Seminar at the NCSU

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
North Carolina State University
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

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

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

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

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

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

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

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

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

D A T A

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

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

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.

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

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)

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)

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
,
lim
θ→∞
MRS(θ) = BKK

Foreign-owned capital — an imperfect substitute?
Product variety in non-tradeable goods (e.g., retail services)

Product variety in tradeable goods (FDI inflows replacing imports)

Foreign presence in sectors complementary with others

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)

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.)

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.

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, 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

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

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

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

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

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

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

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 ↑

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 — direct upward impact on MPKA(t + 1)
k∗
A ↑ while k∗
B ↓ if ρz large enough

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

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)

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

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

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

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

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