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Export, FDI and the welfare gains from trade liberalization
Journal Pre-proof Export, FDI and the welfare gains from trade liberalization Puyang Sun, Yong Tan, Guang Yang PII:
S0264-9993(19)30307-4
DOI:
https://doi.org/10.1016/j.econmod.2020.01.003
Reference:
ECMODE 5119
To appear in:
Economic Modelling
Received Date: 1 March 2019 Revised Date:
25 October 2019
Accepted Date: 3 January 2020
Please cite this article as: Sun, P., Tan, Y., Yang, G., Export, FDI and the welfare gains from trade liberalization, Economic Modelling (2020), doi: https://doi.org/10.1016/j.econmod.2020.01.003. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Export, FDI and the Welfare Gains from Trade Liberalization† Puyang Sun1
Yong Tan2‡
Guang Yang1
1: Department of Economics, Nankai University 2: School of International Economics & Trade, Nanjing University of Finance and Economics
Abstract This paper extends Melitz and Redding (2015) to analyze the welfare gains from trade liberalization by adding foreign direct investment(FDI). Our model predicts that with FDI activities, welfare gains from trade liberalization will be strictly lower than those in a model without FDI, but only takes exports into account. In addition, the calibrated model indicates that with FDI activities, aggregate welfare reaches its maximum when the fixed export costs are positive rather than 0. Furthermore, we decompose the welfare gains induced by trade liberalization from continuing exporters, and switchers. The results show that in any case, with or without FDI, continuing exporters contribute a larger share to welfare gains than status switching firms. Keywords: FDI · Welfare Gains · Trade Liberalization JEL Classifications: F12·F13·F41
†
Contact information: [email protected] (P. Sun), yongtan [email protected] (Y. Tan), [email protected] (G.Yang). We are grateful to Lorenzo Caliendo, Yi Lu, Larry Qiu, Joel Rodrigue for their invaluable comments and feedback. We are also grateful to the editor and two anonymous referees for providing valuable comments. We would like to thank participants at CCER Summer Conference in Yantai (2016), and CTRG conference in Nanjing (2016). Yong Tan acknowledges the financial support from the Natural Science Foundation of China (71703067), National (Major) Social Science Foundation of China (18VSJ017). Guang Yang acknowledges the financial support from Social Science Foundation of China(18CJL013). All authors have equal contribution in this paper. If you have any questions, please contact Yong Tan, who is the corresponding author. ‡ Corresponding Author: Yong Tan is the corresponding authors
1
1. Introduction In the last three decades, a central element of economic globalization has been the growth in multinational production (henceforth, MP). From 1990 to 2006, the annual growth rate of global foreign direct investment (henceforth, FDI) was 17%; during the same period, world exports grew by only 8% (Irarrazabal et al., 2013). According to the World Investment Report, by 2006, 10% of the world’s GDP was comprised of value added from MP. The remarkable growth of FDI and its interaction with exports has drawn considerable attention from researchers (e.g. Helpman et al., 2004; Irarrazabal et al., 2013; Ramondo and Rodriguez-Clare, 2013). Further, the question of how much a country gains from trade liberalization, a decrease in the variable trade cost, lies at the core of research in international trade. Arkolakis et al. (2012) and Melitz and Redding (2015) evaluate the gains from trade liberalization in economies with homogeneous and heterogeneous firms, respectively. However, FDI is prohibited in their works, which leaves the gains unclear when firms face FDI options. Ethier (1986) finds a substitution relationship between FDI and exports. Firms that are engaged in FDI are not necessarily affected by trade liberalization.1 As such, gains from trade liberalization are overestimated if firm-level FDI activities are not considered. Given the rapid growth of FDI and its influence on welfare gains during trade liberalization, how to correctly measure welfare gains from trade liberalization is not only of academic interest; it is also of policy importance. 1
Trade liberalization only affects a firm that is engaged in FDI if it switches its status from FDI to exporting due to variable trade cost reductions.
2
Pioneer research documents welfare gains from trade liberalization from different perspectives: consumers gain from more variety (Broda and Weinstein, 2006; Goldberg et al, 2009); productivity gains from exporting a large variety of goods (Feenstra and Kee, 2008) and welfare gains from reduced markups (Feenstra and Weinstein, 2009; Edmond et al., 2015). In contrast, Arkolakis et al. (2012) (henceforth, ACR) introduce a way to measure the aggregate welfare gains from trade liberalization.2 However, Melitz and Redding (2015) show that ACR underestimate gains from trade liberalization by focusing on an economy with homogeneous firms. Specifically, Melitz and Redding (2015) demonstrate that the aggregate welfare level can be measured by real income, i.e., the nominal income divided by the price index. Moving from an economy with homogeneous firms to one with heterogeneous firms, the trade induced welfare gains will increase. Intuitively, in equilibrium, nominal income is determined by aggregate output, and the price index depends on the revenue-weighted average firm-level productivity.3 Trade liberalization, on the one hand increases aggregate output by encouraging firm-level exporting participation; on the other hand, it leads to a disproportionately faster growth of more productive firms.4 Therefore, as nominal income increases, and the price index decreases. The aggregate welfare level, in turn increases. In this paper, we attempt to measure the gains from trade similar to Melitz and Redding (2015) by allowing firm-level FDI activities. Following Helpman et al. 2
ACR (2012) extend the idea of Eaton and Kortum (2002) to show that when certain conditions are satisfied, the aggregate welfare gains from trade liberalization can be measured using a country’s domestic trade share and its elasticity of trade with respect to variable trade costs. 3 Nominal income increases in the aggregate output and price index decreases with average firm-level productivity. 4 Throughout this paper, trade liberalization refers to reductions in variable trade cost, τ .
3
(2004), when an economy moves from autarky to free trade, the most productive firms choose to conduct FDI, followed by firms engaged in exporting, and those that only serve the domestic market, while the least productive firms exit. The FDI activities change the trade elasticity measured in Melitz and Redding (2015), in which trade elasticity with respect to variable trade costs is determined only by the export productivity cutoff, ϕx . In contrast, with the FDI option, this elasticity is jointly determined by the productivity cutoffs of exporting, ϕx , and FDI, ϕI .5 This implies that the aggregate output and average productivity growth induced by trade liberalization are smaller in cases with FDI activities. As such, the welfare gains from trade liberalization are overestimated by Melitz and Redding (2015). Further, in this paper we estimate the trajectory of welfare gains by gradually lowering the variable trade cost, τ . The results show that although the welfare level is always higher in the case with FDI than that without FDI, the welfare gains from trade liberalization are smaller in the case with FDI. Specifically, our calibration results show that when the variable trade cost, τ , decreases from 3 to 1.25, the welfare gains in the case with FDI are 3 percentage points lower than those in the case with exporting only. We further decompose the welfare gains into different group of firms in order to investigate the source of gains. The results demonstrate that with FDI activities, gains from continuing exporters contribute 57% of the aggregate welfare gains, and status-switching firms contribute the remaining 43% of welfare gains (of which 78% is from the switching of non-exporting firms to exporting firms, and 21% from the switching of FDI firms to exporting firms). By comparison, when FDI is prohibited, continuing exporters contribute 74% of 5
This is because a decrease in variable trade costs would decrease the export productivity cutoff, ϕx , and increase the FDI productivity cutoff, ϕI .
4
the aggregate welfare gains. These findings are not only of research interest; they are also of policy importance. Since FDI revenue varies across economies, an economy with a higher FDI share would expect lower welfare gains from trade liberalization. In addition, FDI activities exhibit heterogeneities across industries, i.e., FDI is more popular in some industries, e.g., textile and cloths, leather, and mining industries than in others. To maximize social welfare, policymakers may want to decrease the variable export cost, τ , more in industries with fewer FDI activities.6 After understanding the source of welfare gains, we conduct further counterfactual experiments by gradually changing the fixed export costs, variable trade costs, and fixed FDI costs. The calibration results demonstrate that when gradually increasing the fixed export costs in an economy with heterogeneous firms, welfare reaches its maximum at a positive fixed export cost. This is because a positive fixed export cost drives more firms to conduct FDI instead of exporting.7 More FDI firms increase the aggregate output and average productivity. This, in turn, raises the social welfare level. This work is related to a number of papers which empirically or numerically quantify the gains from trade through different channels (Broda et al., 2006; Broda and Weinstein, 2006; Goldberg et al, 2009; Feenstra and Weinstein, 2009; Edmond et al., 2015; Fajgelbaum and Khandelwal, 2014). In contrast to these works, our 6
Since FDI firms will not be affected by trade liberalization, the reduction in variable export costs will generate fewer welfare gains in industries in which more firms are engaged in FDI activities. 7 In the case with FDI activities, zero fixed export costs will lead to excessive entry into exporting, i.e., some FDI firms will switch to exporting, and some nonexporters will start exporting. This lowers firm-level output. Suzumura and Kiyono (1987) show that the excessive entry will decrease firm-level output, and hence, lower social welfare. Our result is in line with Suzumura and Kiyono (1987), and we thank an anonymous referee for pointing out this issue.
5
study evaluates the aggregate welfare gains from trade liberalization. This feature makes our paper closely related to Melitz and Redding (2015). However, our work differs from Melitz and Redding (2015) in three respects. First, we examine the aggregate welfare gains from trade liberalization in a framework with FDI activities, which are the central elements of the economic globalization. Second, we decompose the welfare gains into different groups of firms to clarify the source of the gains; Third, we calibrate the model to detect optimal export fixed costs. We find that in the case with FDI activities, the optimal export fixed costs are strictly positive. Our work is also distinct from Irarrazabal et al. (2013) and Ramondo and Rodriguez-Clare (2013) in two respects. First, we do not discuss FDI geography gravity; instead we focus on the welfare effects of the substitutability between FDI and exports. Second, in a more general setting with FDI activities, we find that economies consisting of heterogeneous and homogeneous firms benefit differently from trade liberalization.8 This paper proceeds as follows: In section 2 we introduce the model with FDI. Section 3 outlines the welfare gains in response to trade liberalization when FDI activities are allowed. Section 4 decomposes the welfare gains from different firms to clarify where the gains come from. In section 5, we calibrate the welfare gains from variable trade cost reductions, fixed trade cost reductions, and fixed FDI cost reductions. Section 6 concludes. 8
In Ramondo and Rodriguez-Clare (2013), the gains from openness are invariant to economies with heterogeneous and homogeneous firms.
6
2. Model 2.1. A Model with Heterogeneous Firms and FDI Following Helpman et al. (2004), we assume that there are two countries, the home country, H, and the foreign country, F . The two countries are assumed to be symmetric, i.e. identical in size, labor supply, etc. After paying a sunk entry cost, fe , firms draw their productivity from a Pareto distribution, G(·). Based on a productivity draw, each firm decides to either stay in the market or exit. If a firm chooses to stay in the market, it will further decide whether to serve the foreign market and, if so, whether to do so through exporting or FDI.9 Each firm produces a differentiated variety, and preferences in both the home and foreign country have the standard CES form, with an elasticity of substitution, σ = 1/(1 − ρ) > 1. These preferences generate a demand function Ap−σ for every firm. A is a demand shifter in the home and foreign countries.10 Since the home and foreign countries are identical, we focus our discussion on the home country, H, even though all results are equally applicable to the foreign country, F . Denote ϕTd,τ , ϕTs,τ and ϕTI,τ as the productivity cutoffs for serving the domestic market, exporting, and FDI, at trade costs, τ, respectively. The zero profit 9
Intuitively, the least productive firms exit the market immediately after their productivity draw, low productivity firms serve the domestic market only, firms with a relatively high level of productivity draw export to the foreign market, and the most efficient firms serve the foreign market through FDI. σ 10 In particular, A = ωL P P , where ω is the wage level, L is the aggregate labor supply, and P denotes the price index.
7
conditions for serving the domestic market, exporting and FDI are as follows:
rI
!σ−1 rd ϕTd,τ R σ − 1 P ϕTd,τ = = wfd σ σ σ w !σ−1 rx ϕTx,τ R σ − 1 P ϕTx,τ = = wfx σ σ σ τw ϕTI,τ rx ϕTI,τ − wfI = − wfx σ σ
(1)
(2) (3)
where rd ϕTx,τ denotes the revenue of firms with the cutoff productivity ϕTd,τ in the home country; rx ϕTx,τ denotes the export revenue in foreign market with productivity ϕTx,τ ; and rI ϕTI,τ measures the FDI revenue in the foreign market with productivity, ϕTI,τ . fd , fx , and fI are the fixed production costs in the domestic market, export, and FDI, respectively. w is the wage level. Equations (1)-(3) define the productivity cutoffs of staying in the market, starting exporting and FDI, respectively.11 For potential entrants, the expected profit is equal to the entry cost, which gives the free entry condition as follows:
fd J ϕTd,τ + fx J ϕTx,τ + fI J ϕTI,τ = fe 11
These cutoffs are also depicted in Figure A1 in the online Appendix.
8
(4)
where, fd J ϕTd,τ =
fx J ϕTx,τ =
fI J ϕTI,τ =
Z
ϕmax
ϕT d,τ
Z
ϕmax
"
ϕT x,τ
Z
ϕmax
ϕ ϕTx,τ
ϕT I,τ
ϕ ϕTd,τ
ϕ ϕTI,τ
!σ−1
− 1 dG(ϕ) σ−1
# − 1 dG(ϕ)
!σ−1
− 1 dG(ϕ)
Similar to Melitz and Redding (2015), with all the notations introduced above, the number of active firms can be expressed as: R L M = 1 − G ϕTd,τ Me = = r σF T
(5)
where, M is the number of active firms, and Me is the number of potential entrants. L is the total labor supply in the home country. r and F T denote the average revenue earned by active firms and the average fixed costs paid by all firms, respectively. In particular, fe + fd + χx,τ fx + χI,τ fI 1 − G ϕTd,τ G ϕTI,τ − G ϕTx,τ = 1 − G ϕTd,τ 1 − G ϕTI,τ = 1 − G ϕTd,τ
FT = χx,τ χI,τ
(6)
where χx,τ and χI,τ denote the share of firms that are engaged in export and FDI, respectively. Before we proceed further, it is worthwhile to note three differences between the model with FDI and the model without FDI (e.g. Melitz and Redding, 2015).
9
First, given that all parameters are identical in the two models, the number of active firms will be smaller in the model with FDI than in the model without FDI. By allowing FDI, the expected profit for potential entrants is higher than that in a setting where firms can only export. Higher profits encourage entry and hence intensify the competition.12 Second, the welfare gains will be smaller in the case with FDI activities than those in Melitz and Redding (2015). This is because a portion of firms with the highest levels of productivity are engaged in FDI, and some of them are not affected by trade liberalization (a decrease in variable trade cost, τ ) if they do not switch from FDI to exporting. Third, moving from an autarkic economy to an open economy, the model with FDI will imply greater welfare gains.13
3. Welfare Analysis In this section, we investigate the welfare gains from trade liberalization. Similar to Melitz and Redding (2015), we represent the aggregate welfare in a setting with FDI as follows:
T WHet,F DI =
1 σ−1
w σ − 1 L(1 + χx,τ + χI,τ ) T σ−1 = ϕ e T P σ σF | t,τ{z } | {z } Γ2
(7)
Γ1
ϕ eTt,τ =
1 1 + χx,τ + χI,τ
h
ϕ eTd,τ
σ−1
+ χx,τ τ −1 ϕ eTx,τ
12
σ−1
+ χI,τ ϕ eTI,τ
σ−1 i
The higher expected profit shifts up the free entry curve, which increases the zero profit cutoff ϕTd,τ . 13 The second and third points can be seen in Figure A2 in the online Appendix.
10
T where, WHet,F DI denotes aggregate welfare in the home (foreign) country when
firms can choose to conduct FDI.14 ϕ eTt,τ is the weighted average of ϕ eTx,τ , ϕ eTd,τ and ϕ eTI,τ , which are the average productivity of all active firms, firms serving foreign markets (through exporting and FDI), and firms engaged in FDI, respectively. In particular,
ϕ eTd,τ = ϕ eTx,τ = ϕ eTI,τ =
Z
ϕmax
" ϕσ−1
ϕT d,τ
Z
ϕmax
" ϕσ−1
ϕT x,τ
Z
ϕmax
" ϕσ−1
ϕT I,τ
dG(ϕ) 1 − G ϕTd,τ dG(ϕ) 1 − G ϕTx,τ dG(ϕ) 1 − G ϕTI,τ
1 # σ−1
(7.1) 1 # σ−1
(7.2) 1 # σ−1
(7.3)
Equation (7) indicates a difference from Melitz and Redding (2015); two new terms appear in the aggregate welfare expression, χI,τ , and ϕTI,τ . An decrease in variable trade costs, τ , will change the share of firms that are engaged in FDI and the FDI productivity cutoff. Similarly, we can rewrite the aggregate welfare calculation when FDI is prohibited:
T WHet,EXP
ϕ eTt,τ
1 w σ − 1 L(1 + χx,τ ) T σ−1 σ−1 = = ϕ et,τ P σ σF T h σ−1 σ−1 i 1 T −1 T = ϕ ed,τ + χx,τ τ ϕ ex,τ 1 + χx,τ
(8)
It is easy to show that aggregate welfare is higher in the case with FDI than 14
Similar to Melitz and Redding (2015), Γ1 and Γ2 measure the nominal income and price L(1+χx,τ ) index, respectively. The only difference is that in Melitz and Redding (2015), Γ1 = . σF T Notice that Γ1 is a measure of the aggregate output, which equals to the total expenditure in each country. As such, the welfare measured in equation (7) takes into account of both import and export tariffs.
11
without FDI: T WHet,F DI = T WHet,EXP 1 σ−1 h σ−1 σ−1 i σ−1 f −1 T −1 T T e + χI,τ τ ϕ eI,τ + χx,τ τ ϕ ex,τ ed,τ + fd + χx,τ fx ϕ 1−G(ϕT d,τ ) >1 h σ−1 σ−1 i fe T −1 T + χx,τ τ ϕ ex,τ ϕ ed,τ + fd + χx,τ fx + χI,τ fI 1−G(ϕT d,τ )
(9) Inequality (9) implies that in moving from autarky to an open economy, welfare gains are smaller when FDI is prohibited. 3.1. Welfare Gains from Trade Liberalization Now we are ready to evaluate the gains from trade liberalization. We set all parameters identical to Melitz and Redding (2015). That is, we set the elasticity of substitution rate, σ = 4, the wage rate, ω = 1, the labor force, L = 153.889, the Pareto distribution parameter, ϕmin = 1, and k = 4.25.15 In addition, the fixed cost of entry, fe , domestic production, fd , export, fx , are set to be 1, 1, and 0.545, respectively. Finally, we set the fixed cost of FDI as 20.16 Using equations (1) - (6), we can compute the share of exporting firms, FDI firms, and the corresponding productivity cutoffs. We gradually decrease variable trade costs, τ , to measure the welfare gains from trade liberalization. The results are presented in Table 1: −k ϕ The Pareto distribution function is given by G(ϕ) = 1 − ϕmin , where ϕmin denotes the minimum productivity and k is the Pareto distribution parameter, which governs the shape of the distribution. 16 This value is not picked randomly. It cannot be too large or too small relative to fixed export costs. If it is too large, no firms will choose to conduct FDI, and if it is too small no firms will choose to export. 15
12
[Table 1 is to be here] In Table 1, Welfare A , Welfare EXP and Welfare F DI denote the welfare level in autarky, with exporting only and with exporting and FDI, respectively. The results in the first row show that when the variable trade costs, τ , converge to infinity, Welfare EXP =Welfare A , and the welfare with FDI is 6% higher than that in the autarky.17 This relationship continues to hold when the trade costs decrease to 3 (τ = 3). The third row of Table 1 implies that when the trade costs further decrease to τ = 1.25, the welfare levels in the case without FDI and in the case with FDI are 10% and 14% higher than that in autarky, respectively. In sum, Table 1 delivers two pieces of information. First, the welfare level is always higher when FDI is not prohibited than that in the case with exports only; Second, trade liberalization brings larger welfare gains for the economy with export only ((1.10 − 1)/1 = 10% higher) than in the economy with both export and FDI ((1.14 − 1.06)/1.06 = 8%).
4. Decomposition of Welfare Gains In an economy with FDI, welfare gains from trade liberalization can be attributed to three sources. First, the economy benefits from a portion of nonexporters (with relative high productivity) start to export. Second, the economy gains from increasing foreign sales from continuing exporters. Third, the switching of a fraction of firms from conducting FDI to exporting also increases the welfare level. In this section, we decompose the aggregate welfare gains from trade 17
Notice that the fixed FDI costs, fI , is fixed at 20 during the decrease of the variable trade costs. This implies that the most productive firms can always choose to conduct FDI.
13
liberalization to the three groups of firms: 1. nonexporters; 2. exporters; 3. firms engaged in FDI. According to equation (7), when the variable trade costs decrease from a particular level, τ1 , to τ2 (τ2 < τ1 ), the ratio of aggregate welfare under these two different variable trade costs can be written as: 1 " σ−1 # σ−1 T T T ϕ WHet,F (τ ) e F 1 + χ + χ 2 x,τ2 I,τ2 τ1 t,τ2 DI = σ−1 T T 1 + χ + χ F WHet,F (τ ) x,τ1 I,τ1 τ2 ϕ eTt,τ1 DI 1
(10)
Our decomposition procedures are straightforward. First, we assume that nonexporters and FDI firms do not switch to exporting when the variable trade costs decrease from τ1 to τ2 , and calculate the gains for continuing exporters in response to trade liberalization. Second, we compute the new survival, export and FDI productivity cutoffs under the trade costs τ2 . With these new cutoffs, we can calculate the welfare gains from switchers: (1) nonexporters that start exporting (2) nonexporters that exit (3) FDI firms switch to exporting. Mathematically, the welfare gains are written as T T T WHet,F WHet,F DI (τ2,keep ) WHet,F DI (τ2 ) DI (τ2 ) = T T T WHet,F WHet,F DI (τ1 ) DI (τ1 ) WHet,F DI (τ2,keep )
(11)
T where WHet,F DI (τ2,keep ) is the welfare level at the trade cost level, τ2 , without any T switching. In comparison, WHet,F DI (τ2 ) denotes the welfare level at the trade cost,
τ2 , after accounting for all possible switching. As such, the first component in the RHS of equation (11) measures the welfare gains for continuing exporters, while the second term captures the welfare gains generated by switchers. Later, the second term will be further decomposed into the gains from nonexporters and FDI
14
firms, respectively. T WHet,OF DI (τ2,keep ) T WHet,OF DI (τ1 )
σ−1 ϕ eTt,τ2 σ−1 ϕ eTt,τ1
"
ϕ eTd,τ1
σ−1
+ χx,τ1 τ2−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
ϕ eTd,τ1
σ−1
+ χx,τ1 τ1−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
=
=
1 # σ−1
"
1 σ−1 # σ−1
σ−1 (12)
where ϕ eTd,τi , ϕ eTx,τi , and ϕ eTt,τi , i = 1, 2, are productivity cutoffs as defined in equations (7.1)-(7.3). Note that in equation (12), we assume switching is not possible, and hence there is no change in productivity cutoffs. Similarly, the welfare gains from switchers can be written as follows: 1 " σ−1 σ−1 # σ−1 −1 T T T T T ϕ e + χ τ ϕ e + χ ϕ e (τ ) WHet,OF F 1 + χ + χ x,τ I,τ 2 2 2 2 x,τ2 I,τ2 x,τ2 I,τ2 τ1 d,τ2 DI = σ−1 σ−1 T T −1 T T 1 + χ F + χ WHet,OF (τ ) x,τ1 I,τ1 τ2 ϕ ed,τ1 + χx,τ2 τ2 ϕ ex,τ1 + χI,τ2 ϕ eTI,τ1 DI 2,keep (13)
After some cumbersome algebra,18 we write the welfare gains as follows: T T T WHet,F WHet,F WHet,F DI (τ2 ) DI (τ2,keep ) DI (τ2 ) ln T = ln + ln T T WHet,F DI (τ1 ) WHet,F WHet,F DI (τ1 ) DI (τ2,keep )
18
The details are in the Appendix.
15
(14)
=
σ−1 i χx,τ1 h −1 T σ−1 τ2 ϕ ex,τ2 − τ1−1 ϕ eTx,τ1 |σ − 1 {z }
+
σ−1 i σ−1 1 eTx,τ2 − χx,τ1 τ2−1 ϕ eTx,τ2 χx,τ2 − χx,τ 1 + χx,τ1 fx − χx,τ 2 fx + χx,τ2 τ2−1 ϕ |σ − 1 {z }
Gains of continuing Exporters
h
Gains from swithing (nonexport to export)
σ−1 σ−1 i 1 χI,τ2 − χI,τ 1 + χI,τ1 fI − χI,τ 2 fI + χI,τ2 τ2−1 ϕ eTI,τ2 − χI,τ1 τ2−1 ϕ eTI,τ2 |σ − 1 {z } h
Gains from swithing (FDI to exporters)
+
σ−1 1 ∆ ϕ eTd |σ − 1 {z }
Gains from switching (exit)
The components on the RHS of equation (14) give the welfare contributions of each group. In particular, when the variable trade costs, τ , decrease from 3 to 1, we calculate the associated welfare gains from each group of firms. The results are reported in Panel A of Table 2: [Table 2 is here] The results indicate that the aggregate welfare with FDI will increase by 16%. Continuing exporters contribute 57% of the total welfare gains, while switchers contribute 43% of welfare gains. Further, within the 6.88% (=43% × 16%) welfare gains, most are caused by firms switching from nonexporting to exporting, which accounts for 78% of the gains, while the firms switching from FDI to exporting only contribute 21% of the gains.19 For comparison purposes, we repeat the exercise for the model without FDI in 19
Exit firms account for 1% of the welfare gains among all switchers. The results are consistent with our intuition: switching from nonexporting to exporting contributes more to welfare gains than switching from FDI to exporting. The former increases foreign sales more (decreases the domestic trade share more) than the latter and, hence, according to Arkolakis et al. (2012) the former contributes more to welfare gains.
16
Panel B of Table 2. The results indicate that when FDI is prohibited, the aggregate welfare gains are larger, 19% compared to 16% – in response to a variable trade cost decrease. This is because more continuing firms directly benefit from the variable cost reduction. The above results convey an important piece of information: compared with continuing exporters, the switching of FDI firms contributes a relatively trivial share to welfare gains.
5. Calibrating the Influence of Trade Liberalization In this section, we calibrate the model with FDI to numerically evaluate the influence of trade liberalization on an economy. We first increase the fixed exporting costs from 0 to 1 and compare the welfare changes in economies with homogeneous and heterogeneous firms. Next, we increase the variable export costs, τ , to compare the welfare changes in the homogeneous and heterogeneous economies. Finally, we increase the fixed FDI investment costs to evaluate the influence of investment liberalization on welfare. 5.1. Welfare Gains from Fixed Export Cost Reductions We first calibrate the influence of fixed export cost reductions on welfare. We are interested in two questions. First, in the model with FDI, how different do the economies with homogeneous and heterogeneous firms respond to fixed export cost reductions? Second, how do the gains differ from those reported in Melitz and Redding (2015)? In the calibration, we set all parameters identical to those in Melitz and Red-
17
ding (2015),and increase the fixed export costs from 0 to 1.20 Figure 1 depicts the changes in welfare gains, export probability, average productivity and the domestic trade share in response to a fixed cost increase. Figure 1: The Influence of Export Fixed Cost Reductions Panel B
1 1.08
Probability of exporting
Welfare gains from trade
Panel A
1.06 1.04 1.02 1
0
0.25
0.5
0.75
0.8 0.6 0.4 0.2 0
1
0
1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1
0.25
0.5
0.75
1
Fixed exporting cost Panel D
1 Domestic trade share
Weighted average productivity
Fixed exporting cost Panel C
0
0.25
0.5
0.75
0.95 0.9 0.85 0.8
1
Fixed exporting cost Note: Variable trade costs=1.83
0
0.25
0.5
0.75
1
Fixed exporting cost
In Panels A − Panel D of Figure 1, the solid and dashed curves depict the patterns of different variables across heterogeneous and homogeneous economies, respectively. Figure 1 first indicates that the welfare gains and weighted average productivity are always higher in the economy with heterogeneous firms than in the economy with homogeneous firms when facing different levels of fixed export cost (Panel A and C). Second, the export probability decreases in both economies when facing an increase in fixed export costs (Panel B). Third, the domestic trade 20 Notice that the fixed cost for FDI is much higher than that associated with exporting. This setting is consistent with the fact that FDI activities require a higher fixed cost relative to exporting. Secondly, we need to set the fixed FDI cost higher to guarantee that not every firm serves the foreign markets through FDI.
18
share, which is calculated as domestic sales divided by total sales, increases with fixed export costs in both economies in both economies.21 When we focus on trends in the economy composed of heterogeneous firms, we find some patterns that are in striking contrast to those in Melitz and Redding (2015).22 Panel A, for instance, indicates that when facing an increase in the fixed export cost, welfare first increases and then decreases. The average weighted productivity also manifests a similar inverted-U shape (Panel C). The intuition is that when the fixed exporting costs gradually increase from 0, some productive exporters with sufficiently high productivity will switch to FDI. After these firms switch from exporting to FDI, they sell more in foreign markets,23 which has two direct consequences: it decreases the domestic trade share (the decreasing part in Panel D), and increases the aggregate income as consumers earn more income from foreign sales.24 Both effects result in a welfare increase. When the fixed export cost increases even further, more firms stop exporting, which decreases foreign sales and drives both average productivity and welfare down. Therefore, aggregate welfare eventually declines in response to further fixed export cost increases. An implication of Figure 1 is that in order to maximize welfare in an economy with heterogeneous firms, moderate positive fixed export costs are necessary when FDI is not prohibited. 21
The domestic trade share initially decreases in the economy with heterogeneous firms when fixed export costs increase. 22 The corresponding results for an economy without FDI are shown in Figure A3 in the Appendix. 23 This switching prevents excessive entry into the foreign market, which would otherwise lead to lower foreign sales (see, Suzumura and Kiyono, 1987). 24 This is also consistent with Arkolakis et al. (2012) that given the trade elasticity, the welfare is decreasing in domestic trade share.
19
5.2. The Influence of Export Variable Cost Reductions We next calibrate the model to evaluate the influence of variable export cost reductions on economies with heterogeneous and homogeneous firms, respectively. In this numerical exercise, we again set all parameters equal to those values in the previous section, except that fixed export costs are set to fx = 0.76 ( rather than varying between 0 and 1), and the variable export costs will increase from 1 to 3 as in Melitz and Redding (2015). The influence of variable export costs based on aggregate welfare, export probability, weighted average productivity, and domestic trade share are depicted in Figure 2.25 Figure 2: The Influence of Export Variable Cost Reductions Panel A
Panel B
1.2
Probability of exporting
Welfare gains from trade
1
1.15 1.1 1.05 1
1
1.5
2
2.5
0.8 0.6 0.4 0.2 0
3
1
1.2 1.175 1.15 1.125 1.1 1.075 1.05 1.025 1
1.5
2
2.5
3
Variable trade cost Panel D
1 Domestic trade share
Weighted average productivity
Variable trade cost Panel C
1
1.5
2
2.5
0.8
0.6
0.4
3
Variable trade cost Note: Fixed exporting cost=0.545
1
1.5
2
2.5
3
Variable trade cost
In contrast to the influence of fixed export cost on these aggregate variables, increasing variable trade costs cause a steady decline in welfare, export probability, weighted average productivity, and increase the domestic trade share for 25
We depict the results without FDI in Figure A4 of the Appendix.
20
both economies. The only exception is weighted average productivity, which only declines in the economy with heterogeneous firms. Although these results seem to contradict the patterns exhibited in Figure 1, we have good explanations for these observed trends. When variable export costs increase from 1, some productive firms switch from export to FDI. However, this switching does not largely change firm-level sales in foreign markets, as FDI variable costs, which take a value of 1, are only slightly lower than that associated with exporting. Therefore, foreign sales decrease because less productive firms stop exporting, and these firms dominate those switching from export to FDI. The results indicate that in order to maximize welfare and weighted average productivity in an economy with heterogeneous firms, variable trade costs should be reduced to 1. 5.3. The Influence of FDI Fixed Cost Reductions Finally, we assess the influence of FDI fixed cost reductions on aggregate welfare, weighted average productivity, average FDI propensity, and domestic sales. In this calibration, all parameters are set to the same values as those in the previous section, while fixed FDI costs, fI , increase from 15 to 200. The calibrated results are depicted in Figure 3 with the solid and dashed curves denoting economies with heterogeneous and homogeneous firms, respectively: The figure shows that firm-level productivity in the homogeneous economy has been set to equalize the weighted average productivity of firms in the heterogeneous economy in autarky. No firms will conduct FDI in the homogeneous economy, as firm-level productivity is not sufficiently high to overcome the high
21
Figure 3: The Influence of FDI Fixed Cost Reductions Panel A
Panel B
Probability of FDI
Welfare gains from FDI
1.08 1.06 1.04 1.02
0.1 0.08 0.06 0.04 0.02 0
1 15 40 65 90 115 140 165 190
15 40 65 90 115 140 165 190
1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1 15 40 65 90 115 140 165 190
Fixed FDI cost Panel D
0.9 Domestic trade share
Weighted average productivity
Fixed FDI cost Panel C
0.88
0.86
0.84
Fixed FDI cost
15 40 65 90 115140165190 Fixed FDI cost
FDI fixed costs.26 As such, changes in FDI fixed cost have a trivial impact on the homogeneous economy. In contrast, in the economy with heterogeneous firms, the most productive firms will conduct FDI instead of exporting. Changes in the fixed FDI costs will thus significantly affect the heterogeneous economy. For instance, Panel A shows that the aggregate welfare level declines as FDI fixed costs increase. This is because weighted average productivity also decreases with FDI fixed costs (shown in Panel C). Meanwhile, Panel B indicates the probability that FDI is also decreasing as FDI fixed costs increase, and hence the domestic trade share increases with FDI fixed costs (Panel D). Intuitively, when FDI fixed costs rise, a portion of firms will switch from FDI to exporting. This switching reduces firm-level sales in foreign markets, and hence decreases weighted average produc26
In the homogeneous economy, firm-level productivity is not sufficiently high to allow firms to conduct FDI. If we change some parameters, such as fI = fx , all firms will conduct FDI after investment liberalization.
22
tivity, as well as the foreign share. All of these facts predict a decline in aggregate welfare.
6. Conclusions In this paper, we investigate the welfare gains from trade liberalization when FDI activities are allowed. The results indicate that welfare gains are lower with FDI than those without FDI when considering marginal changes in variable trade costs. This implies that the welfare gains from trade liberalization have been overestimated if they do not take FDI into account. We further decompose the welfare gains into different groups of firms. The results indicate that the continuing exporters contribute the most to welfare gains in response to trade liberalization. In contrast, firms that switches to FDI only contribute a trivial share of the welfare gains. This explains why the welfare gains are lower with FDI activities. This finding show that economies benefit differently from trade liberalization, i.e., those with a larger share of FDI benefit less. In addition, the welfare gains are disproportionately large for industries with a small share of FDI. Meanwhile, we compare the welfare gains in an economy with homogeneous firms vs. heterogeneous firms. The results show that the welfare gains from trade liberalization are always higher in the economy with heterogeneous firms. However, when FDI is not prohibited, the welfare difference between the two economies narrows. This suggests that Melitz and Redding (2015) overestimate the gains from a heterogeneous economy. In addition, the calibrated results demonstrate that zero fixed export costs do not maximize aggregate welfare in an economy with FDI activities. Instead, slightly positive fixed export costs will maximize the aggregate welfare by driving 23
some firms to switch from exporting to FDI. This finding has important policy implications: to increase foreign sales by encouraging firm-level FDI activities, policymakers can either decease fixed FDI costs or slightly increase the fixed export costs. This finding implies that that a certain low level of export/import clearance cost is optimal for social welfare. Lastly, aggregate welfare is monotonically decreases with variable trade costs and fixed FDI costs. Therefore, policymakers may want to lower both types of costs jointly to maximize social welfare.
24
Appendix(Figures and Tables) Figure A1: Productivity Cutoffs
In Figure A1, the three upward sloped lines A, B and C, denote the profit from serving the domestic market, serving the foreign market through exports, and serving the foreign market through FDI, respectively. Firms with productivity, ϕ ∈ [0, ϕTd,τ ), exit; firms will only serve the domestic market if their productivity is between [ϕTd,τ , ϕTx,τ ); firms will start to export if their productivity is between [ϕx,τ , ϕI,τ ); and firms whose productivity is above ϕTI,τ engage in FDI. When the variable trade cost, τ , decreases, firm-level profit associated with exporting increases. Therefore, the solid curve B shifts up to the dash curve B 0 . The productivity cutoff for export and FDI changes from ϕTx,τ to ϕTx,τ 0 and ϕTI,τ to ϕTI,τ 0 , respectively. When FDI is prohibited, firms whose productivity, ϕ > ϕTx,τ 0 , will benefit from a reduction in trade costs. In contrast, when FDI is possible, firms
25
Figure A2: Shifting of Productivity Cutoffs
with productivity, ϕ ∈ [ϕTx,τ 0 , ϕTI,τ 0 ] will benefit from the trade cost reduction, while firms with productivity ϕ > ϕI,τ 0 are not affected. Therefore, the welfare gains from trade liberalization will be smaller in the case with FDI. Similarly, when an economy moves from autarky to an open economy, firms with productivity, ϕ > ϕTI,τ , will chose to conduct FDI instead of exporting because profits from FDI are greater than those from exporting. As such, when FDI is allowed, moving from autarky to an open economy brings larger welfare gains.
26
Table A3: The Influence of Export Fixed Cost Reductions (Without OFDI) Panel A
Panel B
1 Probability of exporting
Welfare gains from trade
1.05 1.04 1.03 1.02 1.01 1
0
0.25
0.5
0.75
0.8 0.6 0.4 0.2 0
1
0
1.04
0.5
0.75
1
1
1.03 1.02 1.01 1
0.25
Fixed exporting cost Panel D
Domestic trade share
Weighted average productivity
Fixed exporting cost Panel C
0
0.25
0.5
0.75
1
0.95
0.9
0.85
0
Fixed exporting cost Note: Variable trade costs=1.83
0.25
0.5
0.75
1
Fixed exporting cost
Table A4: The Influence of Export Variable Cost Reductions (Without OFDI) Panel A
Panel B
1 Probability of exporting
Welfare gains from trade
1.2 1.15 1.1 1.05 1
1
1.5
2
2.5
0.8 0.6 0.4 0.2 0
3
1
2
2.5
3
1
1.125 1.1 1.075 1.05 1.025 1
1.5
Variable trade cost Panel D
Domestic trade share
Weighted average productivity
Variable trade cost Panel C
1
1.5
2
2.5
0.8
0.6
0.4
3
Variable trade cost Note: Fixed exporting cost=0.545
1
1.5
2
2.5
Variable trade cost
27
3
Table 1: Welfare Gains from Trade Liberalization
Trade Cost
W elf areEXP /W elf areA (without OFDI) τ → inf 1 τ =3 1 τ = 1.25 1.10 Welfare Change (10%) 10%
W elf areOF DI /W elf areA (with OFDI) 1.06 1.06 1.14 8%
Table 2: Welfare Decomposition
Panel A: With FDI Welfare Gains
Continuing Exporters
16%
57%
Switchers Exit
43% Nonexport to Export
FDI to Export
1%
78%
21%
Panel B: Without FDI Welfare Gains
Continuing Exporters
19%
74%
Switchers Exit
26% Nonexport to Export
FDI to Export
3%
97%
0%
Proofs The Decomposition With FDI option, the aggregate welfare can be written as:
T WHet,OF DI (τ )
1 σ − 1 L(1 + χx,τ + χI,τ ) T σ−1 σ−1 = ϕ et,τ σ σF T
(A1)
where χx,τ and χI,τ are defined as the proportion of firms engaging in export and FDI under the trade cost level, τ, respectively. 28
The welfare increase caused by variable trade cost, τ, decreases from τ1 to τ2 is T WHet,OF DI (τ2 ) T WHet,OF DI (τ1 )
" =
1 + χx,τ2 + 1 + χx,τ1 +
χI,τ2 FτT1 χI,τ1 FτT2
σ−1 ϕ eTt,τ2 σ−1 ϕ eTt,τ1
1 # σ−1
(A2)
eTx,τ eTd,τ , ϕ where ϕ eTt,τ denotes the weighted average of the three productivity cutoffs, ϕ and ϕ eTI,τ ,(write the expressions of the average.) under trade cost, τ as in equation (2). T T T WHet,OF WHet,OF DI (τ2 ) DI (τ2 ) WHet,OF DI (τ2,keep ) = T T T WHet,OF WHet,OF DI (τ1 ) DI (τ2,keep ) WHet,OF DI (τ1 )
T WHet,OF DI (τ2,keep ) = T WHet,OF DI (τ1 )
"
ϕ eTt,τ1 "
=
ϕ eTt,τ2
1 σ−1 # σ−1
(A3)
σ−1
ϕ eTd,τ1
σ−1
+ χx,τ1 τ2−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
ϕ eTd,τ1
σ−1
+ χx,τ1 τ1−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
1 σ−1 # σ−1
σ−1
" σ−1 σ−1 # −1 T T T T T ϕ e + χ τ ϕ e + χ ϕ e (τ ) WHet,OF F 1 + χ + χ x,τ I,τ 2 2 2 2 x,τ2 I,τ2 x,τ2 I,τ2 τ1 DI d,τ2 = σ−1 σ−1 T T −1 T T 1 + χ + χ F WHet,OF (τ ) x,τ1 I,τ1 τ2 ϕ ed,τ1 + χx,τ2 τ2 ϕ ex,τ1 + χI,τ2 ϕ eTI,τ1 DI 2,keep (A4) We can further decompose equation (A4) into two parts: one is welfare gains from nonexport switching firms, the other is welfare gains from FDI swiching firms. In particular:
29
T WHet,OF DI (τ2 ) ln T (A5) WHet,OF DI (τ2,keep ) " σ−1 σ−1 # ϕ eTd,τ2 + χx,τ2 τ2−1 ϕ eTx,τ2 + χI,τ2 ϕ eTI,τ2 FτT1 1 + χx,τ2 + χI,τ2 1 ln + ln T + ln = σ−1 σ−1 σ−1 1 + χx,τ1 + χI,τ1 F τ2 + χx,τ2 τ2−1 ϕ eTx,τ1 + χI,τ2 ϕ eTI,τ1 ϕ eTd,τ1 1 ≈ [∆ϕ eTd,τ2 + χx,τ2 + χI,τ2 − χx,τ1 − χI,τ1 + FτT1 − FτT2 σ−1 σ−1 σ−1 + χx,τ2 τ2−1 ϕ eTx,τ2 + χI,τ2 ϕ eTI,τ2 − χx,τ2 τ2−1 ϕ eTx,τ1 − χI,τ2 ϕ eTI,τ1 ]
Substitute FτT =
fe 1−G(ϕT d,τ )
FτT1 − FτT2 = −
+ fd + χx,τ fx + χx,τ fI into equation (A5) and obtain:
fe + fd + χx,τ1 fx + χx,τ1 fI 1 − G(ϕTd,τ1 ) fe + fd + χx,τ2 fx + χx,τ2 fI 1 − G(ϕTd,τ2 )
!
We can rewrite equation (A5) as
ln
T WHet,OF 1 DI (τ2 ) ≈ [∆ϕ eTd,τ2 + χx,τ2 + χI,τ2 − χx,τ1 − χI,τ1 T σ−1 WHet,OF DI (τ2,keep )
(A6)
+ χx,τ1 fx + χI,τ1 fI − χx,τ2 fx − χI,τ2 fI σ−1 σ−1 + χx,τ2 τ2−1 ϕ eTx,τ2 + χI,τ2 ϕ eTI,τ2 − χx,τ2 τ2−1 ϕ eTx,τ1 − χI,τ2 ϕ eTI,τ1 ] 1 [∆ϕ eTd,τ2 + χx,τ2 − χx,τ1 + χx,τ1 fx − Within equation (A6), the component σ−1 σ−1 σ−1 eTx,τ1 ] is the welfare increase caused by χx,τ2 fx + χx,τ2 τ2−1 ϕ eTx,τ2 − χx,τ2 τ2−1 ϕ
the switching of nonexport firms: a portion of nonexport firms exit, and another 1 [χI,τ2 − χI,τ1 + portion of nonexport firms switch to export. The component: σ−1 χI,τ1 fI − χI,τ2 fI + χI,τ2 ϕ eTI,τ2 − χI,τ2 ϕ eTI,τ1 ], is the welfare increase caused by the
30
switching of FDI firms: a portion of FDI firms switch to export in response to a variable trade cost decrease.
31
Reference Arkolakis, C., A. Costinot and A. Rodrigues-Clare, 2012. New Trade Model, Same Old Gains? American Economic Review, 99, 94–130. Broda, C., J. Greenfield, and D. Weinstein, 2006. From Groundnuts to Globalization: A Structural Estimantion of Trade and Growth, NBER Working paper 12512, Broda, C. and D. Weinstein, 2006. Globalization and the Gains from Variety, Quarterly Journal of Economics, 121, 541–585. Eaton, Jonathan and Kortum, Samuel 2002. Technology, Geography, and Trade. Econometrica, 70, 1741-1779. Edmond, C., V. Midrigan, and Y. Xu, 2015. Competition, Markups, and the Gains from International Trade, American Economic Review, 105, 3183-3221. Ethier, W.J., 1986. The Multinational Firm The Quarterly Journal of Economics, 101(4), 805–834. Fajgelbaum, P. and A. Khandelwal, 2014. Measuring the Unequal Gains from Trade, Working paper. Feenstra, R. and D. Weinstein, 2009. Globalization, Competition, and the US Price Level, Unpublished. Feenstra, R. and H. Kee, 2008. Export Variety and Country Productivity: Estimating the Monopolistic Competition Model with Endogenous Productivity, Journal of International Economics, 74, 500–518. 32
Goldberg, P., A. Khandelwal, N. Pavcnik and P. Topalova, 2009. Trade Liberalization and New Imported Inputs, American Economic Review, 99, 494–500. Helpman, E., M. Melitz, and S. Yeaple, 2004. Export Versus FDI with Hetergeneous Firms, American Economic Review, 94, 300–316. Irarrazabal, A., A. Moxnes, and L.D. Opromolla 2013. The Margins of Multinational Production and the Role of Intra-Firm Trade Journal of Political Economy, 121, 74–126. Suzumura, K., K. Kiyono 1987. Entry Barriers and Economic Welfare The Review of Economic Studies, 54(1), 157–167. Melitz, M. and S. Redding, 2015. New Trade Models, New Welfare Implications, American Economic Review, 105, 1105–1146. Ramondo, N. and A. Rodriguez-Clare, 2013. Trade, Multinational Production, and the Gains from Oppeness, Journal of Political Economy, 121, 273–322. World Investment Report 2012. Transitional Corporations, Agricultural Production and Development. Geneva: United Nations
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Highlights:
1. Gains from trade liberalization will be larger when foreign direct invest (FDI) is an available choice for firms; 2. However, gains from tariff reduction (export liberalization) are smaller when a fraction of firms are engaged in FDI; 3. The decomposition of the gains from trade liberalization shows that most gains are from firms which switch their exporting mode; 4. Resource reallocation is the key determinant of the gains from trade liberalization;
S0264-9993(19)30307-4
DOI:
https://doi.org/10.1016/j.econmod.2020.01.003
Reference:
ECMODE 5119
To appear in:
Economic Modelling
Received Date: 1 March 2019 Revised Date:
25 October 2019
Accepted Date: 3 January 2020
Please cite this article as: Sun, P., Tan, Y., Yang, G., Export, FDI and the welfare gains from trade liberalization, Economic Modelling (2020), doi: https://doi.org/10.1016/j.econmod.2020.01.003. This is a PDF file of an article that has undergone enhancements after acceptance, such as the addition of a cover page and metadata, and formatting for readability, but it is not yet the definitive version of record. This version will undergo additional copyediting, typesetting and review before it is published in its final form, but we are providing this version to give early visibility of the article. Please note that, during the production process, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. © 2020 Published by Elsevier B.V.
Export, FDI and the Welfare Gains from Trade Liberalization† Puyang Sun1
Yong Tan2‡
Guang Yang1
1: Department of Economics, Nankai University 2: School of International Economics & Trade, Nanjing University of Finance and Economics
Abstract This paper extends Melitz and Redding (2015) to analyze the welfare gains from trade liberalization by adding foreign direct investment(FDI). Our model predicts that with FDI activities, welfare gains from trade liberalization will be strictly lower than those in a model without FDI, but only takes exports into account. In addition, the calibrated model indicates that with FDI activities, aggregate welfare reaches its maximum when the fixed export costs are positive rather than 0. Furthermore, we decompose the welfare gains induced by trade liberalization from continuing exporters, and switchers. The results show that in any case, with or without FDI, continuing exporters contribute a larger share to welfare gains than status switching firms. Keywords: FDI · Welfare Gains · Trade Liberalization JEL Classifications: F12·F13·F41
†
Contact information: [email protected] (P. Sun), yongtan [email protected] (Y. Tan), [email protected] (G.Yang). We are grateful to Lorenzo Caliendo, Yi Lu, Larry Qiu, Joel Rodrigue for their invaluable comments and feedback. We are also grateful to the editor and two anonymous referees for providing valuable comments. We would like to thank participants at CCER Summer Conference in Yantai (2016), and CTRG conference in Nanjing (2016). Yong Tan acknowledges the financial support from the Natural Science Foundation of China (71703067), National (Major) Social Science Foundation of China (18VSJ017). Guang Yang acknowledges the financial support from Social Science Foundation of China(18CJL013). All authors have equal contribution in this paper. If you have any questions, please contact Yong Tan, who is the corresponding author. ‡ Corresponding Author: Yong Tan is the corresponding authors
1
1. Introduction In the last three decades, a central element of economic globalization has been the growth in multinational production (henceforth, MP). From 1990 to 2006, the annual growth rate of global foreign direct investment (henceforth, FDI) was 17%; during the same period, world exports grew by only 8% (Irarrazabal et al., 2013). According to the World Investment Report, by 2006, 10% of the world’s GDP was comprised of value added from MP. The remarkable growth of FDI and its interaction with exports has drawn considerable attention from researchers (e.g. Helpman et al., 2004; Irarrazabal et al., 2013; Ramondo and Rodriguez-Clare, 2013). Further, the question of how much a country gains from trade liberalization, a decrease in the variable trade cost, lies at the core of research in international trade. Arkolakis et al. (2012) and Melitz and Redding (2015) evaluate the gains from trade liberalization in economies with homogeneous and heterogeneous firms, respectively. However, FDI is prohibited in their works, which leaves the gains unclear when firms face FDI options. Ethier (1986) finds a substitution relationship between FDI and exports. Firms that are engaged in FDI are not necessarily affected by trade liberalization.1 As such, gains from trade liberalization are overestimated if firm-level FDI activities are not considered. Given the rapid growth of FDI and its influence on welfare gains during trade liberalization, how to correctly measure welfare gains from trade liberalization is not only of academic interest; it is also of policy importance. 1
Trade liberalization only affects a firm that is engaged in FDI if it switches its status from FDI to exporting due to variable trade cost reductions.
2
Pioneer research documents welfare gains from trade liberalization from different perspectives: consumers gain from more variety (Broda and Weinstein, 2006; Goldberg et al, 2009); productivity gains from exporting a large variety of goods (Feenstra and Kee, 2008) and welfare gains from reduced markups (Feenstra and Weinstein, 2009; Edmond et al., 2015). In contrast, Arkolakis et al. (2012) (henceforth, ACR) introduce a way to measure the aggregate welfare gains from trade liberalization.2 However, Melitz and Redding (2015) show that ACR underestimate gains from trade liberalization by focusing on an economy with homogeneous firms. Specifically, Melitz and Redding (2015) demonstrate that the aggregate welfare level can be measured by real income, i.e., the nominal income divided by the price index. Moving from an economy with homogeneous firms to one with heterogeneous firms, the trade induced welfare gains will increase. Intuitively, in equilibrium, nominal income is determined by aggregate output, and the price index depends on the revenue-weighted average firm-level productivity.3 Trade liberalization, on the one hand increases aggregate output by encouraging firm-level exporting participation; on the other hand, it leads to a disproportionately faster growth of more productive firms.4 Therefore, as nominal income increases, and the price index decreases. The aggregate welfare level, in turn increases. In this paper, we attempt to measure the gains from trade similar to Melitz and Redding (2015) by allowing firm-level FDI activities. Following Helpman et al. 2
ACR (2012) extend the idea of Eaton and Kortum (2002) to show that when certain conditions are satisfied, the aggregate welfare gains from trade liberalization can be measured using a country’s domestic trade share and its elasticity of trade with respect to variable trade costs. 3 Nominal income increases in the aggregate output and price index decreases with average firm-level productivity. 4 Throughout this paper, trade liberalization refers to reductions in variable trade cost, τ .
3
(2004), when an economy moves from autarky to free trade, the most productive firms choose to conduct FDI, followed by firms engaged in exporting, and those that only serve the domestic market, while the least productive firms exit. The FDI activities change the trade elasticity measured in Melitz and Redding (2015), in which trade elasticity with respect to variable trade costs is determined only by the export productivity cutoff, ϕx . In contrast, with the FDI option, this elasticity is jointly determined by the productivity cutoffs of exporting, ϕx , and FDI, ϕI .5 This implies that the aggregate output and average productivity growth induced by trade liberalization are smaller in cases with FDI activities. As such, the welfare gains from trade liberalization are overestimated by Melitz and Redding (2015). Further, in this paper we estimate the trajectory of welfare gains by gradually lowering the variable trade cost, τ . The results show that although the welfare level is always higher in the case with FDI than that without FDI, the welfare gains from trade liberalization are smaller in the case with FDI. Specifically, our calibration results show that when the variable trade cost, τ , decreases from 3 to 1.25, the welfare gains in the case with FDI are 3 percentage points lower than those in the case with exporting only. We further decompose the welfare gains into different group of firms in order to investigate the source of gains. The results demonstrate that with FDI activities, gains from continuing exporters contribute 57% of the aggregate welfare gains, and status-switching firms contribute the remaining 43% of welfare gains (of which 78% is from the switching of non-exporting firms to exporting firms, and 21% from the switching of FDI firms to exporting firms). By comparison, when FDI is prohibited, continuing exporters contribute 74% of 5
This is because a decrease in variable trade costs would decrease the export productivity cutoff, ϕx , and increase the FDI productivity cutoff, ϕI .
4
the aggregate welfare gains. These findings are not only of research interest; they are also of policy importance. Since FDI revenue varies across economies, an economy with a higher FDI share would expect lower welfare gains from trade liberalization. In addition, FDI activities exhibit heterogeneities across industries, i.e., FDI is more popular in some industries, e.g., textile and cloths, leather, and mining industries than in others. To maximize social welfare, policymakers may want to decrease the variable export cost, τ , more in industries with fewer FDI activities.6 After understanding the source of welfare gains, we conduct further counterfactual experiments by gradually changing the fixed export costs, variable trade costs, and fixed FDI costs. The calibration results demonstrate that when gradually increasing the fixed export costs in an economy with heterogeneous firms, welfare reaches its maximum at a positive fixed export cost. This is because a positive fixed export cost drives more firms to conduct FDI instead of exporting.7 More FDI firms increase the aggregate output and average productivity. This, in turn, raises the social welfare level. This work is related to a number of papers which empirically or numerically quantify the gains from trade through different channels (Broda et al., 2006; Broda and Weinstein, 2006; Goldberg et al, 2009; Feenstra and Weinstein, 2009; Edmond et al., 2015; Fajgelbaum and Khandelwal, 2014). In contrast to these works, our 6
Since FDI firms will not be affected by trade liberalization, the reduction in variable export costs will generate fewer welfare gains in industries in which more firms are engaged in FDI activities. 7 In the case with FDI activities, zero fixed export costs will lead to excessive entry into exporting, i.e., some FDI firms will switch to exporting, and some nonexporters will start exporting. This lowers firm-level output. Suzumura and Kiyono (1987) show that the excessive entry will decrease firm-level output, and hence, lower social welfare. Our result is in line with Suzumura and Kiyono (1987), and we thank an anonymous referee for pointing out this issue.
5
study evaluates the aggregate welfare gains from trade liberalization. This feature makes our paper closely related to Melitz and Redding (2015). However, our work differs from Melitz and Redding (2015) in three respects. First, we examine the aggregate welfare gains from trade liberalization in a framework with FDI activities, which are the central elements of the economic globalization. Second, we decompose the welfare gains into different groups of firms to clarify the source of the gains; Third, we calibrate the model to detect optimal export fixed costs. We find that in the case with FDI activities, the optimal export fixed costs are strictly positive. Our work is also distinct from Irarrazabal et al. (2013) and Ramondo and Rodriguez-Clare (2013) in two respects. First, we do not discuss FDI geography gravity; instead we focus on the welfare effects of the substitutability between FDI and exports. Second, in a more general setting with FDI activities, we find that economies consisting of heterogeneous and homogeneous firms benefit differently from trade liberalization.8 This paper proceeds as follows: In section 2 we introduce the model with FDI. Section 3 outlines the welfare gains in response to trade liberalization when FDI activities are allowed. Section 4 decomposes the welfare gains from different firms to clarify where the gains come from. In section 5, we calibrate the welfare gains from variable trade cost reductions, fixed trade cost reductions, and fixed FDI cost reductions. Section 6 concludes. 8
In Ramondo and Rodriguez-Clare (2013), the gains from openness are invariant to economies with heterogeneous and homogeneous firms.
6
2. Model 2.1. A Model with Heterogeneous Firms and FDI Following Helpman et al. (2004), we assume that there are two countries, the home country, H, and the foreign country, F . The two countries are assumed to be symmetric, i.e. identical in size, labor supply, etc. After paying a sunk entry cost, fe , firms draw their productivity from a Pareto distribution, G(·). Based on a productivity draw, each firm decides to either stay in the market or exit. If a firm chooses to stay in the market, it will further decide whether to serve the foreign market and, if so, whether to do so through exporting or FDI.9 Each firm produces a differentiated variety, and preferences in both the home and foreign country have the standard CES form, with an elasticity of substitution, σ = 1/(1 − ρ) > 1. These preferences generate a demand function Ap−σ for every firm. A is a demand shifter in the home and foreign countries.10 Since the home and foreign countries are identical, we focus our discussion on the home country, H, even though all results are equally applicable to the foreign country, F . Denote ϕTd,τ , ϕTs,τ and ϕTI,τ as the productivity cutoffs for serving the domestic market, exporting, and FDI, at trade costs, τ, respectively. The zero profit 9
Intuitively, the least productive firms exit the market immediately after their productivity draw, low productivity firms serve the domestic market only, firms with a relatively high level of productivity draw export to the foreign market, and the most efficient firms serve the foreign market through FDI. σ 10 In particular, A = ωL P P , where ω is the wage level, L is the aggregate labor supply, and P denotes the price index.
7
conditions for serving the domestic market, exporting and FDI are as follows:
rI
!σ−1 rd ϕTd,τ R σ − 1 P ϕTd,τ = = wfd σ σ σ w !σ−1 rx ϕTx,τ R σ − 1 P ϕTx,τ = = wfx σ σ σ τw ϕTI,τ rx ϕTI,τ − wfI = − wfx σ σ
(1)
(2) (3)
where rd ϕTx,τ denotes the revenue of firms with the cutoff productivity ϕTd,τ in the home country; rx ϕTx,τ denotes the export revenue in foreign market with productivity ϕTx,τ ; and rI ϕTI,τ measures the FDI revenue in the foreign market with productivity, ϕTI,τ . fd , fx , and fI are the fixed production costs in the domestic market, export, and FDI, respectively. w is the wage level. Equations (1)-(3) define the productivity cutoffs of staying in the market, starting exporting and FDI, respectively.11 For potential entrants, the expected profit is equal to the entry cost, which gives the free entry condition as follows:
fd J ϕTd,τ + fx J ϕTx,τ + fI J ϕTI,τ = fe 11
These cutoffs are also depicted in Figure A1 in the online Appendix.
8
(4)
where, fd J ϕTd,τ =
fx J ϕTx,τ =
fI J ϕTI,τ =
Z
ϕmax
ϕT d,τ
Z
ϕmax
"
ϕT x,τ
Z
ϕmax
ϕ ϕTx,τ
ϕT I,τ
ϕ ϕTd,τ
ϕ ϕTI,τ
!σ−1
− 1 dG(ϕ) σ−1
# − 1 dG(ϕ)
!σ−1
− 1 dG(ϕ)
Similar to Melitz and Redding (2015), with all the notations introduced above, the number of active firms can be expressed as: R L M = 1 − G ϕTd,τ Me = = r σF T
(5)
where, M is the number of active firms, and Me is the number of potential entrants. L is the total labor supply in the home country. r and F T denote the average revenue earned by active firms and the average fixed costs paid by all firms, respectively. In particular, fe + fd + χx,τ fx + χI,τ fI 1 − G ϕTd,τ G ϕTI,τ − G ϕTx,τ = 1 − G ϕTd,τ 1 − G ϕTI,τ = 1 − G ϕTd,τ
FT = χx,τ χI,τ
(6)
where χx,τ and χI,τ denote the share of firms that are engaged in export and FDI, respectively. Before we proceed further, it is worthwhile to note three differences between the model with FDI and the model without FDI (e.g. Melitz and Redding, 2015).
9
First, given that all parameters are identical in the two models, the number of active firms will be smaller in the model with FDI than in the model without FDI. By allowing FDI, the expected profit for potential entrants is higher than that in a setting where firms can only export. Higher profits encourage entry and hence intensify the competition.12 Second, the welfare gains will be smaller in the case with FDI activities than those in Melitz and Redding (2015). This is because a portion of firms with the highest levels of productivity are engaged in FDI, and some of them are not affected by trade liberalization (a decrease in variable trade cost, τ ) if they do not switch from FDI to exporting. Third, moving from an autarkic economy to an open economy, the model with FDI will imply greater welfare gains.13
3. Welfare Analysis In this section, we investigate the welfare gains from trade liberalization. Similar to Melitz and Redding (2015), we represent the aggregate welfare in a setting with FDI as follows:
T WHet,F DI =
1 σ−1
w σ − 1 L(1 + χx,τ + χI,τ ) T σ−1 = ϕ e T P σ σF | t,τ{z } | {z } Γ2
(7)
Γ1
ϕ eTt,τ =
1 1 + χx,τ + χI,τ
h
ϕ eTd,τ
σ−1
+ χx,τ τ −1 ϕ eTx,τ
12
σ−1
+ χI,τ ϕ eTI,τ
σ−1 i
The higher expected profit shifts up the free entry curve, which increases the zero profit cutoff ϕTd,τ . 13 The second and third points can be seen in Figure A2 in the online Appendix.
10
T where, WHet,F DI denotes aggregate welfare in the home (foreign) country when
firms can choose to conduct FDI.14 ϕ eTt,τ is the weighted average of ϕ eTx,τ , ϕ eTd,τ and ϕ eTI,τ , which are the average productivity of all active firms, firms serving foreign markets (through exporting and FDI), and firms engaged in FDI, respectively. In particular,
ϕ eTd,τ = ϕ eTx,τ = ϕ eTI,τ =
Z
ϕmax
" ϕσ−1
ϕT d,τ
Z
ϕmax
" ϕσ−1
ϕT x,τ
Z
ϕmax
" ϕσ−1
ϕT I,τ
dG(ϕ) 1 − G ϕTd,τ dG(ϕ) 1 − G ϕTx,τ dG(ϕ) 1 − G ϕTI,τ
1 # σ−1
(7.1) 1 # σ−1
(7.2) 1 # σ−1
(7.3)
Equation (7) indicates a difference from Melitz and Redding (2015); two new terms appear in the aggregate welfare expression, χI,τ , and ϕTI,τ . An decrease in variable trade costs, τ , will change the share of firms that are engaged in FDI and the FDI productivity cutoff. Similarly, we can rewrite the aggregate welfare calculation when FDI is prohibited:
T WHet,EXP
ϕ eTt,τ
1 w σ − 1 L(1 + χx,τ ) T σ−1 σ−1 = = ϕ et,τ P σ σF T h σ−1 σ−1 i 1 T −1 T = ϕ ed,τ + χx,τ τ ϕ ex,τ 1 + χx,τ
(8)
It is easy to show that aggregate welfare is higher in the case with FDI than 14
Similar to Melitz and Redding (2015), Γ1 and Γ2 measure the nominal income and price L(1+χx,τ ) index, respectively. The only difference is that in Melitz and Redding (2015), Γ1 = . σF T Notice that Γ1 is a measure of the aggregate output, which equals to the total expenditure in each country. As such, the welfare measured in equation (7) takes into account of both import and export tariffs.
11
without FDI: T WHet,F DI = T WHet,EXP 1 σ−1 h σ−1 σ−1 i σ−1 f −1 T −1 T T e + χI,τ τ ϕ eI,τ + χx,τ τ ϕ ex,τ ed,τ + fd + χx,τ fx ϕ 1−G(ϕT d,τ ) >1 h σ−1 σ−1 i fe T −1 T + χx,τ τ ϕ ex,τ ϕ ed,τ + fd + χx,τ fx + χI,τ fI 1−G(ϕT d,τ )
(9) Inequality (9) implies that in moving from autarky to an open economy, welfare gains are smaller when FDI is prohibited. 3.1. Welfare Gains from Trade Liberalization Now we are ready to evaluate the gains from trade liberalization. We set all parameters identical to Melitz and Redding (2015). That is, we set the elasticity of substitution rate, σ = 4, the wage rate, ω = 1, the labor force, L = 153.889, the Pareto distribution parameter, ϕmin = 1, and k = 4.25.15 In addition, the fixed cost of entry, fe , domestic production, fd , export, fx , are set to be 1, 1, and 0.545, respectively. Finally, we set the fixed cost of FDI as 20.16 Using equations (1) - (6), we can compute the share of exporting firms, FDI firms, and the corresponding productivity cutoffs. We gradually decrease variable trade costs, τ , to measure the welfare gains from trade liberalization. The results are presented in Table 1: −k ϕ The Pareto distribution function is given by G(ϕ) = 1 − ϕmin , where ϕmin denotes the minimum productivity and k is the Pareto distribution parameter, which governs the shape of the distribution. 16 This value is not picked randomly. It cannot be too large or too small relative to fixed export costs. If it is too large, no firms will choose to conduct FDI, and if it is too small no firms will choose to export. 15
12
[Table 1 is to be here] In Table 1, Welfare A , Welfare EXP and Welfare F DI denote the welfare level in autarky, with exporting only and with exporting and FDI, respectively. The results in the first row show that when the variable trade costs, τ , converge to infinity, Welfare EXP =Welfare A , and the welfare with FDI is 6% higher than that in the autarky.17 This relationship continues to hold when the trade costs decrease to 3 (τ = 3). The third row of Table 1 implies that when the trade costs further decrease to τ = 1.25, the welfare levels in the case without FDI and in the case with FDI are 10% and 14% higher than that in autarky, respectively. In sum, Table 1 delivers two pieces of information. First, the welfare level is always higher when FDI is not prohibited than that in the case with exports only; Second, trade liberalization brings larger welfare gains for the economy with export only ((1.10 − 1)/1 = 10% higher) than in the economy with both export and FDI ((1.14 − 1.06)/1.06 = 8%).
4. Decomposition of Welfare Gains In an economy with FDI, welfare gains from trade liberalization can be attributed to three sources. First, the economy benefits from a portion of nonexporters (with relative high productivity) start to export. Second, the economy gains from increasing foreign sales from continuing exporters. Third, the switching of a fraction of firms from conducting FDI to exporting also increases the welfare level. In this section, we decompose the aggregate welfare gains from trade 17
Notice that the fixed FDI costs, fI , is fixed at 20 during the decrease of the variable trade costs. This implies that the most productive firms can always choose to conduct FDI.
13
liberalization to the three groups of firms: 1. nonexporters; 2. exporters; 3. firms engaged in FDI. According to equation (7), when the variable trade costs decrease from a particular level, τ1 , to τ2 (τ2 < τ1 ), the ratio of aggregate welfare under these two different variable trade costs can be written as: 1 " σ−1 # σ−1 T T T ϕ WHet,F (τ ) e F 1 + χ + χ 2 x,τ2 I,τ2 τ1 t,τ2 DI = σ−1 T T 1 + χ + χ F WHet,F (τ ) x,τ1 I,τ1 τ2 ϕ eTt,τ1 DI 1
(10)
Our decomposition procedures are straightforward. First, we assume that nonexporters and FDI firms do not switch to exporting when the variable trade costs decrease from τ1 to τ2 , and calculate the gains for continuing exporters in response to trade liberalization. Second, we compute the new survival, export and FDI productivity cutoffs under the trade costs τ2 . With these new cutoffs, we can calculate the welfare gains from switchers: (1) nonexporters that start exporting (2) nonexporters that exit (3) FDI firms switch to exporting. Mathematically, the welfare gains are written as T T T WHet,F WHet,F DI (τ2,keep ) WHet,F DI (τ2 ) DI (τ2 ) = T T T WHet,F WHet,F DI (τ1 ) DI (τ1 ) WHet,F DI (τ2,keep )
(11)
T where WHet,F DI (τ2,keep ) is the welfare level at the trade cost level, τ2 , without any T switching. In comparison, WHet,F DI (τ2 ) denotes the welfare level at the trade cost,
τ2 , after accounting for all possible switching. As such, the first component in the RHS of equation (11) measures the welfare gains for continuing exporters, while the second term captures the welfare gains generated by switchers. Later, the second term will be further decomposed into the gains from nonexporters and FDI
14
firms, respectively. T WHet,OF DI (τ2,keep ) T WHet,OF DI (τ1 )
σ−1 ϕ eTt,τ2 σ−1 ϕ eTt,τ1
"
ϕ eTd,τ1
σ−1
+ χx,τ1 τ2−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
ϕ eTd,τ1
σ−1
+ χx,τ1 τ1−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
=
=
1 # σ−1
"
1 σ−1 # σ−1
σ−1 (12)
where ϕ eTd,τi , ϕ eTx,τi , and ϕ eTt,τi , i = 1, 2, are productivity cutoffs as defined in equations (7.1)-(7.3). Note that in equation (12), we assume switching is not possible, and hence there is no change in productivity cutoffs. Similarly, the welfare gains from switchers can be written as follows: 1 " σ−1 σ−1 # σ−1 −1 T T T T T ϕ e + χ τ ϕ e + χ ϕ e (τ ) WHet,OF F 1 + χ + χ x,τ I,τ 2 2 2 2 x,τ2 I,τ2 x,τ2 I,τ2 τ1 d,τ2 DI = σ−1 σ−1 T T −1 T T 1 + χ F + χ WHet,OF (τ ) x,τ1 I,τ1 τ2 ϕ ed,τ1 + χx,τ2 τ2 ϕ ex,τ1 + χI,τ2 ϕ eTI,τ1 DI 2,keep (13)
After some cumbersome algebra,18 we write the welfare gains as follows: T T T WHet,F WHet,F WHet,F DI (τ2 ) DI (τ2,keep ) DI (τ2 ) ln T = ln + ln T T WHet,F DI (τ1 ) WHet,F WHet,F DI (τ1 ) DI (τ2,keep )
18
The details are in the Appendix.
15
(14)
=
σ−1 i χx,τ1 h −1 T σ−1 τ2 ϕ ex,τ2 − τ1−1 ϕ eTx,τ1 |σ − 1 {z }
+
σ−1 i σ−1 1 eTx,τ2 − χx,τ1 τ2−1 ϕ eTx,τ2 χx,τ2 − χx,τ 1 + χx,τ1 fx − χx,τ 2 fx + χx,τ2 τ2−1 ϕ |σ − 1 {z }
Gains of continuing Exporters
h
Gains from swithing (nonexport to export)
σ−1 σ−1 i 1 χI,τ2 − χI,τ 1 + χI,τ1 fI − χI,τ 2 fI + χI,τ2 τ2−1 ϕ eTI,τ2 − χI,τ1 τ2−1 ϕ eTI,τ2 |σ − 1 {z } h
Gains from swithing (FDI to exporters)
+
σ−1 1 ∆ ϕ eTd |σ − 1 {z }
Gains from switching (exit)
The components on the RHS of equation (14) give the welfare contributions of each group. In particular, when the variable trade costs, τ , decrease from 3 to 1, we calculate the associated welfare gains from each group of firms. The results are reported in Panel A of Table 2: [Table 2 is here] The results indicate that the aggregate welfare with FDI will increase by 16%. Continuing exporters contribute 57% of the total welfare gains, while switchers contribute 43% of welfare gains. Further, within the 6.88% (=43% × 16%) welfare gains, most are caused by firms switching from nonexporting to exporting, which accounts for 78% of the gains, while the firms switching from FDI to exporting only contribute 21% of the gains.19 For comparison purposes, we repeat the exercise for the model without FDI in 19
Exit firms account for 1% of the welfare gains among all switchers. The results are consistent with our intuition: switching from nonexporting to exporting contributes more to welfare gains than switching from FDI to exporting. The former increases foreign sales more (decreases the domestic trade share more) than the latter and, hence, according to Arkolakis et al. (2012) the former contributes more to welfare gains.
16
Panel B of Table 2. The results indicate that when FDI is prohibited, the aggregate welfare gains are larger, 19% compared to 16% – in response to a variable trade cost decrease. This is because more continuing firms directly benefit from the variable cost reduction. The above results convey an important piece of information: compared with continuing exporters, the switching of FDI firms contributes a relatively trivial share to welfare gains.
5. Calibrating the Influence of Trade Liberalization In this section, we calibrate the model with FDI to numerically evaluate the influence of trade liberalization on an economy. We first increase the fixed exporting costs from 0 to 1 and compare the welfare changes in economies with homogeneous and heterogeneous firms. Next, we increase the variable export costs, τ , to compare the welfare changes in the homogeneous and heterogeneous economies. Finally, we increase the fixed FDI investment costs to evaluate the influence of investment liberalization on welfare. 5.1. Welfare Gains from Fixed Export Cost Reductions We first calibrate the influence of fixed export cost reductions on welfare. We are interested in two questions. First, in the model with FDI, how different do the economies with homogeneous and heterogeneous firms respond to fixed export cost reductions? Second, how do the gains differ from those reported in Melitz and Redding (2015)? In the calibration, we set all parameters identical to those in Melitz and Red-
17
ding (2015),and increase the fixed export costs from 0 to 1.20 Figure 1 depicts the changes in welfare gains, export probability, average productivity and the domestic trade share in response to a fixed cost increase. Figure 1: The Influence of Export Fixed Cost Reductions Panel B
1 1.08
Probability of exporting
Welfare gains from trade
Panel A
1.06 1.04 1.02 1
0
0.25
0.5
0.75
0.8 0.6 0.4 0.2 0
1
0
1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1
0.25
0.5
0.75
1
Fixed exporting cost Panel D
1 Domestic trade share
Weighted average productivity
Fixed exporting cost Panel C
0
0.25
0.5
0.75
0.95 0.9 0.85 0.8
1
Fixed exporting cost Note: Variable trade costs=1.83
0
0.25
0.5
0.75
1
Fixed exporting cost
In Panels A − Panel D of Figure 1, the solid and dashed curves depict the patterns of different variables across heterogeneous and homogeneous economies, respectively. Figure 1 first indicates that the welfare gains and weighted average productivity are always higher in the economy with heterogeneous firms than in the economy with homogeneous firms when facing different levels of fixed export cost (Panel A and C). Second, the export probability decreases in both economies when facing an increase in fixed export costs (Panel B). Third, the domestic trade 20 Notice that the fixed cost for FDI is much higher than that associated with exporting. This setting is consistent with the fact that FDI activities require a higher fixed cost relative to exporting. Secondly, we need to set the fixed FDI cost higher to guarantee that not every firm serves the foreign markets through FDI.
18
share, which is calculated as domestic sales divided by total sales, increases with fixed export costs in both economies in both economies.21 When we focus on trends in the economy composed of heterogeneous firms, we find some patterns that are in striking contrast to those in Melitz and Redding (2015).22 Panel A, for instance, indicates that when facing an increase in the fixed export cost, welfare first increases and then decreases. The average weighted productivity also manifests a similar inverted-U shape (Panel C). The intuition is that when the fixed exporting costs gradually increase from 0, some productive exporters with sufficiently high productivity will switch to FDI. After these firms switch from exporting to FDI, they sell more in foreign markets,23 which has two direct consequences: it decreases the domestic trade share (the decreasing part in Panel D), and increases the aggregate income as consumers earn more income from foreign sales.24 Both effects result in a welfare increase. When the fixed export cost increases even further, more firms stop exporting, which decreases foreign sales and drives both average productivity and welfare down. Therefore, aggregate welfare eventually declines in response to further fixed export cost increases. An implication of Figure 1 is that in order to maximize welfare in an economy with heterogeneous firms, moderate positive fixed export costs are necessary when FDI is not prohibited. 21
The domestic trade share initially decreases in the economy with heterogeneous firms when fixed export costs increase. 22 The corresponding results for an economy without FDI are shown in Figure A3 in the Appendix. 23 This switching prevents excessive entry into the foreign market, which would otherwise lead to lower foreign sales (see, Suzumura and Kiyono, 1987). 24 This is also consistent with Arkolakis et al. (2012) that given the trade elasticity, the welfare is decreasing in domestic trade share.
19
5.2. The Influence of Export Variable Cost Reductions We next calibrate the model to evaluate the influence of variable export cost reductions on economies with heterogeneous and homogeneous firms, respectively. In this numerical exercise, we again set all parameters equal to those values in the previous section, except that fixed export costs are set to fx = 0.76 ( rather than varying between 0 and 1), and the variable export costs will increase from 1 to 3 as in Melitz and Redding (2015). The influence of variable export costs based on aggregate welfare, export probability, weighted average productivity, and domestic trade share are depicted in Figure 2.25 Figure 2: The Influence of Export Variable Cost Reductions Panel A
Panel B
1.2
Probability of exporting
Welfare gains from trade
1
1.15 1.1 1.05 1
1
1.5
2
2.5
0.8 0.6 0.4 0.2 0
3
1
1.2 1.175 1.15 1.125 1.1 1.075 1.05 1.025 1
1.5
2
2.5
3
Variable trade cost Panel D
1 Domestic trade share
Weighted average productivity
Variable trade cost Panel C
1
1.5
2
2.5
0.8
0.6
0.4
3
Variable trade cost Note: Fixed exporting cost=0.545
1
1.5
2
2.5
3
Variable trade cost
In contrast to the influence of fixed export cost on these aggregate variables, increasing variable trade costs cause a steady decline in welfare, export probability, weighted average productivity, and increase the domestic trade share for 25
We depict the results without FDI in Figure A4 of the Appendix.
20
both economies. The only exception is weighted average productivity, which only declines in the economy with heterogeneous firms. Although these results seem to contradict the patterns exhibited in Figure 1, we have good explanations for these observed trends. When variable export costs increase from 1, some productive firms switch from export to FDI. However, this switching does not largely change firm-level sales in foreign markets, as FDI variable costs, which take a value of 1, are only slightly lower than that associated with exporting. Therefore, foreign sales decrease because less productive firms stop exporting, and these firms dominate those switching from export to FDI. The results indicate that in order to maximize welfare and weighted average productivity in an economy with heterogeneous firms, variable trade costs should be reduced to 1. 5.3. The Influence of FDI Fixed Cost Reductions Finally, we assess the influence of FDI fixed cost reductions on aggregate welfare, weighted average productivity, average FDI propensity, and domestic sales. In this calibration, all parameters are set to the same values as those in the previous section, while fixed FDI costs, fI , increase from 15 to 200. The calibrated results are depicted in Figure 3 with the solid and dashed curves denoting economies with heterogeneous and homogeneous firms, respectively: The figure shows that firm-level productivity in the homogeneous economy has been set to equalize the weighted average productivity of firms in the heterogeneous economy in autarky. No firms will conduct FDI in the homogeneous economy, as firm-level productivity is not sufficiently high to overcome the high
21
Figure 3: The Influence of FDI Fixed Cost Reductions Panel A
Panel B
Probability of FDI
Welfare gains from FDI
1.08 1.06 1.04 1.02
0.1 0.08 0.06 0.04 0.02 0
1 15 40 65 90 115 140 165 190
15 40 65 90 115 140 165 190
1.1 1.09 1.08 1.07 1.06 1.05 1.04 1.03 1.02 1.01 1 15 40 65 90 115 140 165 190
Fixed FDI cost Panel D
0.9 Domestic trade share
Weighted average productivity
Fixed FDI cost Panel C
0.88
0.86
0.84
Fixed FDI cost
15 40 65 90 115140165190 Fixed FDI cost
FDI fixed costs.26 As such, changes in FDI fixed cost have a trivial impact on the homogeneous economy. In contrast, in the economy with heterogeneous firms, the most productive firms will conduct FDI instead of exporting. Changes in the fixed FDI costs will thus significantly affect the heterogeneous economy. For instance, Panel A shows that the aggregate welfare level declines as FDI fixed costs increase. This is because weighted average productivity also decreases with FDI fixed costs (shown in Panel C). Meanwhile, Panel B indicates the probability that FDI is also decreasing as FDI fixed costs increase, and hence the domestic trade share increases with FDI fixed costs (Panel D). Intuitively, when FDI fixed costs rise, a portion of firms will switch from FDI to exporting. This switching reduces firm-level sales in foreign markets, and hence decreases weighted average produc26
In the homogeneous economy, firm-level productivity is not sufficiently high to allow firms to conduct FDI. If we change some parameters, such as fI = fx , all firms will conduct FDI after investment liberalization.
22
tivity, as well as the foreign share. All of these facts predict a decline in aggregate welfare.
6. Conclusions In this paper, we investigate the welfare gains from trade liberalization when FDI activities are allowed. The results indicate that welfare gains are lower with FDI than those without FDI when considering marginal changes in variable trade costs. This implies that the welfare gains from trade liberalization have been overestimated if they do not take FDI into account. We further decompose the welfare gains into different groups of firms. The results indicate that the continuing exporters contribute the most to welfare gains in response to trade liberalization. In contrast, firms that switches to FDI only contribute a trivial share of the welfare gains. This explains why the welfare gains are lower with FDI activities. This finding show that economies benefit differently from trade liberalization, i.e., those with a larger share of FDI benefit less. In addition, the welfare gains are disproportionately large for industries with a small share of FDI. Meanwhile, we compare the welfare gains in an economy with homogeneous firms vs. heterogeneous firms. The results show that the welfare gains from trade liberalization are always higher in the economy with heterogeneous firms. However, when FDI is not prohibited, the welfare difference between the two economies narrows. This suggests that Melitz and Redding (2015) overestimate the gains from a heterogeneous economy. In addition, the calibrated results demonstrate that zero fixed export costs do not maximize aggregate welfare in an economy with FDI activities. Instead, slightly positive fixed export costs will maximize the aggregate welfare by driving 23
some firms to switch from exporting to FDI. This finding has important policy implications: to increase foreign sales by encouraging firm-level FDI activities, policymakers can either decease fixed FDI costs or slightly increase the fixed export costs. This finding implies that that a certain low level of export/import clearance cost is optimal for social welfare. Lastly, aggregate welfare is monotonically decreases with variable trade costs and fixed FDI costs. Therefore, policymakers may want to lower both types of costs jointly to maximize social welfare.
24
Appendix(Figures and Tables) Figure A1: Productivity Cutoffs
In Figure A1, the three upward sloped lines A, B and C, denote the profit from serving the domestic market, serving the foreign market through exports, and serving the foreign market through FDI, respectively. Firms with productivity, ϕ ∈ [0, ϕTd,τ ), exit; firms will only serve the domestic market if their productivity is between [ϕTd,τ , ϕTx,τ ); firms will start to export if their productivity is between [ϕx,τ , ϕI,τ ); and firms whose productivity is above ϕTI,τ engage in FDI. When the variable trade cost, τ , decreases, firm-level profit associated with exporting increases. Therefore, the solid curve B shifts up to the dash curve B 0 . The productivity cutoff for export and FDI changes from ϕTx,τ to ϕTx,τ 0 and ϕTI,τ to ϕTI,τ 0 , respectively. When FDI is prohibited, firms whose productivity, ϕ > ϕTx,τ 0 , will benefit from a reduction in trade costs. In contrast, when FDI is possible, firms
25
Figure A2: Shifting of Productivity Cutoffs
with productivity, ϕ ∈ [ϕTx,τ 0 , ϕTI,τ 0 ] will benefit from the trade cost reduction, while firms with productivity ϕ > ϕI,τ 0 are not affected. Therefore, the welfare gains from trade liberalization will be smaller in the case with FDI. Similarly, when an economy moves from autarky to an open economy, firms with productivity, ϕ > ϕTI,τ , will chose to conduct FDI instead of exporting because profits from FDI are greater than those from exporting. As such, when FDI is allowed, moving from autarky to an open economy brings larger welfare gains.
26
Table A3: The Influence of Export Fixed Cost Reductions (Without OFDI) Panel A
Panel B
1 Probability of exporting
Welfare gains from trade
1.05 1.04 1.03 1.02 1.01 1
0
0.25
0.5
0.75
0.8 0.6 0.4 0.2 0
1
0
1.04
0.5
0.75
1
1
1.03 1.02 1.01 1
0.25
Fixed exporting cost Panel D
Domestic trade share
Weighted average productivity
Fixed exporting cost Panel C
0
0.25
0.5
0.75
1
0.95
0.9
0.85
0
Fixed exporting cost Note: Variable trade costs=1.83
0.25
0.5
0.75
1
Fixed exporting cost
Table A4: The Influence of Export Variable Cost Reductions (Without OFDI) Panel A
Panel B
1 Probability of exporting
Welfare gains from trade
1.2 1.15 1.1 1.05 1
1
1.5
2
2.5
0.8 0.6 0.4 0.2 0
3
1
2
2.5
3
1
1.125 1.1 1.075 1.05 1.025 1
1.5
Variable trade cost Panel D
Domestic trade share
Weighted average productivity
Variable trade cost Panel C
1
1.5
2
2.5
0.8
0.6
0.4
3
Variable trade cost Note: Fixed exporting cost=0.545
1
1.5
2
2.5
Variable trade cost
27
3
Table 1: Welfare Gains from Trade Liberalization
Trade Cost
W elf areEXP /W elf areA (without OFDI) τ → inf 1 τ =3 1 τ = 1.25 1.10 Welfare Change (10%) 10%
W elf areOF DI /W elf areA (with OFDI) 1.06 1.06 1.14 8%
Table 2: Welfare Decomposition
Panel A: With FDI Welfare Gains
Continuing Exporters
16%
57%
Switchers Exit
43% Nonexport to Export
FDI to Export
1%
78%
21%
Panel B: Without FDI Welfare Gains
Continuing Exporters
19%
74%
Switchers Exit
26% Nonexport to Export
FDI to Export
3%
97%
0%
Proofs The Decomposition With FDI option, the aggregate welfare can be written as:
T WHet,OF DI (τ )
1 σ − 1 L(1 + χx,τ + χI,τ ) T σ−1 σ−1 = ϕ et,τ σ σF T
(A1)
where χx,τ and χI,τ are defined as the proportion of firms engaging in export and FDI under the trade cost level, τ, respectively. 28
The welfare increase caused by variable trade cost, τ, decreases from τ1 to τ2 is T WHet,OF DI (τ2 ) T WHet,OF DI (τ1 )
" =
1 + χx,τ2 + 1 + χx,τ1 +
χI,τ2 FτT1 χI,τ1 FτT2
σ−1 ϕ eTt,τ2 σ−1 ϕ eTt,τ1
1 # σ−1
(A2)
eTx,τ eTd,τ , ϕ where ϕ eTt,τ denotes the weighted average of the three productivity cutoffs, ϕ and ϕ eTI,τ ,(write the expressions of the average.) under trade cost, τ as in equation (2). T T T WHet,OF WHet,OF DI (τ2 ) DI (τ2 ) WHet,OF DI (τ2,keep ) = T T T WHet,OF WHet,OF DI (τ1 ) DI (τ2,keep ) WHet,OF DI (τ1 )
T WHet,OF DI (τ2,keep ) = T WHet,OF DI (τ1 )
"
ϕ eTt,τ1 "
=
ϕ eTt,τ2
1 σ−1 # σ−1
(A3)
σ−1
ϕ eTd,τ1
σ−1
+ χx,τ1 τ2−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
ϕ eTd,τ1
σ−1
+ χx,τ1 τ1−1 ϕ eTx,τ1
σ−1
+ χI,τ1 ϕ eTI,τ1
1 σ−1 # σ−1
σ−1
" σ−1 σ−1 # −1 T T T T T ϕ e + χ τ ϕ e + χ ϕ e (τ ) WHet,OF F 1 + χ + χ x,τ I,τ 2 2 2 2 x,τ2 I,τ2 x,τ2 I,τ2 τ1 DI d,τ2 = σ−1 σ−1 T T −1 T T 1 + χ + χ F WHet,OF (τ ) x,τ1 I,τ1 τ2 ϕ ed,τ1 + χx,τ2 τ2 ϕ ex,τ1 + χI,τ2 ϕ eTI,τ1 DI 2,keep (A4) We can further decompose equation (A4) into two parts: one is welfare gains from nonexport switching firms, the other is welfare gains from FDI swiching firms. In particular:
29
T WHet,OF DI (τ2 ) ln T (A5) WHet,OF DI (τ2,keep ) " σ−1 σ−1 # ϕ eTd,τ2 + χx,τ2 τ2−1 ϕ eTx,τ2 + χI,τ2 ϕ eTI,τ2 FτT1 1 + χx,τ2 + χI,τ2 1 ln + ln T + ln = σ−1 σ−1 σ−1 1 + χx,τ1 + χI,τ1 F τ2 + χx,τ2 τ2−1 ϕ eTx,τ1 + χI,τ2 ϕ eTI,τ1 ϕ eTd,τ1 1 ≈ [∆ϕ eTd,τ2 + χx,τ2 + χI,τ2 − χx,τ1 − χI,τ1 + FτT1 − FτT2 σ−1 σ−1 σ−1 + χx,τ2 τ2−1 ϕ eTx,τ2 + χI,τ2 ϕ eTI,τ2 − χx,τ2 τ2−1 ϕ eTx,τ1 − χI,τ2 ϕ eTI,τ1 ]
Substitute FτT =
fe 1−G(ϕT d,τ )
FτT1 − FτT2 = −
+ fd + χx,τ fx + χx,τ fI into equation (A5) and obtain:
fe + fd + χx,τ1 fx + χx,τ1 fI 1 − G(ϕTd,τ1 ) fe + fd + χx,τ2 fx + χx,τ2 fI 1 − G(ϕTd,τ2 )
!
We can rewrite equation (A5) as
ln
T WHet,OF 1 DI (τ2 ) ≈ [∆ϕ eTd,τ2 + χx,τ2 + χI,τ2 − χx,τ1 − χI,τ1 T σ−1 WHet,OF DI (τ2,keep )
(A6)
+ χx,τ1 fx + χI,τ1 fI − χx,τ2 fx − χI,τ2 fI σ−1 σ−1 + χx,τ2 τ2−1 ϕ eTx,τ2 + χI,τ2 ϕ eTI,τ2 − χx,τ2 τ2−1 ϕ eTx,τ1 − χI,τ2 ϕ eTI,τ1 ] 1 [∆ϕ eTd,τ2 + χx,τ2 − χx,τ1 + χx,τ1 fx − Within equation (A6), the component σ−1 σ−1 σ−1 eTx,τ1 ] is the welfare increase caused by χx,τ2 fx + χx,τ2 τ2−1 ϕ eTx,τ2 − χx,τ2 τ2−1 ϕ
the switching of nonexport firms: a portion of nonexport firms exit, and another 1 [χI,τ2 − χI,τ1 + portion of nonexport firms switch to export. The component: σ−1 χI,τ1 fI − χI,τ2 fI + χI,τ2 ϕ eTI,τ2 − χI,τ2 ϕ eTI,τ1 ], is the welfare increase caused by the
30
switching of FDI firms: a portion of FDI firms switch to export in response to a variable trade cost decrease.
31
Reference Arkolakis, C., A. Costinot and A. Rodrigues-Clare, 2012. New Trade Model, Same Old Gains? American Economic Review, 99, 94–130. Broda, C., J. Greenfield, and D. Weinstein, 2006. From Groundnuts to Globalization: A Structural Estimantion of Trade and Growth, NBER Working paper 12512, Broda, C. and D. Weinstein, 2006. Globalization and the Gains from Variety, Quarterly Journal of Economics, 121, 541–585. Eaton, Jonathan and Kortum, Samuel 2002. Technology, Geography, and Trade. Econometrica, 70, 1741-1779. Edmond, C., V. Midrigan, and Y. Xu, 2015. Competition, Markups, and the Gains from International Trade, American Economic Review, 105, 3183-3221. Ethier, W.J., 1986. The Multinational Firm The Quarterly Journal of Economics, 101(4), 805–834. Fajgelbaum, P. and A. Khandelwal, 2014. Measuring the Unequal Gains from Trade, Working paper. Feenstra, R. and D. Weinstein, 2009. Globalization, Competition, and the US Price Level, Unpublished. Feenstra, R. and H. Kee, 2008. Export Variety and Country Productivity: Estimating the Monopolistic Competition Model with Endogenous Productivity, Journal of International Economics, 74, 500–518. 32
Goldberg, P., A. Khandelwal, N. Pavcnik and P. Topalova, 2009. Trade Liberalization and New Imported Inputs, American Economic Review, 99, 494–500. Helpman, E., M. Melitz, and S. Yeaple, 2004. Export Versus FDI with Hetergeneous Firms, American Economic Review, 94, 300–316. Irarrazabal, A., A. Moxnes, and L.D. Opromolla 2013. The Margins of Multinational Production and the Role of Intra-Firm Trade Journal of Political Economy, 121, 74–126. Suzumura, K., K. Kiyono 1987. Entry Barriers and Economic Welfare The Review of Economic Studies, 54(1), 157–167. Melitz, M. and S. Redding, 2015. New Trade Models, New Welfare Implications, American Economic Review, 105, 1105–1146. Ramondo, N. and A. Rodriguez-Clare, 2013. Trade, Multinational Production, and the Gains from Oppeness, Journal of Political Economy, 121, 273–322. World Investment Report 2012. Transitional Corporations, Agricultural Production and Development. Geneva: United Nations
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Highlights:
1. Gains from trade liberalization will be larger when foreign direct invest (FDI) is an available choice for firms; 2. However, gains from tariff reduction (export liberalization) are smaller when a fraction of firms are engaged in FDI; 3. The decomposition of the gains from trade liberalization shows that most gains are from firms which switch their exporting mode; 4. Resource reallocation is the key determinant of the gains from trade liberalization;