers of investment across the distribution – some factors might matter when there is very low investment, others when there is very high investment, and others when there is moderate investment – and may not adequately account for important nonlinearities in factors.
We use unconditional quantile regressions (UQRs), which are well suited to uncover nonlinearities and appropriate for a heavily skewed, fat-tailed distribution. Unconditional quantile regressions, which characterise the marginal effects across the distribution of investment independent of other variables, allow us to describe the relation of covariates and investment at different points of the investment distribution. Rather than reduce the effect of outliers on coefficient estimates of various factors on average investment, unconditional quantile regressions can reveal nonlinearities in effects.
Implementing unconditional quantile regressions is relatively straightforward. We apply the Firpo et al. (2009) method of running least squares regressions of a recentred influence function at a range of investment quantiles on proposed investment determinants drawn from the literature. The coefficient estimates reveal how determinants affect the contribution of an observation to a specific investment quantile, such as very low investment at the 30th quantile or very high investment at the 95th quantile.
We draw from the broad range of theories that suggest that international investment depends on barriers such as information and familiarity as well as hedging motives, transactions costs, and governance (e.g. Bekaert and Wang 2009, Chan et al. 2005, Coeurdacier and Rey 2013, Lane and Milesi-Feretti 2008). Figure 3 shows unconditional quantile regression coefficient estimates plotted as the circles for a select set of the comprehensive set of bilateral, investor country, and investment destination characteristics across a range from low relative investment weight (quantile 30) to very high relative investment weight (quantile 95). Vertical lines extending from the circles (sometimes so small that they are hidden behind the circles) show 95% confidence bounds for the unconditional quantile regression marginal effects. For comparison, the solid blue horizontal line in each subplot shows the coefficient estimate from a full sample OLS regression, and the dashed line shows the associated 95% confidence bound.
Figure 3 Select determinants of relative investment weight
The unconditional quantile regression estimates show clear nonlinearities in the drivers of investment. The marginal effects of all the determinants vary across the distribution of relative weight. The graphical presentation here, along with a closer look at the tabulated results in the accompanying paper, reveals that while some determinants are statistically significant on average (from the OLS regression), many other coefficient estimates are only significant at distinct portions of the relative weight distribution. In fact, in our comprehensive set of determinants, there are only two variables that are significant on average as well as across the entire distribution. Many coefficients that are significant in a least squares regression are not significant drivers at other points of the relative weight distribution. On the other hand, there are several variables that are not statistically significant in a least squares regression – and therefore at risk of being dismissed by researchers – that the unconditional quantile regression results reveal are statistically significant at other points of the distribution. The differences in estimates have important implications for understanding not just which determinants drive investment, but how. For example, the bilateral trade ordinary least squares (OLS) estimate is positive but insignificant. But unconditional quantile regression estimates reveal that at the left part of the distribution, where investment is low (and, presumably, barriers are high), more trade between two countries is associated with more investment.
Implications
Considering the nonlinear effects of determinants across the distribution of relative investment weights, we propose a pecking order in barriers that helps explain cross-border equity investment. When direct barriers are severe, improvements in governance factors such as rule of law and expropriation risk can increase investment. Only when severe barriers are ameliorated can factors such as firm-specific information, transaction costs and hedging motives become more important.
Understanding these nonlinearities has important implications for research on international investment. On the empirical side, the emphasis has been on micro datasets (e.g. Bekaert et al. 2017, Maggiori et al. 2020) that necessarily use a particular slice of the investment distribution. A recognition that results supporting various theories depend on the particular slice of the distribution should help link micro and macro evidence. Relatedly, reliance on a specific dataset might mask the effect of important nonlinearities in factors that drive international investment.
Our results highlight that some theories are more likely to find empirical support at certain parts of the distribution, so in a sense the choice of a dataset will drive many results. For theorists, our evidence might expand models currently focused exclusively on information (van Nieuwerburgh and Veldkamp 2009, De Marco et al. 2022, Valchev 2017) to models exploring the nonlinearities of effects that vary through the investment distribution.
Source : VOXeu
