Real Interest Rates and Productivity in Small Open Economies - - PowerPoint PPT Presentation
Real Interest Rates and Productivity in Small Open Economies Tommaso Monacelli (Universit Bocconi, IGIER and CEPR) (joint with D. Siena and L. Sala) Banque de France - September 2019 Capital flows, real interest rates and productivity EZ
Tommaso Monacelli (Università Bocconi, IGIER and CEPR) (joint with D. Siena and L. Sala) Banque de France - September 2019
EZ periphery: slowdown in TFP associated to lower real
interest rates and capital inflows (Reis 2013, Gopinath et al, 2016)
EZ periphery: slowdown in TFP associated to lower real
interest rates and capital inflows (Reis 2013, Gopinath et al, 2016)
Puzzle: capital should flow towards countries where TFP
growth is positive
Puzzle: capital should flow towards countries where TFP
growth is positive
In EZ periphery: slowdown in TFP associated to lower real
interest rates (Euro convergence)
Emerging Markets
productivity booms + appreciating real ex. rates
Emerging Markets
productivity booms + appreciating real ex. rates
cycles (Mendoza 1991; Neumeyer and Perri 2005; Uribe and Yue 2006)
Emerging Markets
productivity booms + appreciating real ex. rates
cycles (Mendoza 1991; Neumeyer and Perri 2005; Uribe and Yue 2006)
Recurrent insight: hard for real interest rate shocks to account
for EM business cycles unless correlated with TFP shocks
Emerging Markets
productivity booms + appreciating real ex. rates
cycles (Mendoza 1991; Neumeyer and Perri 2005; Uribe and Yue 2006)
Recurrent insight: hard for real interest rate shocks to account
for EM business cycles unless correlated with TFP shocks
No analysis of the effects of real interest rates (shocks) on
TFP
Figure:
Cross-correlation between real interest rate (t+j) and log GDP(t)
Real interest rates and GDP
Cross-correlation between real interest rate (t+j) and log TFP(t)
Real interest rates and TFP
(⇑ real int. rate):
GDP and TFP fall in EMEs GDP and TFP rise in EZ periphery
Two key competing effects:
Two key competing effects:
Cleansing
→ ⇑ return from lending ("being idle") → Marginally productive firms exit market − → TFP ⇑
Two key competing effects:
Cleansing
→ ⇑ return from lending ("being idle") → Marginally productive firms exit market − → TFP ⇑
Original sin (firms borrow in foreign currency)
by future appreciation) → ⇓Return from saving in foreign currency → Idle (less productive) firms enter production → TFP ⇓
Two key competing effects:
Cleansing
→ ⇑ return from lending ("being idle") → Marginally productive firms exit market − → TFP ⇑
Original sin (firms borrow in foreign currency)
by future appreciation) → ⇓Return from saving in foreign currency → Idle (less productive) firms enter production → TFP ⇓
Two key competing effects:
Cleansing
→ ⇑ return from lending ("being idle") → Marginally productive firms exit market − → TFP ⇑
Original sin (firms borrow in foreign currency)
by future appreciation) → ⇓Return from saving in foreign currency → Idle (less productive) firms enter production → TFP ⇓
firms’ productivity dispersion (market concentration) to rationalize evidence in EMEs vs AEs
Structural VAR analysis of RR shocks on productivity
Structural VAR analysis of RR shocks on productivity Literature on EMEs (eg: Neumeyer and Perri 2005; Uribe and
Yue 2006)
cycle
Yt = TFPt · K α
t N1−α t
stock (Fernald 2012)
Yt = TFPt · K α
t N1−α t
stock (Fernald 2012)
Two types of capital:
i) Buildings : δj
q = 10% annually
ii) Equipment: δj
q = 2.5% annualy
K j
t+1 = (1 − δj q)K j t + I j t+1
RREM
t
= RUS
t
TB rate
−EπUS
t
+ Spreadt
EMBI + spread
RRAE
t
= {90-day interbank rate} - EπAE
t expected inflation
RREM
t
= RUS
t
TB rate
−EπUS
t
+ Spreadt
EMBI + spread
RRAE
t
= {90-day interbank rate} - EπAE
t expected inflation
Yt = A · Yt−1 + B · εt Yt ≡ TFPt GDPt NXt REERt RRt
Triangular factorization: RRt ordered last Bayesian stochastic pooling to compute IRFs (Canova and
Pappa 2007)
Country-specific impulse response of variable r to εRR t
has prior distribution: αr
ι,h
country ι horizon h
= µr
h
IR
+vr
ι,h
where vr
ι,h ∼ N (0, τr h)
where h is the impulse response horizon, h = 0, 1, ..., H and ι is the country identifier
Country-specific impulse response of variable r to εRR t
has prior distribution: αr
ι,h
country ι horizon h
= µr
h
IR
+vr
ι,h
where vr
ι,h ∼ N (0, τr h)
where h is the impulse response horizon, h = 0, 1, ..., H and ι is the country identifier
Diffuse prior for µr h Assume τr h = δr /h, where δr is the observed dispersion of the
impulse responses for variable r across countries.
Country-specific impulse response of variable r to εRR t
has prior distribution: αr
ι,h
country ι horizon h
= µr
h
IR
+vr
ι,h
where vr
ι,h ∼ N (0, τr h)
where h is the impulse response horizon, h = 0, 1, ..., H and ι is the country identifier
Diffuse prior for µr h Assume τr h = δr /h, where δr is the observed dispersion of the
impulse responses for variable r across countries.
Under a Normal-Wishart prior for each country-specific VAR,
the posterior for µr
h is
µr
h|τr h, ˆ
Σui ∼ N(˜ µr
h, ˜
V r
µ,h)
where ˜ µr
h = ˜
V r
µ,h · N
ι=0
( ˆ V r
αι,h + τr h)−1 ˆ
αr
ι,h
˜ V r
µ,h = ( N
ι=0
( ˆ V r
αι,h + τr h)−1)−1
ˆ Σuι is the estimated variance-covariance matrix of the reduced form residuals ut in the VAR for country ι, ˆ αr
ι,h is the country
ι-specific OLS estimator of αr
ι,h and ˆ
V r
αι,h its variance.
Advanced economies (EZ periphery): ↑ RRt → ↑TFP
In response to a positive real int. rate innovation ("capital
In response to a positive real int. rate innovation ("capital
Structural evidence for EZ periphery in line with "EZ-entry
narrative": ↓ real int. rates → ↓ productivity
Need to rationalize different effects of real int. rate shocks
Need to rationalize different effects of real int. rate shocks
Main features relative to classic RBC literature in EM
business cycles
Two goods: H (domestic) and F (imported)
Two goods: H (domestic) and F (imported) Two agents:
productivity (Entrepreneur)
Two goods: H (domestic) and F (imported) Two agents:
productivity (Entrepreneur)
Two goods: H (domestic) and F (imported) Two agents:
productivity (Entrepreneur)
Firms belonging to the family borrow/lend to each other at
the (exogenous) real interest rate r ∗
t .
Two goods: H (domestic) and F (imported) Two agents:
productivity (Entrepreneur)
Firms belonging to the family borrow/lend to each other at
the (exogenous) real interest rate r ∗
t . Borrowing frictions based on collateral
Continuum indexed by i∈ [0, 1] Draw productivity zi,t−1 before end of period t − 1 → Affect
future output yi,t = At−1 · zi,t−1
drawn at t-1
ki,t−1
α · l1−α i,t
Continuum indexed by i∈ [0, 1] Draw productivity zi,t−1 before end of period t − 1 → Affect
future output yi,t = At−1 · zi,t−1
drawn at t-1
ki,t−1
α · l1−α i,t Draw from Pareto distribution
z ∼ Ψ(z) = 1 − z−η η > 1 shape
parameter
Continuum indexed by i∈ [0, 1] Draw productivity zi,t−1 before end of period t − 1 → Affect
future output yi,t = At−1 · zi,t−1
drawn at t-1
ki,t−1
α · l1−α i,t Draw from Pareto distribution
z ∼ Ψ(z) = 1 − z−η η > 1 shape
parameter Timing generates motive for borrowing and lending: less
productive firms have incentive to lend to more productive firms
Pt
=
H,t + (1 − γ)P1−θ F ,t
1−θ
ǫt
real ex rate
≡ P∗
t
Pt = PF ,t Pt qt
goods
≡ PH,t Pt =
t
γ
1−θ
= q(ǫt)
Conditional on borrowing, firm i faces collateral constraint:
di,t
foreign good
≤ χ · ki,t ǫt
rate
→Original sin: can borrow only in foreign goods
Profits at time t (after handing back net worth to the family)
Γi,t
goods
= qtyi,t + (1 − δ)ki,t−1
capital
hand"
− wtli,t
cost
− (1 + r ∗
t−1)ǫtdi,t−1
debt
− qt−1nt−1
to the family
Firm i’s problem divided into 2 stages
Firm i’s problem divided into 2 stages
li,t = l(At−1, wt, zi,t−1) · ki,t−1
capital
where l(At−1, wt, zi,t−1) ≡ max
li,t {qtyi,t − wtli,t}
= wt 1 − α − 1
α
(At−1qt)
1 α zi,t−1
Choice of labor affects only time-t profits and is made after
state Si,t is observed→ li,t maximizes Γi,t state by state.
demand)
Define
Rt ≡ (1 + r ∗
t ) · ǫt+1
ǫt
in domestic CPI units
Firm i chooses {ki,t, di,t} before end of time t after
receiving net wealth nt and after drawing next period productivity zi,t max
{ki,t,di,t} Et Mt,t+1 common across firms
1 α wt+1
1−α
− 1−α
α zi,t
+1 − δ
+ (1 + r ∗
t )ǫt+1
ǫt
· (qtnt − ki,t) subject to di,t ≤ χ · ki,t ǫt ki,t
goods
= ntqt + ǫt · di,t
goods
Optimal capital and debt choices linear in net worth and at
the corner νt > 0
binding borrowing constraint
: ki,t = λ · qtnt
to the maximum
: di,t = (λ − 1) · qtnt ǫt νt = 0 : EtMt,t+1
1 α wt+1
1−α
− 1−α
α αzi,t
+ (1 − δ) − Rt
Can solve for common threshold value of productivity zt
zt = Et {Mt,t+1 [Rt − 1 + δ]} Et
1 α wt+1
1−α
− 1−α
α
= z
ǫt+1 ǫt
Choice of capital and debt
ki,t
= λ · qtnt if zi,t > zt ∈ (0, λqtnt] if zi,t = zt if zi,t < zt di,t
=
(λ−1)·qtnt ǫt
if zi,t > zt
[−qtnt,(λ−1)·qtnt] ǫt
if zi,t = zt −qtnt if zi,t < zt
Key result: threshold productivity is increasing in Rt
zt = z(Rt, ..); ∂zt Rt > 0
Key result: threshold productivity is increasing in Rt
zt = z(Rt, ..); ∂zt Rt > 0
saving → ↑ incentive for marginal firm to remain "idle" → ↑ zt → ⇑ average TFP
Key result: threshold productivity is increasing in Rt
zt = z(Rt, ..); ∂zt Rt > 0
saving → ↑ incentive for marginal firm to remain "idle" → ↑ zt → ⇑ average TFP
depreciation (↑ ǫt) (i) Expected appreciation →Return from lending falls (in units of domestic CPI goods) → Marginal firm has incentive to enter → ⇓ average TFP (ii) Tighten balance sheet of incumbent firms (↓ qt)
Wealth/net worth
Nt =
1
0 ntdi = nt ·
∞
ψ(z)dz = nt
Allocation of net worth into capital
Kt =
= λ · Nt · [1 − Ψ(zt)]
Allocation of net worth into debt
ǫtDt =
1
0 ǫtdi,t di
= Nt · [λ(1 − Ψ(zt)) − 1]
Labor
Lt =
1
0 Li,tdi =
wt 1 − α − 1
α
[qtAt−1]
1 α Kt−1
∞
z t−1 zψ(z)dz
[1 − Ψ(zt−1)]
productivity Profits
Γt =
1
0 Γi,tdi
= [(Πt − Rt−1 + 1 − δ) [1 − Ψ(zt−1)]λ + (Rt−1 − 1)] Nt−1
Wealth and aggregate profits of individual firms returned to
the Entrepreneur ("family").
Family consumes
C e
t =
1 θ C θ−1 θ
H,t + (1 − γ)
1 θ C θ−1 θ
F ,t
θ−1
Family solves simple intertemporal problem (after
aggregation) max
{Ct,Nt,CH,t,CF ,t} Et ∞
s=0
χt+s ln C e
t+s
C e
t + Nt = Γt + Nt−1
Γt = [(Πt − Rt−1 + 1 − δ) [1 − Ψ(zt−1)]λ + (Rt−1 − 1)] Nt−1 Πt ≡ α (qtAt−1)
1 α
wt 1 − α − 1−α
α ∞
z t−1 zψ(z)dz
[1 − Ψ(zt−1)]
productivity
Compare baseline RBC small open economy vs. one-good
version of our model
Notice: no relative price / valuation effect on borrowing
constraint
Compare baseline RBC small open economy vs. one-good
version of our model
Notice: no relative price / valuation effect on borrowing
constraint
Baseline calibration
log(1 + r ∗
t ) = ρ∗ log(1 + r ∗ t−1) + ε∗ t .
(1) Parameter Description Value α
capital share
0.32 δ
K depreciation
0.025 φ
inverse Frisch
1.5 χ
2/3 γ
home bias
0.8 θ trade elasticity 1 η Pareto distribution 3
AR real int. rate
0.96
5 10
quarters
Output
% d e v s . f r
s . s .
5 10
quarters
Consumption 5 10
5 Inv estment
% d e v s . f r
s . s .
5 10 0.01 0.02 0.03 0.04 Av erage Productiv ity
Baseline RBC Model Cleansing Model, η=1.5
Capital outflow shock: responses to a rise in r ∗
t
How large is the cleansing effect? Need a sufficiently
dispersed distribution of firms
The lower η, i.e., the larger the heterogeneity across firms,
the higher the number of firms exiting (or entering) the market at the margin
1 1.5 2 2.5 3 1 2 3 4 5 6 7 8 9 10 Probability density function - firm distribution 2 4 6 8 10
Output η=1.5 η=3 η=10 η=∞
η → ∞: recover RBC version of the model
Dispersion of log(TFPR) - log(sector mean of TFPR)
TFPRi,s = Pi,sYi,s K α
i,s (wLi,s)
Model with financial frictions and firms’ heterogeneity:
is the degree of heterogeneity)
Model with financial frictions and firms’ heterogeneity:
is the degree of heterogeneity)
Model with financial frictions and firms’ heterogeneity:
is the degree of heterogeneity)
Intuition: model incorporates only "cleansing channel" of real
interest rate changes → Negative comovement between Y and TFP
10 20 30 40
% dev. from SS
Output
10 20 30 40
0.1 0.2 0.3 0.4 0.5 0.6 % dev. from SS
Average Productivity
10 20 30 40
0.5 % dev. from SS
Consumption
10 20 30 40
5 % dev. from SS
Investment
10 20 30 40
2 4 6 8 10 12 % dev. from SS
Real Exchange Rate
10 20 30 40
0.01 0.02 0.03 0.04 Level
Net Exports / GDP θ=0.3 θ=1 θ=1.5
Capital outflow shock: model with cleansing + original sin
Method of moments: match impulse responses Estimate 4 parameters:
θ
elasticty
, η
shap / e
, ρr1, ρr2
Keep the model simple (no DSGE frictions)
Estimated parameter values Trade elasticity θ Pareto distribution η ρ∗
1
ρ∗
2
EMEs 0.353 1.046 0.821
(0.0259) (0.0417) (0.1274) (0.1360)
AEs 0.430 6.021 1.078
(0.0497) (0.0297) (0.0086) (0.0496)
Low trade elasticity of substitution Larger dispersion of firms’ productivity distribution in EMEs
Real interest rate (≈ capital flow) shocks: opposite effect on
productivity in EMEs vs AEs
Real interest rate (≈ capital flow) shocks: opposite effect on
productivity in EMEs vs AEs
Model that can rationalize both facts, and be consistent
with relevant role of RR shocks for EMEs
Real interest rate (≈ capital flow) shocks: opposite effect on
productivity in EMEs vs AEs
Model that can rationalize both facts, and be consistent
with relevant role of RR shocks for EMEs
Ingredients: cleansing (cum financial frictions) + original sin
+ low trade elasticity of substitution
Real interest rate (≈ capital flow) shocks: opposite effect on
productivity in EMEs vs AEs
Model that can rationalize both facts, and be consistent
with relevant role of RR shocks for EMEs
Ingredients: cleansing (cum financial frictions) + original sin
+ low trade elasticity of substitution
Importance of cross-country (EMEs vs AEs) differences in
dispersion of firms’ productivity distribution