Real Business Cycles in Emerging Economies

Real Business Cycles in Emerging Economies:
the Role of Interest Rates and Exchange Rates
Sihao CHEN, Kang SHI, Juanyi XU
HKUST, CUHK, HKUST
IMES, HKUST, Feb. 22, 2018
(Institute) IMES, HKUST, Feb. 22, 2018 1 / 43

Motivation
Understanding real business cycle in emerging market economies is a
central issue in international macroeconomics. Current literatures
focus on the excess consumption volatility or counter-cyclical trade
balance. Permanent productivity shocks and interest rate shocks are
proposed to explain aggregate ‡uctuations in emerging economies.
Real exchange rate (RER) dynamics and its comovement with other
macroeconomics variables are usually not explored as most papers
focus on one-sector RBC models.
Since most emerging market economies are small open economies
subject to external shocks to interest rate, demand, and terms of
trade, It seems nontrivial to include RER in the study of emerging
market business cycle.
Moreover, as shown in Mendoza (2012) and Bianchi(2011), RER
changes can induce sharp and sudden adjustments in access to foreign
…nancing, and play important roles in emerging marker crisis.

Questions
Are RER dynamics and its comovement with aggregate variables
di¤erent between emerging market economies and developed small
open economies?
Can a standard two-sector model with non-tradable goods explain the
behavior of RER and aggregate moments related to RER?
Can permanent productivity shocks or interest rate shocks help to
explain RER dynamics? Do they remain important in explaining
aggregate ‡uctuations in emerging market economies when RER data
are included in the estimation?

Stylized facts of RER behavior in emerging market
economies
RER volatility relative to output and RER persistence in emerging
economies are similar to that of developed small open economies. In
other words, RER is quite volatile and very persistent.
However, the comovement between RER and other macroeconomic
aggregates are quite di¤erent between emerging economies and
developed SOE.
1 Real exchange rates are positively correlated with consumption and
output in emerging economies, while in developed economies it is
counter-cyclical.
2 More importantly, there exists signi…cant and negative correlation
between real interest rate and real exchange rate in emerging
economies. And this correlation is close to zero in developed SOEs.
3 Real interest rates are countercyclical in emerging markets while
acyclical in developed SOEs.

Facts
σ(gY )
σ(gC )
σ(gY )
σ(gI )
σ(gY )
σ(tby)
σ(gY )
σ(RER)
σ(gY )
σ(R)
σ(gY )
Emerging markets 1.93 1.34 2.84 2.14 7.21 2.31
Small developed economies 0.90 0.92 3.40 3.79 6.95 2.34
ρ(gY , RER) ρ(gC , RER) ρ(tby, RER) ρ(R, RER) ρ(R, gY ) ρ(RER)
Emerging markets 0.07 0.13 -0.46 -0.17 -0.17 0.86
Small developed economies -0.13 -0.04 -0.40 0.02 0.08 0.94
Note: ratio is the average of emerging markets or the average of small developed economies.
Table: 1 Comparison of Business Cycle Moments

corr(gY , RER) corr(gC , RER) corr(gI , RER) corr(tby, RER)
Argentina -0.26 -0.21 -0.29 -0.56
p value 0.02 0.06 0.01 0.00
Brazil 0.09 0.22 0.24 -0.68
p value 0.46 0.06 0.04 0.00
Chile 0.07 0.23 0.00 -0.29
p value 0.57 0.04 0.98 0.01
Colombia -0.07 -0.04 -0.14 -0.10
p value 0.53 0.75 0.23 0.36
Indonesia 0.70 0.09 0.47 -0.67
p value 0.00 0.46 0.00 0.00
Israel -0.09 0.08 -0.16 -0.56
p value 0.42 0.50 0.16 0.00
Korea 0.28 0.32 0.25 -0.46
p value 0.00 0.00 0.00 0.00
Malaysia -0.07 0.26 -0.09 -0.67
p value 0.75 0.23 0.66 0.00
Mexico 0.20 0.33 0.26 -0.55
p value 0.07 0.00 0.02 0.00
Peru -0.13 0.02 -0.07 -0.64
p value 0.23 0.83 0.51 0.00
Philippines 0.28 0.29 0.13 -0.51
p value 0.19 0.17 0.54 0.01
South Africa -0.10 0.08 -0.09 0.13
p value 0.24 0.33 0.27 0.13
Thailand 0.07 0.09 0.03 -0.49
p value 0.55 0.41 0.77 0.00
Turkey 0.06 0.12 0.20 -0.36
p value 0.58 0.29 0.07 0.00
Average 0.07 0.13 0.05 -0.46
Table: 2: Correlations with real exchange rate: Emerging markets

corr(gY , R) corr(gC , R) corr(gI , R) corr(tby, R) corr(RER, R)
Argentina 0.12 0.08 0.26 0.75 -0.19
p value 0.29 0.48 0.02 0.00 0.10
Brazil -0.15 -0.33 -0.24 0.07 -0.53
p value 0.24 0.01 0.06 0.55 0.00
Chile -0.05 -0.06 -0.08 -0.08 0.15
p value 0.70 0.67 0.56 0.56 0.28
Colombia 0.01 0.07 -0.12 0.00 -0.45
p value 0.91 0.57 0.34 0.99 0.00
Korea -0.13 -0.07 -0.27 0.14 -0.35
p value 0.41 0.67 0.10 0.37 0.02
Malaysia -0.22 -0.16 -0.29 0.14 0.06
p value 0.08 0.20 0.02 0.28 0.62
Mexico -0.17 -0.25 -0.20 0.87 -0.53
p value 0.13 0.03 0.08 0.00 0.00
Peru -0.34 -0.21 -0.38 -0.69 0.07
p value 0.01 0.11 0.00 0.00 0.57
South Africa -0.18 -0.20 -0.22 0.64 0.14
p value 0.14 0.09 0.06 0.00 0.24
Thailand -0.46 -0.36 -0.41 0.67 0.39
p value 0.01 0.03 0.01 0.00 0.02
Turkey -0.25 -0.14 -0.32 0.70 -0.64
p value 0.04 0.27 0.01 0.00 0.00
Average -0.17 -0.15 -0.21 0.29 -0.17
Table: 3: Correlations with interest rate: Emerging markets

corr(Y , RER) corr(C , RER) corr(I, RER) corr(tby, RER)
Argentina 0.49 0.61 0.46 -0.55
p value 0.00 0.00 0.00 0.00
Brazil 0.42 0.39 0.45 -0.19
p value 0.00 0.00 0.00 0.10
Chile 0.58 0.11 0.15 0.06
p value 0.00 0.34 0.18 0.58
Colombia 0.00 -0.08 0.07 -0.01
p value 0.97 0.46 0.50 0.93
Indonesia 0.42 0.31 -0.03 -0.34
p value 0.00 0.01 0.83 0.00
Israel 0.32 0.32 0.24 0.01
p value 0.00 0.00 0.03 0.97
Korea 0.41 0.49 0.40 -0.25
p value 0.00 0.00 0.00 0.00
Malaysia 0.23 -0.20 -0.09 -0.20
p value 0.27 0.35 0.65 0.34
Mexico 0.66 0.73 0.72 -0.39
p value 0.00 0.00 0.00 0.00
Peru 0.08 0.46 0.10 -0.20
p value 0.47 0.00 0.36 0.08
Philippines 0.32 0.17 0.43 -0.10
p value 0.12 0.42 0.03 0.64
South Africa -0.08 0.16 -0.04 -0.13
p value 0.36 0.05 0.61 0.13
Thailand 0.39 0.41 0.35 -0.25
p value 0.00 0.00 0.00 0.02
Turkey 0.33 0.48 0.25 -0.23
p value 0.00 0.00 0.02 0.03
Average 0.33 0.31 0.25 -0.20
Table: 4: Correlations with detrended real exchange rate: Emerging markets

corr(Y , R) corr(C , R) corr(I, R) corr(tby, R) corr(RER, R)
Argentina -0.57 -0.60 -0.53 0.53 -0.66
p value 0.00 0.00 0.00 0.09 0.00
Brazil -0.16 -0.20 -0.12 0.05 -0.39
p value 0.21 0.10 0.33 0.68 0.00
Chile 0.37 -0.10 0.00 0.20 0.44
p value 0.01 0.49 1.00 0.14 0.00
Colombia -0.04 -0.01 -0.26 0.35 -0.17
p value 0.77 0.93 0.04 0.00 0.19
Korea -0.69 -0.75 -0.68 0.51 -0.57
p value 0.00 0.00 0.00 0.00 0.00
Malaysia -0.52 -0.61 -0.57 0.56 -0.53
p value 0.00 0.00 0.00 0.00 0.00
Mexico -0.30 -0.31 -0.47 0.23 -0.69
p value 0.01 0.01 0.00 0.05 0.00
Peru -0.07 -0.21 0.15 -0.04 -0.26
p value 0.58 0.10 0.24 0.77 0.04
South Africa -0.02 0.04 0.05 0.03 -0.16
p value 0.84 0.75 0.66 0.77 0.17
Thailand -0.62 -0.68 -0.59 0.38 -0.10
p value 0.00 0.00 0.00 0.02 0.55
Turkey -0.17 -0.30 -0.28 0.44 -0.13
p value 0.16 0.01 0.02 0.00 0.30
Average -0.25 -0.34 -0.30 0.30 -0.29
Table: 5: Correlations with detrended interest rate: Emerging markets

Performance of a standard two-sector model
Model feature
1 Tradable and non-tradable sector, but tradable goods are homogeneous.
2 Five shocks are introduced, including permanent productivity shock,
country premium shock and stationary sector-speci…c technology
shocks.
RER and real interest rate data are included in the Bayesian
estimation (Mexican data)
1 Get the RER persistence, but underestimate the RER volatility relative
to output.
2 Underestimate the signi…cant negative correlation between RER and
real interest rate, as well as the negative comovement between RER
and tby/GDP ratio.
3 Fail to generate excess consumption volatility and the countercyclical
real interest rate.

Why the model does not do well?
The model relies on transitory technology shocks to drive output and
consumption ‡uctuations, as well as the RER dynamics
A positive AN shock leads to
RER depreciation since PN decrease;
So it is not surprising this model cannot fully explain the negative
comovement of RER and real interest rate.
Also, this benchmark model fails to generate the countercyclical
behavior of real interest rate.

Consumption smoothing since it is a transitory shock - so cannot
generate excess consumption smoothing;

Consumption smoothing since it is a transitory shock - so cannot
generate excess consumption smoothing;
Trade balance will increase - implying real interest rate will decrease.

How to improve the performance?
Ideally, need some shocks that will a¤ect RER and real interest rate
together. How about country premium shock?
A positive interest rate shock leads to increase of real interest rate
and decrease in consumption demand. So the demand for
non-tradable goods decrease, and PN decrease.
Seems to be working, but quantitatively too small!
We need more RER ‡uctuations!

RER ‡uctuation - deviation from LOOP in tradable goods
In empirical literature on RER, the dominant view is that relative
prices of tradable goods account for most of the RER variability. For
example, Engel (1999, 2000); Betts and Kehoe (2005)
Later some papers argue that relative price of non-tradable to
tradable goods are still important in explaining RER ‡uctuations. For
example, Mendoza (2005a) and Betts and Kehoe (2008)
So it seems reasonable to introduce di¤erentiated home and imported
tradable goods and allow for deviation from LOOP in tradable goods
to account for RER dynamics.

Performance of the imperfect substitution model
Model feature
1 Domestic produced tradable goods and imported tradable goods are
imperfect substitutes.
2 So home tradable goods price ‡uctuations will contribute to RER
variability.
Bayesian estimation result (Mexico data)
1 Can match the negative correlation between RER and real interest rate,
as well as the negative comovement between RER and tby/GDP ratio.
2 Can generate excess consumption volatility (permanent technology
shock plays more important role in output ‡uctuations) and the
countercyclical real interest rate qualitatively, but not quantitatively.
3 Also do better in match the RER volatility to output. But overestimate
the output and RER volatility.

Why does the imperfect substitution model do better?
The main reason for the improvement comes from the dominant role
of country premium shock in explaining both RER and real interest
rate.
In the imperfect substitution model, from the IRF we can see that the
RER depreciation after a positive country premium shock is much
larger. Why?
With di¤erentiated home and imported tradable goods, decrease in
consumption and investment can be generated through the decrease of
domestic tradable goods price, as well as decrease in non-tradable
goods price.
It also helps to generate the negative comovement of real interest rate
and output/consumption.

rate.
larger. Why?
goods price.
Compared to the benchmark model, the demand e¤ect of interest rate
shock will now induce additional relative price changes and RER
‡uctuations.

rate.
larger. Why?
goods price.
Compared to the benchmark model, the demand e¤ect of interest rate
shock will now induce additional relative price changes and RER
‡uctuations.
Consistent with this intuition, the RER ‡uctuations depends on the
elasticity of substitution between home and imported tradable goods.

How to improve the performance further?
To get more signi…cant negative comovement between real interest
rate and output/consumption, interest rate shocks need to play more
important role in the supply side.
Financial friction will help.
It seems working capital constraint itself is not enough, consistent with
Chang and Fernandez (2013)’s …nding.
This will also help to reduce the excess volatility of RER because it is
also constrained by supply side factors.

Collateral constraint with collateral value a¤ected by RER in small
open economy, as emphasized in Mendoza (2002,2005, 2010) and
Bianchi (2011)

Collateral constraint with collateral value a¤ected by RER in small
open economy, as emphasized in Mendoza (2002,2005, 2010) and
Bianchi (2011)
Moreover, since investment goods are tradable goods, internaaction of
RER ‡uctuation and collateral constraint can help to match the
negative comovement of RER and real interest rate.

Performance of the collateral constraint model
Model feature
1 Entrepreneurs own the capital and use the value of capital stock as
collateral to …nance their borrowing from the international …nancial
market.
2 Since only tradable goods are used as investment goods, pecuniary
e¤ect induced by RER changes will a¤ect …rms’borrowing capacity.
3 There is still working capital constraint on wage bill and imperfect
substitution.
Bayesian estimation result (Mexico data)
1 Quantitatively match the volatility of output, consumption, RER and
real interest rate.
2 Improve on the negative correlation between real interest rate and
output/consumption.
3 Country premium shocks plays dominant role in driving ‡uctuations of
all variables, including RER.

The country premium shock
So the country premium shock is important in explaining RER
dynamics and comovement with other macroeconomic variables in the
emerging market economies!
We provide another argument for the importance of country premium
shock in explaining RBC in emerging economies, from the perspective
of RER ‡uctuations and its comovement with real interest rate
induced by …nancial frictions.

Literature Reviews
On emerging market studies:
1 Permanent technology shock: Aguiar and Gopinath (2007).
2 Financial friction: Neumeyer and Perri (2005); Uribe and Yue (2006);
Garcia-Cicco et al. (2010); Chang and Fernandez (2013); Hevia (2014)
3 Include RER data into estimation: Seoane (2016).
4 Include real interest rate data into estimation: Akinci (2014).
5 Collateral constraints with pecuniary e¤ect of relative price change in
small open economy: Mendoza (2010), Bianchi (2011) and Korinek
(2011).

Main contribution of our paper
We show that the comovement between RER and macroeconomics
aggregates, especially the real interest rate is di¤erent between
emerging economies and developed SOEs. So we include both RER
and real interest rate data into the estimation.
We show that deviation from LOOP is important to explain RER
dynamics in emerging market economies.
We argue the importance of country premium shock from the
perspective of RER dynamics and comovement induced by …nancial
friction.

Two sector model: Extension of Garcia-Cicco et al(2010)
Household GHH preference:
E0
∞
∑
t=0
βt
vt [ Ct
Xt 1
Λτ 1lt
τ]1 γX
1 γ
t 1 1
1 γ
(1)
There are two sectors: tradable and non-tradable sector, but tradable
goods are homogeneous.
Ct = [ω
1
κ C
T κ 1
κ
t + (1 ω)
1
κ C
N κ 1
κ
t ]
κ
κ 1
Pc
t = [ω(PT
t )1 κ
+ (1 ω)(PN
t )1 κ
]
1
1 κ
Let PT
t be the numeraire. Assume all investment goods are tradable
goods. Households’real budget constraint:
Pc
t Ct +Dh
t +IN
t +IT
t =
Dh
t+1
1 + rt
+wt lt +RK ,N
t KN
t +RK ,T
t KT
t +Πt (2)
where Dh
t is the debt holding of households at time t. They borrow debt
from the bank/…nancial intermediary.

Two sector model:
The bank borrow money from international debt market. Following
Schimitt-Grohe and Uribe (2003), domestic interest rate is external-debt elastic.
1 + rt = 1 + r +ψ[ exp (
eDt+1
Xt
d)] + µt (3)
where eDt+1 is the aggregate level of external debt. µt is the country-premium
shock.
The capital motion is given by
Kj
t+1= (1 δ)Kj
t +Ij
t
φj
2
(
Kj
t+1
Kj
t
g)2
Kj
t (4)
Households choose labor supply, consumption, debt holding and investment to
maximize the utility subject to the b.c, and capital motion.

Two sector model:
Firms and equilibrium conditions
In both sectors, …rms are competitive. For j producer, j 2 fT, Ng, the
production function is:
Y j
t = Aj
t (Kj
t )1 αj
(X t lj
t )αj
(5)
The working capital constraint following Schmitt-Grohe and Uribe (2016), …rm
need to hold j wt lj
t units of real money to pay for wage bill
MBj
t
j
wt lj
t (6)
Net pro…t of …rms could be speci…ed as
Πj
t = Pj
t Y j
t wt lj
t RK ,j
t Kj,s
t (MBj
t MBj
t 1)+
Df ,j
t+1
1 + rt
Df ,j
t (7)
where Df ,j
t is sector j …rms’holding of debt, again borrowed from the
…nancial intermediary.

Two sector model:
Firms choose lj
t , Kj
t+1, MBj
t and Dj
t+1 to maximize pro…t
max
lj
t ,K j
t+1,MBj
t ,Dj
t+1
E0Σ∞
t=0[βt
λt X
γ
t 1Πj
t ]
subject to the working capital constraint.
λt X
γ
t 1 is the stochastic discount factor, and Lagrangian equation is
L = E0Σ∞
t=0βt
λt X
γ
t 1
2
4
pj
t Y j
t wt lj
t RK ,j
t Kj
t (MBj
t MBj
t 1)
+
Df ,j
t+1
1+rt
Df ,j
t + ςj
t MBj
t
j wt lj
t
3
5 (8)
We can then get …rms’optimality conditions.
Finally, consider bank’s balance sheet and labor and goods market
equilibrium conditions.
Five shocks:
n
vt , gt = Xt
Xt 1
, µt , AT
t , AN
t
o

Calibration
Value Meaning Source
β = 0.98 quarterly discount factor AG,2007
γ = 2 curvature of period utility function AG,2007
Λ = 2.2 parameter to ensure the allocation of labor in steady state calibrated
τ = 1.6 1/(τ 1) is the labor supply elasticity GPU,2010
αT = αN = 0.68 labor income share AG,2007
δT ,ss
= δN,ss
= 0.05 capital depreciation rate AG,2007
ln RER = 0.016 steady state level of real e¤ective exchange rate calibrated
tby = 0.02 steady state level of trade balance to GDP ratio calibrated
AG denotes Aguiar and Gopinath (2007); GPU denotes Garcia-Cicco, Pancrazi and Uribe (2010)
Table: 6 Parameters for benchmark model

Estimation strategy
Data: Mexico 1994Q1- 2012Q4. gY
t , gC
t , gI
t are approximated by …rst
order di¤erence of logged variables.
GDPdata
t =
Y T
t + PN
t Y N
t
Pc
t
; Idata
t =
(IT
t + IN
t )
Pc
t
tbydata
t =
TBt
Pc
t GDPt
; REERdata
t =
Pc
t
Pt
The measurement equations are given by
2
6
6
6
6
6
6
4
gY
t
gC
t
gI
t
tbyt
ln Rt
ln RERt
3
7
7
7
7
7
7
5
=
2
6
6
6
6
6
6
4
∆ ln GDPdata
t
∆ ln Ct
∆ ln Idata
t
tbydata
t
ln Rt
ln RERdata
t
3
7
7
7
7
7
7
5
+
2
6
6
6
6
6
6
4
ln gt 1
ln gt 1
ln gt 1
0
0
0
3
7
7
7
7
7
7
5

Estimation result
gY gC gI tby RER R
Standard Deviations*:
model 1.97 1.00 2.05 1.34 5.49 0.49
data 1.36 1.25 3.08 2.20 8.89 0.72
Correlation with gY :
model 0.86 0.63 -0.10 0.28 0.07
data 0.87 0.83 0.02 0.20 -0.17
Correlation with gC :
model 0.80 -0.21 0.29 0.01
data 0.80 -0.04 0.33 -0.24
Correlation with RER
model -0.17 -0.26
data -0.58 -0.51
First Order Autocorr.:
model 0.13 0.12 -0.01 0.88 0.91 0.94
data 0.46 0.35 0.36 0.95 0.86 0.95
* Standard deviation is the standard deviation relative to output.
Table: 8 Standard model business cycle moment: Mexico

Estimation result
AH AN g v µ
gY 1.24 50.64 41.10 0.06 6.54
gC 0.42 22.99 51.24 0.13 24.69
gI 0.19 5.81 8.81 0.09 85.07
tby 0.12 0.17 20.44 0.03 79.25
RER 20.95 40.30 14.27 0.14 20.73
R 0.24 0.37 23.35 0.04 75.89
Table: 9 Variance decomposition: Standard models

IRF
0 10 20 30 40
-0.01
0
0.01
0.02
Output growth
0 10 20 30 40
-5
0
5
10
10-3Consumption growth
0 10 20 30 40
-0.01
0
0.01
0.02
Investment growth
0 10 20 30 40
-2
0
2
10-3Trade balance to GDP ratio
0 10 20 30 40
-0.05
0
0.05
RER
0 10 20 30 40
-1
-0.5
0
10-3 R
0 10 20 30 40
0
0.01
0.02
Nontradable output
0 10 20 30 40
0
0.02
0.04
0.06
Tradable output
0 10 20 30 40
0
0.01
0.02
0.03
tradable consumption
imperf ect substitution model
benchmark model
0 10 20 30 40
-0.05
0
0.05
Nontradable price
0 10 20 30 40
-5
0
5
10-3Home tradable price
0 10 20 30 40
0
0.005
0.01
Comsumption home tradable
Figure: One standard deviation AT shock

IRF
0 10 20 30 40
-0.01
0
0.01
0.02
Output growth
0 10 20 30 40
-0.01
0
0.01
0.02
Consumption growth
0 10 20 30 40
-0.01
0
0.01
0.02
Investment growth
0 10 20 30 40
-4
-2
0
2
0 10 20 30 40
-0.015
-0.01
-0.005
0
RER
0 10 20 30 40
-2
-1
0
1
10-4 R
0 10 20 30 40
0
0.005
0.01
0.015
Nontradable output
0 10 20 30 40
0
0.005
0.01
Tradable output
0 10 20 30 40
0
0.005
0.01
imperfect substitution model
benchnmarkmodel
0 10 20 30 40
-0.02
-0.01
0
Nontradable price
0 10 20 30 40
-4
-2
0
10-3Home tradable price
0 10 20 30 40
0
0.005
0.01
Figure: One standard deviation AN shock

IRF
0 10 20 30 40
0
0.005
0.01
Output grow th
0 10 20 30 40
0
0.005
0.01
0.015
Consumption grow th
0 10 20 30 40
0
0.01
0.02
0.03
Inv estment grow th
0 10 20 30 40
-10
-5
0
5
10
-3Trade balance to GDP ratio
0 10 20 30 40
-0.02
0
0.02
0.04
RER
0 10 20 30 40
0
0.5
1
10
-3 R
0 10 20 30 40
0
0.02
0.04
Nontradable output
0 10 20 30 40
0
0.02
0.04
0.06
Tradable output
0 10 20 30 40
0
0.02
0.04
0 10 20 30 40
0
0.02
0.04
0.06
Nontradable price
benchm ark m odel
im perf ect substitution m odel
0 10 20 30 40
0
0.02
0.04
0.06
Home tradable price
0 10 20 30 40
0
0.02
0.04
0.06
Com sumption home tradable
Figure: One standard deviation g shock

IRF
0 10 20 30 40
-10
-5
0
5
10-3 Output growth
0 10 20 30 40
-0.02
-0.01
0
0.01
Consumption growth
0 10 20 30 40
-0.04
-0.02
0
0.02
Investment growth
0 10 20 30 40
-0.01
0
0.01
0.02
Trade balance to GDP ratio
0 10 20 30 40
-0.05
0
0.05
RER
0 10 20 30 40
0
2
4
10-3 R
0 10 20 30 40
-0.01
-0.005
0
Nontradable output
0 10 20 30 40
-0.01
0
0.01
Tradable output
0 10 20 30 40
-0.02
-0.01
0
imperfect substitutionmodel
benchmarkmodel
0 10 20 30 40
-0.1
-0.05
0
0.05
Nontradable price
0 10 20 30 40
-0.05
0
0.05
Home tradable price
0 10 20 30 40
-10
-5
0
5
10-3Comsumption home tradable
Figure: One standard deviation µ shock

"Imperfect Substitution Model"
Tradable consumption goods
CT
t = [ξ
1
θ (CH
t )
θ 1
θ + (1 ξ)
1
θ (CF
t )
θ 1
θ ]
θ
θ 1 (9)
The demands of domestic tradable and foreign tradable are:
CH
t = ξ(
PH
t
PT
t
) θ
CT
t (10)
CF
t = (1 ξ)(
PF
t
PT
t
) θ
CT
t (11)
The tradable goods’price index:
PT
t = [ξ(PH
t )1 θ
+ (1 ξ)(PF
t )1 θ
]
1
1 θ (12)

Estimation result: "Imperfect Substitution Model"
gY gC gI tby RER R
model 1.85 1.04 2.51 1.60 10.83 0.69
data 1.36 1.25 3.08 2.20 8.89 0.72
model 0.96 0.86 -0.25 0.33 -0.05
data 0.87 0.83 0.02 0.20 -0.17
model 0.88 -0.26 0.34 -0.06
data 0.80 -0.04 0.33 -0.24
model -0.85 -0.45
data -0.58 -0.51
model 0.10 0.09 -0.03 0.95 0.95 0.96
data 0.46 0.35 0.36 0.95 0.86 0.95
Table: 11 Business cycle in Mexico: imperfect substitution model

Estimation result: "Imperfect Substitution Model"
AH AN v g CS µ
gY 0.87 8.94 0.00 61.73 0.02 27.38
gC 0.17 4.39 0.09 63.26 0.01 31.78
gI 0.98 3.24 0.17 43.59 0.01 51.72
tby 0.01 0.01 0.00 59.42 0.03 40.53
RER 0.01 0.32 0.00 59.29 0.06 40.27
R 0.00 0.00 0.00 10.07 0.00 89.92
Table: 12 Variance decomposition: imperfect substitution model

Role of trade elasticity
5 10 15 20 25 30 35 40 45 50
-0.05
-0.04
-0.03
-0.02
-0.01
0
0.01
RER
=1.27
=5
=10
=20
=50
=100
Figure: Response to one standard deviation of µ shock.

"Collateral Constraint Model"
Entrepreneur There are two sector j = fH, Ng. anb the objective function is
E
∞
∑
t=0
βe,t
(
(Cj
et )1 γ
1 γ
)
(13)
Production is identical to equation (5), capital motion is identical to equation
(4). The …rms still face the working capital constraint (6).
MBj
t
j
wt lj
t (14)
The entrepreneur makes investment, owns the capital and this capital can be used
as collateral
Df ,j
t+1 θj
t Et [qj
k,t+1Kj
t+1] (15)
where θj
t is the collateral shock. qj
k,t+1 is the shadow price of capital in
consumption units. Since only tradable goods are used as investment goods, it is
determined by the price of domestic tradable goods. PH
t = qj
kt . So the relative
price change will have a pecuniary e¤ect on the borrowing capacity of …rms.

"Collateral Constraint Model"
The entrepreneur’s pro…t:
Pj
t Cj
et = Pj
t Y j
t PH
t Ij
t wt lj
t +
Df ,j
t+1
1 + rt
Df ,j
t (MBj
t MBj
t 1) (16)
They choose Cj
et , lj
t , Ij
t , Df ,j
t+1, MBj
t to maximize utility function, subject to
capital motion, collateral constraint, and working capital constraint.
From the optimality condition of entrepreneurs, we got
µj
ct =
rt
1 + rt
+µj
bt (17)
where µj
ct is the shadow price of working capital constraint, and µj
bt is the
shadow price of collateral constraint. Compared with standard model without
collateral constraint, the wedge contents another term µj
bt which is the marginal
value of collateral.

Estimation result: "Collateral Constraint Model"
gY gC gI tby RER R
model 1.44 1.19 2.52 1.75 8.86 0.93
data 1.36 1.25 3.08 2.20 8.89 0.72
model 0.91 0.80 -0.23 0.38 -0.11
data 0.87 0.83 0.02 0.20 -0.17
model 0.78 -0.25 0.42 -0.11
data 0.80 -0.04 0.33 -0.24
model -0.84 -0.49
data -0.58 -0.51
model 0.26 0.26 0.10 0.94 0.87 0.97
data 0.46 0.35 0.36 0.95 0.86 0.95
Table: 14 Business cycle in Mexico: collateral constraint model

Estimation result: "Collateral Constraint Model "
AH AN v g CS µ θH
θN
gY 0.66 17.66 0.02 24.63 0.40 55.68 0.23 0.08
gC 0.09 6.64 0.05 18.64 0.11 73.54 0.15 0.04
gI 2.06 7.64 0.02 11.68 0.05 77.54 0.78 0.06
tby 0.02 0.02 0.06 1.48 0.12 98.23 0.03 0.00
RER 0.05 1.48 0.04 5.34 0.28 92.37 0.07 0.00
R 0.00 0.00 0.01 0.01 0.01 99.97 0.00 0.00
Table: 15 Variance decomposition: collateral constraint models

IRF
0 10 20 30 40
0
0.005
0.01
Output grow th
0 10 20 30 40
0
0.01
0.02
Consumption grow th
0 10 20 30 40
0
0.01
0.02
0.03
Inv estment grow th
0 10 20 30 40
-10
-5
0
5
0 10 20 30 40
0
0.02
0.04
RER
0 10 20 30 40
-2
0
2
4
10
-4 R
0 10 20 30 40
0
0.02
0.04
Nontradable output
0 10 20 30 40
0
0.02
0.04
0.06
Tradable output
0 10 20 30 40
0
0.02
0.04
0 10 20 30 40
0
0.02
0.04
0.06
Nontradable price
collateral constraint model I
0 10 20 30 40
0
0.02
0.04
0.06
Home tradable price
0 10 20 30 40
0
0.02
0.04
0.06
Figure: One standard deviation g shock

IRF
0 10 20 30 40
-10
-5
0
5
10-3 Output growth
0 10 20 30 40
-0.02
-0.01
0
0.01
Consumption growth
0 10 20 30 40
-0.04
-0.02
0
0.02
Investment growth
0 10 20 30 40
-5
0
5
10
0 10 20 30 40
-0.05
0
0.05
RER
0 10 20 30 40
0
2
4
10-3 R
0 10 20 30 40
-10
-5
0
10-3Nontradable output
0 10 20 30 40
-0.01
-0.005
0
Tradable output
0 10 20 30 40
-0.03
-0.02
-0.01
0
collateral constraint model I
0 10 20 30 40
-0.1
-0.05
0
0.05
Nontradable price
0 10 20 30 40
-0.05
0
0.05
Home tradable price
0 10 20 30 40
-10
-5
0
5
10-3Comsumption home tradable
Figure: One standard deviation µ shock

Conclusion
In this paper we document the di¤erent comovement of RER and
other macroeconomic aggregates between emerging economies and
developed SOE, especially the negative correlation between RER and
real interest rate.
Motivated by this evidence, we include the RER and real interest rate
data in the estimation of a two-sector model with imperfect
substitution between tradable and non-tradable goods and collateral
constraint with pecuniary e¤ect induced by relative price changes.
Estimation result shows that the model performs reasonably well in
explaining RER dynamics and its comovement with macroeconomics
aggregates, such as real interest rate and tby/GDP ratio.
Country premium shock is the main driving force of RER and real
interest rate variation and this helps to generate the negative
comovement between these two variables. So our paper provides
another evidence supporting the important role of country premium
shock in explaining emerging market business cycle.

Real Business Cycles in Emerging Economies

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