\documentclass[12pt]{article} \usepackage{amssymb} \usepackage{graphicx} %\usepackage[dcucite]{harvard} \usepackage{amsmath} \usepackage{color}\usepackage{setspace} \usepackage{booktabs} \usepackage{hyperref} \usepackage[T1]{fontenc} \usepackage{threeparttable} \usepackage{array} \usepackage{comment} \usepackage{longtable} \usepackage{subcaption} \usepackage{adjustbox} \usepackage{tikz} \usetikzlibrary{decorations.pathreplacing} \usepackage{natbib} %\usepackage{apacite} \usepackage{indentfirst} \usepackage{tikz} \usetikzlibrary{arrows,shapes,positioning,shadows,trees} \usepackage[table]{colortbl}% http://ctan.org/pkg/xcolor \tikzset{ basic/.style = {draw, text width=2cm, drop shadow, font=\sffamily, rectangle}, root/.style = {basic, rounded corners=2pt, thin, align=center, fill=teal!50, text width=20em}, level 2/.style = {basic, rounded corners=6pt, thin,align=center, fill=teal!35, text width=6.5em}, level 3/.style = {basic, thin, align=center, fill=teal!10, text width=6.5em} } \setlength{\topmargin}{0.1in} \setlength{\headheight}{0in} \setlength{\headsep}{0in} \setlength{\topskip}{0in} \setlength{\textheight}{8.5in} \setlength{\oddsidemargin}{0in} \setlength{\evensidemargin}{0in} \setlength{\textwidth}{6.5in} \newcommand\inv[1]{#1\raisebox{1.15ex}{$\scriptscriptstyle-\!1$}} \makeatletter \setlength{\@fptop}{0pt} \makeatother \begin{document} \thispagestyle{empty} { % set font to helvetica (arial) to make it 508-compliant \fontfamily{phv}\selectfont \begin{center} {\Large \textbf{PHANTOM FDI: A STRUCTURAL GRAVITY ANALYSIS USING MREID}\\} %{\Large Comparing Armington Elasticities Across Methods and Aggregations: The Case of Fish\\} \vspace{0.75in} {\Large Saad Ahmad \\Jeffrey Bergstrand\\ Jordi Paniagua \\ Heather Wickramarachi}\\ \vspace{0.75in} \vspace{0.75in} {\large ECONOMICS WORKING PAPER SERIES}\\ Working Paper 2025--08--C \\ \vspace{0.5in} U.S. INTERNATIONAL TRADE COMMISSION \\ 500 E Street SW \\ Washington, DC 20436 \\ \vspace{0.25in} August 2025 \end{center} \vfill \noindent The views expressed solely represent the opinions and professional research of the authors. The content of the working paper is not meant to represent the views of the U.S. International Trade Commission, any of its individual Commissioners, or the United States government. Please address correspondence to saad.ahmad@usitc.gov. \newpage \thispagestyle{empty} % remove headers, footers, and page numbers from cover page \begin{flushleft} Phantom FDI: A Structral Gravity Analysis Using MREID \\ Saad Ahmad, Jeffrey Bergstrand, Jordi Paniagua and Heather Wickramarachi \\ Office of Economics Working Paper 2025--08--C\\ August 2025\\~\\ \end{flushleft} \vfill \begin{abstract} \noindent Foreign direct investment (FDI) measured by public sources includes investments made by firms for financial and accounting related (or nonproduction-based) reasons, typically concentrated in offshore financial centers (OFCs). Recent studies suggest that profit-shifting may also occur in non-OFC regions. Consequently, many datasets used to understand the economic factors behind a firm's decision to shift production activities across countries may still contain such ``phantom FDI.'' As a result, researchers have developed analytical methods to remove phantom FDI flows and improve the accuracy of FDI measures. In this paper, we propose a structural gravity approach to identify and measure phantom FDI using the new Multinational Revenue, Employment, and Investment Database (MREID). We use this approach to provide estimates of phantom FDI for a number of developed countries in our sample. Our baseline results are then validated using an alternative production-function approach. \end{abstract} \vfill \begin{flushleft} Saad Ahmad, Office of Economics\\ \href{mailto:saad.ahmad@usitc.gov}{saad.ahmad@usitc.gov}\\ \vspace{0.25in} Jeffrey Bergstrand, University of Notre Dame\\ \href{mailto:jbergstr@nd.edu}{jbergstr@nd.edu}\\ \vspace{0.25in} Jordi Paniagua, University of Valencia\\ \href{mailto:jordi.paniagua@uv.es}{jordi.paniagua@uv.es}\\ \vspace{0.25in} Heather Wickramarachi, Office of Industry and Competitiveness Analysis \href{mailto:heather.wickrama@usitc.gov}{heather.wickrama@usitc.gov}\\ \vspace{0.75in} \end{flushleft} } % end of helvetica (arial) font \clearpage \newpage \doublespacing \setcounter{page}{1} \section{Introduction} In an effort to capture production-based foreign direct investment (FDI) of multinationals, many FDI datasets allow researchers to isolate FDI flows related to special purpose entities (SPEs). These SPEs are often set up in offshore financial centers (OFCs), but have little impact on ``real'' economic activity. As a result, researchers often exclude these financial or profit-shifting flows from their analyses, allowing for a more explicit analysis to be conducted on the ``real'' elements behind FDI flows. Data sources that provide this level of granularity include the OECD, Eurostat, and the International Monetary Fund’s Balance of Payments/International Investment Position (BOP/IIP) data. The United Nations Conference on Trade and Development (UNCTAD) also directly excludes SPEs from their reported FDI data whenever feasible. In theory, FDI data without SPEs should do a better job in matching "real" indicators of multinational activity (sales, assets). \footnote{The IMF’s Coordinated Direct Investment Survey (CDIS) does not offer this distinction.} While identifying and excluding OFCs is a necessary step in capturing production-based FDI, it is not sufficient on its own. Recent research shows that profit-shifting activities might occur from Multinational Enterprises (MNEs) transferring their intangible assets to subsidiaries in low-tax jurisdictions \citep{santacreu2024impact}. So, even after the exclusion of OFCs, the FDI datasets used in the literature can still contain phantom (or conduit) FDI \citep{casella2024measuring}. Given these circumstances, analytical methods continue to be developed to remove conduit FDI flows from bilateral data so that FDI flows can be measured more precisely in economic studies. These methods, as noted in \citet{casella2024measuring} and \citet{brandt2023illicit}, involve the use of estimation techniques and alternative data to detect and exclude phantom FDI. This paper contributes to this literature by introducing a well-established theoretical approach (structural gravity) to identify and measure ``Phantom FDI.''\footnote{The gravity equation is a widely used model in the international trade literature that predicts trade and investment flows between two countries is related to their economic sizes and the bilateral frictions between them}. Expanding on \citet{damgaard2024real}, we define phantom FDI as investment in empty corporate shells or subsidiaries where the investment is not motivated by considerations related to local production and is thus not explicitly tied to local economic activities. Our first contribution is on identifying phantom FDI in the outward investment activities of U.S. MNEs in various destination countries. To validate our results, we also use a production-function approach that delivers estimates similar to those using the gravity-equation approach for the U.S. MNEs. A second contribution is an application of our methods to identify inward phantom FDI of a very large set of advanced countries. The third contribution, and one of the advantages of combining our methods with the exhaustive Multinational Revenue, Employment, and Investment Database (MREID) described in \citet{ahmad2023mreid}, is evaluating phantom FDI for multiple measures of FDI: numbers of affiliates, revenues, and investments in total assets, fixed assets, tangible fixed assets, and intangible fixed assets. The paper is organized as follows. Section \ref{sec:back} reviews the literature on phantom FDI. Section \ref{sec:methodd} describes our methods to estimate phantom FDI. Section \ref{sec:data} describes the various measures of MNEs' activities provided by MREID. Section \ref{sec:results} reports the main results using outward U.S. FDI while section \ref{sec:globalinward} explores this approach for non-U.S. countries. Section \ref{sec:conclusions} concludes. \section{Literature Background\label{sec:back}} The identification of phantom foreign direct investment (FDI) can be approached using several methods, each with a distinctive statistical foundation. The most common methods are those proposed by the International Monetary Fund (IMF) and the United Nations Conference on Trade and Development (UNCTAD). The IMF method, proposed by \citet{damgaard2024real}, estimates both real and phantom FDI by utilizing reported data on SPEs. This method incorporates known information to isolate phantom investments. The IMF method uses Orbis data from 2016 to match ``real'' FDI, interpreted as Multinational Production (MNP), with OECD statistics. This approach assumes that Orbis data reflects the structure and changes in FDI accurately, even if it may not be precise in terms of absolute levels. By relying on these datasets, the method seeks to identify the genuine economic activity underlying FDI flows, distinguishing it from phantom FDI, which is typically designed for tax optimization rather than actual production. They find that phantom FDI has grown at a faster pace than real FDI over the last decade and accounts for around \$15 trillion, almost 40 percent of total global FDI. In contrast, UNCTAD offers the ``implied investment method,'' as discussed by \citet{bolwijn2018establishing} and \citet{casella_looking_2019}. This approach establishes a direct linear relationship between the logarithm of FDI stock (either inward or outward) and the logarithm of gross domestic product (GDP). The UNCTAD method introduces a distinct analytical approach to derive bilateral FDI stocks by ultimate investors. This method is grounded in Markov chain results, which provide a probabilistic model for tracing FDI flows back to their ultimate sources. Unlike traditional methods, which may rely on reported data or correlations with economic variables like GDP, Casella's approach offers a novel way to map FDI more accurately by capturing the flow of investments across borders through a sequence of intermediate steps. Looking at a dozen recipient countries, the estimated distribution used in \citet{casella_looking_2019} more clearly reflects the reported distribution of ultimate investors than it does for bilateral FDI accounting for direct investors. This indicates that their methodology accounts for the substantial conduit FDI normally reflected in bilateral statistics. Both methodologies, however, are inherently ``a-theoretical,'' as they are based on statistical correlations rather than an underlying economic theory. They integrate empirical data with estimation techniques to differentiate between real economic activity and phantom investments designed for tax optimization or regulatory arbitrage. Other methods for identifying and analyzing phantom FDI expand upon different analytical frameworks and datasets. The OECD Economic Impact Assessment, as developed by \citet{turban2020set}, uses a fully estimated method that diverges from the implied investment approach. Instead, conduit FDI is estimated by extrapolating data from economies that report on ultimate investors. This method employs a set of matrices that map the locations of profit and economic activities of multinational enterprises (MNEs), offering a comprehensive view of global FDI patterns. \citet{haberly2015regional} apply principal component analysis (PCA) to decompose the global bilateral FDI anomaly matrix into its primary constituent sub-networks. This approach allows for the identification of regional blocks and imperial legacies, helping to map the global offshore FDI network and reveal the structural patterns that contribute to the concentration of FDI in specific regions or countries. Furthermore, UNCTAD’s \citeyear{publications_world_2015} World Investment Report introduces an FDI-driven approach through the Offshore Investment Matrix. This method categorizes self-declared SPE countries and tax havens, focusing on identifying the role of these jurisdictions in facilitating offshore investment, thereby offering another perspective on the relationship between FDI and phantom investment. Each of these methodologies provides unique insights into the complexities of global FDI flows and their implications for economic governance. Related to the identification of phantom FDI, \cite{guvenen2022offshore} employ a profit-shifting method using firm-level data to reattribute earnings between U.S. Direct Investment Abroad (USDIA) and the respective foreign affiliates of U.S. multinational enterprises (MNEs). This reattribution method is based on a theoretical model of profit-maximizing firms, wherein the total worldwide earnings of an MNE are distributed among its parent company and affiliates according to their shares of the MNE’s global wage bill, physical capital stock, or intangible capital stock. The key innovation in this approach lies in its foundation on economic theory, unlike the other methods that rely more heavily on empirical data correlations. By attributing profits according to these measurable factors, the model allows for a more realistic estimate of where profits are actually generated, as opposed to where they are reported for tax purposes. This method helps uncover the extent of profit shifting within MNEs, providing a clearer picture of the actual economic contributions of both the parent companies and their foreign affiliates. Their results show that the largest sectors involved in profit shifting are computers, petroleum and chemicals, pharmaceuticals, and R\&D, largely due to the shifting of intellectual property. They find that R\&D-intensive industries have experienced faster productivity growth compared to non-R\&D-intensive industries, suggesting that the decline in productivity is primarily driven by non-R\&D-intensive industries. Further, they estimate that 38 percent of the profits reported by US MNEs as being earned abroad can be considered as generated in the US; accordingly, accounting for profit shifting reduces the return on US direct investment abroad. The impact of this profit shifting in the United States has been significant. \cite{clausing2020profit} estimates that one-third of U.S. corporate income taxes, equivalent to \$100 billion in revenue, are lost annually due to this practice. \cite{torslov2023missing} estimate that the amount of globally shifted profit is 36\% of multinational profit and calculate that the U.S. loses around 15\% of its corporate tax revenues due to the relocation of profits to low-tax jurisdictions. Further, fiscal authorities of high-tax countries may lack the incentives to combat profit shifting to tax havens \citep{torslov2023externalities}. \section{Methodology \label{sec:methodd}} \subsection{The Gravity Equation for Trade and FDI} In this paper, we employ well-established theoretical foundations for ``structural gravity'' (cf., \citet{anderson2003gravity}, \cite{Baieretal2017} and \cite{anderson2019}) to address the phantom FDI issue. The gravity equation is a widely used model in the international trade literature that (initially) predicted bilateral trade flows between two countries based on their economic sizes and the distance between them. Similar to Newton’s Law of Gravitation, the (naive) trade gravity model suggests that trade between two countries is proportional to their economic masses — typically represented by exporter and importer GDPs — and inversely related to the trade costs, which often were captured by geographic distance, tariffs, and other trade barriers. %The model accounts for both supply and demand effects, with larger economies expected to trade more due to their greater production capacity and consumption needs, cf., \citet{anderson1979theoretical} and \citet{bergstrand1985gravity}. \cite{Tinbergen1962} was the first to use the gravity equation applied to bilateral aggregate trade flows, estimating for a single year using Ordinary Least Squares (OLS) and positive trade flows: \begin{equation}\label{Eq1} \ln TRADE_{ij} = \beta_0 + \beta_1 \ln Y_{i} + \beta \ln Y_{j} + \beta_3 \ln Dist_{ij} + \beta_4 EIA_{ij} + \ln \epsilon_{ij} \end{equation} where $\ln TRADE_{ij}$ was the natural logarithm of the (nominal) bilateral trade flow (in U.S. dollars) from country $i$ to country $j$, $Y_i$ ($Y_j$) was nominal GDP in U.S. dollars in country $i$ ($j$), $Dist_{ij}$ was the bilateral distance in nautical miles between the two countries' economic centers, $EIA_{ij}$ was a dummy variable taking the value 1 if the two countries had an economic integration agreement, or EIA (such as a free trade agreement) and 0 otherwise, and $\epsilon_{ij}$ was an error term. A multitude of studies over subsequent years estimated gravity equations similar to equation \eqref{Eq1}, especially to find estimates of $\beta_4$, the coefficient on the presence or absence of an EIA. Along the way, researchers introduced additional control variables, such as dummies for having a common land border, common official language, and/or common legal origins, or being an island or landlocked. However, formal theoretical \textit{microeconomic} foundations for the gravity equation did not surface until 1979 with the models in \cite{anderson1979theoretical} and \cite{bergstrand1985gravity}. While focusing on different dimensions of the theoretical foundation for equation \eqref{Eq1}, both papers provided complementary elements that -- once properly synthesized in \cite{anderson2003gravity} -- led to what is now referred to as ``structural gravity,'' cf., the Introduction in \cite{Bergstrand2019} or Online Supplement Appendix B in \cite{Bergstrandetal2023}. A standard structural gravity equation for a given year can be represented as: \begin{eqnarray}\label{Eq2} TRADE_{ij} = \frac{Y_{i} E_{j}}{Y^W} \left( \frac{t_{ij}}{\Pi_{i}{P_{j}}} \right)^{1-\sigma} \epsilon^T_{ij}, %if FDI_{ijt}=\omega_{ijt}M_{it} > 1 \end{eqnarray} where $Y_{i}$ ($E_{j}$) is nominal GDP (aggregate expenditures) in $i$ ($j$), $Y^W$ is world GDP (captured by a constant), $t_{ij}$ is an \textit{ad valorem} measure of bilateral trade costs (which can be replaced by an EIA dummy), and $\Pi_{i}$ ($P_{j}$) is the outward (inward) multilateral price index of producers (consumers) in country $i$ ($j$), cf., \cite{Baieretal2017}. This trade gravity equation has become a workhorse for understanding determinants of bilateral trade flows. In the presence of zeros and potential heteroskedasticity, researchers in this area now commonly estimate equation \eqref{Eq2} by Poisson pseudo maximum likelihood (PPML), cf., \cite{Baieretal2017}. A key strength of the structural gravity model is that it is rooted in economic theory and accommodates frictions and policy variables empirically while maintaining a microeconomic foundation. This allows researchers to evaluate the effects of trade agreements, tariffs, or non-tariff barriers on bilateral trade flows by explicitly modeling the costs associated with moving goods between countries. The model's consistent structural form facilitates the estimation of elasticities of bilateral trade with respect to bilateral trade costs, and it is robust to various extensions, such as incorporating multiple sectors, heterogeneous firms, or additional dimensions of trade costs like cultural and institutional differences. Another key advantage of the gravity equation is its flexibility in accommodating non-trade bilateral flows, such as foreign direct investment (FDI) and migration, making it a versatile tool for analyzing various forms of bilateral economic interactions between countries. When applied to FDI, the gravity model effectively captures the determinants of cross-border investment flows by accounting for both the size of a pair of economies and the costs associated with one country investing abroad in another country. The first formal theoretical economic foundation for the gravity equation applied to bilateral FDI was \citet{Bergstrand2007}, which solved for a gravity equation using a Knowledge-and-Physical-Capital extension of the Knowledge Capital model of \cite{Markusen2002}. Similar to trade flows, larger economies are expected to engage in higher volumes of FDI, while geographic distance, institutional barriers, and other frictions can impede investment. The model can be extended to include additional factors that affect FDI, such as bilateral investment treaties, regulatory environments, or political risk, allowing researchers to assess how these variables influence capital allocation across borders. This adaptability makes the gravity equation a powerful framework for studying FDI in addition to its traditional application to trade. \cite{anderson2019} solved for a structural gravity equation for FDI akin to equation \eqref{Eq2}. Ignoring the transition dynamics in \cite{anderson2019}, the determinants of the (steady state) bilateral FDI from origin country $i$ to affiliates in destination country $j$ in some year ($FDI_{ij}$) is the gravity equation: \begin{eqnarray}\label{Eq3} FDI_{ij} = \frac{\beta \phi^2\eta_{i}^2}{1-\beta + \beta \delta_{j,M}} \omega_{ijt} \frac{E_{i}}{P_{i}} \frac{Y_{j}}{M_{i}} \epsilon^F_{ij}, \end{eqnarray} if $FDI_{ij}=\omega_{ij}M_{i} > 1$ (and 0 otherwise), where $E_{i}$ is total expenditures in origin country $i$ (on consumption goods, physical capital investments, and technology capital investments), $P_{i}$ is a multilateral index of prices in country $i$ on all types of goods, $Y_{j}$ is a measure of national output in destination country $j$, $M_{i}$ is the technology capital stock in $i$, $\omega_{ij}$ is a measure of (policy and non-policy) openness of country $j$ to country $i$'s technology capital, $\beta$ is the standard time-discount factor, $\phi$ is the (Cobb-Douglas) share of the global technology capital stock used in production of output, $\eta_{i}$ is the share of country $i$'s technology capital as a share of country $j$'s global technology capital stock, and $\delta_{j,M}$ is the technology capital ``adjustment cost,'' analogous to the standard physical capital adjustment costs (in the physical capital accumulation literature). In empirical analysis, the structural gravity equation is often estimated using data on bilateral trade, FDI, GDP, distance measures between countries, and other bilateral costs discussed above. Recently, \citet{bergstrand2024deep} have investigated the partial and general equilibrium effects of various provisions in ``deep'' trade agreements on bilateral trade, bilateral FDI stocks, and various measures of MNEs' ``activities'' (i.e., affiliates costs, revenues, employment, and assets) using the structural gravity-equation approach. %By controlling for country-specific factors through fixed effects, researchers can isolate the impact of trade costs on trade flows. The model's flexibility also allows for including exporter and importer fixed effects, which capture country-specific multilateral resistance terms, accounting for a country's trade openness relative to the rest of the world. Overall, the structural gravity equation is a powerful tool for understanding the determinants of FDI patterns and the effects of international policies in a globalized economy. We will use equation \eqref{Eq3} as the theoretical gravity equation undergirding the empirical specifications that follow. \subsection{Measuring Phantom FDI with Structural Gravity} We next explain how ``phantom FDI'' can be identified using the structural gravity approach discussed in the previous section. Based on the theoretical model given in \eqref{Eq3}, we specify our baseline gravity equation as: \begin{equation}\label{eq:gravity1} FDI_{ij}=\exp\left(\alpha +\lambda_i + \lambda_j + \beta \omega_{ij} \right)\times \epsilon_{j}, \end{equation} where $FDI_{ij}$ represents a measure of MNE activity taking place between the Global Ultimate Owner (GUO) in source country $i$ and its affiliate in country $j$. Consistent with equation \eqref{Eq3}, the RHS includes $\omega_{ij}$ where openness is captured by standard gravity-equation variables (log of distance and dummies for common language, common legal origin, island, and landlocked). We also include the following policy-related dummies in $\omega_{ij}$ : if $i$ and $j$ are members of the World Trade Organization, if they are members of the European Union; if they have a free trade agreement between them; and if they have a bilateral investment treaty between them. $\lambda_i$ ($\lambda_j$) represent the fixed effects for the source (host) country with $\lambda_i$ capturing total expenditures and prices in source $i$ and $\lambda_j$ accounting for the GDP of host $j$ along with the influence of $\delta_{j,M}$ on bilateral FDI. Following best practices, the above specification is estimated using Poisson pseudo maximum likelihood (PPML). The predicted values of $FDI_{ij}$ from the estimation of \eqref{eq:gravity1} gives us a measure of potential FDI---the level of FDI that should be taking place between source $i$ and host $j$ if there were no other factors determining bilateral FDI beyond those listed in \eqref{Eq3}. In reality, unobservable factors can cause observed FDI to differ from predicted FDI. So in cases where observed FDI is higher than predicted FDI, we compute Phantom FDI as: \begin{equation} \label{eq:phantom1a} FDI_{ij}^{Phantom}=FDI_{ij}-\widehat{FDI_{ij}} . \end{equation} It is worthwhile here to take stock of the underlying assumptions behind our Phantom FDI measure. First, we consider any $FDI_{ij}$ that exceeds the Potential FDI predicted from \eqref{eq:gravity1} as lacking microeconomic foundations and so is classified as non-productive or phantom FDI.\footnote{Since the focus of the paper is on identifying phantom FDI, we do not analyze the cases where $FDI_{ij}$ is less than Potential FDI, so that non-economic factors are suppressing FDI.} Secondly, our strategy to identify phantom FDI rests on the explanatory variables being uncorrelated with the error term in \ref{eq:gravity1}. If that is the case, then the standard gravity variables predict the real FDI that should be taking place between two countries, while the residual is capturing non-economic considerations. Thirdly, our measure of Phantom FDI is bilateral in nature and so should not be affected by the inclusion of country-specific fixed effects, such as their tax treatment of MNEs, as that should attract inward FDI to the host country from all source countries.\footnote{A future extension would be to explore the effect tax rates and other country-specific policies may have on $\lambda_j$ in a second stage regression.} Lastly, our method focuses positive Phantom FDI, that is, when the residual is positive or $FDI_{ij}>\widehat{FDI_{ij}}$. By construction, there is an equal amount of negative Phantom FDI because the mean of the error term is zero. However, one of the advantages of the structural gravity equation is that the PPML estimator is robust to heteroskedasticity \citep{silva2006log}. Therefore, positive and negative Phantom FDI may have different variances. We can exploit this feature of the PPML estimator to identify Phantom FDI with the positive error terms by assuming that the negative error term has a lower variance (i.e., it is normally distributed) in the vein of \cite{rigobon2003identification}. Along with levels, we also calculate ``FDI ratio'' for each destination with: \begin{equation} \label{eq:ratio2} {FDI}_{ij}^{Ratio}\equiv\frac{FDI_{ij}}{\widehat{FDI}_{ij}}. \end{equation} The FDI ratio in equation \eqref{eq:ratio2} gives us a ranking of countries with actual FDI higher or lower than the theoretically predicted FDI from the gravity equation. The FDI ratio can be informative; if the predicted value of FDI is very low, the FDI ratio will be very high. Moreover, $FDI^{Ratio}_{ij}$ ``normalizes'' the relative importance of phantom FDI across countries so that the economic sizes of countries do not distort the importance of phantom FDI. %We omit any measure to explicitly capture variation across $j$ in $\delta_{j,M}$, the variable representing the technology-capital adjustment-cost factor because of lack of data on this variable; instead, we assume this factor is constant across countries. %In this section, we choose the United States (USA) as the origin country ($i$) and provide a methodology to estimate the values of bilateral phantom FDI to various recipient destinations ($j$). %Because we have a single origin country, there is no variation in the $i$ variables in equation \eqref{Eq3}; these variables are subsumed in the constant. Consequently, for our cross-sectional empirical specification in this case, we need only measures of variables that vary across $j=1,...,N$ countries in a particular year: $Y_j$ (nominal GDP in $j$), $\delta_{j,M}$ (technology-capital adjustment-cost factor in $j$), and $\omega_{ij}$ (bilateral variables that either enhance or diminish openness to FDI across the two countries). Consequently, all this suggests the following specification using Poisson pseudo maximum likelihood (PPML) estimation: %Focusing on the Phantom FDI from a single country of origin (e.g., the USA), we can estimate the following equation for a cross-section of data containing only the flows originating in the US. %\begin{equation} \label{eq:gravity2} %FDI_{USA,j}=\exp\left(\beta_0 + \beta_1\ln GDP_j + \beta_2 \omega_{USA,j} \right)\times \epsilon_{j}, %\end{equation} %where $FDI_{USA,j}$ represents a measure of MNE activity of Global Ultimate Owners (GUOs) based in the USA with affiliates in country $j$. Consistent with equation \eqref{Eq3}, the RHS includes destination GDP and $\omega_{USA,j}$ where the latter measure of openness is captured by standard gravity-equation variables (log of distance and dummies for common language, common legal origin, island, and landlocked). We also include in $\omega_{USA,j}$ policy-related dummies: membership of $j$ in the World Trade Organization, membership of $j$ in the European Union, a common free trade agreement, and a common bilateral investment treaty. We omit any measure to explicitly capture variation across $j$ in $\delta_{j,M}$, the variable representing the technology-capital adjustment-cost factor because of lack of data on this variable; instead, we assume this factor is constant across countries. %In equation \eqref{eq:gravity2}, we cannot include country-fixed effects due to collinearity. Instead, we introduce observables for the destination country, $\chi_{ij}$, which represents bilateral variables that have an observed effect on FDI flows between the origin (USA) and destination ($j$) countries. %We denote the predicted value of $FDI_{USA,j}$ as the ``Potential FDI'' for U.S. outward FDI to country $j$ and refer to it as $\widehat{FDI}_{USA,j}$. Then, we compute the ``Phantom FDI'' for US outward FDI as: %\begin{equation} \label{eq:phantom1} %{FDI}_{USA,j}^{Phantom}\equiv FDI_{USA,j}-\widehat{FDI}_{USA,j}. %\end{equation} %Hence, any $FDI_{USA,j}$ that exceeds that associated with the Potential FDI based upon the microeconomic founded FDI value is ``non-economic'' FDI and interpreted as non-productive FDI or phantom FDI. Note that our strategy to identify phantom FDI rests on the explanatory variables being uncorrelated with the error term in \ref{eq:gravity2}. Under these conditions, the standard gravity variables predict the real FDI that should be taking place between two countries, while the positive residuals give us our measure of phantom FDI.\footnote{Since the focus of the paper is on identifying phantom FDI, we do not analyze the cases where $FDI_{USA,j}$ is less than Potential FDI, so that non-economic factors are suppressing FDI.} %We also calculate ``FDI ratio'' for each destination with: %\begin{equation} \label{eq:ratio2} %{FDI}_{USA,j}^{Ratio}\equiv\frac{FDI_{USA,j}}{\widehat{FDI}_{USA,j}}. %\end{equation} %The FDI ratio in equation \eqref{eq:ratio2} gives us a ranking of countries with actual FDI higher or lower than the theoretically predicted FDI from the gravity equation. The FDI ratio can be informative; if the predicted value of FDI is very low, the FDI ratio will be very high. Moreover, $FDI^{Ratio}_{USA,j}$ ``normalizes'' the relative importance of phantom FDI across countries so that the economic sizes of countries do not distort the importance of phantom FDI. %\subsection{Robustness Method 1: Structural Gravity Using All Country-Pairs} %It is also possible to estimate the amount of phantom FDI for numerous origin-destination country pairs. In this case, we need to first estimate the bilateral phantom FDI across country-pairs. %Then, we can aggregate for any destination country $j$ its multilateral phantom FDI (i.e., the sum of bilateral inward phantom FDI values from all $i=1,...,N$ origin countries ($i \neq j$)). %Using the same theoretical framework from above, we can estimate for any given year: %Our focus is to compute bilateral Phantom FDI with the assistance of the gravity equation. To do so, we estimate in a first step the following equation: %where FDI represents a measure of MNE activities of Global Ultimate Owners (GUOs) based in country $i$ with affiliates in country $j$, $\omega_{ij}$ represents the same bilateral variables that we examined earlier between the origin ($i$) and destination ($j$) countries, and $\lambda_i$ ($\lambda_j$) represents a country fixed effect for the home (host) country. In this specification, $\lambda_j$ embeds the influence of $\delta_{j,M}$ in equation \eqref{eq:gravity2}. It also includes country-specific factors, such as tax rates, that can help attract inward FDI to the host country from all source countries. We note here that our measure of Phantom FDI is bilateral in nature and so should not be affected by the inclusion of country-specific fixed effects. \footnote{$\lambda_j$ in these estimations also accounts for country-specific factors such as low tax rates that may make the country more attractive for phantom FDI from all source countries. A future extension would be to explore the effect tax rates and other policies can have on $\lambda_j$ in a second stage regression.} %Again, we will denote the predicted value of $FDI_{ij}$ as the ``Potential FDI'' for the country-pair $ij$ and refer to it as $\widehat{FDI_{ij}}$: %\begin{equation} \label{eq:phantom2} %{FDI}_{j}^{Phantom}\equiv\sum_{i=1,i\neq %j}^N\left(FDI_{ij}-%\widehat{FDI_{ij}}\right) . %\end{equation} %where $\widehat{FDI_{ij}}$ is the predicted FDI flow from equation \eqref{eq:gravity1}. We can then compare the values of $FDI_{USA,j}^{Phantom}$ estimated using equations \eqref{eq:gravity2} and \eqref{eq:phantom1} with the values of $FDI_{USA,j}^{Phantom}$ estimated using equations \eqref{eq:gravity1} and \eqref{eq:phantom1a}. \section{Data description \label{sec:data}} \subsection{MREID} The Multinational Revenue, Employment, and Investment Database (MREID), constructed by \citet{ahmad2023mreid}, provides comprehensive and consistent information on both international \emph{and domestic} revenues, employment, and investment of affiliates operated by MNEs of a source country in a host destination. This information is provided at the bilateral level for the pairings of 185 countries across 25 industries, and (initially) 12 years (2010-2021). Covering a wide range of agriculture, mining, energy, manufacturing and services industries, MREID provides a novel and comprehensive panel of sectoral-level bilateral foreign direct investment (and domestic investment) and foreign affiliate sales activities; we use the term ``foreign direct investment'' (FDI) broadly for now, but also narrow the definition later. Furthermore, MREID can distinguish greenfield investment from merger and acquisition (M\&A) investment. Since MREID is based on firm-level data, it allows us to bypass some of the issues present in official FDI statistics related to offshore activities.\footnote{The underlying firm-level data used in MREID comes from Orbis. Orbis is Moody's flagship-company database with data from more than 425 million companies worldwide. It focuses on private company information and presents companies' variables in a comparable formats; information is sourced from over 170 different providers but is standardized into comparable cross-country information.} %Firm-level data in Orbis allows us to bypass some of the issues that plague official FDI statistics of major sources, such as that of the IMF with regards to offshore activites. We use the ``Global Ultimate Owner'' (GUO) variable in Orbis to identify the foreign ownership of affiliates. This variable allows us to track firms that invest in foreign countries. One of the limitations of the Orbis web interface is that the GUO variable is only available for the ``current'' day. To overcome this limitation, we followed the approach in \cite{kalemli2022construct} and used the M\&A module in Orbis to track these changes over time. With this procedure, we obtained accurate FDI data without accessing historical days; the consequent limitation is a 10-year rolling period.\footnote{This procedure allows the construction of a comparable companion dataset recording M\&A data. Whenever an affiliate enters the database within the observation period of 2010-2021, it is flagged as a greenfield investment; hence, we also have a second companion database on greenfield investment. We limited our search to affiliates with more than USD 1 million in sales or in total assets in at least one year in the sample. We also implemented criteria to detect exits from the market. \citet{ahmad2023mreid} provides extensive details on the search strategy.} %The dimensions of our database are as follows. MREID (initially) spans 12 years, 2010-2021. It contains financial data of 362,845 parent companies (GUOs) with 1,132,707 domestic and foreign affiliates. Of those, 351,66 are foreign affiliates of 70,661 parent companies, and the rest are domestic affiliates. Raw data from 25 sectors are combined and, after undergoing data cleaning, we have approximately 27,000 raw observations per year at the country-sector (two-digit) level. MREID has data on FDI for 185 countries; hence, there are potentially 34,410 (=184x185) bilateral FDI ``measures'' of activity. However, FDI data are characterized by many zeros; hence, the raw MREID database is unbalanced. For the estimates of U.S. phantom FDI, we restrict the analysis to 111 destinations with non-zero FDI in the year 2019. \subsection{U.S. Outward FDI Trends} Since our primary focus is on identifying phantom FDI in the investment activities of U.S. MNEs, we next describe the outward FDI measures found in MREID for U.S. firms. In Table 1, ``affiliates'' refers to the number of affiliates. This forms the basis for our benchmark results later. We note that from 2010 to 2019 there has been nearly a doubling of U.S. affiliates as well as a sharp jump in revenues, assets and employment of U.S. multinationals. The global pandemic that began in 2020 saw a decline in the overseas economic activity of U.S. firms as countries imposed stringent measures to stop the spread of the COVID-19 virus. \begin{table}[!ht] \centering \caption{Annual Outward FDI of U.S. MNEs in MREID} \begin{tabular}{|l|c|c|c|c|c|} \hline Year & Affiliates & Revenue & Employees & Total Assets & Fixed Assets \\ \hline 2010 & 50,689 & 515 & 682,641 & 4,069 & 728 \\ \hline 2011 & 54,127 & 1,945 & 3,248,606 & 7,854 & 2,614 \\ \hline 2012 & 57,667 & 3,151 & 4,572,539 & 10,313 & 3,996 \\ \hline 2013 & 61,485 & 3,408 & 4,991,396 & 13,103 & 4,689 \\ \hline 2014 & 65,787 & 3,569 & 5,343,777 & 13,695 & 4,881 \\ \hline 2015 & 70,308 & 3,450 & 5,998,080 & 14,143 & 6,371 \\ \hline 2016 & 74,924 & 3,624 & 6,339,269 & 16,326 & 7,905 \\ \hline 2017 & 79,878 & 4,467 & 6,785,568 & 19,900 & 9,415 \\ \hline 2018 & 85,075 & 5,016 & 7,192,457 & 27,228 & 15,591 \\ \hline 2019 & 90,033 & 4,965 & 7,190,422 & 21,810 & 10,497 \\ \hline 2020 & 93,377 & 4,768 & 7,139,845 & 23,636 & 11,390 \\ \hline 2021 & 94,421 & 2,022 & 2,966,898 & 13,041 & 4,290 \\ \hline \multicolumn{6}{l}{{\footnotesize{}{}Note: Revenues, Total Assets and Fixed Assets in Billions of dollars.}}\tabularnewline \end{tabular} \end{table} Figure \ref{fig:MREIDUSA} shows the top destination countries of American outward investment for several variables of the MREID dataset.\footnote{The public MREID dataset does not distinguish between tangible and intangible fixed assets.} Most of the American affiliates concentrate in Western Europe. As shown in Figure \ref{fig:affiliatesUSA}, the following are the rankings of the top destinations for American affiliates abroad: United Kingdom (1st), Netherlands (2nd), Germany (3rd), and France (7th). Emerging economies like Brazil (4th) and India (6th) also occupy the top list. Even in Orbis data, which mostly captures ``real'' FDI, tax havens appear to be a significant investment hub for American foreign affiliates. Luxembourg (5th) and Singapore (8th), usually classified as tax havens, appear as top destinations for U.S. MNEs. \begin{figure} \caption{USA's Outward FDI (MREID dataset)} % Alt Text: Figure 1 is comprised of six seperate bar charts showing the top destination countries of American outward investment for several variables of the MREID. Figure 1(a) shows number of affiliates, figure 1(b) shows revenues, figure 1(c) shows total assets, figure 1(d) shows fixed assets, figure 1(e) shows tangible fixed assets, and figure 1(f) shows intangible fixed assets. \label{fig:MREIDUSA} \centering \centering \hfill \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Number of Affiliates} \label{fig:affiliatesUSA} \includegraphics[width=\textwidth]{figures/bar_extensive.png}{a} \end{subfigure} \hfill \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Revenues from Affiliates} \label{fig:revenuesUSA} \includegraphics[width=\textwidth]{figures/bar_revenue}{b} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \caption[]{USA's Outward FDI (MREID dataset) (cont.)} \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Total Assets in Foreign Countries} \label{fig:totalassetsUSA} \includegraphics[width=\textwidth]{figures/bar_totalassets.png}{c} \end{subfigure} \hfill \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Fixed Assets in Foreign Countries} \label{fig:fixedassetsUSA} \includegraphics[width=\textwidth]{figures/bar_fixedassets.png}{d} \end{subfigure} \hfill \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure} \ContinuedFloat \caption[]{USA's Outward FDI (MREID dataset) (cont.)} \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Tangible Fixed Assets in Foreign Countries \label{fig:tangibleUSA}} \includegraphics[width=\textwidth]{figures/bar_tangible.png} \end{subfigure} \hfill \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Inangible Fixed Assets in Foreign Countries \label{fig:intangibleUSA}} \includegraphics[width=\textwidth]{figures/bar_intangible.png} \end{subfigure} \end{figure} Focusing on revenues in Figure \ref{fig:revenuesUSA}, we observe several interesting traits. Singapore has the second highest concentration of U.S. MNEs' foreign revenues, only after the United Kingdom (1st). Netherlands (3rd), known for favorable holdings regulations, and Ireland (4th), with one of the lowest corporate tax rates in the EU, follow. The picture of American assets abroad (total assets in Figure \ref{fig:totalassetsUSA} and fixed assets in \ref{fig:fixedassetsUSA}) depicts a similar pattern, with Luxembourg, the Netherlands, Ireland, and Singapore occupying the top ranks. When we distinguish between tangible (Figure \ref{fig:tangibleUSA}) and intangible fixed assets (Figure \ref{fig:intangibleUSA}), we observe similar distributions. The Netherlands is the absolute champion in tangible fixed assets, followed by the United Kingdom. Ireland and Singapore (with the United Kingdom between them) lead the country ranking with most of the U.S. foreign intangible fixed assets. MREID allows us to examine the sectors that are the targets of U.S. MNE activity. Table 2 lists the top 10 country-sectors receiving U.S. investment based on total assets. Finance and Insurance (NAICS 52) and Management of Companies and Enterprises (NAICS 55) are the two main sectors. Given that NAICS 55 mainly comprises activities related to holding companies, Table 2 suggests that tax avoidance may be a significant motivation for outward U.S. investment in known tax havens such Luxembourg, Netherlands, and Ireland. \begin{table}[!ht] \centering \caption{Outward FDI of U.S. MNEs by Top Destinations and Sectors} \begin{tabular}{|l|l|l|l|l|l|l|} \hline Country & NAICS & Affiliates & Revenue & Employees & Total Assets & Fixed Assets \\ \hline UK & 52 & 1,497 & 85 & 78,209 & 3,363 & 174 \\ \hline UK & 55 & 2,239 & 78 & 105,788 & 1,913 & 854 \\ \hline Luxembourg & 55 & 2,576 & 36 & 4,647 & 1,591 & 1,334 \\ \hline Netherlands & 55 & 2,029 & 89 & 71,602 & 1,262 & 1,117 \\ \hline China & 52 & 78 & 14 & 29,330 & 536 & 494 \\ \hline Japan & 52 & 50 & 54 & 13,382 & 458 & 2 \\ \hline Ireland & 52 & 385 & 14 & 14,962 & 326 & 64 \\ \hline UK & 56 & 2,384 & 67 & 712,368 & 302 & 178 \\ \hline Ireland & 55 & 243 & 19 & 14,044 & 266 & 206 \\ \hline Germany & 55 & 621 & 32 & 92,393 & 214 & 128 \\ \hline \multicolumn{7}{l}{{\footnotesize{}{}Notes: Revenues, Total Assets and Fixed Assets in Billions of dollars. All variables averaged over time.}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}NAICS sectors 55: Management of Companies and Enterprises.}} \tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}NAICS sectors 52: Finance and Insurance.}}\tabularnewline \end{tabular} \end{table} \subsection{Other Data Sources for Regressions} The gravity regressions use covariates to control for country-pair heterogeneity, specifically for factors that influence $\omega_{ij}$. For our benchmark regressions that estimates U.S. bilateral outward FDI, we include the following variables: the log of (nominal) gross domestic product (GDP) at the destination (ln GDP), the log of the physical distance (weighted by population) between the home and host countries (ln Distance), a dummy variable that takes the value of 1 if the host is an island and zero otherwise (Island), a dummy variable that takes the value of 1 if the host is a landlocked country and zero otherwise (Landlocked), a binary indicator that takes a value of 1 if the home and host countries share a common legal system and zero otherwise (Common Legal Origin), a dummy variable that takes the value of 1 if the home and host countries share a common language and zero otherwise (Common Language), a binary indicator that takes a value of 1 if the host country is a member of the World Trade Organization and zero otherwise (WTO Member), a binary variable with the value of 1 if the host country is a member of the European Union and zero otherwise (EU Member), a dummy variable that takes the value of 1 if the home and host countries have a free trade agreement in force and zero otherwise (FTA), and a binary indicator with the value of 1 if the home and host countries have a bilateral investment treaty in force and zero otherwise (BIT). The source for all variables (except BIT) is the Dynamic Gravity Dataset (DGD) at the USITC's Gravity Portal \citep{Gurevich2018dynamic}. BIT came from UNCTAD. \section{Phantom FDI in outward U.S. investment activities \label{sec:results}} \subsection{Benchmark Estimates with Structural Gravity} Table \ref{tab:global} presents the gravity-equation coefficient estimates of \eqref{eq:gravity1} for various measures of U.S. outward FDI activity. Each column in table \ref{tab:global} represents a different FDI measure in MREID: number of affiliates, revenues, total assets, fixed assets, tangible fixed assets, and intangible fixed assets. The right-hand-side (RHS) variables of interest include traditional gravity model components like geographic distance, common legal origin, contiguity, colonial history, free trade agreements, and bilateral investment treaties. Recall that these regressions also include home and host country fixed effects, $\lambda_i$ and $\lambda_j$, respectively. We find that the coefficient estimates for distance are negative and statistically significant across all specifications, indicating that greater geographic distance reduces FDI---consistent with the predictions of the gravity model. Contiguity, colonial history, and shared legal origin display various relationships across the dependent variables. However, the only statistically significant coefficients for these variables are positive (as expected). %though not uniformly across all outcomes. Notably, the variable capturing colonial history has a strong positive impact on tangible fixed assets, suggesting that historical ties may influence specific types of capital allocation. In these results, only fixed asset investments have a statistically significant relationship with the FTA variable, and it is negative.\footnote{For more evidence of FTAs having negative effects on FDI, see \cite{Bergstrand2007} and \cite{bergstrand2024deep}.} Since the results reported in Table \ref{tab:global} use both origin and destination country fixed effects, they can account for any unobserved heterogeneity at the country-level. This is reflected in the relatively high $R^2$ values seen across specifications and indicates that the gravity model explains a substantial portion of the observed variance in the activities of MNEs across destination countries. The good fit of the gravity model suggests that we should obtain accurate estimates of phantom FDI. We now turn to our estimates of phantom FDI for U.S. MNEs using the gravity estimates in table \ref{tab:global}. Table \ref{tab:quantification_all_USA} provides values of the total FDI and the phantom FDI linked to U.S. foreign affiliates. The table showcases different FDI components, including numbers of affiliates,revenues, total assets, fixed assets, tangible fixed assets, and intangible fixed assets. The first row reports the actual values in MREID across these FDI measures. For instance, foreign affiliates of U.S. MNES collectively represent 89,901 units, with total revenues of \$4,964,481 million and total assets of \$21,801,645 million. Among these assets, \$10,493,457 million are fixed assets, while tangible and intangible fixed assets account for \$1,837,439 million and \$769,051 million, respectively. The second row highlights the level of FDI that can be classified as phantom FDI based on calculations from equation \eqref{eq:phantom1a}. The bottom row provides the shares of total U.S. FDI that we estimate to be as phantom FDI. We find that Phantom FDI constitutes a significant share of total FDI across various categories, notably making up 23.3\% of total revenues, 25.4\% of total assets, 18.4\% of fixed assets, and an even higher proportion of intangible assets (32.0\%). We note here that the share of phantom FDI in total revenues of U.S. affiliates is close to what was found by Guvenen et al. (2022). Overall, Table \ref{tab:quantification_all_USA} underscores the pervasive influence of phantom FDI within U.S. outward FDI, reflecting both tax-motivated structures and strategic financial positioning of U.S. MNEs. \begin{table}[htbp] \centering \global\long\def\sym#1{\ifmmode^{#1}\else$^{#1}$\fi}% \caption{Gravity-Equation Coefficient Estimates (All Country-Pairs) \label{tab:global}} \scalebox{0.9}{% \begin{tabular}{lcccccc} \toprule & \multicolumn{1}{c}{(1)} & \multicolumn{1}{c}{(2)} & \multicolumn{1}{c}{(3)} & \multicolumn{1}{c}{(4)} & \multicolumn{1}{c}{(5)} & \multicolumn{1}{c}{(6)}\tabularnewline & \multicolumn{1}{c}{Affiliates} & \multicolumn{1}{c}{Revenues} & \multicolumn{1}{c}{Total assets} & \multicolumn{1}{c}{Fixed assets} & \multicolumn{1}{c}{Tangible fixed} & \multicolumn{1}{c}{Intangible fixed}\tabularnewline \midrule lnDistance & -0.5761\sym{{*}{*}{*}} & -0.4003\sym{{*}{*}{*}} & -0.3754\sym{{*}{*}{*}} & -0.4862\sym{{*}{*}{*}} & -0.3703\sym{{*}{*}{*}} & -0.3063\sym{*}\tabularnewline & (0.05) & (0.05) & (0.10) & (0.09) & (0.08) & (0.16)\tabularnewline \addlinespace Common Legal Origin & 0.3707\sym{{*}{*}} & 0.2911 & 0.3936\sym{*} & -0.0850 & -0.4595 & 1.2459\sym{{*}{*}{*}}\tabularnewline & (0.17) & (0.20) & (0.23) & (0.25) & (0.31) & (0.33)\tabularnewline \addlinespace Contiguity & 0.5557\sym{{*}{*}{*}} & 0.2581 & 0.4727\sym{*} & 0.0964 & 0.6769\sym{{*}{*}{*}} & -0.0637\tabularnewline & (0.11) & (0.17) & (0.27) & (0.27) & (0.24) & (0.34)\tabularnewline \addlinespace Colony & 0.4113\sym{{*}{*}{*}} & 0.5161\sym{{*}{*}{*}} & 0.2472 & 0.1018 & 1.3021\sym{{*}{*}{*}} & -0.4863\tabularnewline & (0.15) & (0.20) & (0.22) & (0.25) & (0.27) & (0.37)\tabularnewline \addlinespace FTA & -0.1139 & 0.0573 & -0.0608 & -0.4031\sym{*} & 0.0830 & -0.2357\tabularnewline & (0.13) & (0.14) & (0.18) & (0.21) & (0.16) & (0.34)\tabularnewline \addlinespace BIT & 0.0035 & -0.2467 & -0.2502 & -0.0572 & -0.0187 & 0.2454\tabularnewline & (0.15) & (0.18) & (0.22) & (0.17) & (0.16) & (0.31)\tabularnewline \midrule Observations & 3225 & 3225 & 3225 & 3135 & 3135 & 3077\tabularnewline $R^{2}$ & 0.888 & 0.825 & 0.838 & 0.883 & 0.824 & 0.781\tabularnewline \midrule \multicolumn{7}{l}{{\footnotesize{}{}PPML, Robust standard errors in (), clustered by country pair}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}Cross section, year 2019. Origin and destination country fixed effects included}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}\sym{*} $p<0.10$, \sym{{*}{*}} $p<0.05$, \sym{{*}{*}{*}} $p<0.01$}}\tabularnewline \end{tabular}} \end{table} \begin{table}[t] \caption{Quantification (USA using All Country-Pairs)\label{tab:quantification_all_USA}} \centering \scalebox{0.8}{ \begin{tabular}{lcccccc} & Affiliates & Revenue & Total Assets & Fixed Assets & Tangible & Intangible\tabularnewline \hline Total FDI & 89,901 & 4,964,481 & 21,801,645 & 10,493,457 & 1,837,439 & 769,051 \tabularnewline Phantom FDI & 15,542 & 1,159,094 & 5,553,177 & 1,931,544 & 380,683 & 245,789 \tabularnewline Phantom FDI/Total FDI & 0.178 & 0.233 & 0.254 & 0.184 & 0.207 & 0.320\tabularnewline \hline \multicolumn{7}{l}{Notes: Affiliates: number of foreign affiliates. Rest of variables in million USD}\tabularnewline \end{tabular}} \end{table} While Table \ref{tab:quantification_all_USA} provides the aggregate value of phantom FDI undertaken by U.S. MNEs, we can also explore the level of outward U.S. phantom FDI by host countires. Figure \ref{fig:phantom_all_USA} shows the details of phantom FDI for the first 35 country destinations of American FDI using all countries in the sample. The figure reports the level of phantom FDI being generated by foreign affiliates of U.S. GUOs across these FDI categories: numbers of affiliates, revenues, total assets, fixed assets, tangible fixed assets, and intangible fixed assets. Figure \ref{fig:phantom_extensive_all_US} shows that the United Kingdom, Luxembourg, and Netherlands are the top three destinations of U.S. outward phantom FDI, based on their number of U.S. affiliates. The actual number of U.S. affiliates in these three countries exceeds the number predicted by structural gravity by more than 10,000 affiliates. Focusing on the revenues of foreign affiliates of U.S. MNEs, Figure \ref{fig:phantom_revenue_all_US} shows that Ireland, Netherlands, and Singapore are the top three destinations for U.S. outward Phantom FDI with actual revenues exceeding predicted revenues by around \$300 billion, \$150 billion, and \$100 billion respectively. Rounding out the top 10 countries associated with Phantom revenues are the United Kingdom, Belgium, Germany, Luxembourg, Japan, India, and Italy. Moving towards the assets of U.S. foreign affiliates, figure \ref{fig:phantom_totalassets_all_US} finds a similar pattern with Luxembourg, UK, and Ireland being the top three destinations of U.S. outward Phantom FDI. For each of these three countries, the actual value of total assets held by U.S. MNEs through their foreign affiliates in MREID exceeded the value predicted by structural gravity by more that a \$1 trillion. Results are similar when we move beyond total assets, as seen in figure \ref{fig:phantom_fixedassets_all_US}, to fixed assets, with Luxembourg, Ireland, and Netherlands being the top three destinations of U.S. outward Phantom FDI. MREID also allows us to distinguish between fixed assets as either tangible or intangible. Figures \ref{fig:phantom_tangible_all_US} and \ref{fig:phantom_intangible_all_US} highlight a diverse set of motivations may be behind phantom FDI. Both Netherlands and the Ireland are considered to have favorable investment regimes. Yet, U.S. MNEs prefer to hold tangible assets in the Netherlands and keep intangible assets in Ireland. This reflects the importance of tax considerations and the regulatory and legal environment facilitating holding structures, emphasizing the role of firm-specific optimization strategies in shaping FDI in this category. Future studies can further focus on these differences to better understand how certain polices are better at attracting investments aimed at maximizing global profits through tax mitigation strategies. %Finally, investments in intangible fixed assets, such as intellectual property, show a complex pattern driven by a mix of political risk and tax considerations. At the same time, Ireland's tax-friendly policies and traditional tax havens like Bermuda continue to draw intangible investments, emphasizing the role of tax optimization in shaping FDI flows in this category. %The analysis of FDI ratios using our model reveals several important findings regarding the locations where U.S. outward FDI is directed, particularly concerning tax havens and the strategic factors influencing investment flows. First, gravity models successfully identify traditional tax havens such as Bermuda, the Cayman Islands, Barbados, Luxembourg, Singapore, and the Marshall Islands as key destinations for revenue-related FDI. These locations are known for their favorable tax regimes, attracting investments aimed at maximizing profit through tax minimization strategies. %The results in terms of ranking are similar to those reported in Figure \ref{fig:phantomUSA}, which used only the United States as the origin country in the gravity-equation estimation. %However, as expected from the summary reported in Table \ref{tab:quantification_all_USA}. \renewcommand\figureplace{\floatplace{figure}} \begin{figure} \caption{USA's Outward Phantom FDI (using Structural Gravity with All Country-Pairs)} % Alt Text: Figure 2 is comprised of six seperate bar charts showing the top destination countries recieving Phantom FDI from American MNEs. Figure 2(a) shows number of affiliates, figure 2(b) shows revenues, figure 2(c) shows total assets, figure 2(d) shows fixed assets, figure 2(e) shows tangible fixed assets, and figure 2(f) shows intangible fixed assets. \label{fig:phantom_all_USA} \centering \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Number Affiliates} \label{fig:phantom_extensive_all_US} \includegraphics[width=1\textwidth]{figures/phantom_extensive_all_US} \end{subfigure} \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Revenue from affiliates} \label{fig:phantom_revenue_all_US} \includegraphics[width=1\textwidth]{figures/phantom_revenue_all_US} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \centering \caption{USA's Outward Phantom FDI (using Structural Gravity with all countries) (cont.)} \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Total Assets} \label{fig:phantom_totalassets_all_US} \includegraphics[width=1\textwidth]{figures/phantom_totalassets_all_US} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Fixed Assets } \label{fig:phantom_fixedassets_all_US} \includegraphics[width=1\textwidth]{figures/phantom_fixedassets_all_US} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \centering \caption{USA's Outward Phantom FDI (using Structural Gravity with all countries) (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Tangible Fixed Assets \label{fig:phantom_tangible_all_US}} \includegraphics[width=1\textwidth]{figures/phantom_tangible_all_US} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Intangible Fixed Assets \label{fig:phantom_intangible_all_US}} \includegraphics[width=1\textwidth]{figures/phantom_intangible_all_US} \end{subfigure} \end{figure} \begin{comment} Table \ref{tab:US} presents gravity-equation coefficient estimates for various measures of U.S. outward FDI activity based upon the estimation of equation \eqref{eq:gravity2}. These various measures of FDI serve as the dependent variables. Each column represents a different FDI measure: number of affiliates, revenues, total assets, fixed assets, tangible fixed assets, and intangible fixed assets. The right-hand-side (RHS) variables include the standard gravity-model independent variables described earlier. % such as the GDP of the destination country, geographic %distance, and additional factors like whether the destination country %is an island, landlocked, or shares a common legal origin with the USA. \begin{table}[htbp] \centering \global\long\def\sym#1{\ifmmode^{#1}\else$^{#1}$\fi}% \caption{Gravity-Equation Coefficient Estimates (U.S. Bilateral Outward FDI) \label{tab:US}} \scalebox{0.8}{ % \begin{tabular}{lcccccc} \toprule & \multicolumn{1}{c}{(1)} & \multicolumn{1}{c}{(2)} & \multicolumn{1}{c}{(3)} & \multicolumn{1}{c}{(4)} & \multicolumn{1}{c}{(5)} & \multicolumn{1}{c}{(6)}\tabularnewline & \multicolumn{1}{c}{Affiliates} & \multicolumn{1}{c}{Revenues} & \multicolumn{1}{c}{Total assets} & \multicolumn{1}{c}{Fixed assets} & \multicolumn{1}{c}{Tangible fixed} & \multicolumn{1}{c}{Intangible fixed}\tabularnewline \midrule lnGDP (destination) & 0.7057\sym{***}& 0.7360\sym{***}& 0.4822\sym{***}& 0.2185 & 0.4754\sym{***}& 0.4717\sym{**} \\ & (0.09) & (0.10) & (0.17) & (0.21) & (0.18) & (0.22) \\ \addlinespace lnDistance & 0.0019 & 0.6906 & -0.1522 & 0.0456 & -0.1732 & -0.0281 \\ & (0.47) & (0.62) & (0.54) & (0.87) & (0.45) & (0.78) \\ \addlinespace Island & 0.0418 & 0.1285 & 1.3039\sym{**} & -0.2371 & 0.8254 & -0.1861 \\ & (0.31) & (0.54) & (0.59) & (0.84) & (0.52) & (0.98) \\ \addlinespace Landlocked & 0.6787 & -0.3597 & 1.0477 & 0.9494 & -1.7743 & -0.5926 \\ & (0.43) & (0.63) & (0.88) & (0.92) & (1.11) & (0.83) \\ \addlinespace Common Legal Origin & 1.0951\sym{***}& 0.6388 & 0.8742 & 2.1177\sym{**} & 0.2886 & -0.2981 \\ & (0.40) & (0.73) & (0.97) & (1.01) & (0.68) & (1.22) \\ \addlinespace Common Language & 0.3062 & 0.0647 & -0.1205 & -0.0551 & -1.2690 & 1.8468\sym{*} \\ & (0.34) & (0.49) & (0.92) & (0.99) & (0.95) & (0.96) \\ \addlinespace WTO member & 0.7498 & 0.0087 & -0.3465 & -0.0137 & 0.0896 & -2.2579\sym{**} \\ & (0.86) & (0.88) & (1.01) & (0.95) & (1.04) & (1.11) \\ \addlinespace EU member & 1.6983\sym{***}& 1.8268\sym{***}& 2.5764\sym{***}& 4.1878\sym{***}& 2.8493\sym{***}& 4.5283\sym{***}\\ & (0.32) & (0.34) & (0.50) & (0.81) & (0.62) & (0.81) \\ \addlinespace FTA & 0.4875 & 1.4415\sym{*} & 1.7662\sym{**} & 3.2050\sym{**} & 2.5970\sym{***}& 2.9064\sym{***}\\ & (0.75) & (0.81) & (0.74) & (1.25) & (0.72) & (1.04) \\ \addlinespace BIT & -0.3432 & -1.1001\sym{***}& -2.8495\sym{***}& -3.7125\sym{***}& -2.3713\sym{**} & -3.0056\sym{***}\\ & (0.33) & (0.42) & (0.71) & (0.77) & (1.00) & (0.69) \\ \midrule Observations & 111 & 111 & 111 & 111 & 111 & 111\tabularnewline $R^{2}$ & 0.808 & 0.737 & 0.729 & 0.638 & 0.554 & 0.619\tabularnewline \midrule \multicolumn{7}{l}{Robust {\footnotesize{}{}US outward FDI, year 2019}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}PPML, Robust standard errors in parenthesis, clustered by country pair}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}\sym{*} $p<0.10$, \sym{{*}{*}} $p<0.05$, \sym{{*}{*}{*}} $p<0.01$}}\tabularnewline \end{tabular}} \end{table} GDP of the destination country has a positive and statistically significant effect in all but one specification, suggesting that U.S. outward FDI tends to flow to larger economies, consistent with our theoretical foundations. Interestingly, the coefficient estimate for distance is insignificant, which is uncommon for most gravity-equation coefficient estimates. However, this is explained by the presence of numerous binary RHS variables reflecting ``policy'' connections. In particular, the coefficient estimate for whether destination country $j$ is a European Union (EU) member is highly correlated with the distance variable. In the Appendix, we show that the exclusion of policy-related bilateral variables restores the distance coefficient estimate to standard negative values. This multicollinearity bias is not a concern for our purposes, since our focus is only on the ``predicted'' FDI value (or potential FDI). As shown in Appendix Table 7, the correlation coefficient between the predicted values of the two specifications, for each of the six measures of activity, is 0.999. We will also see later in the first robustness analysis that distance will have the expected negative effect when we use a much larger cross-section. Common legal origin has a large, positive, and statistically significant effect on FDI measures, as does the membership of the destination country in the EU. Common membership in an economic integration agreement (FTA) has a significant effect; in many FTAs, investment provisions can positively affect bilateral FDI. The negative and statistically significant effects of bilateral investment treaties (BITs) are likely attributable here to the selection of BITs by the U.S. government into host countries with weak institutional protections and associated low levels of FDI (such as many developing countries). %which may reflect the modern ability of %firms to overcome geographic barriers in FDI. Membership of the destination country in the European Union and the existence of free trade agreements show strong positive effects across several specifications, indicating that institutional and policy ties play a key role in facilitating U.S. outward FDI. %The impact of bilateral investment treaties (BIT) is notably negative and significant, suggesting that BITs may not promote U.S. outward FDI, which could reflect complexities in investment protection or compliance costs. The relatively high $R^{2}$ values across specifications indicate that the model explains a substantial portion of the variance in U.S. FDI flows across destination countries. The results of applying our methodology to identify bilateral outward phantom FDI for U.S. MNEs in foreign countries are summarized in two figures below. Figure \ref{fig:potentialsUSA} reports the FDI ``ratios'' identified using equation \eqref{eq:ratio2}. Figure \ref{fig:phantomUSA} reports the \textit{value} of U.S. outward phantom FDI based upon our model. Both figures report the results for the numbers of affiliates, revenues, total assets, fixed assets, tangible fixed assets, and intangible fixed assets for foreign affiliates of U.S. GUOs. Figure \ref{fig:potentialsUSA} reports the ``FDI ratios'' for U.S. outward FDI. Except possibly for Ukraine, the ranking of ratios obtained for the number of affiliates in Figure \ref{fig:potential_extensive} are in line with economic intuition. Ukraine, Singapore, and Luxembourg lead the ranking of the ratios of U.S. foreign affiliates. The number of foreign affiliates in Ukraine, Singapore, and Luxembourg is 9, 7, and 6 times higher than expected from theory, respectively. \renewcommand\figureplace{\floatplace{figure}} \begin{figure} \caption{USA's FDI ratios ($FDI^{Ratio}>1$)} % Alt Text: Figure 23 is comprised of six line charts showing aggregate revenue, employees, total assets, fixed assets, number of affiliates, and revenue over time, from 2010 to 2022. \label{fig:potentialsUSA} \centering \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Number Affiliates} \label{fig:potential_extensive} \includegraphics[width=1\textwidth]{figures/potential_extensive} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \caption{Revenue from affiliates} \label{fig:potential_revenue} \includegraphics[width=1\textwidth]{figures/potential_revenue} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \caption{USA's FDI ratios ($FDI^{Ratio}>1$) (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Total Assets} \label{fig:potential_totalassets} \includegraphics[width=1\textwidth]{figures/potential_totalassets} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Fixed Assets } \label{fig:potential_fixedassets} \includegraphics[width=1\textwidth]{figures/potential_fixedassets} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure} \ContinuedFloat \caption{USA's FDI ratios ($FDI^{Ratio}>1$) (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Tangible Fixed Assets \label{fig:potential_tangible}} \includegraphics[width=1\textwidth]{figures/potential_tangible} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Intangible Fixed Assets \label{fig:potential_intangible}} \includegraphics[width=1\textwidth]{figures/potential_intangible} \end{subfigure} \end{figure} \renewcommand\figureplace{\floatplace{figure}} U.S. FDI ratios of revenues (Figure \ref{fig:potential_revenue}), total assets (Figure \ref{fig:potential_totalassets}), fixed assets (Figure \ref{fig:potential_fixedassets}), tangible fixed assets (Figure \ref{fig:potential_tangible}) and intangible fixed assets (Figure \ref{fig:potential_intangible}) reveal interesting characteristics. For affiliate revenues, Bermuda, Barbados, Luxembourg, Singapore, Ireland, Ukraine, the Cayman Islands, and Russia lead the ranking of FDI ratios. All these countries have been categorized as tax havens or have beneficial corporate tax conditions. The revenues obtained by American affiliates in Bermuda are nearly 20 times higher than predicted by theory. In the rest of the leading countries, US affiliates have around five times higher revenues than expected. The same countries lead the ranking of total assets (Ukraine, Russia, Singapore, Luxembourg, Ireland) with actual FDI values more than ten times than expected for the two leading countries. Fixed assets are led by Russia, with an actual value of more than 60 times than expected, followed by Ukraine (nearly $\times40$ times). The rest of the countries in the ranking show much lower ratios regarding fixed assets. The ranking of FDI ratios of tangible fixed assets is led by the Marshall Islands, followed by the Netherlands, India, Ukraine, and Russia. Another former Soviet Republic, Georgia, leads the intangible asset ranking, followed by Russia, Ukraine and Norway. The analysis of FDI ratios using our model reveals several important findings regarding the locations where U.S. outward FDI is directed, particularly concerning tax havens and the strategic factors influencing investment flows. First, gravity models successfully identify traditional tax havens such as Bermuda, the Cayman Islands, Barbados, Luxembourg, Singapore, and the Marshall Islands as key destinations for revenue-related FDI. These locations are known for their favorable tax regimes, attracting investments aimed at maximizing profit through tax minimization strategies. Moreover, when examining the distribution of FDI based on the number of affiliates, total assets, and fixed assets, the data suggest that geo-strategic risks play a significant role. For instance, countries like Ukraine, especially in politically uncertain periods such as 2019, emerge as important considerations for multinational firms. These firms may be motivated by proximity to markets or natural resources but must weigh these benefits against the risks posed by political instability or geo-political tensions. The findings regarding tangible fixed assets highlight a diverse set of motivations for FDI. While tax havens continue attracting investment, countries with favorable holding laws, such as the Netherlands, stand out as major destinations. This reflects the importance of tax considerations and the regulatory and legal environment facilitating holding structures, allowing firms to manage their global assets efficiently. Finally, investments in intangible fixed assets, such as intellectual property, show a complex pattern driven by a mix of political risk and tax considerations. Countries like Russia and Georgia, with higher political risks, attract FDI in intangibles, possibly due to strategic positioning or market potential. Overall, the results of our analysis for U.S. affiliates suggest that most conduit FDI of American affiliates is channeled through the area of Russian influence, as well as tax havens. At the same time, Ireland's tax-friendly policies and traditional tax havens like Bermuda continue to draw intangible investments, emphasizing the role of tax optimization in shaping FDI flows in this category. We focus next on Figure \ref{fig:phantomUSA}, \textit{values} (in millions of U.S. dollars, or USD) of phantom FDI. Regarding the number of affiliates in Figure \ref{fig:phantom_extensive}, the Netherlands, Luxembourg, Brazil, Singapore, and India lead the ranking of the United States' phantom outward FDI. For the first three countries, actual FDI exceeds potential FDI by more than 3,000 affiliates. Note that Ukraine occupies the 9th place with around 500 more American affiliates than expected. \renewcommand\figureplace{\floatplace{figure}} \begin{figure} \caption{USA's Outward Phantom FDI} % Alt Text: Figure 23 is comprised of six line charts showing aggregate revenue, employees, total assets, fixed assets, number of affiliates, and revenue over time, from 2010 to 2022. \label{fig:phantomUSA} \centering \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Number of Affiliates} \label{fig:phantom_extensive} \includegraphics[width=1\textwidth]{figures/phantom_extensive} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Revenues from Affiliates} \label{fig:phantom_revenue} \includegraphics[width=1\textwidth]{figures/phantom_revenue} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \centering \caption{USA's Outward Phantom FDI (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Total Assets} \label{fig:phantom_totalassets} \includegraphics[width=1\textwidth]{figures/phantom_totalassets} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Fixed Assets } \label{fig:phantom_fixedassets} \includegraphics[width=1\textwidth]{figures/phantom_fixedassets} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \centering \caption{USA's Outward Phantom FDI (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Tangible Fixed Assets \label{fig:phantom_tangible}} \includegraphics[width=1\textwidth]{figures/phantom_tangible} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Intangible Fixed Assets \label{fig:phantom_intangible}} \includegraphics[width=1\textwidth]{figures/phantom_intangible} \end{subfigure} \end{figure} The values of U.S. outward phantom revenues (Figure \ref{fig:phantom_revenue}), total assets (Figure \ref{fig:phantom_totalassets}), fixed assets (Figure \ref{fig:phantom_fixedassets}), tangible fixed assets (Figure \ref{fig:phantom_tangible}) and intangible fixed assets (Figure \ref{fig:phantom_intangible}) reveal noteworthy characteristics. Phantom FDI revenues from American affiliates abroad is highest in Singapore, Ireland, Netherlands, and Luxembourg. American foreign affiliates' revenues in Singapore exceed 400,000 USD million the predicted revenues of the gravity equation. The same countries lead the ranking of phantom FDI for total and fixed assets (Luxembourg, Netherlands, Ireland, and Singapore, in that order for both assets). Tangible fixed assets are dominated by the Netherlands, which has phantom FDI of 800,000 USD million. On the other hand, intangible fixed assets are estimated to be dominated by Ireland, with over 250,000 USD million in phantom FDI, followed at a large distance by Singapore, Netherlands, Australia, Luxembourg, and Bermuda. Table \ref{tab:quantificationUSA} provides values of the total FDI and the phantom FDI linked to U.S. foreign affiliates. The table showcases different FDI components, including numbers of affiliates, revenues, total assets, fixed assets, tangible fixed assets, and intangible fixed assets. \begin{table} \caption{Quantification (USA)\label{tab:quantificationUSA}} \centering \scalebox{0.8}{ \begin{tabular}{lcccccc} & Affiliates & Revenue & Total Assets & Fixed Assets & Tangible & Intangible\tabularnewline \hline Total FDI & 89,901 & 4,964,481 & 21,801,645 & 10,493,457 & 1,837,439 & 769,051 \tabularnewline Phantom FDI & 21,728 & 1,585,292 & 7,938,508 & 5,259,637 & 1,098,088 & 411,937\tabularnewline Phantom FDI/Total FDI & 0.242 & 0.319 & 0.364 & 0.501 & 0.597 & 0.535\tabularnewline \hline \multicolumn{7}{l}{Notes: Affiliates: number of foreign affiliates. Rest of variables in million USD}\tabularnewline \end{tabular}} \end{table} The first row reports the total FDI across these categories. For instance, U.S. affiliates collectively represent 89,901 units, with total revenues of \$4,964,481 million and total assets of \$21,801,645 million. Among these assets, \$10,493,457 million are fixed assets, while tangible and intangible fixed assets account for \$1,837,439 million and \$769,051 million, respectively. The second row highlights the substantial portion of FDI classified as phantom. The values for phantom FDI in revenues are similar to those reported by \citet{guvenen2022offshore}. The bottom row of the table provides the shares of total FDI that we estimated as phantom FDI. Phantom FDI constitutes a significant share of total FDI across various categories, notably making up 36.4\% of total assets, 50.1\% of fixed assets, and an even higher proportion of tangible (59.7\%) and intangible (53.5\%) assets. These figures underscore the pervasive influence of phantom FDI within U.S. outward foreign direct investment, reflecting both tax-motivated structures and strategic financial positioning. \end{comment} \begin{comment} \subsection{Robustness Method 1: Structural Gravity using All Countries} Section \ref{sec:methodd} described the methodology for estimating phantom FDI using the gravity equation for a much larger cross-section sample using equation \eqref{eq:gravity1}. Table \ref{tab:global} presents the gravity-equation coefficient estimates for various independent variables across six specifications. Each column corresponds to a different outcome variable: number of affiliates, revenues, fixed assets, tangible fixed assets, and intangible fixed assets. Recall that these regressions include home and host country fixed effects, $\lambda_i$ and $\lambda_j$, respectively. The independent variables of interest include traditional gravity model components like geographic distance, common legal origin, contiguity, colonial history, free trade agreements, and bilateral investment treaties. The coefficient estimates for distance are now negative and statistically significant across all specifications, indicating that greater geographic distance reduces FDI, consistent with the predictions of the gravity model. Contiguity, colonial history, and shared legal origin display various relationships across the dependent variables. However, the only statistically significant coefficients for these variables are positive (as expected). %though not uniformly across all outcomes. Notably, the variable capturing colonial history has a strong positive impact on tangible fixed assets, suggesting that historical ties may influence specific types of capital allocation.\footnote{Note that the variables included in Table \ref{tab:global} are slightly different from those in Table \ref{tab:US} because the host and home country fixed effects are collinear with country-specific variables, including island, landlocked, WTO member (host), and EU member (host).} In these results, only fixed asset investments have a statistically significant relationship with the FTA variable, and it is negative.\footnote{For more evidence of FTAs having negative effects on FDI, see \cite{Bergstrand2007} and \cite{bergstrand2024deep}.} The results reported in Table \ref{tab:global} use origin and destination country fixed effects to account for multilateral resistance terms. These fixed effects control better for unobserved heterogeneity than the observable variables included in Table \ref{tab:US}. Thus, this specification is not only closer to the theory outlined earlier but has better predictive power. Importantly, the values of the $R^2$ are higher in all instances using all countries in Table \ref{tab:global} than using only one country (the USA) in Table \ref{tab:US}. The better fit suggests that we should obtain better estimates of U.S. phantom FDI. The more precise estimates using all countries yield more conservative values of U.S. outward phantom FDI, which are summarized in Table \ref{tab:quantification_all_USA}, than the single case (reported in Table \ref{tab:quantificationUSA}). The phantom FDI for the number of affiliates is now 17.8\% of the total, 6.4 percentage points lower than the single country estimate. The estimates of phantom FDI for revenues using all countries in the sample are 23.3\%, which is 8.6 percentage points lower than the single country estimate. \begin{table}[htbp] \centering \global\long\def\sym#1{\ifmmode^{#1}\else$^{#1}$\fi}% \caption{Gravity-Equation Coefficient Estimates (All Country-Pairs) \label{tab:global}} \scalebox{0.9}{% \begin{tabular}{lcccccc} \toprule & \multicolumn{1}{c}{(1)} & \multicolumn{1}{c}{(2)} & \multicolumn{1}{c}{(3)} & \multicolumn{1}{c}{(4)} & \multicolumn{1}{c}{(5)} & \multicolumn{1}{c}{(6)}\tabularnewline & \multicolumn{1}{c}{Affiliates} & \multicolumn{1}{c}{Revenues} & \multicolumn{1}{c}{Total assets} & \multicolumn{1}{c}{Fixed assets} & \multicolumn{1}{c}{Tangible fixed} & \multicolumn{1}{c}{Intangible fixed}\tabularnewline \midrule lnDistance & -0.5761\sym{{*}{*}{*}} & -0.4003\sym{{*}{*}{*}} & -0.3754\sym{{*}{*}{*}} & -0.4862\sym{{*}{*}{*}} & -0.3703\sym{{*}{*}{*}} & -0.3063\sym{*}\tabularnewline & (0.05) & (0.05) & (0.10) & (0.09) & (0.08) & (0.16)\tabularnewline \addlinespace Common Legal Origin & 0.3707\sym{{*}{*}} & 0.2911 & 0.3936\sym{*} & -0.0850 & -0.4595 & 1.2459\sym{{*}{*}{*}}\tabularnewline & (0.17) & (0.20) & (0.23) & (0.25) & (0.31) & (0.33)\tabularnewline \addlinespace Contiguity & 0.5557\sym{{*}{*}{*}} & 0.2581 & 0.4727\sym{*} & 0.0964 & 0.6769\sym{{*}{*}{*}} & -0.0637\tabularnewline & (0.11) & (0.17) & (0.27) & (0.27) & (0.24) & (0.34)\tabularnewline \addlinespace Colony & 0.4113\sym{{*}{*}{*}} & 0.5161\sym{{*}{*}{*}} & 0.2472 & 0.1018 & 1.3021\sym{{*}{*}{*}} & -0.4863\tabularnewline & (0.15) & (0.20) & (0.22) & (0.25) & (0.27) & (0.37)\tabularnewline \addlinespace FTA & -0.1139 & 0.0573 & -0.0608 & -0.4031\sym{*} & 0.0830 & -0.2357\tabularnewline & (0.13) & (0.14) & (0.18) & (0.21) & (0.16) & (0.34)\tabularnewline \addlinespace BIT & 0.0035 & -0.2467 & -0.2502 & -0.0572 & -0.0187 & 0.2454\tabularnewline & (0.15) & (0.18) & (0.22) & (0.17) & (0.16) & (0.31)\tabularnewline \midrule Observations & 3225 & 3225 & 3225 & 3135 & 3135 & 3077\tabularnewline $R^{2}$ & 0.888 & 0.825 & 0.838 & 0.883 & 0.824 & 0.781\tabularnewline \midrule \multicolumn{7}{l}{{\footnotesize{}{}PPML, Robust standard errors in (), clustered by country pair}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}Cross section, year 2019. Origin and destination country fixed effects included}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}\sym{*} $p<0.10$, \sym{{*}{*}} $p<0.05$, \sym{{*}{*}{*}} $p<0.01$}}\tabularnewline \end{tabular}} \end{table} \begin{table} \caption{Quantification (USA using All Country-Pairs)\label{tab:quantification_all_USA}} \centering \scalebox{0.8}{ \begin{tabular}{lcccccc} & Affiliates & Revenue & Total Assets & Fixed Assets & Tangible & Intangible\tabularnewline \hline Total FDI & 89,901 & 4,964,481 & 21,801,645 & 10,493,457 & 1,837,439 & 769,051 \tabularnewline Phantom FDI & 15,542 & 1,159,094 & 5,553,177 & 1,931,544 & 380,683 & 245,789 \tabularnewline Phantom FDI/Total FDI & 0.178 & 0.233 & 0.254 & 0.184 & 0.207 & 0.320\tabularnewline \hline \multicolumn{7}{l}{Notes: Affiliates: number of foreign affiliates. Rest of variables in million USD}\tabularnewline \end{tabular}} \end{table} The quantification of phantom FDI for total assets (25.4\%), fixed assets (18.4\%), tangible fixed assets (20.7\%), and intangible fixed assets (32.0\%), are 11, 31.7, 39, and 21.5 percentage points lower, respectively. Figure \ref{fig:phantom_all_USA} shows the details of phantom FDI for the first 35 country destinations of American foreign investment using all countries in the sample. The results in terms of ranking are similar to those reported in Figure \ref{fig:phantomUSA}, which used only the United States as the origin country in the gravity-equation estimation. %However, as expected from the summary reported in Table \ref{tab:quantification_all_USA}. \renewcommand\figureplace{\floatplace{figure}} \begin{figure} \caption{USA's Outward Phantom FDI (using Structural Gravity with All Country-Pairs)} % Alt Text: Figure 3 is a bar chart showing the top destinations for U.S. phantom FDI based on the production-function approach. \label{fig:phantom_all_USA} \centering \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Number Affiliates} \label{fig:phantom_extensive_all_US} \includegraphics[width=1\textwidth]{figures/phantom_extensive_all_US} \end{subfigure} \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Revenue from affiliates} \label{fig:phantom_revenue_all_US} \includegraphics[width=1\textwidth]{figures/phantom_revenue_all_US} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \centering \caption{USA's Outward Phantom FDI (using Structural Gravity with all countries) (cont.)} \begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Total Assets} \label{fig:phantom_totalassets_all_US} \includegraphics[width=1\textwidth]{figures/phantom_totalassets_all_US} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Fixed Assets } \label{fig:phantom_fixedassets_all_US} \includegraphics[width=1\textwidth]{figures/phantom_fixedassets_all_US} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure}\ContinuedFloat \centering \caption{USA's Outward Phantom FDI (using Structural Gravity with all countries) (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Tangible Fixed Assets \label{fig:phantom_tangible_all_US}} \includegraphics[width=1\textwidth]{figures/phantom_tangible_all_US} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \subcaption{Intangible Fixed Assets \label{fig:phantom_intangible_all_US}} \includegraphics[width=1\textwidth]{figures/phantom_intangible_all_US} \end{subfigure} \end{figure} For example, regarding revenues, the top 3 phantom destinations are Ireland, Singapore, and the Netherlands in both cases. However, in Figure \ref{fig:phantom_revenue_all_US}, the U.S. phantom FDI corresponding to revenues in Singapore exceeds \$400,000 million. By contrast, the results for U.S. phantom FDI corresponding to revenues in Singapore exceeded \$100,000 million in Figure \ref{fig:phantom_revenue}. Focusing on intangible fixed assets, the top 3 phantom destinations are Ireland, Singapore, and the Netherlands in both cases. However, in Figure \ref{fig:phantom_intangible_all_US}, the U.S. phantom FDI corresponding to intangible assets in Ireland is around \$175,000 million. The results for U.S. phantom FDI corresponding to intangible assets in Ireland was \$250,000 million in Figure \ref{fig:phantom_intangible}. \end{comment} \subsection{Estimates with a Production-Function Approach} %As a first robustness analysis of our estimates of phantom FDI, we also consider measuring As a robustness exercise, we next apply a production-function approach to measure U.S. phantom FDI to various destinations ($j$) using the data from MREID. The methodology we use is similar to the methodology developed in \citet{guvenen2022offshore}. In this approach, we impute the revenues of each destination's foreign affiliates of U.S. MNEs. We do this by estimating the relationship between the revenues of these U.S. foreign affiliates with the capital and labor inputs used by these foreign affiliates. Specifically, we use the Cobb-Douglas production function: \[ R_{USA,j}^{imp} = \gamma K_{j}^{\alpha} L_{j}^{1-\alpha} \] where \( R_{USA,j}^{imp} \) represents the imputed revenue for U.S. affiliates in \( j \), \( K_{j} \) denotes the capital stock, and \( L_{j} \) represents labor stock. The parameters \( \alpha \) and \( 1 - \alpha \) represent, respectively, the share of income going to capital and to labor, %the elasticity of output with respect to capital and labor, respectively and \( \gamma \) is a constant term representing productivity. This approach estimates revenues based on observable inputs and can be compared to \textit{actual} reported revenues ($R^{act}_{USA,j}$) to identify potential discrepancies associated with phantom FDI. We choose $\alpha=0.4$ and calibrate $\gamma=25.933$ to match U.S. domestic revenues and factor endowments. Accordingly, phantom FDI can be represented by: \begin{equation}\label{Eq4} {R}_{USA,j}^{Phantom}\equiv R^{act}_{USA,j}-R^{imp}_{USA,j}. \end{equation} The results obtained with the production-function approach reported in Figure \ref{fig:phantom_production} are qualitatively and quantitatively similar to those obtained with the gravity-equation approach in section \ref{sec:results}. %(reported in Figure \ref{fig:phantom_revenue}). Singapore and Ireland are the leading countries in both cases. The gravity-equation approach seems more conservative than the production-function approach regarding Singapore's phantom FDI. The production-function result indicates that American affiliates' actual revenues in Singapore exceed by more than \$500,000 million the predicted revenues. With the structural gravity estimate using all countries, the estimate is around \$100,000 million. Considering that Singapore's GDP was \$377,000 million in 2019, the structural gravity approach seems more reasonable. \begin{figure} \caption{Phantom Revenues (Production-Function Approach)\label{fig:phantom_production} } \includegraphics[scale=0.4]{figures/phantom_revenue_production} \end{figure} Table \ref{tab:quantificationUSArob} quantifies the total revenues from all destinations using the production-function approach and comparing the results to those obtained earlier with the gravity-equation approach. The results confirm that Phantom FDI, as measured by the revenues of U.S. foreign affiliates, are much lower using the structural gravity approach than the production-function approach. \begin{table} \caption{Gravity-Equation vs. Production-Function Approaches for Phantom FDI\label{tab:quantificationUSArob}} \centering % \begin{tabular}{lcc} & Structural Gravity & Production Function \tabularnewline \hline Total FDI & 4,964,481 & 4,964,481 \tabularnewline Phantom FDI & 1,159,094 & 1,906,369\tabularnewline Phantom FDI Fraction & 0.233 & 0.384\tabularnewline \hline \multicolumn{3}{l}{Million USD}\tabularnewline \end{tabular} \end{table} %confirming the robustness of the gravity model's ability to detect phantom FDI, albeit with slightly more conservative estimates. The structural gravity approach delivers the most conservative estimates, with only 23.3\% of phantom FDI in terms of revenues, 12.4 percentage points lower than the production-function approach. These results suggest that the production-function approach in previous studies in the literature might overestimate the value of phantom FDI. This might be due to two reasons. On the one hand, there might be uncertainty regarding the parameter $\gamma$ used to calibrate the production function. Furthermore, the production-function approach does not control for third-country effects. Interestingly, when we do not control for these effects, the one-country gravity-equation and the production-function approaches yield closer results than when using structural gravity with all country pairs. \section{Inward Multilateral Phantom FDI for Non-U.S. Countries}\label{sec:globalinward} We can also use our structural gravity-equation results to provide estimates of inward multilateral phantom FDI for non-U.S. countries. Using our estimates from structural gravity of bilateral phantom FDI, we can calculate: \begin{equation} \label{eq:phantom2} {FDI}_{j}^{Phantom}\equiv\sum_{i=1,i\neq j}^N\left(FDI_{ij}-\widehat{FDI_{ij}}\right) . \end{equation} where $\widehat{FDI_{ij}}$ is the predicted FDI flow from equation \eqref{eq:gravity1}. The results of applying our gravity-equation methodology to identify phantom FDI on a global scale are reported in Figure \ref{fig:globalphantom}, which contains the results for the numbers of affiliates, revenues, total assets, fixed assets, tangible fixed assets, and intangible fixed assets. \begin{comment} Figure \ref{fig:globalpotentials} reports for FDI potentials for global FDI. Regarding the number of affiliates in Figure \ref{fig:potential_extensive_all}, Belarus (1s), Israel (2nd), El Salvador (3rd), Kazakhstan (4th), and Algeria (5th) lead the ranking of the FDI gravity ratio. The value of the ratio suggest, for instance, that the actual inward FDI in Belrus is around 100 times higher that the predicted theoretical value obtained from the gravity equation. Most of the countries that lead this ranking are relatively small countries, with a small predicted value of FDI by the gravity equation. This small value is the denominator of equation \eqref{eq:ratio1}, hence the large value of the ratios. \begin{figure} \caption{Global FDI potentials ($FDI_{ratio}>1$)} % Alt Text: Figure 23 is comprised of six line charts showing aggregate revenue, employees, total assets, fixed assets, number of affiliates, and revenue over time, from 2010 to 2022. \label{fig:globalpotentials} \centering \centering \hfill{}\begin{subfigure}[b]{0.475\textwidth} \centering \caption{Number Affiliates} \label{fig:potential_extensive_all} \includegraphics[width=1\textwidth]{figures/potential_extensive_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.475\textwidth} \centering \caption{Revenue from affiliates} \label{fig:potential_revenue_all} \includegraphics[width=1\textwidth]{figures/potential_revenue_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.475\textwidth} \centering \caption{Total Assets} \label{fig:potential_totalassets_all} \includegraphics[width=1\textwidth]{figures/potential_totalassets_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.475\textwidth} \centering \caption{Fixed Assets } \label{fig:potential_fixedassets_all} \includegraphics[width=1\textwidth]{figures/potential_fixedassets_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.475\textwidth} \centering \caption{Tangible Assets \label{fig:potential_tangible_all}} \includegraphics[width=1\textwidth]{figures/potential_tangible_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.475\textwidth} \centering \caption{Inangible Assets \label{fig:potential_intangible_all}} \includegraphics[width=1\textwidth]{figures/potential_intangible_all} \end{subfigure} \end{figure} The value of the FDI potential (ratios) of revenues (Figure \ref{fig:potential_revenue_all}), total assets (Figure \ref{fig:potential_totalassets_all}), fixed assets (Figure \ref{fig:potential_fixedassets_all}), tangible assets (Figure \ref{fig:potential_tangible_all}) and intangible assets (Figure \ref{fig:potential_intangible_all}) show similar patterns with small countries leading the FDI potential ranking. The only exception is Russia, that leads the FDI potential ranking for revenues, followed by Moldova and ranks second intangible assets, precede by Serbia. Moldova, a former Soviet Republic, leads the ranking in total and fixed assets, followed by Dominican Republic and Albania, respectively. Côte d'Ivorie, Israel and Ukraine lead the ranking of tangible assets. \end{comment} Figure \ref{fig:globalphantom} reports the inward multilateral phantom FDI for numerous non-U.S. countries. Regarding the number of affiliates in Figure \ref{fig:phantom_extensive_all}, China (1st), United Kingdom (2nd), and Netherlands (3rd) lead the ranking of the phantom FDI. The value of phantom FDI suggests, for instance, that the number of foreign affiliates in China exceeds by more than 9,000 affiliates the predicted theoretical value obtained from the gravity equation. However, the value of the phantom FDI is \textit{not} a ratio; thus, small countries are weighted relatively less with this approach. The value of phantom FDI of revenues (Figure \ref{fig:phantom_revenue_all}), total assets (Figure \ref{fig:phantom_totalassets_all}), fixed assets (Figure \ref{fig:phantom_fixedassets_all}), tangible fixed assets (Figure \ref{fig:phantom_tangible_all}) and intangible fixed assets (Figure \ref{fig:phantom_intangible_all}) show a different picture from the rankings in Figure \ref{fig:phantom_extensive_all}. China is followed by the United Kingdom, Singapore, France, and Ireland in ranking phantom FDI by revenues. The revenues of non-U.S. foreign affiliates in China exceed the FDI potential by 800,000 million USD. The United Kingdom, Luxembourg, Hong Kong and China lead the rankings in total assets, and Luxembourg, IK and Netherlands in fixed assets. The Netherlands, the UK, and Australia lead the tangible fixed asset ranking. Ireland, Netherlands, and Brazil lead the ranking using fixed intangible assets. Finally, Table \ref{tab:quantificationALL} reports the fractions of total FDI that are estimated to be phantom FDI for each of the six dependent variables. \\ %The results obtained on a global scale hint at a mix of Phantom FDI and outperforming economic activity in certain countries, which is not entirely captured by aggregating the results for all possible origins. \begin{table}[h] \caption{Quantification (Inward Multilateral FDI for Non-U.S. Countries)\label{tab:quantificationALL}} \centering \scalebox{0.8}{ \begin{tabular}{lcccccc} & Affiliates & Revenue & Total Assets & Fixed Assets & Tangible & Intangible\tabularnewline \hline Total FDI & 331,642 & 19,700,000 & 68,600,000 & 27,300,000 & 6,008,717 & 2,074,382 \tabularnewline Phantom FDI & 75,730 & 6,367,864 & 23,900,000 & 7,810,626 & 2,159,687 & 935,735 \tabularnewline Phantom FDI/Total FDI & 0.228 & 0.323 & 0.349 & 0.285 & 0.359 & 0.451\tabularnewline \hline \multicolumn{7}{l}{Notes: Affiliates: number of foreign affiliates. Rest of variables in million USD}\tabularnewline \end{tabular}} \end{table} \section{Conclusion \label{sec:conclusions}} This paper applies a structural gravity approach to identify and quantify the presence of phantom FDI, which refers to investment flows that are motivated by factors other than those related to the production opportunities in host country. %By integrating the gravity model with theoretical foundations and validating the approach using a production function, we provide robust evidence on the global distribution of FDI, including a specific focus on U.S. outward FDI. Focusing on the United States, our findings demonstrate that the structural gravity approach identifies several key destinations as significant recipients of Phantom FDI: Luxembourg, Netherlands, Ireland, Singapore and the United Kingdom. Some of these countries have been identified as prominent tax havens in other studies \citep{damgaard2024real}. Regarding the dollar value of Phantom FDI, Ireland, Singapore, and the Netherlands rank first in terms of affiliate revenues. Moreover, the results indicate that the decision to hold assets in overseas subsidiaries are influenced by a mix of policy advantages, geo-strategic factors, and favorable tax holding laws, with the Netherlands and Ireland standing out as key destinations for U.S. MNEs. %Intangible assets, meanwhile, are driven by political risks (e.g., Russia and Georgia), tax-friendly policies (e.g., Ireland), and traditional tax havens (e.g., Bermuda), highlighting the diverse factors influencing these investment decisions. Furthermore, the analysis reveals that geo-strategic risks, as present in countries like Ukraine, play a significant role in shaping FDI flows related to numbers of affiliates. This underscores the importance of political and geographical considerations in addition to tax factors. %Moreover, the results indicate that tangible fixed assets are influenced by a mix of tax advantages, geo-strategic factors, and favorable holding laws, with the Netherlands standing out as a key destination. Intangible assets, meanwhile, are driven by political risks (e.g., Russia and Georgia), tax-friendly policies (e.g., Ireland), and traditional tax havens (e.g., Bermuda), highlighting the diverse factors influencing these investment decisions. Overall, this study suggests that the structural gravity framework -- founded upon well-established theoretical foundations -- is useful in identifying phantom FDI flows. We show that the results using structural gravity-equation estimates are more conservative -- and perhaps more realistic -- than previous approaches used by the literature, cf., \cite{guvenen2022offshore}. This provides a valuable framework for researchers wanting to better understand the underlying drivers of FDI and to assess the importance of political and geographical considerations, in addition to tax factors, that are behind these Phantom FDI flows. \renewcommand\figureplace{\floatplace{figure}} \begin{figure} \caption{Inward Phantom FDI of Non-U.S. Countries, 2019} % Alt Text: Figure 4 is comprised of six seperate bar charts showing the top destination countries recieving Phantom FDI from non-US MNEs. Figure 4(a) shows number of affiliates, figure 4(b) shows revenues, figure 4(c) shows total assets, figure 4(d) shows fixed assets, figure 4(e) shows tangible fixed assets, and figure 4(f) shows intangible fixed assets. \label{fig:globalphantom} \centering \centering \begin{subfigure}[b]{0.9\textwidth} \centering \caption{Number Affiliates} \label{fig:phantom_extensive_all} \includegraphics[width=1\textwidth]{figures/phantom_extensive_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \caption{Revenue from affiliates} \label{fig:phantom_revenue_all} \includegraphics[width=1\textwidth]{figures/phantom_revenue_all} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure} \ContinuedFloat \caption{Inward Phantom FDI of Non-U.S. Countries, 2019 (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \caption{Total Assets} \label{fig:phantom_totalassets_all} \includegraphics[width=1\textwidth]{figures/phantom_totalassets_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \caption{Fixed Assets } \label{fig:phantom_fixedassets_all} \includegraphics[width=1\textwidth]{figures/phantom_fixedassets_all} \end{subfigure} \end{figure} \addtocounter{postfigure}{-1} \renewcommand\figureplace{} \begin{figure} \ContinuedFloat \caption{Inward Phantom FDI of Non-U.S. Countries, 2019 (cont.)} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \caption{Tangible Fixed Assets \label{fig:phantom_tangible_all}} \includegraphics[width=1\textwidth]{figures/phantom_tangible_all} \end{subfigure} \hfill{}\begin{subfigure}[b]{0.9\textwidth} \centering \caption{Inangible Fixed Assets \label{fig:phantom_intangible_all}} \includegraphics[width=1\textwidth]{figures/phantom_intangible_all} \end{subfigure} \end{figure} \singlespacing \newpage \bibliographystyle{apalike} \bibliography{sample} \newpage \appendix \doublespacing \section{Additional Tables} \setcounter{table}{0} \setcounter{figure}{0} %\setcounter{postfigure}{0} \counterwithin{figure}{section} \counterwithin{table}{section} %The coefficient estimates of the policy variables reported in Table \ref{tab:US} might be biased, as this cross-section analysis does not control adequately for endogeneity bias, cf., \cite{BaierBergstrand2007}. However, this analysis aims to predict FDI accurately rather than to estimate the unbiased effects of policy interventions. Nonetheless, as a sensitivity analysis, we provide the gravity-equation estimates for U.S. outward FDI \textit{without} the potentially endogenous policy-related variables here. As shown in the bottom panel of Table \ref{tab:sens}, the predicted values of FDI from both specifications are highly correlated for all six dependent variable values (0.9999). \begin{table}[htbp]\centering \def\sym#1{\ifmmode^{#1}\else\(^{#1}\)\fi} \caption{Sensitivity Analysis: Restricted Model and Correlations \label{tab:sens}} \scalebox{0.8}{ % \begin{tabular}{l*{6}{c}} \toprule & \multicolumn{1}{c}{(1)} & \multicolumn{1}{c}{(2)} & \multicolumn{1}{c}{(3)} & \multicolumn{1}{c}{(4)} & \multicolumn{1}{c}{(5)} & \multicolumn{1}{c}{(6)}\tabularnewline & \multicolumn{1}{c}{Affiliates} & \multicolumn{1}{c}{Revenues} & \multicolumn{1}{c}{Total assets} & \multicolumn{1}{c}{Fixed assets} & \multicolumn{1}{c}{Tangible fixed} & \multicolumn{1}{c}{Intangible fixed}\tabularnewline \midrule lnGDP & 0.7053\sym{***}& 0.7324\sym{***}& 0.5847\sym{***}& 0.4791\sym{***}& 0.5517\sym{***}& 0.5758\sym{***}\\ & (0.10) & (0.08) & (0.11) & (0.11) & (0.11) & (0.10) \\ \addlinespace lnDistance & -0.7471\sym{**} & -0.2782 & -1.0589\sym{**} & -1.3208\sym{*} & -1.2253 & -0.6463\sym{*} \\ & (0.35) & (0.45) & (0.49) & (0.70) & (0.80) & (0.35) \\ \addlinespace Island & 0.2444 & 0.3634 & 1.2606\sym{**} & 0.5775 & 0.2974 & 0.2631 \\ & (0.46) & (0.34) & (0.50) & (0.59) & (0.96) & (0.58) \\ \addlinespace Landlocked & 0.7064 & -0.4498 & 1.2063 & 1.3012 & -1.6339 & -1.0213 \\ & (0.46) & (0.68) & (0.92) & (0.95) & (1.01) & (0.97) \\ \addlinespace Common Legal Origin & 1.9260\sym{***}& 0.9659\sym{**} & 1.8395\sym{***}& 2.3577\sym{***}& 1.3562 & 0.4432 \\ & (0.49) & (0.42) & (0.66) & (0.90) & (1.26) & (0.54) \\ \addlinespace Common Language & -0.3969 & -0.0787 & -0.5662 & -1.0605 & -1.5025 & 0.9725 \\ & (0.39) & (0.45) & (0.75) & (0.99) & (1.33) & (0.76) \\ \midrule Correlation & 0.9999 &0.9999 & 0.9999 &0.9999 & 0.9999 & 0.9999 \\ Observations & 111 & 111 & 111 & 111 & 111 & 111 \\ R$^2$ & 0.678 & 0.572 & 0.554 & 0.364 & 0.358 & 0.282 \\ \bottomrule \multicolumn{7}{l}{Robust {\footnotesize{}{}US outward FDI, year 2019. Correlations with the predicted values of the unrestricted regressions}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}PPML, Robust standard errors in parenthesis, clustered by country pair}}\tabularnewline \multicolumn{7}{l}{{\footnotesize{}{}\sym{*} $p<0.10$, \sym{{*}{*}} $p<0.05$, \sym{{*}{*}{*}} $p<0.01$}}\tabularnewline \end{tabular} } \end{table} %Consequently, a comparison of the results reported in Table \ref{tab:US} and those reported in Table \ref{tab:sens} suggest that the potentially endogenous policy-related variables did not bias the \textit{predictions} from the gravity equation. The correlation of the predictions is close to one in all cases. Interestingly, the distance coefficient is now negative and statistically significant for the numbers of affiliates, total assets, fixed assets, and intangible fixed assets. %The effect of common language on the other hand is non-significant. \end{document}