Welfare gains from openness to FDI flows

Beyond risk sharing: FDI and tangible gains from
financial integration
Alexander McQuoid Jacek Rothert Katherine A. Smith
USNA, Economics USNA, Economics USNA, Economics
FAME | GRAPE
June 2022
Econometric Society — 2022 North American Summer Meeting
The views expressed are those of the authors and do not necessarily reflect
the views of the U.S. Department of Defense.
McQuoid-Rothert-Smith (MRS) Beyond Risk Sharing: FDI welfare gains June 2022 1 / 38

Welfare gains from financial integration
Previous estimates in macro models:
1 risk sharing — u0(c) = u0(c∗) — ≈ 1% of C
Backus-Kehoe-Kydland (1992); akin to Lucas (1985)
2 cons. smoothing — u0(ct) = u0(ct+1)βR∗ — ≈ 1% of C
Gourinchas and Jeanne (2006)
3 capital scarcity (K jumps to steady-state): ≤ 5% of C
Gourinchas and Jeanne (2006)
4 FDI - potentially very large
McGrattan and Prescott (2010)

FDI flows over the international business cycle
Implicit assumption in (almost) entire int’l business cycle lit:
elasticity of substitution btw. k and k∗ = ∞
⇒ gross FDI flows indeterminate; only net flows matter
Important limitation, because:
gross flows as a % of investment almost tripled over the last 30 years
inflows and outflows positively correlated over the business cycle
inflows and outflows at a country-level: Broner et al. (2013);
bilateral flows between country-pairs: new evidence from the EU
Net FDI inflow of 10 mln into FRA can mean:
DEU buys 10 mln K in FRA
DEU buys 20 mln K in FRA, while FRA buys 10 mln K in DEU
DEU sells 10 mln K owned in FRA; FRA sells 20 mln K owned in DEU

Gross FDI flows / GDP - EU+UK vs. ROW
0
10
20
30
40
50
1970 1980 1990 2000 2010 2020
Year
World (minus EU28) EU 28
5 Yr MA - Gross FDI Flows as % of Fixed Capital Formation

Gross FDI flows / GDP - only current Eurozone members
0
10
20
30
40
5
Yr
MA
-
Gross
FDI
Flows
as
%
of
Fixed
Capital
1970 1980 1990 2000 2010 2020
Year

Contributions of our paper
Framework — gross FDI flows in the int’l business cycle framework
extension of BKK ’92
elast. of subst. btw. k and k∗ < ∞ — K-ownership matters!
Evidence — positive co-movement of gross FDI flows in the EU
identifies elast. of subst. btw. k and k∗,
which needs to be much lower than ∞ (around 1.2).
Welfare gains from openness to FDI can be very large - up to 30% of C
far beyond the 1% from risk-sharing.
Fresh look at the BKK puzzle — ρ(c, c∗) < ρ(y, y∗)

Domestic vs. foreign ownership - (im)perfect substitutes?
Implicit assumption in (almost) entire int’l business cycle lit:
elasticity of substitution btw. k and k∗ = ∞
⇒ gross FDI flows indeterminate; only net flows matter
Micro evidence to the contrary
Goolsbee and Gross (2000); Goolsbee (2004); Chun and Mun (2006)
imperfect substitution between capital varieties
Related macro literature
Hoxa et al. (2013): consider diff. values for e.o.s. btw. K-goods;
McGrattan and Prescott (2010): technology capital
Our approach
allow for the possibility that elast. of subst. < ∞
estimate it to match gross FDI co-movement (let the data decide)

D A T A

FDI in the European Union
Why European Union?
empirically, closest to free int’l capital mobility
records of bilateral FDI flows
Data
27 current EU members plus Iceland, Norway, Switzerland, UK
by country: total inflows and outflows, quarterly
by country pair: bilateral flows, OECD, annual, 1986-2016
only years when both countries were in the EU

Country-level statistics
ρ(FDIi/FDIo) ρ(FDIi, I) ρ(FDIo, I) ρ( I
GDP , S
GDP )
Bulgaria 0.587 0.511 0.134 0.158
Denmark 0.696 0.338 0.020 0.675
Finland 0.602 0.090 0.097 0.109
Germany 0.943 0.094 0.119 -0.267
Greece 0.300 0.462 -0.068 0.880
Luxembourg 0.981 0.157 0.235 0.200
United Kingdom 0.720 0.211 0.141 0.289
Sample Average 0.782 0.102 0.039 0.260
Sample Median 0.851 0.090 0.020 0.389
Residuals from HP-filter; average and median across all countries

Country-pair correlations
GDP, Consumption, Investment and Gross FDI Correlations
Correlation of Interest Mean Median
corr(y, y∗) 0.62 0.65
corr(c, c∗) 0.45 0.47
corr(i, i∗) 0.43 0.45
corr(FDI, FDI∗) 0.53 0.60
Residuals from HP-filter; all country-pairs

EMU vs. non-EMU members
Total Bilateral
flows flows
(by country) (country pairs)
EMU
Average 0.86 0.47
Median 0.90 0.55
non-EMU
Average 0.71 0.56
Median 0.73 0.64
Bilateral flows: EMU means that both countries are in the Eurozone

Prior to 2008 vs. post-2008
Total Bilateral
flows flows
(by country) (country pairs)
pre-2008
Average 0.82 0.36
Median 0.88 0.40
post-2008
Average 0.79 0.44
Median 0.87 0.56

Main takeaway
Correlation of gross FDI flows positive
inflows and outflows at a country level
bilateral flows at a country-pair level
robust pattern, consistent with prior evidence
A model where residents / companies from one country can own
capital located in another country, should generate a positive
co-movement of gross FDI flows

M O D E L

Extension of BKK (1992)
Two countries: i = A, B
GDPi = ezi · F

K̃i, Li

= Ci + Ii + NXi
Part of K located in i owned by residents of −i (foreigners):
Ki = ki + k∗
i (foreign-owned)

Extension of BKK (1992)
Two countries: i = A, B
GDPi = ezi · F

K̃i, Li

= Ci + Ii + NXi
Part of K located in i owned by residents of −i (foreigners):
Ki = ki + k∗
i (foreign-owned)
New – ownership matters — effective capital stock:
K̃i =
h
ω
1
θ ki
θ−1
θ + (1 − ω)
1
θ k∗
i
θ−1
θ
i θ
θ−1
Ki if θ ∞,
lim
θ→∞
MRS(θ) = BKK

Resource constraints
Laws of motion for capital stocks
ki

st

= (1 − δ)ki

st−1

+ xi

st

k∗
i

st

= (1 − δ)k∗
i

st−1

+ x∗
i

st

xi purchases of i-located capital goods by i residents
x∗
i purchases of i-located capital goods by −i residents
Global resource constraint
CA + CB + xA + x∗
A
| {z }
IA
+ xB + x∗
B
| {z }
IB
= YA + YB (1)

FDI - gross vs. net
ki

st

= (1 − δ)ki

st−1

+ xi

st

k∗
i

st

= (1 − δ)k∗
i

st−1

+ x∗
i

st

YA + YB = CA + CB + xA + x∗
A
| {z }
IA
+ xB + x∗
B
| {z }
IB
Gross FDI inflows to country A = x∗
A
Gross FDI outflows from country A = x∗
B
NET FDI flows to country A = x∗
A − x∗
B (common focus in the lit.)

Firms
In country i = A, B, a representative firm maximizes profits by solving:
max
K̃i,Li,ki,k∗
i
ezi
· F

K̃i, Li

− wiLi − riki − r∗
i k∗
i
subject to K̃i =
h
ω
1
θ ki
θ−1
θ + (1 − ω)
1
θ k∗
i
θ−1
θ
i θ
θ−1
.
Yields:
ri = MPKi ·
∂K̃i
∂ki
and r∗
i = MPKi ·
∂K̃i
∂k∗
i

Households
Household A, endowed with a unit of labor, solves:
max
∞
X
t=1
βt

X
st
π

st

ψ

st

U

c(st
)

#
subject to:
c(st
) + xA

st

+ x∗
B

st

+ d

st−1

≤ w(st
) + rA

st

kA

st−1

+

1 − κF

r∗
B

st

k∗
B

st−1

+ q

st

d

st

+ T

st

−
κD
2 · (1 − κD)
d

st
2
kA

st

≤ (1 − δ)kA

st−1

+ xA

st

k∗
B

st

≤ (1 − δ)k∗
B

st−1

+ x∗
B

st


Model: Government
T are lump-sum transfers, taken as given by the household, and given by:
T

st

= κF
· r∗
A

st

k∗
A

st−1

+
κD
2 · (1 − κD)
d

st
2
Capital controls and financial integration
0 ≤ κF , κD ≤ 1 — international financial frictions
κD = cost of ending a period with a non-zero net foreign debt
κF tax imposed on return to capital earned by foreign owners
κF = κD = 0 markets are complete and CE=SP
κF = 0 but κD = 1 FDI but no debt (incomplete risk sharing)
κF = 1 but κD = 0 no FDI but debt
κF = κD = 1 financial autarky.

Competitive Equilibrium
A competitive equilibrium consists of price and allocation functions:
h
Ci(st
), K̃i(st
), ki(st
), k∗
i (st
), Yi(st
), xi(st
), x∗
i (st
)
i
i,j=A,B
and h
ri(st
), r∗
i (st
), wi(st
), q(st
), Ti(st
)
i
i,j=A,B
such that, given prices, allocations solve the utility and profit maximization
problems, and all markets clear.

FOCs
Inter-temporal Euler equations for the household in country A:
U0
(Ct) = βEt
ψt+1
ψt
U0
(Ct+1) [1 − δ + rA,t+1]
U0
(Ct) = βEt
ψt+1
ψt
U0
(Ct+1)
h
1 − δ + r∗
B,t+1(1 − κF
)
i

Functional forms
Utility
U(C) =
C1−σ
1 − σ
Production
F

K̃, L

= K̃α
L1−α

Parameters
1 β = 0.96, σ = 2, δ = 0.06, α = 0.3, κF = 0
2 TFP (z) and demand (ψ) shocks:
zt = ρzzt−1 + z
t ,
z
t
z∗
t
!
∼ N (0, Σz) , Σz =

σz σz,z∗
σz,z∗ σz∗
#
Symmetry: σz = σz∗ ; yields 3 parameters: σz, ρz, σz,z∗
Similar for demand shocks: σψ, ρψ, σψ,ψ∗
Moments:
σ(GDP), ρ(GDPt, GDPt−1), ρ(GDP, GDP∗
)
σ(C), ρ(Ct, Ct−1), ρ(C, C∗
)
3 Effective capital stock: θ and ω (jointly)
correlation of bilateral FDI flows
average
F DIi→j +F DIj→i
GDPi+GDPj

Int’l financial integration and welfare
Move towards int’l financial integration = reduction in κF and/or κD.
Current version
End point — κF = 0 and κD = 0
Start point — κF = 0.9 and κD = 0.999
Welfare — % increase in steady-state C
Future
Start point
κF
calibrated to match average ratio of FDI/GDP in the 1970’s
κD
calibrated to match sdev(NX/GDP) in the 1970’s
Welfare
global methods to compute welfare gains along the transition and
separate into non-stochastic (steady-state) and stochastic (risk-sharing)

Results - identification of θ
2 4 6 8 10
- elast. of subst. between K-ownership
-1
-0.5
0
0.5
1
corr
(FDI
in,FDI
out)
0
10
20
30
40
50
60
%
C
change
due
to
integration
corr(FDI in,FDI out) - data
corr(FDI in,FDI out) - model
welfare gain (right axis)

FDI co-movement in the model — demand shock
HH A more patient — saves more
kA ↑ ⇒ K̃A ↑ ⇒ MPKA(t + 1) ↓
k∗
B ↑ ⇒ FDIA→B ↑
Case 1 - θ high
increase in ∂K̃A
∂k∗
A
small
r∗
A ≡ MPKA · ∂K̃A
∂k∗
A
↓ ⇒ FDIB→A ↓
Case 2 - θ low
increase in ∂K̃A
∂k∗
A
large
r∗
A ≡ MPKA · ∂K̃A
∂k∗
A
↑ ⇒ FDIB→A ↑

Impulse responses - demand shock - high θ
-shock; = 15
0 10 20 30 40
0
0.05
0.1
kA
0 10 20 30 40
-0.06
-0.04
-0.02
0
kAstar
0 10 20 30 40
0
0.05
0.1
kBstar
0 10 20 30 40
-0.02
-0.01
0
0.01
kB
0 10 20 30 40
0
0.2
0.4
FDI out
0 10 20 30 40
-0.15
-0.1
-0.05
0
FDI in

Impulse responses - demand shock - low θ
-shock; = 0.5
0 10 20 30 40
0
0.02
0.04
0.06
kA
0 10 20 30 40
-0.01
0
0.01
0.02
0.03
kAstar
0 10 20 30 40
0
0.02
0.04
0.06
0.08
kBstar
0 10 20 30 40
-0.01
0
0.01
0.02
0.03
kB
0 10 20 30 40
0
0.2
0.4
FDI out
0 10 20 30 40
-0.05
0
0.05
FDI in

FDI co-movement in the model — supply shock
1 Temporary — ρz = 0
similar intuition to demand shock
zA ↑ ⇒ MPKA(t) ↑ ⇒ ∆IncomeA ∆IncomeB 0
A increases savings more than B
no direct impact on MPKt+1 other than via increase in K̃t+1
2 Persistent — ρz 0
additional effect — impact on MPKt+1

Impulse responses - persistent supply shock - high θ
z-shock; = 15
0 10 20 30 40
0
0.02
0.04
0.06
kA
0 10 20 30 40
-0.02
0
0.02
0.04
0.06
kAstar
0 10 20 30 40
-0.05
0
0.05
kBstar
0 10 20 30 40
-0.03
-0.02
-0.01
0
0.01
kB
0 10 20 30 40
-0.4
-0.2
0
0.2
0.4
FDI out
0 10 20 30 40
-0.2
0
0.2
0.4
0.6
0.8
FDI in

Impulse responses - persistent supply shock - low θ
z-shock; = 0.5
0 10 20 30 40
0
0.02
0.04
0.06
kA
0 10 20 30 40
0
0.02
0.04
kAstar
0 10 20 30 40
-0.02
0
0.02
0.04
kBstar
0 10 20 30 40
-0.04
-0.02
0
0.02
kB
0 10 20 30 40
-0.2
0
0.2
FDI out
0 10 20 30 40
0
0.2
0.4
FDI in

Results
θ σ(y) ρ(y, y∗
) σ(c) ρ(c, c∗
) ρ(fdi, fdi∗
) ρ(S, I) ∆C
0.90 2.37 0.62 0.84 0.46 0.51 0.88 0.34
1.25 2.41 0.62 0.88 0.45 0.45 0.88 0.26
2.50 2.41 0.62 0.88 0.45 0.21 0.89 0.08
5.00 2.41 0.62 0.88 0.45 -0.41 0.91 0.01
Full Estimation (θ estimated)
1.20 2.42 0.62 0.96 0.48 0.45 0.88 0.27

BKK puzzle and FDI co-movement (only TFP shocks!)
5 10 15 20
0.75
0.8
0.85
0.9
0.95
corr(c,c*)
corr(y,y*)
5 10 15 20
0.9
0.92
0.94
0.96
0.98
1
corr(c,c*)
corr(y,y*)
//
5 10 15 20
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
corr(fdi,fdi*)
5 10 15 20
-0.6
-0.4
-0.2
0
0.2
corr(fdi,fdi*)
Left column: κD = 1 (no debt, only FDI)
Right column: κD = 0 (complete markets)

Implications of our mechanism
Consider the model without debt – κD = 1.0
5 10 15 20
0.75
0.8
0.85
0.9
0.95
corr(c,c*)
corr(y,y*)
5 10 15 20
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
corr(fdi,fdi*)
If θ varies across country-pairs ⇒ ρ(fdi, fdi∗) varies across country-pairs
Country pairs with lower θ will have
higher ρ(fdi, fdi∗)
higher ρ(y, y∗) − ρ(c, c∗) — (less risk-sharing)

FDI co-movements vs. lack of risk-sharing
-1
-.5
0
.5
1
-.5 0 .5 1
y_minus_c
corr_fdi_fdistar_cycln Fitted values
Vertical axis: ρ(fdi, fdi∗)
Horizontal axis: ρ(y, y∗) minus ρ(c, c∗)

Final Remarks
Gross FDI flows missing in the international business cycles literature
⇒ net inflows to A imply net outflows from B
Robust empirical evidence of positive co-movement of FDI flows
We offer:
flexible framework to study gross FDI flows in the IBC model
one extra parameter that we can identify using FDI co-movement
capital diversity channel
Calibrated elast. of subst. btw. k and k∗ low
⇒ welfare gains from openness to FDI can be very large

Welfare gains from openness to FDI flows

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