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Foreign Direct Investment over the International
Business Cycle
Alexander McQuoid Jacek Rothert Katherine A. Smith
USNA, Economics USNA, Economics USNA, Economics
FAME | GRAPE
Nov 2022
SEA 92nd Annual 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) FDI over IBC Nov 2022 1 / 47
FDI flows and stocks: data vs. macro models
Data
gross FDI positions as a % of GDP almost quadrupled since 1990
almost ten times greater than net positions
inflows and outflows positively correlated over the business cycle
Broner et al. (2013): positive corr. of total capital inflows and outflows
This paper: similar pattern for FDI
Implicit assumption in (almost all) macro models
elasticity of substitution btw. k and k∗ = ∞
⇒ gross FDI flows indeterminate; only net flows matter
Important limitation — 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
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 2 / 47
Gross vs. Net Capital Positions - Total
−2
0
2
4
6
Relative
to
GDP
1970 1980 1990 2000 2010 2020
Year
Gross Position Total Assets
Total Liabilities Net IIP − US
Net IIP − Japan
G7 Investment Positions
Source: IMF
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 3 / 47
Contributions of our paper
Framework — gross FDI flows in the int’l business cycle framework
extension of Backus-Kehoe-Kydland (JPE, 1992)
foundation for 100+ papers in the last 30 years
elast. of subst. btw. k and k∗ ≤ ∞ — K-ownership matters!
Evidence — positive co-movement of gross FDI flows in the data
identifies elast. of subst. btw. k and k∗,
which needs to be much lower than ∞.
Welfare gains from openness to FDI can be large
if elast. of subst. btw k and k∗ low
FDI costs ↓ → more efficient alloc. of K → Solow residual ↑
new channel - capital diversity
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 4 / 47
Balance of Payments (very(!) simplified)
Current account
(+) Exports
(-) Imports
(+) income from abroad (net) and other small items (net)
Capital and financial account
(+) Purchase of domestic assets by foreign residents (capital inflows)
short-term: portfolio investment
long-term: direct investment (FDI)
(-) Purchase of foreign assets by domestic residents (capital outflows)
Current account + Capital and financial account = 0
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 5 / 47
Portfolio vs. Direct Investment Flows
Direct investment
“Financial transactions related to long-term capital investment in a
business (e.g. purchase of machinery, buildings and factories), where the
investor has significant – 10 per cent or more – voting power in the
business (i.e. through ownership of ordinary shares or voting stock)”
Portfolio investment
“The purchase of equity or debt (shares or bonds) in a business. In
contrast to direct investment, portfolio investment occurs when the
investor does not have an influence in the operation of the business.”
Source: Reserve Bank of Australia
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 6 / 47
Gross vs. Net Capital Positions - Equity
0
.5
1
1.5
2
Relative
to
GDP
1970 1980 1990 2000 2010 2020
Year
Gross Equity Position Equity Assets
Equity Liabilities Net Equity
G7 International Equity Positions
Source: IMF
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 7 / 47
Gross Equity Assets - FDI and Portfolio
0
.5
1
Relative
to
GDP
1970 1980 1990 2000 2010 2020
Year
Gross Equity Assets FDI Assets
Portfolio Equity Assets
G7 Equity Assets
Source: IMF
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 8 / 47
Literature
Capital flows in open economy macro (too many papers to list)
Long vs. short NET positions in debt vs. equity
Does FDI crowd out domestic investment?
NET FDI as an explanatory variable
Portfolio diversification
focus on short-term portfolio flows
Scant literature where gross FDI positions are well defined
McGrattan and Prescott (2012): technology/intangible capital
Our paper
flexible business cycle framework with well defined gross capital flows
identification of the key parameter
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 9 / 47
Literature
Welfare effects of financial openness
risk sharing — u0(c) = u0(c∗) — ≈ 1% of C
cons. smoothing — u0(ct) = u0(ct+1)βR∗ — ≈ 1% of C
capital scarcity (K jumps to steady-state): ≤ 5% of C
FDI - potentially very large
McGrattan and Prescott (2010): > 40% of C
Our paper
“New” source of welfare gains from FDI openness - additional
5%-10% on top of the first three
similar to love for variety in trade models
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 10 / 47
D A T A
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 11 / 47
Data sources
IMF, Annual Data, 1970-2020
Gross FDI and Portfolio flows - Balance of Payments
NIPA aggregates (GDP, C, I, EX, IM) - International Financial Statistics
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 12 / 47
FDI flows relative to Domestic Investment
1970s 1980s 1990s 2000s 2010s
Gross FDI Flows Median 0.034 0.047 0.123 0.216 0.192
Std Dev 0.048 0.065 0.202 0.287 0.134
Net FDI Flows Median 0.000 -0.009 -0.023 -0.042 -0.034
Std Dev 0.028 0.026 0.064 0.114 0.107
FDI Inflows Median 0.018 0.022 0.055 0.095 0.078
Std Dev 0.030 0.030 0.079 0.137 0.088
FDI Outflows Median 0.021 0.032 0.065 0.134 0.115
Std Dev 0.025 0.040 0.127 0.170 0.083
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 13 / 47
Correlations between FDI Inflows and FDI Outflows
(1) (2) (3) (4) (5) (6) (7) (8)
FDI In FDI Out FDI In FDI Out FDI In FDI Out FDI In FDI Out
FDI Outflows 0.761**** 0.317*** 0.707**** 0.455****
(0.0724) (0.106) (0.0525) (0.0702)
FDI Inflows 0.733**** 0.288** 0.705**** 0.470****
(0.0835) (0.118) (0.0698) (0.0874)
Standard Errors Robust Robust Robust Robust Robust Robust Robust Robust
Country-Specific Trend Yes Yes Yes Yes Yes Yes Yes Yes
Year Dummies No No Yes Yes No No Yes Yes
Time Period 1970-2010 1970-2010 1970-2010 1970-2010 1970-2020 1970-2020 1970-2020 1970-2020
Observations 248 248 248 248 332 332 332 332
We follow Broner et al. (2013) who look at total capital inflows and
outflows
For both FDI inflows and outflows, we de-mean and standardize each
series.
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 14 / 47
Unconditional correlations - FDI (in and out) and GDP
Corr. with GDP
Gross FDI Inflows Outflows Net ρ(In, Out)
Canada 0.663 0.663 0.437 0.454 0.508
Germany 0.153 0.093 0.209 -0.018 0.439
France 0.538 0.581 0.432 -0.228 0.449
United Kingdom 0.289 0.139 0.350 -0.300 0.599
Italy 0.513 0.440 0.489 -0.093 0.643
Japan 0.320 -0.187 0.458 -0.528 0.165
United States 0.244 0.409 0.041 0.317 0.467
Median 0.320 0.409 0.432 -0.093 0.467
Std Dev 0.184 0.302 0.164 0.345 0.154
Note: HP-filtered series; FDI series as a percent of GDP
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 15 / 47
Main takeaway
Gross FDI flows
positive business cycle co-movement of inflows and outflows
robust pattern, consistent with prior evidence for total capital flows
⇒ 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
Gross FDI positions
orders of magnitude larger than net
⇒ suggests less than perfect substitution between domestic and
foreign ownership (at the aggregate level)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 16 / 47
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): intangible, technology capital
Our approach
allow for the possibility that elast. of subst. < ∞
estimate it to match gross FDI co-movement (let the data decide)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 17 / 47
M O D E L
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 18 / 47
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)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 19 / 47
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
,
lim
θ→∞
MRS(θ) = BKK
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 19 / 47
Foreign-owned capital — an imperfect substitute?
Product variety in non-tradeable goods (e.g., retail services)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 20 / 47
Foreign-owned capital — an imperfect substitute?
Product variety in tradeable goods (FDI inflows replacing imports)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 21 / 47
Foreign-owned capital — an imperfect substitute?
Foreign presence in sectors complementary with others
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 22 / 47
Resource constraints
Laws of motion for capital stocks
ki

st

= (1 − δ)ki

st−1

+ xi

st

− φD

ki(st
), ki(st−1
)

k∗
i

st

= (1 − δ)k∗
i

st−1

+ x∗
i

st

− φF

k∗
i (st
), k∗
i (st−1
)

xi purchases of i-located capital goods by i residents
x∗
i purchases of i-located capital goods by −i residents
φ(·, ·) - investment adjustment costs
Global resource constraint
CA + CB + xA + x∗
A
| {z }
IA
+ xB + x∗
B
| {z }
IB
= YA + YB (1)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 23 / 47
FDI - gross vs. net
ki

st

= (1 − δ)ki

st−1

+ xi

st

− φD

ki(st
), ki(st−1
)

k∗
i

st

= (1 − δ)k∗
i

st−1

+ x∗
i

st

− φF

k∗
i (st
), k∗
i (st−1
)

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.)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 24 / 47
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
where MPKi = ∂GDPi/∂K̃i.
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 25 / 47
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

McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 26 / 47
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.
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 27 / 47
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.
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 28 / 47
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
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 29 / 47
Functional forms
Utility
U(C, L) =
[C1−η(1−L)η
]
1−σ
1−σ — Cobb-Douglas (CD)
U(C, L) = C1−σ
1−σ − ηL1+γ
1+γ — Separable (SEP)
U(C, L) =
[C−η·L1+γ
]
1−σ
1−σ — GHH
Production
F

K̃, L

= K̃α
L1−α
Investment adjustment costs
φD(kt, kt−1) =
φD
2

kt
kt−1
− 1
2
kt−1
φF (k∗
t , k∗
t−1) =
φF
2
k∗
t
k∗
t−1
− 1
!2
k∗
t−1
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 30 / 47
Imposed and calibrated parameters
1 β = 0.96, σ = 2, δ = 0.06, α = 0.33, γ = 2
2 κF = 0
3 η calibrated so that steady-state ` = 0.33
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 31 / 47
Estimated parameters
Stochastic processes in country i = A, B
zi,t = ρzzi,t−1 + z
i,t
z
A,t
z
B,t
!
∼ N (0, Σz) , Σz =

σ2
z σ2
z · ρz,z∗
σ2
z · ρz,z∗ σ2
z
#
Three parameters to be estimated: σz, ρz, ρz,z∗
Similar for demand shocks: σψ, ρψ, ρψ,ψ∗
Domestic and foreign investment adj. costs parameters — φD and φF
Elast. of substitution θ (re-calibrate home bias to match average K∗
GDP )
Cost of non-zero debt — κD
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 32 / 47
Method of moments estimation
Important moments and key parameters:
σ(y), ρ(yt, yt−1), ρ(y, y∗) — z-shocks
σ(c)/σ(y), ρ(ct, ct−1), ρ(c, c∗) — ψ-shocks
σ(inv)/σ(y), ρ(invt, invt−1), ρ(inv, inv∗) — ψ-shocks and φD
σ(fdi)/σ(y), σ(nx)/σ(y), ρ(fdi, fdi∗) — θ, κD, and φF
1 Restricted — only moments listed above
2 Unrestricted — add co-movement of FDI inflows and outflows with
GDP, INV, and C
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 33 / 47
Openness to FDI and welfare
Welfare effects — % ∆C in steady-state
End point — κF = 0
Start point — κF = κ̄ calibrated so that
FDI
GDP (κ̄) = 0.5 · FDI
GDP (0) ⇒ % ∆C - low
FDI
GDP (κ̄) = 0.1 · FDI
GDP (0) ⇒ % ∆C - high
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 34 / 47
Capital diversity estimates
Restricted Set Full Set
Parameter CD SEP GHH CD SEP GHH
θ 1.08 1.64 2.10 2.16 2.46 2.30
% ∆C - low 5.90 4.54 6.07 4.23 3.55 5.69
% ∆C - high 18.87 9.84 10.07 6.86 5.21 8.70
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 35 / 47
θ, FDI co-movement, and welfare gains from openness
2 4 6 8 10 12 14
- elast. of subst. between K-ownership
-1
-0.5
0
0.5
1
corr
(FDI
in,FDI
out)
0
0.05
0.1
0.15
0.2
%
C
change
due
to
integration
corr(FDI in,FDI out) - data
corr(FDI in,FDI out) - model
welfare gain ( C) - right axis
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 36 / 47
FDI co-movement in the model — demand shock
HH A more patient — saves more
kA ↑ ⇒ ∂K̃A
∂k∗
A
↑ but 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 ↑
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 37 / 47
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
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 38 / 47
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
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 39 / 47
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 — direct upward impact on MPKA(t + 1)
k∗
A ↑ while k∗
B ↓ if ρz large enough
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 40 / 47
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
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 41 / 47
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
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 42 / 47
BKK puzzle and FDI co-movement (only TFP shocks!)
5 10 15 20
- elast. of subst. between K-ownership
0.75
0.8
0.85
0.9
0.95
corr(c,c*)
corr(y,y*)
5 10 15 20
- elast. of subst. between K-ownership
0.9
0.92
0.94
0.96
0.98
1
corr(c,c*)
corr(y,y*)
//
5 10 15 20
- elast. of subst. between K-ownership
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
corr(fdi,fdi*)
5 10 15 20
- elast. of subst. between K-ownership
-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)
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 43 / 47
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 estimated using FDI co-movement
k and k∗
far from perfect substitutes
new source of gains from financial openness — capital diversity
additional 5%-10% on top of risk sharing or eliminating capital scarcity
less than perfect risk-sharing in an open economy
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 44 / 47
Parameter estimates
Restricted Set Full Set
Parameter CD SEP GHH CD SEP GHH
κD 0.044 0.017 0.027 0.466 0.358 0.370
φD 0.314 0.316 0.417 5.365 5.124 3.313
φF 19.951 13.759 11.089 21.257 21.469 15.857
ρψ 0.536 0.420 0.444 0.211 0.246 0.189
ρψ,ψ∗ -0.263 -0.021 -0.072 0.269 0.383 0.034
ρz 0.976 0.982 0.919 0.979 0.987 0.937
ρz,z∗ 0.483 0.458 0.493 0.246 0.257 0.214
σψ 2.223 1.567 6.523 4.070 3.698 9.373
σz 0.662 0.925 0.500 0.716 1.002 0.500
θ 1.081 1.644 2.103 2.158 2.460 2.296
% ∆C - low 5.899 4.535 6.066 4.225 3.555 5.694
% ∆C - high 18.869 9.844 10.066 6.861 5.208 8.695
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 45 / 47
Data vs. Model Moments - part 1
Restricted Set (*) Full Set
Moment Data CD SEP GHH CD SEP GHH
(*) ρ(ct, ct−1) 0.87 0.89 0.93 0.82 0.84 0.89 0.69
(*) ρ(c, c∗) 0.34 0.42 0.47 0.32 0.27 0.31 0.17
ρ(fdit, fdit−1) 0.15 0.95 0.95 0.94 0.65 0.66 0.72
(*) ρ(fdi, fdi∗) 0.59 0.52 0.52 0.58 0.45 0.44 0.50
ρ(fdi∗
t , fdi∗
t−1) 0.58 0.96 0.95 0.95 0.65 0.64 0.72
ρ(inv, fdi) 0.13 0.32 0.27 0.32 0.72 0.71 0.67
ρ(invt, fdit−1) 0.30 0.25 0.22 0.27 0.27 0.27 0.28
ρ(inv, fdi∗) 0.61 0.55 0.60 0.64 0.66 0.68 0.70
ρ(invt, fdi∗
t−1) 0.51 0.42 0.45 0.45 0.32 0.33 0.34
(*) ρ(invt, invt−1) 0.70 0.62 0.59 0.65 0.43 0.44 0.46
(*) ρ(inv, inv∗) 0.40 0.38 0.38 0.34 0.57 0.61 0.61
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 46 / 47
Data vs. Model Moments - part 2
Restricted Set (*) Full Set
Moment Data CD SEP GHH CD SEP GHH
ρ(y, fdi) 0.26 0.49 0.49 0.51 0.42 0.44 0.37
ρ(yt, fdit−1) 0.42 0.45 0.42 0.48 0.29 0.26 0.39
ρ(y, fdi∗) 0.69 0.91 0.88 0.87 0.70 0.69 0.68
ρ(yt, fdi∗
t−1) 0.70 0.87 0.84 0.84 0.68 0.66 0.67
ρ(y, fdi + fdi∗) 0.57 0.80 0.78 0.77 0.66 0.66 0.61
(*) ρ(yt, yt−1) 0.79 0.92 0.90 0.95 0.90 0.86 0.95
(*) ρ(y, y∗) 0.46 0.40 0.36 0.43 0.31 0.28 0.30
(*) sd(nx)/sd(y) 1.06 1.08 1.05 1.05 1.01 0.99 0.94
(*) sd(c)/sd(y) 1.13 0.93 0.85 1.05 0.98 0.91 1.13
(*) sd(fdi)/sd(y) 0.85 0.82 0.81 0.82 0.85 0.84 0.88
(*) sd(inv)/sd(y) 2.82 2.81 2.80 2.83 2.75 2.74 2.75
(*) sd(y) 3.12 3.11 3.12 3.13 3.13 3.14 3.18
McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 47 / 47

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Presentation at the 92nd annual meeting of the Southern Economic Association

  • 1. Foreign Direct Investment over the International Business Cycle Alexander McQuoid Jacek Rothert Katherine A. Smith USNA, Economics USNA, Economics USNA, Economics FAME | GRAPE Nov 2022 SEA 92nd Annual 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) FDI over IBC Nov 2022 1 / 47
  • 2. FDI flows and stocks: data vs. macro models Data gross FDI positions as a % of GDP almost quadrupled since 1990 almost ten times greater than net positions inflows and outflows positively correlated over the business cycle Broner et al. (2013): positive corr. of total capital inflows and outflows This paper: similar pattern for FDI Implicit assumption in (almost all) macro models elasticity of substitution btw. k and k∗ = ∞ ⇒ gross FDI flows indeterminate; only net flows matter Important limitation — 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 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 2 / 47
  • 3. Gross vs. Net Capital Positions - Total −2 0 2 4 6 Relative to GDP 1970 1980 1990 2000 2010 2020 Year Gross Position Total Assets Total Liabilities Net IIP − US Net IIP − Japan G7 Investment Positions Source: IMF McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 3 / 47
  • 4. Contributions of our paper Framework — gross FDI flows in the int’l business cycle framework extension of Backus-Kehoe-Kydland (JPE, 1992) foundation for 100+ papers in the last 30 years elast. of subst. btw. k and k∗ ≤ ∞ — K-ownership matters! Evidence — positive co-movement of gross FDI flows in the data identifies elast. of subst. btw. k and k∗, which needs to be much lower than ∞. Welfare gains from openness to FDI can be large if elast. of subst. btw k and k∗ low FDI costs ↓ → more efficient alloc. of K → Solow residual ↑ new channel - capital diversity McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 4 / 47
  • 5. Balance of Payments (very(!) simplified) Current account (+) Exports (-) Imports (+) income from abroad (net) and other small items (net) Capital and financial account (+) Purchase of domestic assets by foreign residents (capital inflows) short-term: portfolio investment long-term: direct investment (FDI) (-) Purchase of foreign assets by domestic residents (capital outflows) Current account + Capital and financial account = 0 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 5 / 47
  • 6. Portfolio vs. Direct Investment Flows Direct investment “Financial transactions related to long-term capital investment in a business (e.g. purchase of machinery, buildings and factories), where the investor has significant – 10 per cent or more – voting power in the business (i.e. through ownership of ordinary shares or voting stock)” Portfolio investment “The purchase of equity or debt (shares or bonds) in a business. In contrast to direct investment, portfolio investment occurs when the investor does not have an influence in the operation of the business.” Source: Reserve Bank of Australia McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 6 / 47
  • 7. Gross vs. Net Capital Positions - Equity 0 .5 1 1.5 2 Relative to GDP 1970 1980 1990 2000 2010 2020 Year Gross Equity Position Equity Assets Equity Liabilities Net Equity G7 International Equity Positions Source: IMF McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 7 / 47
  • 8. Gross Equity Assets - FDI and Portfolio 0 .5 1 Relative to GDP 1970 1980 1990 2000 2010 2020 Year Gross Equity Assets FDI Assets Portfolio Equity Assets G7 Equity Assets Source: IMF McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 8 / 47
  • 9. Literature Capital flows in open economy macro (too many papers to list) Long vs. short NET positions in debt vs. equity Does FDI crowd out domestic investment? NET FDI as an explanatory variable Portfolio diversification focus on short-term portfolio flows Scant literature where gross FDI positions are well defined McGrattan and Prescott (2012): technology/intangible capital Our paper flexible business cycle framework with well defined gross capital flows identification of the key parameter McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 9 / 47
  • 10. Literature Welfare effects of financial openness risk sharing — u0(c) = u0(c∗) — ≈ 1% of C cons. smoothing — u0(ct) = u0(ct+1)βR∗ — ≈ 1% of C capital scarcity (K jumps to steady-state): ≤ 5% of C FDI - potentially very large McGrattan and Prescott (2010): > 40% of C Our paper “New” source of welfare gains from FDI openness - additional 5%-10% on top of the first three similar to love for variety in trade models McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 10 / 47
  • 11. D A T A McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 11 / 47
  • 12. Data sources IMF, Annual Data, 1970-2020 Gross FDI and Portfolio flows - Balance of Payments NIPA aggregates (GDP, C, I, EX, IM) - International Financial Statistics McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 12 / 47
  • 13. FDI flows relative to Domestic Investment 1970s 1980s 1990s 2000s 2010s Gross FDI Flows Median 0.034 0.047 0.123 0.216 0.192 Std Dev 0.048 0.065 0.202 0.287 0.134 Net FDI Flows Median 0.000 -0.009 -0.023 -0.042 -0.034 Std Dev 0.028 0.026 0.064 0.114 0.107 FDI Inflows Median 0.018 0.022 0.055 0.095 0.078 Std Dev 0.030 0.030 0.079 0.137 0.088 FDI Outflows Median 0.021 0.032 0.065 0.134 0.115 Std Dev 0.025 0.040 0.127 0.170 0.083 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 13 / 47
  • 14. Correlations between FDI Inflows and FDI Outflows (1) (2) (3) (4) (5) (6) (7) (8) FDI In FDI Out FDI In FDI Out FDI In FDI Out FDI In FDI Out FDI Outflows 0.761**** 0.317*** 0.707**** 0.455**** (0.0724) (0.106) (0.0525) (0.0702) FDI Inflows 0.733**** 0.288** 0.705**** 0.470**** (0.0835) (0.118) (0.0698) (0.0874) Standard Errors Robust Robust Robust Robust Robust Robust Robust Robust Country-Specific Trend Yes Yes Yes Yes Yes Yes Yes Yes Year Dummies No No Yes Yes No No Yes Yes Time Period 1970-2010 1970-2010 1970-2010 1970-2010 1970-2020 1970-2020 1970-2020 1970-2020 Observations 248 248 248 248 332 332 332 332 We follow Broner et al. (2013) who look at total capital inflows and outflows For both FDI inflows and outflows, we de-mean and standardize each series. McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 14 / 47
  • 15. Unconditional correlations - FDI (in and out) and GDP Corr. with GDP Gross FDI Inflows Outflows Net ρ(In, Out) Canada 0.663 0.663 0.437 0.454 0.508 Germany 0.153 0.093 0.209 -0.018 0.439 France 0.538 0.581 0.432 -0.228 0.449 United Kingdom 0.289 0.139 0.350 -0.300 0.599 Italy 0.513 0.440 0.489 -0.093 0.643 Japan 0.320 -0.187 0.458 -0.528 0.165 United States 0.244 0.409 0.041 0.317 0.467 Median 0.320 0.409 0.432 -0.093 0.467 Std Dev 0.184 0.302 0.164 0.345 0.154 Note: HP-filtered series; FDI series as a percent of GDP McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 15 / 47
  • 16. Main takeaway Gross FDI flows positive business cycle co-movement of inflows and outflows robust pattern, consistent with prior evidence for total capital flows ⇒ 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 Gross FDI positions orders of magnitude larger than net ⇒ suggests less than perfect substitution between domestic and foreign ownership (at the aggregate level) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 16 / 47
  • 17. 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): intangible, technology capital Our approach allow for the possibility that elast. of subst. < ∞ estimate it to match gross FDI co-movement (let the data decide) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 17 / 47
  • 18. M O D E L McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 18 / 47
  • 19. 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) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 19 / 47
  • 20. 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 , lim θ→∞ MRS(θ) = BKK McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 19 / 47
  • 21. Foreign-owned capital — an imperfect substitute? Product variety in non-tradeable goods (e.g., retail services) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 20 / 47
  • 22. Foreign-owned capital — an imperfect substitute? Product variety in tradeable goods (FDI inflows replacing imports) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 21 / 47
  • 23. Foreign-owned capital — an imperfect substitute? Foreign presence in sectors complementary with others McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 22 / 47
  • 24. Resource constraints Laws of motion for capital stocks ki st = (1 − δ)ki st−1 + xi st − φD ki(st ), ki(st−1 ) k∗ i st = (1 − δ)k∗ i st−1 + x∗ i st − φF k∗ i (st ), k∗ i (st−1 ) xi purchases of i-located capital goods by i residents x∗ i purchases of i-located capital goods by −i residents φ(·, ·) - investment adjustment costs Global resource constraint CA + CB + xA + x∗ A | {z } IA + xB + x∗ B | {z } IB = YA + YB (1) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 23 / 47
  • 25. FDI - gross vs. net ki st = (1 − δ)ki st−1 + xi st − φD ki(st ), ki(st−1 ) k∗ i st = (1 − δ)k∗ i st−1 + x∗ i st − φF k∗ i (st ), k∗ i (st−1 ) 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.) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 24 / 47
  • 26. 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 where MPKi = ∂GDPi/∂K̃i. McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 25 / 47
  • 27. 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 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 26 / 47
  • 28. 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. McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 27 / 47
  • 29. 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. McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 28 / 47
  • 30. 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 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 29 / 47
  • 31. Functional forms Utility U(C, L) = [C1−η(1−L)η ] 1−σ 1−σ — Cobb-Douglas (CD) U(C, L) = C1−σ 1−σ − ηL1+γ 1+γ — Separable (SEP) U(C, L) = [C−η·L1+γ ] 1−σ 1−σ — GHH Production F K̃, L = K̃α L1−α Investment adjustment costs φD(kt, kt−1) = φD 2 kt kt−1 − 1 2 kt−1 φF (k∗ t , k∗ t−1) = φF 2 k∗ t k∗ t−1 − 1 !2 k∗ t−1 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 30 / 47
  • 32. Imposed and calibrated parameters 1 β = 0.96, σ = 2, δ = 0.06, α = 0.33, γ = 2 2 κF = 0 3 η calibrated so that steady-state ` = 0.33 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 31 / 47
  • 33. Estimated parameters Stochastic processes in country i = A, B zi,t = ρzzi,t−1 + z i,t z A,t z B,t ! ∼ N (0, Σz) , Σz = σ2 z σ2 z · ρz,z∗ σ2 z · ρz,z∗ σ2 z # Three parameters to be estimated: σz, ρz, ρz,z∗ Similar for demand shocks: σψ, ρψ, ρψ,ψ∗ Domestic and foreign investment adj. costs parameters — φD and φF Elast. of substitution θ (re-calibrate home bias to match average K∗ GDP ) Cost of non-zero debt — κD McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 32 / 47
  • 34. Method of moments estimation Important moments and key parameters: σ(y), ρ(yt, yt−1), ρ(y, y∗) — z-shocks σ(c)/σ(y), ρ(ct, ct−1), ρ(c, c∗) — ψ-shocks σ(inv)/σ(y), ρ(invt, invt−1), ρ(inv, inv∗) — ψ-shocks and φD σ(fdi)/σ(y), σ(nx)/σ(y), ρ(fdi, fdi∗) — θ, κD, and φF 1 Restricted — only moments listed above 2 Unrestricted — add co-movement of FDI inflows and outflows with GDP, INV, and C McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 33 / 47
  • 35. Openness to FDI and welfare Welfare effects — % ∆C in steady-state End point — κF = 0 Start point — κF = κ̄ calibrated so that FDI GDP (κ̄) = 0.5 · FDI GDP (0) ⇒ % ∆C - low FDI GDP (κ̄) = 0.1 · FDI GDP (0) ⇒ % ∆C - high McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 34 / 47
  • 36. Capital diversity estimates Restricted Set Full Set Parameter CD SEP GHH CD SEP GHH θ 1.08 1.64 2.10 2.16 2.46 2.30 % ∆C - low 5.90 4.54 6.07 4.23 3.55 5.69 % ∆C - high 18.87 9.84 10.07 6.86 5.21 8.70 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 35 / 47
  • 37. θ, FDI co-movement, and welfare gains from openness 2 4 6 8 10 12 14 - elast. of subst. between K-ownership -1 -0.5 0 0.5 1 corr (FDI in,FDI out) 0 0.05 0.1 0.15 0.2 % C change due to integration corr(FDI in,FDI out) - data corr(FDI in,FDI out) - model welfare gain ( C) - right axis McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 36 / 47
  • 38. FDI co-movement in the model — demand shock HH A more patient — saves more kA ↑ ⇒ ∂K̃A ∂k∗ A ↑ but 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 ↑ McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 37 / 47
  • 39. 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 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 38 / 47
  • 40. 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 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 39 / 47
  • 41. 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 — direct upward impact on MPKA(t + 1) k∗ A ↑ while k∗ B ↓ if ρz large enough McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 40 / 47
  • 42. 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 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 41 / 47
  • 43. 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 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 42 / 47
  • 44. BKK puzzle and FDI co-movement (only TFP shocks!) 5 10 15 20 - elast. of subst. between K-ownership 0.75 0.8 0.85 0.9 0.95 corr(c,c*) corr(y,y*) 5 10 15 20 - elast. of subst. between K-ownership 0.9 0.92 0.94 0.96 0.98 1 corr(c,c*) corr(y,y*) // 5 10 15 20 - elast. of subst. between K-ownership -1 -0.8 -0.6 -0.4 -0.2 0 0.2 corr(fdi,fdi*) 5 10 15 20 - elast. of subst. between K-ownership -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) McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 43 / 47
  • 45. 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 estimated using FDI co-movement k and k∗ far from perfect substitutes new source of gains from financial openness — capital diversity additional 5%-10% on top of risk sharing or eliminating capital scarcity less than perfect risk-sharing in an open economy McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 44 / 47
  • 46. Parameter estimates Restricted Set Full Set Parameter CD SEP GHH CD SEP GHH κD 0.044 0.017 0.027 0.466 0.358 0.370 φD 0.314 0.316 0.417 5.365 5.124 3.313 φF 19.951 13.759 11.089 21.257 21.469 15.857 ρψ 0.536 0.420 0.444 0.211 0.246 0.189 ρψ,ψ∗ -0.263 -0.021 -0.072 0.269 0.383 0.034 ρz 0.976 0.982 0.919 0.979 0.987 0.937 ρz,z∗ 0.483 0.458 0.493 0.246 0.257 0.214 σψ 2.223 1.567 6.523 4.070 3.698 9.373 σz 0.662 0.925 0.500 0.716 1.002 0.500 θ 1.081 1.644 2.103 2.158 2.460 2.296 % ∆C - low 5.899 4.535 6.066 4.225 3.555 5.694 % ∆C - high 18.869 9.844 10.066 6.861 5.208 8.695 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 45 / 47
  • 47. Data vs. Model Moments - part 1 Restricted Set (*) Full Set Moment Data CD SEP GHH CD SEP GHH (*) ρ(ct, ct−1) 0.87 0.89 0.93 0.82 0.84 0.89 0.69 (*) ρ(c, c∗) 0.34 0.42 0.47 0.32 0.27 0.31 0.17 ρ(fdit, fdit−1) 0.15 0.95 0.95 0.94 0.65 0.66 0.72 (*) ρ(fdi, fdi∗) 0.59 0.52 0.52 0.58 0.45 0.44 0.50 ρ(fdi∗ t , fdi∗ t−1) 0.58 0.96 0.95 0.95 0.65 0.64 0.72 ρ(inv, fdi) 0.13 0.32 0.27 0.32 0.72 0.71 0.67 ρ(invt, fdit−1) 0.30 0.25 0.22 0.27 0.27 0.27 0.28 ρ(inv, fdi∗) 0.61 0.55 0.60 0.64 0.66 0.68 0.70 ρ(invt, fdi∗ t−1) 0.51 0.42 0.45 0.45 0.32 0.33 0.34 (*) ρ(invt, invt−1) 0.70 0.62 0.59 0.65 0.43 0.44 0.46 (*) ρ(inv, inv∗) 0.40 0.38 0.38 0.34 0.57 0.61 0.61 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 46 / 47
  • 48. Data vs. Model Moments - part 2 Restricted Set (*) Full Set Moment Data CD SEP GHH CD SEP GHH ρ(y, fdi) 0.26 0.49 0.49 0.51 0.42 0.44 0.37 ρ(yt, fdit−1) 0.42 0.45 0.42 0.48 0.29 0.26 0.39 ρ(y, fdi∗) 0.69 0.91 0.88 0.87 0.70 0.69 0.68 ρ(yt, fdi∗ t−1) 0.70 0.87 0.84 0.84 0.68 0.66 0.67 ρ(y, fdi + fdi∗) 0.57 0.80 0.78 0.77 0.66 0.66 0.61 (*) ρ(yt, yt−1) 0.79 0.92 0.90 0.95 0.90 0.86 0.95 (*) ρ(y, y∗) 0.46 0.40 0.36 0.43 0.31 0.28 0.30 (*) sd(nx)/sd(y) 1.06 1.08 1.05 1.05 1.01 0.99 0.94 (*) sd(c)/sd(y) 1.13 0.93 0.85 1.05 0.98 0.91 1.13 (*) sd(fdi)/sd(y) 0.85 0.82 0.81 0.82 0.85 0.84 0.88 (*) sd(inv)/sd(y) 2.82 2.81 2.80 2.83 2.75 2.74 2.75 (*) sd(y) 3.12 3.11 3.12 3.13 3.13 3.14 3.18 McQuoid-Rothert-Smith (MRS) FDI over IBC Nov 2022 47 / 47