Policy Research Working Paper 10338 Deep Trade Agreements and FDI in Partial and General Equilibrium A Structural Estimation Framework Mario Larch Yoto V. Yotov Development Research Group & Macroeconomics, Trade and Investment Global Practice March 2023 Policy Research Working Paper 10338 Abstract This paper quantifies the relationships between deep trade deep trade agreement effects on trade and quantifying the liberalization and foreign direct investment. To this end, it impact of deep trade agreements on foreign direct invest- focuses on the effects of deep trade agreements. The analysis ment through trade. The paper obtains sizeable, positive, relies on a structural framework that simultaneously enables and statistically significant estimates of the effects of deep (i) estimating the direct impact of deep trade agreements on trade agreements on both trade and foreign direct invest- foreign direct investment, (ii) translating the partial deep ment. A counterfactual analysis suggests that together with trade agreement estimates into general equilibrium effects direct and indirect channels deep trade agreements have on foreign direct investment; and (iii) obtaining partial contributed. This paper is a product of the Development Research Group, Development Economics and the Macroeconomics, Trade and Investment Global Practice. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at mario.larch@uni-bayreuth.de and yotov@drexel.edu. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Deep Trade Agreements and FDI in Partial and General Equilibrium: A Structural Estimation Framework * „ Mario Larch Yoto V. Yotov University of Bayreuth Drexel University JEL Classication Codes: F10, F43, O40 Keywords: Foreign Direct Investment (FDI), Trade Liberalization, Deep Trade Agreements. * We are grateful to Vanessa Alviarez for a very thoughtful and constructive discussion of our paper, and for her excellent suggestions during the World Bank's Deep Trade Agreements Conference: Eects Beyond Trade. We also thank Emily Blanchard, Keith Maskus, Gianluca Orece, Nadia Rocha, and Michele Ruta for very useful comments and suggestions. This paper has beneted from support from the World Bank's Umbrella Facility for Trade trust fund nanced by the governments of the Netherlands, Norway, Sweden, Switzerland and the United Kingdom. All errors are our own. „ Contact: LarchDepartment of Law and Economics, University of Bayreuth, CEPII, CESifo, GEP, ifo, mario.larch@uni-bayreuth.de; YotovSchool of Economics, LeBow College of Business, Drexel University, yotov@drexel.edu. 1 Introduction: Motivation and Contributions Most modern preferential trade agreements (PTAs) include a variety of investment provi- sions. As pointed out by Crawford and Kotschwar (2020), Following the entry into force of NAFTA and the GATS, trade negotiators increasingly began to incorporate into PTAs a broad set of investment provisions that liberalize, protect, and regulate investments. (p. 145). The increase, both in absolute and in relative terms, in the number of PTAs with investment provisions is depicted in Figure 1, which comes from Crawford and Kotschwar (2020). Figure 1: Number of PTAs that include investment provisions, 1958-2018 Notes: This gure plots the number of PTAs with and without investment provisions. The g- ure comes from Crawford and Kotschwar (2020). The original source is the WTO RTA database: http://rtais.wto.org, May 2018. Using the World Bank's Database on the Content of Regional Trade Agreements (DCRTA), cf. Hofmann et al. (2019) and Mattoo et al., eds (2020), we complement Figure 1 by plotting the number of country-pairs that have signed a trade agreement that includes investment pro- visions. Figure 2 clearly corroborates the evidence from Figure 1 by depicting a remarkable 1 increase in the country-pairs that have negotiated investment together with trade, especially since the early 1990s as noted in the opening quote from Crawford and Kotschwar (2020). Figure 2: Country-pairs that have PTAs with Investment Provisions, 1958-2017. Notes: This gure plots the number of country pairs that have signed a trade agreement that includes investment provisions. The data used to construct the gure is from the World Bank's Database on the Content of Regional Trade Agreements, https://datatopics.worldbank.org/dta/about-the-project.html. Despite the increase in the number and importance of investment provisions in the ne- gotiations and implementation of PTAs, there is relatively little and mixed evidence on the eectiveness of such provisions in promoting FDI. For example, the authoritative surveys of 1 Eicher et al. (2012) and Blonigen and Piger (2014) on the determinants of FDI do not ac- count for such provisions. Only very recently, some papers (e.g., Kox and Rojas-Romagosa, 2020; Laget et al., 2021) have studied the impact of Deep Trade Agreements (DTAs) and various PTA provisions (disciplines) on FDI, oering mixed evidence on the impact of in- 1 Other examples of studies on determinants of FDI, including studies on the impact of trade liberalization and deep trade agreements on FDI, include Baltagi et al. (2008), Medvedev (2012), Osnago et al. (n.d.), and Di Ubaldo and Gasiorek (2022). 2 2 vestment provisions. Against this backdrop, we make three contributions to the existing literature on the links between deep trade liberalization and FDI. First, we contribute to the debate on whether deep trade agreements with investment provisions stimulate FDI by estimating the direct/partial equilibrium eects of DTAs and DTAs with investment and other provi- sions on FDI. Second, we use our partial estimates to obtain novel general equilibrium (GE) estimates of the eects of DTAs on FDI. Third, within the same structural framework, we obtain estimates of the eects of DTAs on trade ows, and we translate those eects into general equilibrium eects of DTAs on FDI through trade liberalization. 3 Guided by the theoretical model of Anderson et al. (2019), we specify two estimating gravity equationsone for trade and one for FDI, which are (i) consistent with and repre- sentative of a large number studies that quantify the impact of various determinants on FDI (e.g., Eicher et al., 2012; Blonigen and Piger, 2014; Kox and Rojas-Romagosa, 2020; Laget et al., 2021), and (ii) capitalize on the latest developments in the trade gravity literature (e.g., Head and Mayer, 2014; Yotov et al., 2016). Specically, we rely on the Poisson Pseudo- Maximum-Likelihood estimator to account for potential heteroskedasticity in the bilateral trade and FDI data and to take advantage of the information in the zero trade and FDI ows (cf. Santos Silva and Tenreyro, 2006, 2011). In addition, we employ a very rich set of xed eects (including origin-time, destination-time, and directional country-pair xed eects), which control for and absorb all possible country-specic and time-invariant bilateral deter- 2 For example, Lesher and Miroudot (2006) obtain positive eects of investment provisions on FDI, while, more recently, Kox and Rojas-Romagosa (2020) and Laget et al. (2021) do not nd that investment provisions have signicant additional impact on FDI. Moreover, we are not aware of existing work that quanties the full/general equilibrium impact of DTAs and their investment provisions on FDI. 3 The theoretical model of Anderson et al. (2019) suits our objectives well because it (i) oers structural foundations for both our trade and FDI estimating gravity models and (ii) enables us to translate our partial estimates of the eects of DTAs on trade and welfare into GE eects on FDI. Our contributions in relation to Anderson et al. (2019) are twofold. First, from a methodological perspective, they calibrate the model in a cross section while we build a panel data set to estimate some of the structural equations in order to test for and establish causality in the relationships of interest to us. Second, from a policy perspective, Anderson et al. (2019) simulate a world without FDI, while our aim is to quantify the impact of deep trade agreements on FDI. In policy work that is not intended for publication, Anderson et al. (2016) rely on the framework of Anderson et al. (2019) to quantify the eects of CETA. 3 minants of trade and FDI. Thus, mitigating omitted variable bias and endogeneity concerns with the key variables of interest to us. In addition to PTAs and DTAs, we control for other policy variables such as WTO membership, economic sanctions, and bilateral investment treaties. To perform the empirical analysis we build a balanced panel data set for 89 countries covering more than 96 percent of world GDP and more than 94 percent of FDI throughout the sample period, 1990-2011. Our data set covers foreign direct investment, trade agree- ments, trade ows, gross domestic product (GDP), employment, physical capital, bilateral investment treaties, sanctions, and WTO membership. An important feature of the data set is that we capitalize on the richness of the Database on the Content of Regional Trade Agreements (DCRTA), cf. Hofmann et al. (2019) and Mattoo et al., eds (2020). Specically, the DCRTA enables us to distinguish between several indicator and continuous PTA vari- ables, including a standard dummy variable for PTAs, an indicator variable for DTAs, an indicator for DTAs that include investment provisions, and two continuous variables for the overall depth of DTAs and for the depth of the DTAs with investment provisions. Three main ndings stand out from our estimates of the eects of DTAs on trade. First, we nd that the average impact of PTAs in our sample is not statistically signicant. How- ever, second, we obtain positive and statistically signicant estimates of the eects of deep trade agreements. Specically, our estimates suggest that the DTAs in our sample have led to a 16.1% (std.err. 3.184) increase in bilateral trade among member countries. Finally, our estimates reveal that deeper trade agreements (as measured by the number of provisions) lead to larger increases in the trade ows among DTA members. Depending on the number of provisions that they include, the DTAs in our sample have led to trade increases between 0.576% (std.err. 0.289) and 23.012% (std.err. 12.744). Overall, our estimates of the DTA ef- fects in trade are consistent with ndings from recent studies that have utilized the database on the Content of Regional Trade Agreements and reinforce the view that `depth' matters 4 4 for the eectiveness of PTAs. Similar to our results for trade, the estimates of the eects of DTAs on FDI are also heterogeneous. Specically, we do not obtain signicant estimates of the eects of PTAs and DTAs on FDI. However, when we zoom in on the eects of DTAs that include investment provisions, we obtain a positive, sizable, and statistically signicant estimate, which suggests that, on average, the PTAs with investment provisions in our sample have led to a 34.33% (std.err. 14.535) increase in FDI between their members. This result is consistent with earlier ndings from Lesher and Miroudot (2006). We also obtain positive estimates of the eects on FDI of several other DTA provisions including `labor market regulations', `export taxes', `public procurement' and `state owned enterprises'. This analysis reinforces and complements the ndings of Laget et al. (2021) who study the impact of dierent DTA provisions with rm-level data for the period 2003-2015. Finally, our estimates do not reveal a signicant impact of the increase in the depth (number of provisions) on FDI. In fact, our results suggest that an increase in the number/complexity of some investment provisions (e.g., related to `transparency' and `regulations') may actually decrease FDI. We use the structural model in combination with our estimates of the partial eects of 5 DTAs on trade and FDI in order to quantify the GE impact of DTAs on FDI. We focus the analysis on inward usage of technology FDI per country and outward technology FDI stocks per country used abroad. The main conclusions from this analysis are as follows. DTAs have had large and strongly asymmetric eects on FDI. The DTAs that were in force in 2011 have contributed to about 3% of inward FDI in the world and about 70% of outward FDI. The large average eect of outward FDI is driven by some large outward FDI countries (such as the United States and China), where, consistent with our theoretical model of non-rival 4 We refer the reader to Fernandes et al., eds (2021), an eBook from the World Bank and CEPR, which is a collection of excellent papers that focus on various aspects of the determinants of DTAs and on the DTA eects on trade and other economic outcomes. 5 As discussed in more detail in Section 4.2, a caveat with our GE analysis is that the underlying theory is based on the assumption of non-rival technology FDI, while our data includes all/aggregate FDI ows. While this gap, of course, has implications for the quantitative results, our conclusions about the disproportionately large impact of outward FDI will remain qualitatively the same if applied to better suited data. 5 capital, any change in the technology stock of these countries has a multiplying eect due to the usage in many other countries, resulting in a large boost in outward FDI stock usage abroad. We view our result about the disproportionately large impact of outward FDI as novel and potentially important from a policy perspective, both for the negotiations of trade and investment agreements and for properly quantifying their implications. Finally, we also nd that changes in trade costs due to DTAs have led to additional boosts in FDI through the GE links between trade and FDI in our model. Specically, through their impact on trade costs, the 2011 DTAs in our model have boosted inward FDI by an additional 1 percentage point and outward FDI by 10 additional percentage points, i.e., eects that are about a quarter of the corresponding estimates due to FDI liberalization. By demonstrating that the impact of DTAs on FDI through trade is signicant, we complement some recent work on the GE links between DTAs and trade, cf. Fontagne et al. (2021), and also, from a broader perspective, papers that have studied the GE links between trade liberalization and FDI, cf. Baltagi et al. (2008), Tintelnot (2017), and Anderson et al. (2019). The rest of the paper is organized as follows. Section 2 presents the methodological foundations of our analysis, including the theoretical foundations (in Subsection 2.1), a discussion of the alternative channels through which DTAs impact FDI (in Subsection 2.2), and the specications of our estimating equations for bilateral trade ows and FDI (in Subsection 2.3). Section 3 describes the main variables and the corresponding data sources that we use to construct them. Section 4 presents and discusses our partial estimates (in Subsection 4.1) and our GE results (in Subsection 4.2). Section 5 concludes and we oer a supplementary Appendix that includes the derivations of the theoretical model. 2 Methods In order to quantify the impact of deep trade agreements on FDI, we rely on the theoretical framework of Anderson et al. (2019). While, our current contribution is purely empirical, 6 we nd it helpful to summarize the model of Anderson et al. (2019). We do this in Section 2.1 for two reasons. First, as demonstrated in Section 2.2, it will enable us to describe and decompose several partial and GE channels through which DTAs impact FDI. In addition, in Section 2.3, we will capitalize on the structural equations for bilateral trade ows and FDI in order to specify the corresponding estimating equations, which in turn will deliver our key estimates of the direct impact of DTAs on trade and FDI. 2.1 Theoretical Foundations To motivate and perform the empirical analysis, we rely on the theoretical framework of Anderson et al. (2019), who derive a multi-country dynamic model of trade, investment in 6 physical capital and FDI under the following assumptions. Each country (i, j ∈ N ) produces a single tradeable good (dierentiated by place of origin, Armington, 1969), which, subject to iceberg trade frictions (tij,t ≥ 1), can be used for consumption (Cj,t ) and to build country- specic physical capital (Kj,t ) in any other country. In addition, each country invests in 7 non-rival technology capital (Mj,t ), and the technology capital of one country can be used in all other countries subject to investment frictions (1 ≥ ωij,t ≥ 0).8 The decisions on aggregate consumption (Cj,t ), aggregate investment in physical capital (Ωj,t ), and aggregate investment in technology capital (χj,t ) in each country are made by representative agents who maximize the present discounted value of their lifetime utility subject to a sequence of constraints, as captured by the following consumer optimization 6 We refer the reader to Anderson et al. (2019) for motivation behind some of the assumptions and for details on all derivations. For the convenience of the reader, we enclose the online Appendix from Anderson et al. (2019) along with this paper. 7 The modeling of FDI in form of non-rival technology capital is in the spirit of Markusen (2002), McGrat- tan and Prescott (2009, 2010, 2014) and McGrattan and Waddle (2017). One interpretation of technology capital is akin to the notion of knowledge capital, and possible examples include patents, blue-prints, man- agement skills/practices, etc. 8 If ωij,t = 1, then country j is totally open to the use of foreign technology of country i capital at time t within its borders. If ωij,t = 0, no foreign technology from country i can be used in country j at time t. 7 problem: ∞ max β t ln(Cj,t ) (1) {Cj,t ,Ωj,t ,χj,t } t=0 Kj,t+1 = (1 − δj,K ) Kj,t + Ωj,t for all t, (2) Mj,t+1 = (1 − δj,M ) Mj,t + χj,t for all t, (3) N ϕ 1−αj 1−ϕ Yj,t = pj,t Aj,t Lj,t α j Kj,t (max{1, ωij,t Mi,t })ηi for all t, (4) i=1 Ej,t = Pj,t Cj,t + Pj,t Ωj,t + Pj,t χj,t for all t, (5) Ej,t = Yj,t + ϕηj Yi,t − ϕYj,t ηi for all t, (6) i∈Nji,t i∈Nij,t Kj,0 , Mj,0 given. (7) Equation (1) is the representative agent's intertemporal utility function, where aggregate σ 1−σ σ −1 σ −1 N consumption, Cj,t = i=1 γi σ cij,t σ , comprises of domestic and foreign goods ( cij,t ) from all possible countries. Equation (2) is the transition function for accumulation of physical σ 1−σ σ −1 σ −1 N K capital, where δj,K is the depreciation rate and Ωj,t = i=1 γi σ Iij,t σ denotes the aggregate ow of investment in physical capital in country j at time t as a CES aggre- K 9 gate of investment goods (Iij,t ) from all countries. Similarly, equation (3) is the transition function for accumulation of technology capital, where δj,M is the depreciation rate and σ 1−σ σ −1 σ −1 N M χj,t = i=1 γi σ Iij,t σ denotes the CES-aggregated ow of investments of technology M capital (Iij,t ) in j at time t from all countries, including j itself. Equation (4) is the production value function. Here, pj,t denotes the factory-gate price of good (country) j at time t, Aj,t is the local, country-specic technology, Lj,t is country- specic (internationally immobile) labor, and all other variables are dened earlier. Note N that the last term i=1 (max{1, ωij,t Mi,t })ηi is the global technology stock applied locally. When ωij,t = 0, no foreign technology from country i can be used in country j at time t, and when ωij,t = 1 usage of foreign technology is frictionless. With ωij,t > 0 every unit of 9 The assumption that consumption and investment goods are subject to the same CES aggregation is very convenient analytically. Allowing for heterogeneity in preferences and prices between and within consumption and investment goods requires sectoral treatment and will open additional channels for the interaction between trade liberalization and FDI. 8 foreign technology from country i at time t has ωij,t -times the use in country j . By assuming N i=1 ηi = 1, we impose constant returns to scale. The max-function implements the notion that there is some world knowledge of technology capital freely available to all countries and ensures that there is always some technology capital available for all countries. Equation (5) gives total expenditure in country j at time t, Ej,t , as the sum of spending on consumption (Pj,t Cj,t ), spending on investment in physical capital (Pj,t Ωj,t ), and spending on investment in technology capital (Pj,t χj,t ). Finally, Equation (6) denes disposable income, which is equal to expenditure, as the sum of total nominal output (Yj,t ) plus rents from foreign in- vestments ϕηj i∈Nji,t Yi,t , minus rents accruing to foreign investments ϕYj,t i∈Nij,t ηi , where Nij,t ≡ {i ̸= j, ωij,t Mi,t > 1}. Solving the representative agent's problem delivers the following steady state structural 10 system that describes the relationships between trade, domestic investment, and FDI: 1−σ Yi E j tij Xij = for all i and j (8) Y Πi Pj N 1−σ tij Yi Pj1−σ = for all j, (9) i=1 Πi Y N 1−σ −σ tij Ej Π1 i = for all i, (10) j =1 Pj Y 1 N 1−σ Yj / j =1 Yj pj = for all j, (11) γj Πj N ϕ 1−ϕ 1−α α ηi Yj = pj Aj Lj j Kj j (max{1, ωij Mi }) for all j, (12) i=1 Ej = Yj + ϕηj Yi − ϕYj ηi for all j, (13) i∈Nji,t i∈Nij,t αj β (1 − ϕ) 1 − ϕ i∈Nij,t ηi Y j Kj = for all j, (14) 1 − β + βδj,K Pj value Ei Yj F DIij = Γi ωij for all i and j. (15) Pi Mi 10 Mechanically, the model is solved in two stages. First, for given aggregate variables, the demands for K M cij,t , Iij,t and Iij,t are obtained. Then, the dynamic optimization problem for Cj,t , Ωj,t and χj,t is solved. The focus on the steady state system is consistent with other FDI models, e.g., Head and Ries (2008). 9 Equations (8)-(11) may look familiar, because they represent the structural gravity trade sys- tem of Anderson and van Wincoop (2003). Equation (8) is the standard structural gravity −σ 1−σ equation. Π1 i,t and Pj,t are the multilateral resistance terms (MRTs, outward and inward, respectively), which consistently aggregate bilateral trade costs and decompose their inci- dence on the producers and the consumers in each region. As dened earlier, equations (12) and (13) dene the value of production and the expenditure in country j, respectively. Equation (14) is the solution for physical capital. Intuitively, the direct relationship between Kj and Yj reects the fact that there will be more investment the higher the value of marginal product of physical capital. The inverse relationship between Kj and Pj can be interpreted through the lens of the law of demand, i.e., if Pj is interpreted as the price of investment goods. Alternatively, if Pj is the price of consumption or technology goods, then the intuition for inverse relationship is that there will be less investment when the opportunity cost of it (i.e., investment in consumption or technology goods) is higher. Finally, equation (15) is the structural gravity equation for FDI, where F DIij is the value 2 βϕ2 ηi of the stock of FDI from origin i at destination j , Γi = 1−β +βδi,M is a composite country- specic constant term, and all other variables are dened above. Intuitively, and similar to the gravity model of trade, (15) captures the direct relationship between FDI and the sizes of the source and the destination countries. The explanation for the inverse relationship between FDI and Pj is similar to the relationship between physical capital and Pj . The inverse relationship between FDI and Mi is a reection of the law of diminishing marginal productivity, i.e., the larger the stock of technology capital in country i, the smaller the marginal productivity by an additional unit of investment in technology. Finally, ωij denotes the openness measure for foreign technology of country i in country j .11 The stock of FDI can be dened as: F DIij ≡ ωij Mi . (16) 11 A notable dierence between the FDI gravity model (15) and the standard trade gravity model, as cap- tured by (8), is that the FDI gravity equation does not include explicitly an outward multilateral resistance. The intuitive explanation for this is the non-rival nature of technology capital. 10 For given parameters and variables that are exogenous in the model, i.e., α, β , ϕ, ξ , ηj , γj , σ , δK , δM , Aj,t , Lj,t , tij,t , and ωij,t , we can use system (8)-(15) to simulate the impact of deep trade liberalization on trade and investment in the world. We capitalize on this in Section 4.2. Before that, in Section 2.2, we use (8)-(15) to describe and decompose the partial and GE channels through which DTAs impact FDI. Then, in Section 2.3, we rely on system (8)-(15) to specify the econometric models that will deliver our key estimates of the direct impact of DTAs on trade and FDI. 2.2 On the Links between DTAs and FDI: A Discussion The objective of this section is to describe and decompose the channels through which DTAs aect FDI. To this end, and consistent with the estimation results that we present in Section 4.1, as comparative static shock to system (8)-(15) we consider the formation of a DTA with investment provisions, which is successful in liberalizing both trade and FDI. For clarity and ease of exposition, we consider a specic hypothetical examplea DTA between the US and the EU. Moreover, consistent with the counterfactual analysis that we perform in Section 4.2, we discuss the eects of trade liberalization and investment liberalization sequentially, starting with the eects of investment liberalization, which is captured by an increase of ωij in our model. A decrease in FDI barriers will have a direct eect and several indirect (GE) eects on FDI in system (8)-(15). ˆ Direct DTAs impact on FDI. The direct eect of lower bilateral investment costs be- tween EU and US is captured by equation (15), and it would lead to an immediate increase in FDI between the liberalizing partners. In the empirical analysis below, we will be able to identify the direct impact of DTAs on FDI from our estimating FDI gravity model. Then, we will use our partial estimates of these direct eects to simulate the indirect/GE eects, which we describe next. ˆ First-order GE eect of DTAs on FDI. The removal of FDI barriers (i.e., an increase 11 of ωij ) between US and the EU will lead to higher income, through (12), and higher expenditure, through (13), in the two regions. In turn, via equation (15), the changes of the sizes of the liberalizing partners will lead to more FDI between them and also, ceteris paribus, between each of them and all other countries in the world. These GE size eects are similar to the familiar size eects from the trade gravity literature. ˆ Second-order GE eect of DTAs on FDI. The changes of the sizes of the two regions will lead to changes in the multilateral resistances through system (9)-(10). This relationship is inverse, which means that the MRs will fall. In turn, a lower inward multilateral resistance will stimulate investment via (15). As discussed earlier, the intuition for this result is that the IMR can be interpreted alternatively as the price of investment or the opportunity cost of investment. ˆ Third-order GE eects of DTAs on FDI. Finally, we label the eects of changes in FDI barriers through variables that are not explicitly included in equation (15) as `third-order GE eect of DTAs on FDI'. System (8)-(15) captures at least two such eects. The rst one is via the outward multilateral resistance. As noted earlier, the OMR does not appear explicitly in (15). Nevertheless, it is linked to the other endogenous variables in our model via the MR system (9)-(10). The second one is via physical capital accumulation, which, as captured by equation (14), would respond to the changes in size and the IMR and, in turn, will stimulate further increase in size. Next, we turn to the eects of DTAs on FDI through trade liberalization, e.g., a reduction in the bilateral trade costs (tij ) between US and the EU countries in our model. Naturally, all such eects would be indirect and, similar to the analysis of FDI liberalization, we discuss three GE channels through which trade liberalization could impact FDI. ˆ First-order GE eect of DTAs on FDI. A fall in the barriers between US and the EU will lead to lower inward multilateral resistance, via the direct relationship between 12 bilateral trade frictions and the IMR as captured by equation (9). In turn, a lower inward multilateral resistance will stimulate investment via equation (15). ˆ Second-order GE eect of DTAs on FDI. Triggered by trade liberalization the outward multilateral resistances for US and the EU will decrease (via (9)-(10)). In turn, this will lead to higher factory-gate prices (via (11)) and larger sizes (via (12) and (13)) in the US and the EU. As discussed earlier, larger sizes would stimulate FDI (via (15)). ˆ Third-order GE eects of DTAs on FDI. Finally, similar to the impact of FDI liber- alization, a fall in trade barriers will trigger `third-order GE eect of DTAs on FDI', which are channeled via the OMR, through system (9)-(10), and via physical capital accumulation, as captured by equation (14). In sum, this section demonstrated how our structural system captures and decomposes a series of channels through which DTAs may aect FDI in member and non-member countries. We capitalize on this analysis in Section 4.2, where we simulate the GE eects of DTAs based on our own partial estimates of the eects of DTAs on trade and investment, which we obtain in Section 4.1 based on the econometric models that we specify next. 2.3 From Theory to Empirics A key objective and contribution of this paper is to test for causal links between DTAs, trade, and FDI. Establishing such links, and obtaining estimates of the corresponding direct/partial eects of DTAs on trade and FDI, would also enable us to translate them into GE eects of trade liberalization on FDI through the structural links that we just described in the previous section. In this section, we rely on system (8)-(15) to specify our estimating equations for trade and FDI. Specically, as noted earlier, equation (8) is the standard structural gravity equation from the trade literature, while (15) is our theoretical gravity equation for FDI. To estimate both equations, we will capitalize on the latest developments in the empirical trade 13 12 literature. We start with the estimating equation for bilateral trade ows: Xij,t = exp [ψi,t + ϕj,t + µij + GRAV_TRADEij,t α + DTA_TRADEij,t β ] + ϵij,t , ∀i,j. (17) Here, Xij,t denotes nominal (cf. Baldwin and Taglioni, 2006) exports from i to j at time t. Consistent with theory, Xij,t includes international and domestic trade ows (cf. Yotov, 2022). Estimating equation (17) includes three sets of xed eects. ψi,t and ϕj,t denote exporter- time and importer-time xed eects, respectively, which will account for the country-size and the multilateral resistance terms (cf. Anderson and van Wincoop, 2003) in equation (8), and also for any other observable or unobservable factors that aect trade ows on the exporter or on the importer side. µij denotes a set of pair xed eects, which will control for all time-invariant bilateral trade costs (cf. Egger and Nigai, 2015) and will mitigate endogeneity concerns with respect to the bilateral policy variables in our setting (cf. Baier and Bergstrand, 2007), including DTAs. Our main results will be obtained with directional pair xed eects, which allow for asymmetric time-invariant trade costs depending on the direction of trade ows, i.e., from i to j vs. from j to i. The vector GRAV_TRADEij,t includes a set of time-varying bilateral control variables that control for WTO membership (W T Oij,t ), economic sanctions (SAN CTij,t ), and bilateral investment treaties (BITij,t ). In addition, we also include a full set of time-varying border indicators ( t BRDRij,t ), which would capture any common globalization trends (e.g., im- provements in communication, transportation, communication, etc.). Finally, the vector DTASij,t includes the variables whose estimates would be of central interest to us. Speci- cally, we will dierentiate between the eects of preferential trade agreements (P T Aij,t ), the eects of deep trade agreements (DT Aij,t ), and we will allow for the eects of DTAs to vary depending on their depth (DEP T Hij,t ), which will be measured by the number of provisions that they include. We estimate equation (17) with the Poisson Pseudo-Maximum-Likelihood (PPML) esti- 12 Larch and Yotov (2022) survey the empirical gravity literature and synthesize the best practices for gravity estimations. 14 mator in order to account for the presence of heteroskedasticity in the trade data and to take advantage of the information contained in the zero trade ows, cf. Santos Silva and Tenreyro (2006, 2011). We use three-year interval data, cf. Cheng and Wall (2005) and Egger et al. 13 (2022). Finally, we cluster the standard errors by country pair. Next, guided by equation (15), we specify our estimating gravity equation for FDI as follows: value F DIij,t = exp ψi,t + ϕj,t + µij + GRAV_FDIij,t α ˜ +ϵ ˜ + DTA_FDIij,t β ˜ij,t , ∀i ̸= j. (18) value Here, F DIij,t is the value of FDI stock from origin i to destination j at time t. Capitalizing on the developments in the bilateral trade and FDI literatures, and for consistency with our estimating equation for trade ows, we specify our FDI econometric model to be as close as possible to our estimating equation for trade ows given in equation (17). Specically, we use the same estimator (i.e., PPML), we include the same set of xed eects (i.e., origin- time xed eects (ψi,t ), destination-time xed eects (ϕj,t ), and directional pair xed eects (µij )), and we employ the same set of time-varying policy covariates (i.e., indicators for WTO membership (W T Oij,t ), for bilateral investment treaties (BITij,t ), and for sanctions (SAN CTij,t )). Finally, just as in our trade specication, we rely on three-year interval data and we use the same clustering (i.e., by country pair). Even though, from an econometric perspective, we will use exactly the same set of exporter-time and importer-time xed eects as in our trade equation, the country-time xed eects in the FDI model would proxy and account for dierent variables. Following the 14 existing empirical FDI literature, possible robust determinants of FDI in the country of 13 Cheng and Wall (2005) note that `[f]ixed-eects estimation is sometimes criticized when applied to data pooled over consecutive years on the grounds that dependent and independent variables cannot fully adjust in a single year's time.' (footnote 8, p. 52). Treer (2004) also criticizes trade estimations pooled over consecutive years. He uses three-year intervals. Baier and Bergstrand (2007) use 5-year intervals. Olivero and Yotov (2012) provide empirical evidence that gravity estimates obtained with 3-year and 5-year lags are very similar. Most recently, Egger et al. (2022) show that gravity models with three-way xed eects deliver similar estimates of the common estimates of FTAs. 14 The two leading empirical FDI studies are Eicher et al. (2012) and Blonigen and Piger (2014). The objective of both studies is to identify a set of robust FDI determinants. Both papers utilize Bayesian Model Averaging and each of them comes up with a set of covariates which vary across the four dimensions that 15 origin include corporate tax rate, corruption, and bureaucratic red tape, while possible can- didates at the destination include level of corruption, internal tensions, corporate tax rate, bureaucratic red tape, quality of institutions, etc. Finally, the pair xed eects in (18) will absorb and account for bilateral distance, common ocial language, colonial relationships, which, similar to the trade literature, have been found to be among the most robust FDI determinants by both Eicher et al. (2012) and Blonigen and Piger (2014). There are two dierences between equations (17) and (18). First, we cannot include the set of time-varying border eects ( t BRDRij,t ) in equation (18) since we only use data on international transactions. This is why we use dierent notation for the vector of time- varying gravity covariates (GRAV_FDIij,t ). We also allow for potential dierences in the estimated impact of the common policy covariates by denoting the vector of their estimates ˜. α Second, and more important for our purposes, we use a dierent set of variables to capture the impact of DTAs on FDI in vector DTA_FDIij,t . Specically, in addition to including indicators for PTAs (P T Aij,t ) and DTAs (DT Aij,t ), we add two more covariates. First, motivated by Osnago et al. (n.d.), Crawford and Kotschwar (2020), and Laget et al. (2021), we include a separate indicator variable (IN Vij,t ) that takes a value of one for agreements that include investment provisions. Second, we also account for depth of the investment treaties by using a count variable (IN V _DEP T Hij,t ) for the number of investment provisions within the agreements with investment provisions, i.e., similar to the relationship between P T Aij,t and DEP T Hij,t on the trade side, IN V _DEP T Hij,t is a continuous variable that is equal 15 to zero when IN Vij,t is zero. Estimating equations (17) and (18) will deliver the estimates of the eects of DTAs on trade and investment that we will describe in Section 4.1 and use to obtain GE results in we propose to capture in our study. 15 The inclusion of trade agreement variables in our FDI gravity model is consistent with Eicher et al. (2012) and Blonigen and Piger (2014) who nd that regional trade agreements are among the most important time- varying bilateral determinants of FDI ows. Interestingly, however, neither Eicher et al. (2012) nor Blonigen and Piger (2014) distinguish between the average eects of RTAs and the eects of RTAs covering FDI. As demonstrated by Crawford and Kotschwar (2020) and Laget et al. (2021), FDI chapters and provisions are an important part of contemporary integration eorts. We will provide evidence that such provisions are indeed a very important determinant of FDI. 16 Section 4.2. Before that, we describe our data. 3 Data and Sources To perform the empirical analysis we build a balanced panel data set for 89 countries over the period 1990-2011, covering more than 96 percent of world GDP and for more than 16 94 percent of FDI throughout the sample period. Our data set includes the following variables: foreign direct investment, trade agreements, trade ows, gross domestic product (GDP), employment, physical capital, bilateral investment treaties, sanctions, and WTO membership. We describe the sources to obtain these variables, as well as their construction, in turn next. ˆ FDI Data. We use two sources to construct the FDI variable, (F DIij,t ), which takes a central stage in our analysis. The main source for FDI data is the Bilateral FDI Statis- tics database of the United Nations Conference on Trade and Development (UNCTAD). These data can be accessed at http://unctad.org/en/Pages/DIAE/FDI%20Statistics/ FDI-Statistics-Bilateral.aspx. UNCTAD's FDI data covers inows, outows, inward stock, and outward stock for 206 countries over the period 1990-2011. Data are col- lected from national sources and international organizations and to ensure maximum coverage the data are mirrored. The second source of FDI data is the International Direct Investment Statistics database, which is constructed and maintained by the Or- ganization for Economic Co-operation and Development (OECD). OECD's data oers detailed statistics for inward and outward foreign direct investment ows and positions (stocks) of the OECD countries, including transactions between the OECD members and non-member countries. We use the OECD data to ensure consistency and maxi- mum coverage. Finally, we note that, given our theory, we focus our analysis on FDI 17 stocks (positions), which is also the FDI category for which most data are available. 16 The list of countries and their respective alpha ISO3 codes appear in the rst two columns of Table 5. 17 Anderson et al. (2019) utilize the same sources to construct a cross-section FDI data set. For the 17 ˆ Trada Agreements Data. To account for the presence and depth of trade agree- ments, we use the World Bank's database on deep trade agreements (DTA), cf. Hof- mann et al. (2019) and Mattoo et al., eds (2020), (https://datatopics.worldbank.org/ 18 dta/about-the-project.html). Capitalizing on the rich dimensionality of the DTA database, we construct and utilize several variables for our analysis. P T Aij,t is an indicator variable for the presence of any trade agreement between i and j at time t. DT Aij,t is an indicator denoting the presence of a deep agreement between i and j at time t. DEP T Hij,t is a count variable for the number of provisions in the correspond- ing DTA between i and j . IN Vij,t is an indicator variable that takes a value of one if the DTA between i and j includes investment provisions. Finally, IN V _DEP T Hij,t is a count variable for the number of investment provisions in the corresponding DTA between i and j. For further details on the general features of the DTA database we refer the reader to Hofmann et al. (2019) and Mattoo et al., eds (2020). In addition, for analysis with specic focus the investment provisions in the DTAs, we refer the reader to Crawford and Kotschwar (2020). ˆ Production Data. Data on GDP, employment, and capital stocks are from the Penn World Tables 8.0, cf. Feenstra et al. (2013) (http://www.rug.nl/research/ggdc/data/ o pwt/). For data on GDP, we employ Output-side real GDP at current PPPs (CGDP ), which compares relative productive capacity across countries at a single point in time, as the initial level in our counterfactual experiments, and we use Real GDP using na national-accounts growth rates (CGDP ) for our income-based cross-country growth regressions. We measure employment in eective units by multiplying the Number of persons engaged in the labor force with the Human Capital Index, which is based on average years of schooling. Finally, capital stocks in the Penn World Tables 8.0 estimation analysis in this paper, we also utilize the time variation in the FDI data. In the counterfactual experiments, we rely on the methods of Anderson et al. (2019) to calibrate some parameters and vectors. See Section 4.2 for further details. 18 Specically, we used the DTA 2. Database: Information by Trade agreements. Bilateral observations. 18 are constructed based on accumulating and depreciating past investments using the perpetual inventory method. ˆ Trade Data. Data on international trade ows come from the United Nations Sta- tistical Division (UNSD) Commodity Trade Statistics Database (COMTRADE). We complement the international trade ows data with data on domestic trade ows from Anderson et al. (2020), which we use both for the estimation and for the counterfactual analysis. Anderson et al. (2020) construct domestic trade ows at the aggregate level in two steps. First, they use the ratio between aggregate manufacturing in gross values and total exports of manufacturing goods to construct a multiplier at the country-time level. (Data on gross manufacturing production, which came from the United Nations' IndStat database.) Then, they use this multiplier along with data on aggregate exports to project the values for domestic sales. Availability of data on domestic trade ows predetermined the time coverage of our estimating sample. ˆ Other Data. Finally, in the estimation analysis we employ the following addi- tional covariates as control variables. We control for the presence of bilateral in- vestment treaties with an indicator variable BITij,t , which comes from the UNC- TAD 's data on international investment agreements (IIAs), which can be found at http://investmentpolicyhub.unctad.org/IIA. Data on sanctions come from the Global Sanctions Database (GSDB), cf. Felbermayr et al. (2020) and Kirilakha et al. (2021) (http://www.rug.nl/research/ggdc/data/pwt/). We use the GSDB to include and in- dicator variable (SAN CTij,t ) for the presence of sanctions in our estimations. Finally, data on WTO membership, captured by an indicator variable W T Oij,t in our analysis, come from the Dynamic Gravity Dataset (DGD) of the U.S. International Trade Com- mission, cf. Gurevich and Herman (2018) (http://www.rug.nl/research/ggdc/data/ pwt/). 19 4 Empirical Findings and Analysis Subsection 4.1 presents our partial estimates of the impact of DTAs on trade and FDI. Then, in Subsection 4.2, we translate the partial estimates into corresponding GE eects, and we analyze the total impact of DTAs on FDI within our framework. 4.1 Estimation Results Our estimates of the eects of DTAs on trade are presented in Table 1. As discussed earlier, all estimates are obtained with the PPML estimator with three-way xed eects, includ- ing exporter-time, importer-time, and directional country-pair xed eects. In addition, all specications use time-varying border dummy variables to control for the presence of com- mon globalization trends, and indicator variables for WTO membership (W T Oij,t ), bilateral investment treaties (BITij,t ), and economic sanctions (SAN CTij,t ). In order to highlight the importance of DTAs and their provisions, we develop the estimation analysis in three steps, depending on the denition of the indicator variables designed to capture the impact of trade agreements. The estimates in column (1) include a single indicator variable, P T Aij,t , that reects the presence of a trade agreement of any type (e.g., deep or shallow) between i and j at time t. Several ndings stand out from column (1). Most important for our purposes, we note that, while positive, the estimate on P T Aij,t is economically small and it is not statistically signicant. A possible explanation for this result is that we impose a common eect for all trade agreements in our sample, regardless of their type and depth. We demonstrate that this is indeed the case in column (2) of Table 1. Before that, however, we briey discuss the estimates of the other policy covariates in our specication. First, we note that the estimate of the impact of WTO is positive, large, and statistically signicant. This result is at odds with some of the existing literature, e.g., Rose (2004) and Esteve-Pérez et al. (2020) who nd that WTO membership did not promote international 20 Table 1: Estimates of the Eects of DTAs on Trade (1) (2) (3) PTA DTA DEPTH P T Aij,t 0.083 -0.051 -0.069 (0.057) (0.059) (0.055) DT Aij,t 0.148 0.047 ∗∗ (0.028) (0.059) DEP T Hij,t 0.000 ∗ (0.000) W T Oij,t 0.516 0.526 0.538 ∗∗ ∗∗ ∗∗ (0.044) (0.044) (0.043) BITij,t 0.281 0.288 0.289 ∗∗ ∗∗ ∗∗ (0.099) (0.098) (0.097) SAN CTij,t 0.031 0.028 0.022 (0.024) (0.023) (0.022) N 58,323 58,323 58,323 Notes: This table reports estimates of the eects of trade agree- ments on trade ows over the period 1990-2011. The dependent variable is nominal trade ows. The estimator is PPML. All es- timates are obtained with three-year interval data and three-way xed eects, including exporter-time, importer-time, and direc- tional pair xed eects. In addition, all specications include a full set of time-varying border variables. The estimates of the border dummies and all xed eects, including the constant, are omitted for brevity. The standard errors in all specications are clustered by country pair. The dierence between the three columns are in the set of trade agreement variables. Specically, column (1) reports the average PTA eect across all agreements in the sample. Column (2) adds the eects of DTAs. Finally, in addition to PTAs and DTAs, column (3) introduces a contin- uous variable for DTA depth. The estimate on DEP T Hij,t in column (3) is 0.00047. See text for further details. 21 trade, however, our estimate on W T Oij,t conrms the ndings of Larch et al. (2019) for positive WTO eects when domestic trade ows are used to estimate gravity equations. In robustness analysis, which is available upon request, we conrm that when the model is estimated without domestic trade ows, the estimate of the eects of WTO is smaller and it is not statistically signicant. Second, we obtain a positive, sizable, and statistically signicant estimate of the impact of bilateral investment treaties (BITs) on trade ows. A possible explanation for this result is multinational production. Third, we do not obtain a signicant estimate of the impact of economic sanctions on trade. This result is consistent with estimates from Felbermayr et al. (2020), who argue that average estimates of the eects of sanctions may mask signicant heterogeneity across the eects of sanctions by type. In addition, Kirilakha et al. (2021) demonstrate that the relative importance of trade sanctions has fallen signicantly over time. In robustness analysis, we allowed for dierential eects of dierent types of sanctions. This did not aect our main ndings and conclusions. Finally, the estimates of the time-varying border variables from our specications, which we visualize in Figure 3, reveal signicant globalization eects during the period 1990-2011. Due to the use of pair xed eects, we need to drop one border variable, and we selected the border in 1990 as the baseline. Thus, all other border estimates are obtained as deviations from 1990 and should be interpreted accordingly, i.e., the positive and increasing estimates in Figure 3 capture the positive eects of globalization (smaller impact of borders) on in- ternational trade. The dip in 2002 is probably a reection of the economic recession during this period, while, due to the use of three-year intervals, the deep global economic recession of 2009 is not captured in our graph. In column (2) of Table 1 we allow for heterogeneous eects between shallow vs. deep trade agreements. To this end, we capitalize on the data from World Bank's DCRTA, cf. Hofmann et al. (2019) and Mattoo et al., eds (2020), to dene DT Aij,t as an indicator that takes a value of one for deep trade agreements (i.e., we use the variable `pta_mapped' 22 Figure 3: Common Globalization Eects, 1990-2011. Notes : This gure reports estimates of the impact of globalization on aggregate trade, 1990-2011. These indexes are obtained as the estimates on the time-varying border variables that we include in equation (17). All estimates in the gure are statistically signicant at any conventional level. See text for further details. 23 from the DCRTA database), and it is equal to zero otherwise. Thus, by construction, the observations that take a value of one in the DT Aij,t variable are a subset of the observations that are equal to one in the P T Aij,t dummy from column (1). The main nding from column (2) of Table 1 is encouraging and expected. Specically, we obtain a positive and statistically signicant estimate on DT Aij,t , which suggests that, on average, the deep trade agreements in our sample have led to a 16.1% (std.err. 3.184) increase in bilateral trade among member countries. This result is consistent with and reinforces the general message from Fernandes et al., eds (2021) that DTAs have been eective in stimulating international trade. Finally, in column (3) of Table 1, we use the DTA database to construct a continuous variable (DEP T Hij,t ), which counts the number of provisions within each of the DTAs in our sample. The number of provisions across the DTAs in our sample varies between 12 and 432. The main result from column (3) is that, on average, the deeper the agreement, the more it would promote trade among its members. Specically, we obtain a positive and statistically signicant estimate on DEP T Hij,t (0.00047, std.err. 0.00023), which is consistent with the ndings from Osnago et al. (n.d.). Our estimate suggests that, depending on the number of provisions that they include, the DTAs in our sample have led to trade increases between 0.576% (std.err. 0.289) and 23.012% (std.err. 12.744). We capitalize on this variation in Section 4.2, where we obtain corresponding GE eects on FDI. Our estimates of the eects of DTAs on FDI are presented in Table 2. As discussed earlier, and similar to our trade specication, all estimates are obtained with the PPML es- timator with three-way xed eects, including origin-time, destination-time, and directional pair xed eects. In addition, all specications include indicator variables for WTO member- ship (W T Oij,t ), bilateral investment treaties (BITij,t ), and economic sanctions (SAN CTij,t ). Similar to our approach with trade ows, in order to highlight the importance of DTAs and their provisions for FDI, we develop the estimation analysis sequentially, in four steps. The estimates in column (1) of Table 2 include a single indicator variable, P T Aij,t , that reects the presence of a trade agreement of any type (e.g., deep or shallow) between i and j 24 Table 2: Estimates of the Eects of DTAs on FDI (1) (2) (3) (4) PTA DTA INV DEPTH P T Aij,t -0.029 -0.100 -0.162 -0.134 (0.072) (0.102) (0.101) (0.100) DT Aij,t 0.072 -0.089 -0.120 (0.075) (0.084) (0.083) IN Vij,t 0.295 0.582 ∗∗ ∗ (0.108) (0.251) IN V _DEP T Hij,t -0.010 (0.009) BITij,t 0.017 0.017 0.023 0.028 (0.104) (0.104) (0.107) (0.108) SAN CTij,t -0.019 -0.017 -0.012 -0.012 (0.049) (0.048) (0.048) (0.048) W T Oij,t 0.465 0.476 0.469 0.463 (0.356) (0.353) (0.359) (0.363) N 18,158 18,158 18,158 18,158 Notes: This table reports estimates of the eects of trade agreements on FDI over the period 1990-2011. The dependent variable is the value of FDI stock. The estimator is PPML. All estimates are obtained with three-year interval data and three-way xed eects, including origin-time, destination-time, and directional pair xed eects. The estimates of all xed eects, including the constant, are omitted for brevity. The standard errors in all specications are clustered by country pair. The dierence between the three columns are in the set of trade agreement variables. Specically, column (1) reports the average PTA eect across all agreements in the sample. Column (2) adds the eects of DTAs. Column (3) isolates the DTAs with investment provisions. Finally, in addition to PTAs, DTAs, and DTAs with investment provisions, column (4) introduces a continuous variable for investment depth. See text for further details. 25 at time t. The main result from column (1) is that none of the eects of the policy variables in our model, including the impact of trade agreements and BITs, are statistically signicant. A possible explanation for this result is that some of the most signicant determinants of FDI are country-specic variables on the origin and/or on the destination side (e.g., corporate tax rate, corruption, bureaucratic red tape, quality of institutions, etc.). However, such determinants are fully controlled for and absorbed by the origin-time and the destination- time xed eects in our specication. Moreover, it is also possible (cf. Eicher et al., 2012; Blonigen and Piger, 2014) that a number of time invariant characteristics (e.g., bilateral distance, common ocial language, etc.) are important for FDI. However, similar to the country-specic variables, these eects are also absorbed in our econometric model (by the pair xed eects). Our nding on the insignicant impact of BITs may seem particularly strange, however, this result is common in the related literature, cf. Lesher and Miroudot (2006) and Laget et al. (2021). Next, in column (2) of Table 2 we allow for heterogeneous eects between shallow vs. deep trade agreements by using the same DT A variable which we constructed for our trade regressions. Even though the estimate on DT Aij,t is positive, it is economically small and not statistically signicant. Thus, unlike their signicant impact on trade, our estimates suggest that DTAs per se do not promote FDI. Motivated by Crawford and Kotschwar (2020) and Laget et al. (2021), in our next spec- ication (in column (3) of Table 2), we isolate the eects of DTAs that include investment provisions. To this end, we again rely on the World Bank's DCRTA, cf. Hofmann et al. (2019) and Mattoo et al., eds (2020), which includes 66 possible investment provisions. Based on this information, we construct a dummy variable, IN Vij,t , which takes a value of one if an agreement includes at least one investment provision, and it is equal to zero otherwise. Thus, by construction, the observations that take a value of one in the IN Vij,t indicator are a subset of the observations that are equal to one in the DT Aij,t dummy from column (2). The main nding from column (3) is that we obtain a positive, sizable, and statistically 26 signicant estimate on IN Vij,t , which suggests that, on average, the PTAs with investment provisions in our sample have led to a 34.33% (std.err 14.535) increase in FDI between their members. This result complements the ndings from Laget et al. (2021), who use rm level data for the period 2003-2015 and obtain positive estimates of the eects of provisions related to `intellectual property rights' and `visa and asylum', which vary between 32 and 50 percent, but do not nd signicant eects of investment provisions on FDI. Finally, in column (4) of Table 2 we use the DTA database to construct a continuous variable (IN V _DEP T Hij,t ), which counts the number of investment provisions within each of the DTAs in our sample. The number of investment provisions across the DTAs in our sample varies between 7 and 41. The estimates from column (4) do not reveal a signicant impact of the increase in the depth (number of provisions) on FDI. In fact, and pushing inference to the limit, our estimates suggest that the impact of additional provisions is actually negative. A possible interpretation of this result is that more investment provisions make the agreements more dicult to comply with. Despite the fact that our estimate on IN V _DEP T Hij,t is insignicant, we use it in combination with the positive estimates on IN Vij,t to construct a continuous FDI response to the impact of DTAs. The resulting eects are all positive and vary between 16.4% (std.err. 19.06) and 66.41% (std.err. 32.99), 19 depending on the number of investment provisions. We conclude the econometric analysis with two additional sets of experiments that fur- ther capitalize on the richness of the DCRTA data set to shed light on the links between 20 DTA provisions and FDI. First, we complement the analysis of Laget et al. (2021), who study the impact of several alternative PTA disciplines/provisions on FDI, by investigating the eects of all provision types from DCRTA on aggregate FDI. To this end, we rely on the dummy-variable specication from column (3) of Table 2 by sequentially replacing the 19 Specically, to obtain these bounds, we used the expression ˆIN V (exp(β ˆIN V _DEP T H + β × ij,t ij,t ˆIN V Nmin,max ) − 1) × 100, where β ˆIN V _DEP T H and β are the corresponding estimates from column ij,t ij,t (4) of Table 2), and Nmin,max denotes the minimum (7) and the maximum (42) number of investment provisions in our sample. 20 We are very grateful to Nadia Rocha and Vanessa Alviarez for suggesting to investigate the eects of additional provisions and alternative measures of the depth of DTAs. 27 dummy variable for DTAs with investment provisions (IN Vij,t ) with corresponding indicator variables for each of the other seventeen types of provisions from DCRTA. For brevity, in Table 3 we just summarize our main ndings with respect to the DTA provisions. Table 3: Estimates of the Eects of Alternative DTA Provisions on FDI (1) (2) (3) Provision Description Estimate Standard Error Investment 0.295 0.108 Labor Market Regulations 0.298 0.103 Export Taxes 0.273 0.164 Public Procurement 0.542 0.135 State-Owned Enterprises 0.364 0.134 Movement of Capital 0.182 0.117 Environmental Laws -0.221 0.239 Intellectual Property Rights -0.054 0.124 Visa and Asylum 0.121 0.113 Rules of Origin 0.116 0.147 Services 0.084 0.102 Technical Barriers to Trade 0.034 0.109 Subsidies -0.278 0.235 Sanitary and Phytosanitary -0.063 0.122 Trade Facilitation and Customs -0.246 0.187 Anti-dumping Duties . . Countervailing Duties . . Competition Policy . . Notes: This table reports estimates of the eects of a series of DTA provisions on FDI over the period 1990-2011. Each row corresponds to a separate econometric model based on the specication from column (3) of Table 2 after replacing the dummy variable for DTAs with investment provisions (IN Vij,t ) with corresponding indicator variables for each of the other seventeen types of provisions from DCRTA. The dependent variable is the value of FDI stock. The estimator is PPML. All estimates are obtained with three-year interval data and three-way xed eects, including origin-time, destination-time, directional pair xed eects, and all other control variables from column (3) of Table 2. The estimates of all xed eects and controls are omitted for brevity. The standard errors in all specications are clustered by country pair. See text for further details. The following results stand out from our analysis. First, due to (near) perfect collinear- ity with the DTAs dummy, we could not identify the eects of agreements with provisions covering `antidumping duties', `countervailing duties', and `competition policy'. Our indi- cator for agreements including `competition policy' provisions is perfectly collinear with the DTA dummy, while the correlations between the indicators for agreements with provisions 28 covering `antidumping duties' and `countervailing duties' and the DTA dummy were larger than 0.99. This is why these three types of provisions appear in the bottom panel of Table 3 without corresponding estimates. Second, we obtain positive and statistically signicant estimates for four additional pro- visions, which, together with our estimate for investment provisions, are reported in the top panel of Table 3. Consistent with the result from Laget et al. (2021) for FDI in service- related activities, we nd that `labor market regulations' promote overall FDI. In addition, we obtain a positive eect of provisions related to `export taxes'. We nd this result intu- itive as well. Finally, we obtain large, positive, and statistically signicant estimates of the eects of agreements with provisions that cover `public procurement' and `state owned en- terprises'. A possible explanation for this result is that such provisions ensure transparency and protection from the host state. We are not aware of existing estimates that link `public procurement' and `state owned enterprises' to FDI and, given the size and signicance of our estimates, we view this as an interesting and important channel that deserves a more detailed analysis and investigation. Finally, we do not nd evidence that other provisions, some of which potentially closely related to capital and technology movement, have had a signicant impact on FDI. Specif- ically, our estimates of the eects of provisions related to `intellectual property rights' and `movement of capital' are not statistically signicant. Consistent with Laget et al. (2021), our estimate of the eects of `movement of capital' is sizable and positive, but it is not statistically signicant in our case. Also similar to Laget et al. (2021), we obtain a negative estimate of the eects of provisions related to `environmental laws', but, again, our estimate is not statistically signicant. A possible explanation for the lack of signicance is that the correlation between the indicators for DTAs and agreements with environmental provisions is large, i.e., 0.724. Overall, the estimates in Table 3 indicate that, on average, only a few types of DTA provisions aected FDI directly. In our next experiment, we zoom in on the eects of alternative sets of provisions within 29 the broad category of `investment' provisions. Specically, the DCRTA distinguishes between six types of investment provisions, which are listed in the rst column of Table 4. As before, we start with a dummy-variables specication, as in column (3) of Table 2, by sequentially replacing the dummy variable for DTAs with investment provisions (IN Vij,t ) with corresponding indicator variables for each of the six types of investment provisions from DCRTA. Our results appear in panel A of Table 4, and we see that they are all positive and signicant. In fact, some of the new estimates are identical to our estimate for the overall impact of DTAs with investment provisions. The simple, mechanical explanation for this result is that some of the subcategories of investment provisions (e.g., for `protection' and `liberalization') appear in all DTAs that cover investment. Thus, the indicator variables for such provisions are perfectly collinear with our main dummy variable (IN Vij,t ) from column (3) of Table 2. We do, however, obtain positive estimates for some provision types (e.g., covering `transparency') that are not perfectly collinear with IN Vij,t . Table 4: Estimates of the Eects of Alternative Investment Provisions on FDI A. Indicator B. Depth Provision Description Est. Std.Err. Est. Std.Err. Est. Std.Err. (1) (2) (3) (4) (5) (6) (7) Protection 0.295 0.108 0.378 0.169 -0.007 0.013 Liberalization 0.295 0.108 0.264 0.273 0.007 0.056 Transparency 0.185 0.108 0.461 0.164 -0.141 0.064 Regulation 0.289 0.108 0.532 0.159 -0.128 0.055 Dispute Settlement 0.297 0.108 0.553 0.298 -0.095 0.100 Scope and Denitons 0.295 0.108 0.287 0.392 0.002 0.072 Notes: This table reports estimates of the eects of a series of DTA investment provisions on FDI over the period 1990-2011. Each row in each panel corresponds to a separate econometric model. The results in panel A are based on the specication from column (3) of Table 2 after replacing the dummy variable for DTAs with investment provisions (IN Vij,t ) with corresponding indicator variables for each of the six types of investment provisions from DCRTA. The results in panel B are based on the specication from column (4) of Table 2, where we also allow for dierential eects depending on the number of investment provisions (`depth') within each type. The dependent variable is always the value of FDI stock. The estimator is PPML. All estimates are obtained with three-year interval data and three-way xed eects, including origin-time, destination-time, directional pair xed eects, and all other control variables from columns (3) and (4) of Table 2, respectively. The estimates of all xed eects and controls are omitted for brevity. The standard errors in all specications are clustered by country pair. See text for further details. Since, due to perfect or near-perfect collinearity, we could not obtain informative esti- mates of the eects of all types of investment provisions with an indicator-variable approach, 30 we also allow for additional and dierential eects of such provisions depending on their depth. Specically, in panel B of Table 4 we rely on the specication from column (4) of Table 2 by sequentially replacing the dummy variables for DTAs with investment provisions (IN Vij,t ) and their depth (IN V _DEP T Hij,t ) with the corresponding indicator and contin- uous variables, respectively, for each of the six types of investment provisions. The main message from panel B of Table 4 is consistent with our previous result for no signicant impact of the increase in the depth (number of investment provisions) on FDI. In fact, our estimates of the eect of `depth' for some provision types (e.g., `transparency' and `regula- tion') are negative and statistically signicant, suggesting that more investment provisions and additional complexity may make the agreements more dicult to comply with. In sum, the analysis in this section demonstrated that while trade agreements do not necessarily promote trade and FDI on average, the impact of deep trade agreements on trade and the impact of deep trade agreements that include investment provisions on FDI are positive and statistically signicant. In addition to `investment' provisions, we identied several other types of DTA provisions that have stimulated FDI. We also oered evidence that deeper trade agreements (as measured by the number of provisions) lead to larger trade liberalization eects. However, we do not see evidence that the increase in the number of investment provisions in DTAs has lead to more FDI. In fact, some of our results suggest that additional provisions and added complexity may make DTAs less eective in promoting FDI. Next, in Section 4.2, we rely on the partial estimates from this section to obtain GE eects of DTAs on FDI. 4.2 Counterfactual Analysis This section translates the partial equilibrium estimates from Tables 1 and 2 into GE eects of DTAs on FDI. To this end, we rely on the structural trade and investment system from Section 2.1. We start the analysis by describing the steps that we took to make system (8)-(15) 31 operational for our purposes. For the counterfactual analysis we use as baseline the latest available year in our data set, which is 2011 and was determined by the availability of capital stock data. In order to perform the counterfactual analysis, we need to set values for the parameters. Some parameters are borrowed from the literature: i) the elasticity of substitution is set equal to σ = 6, which is standard in the trade literature, ii) the consumer discount factor is set equal to β = 0.98 (Yao et al., 2012), and iii) the country-specic capital shares of production αj and the country-specic adjustment costs of capital δj are calculated using the Penn World Tables and reported in columns (3) and (4) of Table 5, respectively. We calibrate other parameters in order to match the observed data. The share of tech- nology capital of a country to all destinations as a share from total world technology capital value (ηi ) is calculated using F DIij : value j F DIij ηi = value . (19) i j F DIij in value ϕj is calculated using the relationship between inward FDI (F DIj = i F DIij ) and physical capital in the production function along with FDI and physical capital data and data on the capital shares: in αj × (F DIj /Kj ) ϕj = in . (20) 1 + αj (F DIj /Kj ) The exact values for η and ϕ are given in columns (5) and (6) of Table 5. Table 5: Calibrated Parameters (1) (2) (3) (4) (5) (6) ISO3 Country α δ η ϕ AGO Angola 0.47 0.0528 0.00078 0.056 ARG Argentina 0.57 0.0394 0.00792 0.024 AUS Australia 0.44 0.0375 0.01375 0.052 AUT Austria 0.43 0.0442 0.00521 0.058 AZE Azerbaijan 0.79 0.0725 0.00058 0.041 BEL Belgium 0.38 0.0452 0.00677 0.235 BGD Bangladesh 0.47 0.0407 0.00322 0.003 BGR Bulgaria 0.51 0.0565 0.00093 0.091 BLR Belarus 0.48 0.0506 0.00152 0.031 BRA Brazil 0.44 0.0475 0.02653 0.042 CAN Canada 0.39 0.0371 0.01658 0.057 Continued on next page 32 Table 5  Continued from previous page (1) (2) (3) (4) (5) (6) ISO3 Country α δ η ϕ CHE Switzerland 0.35 0.0568 0.00683 0.190 CHL Chile 0.55 0.0427 0.00305 0.057 CHN China 0.46 0.0530 0.18395 0.009 COL Colombia 0.39 0.0411 0.00536 0.008 CYP Cyprus 0.48 0.0357 0.00117 0.186 CZE Czech Republic 0.49 0.0416 0.00359 0.063 DEU Germany 0.39 0.0389 0.04024 0.031 DNK Denmark 0.37 0.0431 0.00320 0.054 DOM Dominican Republic 0.34 0.0307 0.00097 0.009 ECU Ecuador 0.55 0.0466 0.00160 0.007 EGY Egypt, Arab Rep. 0.62 0.0597 0.00351 0.029 ESP Spain 0.39 0.0375 0.02146 0.047 EST Estonia 0.42 0.0461 0.00030 0.086 ETH Ethiopia 0.47 0.0494 0.00073 0.002 FIN Finland 0.39 0.0412 0.00323 0.049 FRA France 0.37 0.0382 0.03254 0.036 GBR United Kingdom 0.39 0.0379 0.02665 0.083 GHA Ghana 0.47 0.0553 0.00057 0.018 GRC Greece 0.47 0.0335 0.00396 0.014 GTM Guatemala 0.58 0.0454 0.00037 0.030 HKG Hong Kong SAR, China 0.48 0.0435 0.00687 0.228 HRV Croatia 0.34 0.0436 0.00106 0.039 HUN Hungary 0.41 0.0436 0.00229 0.065 IDN Indonesia 0.54 0.0370 0.01334 0.019 IND India 0.50 0.0558 0.04216 0.007 IRL Ireland 0.52 0.0496 0.00238 0.292 IRN Iran, Islamic Rep. 0.74 0.0588 0.01147 0.001 IRQ Iraq 0.70 0.0558 0.00099 0.004 ISR Israel 0.45 0.0448 0.00242 0.026 ITA Italy 0.46 0.0380 0.03135 0.021 JPN Japan 0.39 0.0466 0.07416 0.004 KAZ Kazakhstan 0.58 0.0400 0.00270 0.065 KEN Kenya 0.57 0.0519 0.00049 0.017 KOR Korea, Rep. 0.50 0.0501 0.02197 0.012 KWT Kuwait 0.75 0.0557 0.00204 0.008 LBN Lebanon 0.56 0.0413 0.00134 0.002 LKA Sri Lanka 0.31 0.0446 0.00119 0.001 LTU Lithuania 0.53 0.0418 0.00050 0.058 LUX Luxembourg 0.46 0.0463 0.00649 0.634 LVA Latvia 0.45 0.0336 0.00037 0.051 MAR Morocco 0.51 0.0521 0.00176 0.045 MEX Mexico 0.61 0.0362 0.01590 0.050 MKD North Macedonia 0.47 0.0406 0.00026 0.031 MLT Malta 0.46 0.0529 0.00015 0.219 MYS Malaysia 0.47 0.0596 0.00587 0.034 NGA Nigeria 0.50 0.0581 0.00178 0.050 NLD Netherlands 0.41 0.0401 0.01680 0.109 NOR Norway 0.48 0.0399 0.00348 0.094 NZL New Zealand 0.43 0.0408 0.00124 0.081 OMN Oman 0.70 0.0602 0.00110 0.029 PAK Pakistan 0.47 0.0551 0.00468 0.007 PER Peru 0.69 0.0395 0.00364 0.016 PHL Philippines 0.64 0.0488 0.00485 0.012 POL Poland 0.44 0.0491 0.00746 0.046 PRT Portugal 0.39 0.0351 0.00382 0.043 QAT Qatar 0.81 0.0960 0.00235 0.034 ROM Romania, Socialist Republic of 0.53 0.0518 0.00298 0.049 RUS Russian Federation 0.26 0.0402 0.03052 0.011 SAU Saudi Arabia 0.72 0.0530 0.00976 0.009 SDN Sudan 0.41 0.0664 0.00035 0.008 SER Serbia 0.42 0.0402 0.00103 0.035 SGP Singapore 0.56 0.0533 0.00494 0.182 SVK Slovak Republic 0.46 0.0520 0.00125 0.073 SVN Slovenia 0.33 0.0439 0.00086 0.023 Continued on next page 33 Table 5  Continued from previous page (1) (2) (3) (4) (5) (6) ISO3 Country α δ η ϕ SWE Sweden 0.45 0.0453 0.00408 0.182 SYR Syrian Arab Republic 0.47 0.0552 0.00122 0.003 THA Thailand 0.61 0.0655 0.00946 0.035 TKM Turkmenistan 0.47 0.0430 0.00115 0.001 TUN Tunisia 0.50 0.0474 0.00108 0.005 TUR Türkiye 0.56 0.0554 0.00729 0.037 TZA Tanzania, United Republic of 0.57 0.0435 0.00055 0.032 UKR Ukraine 0.44 0.0308 0.00631 0.013 USA United States 0.40 0.0475 0.17546 0.023 UZB Uzbekistan 0.47 0.0327 0.00099 0.003 VEN Venezuela, RB 0.63 0.0389 0.00366 0.020 VNM Vietnam 0.47 0.0455 0.00507 0.010 ZAF South Africa 0.46 0.0506 0.00419 0.066 ZWE Zimbabwe 0.44 0.0371 0.00004 0.083 Notes : This table reports results from our calibration for some parameters. Column (1) gives the iso3-country codes, column (2) the country names. The country-specic capital shares of production αj are reported in column (3), while in column (4) we give the values of the country-specic adjustment costs of capital δ . The values for the η 's, i.e., the share of technology capital of a country to all destinations, is given in columns (5). Column (6) gives the values for the production share of FDI (ϕ). See text for further details. For the baseline, we calibrate bilateral trade frictions to the power of 1 − σ, i.e., trade −σ openness t1 ij , using data on trade ows, income, and expenditure and solving Equations 1−σ (9) and (10) for given trade costs and calculating a new matrix tij using Equation (8) until convergence, where we normalize all internal trade costs and trade costs for one exporter to one. Given trade costs, we can calculate the inward and outward multilateral resistance indexes using Equations (9) and (10), respectively, where we set the inward MRT for Angola to one. Mj is calibrated using data on income, FDI, and constructed MRTs and the following theory-consistent equation for technology capital: βηj ϕ j Yj η j ϕ2 i Yi Mj = 1 − ϕj ηi + . (21) 1 − β + βδj,M i̸=j, Pj i̸=j, Pj F DIij >1 F DIji >1 With this, we can construct FDI openness (ωij ) using the following equation for FDI ows 34 21 in values: 2 βηi ϕi Yi ηi ϕ2 k Yk ϕj Yj value F DIij = ωij 1 − ϕi ηk + . (22) 1 − β + βδi,M k̸=i, Pi k̸=i, Pi Mi F DIki >1 F DIik >1 Aj /γj , the preference-adjusted technology, is calibrated using Equations (11) and (12). As the value of domestic income and expenditure calculated from the trade data do not perfectly match up, we dene ψj ≡ Ej / Yj + ηj i∈Nji,t ϕi Yi − ϕj Yj i∈Nij,t ηi as an exogenous country-specic parameter that accounts for these trade imbalances. In the spirit of Dekle et al. (2007, 2008), we rst eliminate all exogenous trade imbalances and take the equilibrium without trade imbalances as baseline. In order to highlight the alternative channels through which DTAs aect FDI, and also to capitalize on the full set of our partial estimates, we perform two sets of experiments. First, we rely on our estimates of the dummy variables for DTAs and DTAs with investment provisions from column (2) of Table 1 and column (3) of Table 2, respectively. Then, we also obtain corresponding eects based on the estimates of the continuous depth variables from column (3) of Table 1 and column (4) of Table 2. Consistent with the discussion in Section 2.2, we perform each of the two experiments in two steps. First, we change the vector of FDI frictions. Then, in addition, we change the vector of trade costs. As the DTAs are already in place, we perform an ex-post evaluation, i.e., we assume that in the baseline the agreement is in place and simulate the eect without DTAs as counterfactual. We then report the change from the baseline to the counterfactual, i.e., baseline value minus counterfactual value relative to the counterfactual value. 21 The values of ωij are restricted to be between zero and one. Hence, we normalize each row by the maximum element. Further, all zero FDI ows are leading to zero ωij 's by construction. To avoid this, we set ωij Mi = 1.00001 for those observations. 35 Table 6: Total GE Eects on Inward and Outward FDI Panel A: Dummy DTA variable Panel B: Continuous DTA variable ISO3 FDI lib. FDI and trade lib. FDI lib. FDI and trade lib. inw. FDI outw. FDI inw. FDI outw. FDI inw. FDI outw. FDI inw. FDI outw. FDI (1) (2) (3) (4) (5) (6) (7) (8) (9) AGO 0.12 0.00 0.59 0.00 0.13 0.00 0.42 0.00 ARG 1.15 0.53 2.06 1.55 1.37 0.65 1.95 1.08 AUS 6.93 4.47 7.90 4.85 6.36 3.72 6.97 4.04 AUT 0.99 0.53 1.86 1.75 1.35 0.77 1.91 1.43 AZE 0.24 0.00 1.12 0.01 0.25 0.00 0.82 0.01 BEL 1.01 1.00 1.93 1.45 1.36 1.39 1.95 1.66 BGD 0.24 0.02 1.09 0.17 0.25 0.02 0.80 0.05 BGR 0.92 0.10 1.80 0.26 1.24 0.14 1.78 0.23 BLR 0.22 0.01 1.01 0.10 0.23 0.01 0.72 0.04 BRA 0.60 1.77 1.52 2.58 0.69 2.16 1.28 2.47 CAN 6.16 3.25 7.07 6.29 7.13 3.25 7.72 6.75 CHE 3.47 1.96 4.35 2.62 3.28 2.28 3.84 2.52 CHL 17.97 2.50 18.93 3.04 21.01 3.29 21.65 3.70 CHN 1.43 69.50 2.33 90.59 1.04 51.93 1.61 61.73 COL 1.54 0.52 2.24 0.74 1.58 0.59 2.03 0.72 CYP 0.82 0.06 1.48 0.18 1.13 0.09 1.54 0.16 CZE 1.00 0.14 1.89 0.36 1.35 0.21 1.92 0.34 DEU 1.00 5.31 1.88 10.94 1.35 7.39 1.92 10.53 DNK 1.00 0.42 1.92 1.01 1.35 0.58 1.94 0.91 DOM 10.17 0.06 10.78 0.12 10.23 0.06 10.65 0.12 ECU 0.14 0.00 0.68 0.06 0.15 0.00 0.50 0.02 EGY 0.16 0.02 0.79 0.49 0.17 0.02 0.55 0.17 ESP 0.96 2.14 1.80 4.31 1.31 2.90 1.85 4.11 EST 0.23 0.02 1.09 0.03 0.24 0.02 0.79 0.03 ETH 0.11 0.01 0.48 0.04 0.12 0.01 0.35 0.03 FIN 0.98 0.32 1.84 0.72 1.33 0.47 1.89 0.70 FRA 1.01 3.35 1.95 7.58 1.35 4.89 1.95 7.25 GBR 0.99 3.61 1.90 7.01 1.34 5.02 1.92 6.96 GHA 0.13 0.02 0.63 0.03 0.14 0.02 0.44 0.02 GRC 0.87 0.17 1.66 0.54 1.18 0.24 1.67 0.45 GTM 5.53 0.01 6.02 0.04 5.06 0.01 5.38 0.04 HKG 0.21 0.07 0.93 0.56 0.22 0.07 0.67 0.24 HRV 0.24 0.07 1.00 0.07 0.28 0.11 0.75 0.12 HUN 0.93 0.16 1.81 0.56 1.23 0.23 1.80 0.46 IDN 10.66 2.12 11.47 3.53 8.00 1.65 8.50 2.51 IND 4.31 11.85 5.25 15.97 3.52 9.43 4.11 11.44 IRL 0.97 0.30 1.81 0.74 1.32 0.43 1.87 0.68 IRN 0.10 0.05 0.51 0.54 0.11 0.06 0.34 0.25 IRQ 0.11 0.00 0.46 0.03 0.11 0.00 0.34 0.00 ISR 0.19 0.02 0.90 0.30 0.21 0.02 0.67 0.14 ITA 1.04 4.22 1.99 7.80 1.40 5.82 2.00 7.82 JPN 3.51 27.05 4.39 33.86 3.25 25.62 3.82 29.94 KAZ 0.22 0.01 1.07 0.09 0.23 0.01 0.77 0.04 KEN 0.18 0.00 0.87 0.01 0.20 0.00 0.63 0.01 KOR 10.07 23.79 11.07 26.18 12.10 28.46 12.75 29.89 KWT 0.11 0.00 0.50 0.01 0.12 0.00 0.36 0.00 LBN 0.12 0.03 0.63 0.22 0.13 0.04 0.44 0.13 LKA 0.13 0.02 0.58 0.16 0.14 0.03 0.41 0.09 LTU 0.89 0.02 1.78 0.05 1.19 0.03 1.76 0.05 LUX 0.96 0.99 1.74 1.52 1.31 1.42 1.80 1.74 LVA 0.82 0.00 1.48 0.03 1.12 0.00 1.53 0.02 MAR 5.50 0.07 6.21 0.36 5.20 0.07 5.62 0.19 MEX 8.72 3.60 9.72 8.56 9.77 4.00 10.41 8.88 MKD 6.45 0.10 7.15 0.12 9.84 0.15 10.29 0.16 MLT 0.90 0.01 1.54 0.04 1.26 0.01 1.66 0.03 MYS 10.67 1.22 11.51 2.01 7.71 0.91 8.22 1.41 NGA 0.22 0.00 0.93 0.03 0.23 0.00 0.67 0.01 NLD 1.04 1.81 1.99 5.38 1.40 2.64 2.00 4.64 NOR 1.51 0.70 2.43 1.04 1.64 0.89 2.22 1.16 NZL 7.45 0.29 8.32 0.33 5.33 0.21 5.88 0.25 OMN 5.47 0.05 6.07 0.06 5.16 0.04 5.52 0.05 Continued on next page 36 Table 6  Continued from previous page Panel A: Dummy DTA variable Panel B: Continuous DTA variable ISO3 FDI lib. FDI and trade lib. FDI lib. FDI and trade lib. inw. FDI outw. FDI inw. FDI outw. FDI inw. FDI outw. FDI inw. FDI outw. FDI (1) (2) (3) (4) (5) (6) (7) (8) (9) PAK 5.96 0.13 6.63 0.51 7.67 0.14 8.09 0.32 PER 13.33 0.42 14.26 0.74 12.90 0.39 13.50 0.65 PHL 10.72 0.77 11.59 1.78 7.72 0.59 8.25 1.23 POL 1.01 0.52 1.94 1.44 1.36 0.77 1.95 1.29 PRT 0.86 0.26 1.67 0.87 1.17 0.38 1.69 0.72 QAT 0.16 0.01 0.72 0.02 0.16 0.01 0.51 0.01 ROM 0.19 0.01 0.95 -0.01 0.21 0.02 0.67 0.00 RUS 0.24 0.29 1.13 1.06 0.26 0.31 0.82 0.70 SAU 0.18 0.03 0.87 0.12 0.19 0.04 0.63 0.07 SDN 0.06 0.00 0.26 0.00 0.06 0.00 0.17 0.00 SER 0.23 0.00 1.04 0.00 0.24 0.00 0.74 0.00 SGP 16.96 3.47 17.89 5.02 13.62 2.82 14.18 3.99 SVK 0.91 0.01 1.81 0.08 1.21 0.02 1.79 0.06 SVN 0.88 0.06 1.69 0.10 1.19 0.08 1.69 0.11 SWE 0.96 0.46 1.73 1.23 1.31 0.67 1.79 1.12 SYR 0.11 0.01 0.52 0.09 0.12 0.01 0.37 0.03 THA 10.72 1.56 11.62 3.22 7.78 1.23 8.32 2.34 TKM 0.06 0.01 0.33 0.07 0.07 0.01 0.21 0.04 TUN 0.14 0.01 0.67 0.20 0.15 0.01 0.46 0.10 TUR 0.23 0.05 1.06 0.70 0.24 0.05 0.75 0.33 TZA 0.19 0.00 0.87 0.04 0.20 0.00 0.63 0.01 UKR 0.16 0.02 0.81 0.28 0.17 0.03 0.56 0.11 USA 2.07 72.87 3.01 87.52 2.18 70.94 2.78 83.34 UZB 0.12 0.00 0.55 0.04 0.13 0.00 0.39 0.01 VEN 1.26 0.24 2.12 0.32 1.51 0.30 2.06 0.33 VNM 10.65 0.11 11.39 0.37 7.99 0.09 8.43 0.26 ZAF 0.24 0.02 1.10 0.14 0.25 0.02 0.78 0.08 ZWE 0.12 0.00 0.59 0.00 0.13 0.00 0.41 0.00 World 2.77 72.87 3.67 87.52 2.79 70.94 3.36 83.34 Lib-Countries 3.00 72.87 3.69 87.52 3.01 70.94 3.38 83.34 ROW 0.54 0.01 0.98 0.00 0.64 0.01 0.70 0.00 Notes : This table reports results from our counterfactual analysis. Column (1) gives the iso3-country codes. Panel A reports results based a uniform change in the bilateral FDI frictions between all countries that have signed a DTA with investment provisions that is based on our estimate of 0.295. Columns (2) and (3) report the percentage changes in inward and outward FDI, respectively, when DTAs change FDI frictions, while in columns (4) and (5) in addition to the change in FDI frictions DTAs also change trade frictions. Panel B reports results based on the estimates on the continuous depth variables. Columns (6) and (7) report the percentage changes in inward and outward FDI, respectively, when DTAs change FDI frictions, while in columns (8) and (9) in addition to the change in FDI frictions DTAs also change trade frictions. Given the main purpose of our analysis, and to keep the presentation of our results manageable, we focus the discussion of our counterfactual results on the percentage changes (between the baseline and the counterfactual scenarios) in the stocks of FDI per country. Specically, we construct and report percentage changes in inward and outward FDI stocks, i.e., the percentage changes in technology capital used in total at home and technology 37 capital from one country used abroad: in,b in,c in,c %∆F DI in = (F DIj − F DIj )/F DIj × 100, (23) out,b out,c out,c %∆F DI out = (F DIj − F DIj )/F DIj × 100, (24) where superscript b denote baseline values with DTAs in place, and superscript c the coun- terfactual situation without DTAs in place, and, consistent with our theory, inward FDI and outward FDI stocks per country can be calculated as follows: N in F DIj = i=1 (max{1, ωij Mi })ηi , (25) N F DIiout = j =1 (max{1, ωij Mi })ηi . (26) Note that the inward FDI stock can be seen as the global technology stock applied locally, whereas the outward FDI stock is the usage of a country's technology capital abroad. η determines the usage of FDI abroad of one country, i.e., outward FDI stocks per country will change a lot if this share is large (i.e., η is large), even if the change in technology capital Mi is comparably small. This is a result of the non-rival nature of FDI that we capture. On the other hand side, for inward FDI per country the η 's always sum to one and therefore changes in inward FDI are a weighted average of changes in the ωij Mi 's. Before we discuss our ndings, we draw the reader's attention to a caveat with our GE analysis, which is due to the fact that the underlying theory is based on the assumption of non-rival technology FDI, while our data includes all/aggregate FDI ows. This gap, of course, has implications for the quantitative results. Therefore, the specic indexes that we obtain and report in this section should be interpreted accordingly and with caution. Nevertheless, we believe that the main conclusions and policy implications that we will draw in this section about a disproportionately large impact of outward FDI will remain qualitatively the same if applied to appropriate data on technology FDI. Our ndings are reported in Table 6, where the rst column lists the ISO3 country codes 38 for the countries in our sample, Panel A reports the results from the scenario based on the estimates of the dummy DTA variables, and Panel B reports the eects that are based on the estimates of the continuous depth variables. The results in columns (2) and (3) of Table 6 are obtained in response to a uniform change in the bilateral FDI frictions between all countries that have signed a DTA with investment provisions that is based on our estimate of 0.295 (std.err. 0.108) from column (3) of Table 2. There are several things noteworthy. First, both inward and outward FDI increase for most of the countries. For the countries that have signed a DTA, the eect for inward FDI is on average an about 3% increase, while it amounts to 72% for outward FDI. The huge values for outward FDI are driven by the importance of the United States and China as the largest outward FDI countries. Their technology capital as a share of total world technology capital (i.e., their η 's) is about 18% (see Table 5). Hence, their stocks are used substantially in many countries of the world (the exact usage at the bilateral level also depends on the FDI frictions ω ). Even though the United States and China only increase their technology capital stock (M ) by about 0.7% and 1%, respectively, the eect on their outward FDI stocks is large due to the huge share of their FDI in world FDI and the non-rival nature, allowing to use the technology capital in all countries in the world simultaneously. On the inward FDI side, we see the largest increase for Chile, Singapore, Peru, Thailand, the Philippines, Malaysia, Indonesia, Vietnam, the Dominican Republic and the Republic of Korea. Those are all countries that have many DTAs and also rely substantially on inward FDI. On the other end of the spectrum are countries that are hardly aected, neither on the inward nor on the export side, such as Sudan, Turkmenistan, the Islamic Republic of Iran, and Iraq. Those countries do not have many (or any) DTAs in place and are also relatively closed in terms of FDI. Overall, we see a wide heterogeneity among countries. This is even more extreme for outward FDI, where the importance of the large outward FDI investors is very dominant. The estimates in columns (4) and (5) of Table 6 are obtained when, in addition to the 39 change in bilateral FDI frictions, we also change uniformly the vector of bilateral trade frictions based on our estimate from column (2) of Table 1. Relative to the scenario where only the bilateral FDI frictions are changed (i.e., the results presented in columns (2) and (3) of Table 6), we see qualitatively a very similar picture and quantitatively an increase in both, inward and outward FDI. Specically, on average, trade liberalization has contributed to 0.7 percentage points (or about 25%) increase in inward FDI and about 15 percentage points in outward FDI. These estimates reveal that trade liberalization via DTAs is an important channel to stimulate FDI, thus complementing the results from Anderson et al. (2019), who show that FDI liberalization is important for trade. Panel B of Table 6 reports estimates that are obtained based on the estimates on the continuous depth variables from Section 4.1. The estimates in columns (6) and (7) rely on the estimates from column (4) of Table 2. Allowing for the continuous depth leads overall quantitatively and qualitatively similar results, with heterogeneous changes across countries. Finally, the estimates in columns (8) and (9) of Table 6 are obtained when, in addition to the change in bilateral FDI frictions, we also change the vector of bilateral trade frictions based on our estimate from column (3) of Table 1. Similar to the uniform changes, the additional allowance for changes of bilateral trade frictions leads to larger eects for inward and outward FDI. To sum up, according to our analysis, the DTAs that were in force in 2011 have con- tributed to about 3% of inward FDI in the world and about 70% of outward FDI. The latter is heavily driven by the fact that some countries have large stocks of FDI used in many coun- tries in the world, multiplying the eect of any change in outward FDI of those countries due to changes in frictions. 40 5 Conclusion The objective of this paper was to study the links between deep trade liberalization in the form of DTAs and FDI. To this end, we identied and decomposed three channels through which DTAs impact FDI. First, we obtained signicant direct/partial equilibrium eects of DTAs and their investment provisions on FDI from a theory-motivated FDI gravity model. Second, we translated the partial estimates of the DTA eects on FDI into GE eects. This analysis highlighted the importance of the GE links between DTAs and FDI, and uncovered signicant asymmetries in the response of inward vs. outward FDI in our model. Finally, we performed counterfactual analysis of the impact of deep trade liberalization on FDI, which revealed that, through their impact on trade, DTAs promote FDI additionally. While, as discussed earlier, our counterfactual analysis is subject to criticism on the mismatch between the data used and the underlying theory, we believe that our conclusions about the disproportionately large impact of outward FDI would remain qualitatively the same if applied to appropriate data on technology FDI. We view this nding as novel and potentially important from a policy perspective, both for the negotiations of trade and investment agreements and for properly quantifying their implications. Moreover, we see signicant potential in developing and utilizing data sets on global technology transfers that would generate more precise partial estimates and more informative GE analysis of the links between trade liberalization and FDI and lead to clearer policy recommendations. In addition to the theory on the intensive margin that we utilize here, we expect signicant payos from developing theories that would capture the links between trade liberalization and the extensive margins (both domestic and international) of technology capital and its diusion in the global economy. 41 References Anderson, James E. and Eric van Wincoop, Gravity with Gravitas: A Solution to the Border Puzzle, American Economic Review, 2003, 93 (1), 170192. Anderson, James E., Mario Larch, and Yoto V. Yotov, Trade Liberalization, Growth, and FDI in Canada: A Structural Estimation Framework, unpublished policy report for Global A airs Canada, 2016. , , and , Trade and Investment in the Global Economy: A Multi-country Dynamic Analysis, European Economic Review, 2019, 120 (C). Anderson, James E, Mario Larch, and Yoto V Yotov,  Transitional Growth and Trade with Frictions: A Structural Estimation Framework, Economic Journal, 2020, 130 (630), 15831607. Armington, Paul S., A Theory of Demand for Products Distinguished by Place of Pro- duction, IMF Sta Papers, 1969, 16, 159176. Baier, Scott L. and Jerey H. Bergstrand, Do Free Trade Agreements Actually In- crease Members' International Trade?, Journal of International Economics, 2007, 71 (1), 7295. Baldwin, R.E. and D. Taglioni, Gravity for Dummies and Dummies for Gravity Equa- tions, NBER Working Paper No. 12516, 2006. Baltagi, Badi, Peter Egger, and Michael Pfaermayr, Estimating Regional Trade Agreement Eects on FDI in an Interdependent World, Journal of Econometrics, 2008, 145 (1-2), 194208. Blonigen, Bruce A. and Jeremy Piger, Determinants of Foreign Direct Investment, Canadian Journal of Economics, August 2014, 47 (3), 775812. Cheng, I-Hui and Howard J. Wall, Controlling for Heterogeneity in Gravity Models of Trade and Integration, Federal Reserve Bank of St. Louis Review, 2005, 87 (1), 4963. Crawford, J. and B. Kotschwar, Investment, Chapter 5 in the Handbook of Deep Trade Agreements, Edited by Mattoo, Rocha and Ruta, Washington, DC: World Bank, 2020. Dekle, Robert, Jonathan Eaton, and Samuel Kortum,  Unbalanced Trade, American Economic Review: Papers and Proceedings, 2007, 97, 351355. , , and ,  Global Rebalancing with Gravity: Measuring the Burden of Adjustment, IMF Sta Papers, June 2008, 55 (3), 511540. Di Ubaldo, Mattia and Michael Gasiorek, Non-trade Provisions in Trade Agreements and FDI, European Journal of Political Economy, 2022, p. 102208. Egger, Peter and Sergey Nigai, Structural Gravity with Dummies Only, CEPR Dis- cussion Paper No. DP10427, 2015. 42 Egger, Peter H., Mario Larch, and Yoto V. Yotov,  Gravity Estimations with Interval Data: Revisiting the Impact of Free Trade Agreements, Economica, January 2022, 89 (353), 4461. Eicher, Theo S., Lindy Helfman, and Alex Lenkoski, Robust FDI Determinants: Bayesian Model Averaging in the Presence of Selection Bias, Journal of Macroeconomics, 2012, 34 (3), 637651. Esteve-Pérez, Silviano, Salvador Gil-Pareja, and Rafael Llorca-Vivero,  Does the GATT/WTO Promote Trade? After All, Rose Was Right, Review of World Economics (Weltwirtschaftliches Archiv), May 2020, 156 (2), 377405. Feenstra, Robert C., Robert Inklaar, and Marcel P. Timmer, The Next Generation of the Penn World Table, available for download at http://www.ggdc.net/pwt, 2013. Felbermayr, Gabriel, Aleksandra Kirilakha, Constantinos Syropoulos, Erdal Yal- cin, and Yoto V. Yotov, The Global Sanctions Data Base, European Economic Review, 2020, 129 (C). Fernandes, Ana Margarida, Nadia Rocha, and Michele Ruta, eds, The Economics of Deep Trade Agreements, ISBN: 978-1-912179-46-6, eBook, https://www.worldbank.org/en/research/brief/the-economics-of-deep-trade-agreements- ebook#2, Washington, DC: World Bank, 2021. Fontagne, Lionel, Nadia Rocha, Michele Ruta, and Gianluca Santoni,  A Gen- eral Equilibrium Assessment of the Economic Impact of Deep Trade Agreements, Policy Research Working Paper Series 9630, The World Bank April 2021. Gurevich, Tamara and Peter Herman, The Dynamic Gravity Dataset: 1948-2016, 2018. USITC Working Paper 2018-02-A. Head, K. and J. Ries, FDI as an Outcome of the Market for Corporate Control: Theory and Evidence, Journal of International Economics, 2008, 74 (1), 220. Head, Keith and Thierry Mayer, Gravity Equations: Workhorse, Toolkit, and Cook- book, Chapter 3 in the Handbook of International Economics Vol. 4, eds. Gita Gopinath, Elhanan Helpman, and Kenneth S. Rogo, Elsevier Ltd., Oxford, 2014. Hofmann, Claudia, Alberto Osnago, and Michele Ruta,  The Content of Preferential Trade Agreements, World Trade Review, July 2019, 18 (3), 365398. Kirilakha, Aleksandra, Gabriel Felbermayr, Constantinos Syropoulos, Erdal Yal- cin, and Yoto V. Yotov,  The Global Sanctions Data Base: An Update to Include the Years of the Trump Presidency, in the Research Handbook on Economic Sanctions, Edited by Peter A.G. van Bergeijk, 2021. Kox, Henk L. M. and Hugo Rojas-Romagosa, How Trade and Investment Agreements Aect Bilateral Foreign Direct Investment: Results from a Structural Gravity Model, The World Economy, December 2020, 43 (12). 43 Laget, Edith, Nadia Rocha, and Gonzalo J. Varela,  Deep Trade Agreement and Foreign Direct Investments, Policy Research Working Paper Series 9829, The World Bank November 2021. Larch, Mario and Yoto V. Yotov,  Estimating the Gravity Model of Trade: Lessons From 60 Years of Theory and Applications, Unpublished Manuscript, Bayreuth and Drexel 2022. , José-Antonio Monteiro, Roberta Piermartini, and Yoto Yotov,  On the Eects of GATT/WTO Membership on Trade: They are Positive and Large After All, School of Economics Working Paper Series 2019-4, LeBow College of Business, Drexel University May 2019. Lesher, Molly and Sebastien Miroudot, Analysis of the Economic Impact of Invest- ment Provisions in Regional Trade Agreements, OECD Trade Policy Papers 36, OECD Publishing 2006. Markusen, J.R., Multinational Firms and the Theory of International Trade, Cambridge, Massachusetts: The MIT Press, 2002. Mattoo, Aaditya, Nadia Rocha, and Michele Ruta, eds, Handbook of Deep Trade Agreements, https://openknowledge.worldbank.org/handle/10986/34055, Washing- ton, DC: World Bank, 2020. McGrattan, Ellen R. and Andrea L. Waddle,  The Impact of Brexit on Foreign Invest- ment and Production, Sta Report 542, Federal Reserve Bank of Minneapolis February 2017. McGrattan, Ellen R. and Edward C. Prescott, Openness, Technology Capital, and Development, Journal of Economic Theory, 2009, 144 (6), 24542476. and , Technology Capital and the US Current Account, American Economic Review, 2010, 100 (4), 14931522. McGrattan, Ellen R. and Edward C. Prescott,  A Reassessment of Real Business Cycle Theory, American Economic Review, 2014, 104 (5), 177182. Medvedev, Denis, Beyond Trade: The Impact of Preferential Trade Agreements on FDI Inows, World Development, 2012, 40 (1), 4961. Olivero, María Pía and Yoto V. Yotov, Dynamic Gravity: Endogenous Country Size and Asset Accumulation, Canadian Journal of Economics, 2012, 45 (1), 6492. Osnago, Alberto, Nadia Rocha, and Michele Ruta, Deep Trade Agreements and Vertical FDI: The Devil is in the Details. Rose, Andrew K., Do We Really Know That the WTO Increases Trade?, American Economic Review, 2004, 94 (1), 98114. 44 Santos Silva, J.M.C. and Silvana Tenreyro, The Log of Gravity, Review of Economics and Statistics, 2006, 88 (4), 641658. and , Further Simulation Evidence on the Performance of the Poisson Pseudo- Maximum Likelihood Estimator, Economics Letters, 2011, 112 (2), 220222. Tintelnot, Felix,  Global Production with Export Platforms, The Quarterly Journal of Economics, 2017, 132 (1), 157209. Treer, Daniel, The Long and Short of the Canada-U.S. Free Trade Agreement, American Economic Review, 2004, 94 (4), 870895. Yao, S., C. F. Mela, J. Chiang, and Y. Chen, Determining Consumers' Discount Rates with Field Studies, Journal of Marketing Research, 2012, 49 (6), 822841. Yotov, Yoto V., On the Role of Domestic Trade Flows for Estimating the Gravity Model of Trade, Contemporary Economic Policy, 2022. , Roberta Piermartini, José-Antonio Monteiro, and Mario Larch, An Advanced Guide to Trade Policy Analysis: The Structural Gravity Model, Geneva: UNCTAD and WTO, 2016. 45 Appendix For the convenience of the reader, the following is a replication of the online Appendix from Anderson et al. (2019). It includes all derivations leading to the structural system of trade and investment used in this paper along with some further derivations that may aid intuition and the discussion of our results. A Derivation of System of Equations (8)-(15) This appendix gives derivation details for our system of Equations (8)-(15). First, let us re-state our production function as given in Equation (12), allowing also ϕ to vary by country: N ϕj 1−ϕj 1−α αj ηi Yj,t = pj,t Aj,t Lj,t j Kj,t (max{1, ωij,t Mi,t }) αj , ϕj , ηi ∈ (0, 1). (A1) i=1 Note that we can write max{1, ωij,t Mi,t } = (1 + ωij,t Mi,t + |1 − ωij,t Mi,t |)/2 = (1 + ωij,t Mi,t + ((1 − ωij,t Mi,t )2 )1/2 )/2 .22 The derivative of max{1, ωij,t Mi,t } with respect to Mi,t is given by: ∂ (max{1, ωij,t Mi,t }) (1 − ωij,t Mi,t ) = ωij,t − ωij,t /2 ∂Mi,t ((1 − ωij,t Mi,t )2 )1/2 (1 − ωij,t Mi,t ) ωij,t = 1− . (A2) |1 − ωij,t Mi,t | 2 Using this denition of nominal output, the value marginal product of technology capital at home is given by: ∂Yj,t ϕj ηj Yj,t (1 − ωjj,t Mj,t ) ωjj,t = 1− , (A3) ∂Mj,t max{1, ωjj,t Mj,t } |1 − ωjj,t Mj,t | 2 22 See for example https://math.stackexchange.com/questions/429622/show-that-the-max-x-y-fracxyx-y2. A1 and the value marginal product of Mj,t abroad by: ∂Yi,t ηj ϕi Yi,t (1 − ωji,t Mj,t ) ωji,t = 1− . (A4) ∂Mj,t max{1, ωji,t Mj,t } |1 − ωji,t Mj,t | 2 Note that an alternative way of writing these two conditions is the following:  ηj ϕj Yj,t ωjj,t Mj,t > 1,  ∂Yj,t  if Mj,t = ∂Mj,t   0 if ωjj,t Mj,t ≤ 1.  ηj ϕi Yi,t ωji,t Mj,t > 1,  ∂Yi,t  if Mj,t = ∂Mj,t   0 if ωji,t Mj,t ≤ 1. With these new expressions for the value marginal products, disposable income can be written as: ϕi Yi,t (1 − ωji,t Mj,t ) ωji,t Ej,t = Yj,t + ηj Mj,t 1− (A5) i̸=j max{1, ωji,t Mj,t } |1 − ωji,t Mj,t | 2 ηi Mi,t (1 − ωij,t Mi,t ) ωij,t − ϕj Yj,t 1− , i̸=j max{1, ωij,t Mi,t } |1 − ωij,t Mi,t | 2 which describes expenditure as the sum of total nominal output (Yj,t ) plus rents from foreign ∂Yi,t investments ( i̸=j Mj,t × ∂Mj,t ), minus rents accruing to foreign investments ( i̸=j Mi,t × ∂Yj,t ∂Mi,t ), which are part of nominal output. Rewriting a bit further, we end up with: Ej,t = Yj,t + ηj ϕi Yi,t − ϕj Yj,t ηi . (A6) i̸=j, i̸=j, ωji,t Mj,t >1 ωij,t Mi,t >1 In the next subsection, we rst derive the solution of the dynamic problem. Afterward, we state the steady-state of the system. At the end, we derive our FDI gravity system. A2 A.1 Solving the `Upper Level' This section details the Lagrangian problem and the corresponding rst-order conditions for the `upper level' optimization problem leading to the structural dynamic system of trade, growth, and FDI. We assume a log-intertemporal utility function: ∞ Uj,t = β t ln(Cj,t ), (A7) t=0 and combine the budget constraint given by Equation (5) with the expenditure function given by Equation (A6): Pj,t Cj,t + Pj,t Ωj,t + Pj,t χj,t = Yj,t + ηj ϕi Yi,t − ϕj Yj,t ηi i̸=j, i̸=j, ωji,t Mj,t >1 ωij,t Mi,t >1       1 − ϕj =  Yj,t + ηj ηi  ϕi Yi,t . i̸=j, i̸=j,   ωij,t Mi,t >1 ωji,t Mj,t >1 Further, we replace Yj,t with the production function as formulated in Equation (A1), leading to: Pj,t Cj,t + Pj,t Ωj,t + Pj,t χj,t =     N ϕj 1−ϕj  1 − ϕ j  1−αj αj ηi   pj,t Aj,t Lj,t Kj,t ηi  (max{1, ωij,t Mi,t })  i̸=j,  i=1 ωij,t Mi,t >1 N ϕi −αi αi 1−ϕi ηk +ηj ϕi pi,t Ai,t L1 i,t Ki,t (max{1, ωki,t Mk,t }) . i̸=j, k=1 ωji,t Mj,t >1 A3 In order to end up with only one constraint, we also replace Ωj,t and χj,t by using: Ωj,t = Kj,t+1 − (1 − δj,K ) Kj,t , χj,t = Mj,t+1 − (1 − δj,M ) Mj,t , leading to the following budget constraint: Pj,t Cj,t + Pj,t (Kj,t+1 − (1 − δj,K ) Kj,t ) + Pj,t (Mj,t+1 − (1 − δj,M ) Mj,t ) =     N ϕj 1−ϕj  1 − ϕj  1−αj αj ηi   pj,t Aj,t Lj,t Kj,t ηi  (max{1, ωij,t Mi,t })  i̸=j,  i=1 ωij,t Mi,t >1 N ϕi −αi αi 1−ϕi ηk +ηj ϕi pi,t Ai,t L1 i,t Ki,t (max{1, ωki,t Mk,t }) . i̸=j, k=1 ωji,t Mj,t >1 The corresponding expression for the Lagrangian is: ∞ 1−ϕj 1−α α Lj = β t ln(Cj,t ) + λj,t (1 − ϕj j ηi )pj,t Aj,t Lj,t j Kj,t t=0 i̸=j, ωij,t Mi,t >1 N ϕj ηi × (max{1, ωij,t Mi,t }) i=1 N ϕi −αi αi 1−ϕi ηk +ηj ϕi pi,t Ai,t L1 i,t Ki,t (max{1, ωki,t Mk,t }) i̸=j, k=1 ωji,t Mj,t >1 −Pj,t Cj,t − Pj,t (Kj,t+1 − (1 − δj,K ) Kj,t ) − Pj,t (Mj,t+1 − (1 − δj,M ) Mj,t ) . Take derivatives with respect to Cj,t , Kj,t+1 , Mj,t+1 and λj,t to obtain the following set of rst-order conditions: A4 ∂ Lj βt ! = − β t λj,t Pj,t = 0 for all j and t. (A8) ∂Cj,t Cj,t     ∂ Lj t+1   Yj,t+1 ∂Kj,t+1 1 − ϕj = β λj,t+1   (1 − ϕj )αj Kj,t+1 ηi  i̸=j,   ωij,t+1 Mi,t+1 >1 −β t λj,t Pj,t ! +β t+1 λj,t+1 Pj,t+1 (1 − δj,K ) = 0 for all j and t. (A9)     ∂ Lj t+1   ηj ϕj Yj,t+1 ∂Mj,t+1 1 − ϕj = β λj,t+1  ηi   max{1, ωjj,t+1 Mj,t+1 } i̸=j,   ωij,t+1 Mi,t+1 >1 (1 − ωjj,t+1 Mj,t+1 ) ωjj,t+1 × 1− |1 − ωjj,t+1 Mj,t+1 | 2 + β t+1 λj,t+1 ηj ηj ϕ2 i Yi,t+1 (1 − ωji,t+1 Mj,t+1 ) ωji,t+1 × 1− max{1, ωji,t+1 Mj,t+1 } |1 − ωji,t+1 Mj,t+1 | 2 i̸=j, ωji,t+1 Mj,t+1 >1 − β t λj,t Pj,t ! + β t+1 λj,t+1 Pj,t+1 (1 − δj,M ) = 0 for all j and t. (A10) A5     N ϕj ∂ Lj   1−αj αj 1−ϕj ηi ∂λj,t 1 − ϕj =   pj,t Aj,t Lj,t Kj,t ηi  (max{1, ωij,t Mi,t })  i̸=j,  i=1 ωij,t Mi,t >1 N ϕi −αi αi 1−ϕi ηk +ηj ϕi pi,t Ai,t L1 i,t Ki,t (max{1, ωki,t Mk,t }) i̸=j, k=1 ωji,t Mj,t >1 −Pj,t Cj,t − Pj,t (Kj,t+1 − (1 − δj,K ) Kj,t ) − Pj,t (Mj,t+1 − (1 − δj,M ) Mj,t ) ! =0 for all j and t. (A11) Use the rst-order condition for consumption to express λj,t as: 1 λj,t = . (A12) Cj,t Pj,t Replace this in the rst-order condition for physical capital:     ∂ Lj 1   Yj,t+1 = β t+1 1 − ϕj  (1 − ϕj )αj Kj,t+1 ηi  ∂Kj,t+1 Cj,t+1 Pj,t+1  i̸=j,   ωij,t+1 Mi,t+1 >1 Pj,t −β t Cj,t Pj,t Pj,t+1 ! +β t+1 (1 − δj,K ) = 0 for all j and t. (A13) Cj,t+1 Pj,t+1 Simplify and re-arrange to obtain:       Yj,t+1 Cj,t+1 Pj,t+1 1 − ϕj β  αj (1 − ϕj ) Kj,t+1 − ηi  Cj,t = i̸=j,   ωij,t+1 Mi,t+1 >1 −β (1 − δj,K ) Pj,t+1 for all j and t. (A14) A6 Now replace λj with the expression from the rst-order condition for consumption given in Equation (A12) in the rst-order condition for technology capital given in Equation (A10):     ∂ Lj 1   = β t+1 1 − ϕj ηi  ∂Mj,t+1 Cj,t+1 Pj,t+1   i̸=j,   ωij,t+1 Mi,t+1 >1 ηj ϕj Yj,t+1 (1 − ωjj,t+1 Mj,t+1 ) ωjj,t+1 × 1− max{1, ωjj,t+1 Mj,t+1 } |1 − ωjj,t+1 Mj,t+1 | 2 1 +β t+1 ηj Cj,t+1 Pj,t+1 ηj ϕ2 i Yi,t+1 (1 − ωji,t+1 Mj,t+1 ) ωji,t+1 × 1− max{1, ωji,t+1 Mj,t+1 } |1 − ωji,t+1 Mj,t+1 | 2 i̸=j, ωji,t+1 Mj,t+1 >1 1 −β t Cj,t β t+1 ! + (1 − δj,M ) = 0 for all j and t. (A15) Cj,t+1 Simplify and re-arrange to obtain:       ηj ϕj Yj,t+1 (1 − ωjj,t+1 Mj,t+1 ) ωjj,t+1 1 − ϕj β ηi   max{1, ωjj,t+1 Mj,t+1 } 1− |1 − ωjj,t+1 Mj,t+1 | 2 i̸=j,   ωij,t+1 Mi,t+1 >1 ηj ϕ2 i Yi,t+1 (1 − ωji,t+1 Mj,t+1 ) ωji,t+1 +βηj 1− max{1, ωji,t+1 Mj,t+1 } |1 − ωji,t+1 Mj,t+1 | 2 i̸=j, ωji,t+1 Mj,t+1 >1 Cj,t+1 Pj,t+1 − = Cj,t β (1 − δj,M ) Pj,t+1 for all j and t. (A16) Assuming that for sure ωjj,t+1 Mj,t+1 > 1, i.e., technology stock at home is positive and frictions small (i.e., ωjj,t+1 suciently large), we may simplify as follows: A7   ηj ϕ2     ηj ϕj Yj,t+1 i Yi,t+1 1 − ϕ j β  Mj,t+1 + βηj ηi  Mj,t+1 i̸=j,   ωij,t+1 Mi,t+1 >1 i ̸= j, ωji,t+1 Mj,t+1 > 1 Cj,t+1 Pj,t+1 − = Cj,t −β (1 − δj,M ) Pj,t+1 for all j and t. (A17) Combining the production function given by Equation (A1), the budget constraint given by Equation (5), the expression for Ej,t given in Equation (A6), the expressions for pj,t for each t from Equation (11), and the equations for the trade MRTs Pj,t and Πj,t given by Equations (9) and (10), respectively, with the two rst order conditions for Kj,t+1 and Mj,t+1 as given by Equations (A14) and (A16), respectively, we end up with the following system: N ϕj 1−ϕj 1−α αj ηi Yj,t = pj,t Aj,t Lj,t j Kj,t (max{1, ωij,t Mi,t }) for all j and t, (A18) i=1 Ej,t = Pj,t Cj,t + Pj,t (Kj,t+1 − (1 − δj,K ) Kj,t ) +Pj,t (Mj,t+1 − (1 − δj,M ) Mj,t ) for all j and t, (A19) Ej,t = Yj,t + ηj ϕi Yi,t − ϕj Yj,t ηi for all j and t, (A20) i̸=j, i̸=j, ωji,t Mj,t >1 ωij,t Mi,t >1 1 (Yj,t /Yt ) 1−σ pj,t = for all j and t, (A21) γj Πj,t N Yt = Yj,t for all t, (A22) j =1 A8 N 1−σ 1−σ tij,t Yi,t Pj,t = for all j and t, (A23) i=1 Πi,t Yt N 1−σ −σ tij,t Ej,t Π1 i,t = for all i and t, (A24) j =1 Pj,t Yt       Yj,t+1 Cj,t+1 Pj,t+1 1 − ϕj β  αj (1 − ϕj ) Kj,t+1 − ηi  Cj,t = i̸=j,   ωij,t+1 Mi,t+1 >1 β (δj,K − 1) Pj,t+1 for all j and t. (A25)   ηj ϕ2     ηj ϕj Yj,t+1 i Yi,t+1 1 − ϕj β ηi   Mj,t+1 + βηj Mj,t+1 i̸=j, i̸=j,   ωij,t+1 Mi,t+1 >1 ωji,t+1 Mj,t+1 >1 Cj,t+1 Pj,t+1 − = β (δj,M − 1) Pj,t+1 for all j and t. (A26) Cj,t This is a system of (8 × N + 1) × T equations in the (8 × N + 1) × T unknowns Cj,t , Kj,t , Mj,t , Yj,t , Yt , pj,t , Pj,t , Πj,t , Ej,t and given parameters and exogenous variables Aj,t , ωij,t , Lj,t , αj , β , ϕj , ηj , γj , σ , tij,t , δj,K , and δj,M . A.2 Derivation of the Steady-State In steady-state, values for t+1 and t have to be equal. Hence, we can express physical and technology capital as: Ωj Kj = , (A27) δj,K χj Mj = . (A28) δj,M A9 Further, we can drop the time index for all variables. Let us rst drop time indices in the rst-order condition for physical capital as given in Equation (A25):       Yj Cj P j 1 − ϕj β  αj (1 − ϕj ) Kj − Cj = ηi  i̸=j,   ωij Mi >1 β (δj,K − 1) Pj for all j. ⇒       Yj 1 − ϕj β  αj (1 − ϕj ) Pj Kj − 1 = ηi  i̸=j,   ωij Mi >1 β (δj,K − 1) for all j. ⇒       αj (1 − ϕj ) Yj 1 − ϕj β  (1 − β + βδj,K ) Pj = ηi  i̸=j,   ωij Mi >1 Kj for all j. A10 Let us next drop time indices in the rst-order condition for technology capital as given in Equation (A26):   ηj ϕ2     ηj ϕj Yj i Yi C j Pj 1 − ϕ j β  Mj + βηj ηi  Mj − Cj = i̸=j, i̸=j,   ωij Mi >1 ωji Mj >1 β (δj,M − 1) Pj for all j⇒   ηj ϕ2     ηj ϕj Yj i Yi 1 − ϕj β  Pj Mj + βηj ηi  Pj Mj −1= i̸=j, i̸=j,   ωij Mi >1 ωji Mj >1 β (δj,M − 1) for all j⇒ βηj ϕj Yj ηj ϕ2 i Yi 1 − ϕj ηi + = 1 − β + βδj,M Pj Pj i̸=j, i̸=j, ωij Mi >1 ωji Mj >1 Mj for all j. A11 Hence, the equation system given by Equations (A18)-(A26) simplies to: N ϕj 1−ϕj 1−α α ηi Yj = pj A j L j j Kj j (max{1, ωij Mi }) for all j, (A29) i=1 Ej = Pj Cj + Pj δj,K Kj + Pj δj,M Mj for all j, (A30) E j = Yj + η j ϕi Yi − ϕj Yj ηi for all j, (A31) i̸=j, i̸=j, ωji Mj >1 ωij Mi >1 1 (Yj /Y ) 1−σ pj = for all j, (A32) γj Πj N Y = Yj , (A33) j =1 N 1−σ tij Yi Pj1−σ = for all j, (A34) i=1 Πi Y N 1−σ −σ tij Ej Π1 i = for all i, (A35) j =1 Pj Y       αj (1 − ϕj ) Yj 1 − ϕj Kj = β  ηi   (1 − β + βδj,K ) Pj for all j, (A36) i̸=j,   ωij Mi >1 βηj ϕj Yj ηj ϕ2 i Yi Mj = 1 − ϕj ηi + for all j. (A37) 1 − β + βδj,M Pj Pj i̸=j, i̸=j, ωij Mi >1 ωji Mj >1 1−σ Yi Ej tij Note that trade ows in steady-state are then given by Xij = Y Πi Pj . A.3 Derivation of FDI Gravity Equation The steady state system above yields a convenient gravity representation of FDI that is remarkably similar to the familiar trade gravity system. To obtain it, recall the (steady- A12 state) denition of bilateral FDI stock: F DIij ≡ ωij Mi . (A38) Replacing Mi by the expression given in Equation (A37), we can write: βηi ϕi Yi ηi ϕ2 k Yk F DIij ≡ ωij 1 − ϕi ηk + . (A39) 1 − β + βδi,M Pi Pi k̸=i, k̸=i, ωki Mk >1 ωik Mi >1 Equation (A39) describes physical FDI stocks. To translate (A39) into a stock value FDI equation needed for estimation with data on FDI stock values, dene the value of FDI from country i to country j as the product of the FDI stock times its value marginal product: value ∂Yj F DIij ≡ F DIij × ∂Mi 2 βηi ϕi Yi ηi ϕ2 k Yk ϕj Yj = ωij 1 − ϕi ηk + . (A40) 1 − β + βδi,M Pi Pi Mi k̸=i, k̸=i, ωki Mk >1 ωik Mi >1 Assuming a common production share of FDI across countries, Ei = Yi + ηi ϕ Yj − j ̸=i, ωij Mi >1 ϕYi ηj and using the steady-state solution for technology capital Mi from Equation j ̸=i, ωji Mj >1 (A37), we can write: βϕηi Ei Mi = . (A41) 1 − β + βδi,M Pi Substitute for Mi in Equation (A38) to obtain: βϕηi Ei F DIij = ωij . (A42) 1 − β + βδi,M Pi A13 Translating (A42) into a stock value FDI equation needed for estimation we again multiply with the value marginal product: value ∂Yj βϕηi Ei Yj 2 βϕ2 ηi E i Yj F DIij ≡ F DIij × = ωij ϕηi = ωij . (A43) ∂Mi 1 − β + βδi,M Pi Mi 1 − β + βδi,M Pi Mi Combine Equation (A43) with the denitions of the multilateral resistance terms Pj and Πj given by Equations (A34) and (A35), respectively, to obtain the following FDI gravity system: value 2 βϕ2 ηi Ei Yj F DIij = ωij , (A44) 1 − β + βδi,M Pi Mi 1 N 1−σ 1−σ tji Yj Pi = , (A45) j =1 Πj Y 1 N 1−σ 1−σ tji Ei Πj = . (A46) i=1 Pi Y A14