LTV Policy Simulation in DSGE Model
Iskandar Simorangkir
Nur M. Adhi Purwanto1
Abstract
We develop a small open economy DSGE model with financial frictions and banking sector
as in Gerali et al (2010). We modified the banking sector balance sheet from Gerali et al’s
model to include risk free assets and reserves, in addition to bank’s loan to households and
entrepreneurs, as part of bank’s asset portfolio choices. The main focus of the research is to
understand the transmission mechanism of LTV ratio requirement policy and how it will
interact with monetary policy.
Based on the model simulation, an increase in LTV ratio requirement for households’ lending
will lead to an increase in consumption and housing asset accumulation of the constrained
households. This will lead to a higher growth of aggregate demand. A higher growth in
aggregate demand will increase inflationary pressure and will prompt central bank to
increase the policy rate. The same dynamics applied to an increase in entrepreneur’s LTV
ratio requirement. Because the increase in GDP caused by the increase in entrepreneur’s
LTV ratio requirement is mostly comes from the higher growth of investment, inflationary
pressures is not as significant as in the previous case but central bank still need to respond
by increasing the policy rate.
Keywords: Macroprudential, LTV, DSGE
JEL Classification:
1
Iskandar Simorangkir (iskandarsim@bi.go.id) and Nur M. Adhi Purwato (adhipd@bi.go.id) are researchers in Bank
Indonesia and are responsible for the results and opinions presented in this paper. We would like to express our gratitude to
Mr. Harmanta, Mr. Fajar Oktiyanto and Mr. Andre Raymond that have made valuable contributions in this research.
1
I.
INTRODUCTION
A well-functioning financial system is necessary for an effective monetary policy
transmission. Simultaneously, monetary policy can also influence financial system stability
through its effect on financial condition and behavior of the financial market. Changes in
policy rate will have an effect on how agents in financial markets perceived the future
prospect of the economy and will influence their spending/investment decisions. Despite this,
Blanchard et al (2010) argues that the policy rate is not an appropriate tool to deal with many
financial system imbalances, such as excess leverage, excessive risk taking, or apparent
deviations of asset prices from fundamentals. As an example, they stated that increasing
policy rate to deal with excessively high asset price will result in undesirably higher output
gap. They proposed that macroprudential policy such as cap on loan-to-value ratio to be
employed to address these specific financial system imbalances.
Based on the simulation of the model developed in this research, an increase in LTV
ratio requirement for households’ lending will lead to an increase in consumption and
housing asset accumulation of the constrained households. This will lead to a higher growth
of aggregate demand and inflation. In order to increase households’ lending, the bank
reduces the amount of risk free asset from its portfolio and will cause an increase in its loan
to deposit ratio (LDR). In addition, allocating more assets with higher interest rate will also
increase bank’s profit that will lead to an increase in its capital. A higher growth in aggregate
demand will increase inflationary pressure and will prompt central bank to increase the policy
rate. The same dynamics applied to an increase in entrepreneur’s LTV ratio requirement.
Entrepreneurs will increase their consumption and investment because of the increase in
funding they acquired from the bank. This will lead to an increase in GDP. Because the
increase in GDP is mostly comes from the higher growth of investment, inflationary
pressures is not as significant as in the previous case but central bank still need to respond
by increasing policy rate.
The second chapter of this paper analyzes the theoretical and empirical literatures
related to financial frictions modeling and aggregate commercial bank’s characteristics in
Indonesia, and chapter three explains the model that we developed for this research.
Estimation and simulation result of the model will be presented in chapter four, while
conclusion will close the paper.
2
II.
LITERATURE REVIEW
2.1
Financial Friction in DSGE Model
Based on the current literatures, there are two basic approaches that can be utilized
to incorporate financial frictions into macroeconomic model: financial accelerator and
collateral constraints. Each of these approaches has its own strengths and weaknesses and
a growing numbers of literatures are still debating the merit of each approach.
The premise of the financial accelerator framework is that information asymmetry
between borrower and lender creates an external finance premium, reflecting the difference
between the costs of externally borrowed and internally generated funds. The external
borrowing premium varies intensely with borrower net worth and limits agents’ borrowing.
Borrowers’ net worth is defined as the value of assets minus outstanding obligations. In good
times, borrowers have higher net worth, raising their creditworthiness and lowering external
funding costs. Conversely, in bad times, lower net worth reduces creditworthiness, raising
borrowing costs. The countercyclical behavior of the external finance premium is the
mechanism amplifying and propagating responses of real output and investment to shocks.
For example, the initial response of output to a technology shock is amplified by an
associated increase in asset prices. The rise in asset prices increases borrower net worth,
leading to a decline in the external finance premium, and further boost to spending. The
financial accelerator helps to explain observed large swings in investment and hump-shaped
output responses to moderate interest rate changes.
Similar to the financial accelerator framework, the shock amplifying effect of asset
prices movements that interact with credit market imperfections is also the basic mechanism
in the collateral constraint framework. However, in contrast with the financial accelerator,
borrower net wealth directly affects borrowing limits instead of indirectly through an external
finance premium. In order to provide borrowers with an incentive to repay and for lenders to
rent contracts need to be secured by collateral. Durable assets such as lands, housing, or
capital usually serve as collateral.
The financial accelerator and the collateral constraint framework originally assumed
that borrowers can obtain funds directly from lenders without any financial intermediaries.
Introducing a banking sector into macroeconomic models provides an additional avenue for
incorporating financial frictions specifically linked to the cost of intermediation.
Most of macroprudential policy instruments work through the balance sheet of banks
or borrowers, and an appropriate modeling technique is needed to uncover the relatively
3
unknown effect of these instruments in each agent portfolio choices or spending decisions.
Dynamic Stochastic General Equilibrium (DSGE) model with rigorous treatment on the
microeconomic foundations describing the behavior of economic agents has been
considered to be the appropriate modeling technique for this purpose.2 Macroprudential
policy instruments are aimed to prevent the pro-cyclicality of the financial system, such as
cap on loan to value ratio, cap on debt-to-income ratio, countercyclical capital requirement
and time-varying reserve requirement. These instruments works through financial
intermediaries’ or borrowers’ balance sheet and expected to create a countercyclical
mechanism that would lessen the inherent pro-cyclicality of the financial system. Based on
this, the existence of financial frictions and explicit balance sheet of financial intermediaries
are necessary to properly model the transmission mechanism of macroprudential policy
instruments.
Gerali et al (2010) has published a highly cited paper which describe a closed
economy DSGE model with credit frictions and borrowing constraints, a monopolistically
competitive banking sector and a set of real and nominal frictions as in Christiano et al
(2005). In the model, there are entrepreneurs and two types of households: patient and
impatient households. The households consume, acquire housing asset and provide labor to
entrepreneurs. Entrepreneurs produce undifferentiated intermediate goods using labor
supplied by households and capital. Domestic retailers buy intermediate goods from
entrepreneurs and differentiate it at no cost. Domestic retailers’ prices are sticky. Housing
stock is assumed to be fixed. Patient households deposit their saving in the banks while
impatient households and entrepreneurs borrow from the banks. Both borrower agents are
subjected to binding collateral constraints that are tied to their durable assets (housing
assets for impatient households and capital asset for entrepreneurs). A stylized banks’
balance sheet includes loan to entrepreneurs and loan to household as assets, and deposits
and capital as liabilities. Banks accumulate capital from retained earnings and are subjected
to capital adequacy requirement set by the central bank. Banks are assumed to have some
degree of market power both in deposit and loan market. In the loan market, banks set
different rates for households’ and entrepreneurs’ loan. Margins charged on loan rate
depend on bank capital-to-assets ratio and on degree of interest rate stickiness in each
market.
2.2
2
Indonesia’s Commercial Bank Characteristics
See Roger and Vleck (2011)
4
Based on the current literatures that have tried to incorporate the banking sector in
DSGE model, it is usually assumed that commercial banks’ have a certain amount of market
power in deposit and loan market. Empirical researches in Indonesia have proven the
existence of this market power. One of them is Purwanto (2009) that conclude that the
dynamic of interest rate spread (defined as the difference between weighted average of loan
rate and weighted average of deposit rate) in Indonesia’s banking sector are mostly
influenced by the concentration level of the banking industry. Herfindahl-Hirschman Index
was used to measure Indonesia’s banking industry’s concentration level. Based on panel
model estimation using data from the period of January 2002 – April 2009, the decrease in
interest rate spread during the period is mostly caused by the increase in competition in the
banking sector which is the result of an increase in market share of most banks and a
decline in the market share of banks with large asset.
Another assumption that is also utilized in banking sector modeling is the existence
of commercial banks’ retail interest rate stickiness relative to the dynamic of the policy rate.
From theoretical point of views, this is actually the optimal behavior if the banks are facing
inelastic short term loan/deposit demand function which caused by a high switching cost
(Calem et al., 2006) or the existence of a fixed cost (menu cost) in changing the level of
interest rates (Berger dan Hannan, 1991). Other theoretical reason offered by economist for
interest rate stickiness is the bank’s motive to maintain a good relationship with its
customers by implementing interest rate smoothing to protect costumers from market or
policy rate fluctuations. This arrangement will allow banks to set higher interest rates when
the policy rate is low (Berger and Udell, 1992).
A rigid response of commercial bank’s retail interest rate to a shock from policy rate
can be observed in the impulse response shown in Figure 2.1. This impulse response is
based on bivariate VAR system3 which consist of the following endogenous variables: (1)
Policy rate (BI rate) and consumption loan rate; (2) BI rate and loan rate to
firm/entrepreneurs (weighted average of investment loan rate and working capital loan rate);
and (3) BI rate deposit rate (weighted average of all types of deposit). From Figure 2.1 we
can see a very limited short-term response of commercial bank’s retail interest rate to
changes on the policy rate, especially for consumption loan rate. Deposit rate and loan rate
to firms/entrepreneurs have similar responses. Although the responses of these two interest
rates are not as restricted as consumption loan rate, they still have a relatively high
stickiness.
3
Each VAR system also consists of exogenous variables: reserve ratio for VAR with deposit rate as endogenous variable;
bank’s capital, weight of risky asset in CAR calculation, and total loan for VAR with loan rate as endogenous variable.
5
Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of D(R_PINJAMAN_CONS) to D(BI_RATE)
Response of D(BI_RATE) to D(BI_RATE)
.4
.8
.3
.4
.2
.1
.0
.0
-.4
-.1
-.2
-.8
1
2
3
4
5
6
7
8
9
1
10
2
3
4
5
6
7
8
9
10
Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of D(BI_RATE) to D(BI_RATE)
Response of D(R_DPK) to D(BI_RATE)
1.00
.6
0.75
.4
0.50
.2
0.25
.0
0.00
-.2
-0.25
-0.50
-.4
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
Response to Cholesky One S.D. Innovations ± 2 S.E.
Response of D(R_PINJAMAN_ENT) to D(BI_RATE)
Response of D(BI_RATE) to D(BI_RATE)
.6
.8
.4
.4
.2
.0
.0
-.4
-.2
-.4
-.8
1
2
3
4
5
6
7
8
9
10
1
2
3
4
5
6
7
8
9
10
Figure 1.1 Impulse Response of bivariate VAR system consists of policy rates and commercial bank’s
retail interest rates as the endogenous variables
III.
The Model
The model that we develop is based on Gerali et al’s (2010). The main modifications
are related to the implementation of small open economy assumption and the addition of
government as one of the agent in the model. The model also incorporates standard DSGE
features such as habit persistence in consumption, adjustment cost in investment, sticky
prices and sticky wages.
In the model, there are entrepreneurs and two types of households: patient and
impatient households. The main difference among these three agents is in their discount
factors in which patient households have higher discount factor compared to impatient
households and entrepreneurs. The households consume, acquire and accumulate housing
asset, pay taxes to the government and provide labor to entrepreneurs. Entrepreneurs
produce undifferentiated intermediate goods using labor supplied by households and capital.
6
These goods are then sold to domestic retailers (for domestic market) and exporting retailers
(for foreign market). These two agents then differentiate the homogeneous intermediate
goods at no cost. Both domestic retailers’ and exporting retailer’s prices are sticky. Final
goods producer act as an aggregator that combines intermediate differentiated goods from
domestic retailers and from importing retailers for domestic consumption/investment
purposes.
Capital goods producers and housing producers utilize goods bought from final
goods producers to produce capital and housing asset using technology that are constrained
with investment adjustment cost. The existence of adjustment cost made possible the
condition in which we have different price level for capital assets, housing assets and
consumption goods.
There are two financial instruments that are provided by banks for economic agents
in the model: deposit and loan. Economic agents are facing borrowing constraint if they want
to borrow money from the bank. These borrowing constraints are linked to the value of the
collateral that they have, which are housing assets for impatient households and capital
assets for entrepreneurs. The different in discount factors among economic agents will
ensure the condition in equilibrium in which patient households deposit their money in the
banks and impatient households and entrepreneurs borrow from the banks.
The banks are operating in monopolistic competitive condition in which they have
market power in deciding interest rates for loan and deposit. Loan dispensed by the bank are
financed from total deposits acquired by the banks and from their own capital. We modified
Gerali et al’s model by adding risk free asset and reserve as part of banks’ asset portfolio
choices.
Besides borrowing from domestic commercial banks, entrepreneurs and
government also can borrow from foreign financial entities.
Households and Entrepreneurs
Patient households maximize their utility function by choosing the level of
consumption 𝑐𝑡𝑃 , the amount of leisure time 𝑛𝑡𝑃
and the amount of housing assets they
acquired 𝜒𝑡𝑃 .
max
𝑃
𝑐𝑡𝑃 (𝑖),𝜒𝑡 (𝑖),𝑛𝑡𝑃 (𝑖)
1−𝜎𝑐
𝑃
(𝑐𝑡𝑃 (𝑖)−𝜉𝑐𝑡−1
)
𝑡
∑∞
𝑡=0(𝛽𝑃 ) 𝜀𝑢,𝑡 [
1−𝜎𝑐
+ 𝜀χ,𝑡
𝜒𝑡𝑃 (𝑖)1−𝜎𝜒
1−𝜎𝜒
− 𝜀𝑛,𝑡
𝑛𝑡𝑃 (𝑖)1+𝜎𝑛
]
1+𝜎𝑛
... (3.1)
The parameter 𝜉 determines the level of external habit formation and 𝜀𝑢,𝑡 , 𝜀𝜒,𝑡 , 𝜀𝑛,𝑡 are
intertemporal, housing preference and labor preference shocks that have an AR(1) dynamics
with an iid errors.
7
Patient households revenue comes from labor income 𝑊𝑡 𝑛𝑡𝑃 , interest income from
𝐷 )𝑑
𝑃
deposit (1 + 𝑟𝑡−1
𝑡−1 , and dividend Π𝑡 (they are the owner of banks and retailers). They
spend their income to pay taxes to government𝑇𝑡𝑃 , consume, acquire housing assets and
save the remaining in the form of bank’s deposit𝑑𝑡 . The following is patient households’
budget constraint:
𝑃 (𝑖))
𝐷 )𝑑
𝑃
𝑃𝑡 𝑐𝑡𝑃 (𝑖) + 𝑃𝜒,𝑡 (𝜒𝑡𝑃 (𝑖) − (1 − 𝛿𝜒 )𝜒𝑡−1
+ 𝑑𝑡 (𝑖) = 𝑊𝑡 𝑛𝑡𝑃 (𝑖) + (1 + 𝑟𝑡−1
𝑡−1 (𝑖) − 𝑇𝑡 (𝑖) +
Π𝑡𝑃 (𝑖) ... (3.2)
In the budget constraint equation, consumption and housing asset are multiplied by
their prices to get their nominal values. Parameter 𝛿𝜒 is the depreciation level of the housing
assets own by the households.
Utility function for impatient households is very similar to the patient households’:
max𝐼
𝐼
𝑐𝑡𝐼 (𝑖),𝜒𝑡 (𝑖),𝑛𝑡 (𝑖),𝑏𝑡𝐼 (𝑖)
1−𝜎𝑐
𝐼
(𝑐𝑡𝐼 (𝑖)−𝜉𝑐𝑡−1
)
𝑡
∑∞
𝑡=0(𝛽𝐼 ) 𝜀𝑢,𝑡 [
1−𝜎𝑐
+ 𝜀χ,𝑡
𝜒𝑡𝐼 (𝑖)1−𝜎𝜒
1−𝜎𝜒
− 𝜀𝑛,𝑡
𝑛𝑡𝐼 (𝑖)1+𝜎𝑛
]
1+𝜎𝑛
... (3.3)
To finance their expenditures, besides having revenue from labor income 𝑊𝑡 𝑛𝑡𝐼 , impatient
household also borrow from the bank the amount of 𝑏𝑡𝐼 (𝑖). Because of this, impatient
household also have obligation to pay the previous period loan along with the interest
𝐵𝐼 )𝑏 𝐼
((1 + 𝑟𝑡−1
𝑡−1 ) as part of their expenditures.
𝐼 (𝑖))
𝐵𝐼 )𝑏 𝐼 (𝑖)
𝑃𝑡 𝑐𝑡𝐼 (𝑖) + 𝑃𝜒,𝑡 (𝜒𝑡𝐼 (𝑖) − (1 − 𝛿𝜒 )𝜒𝑡−1
+ (1 + 𝑟𝑡−1
= 𝑊𝑡 𝑛𝑡𝐼 (𝑖) + 𝑏𝑡𝐼 (𝑖) − 𝑇𝑡𝐼 (𝑖) ... (3.4)
𝑡−1
Total amount that can be borrowed by each impatient household is restricted by the
value of the housing assets own by the household multiplied by loan-to-value ratio 𝑚𝑡𝐼 .
(1 + 𝑟𝑡𝐵𝐼 )𝑏𝑡𝐼 (𝑖) ≤ 𝑚𝑡𝐼 𝐸𝑡 [𝑃𝜒,𝑡+1 (1 − 𝛿𝜒 )𝜒𝑡𝐼 (𝑖)] ... (3.5)
From microeconomic point of view (1-𝑚𝑡𝐼 ) can be interpreted as the proportional cost
of collateral repossession for bank in the case of default. From macroeconomic point of view,
the value of 𝑚𝑡𝐼 determine the amount of loan can be supplied by the bank for a certain
household for a certain value of their housing asset. It is assumed that the LTV ratio is not
depend on bank’s individual choices but a stochastic exogenous process that allow us to
study credit-supply restriction to the real sector of the economy.
The utility function of entrepreneurs is only based on the amount of the
consumption, 𝑐𝑡𝐸 :
8
𝑠
𝐸0 ∑∞
𝑠=0(𝛽𝐸 ) (𝜀𝑢,𝑡+𝑠
1−𝜎𝑐
𝐸 (𝑖)−𝜉𝑐 𝐸
(𝑐𝑡+𝑠
𝑡+𝑠−1 )
1−𝜎𝑐
) ... (3.6)
To finance their consumption, entrepreneur produces homogeneous intermediate
goods, 𝑦𝑊,𝑡 , with the following production function:
𝑦𝑊,𝑡 (𝑖) = 𝐴𝑡 [𝑢𝑡 (𝑖)𝑘𝑡−1 (𝑖)]𝛼 𝑛𝑡 (𝑖)1−𝛼 ... (3.7)
Where 𝐴𝑡 is the total factor productivity, 𝑢𝑡 𝜖[0, ∞) is the capital utilization rate, 𝑘𝑡 is the
capital stock and 𝑛𝑡 is the labor input.
To pay for their expenditures which include consumption, labor cost for production
purposes, capital accumulation, capital utilization rate adjustment cost and payment for the
previous period loan, entrepreneurs use revenue from selling their production goods and
from new loan acquired from the bank (𝑏𝑡𝐸 ) and from foreign financial entities (𝑏𝑡∗ ).
𝑃𝑡 𝑐𝑡𝐸 (𝑖) + 𝑊𝑃,𝑡 𝑛𝑃,𝑡 (𝑖) + 𝑊𝐼,𝑡 𝑛𝐼,𝑡 (𝑖) + 𝑃𝑘,𝑡 (𝑘𝑡 (𝑖) − (1 − 𝛿𝑘 )𝑘𝑡−1 (𝑖)) + 𝑃𝑡 𝜓(𝑢𝑡 (𝑖))𝑘𝑡−1 (𝑖) +
𝐸
𝐸 (𝑖)
∗
∗ (𝑖)
+ 𝑒𝑡 (1 + 𝜌𝑡−1 )(1 + 𝑟𝐵,𝑡−1
= 𝑃𝑊,𝑡 A𝑡 [𝑢𝑡 (𝑖)𝑘𝑡−1 (𝑖)]𝛼 [𝑛𝑡 (𝑖)]1−𝛼 +
(1 + 𝑟𝐵,𝑡−1
)𝑏𝑡−1
)𝑏𝑡−1
𝑏𝑡𝐸 (𝑖) + 𝑒𝑡 𝑏𝑡∗ (𝑖) ... (3.8)
Where 𝑃𝑘,𝑡 is the price of the capital goods, 𝑃𝑊,𝑡 is the price of the intermediate goods, 𝛿𝑘 is
the depreciation rate of capital goods, 𝜌𝑡 is the risk premium, 𝑏𝑡𝐸 is the amount of domestic
loan (from the banks), 𝑏𝑡∗ is the amount of foreign loan, 𝑒𝑡 is the exchange rates, 𝜓(𝑢𝑡 (𝑖)) is
the a adjustment cost function for changes in capital utilization.
Similar to impatient household, entrepreneur also subject to borrowing constraint that
is linked to the value of capital stock that they owned:
∗
𝐸
𝐸𝑡 [𝑒𝑡+1 (1 + 𝜌𝑡 )(1 + 𝑟𝐵,𝑡
)𝑏𝑡∗ (𝑖)] + (1 + 𝑟𝐵,𝑡
)𝑏𝑡𝐸 (𝑖) ≤ 𝑚𝑡𝐸 𝐸𝑡 [𝑃𝑘,𝑡+1 (1 − 𝛿𝑘 )𝑘𝑡 (𝑖)] ... (3.9)
Where 𝑚𝑡𝐸 is the ratio of loan-to-value for entrepreneurs with the same characteristics with
the previously mentioned𝑚𝑡𝐼 . Similar to Gerali et al (2010) and Iacoviello (2005), we also
assumed that shocks in the model is sufficiently small so that the variables are always
around their steady state level allowing the model to be solved by assuming a binding
borrowing constraints.
Producers
There are three producers in the model: capital goods producers, housing producers,
and final (consumption) goods producers.
9
Capital good producers operate in a perfectly competitive market and use
consumption goods to produce capital goods. Capital goods are produced from undepreciated previous period capital ((1 − 𝛿𝑘 )𝑘𝑡−1 ) and transformation of consumption goods
(𝑖𝑘,𝑡 ) with the following production function:
1
𝑘𝑡 = (1 − 𝛿)𝑘𝑡−1 + 𝜀𝑖,𝑡 (1 − 2 𝜅𝑘 (𝑖
2
𝑖𝑘,𝑡
𝑘,𝑡−1
− 1) ) 𝑖𝑘,𝑡 ... (3.10)
Where 𝜀𝑖,𝑡 is an AR(1) shock process with an iid error. Previous period capital goods are
directly transformed into new capital goods while transformations of consumption goods into
capital goods are subject to adjustment cost .
𝜅𝐾 > 0 ... (3.11)
The following is the utility function of capital goods producers:
𝑠
max ∑∞
𝑠=0(𝛽𝑝 ) (𝑃𝑘,𝑡+𝑠 𝑘𝑡+𝑠 − (𝑃𝑘,𝑡+𝑠 (1 − 𝛿)𝑘𝑡+𝑠−1 + 𝑃𝑡+𝑠 𝑖𝑘,𝑡+𝑠 )) ... (3.12)
𝑘𝑡
Housing producers have similar characteristics with capital goods producers with
also a similar production function:
1
𝜒𝑡 = (1 − 𝛿𝜒 )𝜒𝑡−1 + 𝜀𝑖𝜒,𝑡 (1 − 2 𝜅𝜒 (𝑖
𝑖𝜒,𝑡
𝜒,𝑡−1
2
− 1) ) 𝑖𝜒,𝑡 ... (3.13)
𝜅𝜒 > 0 ... (3.14)
The utility function is as follows:
𝑠
max ∑∞
𝑠=0(𝛽𝑝 ) (𝑃𝜒,𝑡 𝜒𝑡 − (𝑃𝜒,𝑡 (1 − 𝛿𝜒 )𝜒𝑡−1 + 𝑃𝑡 𝑖𝜒,𝑡 )) ... (3.15)
𝜒𝑡
Final good producer is the agent that combines goods from domestic retailers
𝑦𝐻,𝑡 (𝑗𝐻 ) and importing retailers 𝑦𝐹,𝑡 (𝑗𝐹 ) to produce final goods to be sold in a perfectly
competitive market. The production function of the agent is as follows:
𝑦𝑡 = [𝜂
𝜇
1+𝜇
1
1+𝜇
𝜇
1+𝜇
𝑦𝐻,𝑡 + (1 − 𝜂)
1
1+𝜇
1+𝜇
𝑦𝐹,𝑡 ]
... (3.16)
Where 𝜂 is the home bias parameter, and 𝜇 the parameter that determines elasticity of
substitution between domestic and foreign goods.
10
Optimization of the utility function will result in imported goods (𝑦𝐻,𝑡 ) and domestic
goods (𝑦𝐹,𝑡 ) demand equation, and also the price for the final (consumption) goods (𝑃𝑡 ):
1+𝜇
𝑦𝐻,𝑡 =
−
𝑃
𝜇
𝜂 ( 𝑃𝐻,𝑡 )
𝑡
... (3.17)
1+𝜇
𝑦𝐹,𝑡 = (1 −
𝑃𝑡
1
𝜇
−
−
𝑃
𝜇
𝜂) ( 𝐹,𝑡 )
𝑃𝑡
−
= 𝜂(𝑃𝐻,𝑡 )
1
𝜇
𝑦𝑡 ... (3.18)
−
+ (1 − 𝜂)(𝑃𝐹,𝑡 )
1
𝜇
... (3.19)
Retailers
There are three retailers in the model: domestic retailers, exporting retailers and
importing retailers. Domestic retailers buy undifferentiated intermediate goods from
entrepreneurs, transform them into differentiated goods and sell them to final goods
producer.
Exporting
retailers
also
buy
undifferentiated
intermediate
goods
from
entrepreneurs, transformed them into differentiated goods and sell them in international
market. Importing retailers buy undifferentiated intermediate goods from international
market, transform them into differentiated goods and sell them to final gods producers.
These three retailers assumed to be operating in monopolistic competitive market with price
setting behavior ala Calvo. In each period, there is (1 − 𝜃) probability4 of a certain retailer
will be able to re-optimize its price. For those which cannot re-optimize, their prices are set
according to the last period inflation rate.
For domestic retailers that are not re-optimizing their price, they will set the price
according to the following function: 𝑃𝐻,𝑡 = 𝑃𝐻,𝑡−1 𝜋𝑡−1 . This will result in the following
aggregate price at time t:
1
1−𝜀𝐻
𝑃𝐻,𝑡 = (𝜃𝐻 (𝑃𝐻,𝑡−1 𝜋𝐻,𝑡−1 )
1−𝜀𝐻 1−𝜀𝐻
+ (1 − 𝜃𝐻 ) (𝑃𝐻,𝑡 (𝑖))
)
... (3.20)
Log linearization of the first order condition of domestic retailer’s utility function will
result in the following equation:
1
𝛽
𝑃
𝜋̂𝐻,𝑡 = (1+𝛽 ) 𝜋̂𝐻,𝑡−1 + (1+𝛽
(𝜋̂𝐻,𝑡+1 ) +
)
𝑃
4
𝑃
(1−𝛽𝑃 𝜃𝐻 )(1−𝜃𝐻 )
̂W,t
(P
(1+𝛽𝑃 )𝜃𝐻
̂H,t ) ... (3.21)
−P
𝜃 ∈ [0,1]
11
We have similar arrangement for importing retailers that are not re-optimizing their
price which also used a similar function to determine their price level: 𝑃𝐹,𝑡 = 𝑃𝐹,𝑡−1 𝜋𝑡−1. The
aggregate price level of goods sold by importing retailers at time t is:
1
1−εF
PF,t = (θF (PF,t−1 πF,t−1 )
1−εF 1−εF
+ (1 − θF ) (PF,t (i))
)
... (3.22)
The log linearization of the FOC of importing retailer’s utility function is the following
equation:
1
β
π
̂F,t = (1+β ) π
̂F,t−1 + (1+βP ) (π
̂F,t+1 ) +
P
P
(1−βP θF )(1−θF)
(ŝt
(1+βP )θF
̂F,t ) ...(3.23)
−P
Exporting retailer buy domestic undifferentiated goods differentiate them at no cost
∗
and sell them to the foreign market with a price of 𝑃𝐻,𝑡
, expressed in foreign currency. It is
assumed that the price is sticky in the foreign currency. The demand equation for exporting
goods is:
∗
𝑦𝐻,𝑡
∗
𝑃𝐻,𝑡
−(1+𝜇𝐻∗ )
𝜇𝐻∗
= (𝑃 ∗ )
𝐻,𝑡
∗
𝑦𝐻,𝑡
... (3.24)
Where 𝑦𝐻∗ the output of exporting retailers where:
1+𝜇𝐻∗
1
1
∗
∗ (𝑗 ∗ )1+𝜇𝐻∗
𝑦𝐻,𝑡
= (∫0 𝑦𝐻,𝑡
𝑑𝑗𝐻∗ )
𝐻
... (3.25)
∗
And 𝑃𝐻,𝑡
is
∗
𝑃𝐻,𝑡
=
1 ∗
(∫0 𝑃𝐻,𝑡
−1
−𝜇𝐻∗
(𝑗𝐻∗ )𝜇𝐻∗ 𝑑𝑗𝐻∗ )
... (3.26)
Moreover, it is assumed that foreign demand is given by the following equation:
∗
𝑦𝐻,𝑡
= (1
−(1+𝜇𝐻∗ )
𝜇𝐻∗
𝑃∗
− 𝜂 ∗ ) ( 𝐻,𝑡
)
𝑃𝑡∗
𝑦𝑡∗ ... (3.27)
Similar to the other retailers in the model, price determination of exporting retailers is
based on standard Calvo approach, where the probability of changing the price is (1 − 𝜃) the
probability of not re-optimizing the price is 𝜃. For the ones that are not re-optimizing the
∗
∗
∗
price, they set the price according to the following equation: 𝑃𝐻,𝑡
= 𝑃𝐻,𝑡−1
𝜋𝑡−1
. The aggregate
price at time t is:
12
1
∗
𝑃𝐻,𝑡
=
1−𝜀 ∗
∗
∗
(𝜃𝐻∗ (𝑃𝐻,𝑡−1
𝜋𝐻,𝑡−1
) 𝐻
+ (1 −
∗
1−𝜀𝐻
1−𝜀∗𝐻
∗ (𝑖))
𝜃𝐻∗ ) (𝑃𝐻,𝑡
)
...(3.28)
The log linearization of the FOC of the utility function of exporting retailers will result
in the following equation:
1
β
π
̂∗H,t = (1+β ) π
̂∗H,t−1 + (1+βP ) (π
̂ ∗H,t+1 ) +
P
P
(1−βP θ∗H )(1−θ∗H )
̂W,t
(P
(1+βP )θ∗H
∗
̂H,t
− ŝt +P
) ... (3.29)
Bank
Bank holds a very important function in the financial intermediation process of the
model. The only financial instrument that patient households can use for saving is bank’s
deposit, and the only financial instruments that can be used by impatient households to help
finance their expenditure is bank’s loan. We modified the original model of Gerali et al’s
(2010) in terms of its financial intermediation process by allowing a few agents to have
access to foreign financing. For simplification, we only allow entrepreneurs and government
to have this access.
As with Gerali et al (2010), we assume that the banking sector have a monopolistic
power in the deposit and loan market with rigidities in setting the retail rates in responding to
the dynamic of the policy rates. We design a more detail balance sheet for the banking
sector which includes risk free assets and reserves in addition to bank’s loan to households
and entrepreneur as part of bank’s asset portfolio choices. This is in accordance to the
current condition of Indonesian (aggregate) bank’s balance sheet which includes a
significant amount of excess liquidity held in a form of risk free asset such as Bank
Indonesia’s Certificate (SBI) and Government Bond (SBN). We consider this as a very
important modification since this might influence the transmission mechanism of monetary
and macroprudential policy.
The basic concept of bank’s business process is mostly borrowed from Gerali et al
(2010) with modification to accommodate a more detail balance sheet that has been design
to reflect Indonesia’s current banking industry condition. Each bank consists of three
different units: wholesale, loan branch and deposit branch.
The wholesale unit is assumed to be operating in a perfect competition and manage
the overall balance sheet of the bank:
𝑅𝐹𝑡 + 𝐵𝑡 = (1 − Γt )𝐷𝑡 + 𝐾𝑡𝑏 ... (3.30)
13
Where 𝑅𝐹𝑡 (Risk free Asset), 𝐵𝑡 (Total loan) and 𝐷𝑡 (Deposit) are the choice variables of the
wholesale unit. Γt is the reserve ratio and 𝐾𝑡𝑏 is the bank’s capital.
It is assumed that bank does not have access to outside funding for their capital and
the only way to increase its capital is from retained earnings:
𝑏
𝑏
𝐾𝑡𝑏 = (1 − 𝛿 𝑏 )𝐾𝑡−1
+ 𝑤 𝑏 𝑗𝑡−1
... (3.31)
Where 𝑗𝑡𝑏 is the overall profit of the three unit of the bank, (1 − 𝑤 𝑏 ) proportion of the profit
transferred to patient households as dividend; and 𝛿 𝑏 is the resources used to manage
bank’s capital. The dividend to profit ratio is assumed to be exogenous and constant.
The utility function for the wholesale unit is:
max
{𝑅𝑖𝑠𝑘_𝑓𝑟𝑒𝑒𝑡 ,𝐵𝑡 ,𝐷𝑡 }
𝑠
𝐸0 ∑∞
𝑠=0(𝛽𝑃 )
𝜆𝑃
𝑡+𝑠
[Γt+s 𝐷𝑡+𝑠
𝜆𝑃
𝑡
− Γt+s+1 𝐷𝑡+𝑠+1 + (1 + 𝑟𝑡+𝑠 )𝑅𝐹𝑡+𝑠 − 𝑅𝐹𝑡+𝑠+1 +
𝑏
𝑑
𝑏
−
(1 + 𝑅𝑡+𝑠
)𝐵𝑡+𝑠 − 𝐵𝑡+𝑠+1 + 𝐷𝑡+𝑠+1 − (1 + 𝑅𝑡+𝑠
)𝐷𝑡+𝑠 + Δ𝐾𝑡+𝑠+1
𝑏
𝜅𝐾𝑏
𝐾𝑡+𝑠
(
𝑏
2
𝜔𝑡+𝑠 𝐵𝑡+𝑠
2
𝑏
− 𝑣𝑏,𝑡+𝑠 ) 𝐾𝑡+𝑠
]
... (3.32)
s.t. 𝑅𝐹𝑡 + 𝐵𝑡 = (1 − Γt )𝐷𝑡 + 𝐾𝑡𝑏 ... (3.33)
Where
𝜆𝑃
𝑡+𝑠
𝜆𝑃
𝑡
is the stochastic discount factor, 𝑅𝑡𝑏
is the wholesale loan rate, 𝑅𝑡𝑑
is the
wholesale deposit rate, and 𝑟𝑡 is the policy rate.
FOC of the wholesale unit’s utility function show equations that determine the level of
loan and deposit rate given to loan branch and deposit branch:
𝑅𝑡𝑏 − 𝑟𝑡 = −(𝜔𝑡𝑏 )𝜅𝐾𝑏 (
𝐾𝑡𝑏
𝜔𝑡𝑏 𝐵𝑡
− 𝑣𝑏,𝑡 ) (
𝐾𝑡𝑏
𝜔𝑡𝑏 𝐵𝑡
2
) ... (3.34)
𝑟𝑡 (1 − Γt ) = 𝑅𝑡𝑑 ... (3.35)
When the Capital Adequacy Ratio (𝐶𝐴𝑅 =
𝐾𝑡𝑏
𝜔𝑡𝑏 𝐵𝑡
) is equal to the minimum level ( 𝑣𝑏,𝑡 ),
then wholesale loan rate wil be equal to plicy rate ( 𝑅𝑡𝑏 = 𝑟𝑡 ). While when CAR is above the
minimum level (𝐶𝐴𝑅 > 𝑣𝑏,𝑡 ), the bank will react to lowered it by increasing the total loan 𝐵𝑡
(by lowering the 𝑅𝑡𝑏 ), so that the level of CAR can be close to the minimum level required by
the central bank( 𝐶𝐴𝑅 ≈ 𝑣𝑏,𝑡 ).
When the central bank decide that the minimum reserve requirement is equal to zero
(Γt = 0), then the ratio of the ratio of wholesale unit’s deposit rate to policy rate will be equal
14
to 1(
𝑅𝑡𝑑
𝑟𝑡
= 1), While in the condition of reserve requirement greater than zero (Γt > 0), bank is
facing an increase in opportunity cost and will react by lowering the cost by by lowering the
deposit rate (𝑅𝑡𝑑 ) to decrease the amount of deposit acquired.
Following modification done by Angelini et al (2011), we also include the risky asset
weight variable (𝜔𝑡𝑏 ) to accommodate a more realistic calculation of CAR in the model. This
variable will be multiplied by total loan to get the risk weighted asset value of the bank. The
addition of this variable also made possible the inclusion of default risk as one of the variable
that determine the dynamics of CAR by allowing the weight variable to be determined by the
𝑏𝐸
bank’s loan composition ( 𝑏𝑡𝐼 ) and the default risk (𝑛𝑝𝑙𝑡 ).
𝑡
𝑏
𝜔𝑡𝑏 = 𝜌𝜔 𝜔𝑡−1
+ (1 − 𝜌𝜔 )𝛼𝑎
𝑏𝑡𝐸
𝑏𝑡𝐼
+ (1 − 𝜌𝜔 )𝛼𝑏 𝑛𝑝𝑙𝑡 ... (3.36)
We use non-performing loan as the proxy for default risk and assumed that they have an
AR(1) dynamic with iid error term.
We also add ad hoc equations that determine the dynamic of reserve ratio chosen by
the bank. We firstly determined the dynamic of reserve requirement ratio (Γ̂𝑡𝑟 ) set by the
central bank as follows (after log linearization):
𝑟
Γ̂𝑡𝑟 = 𝜌Γ Γ̂𝑡−1
+ 𝑒̂ Γr ,𝑡 ... (3.37)
This reserve requirement ratio then will influence the amount of excess reserve (𝜀̂𝑡Γ ) held by
the bank:
Γ
𝜀̂𝑡Γ = 𝜌ε 𝜀̂𝑡−1
+ (1 − 𝜌ε ) Γ̂𝑡𝑟 + 𝑒̂Γ,𝑡 ... (3.38)
And the dynamic of the bank’s reserve ratio is as follows:
Γ̂t = 𝜆Γ Γ̂𝑡𝑟 + (1 − 𝜆Γ )𝜀̂𝑡Γ ... (3.39)
In this model, market power of the bank is determine by the (steady state) value of
the elasticity of demand for deposit and loan. The lower the absolute value of the elasticity,
the higher the monopoly power held by the bank. It is assumed that loan that distributed by
the bank is a CES (Constant Elasticity of Substitution) composite basket of a slightly
differentiated product offered by branch of bank-j with elasticity of substitution determined by
bE
the following variables εbH
t , εt . The same mechanism is also assumed for deposit with
variable εdt act as the variable that determines the elasticity of substitution. These three
variables will influence the mark-up and mark-down value of the bank’s retail interest rates.
15
In other words, these three variables will determine the bank’s interest rate spread (the
difference between the policy rate and the bank’s retail interest rate). Following Gerali et al
(2010), it is assumed that these variables have a stochastic process and changes in the
value of the variables are interpreted as changes in the commercial bank’s retail interest
rates that happened outside the influence of the policy rate.
The following are equations for loan demand by entrepreneur (bEt ) and impatient
households (bIt ):
bIt (j)
bEt (j)
rbH
t (j)
=(
rbH
t
rbE
t (j)
=(
rbE
t
−εbH
t
bIt ... (3.40)
)
−εbE
t
)
bEt ... (3.41)
Patient household’s demand for deposit’s (dt ) equation is:
𝑟𝑡𝑑 (𝑗)
𝑑𝑡 (𝑗) = (
𝑟𝑡𝑑
)
−𝜀𝑡𝑑
𝑑𝑡 ... (3.42)
Loan branch received loans (𝐵𝑡 ) from wholesale unit with interest rate equal to 𝑅𝑡𝑏 ,
and then distribute them to households and entrepreneurs by applying two different
markups. To implement interest rate stickiness and to study the implication of imperfect bank
pass-through, it is assumed the loan branch is subjected to quadratic adjustment cost in
setting the loan rates. The cost are determined by parameter 𝜅𝑏𝐸 and 𝜅𝑏𝐻 . The utility
function for the loan branch is as follows:
max𝑏𝐸
𝑏𝐻
(𝑗),𝑟𝑡 (𝑗)}
{𝑟𝑡
𝑠
𝐸0 ∑∞
𝑠=0(𝛽𝑃 )
2
𝑏𝐻 𝐼
1) 𝑟𝑡+𝑠
𝑏𝑡+𝑠 −
𝑏𝐻 (𝑗)
𝜆𝑃
𝜅𝑏𝐻 𝑟𝑡+𝑠
𝑡+𝑠
𝑏𝐻 (𝑗)𝑏 𝐼 (𝑗)
𝑏𝐸 (𝑗)𝑏 𝐸 (𝑗)
𝑏
(𝑗)
[𝑟
+
𝑟
−
𝑅
𝐵
−
(
𝑡+𝑠
𝑡+𝑠
𝑡+𝑠
𝑡+𝑠
𝑡+𝑠
𝑡+𝑠
𝑏𝐻 (𝑗)
𝜆𝑃
2
𝑟𝑡+𝑠−1
𝑡
𝑏𝐸 (𝑗)
𝜅𝑏𝐸 𝑟𝑡+𝑠
(
𝑏𝐸
(𝑗)
2 𝑟𝑡+𝑠−1
−
2
𝑏𝐸 𝐸
− 1) 𝑟𝑡+𝑠
𝑏𝑡+𝑠 ] ... (3.43)
Subject to
𝑏𝑡𝐼 (𝑗) = (
𝑏𝑡𝐸 (𝑗)
𝑟𝑡𝑏𝐻 (𝑗)
=(
𝑟𝑡𝑏𝐻
𝑟𝑡𝑏𝐸 (𝑗)
𝑟𝑡𝑏𝐸
−𝜀𝑡𝑏𝐻
)
−𝜀𝑡𝑏𝐸
)
𝑏𝑡𝐼 ... (3.44)
𝑏𝑡𝐸 ... (3.45)
𝐵𝑡 (𝑗) = 𝑏𝑡 (𝑗) = 𝑏𝑡𝐼 (𝑗) + 𝑏𝑡𝐸 (𝑗) ... (3.46)
16
Similar to loan branch, deposit branch collects deposit (𝑑𝑡 ) from households and
forward them to the wholesale unit and set the deposit rate 𝑟𝑡𝑑 . Utility function of the deposit
branch is as follows:
𝑠
max
𝐸0 ∑∞
𝑠=0(𝛽𝑃 )
𝑑
{𝑟𝑡 (𝑗)}
𝜆𝑃
𝜅
𝑟 𝑑 (𝑗)
𝑡+𝑠
𝑑 (𝑗)𝑑
𝐷
(𝑗) − 𝑑 ( 𝑑𝑡+𝑠
[𝑅𝑡+𝑠
𝐷𝑡+𝑠 (𝑗) − 𝑟𝑡+𝑠
𝑡+𝑠
𝑃
𝜆𝑡
2 𝑟𝑡+𝑠−1 (𝑗)
2
𝑑
− 1) 𝑟𝑡+𝑠
𝑑𝑡+𝑠 ] ... (3.47)
subject to
𝑟𝑡𝑑 (𝑗)
𝑑𝑡 (𝑗) = (
𝑟𝑡𝑑
)
−𝜀𝑡𝑑
𝑑𝑡 ... (3.48)
𝐷𝑡 (𝑗) = 𝑑𝑡 (𝑗) ... (3.49)
Government and Central Bank
Government collects taxes and borrows from domestic market (banks) and foreign
market to finance it’s expenditures.The government’s budget constraint is as follows:
∗
∗
∗
𝑃𝑡 𝑔𝑡 + (1 + 𝑟𝐵,𝑡−1
)𝑒𝑡 𝑏𝐺,𝑡−1
+ (1 + 𝑟𝑡−1 )𝑏𝐺,𝑡−1 = (𝑇𝑡𝑃 + 𝑇𝑡𝐼 ) + 𝑒𝑡 𝑏𝐺,𝑡
+ 𝑏𝐺,𝑡 ... (3.50)
∗
Where 𝑔𝑡 is government expenditures that is modeled as an AR(1) process, 𝑏𝐺,𝑡
is
government foreign financing that is also modeled as an AR(1) process, 𝑇 𝑃 and 𝑇𝑡𝐼 are
taxes collected from patient and impatient households.
In setting the policy rate (𝑟𝑡 ), the central bank are assumed to follow Taylor Rule
based equation:
(1 + 𝑟𝑡 ) = (
1+𝑟𝑡−1 𝜙𝑅
1+𝑟̅
)
𝜋
(( 𝑡 )
𝜋
̅𝑡
𝜙𝜋
𝑦̃
( ̅̃𝑡)
𝑦
𝜙𝑦 1−𝜙𝑅
)
𝜀𝑟,𝑡 ... (3.51)
Where 𝜙𝜋 and 𝜙𝑦 are weight for inflation and output stabilization, 𝑟̅
nominal steady state
interest rate and 𝜀𝑡𝑟 is the i.i.d. shock to monetary policy with normal distribution and
standard deviation 𝜎𝑟 .
Market Clearing Condition
To close the model we need to have equation for market clearing condition for all the
goods produced by final goods producers, for intermediate homogeneous goods produced
by entrepreneurs and housing market. In addition to those equations, because the economy
17
is assumed to be a small open economy we also need to specify balance of payment
equation, the definition of GDP and the risk premium equation. In accordance to SchmittGrohe and Uribe (2003), the risk premium is defined as a function of total foreign loan to
GDP ratio.
Final Goods Producers Output
𝑦𝑡 = 𝑐𝑡 + 𝑖𝑘.𝑡 + 𝑖𝜒,𝑡 + 𝑔𝑡 + 𝜓(𝑢𝑡 )𝑘𝑡−1 ... (3.52)
𝑐𝑡 = 𝛾 𝐼 𝑐𝑡𝐼 + 𝛾 𝑃 𝑐𝑡𝑃 + 𝛾 𝐸 𝑐𝑡𝐸 ... (3.53)
Intermediate Homogenous Goods Market
1
1
∗ (𝑗)𝑑𝑗
= 𝑦𝑊,𝑡 ... (3.54)
∫0 𝑦𝐻,𝑡 (𝑗)𝑑𝑗 + ∫0 𝑦𝐻,𝑡
Housing Market
𝛾 𝑃 𝜒𝑡𝑃 + 𝛾 𝐼 𝜒𝑡𝐼 = 𝜒𝑡 ... (3.55)
Balance of Payment
∗ )𝜌
∗
∗
∗
∗
𝑃𝐹,𝑡 𝑦𝐹,𝑡 + 𝑒𝑡 (1 + 𝑟𝑡−1
𝑡−1 𝑏𝑡𝑜𝑡,𝑡−1 = 𝑒𝑡 𝑃𝐻,𝑡 𝑦𝐻,𝑡 + 𝑒𝑡 𝑏𝑡𝑜𝑡,𝑡 ... (3.56)
Where
∗
∗
𝑏𝑡𝑜𝑡,𝑡
= 𝑏𝑡∗ + 𝑏𝐺,𝑡
... (3.57)
GDP
∗
∗
𝑃𝑡 𝑦̃𝑡 = 𝑃𝑡 𝑦𝑡 + 𝑒𝑡 𝑃𝐻,𝑡
𝑦𝐻,𝑡
− 𝑃𝐹,𝑡 𝑦𝐹,𝑡 ... (3.58)
Risk Premium
(1 + 𝜌𝑡 ) = 𝑒𝑥𝑝 (−𝜚
∗
𝑒𝑡 𝑏𝑡𝑜𝑡,𝑡
𝑃𝑡 𝑦̃𝑡
) 𝜀𝜌,𝑡 ... (3.59)
18
IV.
ESTIMATION AND SIMULATION
4.1
Estimation
For estimation purposes, we use quarterly data from quarter 1, 2004 until quarter 4,
2011. For the real sector, we use the following data: real consumption, real investment,
government expenditure, real export, real import, CPI inflation, import deflator, export
deflator and exchange rate. For external sector, we use the same data utilized by Bank
Indonesia’s core model which are world GDP, USA’s inflation and LIBOR.
For the financial/banking sector we use the following data: policy rate (BI rate),
deposit rate (weighted average), loan rate to households (weighted average), loan rate to
firms/entrepreneurs (weighted average), bank’s risk free asset in the form of BI’s certificates
(SBIs) and government’s bond (SBN), bank’s reserve (including cash in vaults) and nonperforming loan in the banking sector.
In determining the steady state values of the variables in the real sector, we use the
mean of the HP filter values of the variables during the estimation period as our main guide.
We then adjust the values based on our judgment on domestic and external economic
conditions during the period. We also use the same approach in determining the steady
state values for the banking sector variables. In addition we also find guidance from Gunadi
and Budiman (2011) which have done research on the optimal portfolio composition of
commercial banks in Indonesia. A complete list of the steady state values of the variables of
the model can be seen in the appendix (Table A1)
Some of the parameters used in the model are calibrated using the values utilized by
similar models in Bank Indonesia and also from related empirical researches. Capital share
in the production function is set to the value equal to 0.54, in accordance to the estimation of
MODBI model (Medium term forecasting model of Bank Indonesia).The parameter for capital
utilization is based on the value used by Gerali et al (2010). The value of home bias
parameter is determined based on the mean of HP filter values of Indonesia’s import to
absorption ratio during the estimation period. Parameter that govern the elasticity of
substitution between domestic and foreign goods, and elasticity of substitution for export
goods are based on the estimation done by Zhang and Verikios (2006)5. The Calvo
parameters for labor are based on the estimation of BISMA model (2009).
The same approaches that we use to determine the values of the calibrated
parameter are also employed in determining the values of the prior for the estimated
5
We use the CES based estimation that is in accordance with the assumption of the model used in this research.
19
parameters. For
𝜿𝒅 , 𝜿𝒃𝒆
and 𝜿𝒃𝒊
, the prior values are based on the estimation of
immediate pass-through of policy rate to commercial bank’s retail interest rates done by
Harmanta and Purwanto (2012).For the Taylor rule parameter (𝝋𝒓 , 𝝋𝝅 and 𝝋𝒚 ), the prior
values are based on the values used by ARIMBI model (core model of Bank Indonesia).
Prior values for habit persistence parameter are based on the estimation of BISMA model
(2009). A complete list of the prior and posterior values of the estimated parameters can be
seen in the Appendix (Table A3).
4.2
Simulation
In this section, we will discuss the impulse response dynamics of the model. The
discussion is focused on the responses from shock to monetary and LTV ratio policies.
BI Rate
Loan Rate to Household
1
Loan Rate to Firm
0.2
Deposit Rate
0.5
Deposit
0.5
1
0.5
0
0
0
0
-0.2
-0.5
-0.5
-1
0
-0.5
10
20
30
40
10
Bank Capital
20
30
40
Total Loan
0.5
10
20
30
40
10
Loan to Household
1
20
30
40
5
0.5
0
0
20
30
40
-2
LDR
0.5
0
0
-0.5
-1
20
30
40
-1
20
30
40
-5
10
20
30
40
-0.5
Spread Loan rate to firm
10
20
30
40
-2
0.5
0.5
0
0
10
20
30
40
-0.5
10
Exchange Rate
20
30
40
-0.5
10
Output
20
30
40
-1
Consumption
1
0.2
1
0
0
0
-0.5
Housing Investment
10
20
30
40
-1
10
Capital Investment
1
20
30
40
10
Export
0.5
20
20
40
30
40
30
40
-1
10
20
30
Import
0.5
0
0.5
0
0
0
-1
-2
-0.2
10
Total Invesment
0
40
30
0
0.5
30
40
0.5
0
20
20
CAR
0.5
10
10
Spread deposit rate
-0.5
CPI Inflation YoY
-0.5
30
0
10
-0.5
10
40
2
Spread Loan rate to HH
0.5
30
4
-1
10
20
Risk Free
0
0
-0.5
10
Loan to Firm
-0.5
10
20
30
40
-0.5
10
20
30
40
-1
10
20
30
40
-0.5
10
20
Shock R
Figure 4.1. Impulse Responses: Policy (BI) Rate Shock
One percent increase in policy rate will be transmitted to changes in commercial
bank’s retail interest rate. These changes are influenced by the size of the mark-up or markdown and the level of stickiness of each interest rate. Deposit rate has the highest increase
because it has the lowest stickiness level and relatively low mark-down value. Although
commercial bank in Indonesia applies a high mark-up values to household’s loan rate, but it
also has the highest stickiness level. This combination will result in a response of only 0.1%
increase in household’s loan rate. The relatively high stickiness level make the spread of
household loan rate to BI rate decrease 0.6%. This decline in spread only happens for 3
20
40
periods and the spread will return to the steady state value at period 4. The same dynamic
happen to entrepreneur’s loan rate. This rate only increases 0.2% that result in a decline of
0.4% in the spread with BI rate. The spread returns to the steady state level at period 3.
Increase in loan rate will make the demand for loan from households and
entrepreneurs decreases and will result in a 1% decrease in total loan dispensed by the
bank. This will encourage commercial bank to increase risk free asset in its portfolio to avoid
further loss of revenue. In addition, the changes in commercial bank’s portfolio will result in
1% decrease in the aggregate bank’s Loan to Deposit Ratio (LDR).
Increase in deposit rate and loan rate to households will both induced a decrease in
consumption. While increase in the loan rate of both households and entrepreneurs results
in a decrease in investment of capital goods and housing assets. In addition, increase in
entrepreneurs’ loan rate will also result in an increase in exchange rate that will put
pressures to export. Import is also decreasing because the declining consumption and
investment.
BI Rate
Loan Rate to Household
Loan Rate to Firm
Deposit Rate
Deposit
0.2
0.2
0.2
0.1
2
0
0
0
0
0
-0.2
10
20
30
40
-0.2
10
Bank Capital
2
0
1
-0.2
0
20
30
30
40
-0.2
Total Loan
0.2
10
20
40
LDR
10
20
30
40
20
10
Loan to Household
30
40
20
30
40
-2
0
0
0
-2
-5
-1
Spread Loan rate to HH
20
30
40
Spread Loan rate to firm
10
20
30
40
-4
0.05
0.05
2
0.5
0
0
0
0
20
30
40
-0.1
Output
10
20
30
40
-0.05
20
30
40
-0.05
20
30
20
30
40
40
10
20
30
40
0.2
0.2
1
0
0
0
0
0
20
30
40
20
30
Shock mi
40
-0.2
10
20
30
40
-0.2
10
20
30
Impatient HH Consumption
-2
0.2
10
Exchange Rate
10
40
Impatient HH Stock of Housing
5
-0.2
CPI Inflation YoY
10
30
CAR
0.1
10
10
Spread deposit rate
1
0
20
Risk Free
1
10
10
Loan to Firm
5
10
-0.1
40
-1
10
20
30
40
-5
10
20
30
LTV for HH
2
1
0
10
BI rate fixed for 4 quarters
BI rate based on taylor rule
Figure 4.2. Impulse Response: Shock to household's LTV ratio
21
40
An increase in LTV ratio requirement for household loan will lead to an increase in
consumption and housing asset accumulation of the constrained households. This will lead
to a higher growth of aggregate demand and inflation. In order to increase households’
lending, the bank reduces the amount of risk free asset from its portfolio and will cause an
increase in its loan to deposit ratio (LDR). In addition, allocating more assets with higher
interest rate will also increase bank’s profit that will lead to an increase in its capital. A higher
growth in aggregate demand will increase inflationary pressure and will prompt central bank
to increase the policy rate. This will lead to an increase in commercial bank’s retail interest
rates. But this increase is not significant because of the relatively high level of stickiness that
these interest rates have.
BI Rate
Loan Rate to Household
Loan Rate to Firm
Deposit Rate
Deposit
0.1
0.05
0.05
0.05
0.5
0
0
0
0
0
-0.1
10
20
30
40
-0.05
10
Bank Capital
20
30
40
-0.05
Total Loan
10
20
30
40
-0.05
10
Loan to Household
20
30
40
-0.5
Loan to Firm
1
1
1
2
0
0
0
0
0
10
20
30
40
-1
LDR
10
20
30
40
-1
Spread Loan rate to HH
10
20
30
40
-1
Spread Loan rate to firm
10
20
30
40
-2
0.05
0.05
1
0
0
0
0
0
20
30
40
-0.05
Output
10
20
30
40
-0.05
CPI Inflation YoY
10
20
30
40
-0.05
Exchange Rate
10
20
30
40
-1
Entrepreneur Consumption
0.1
0.05
0.2
0.01
0
0
0
0
0
10
20
30
40
-0.1
Capital Investment
2
0
1
10
20
30
20
30
40
-0.05
10
20
30
40
-0.2
10
20
30
20
30
40
10
20
30
40
40
-0.01
10
20
30
40
LTV for Entrepreneur
2
-2
10
40
Intermediate Good Price
0.5
-0.5
30
CAR
0.05
10
10
Spread deposit rate
0.5
-0.5
20
Risk Free
0.2
-0.2
10
40
0
10
20
30
Shock me
40
BI rate fixed for 4 quarters
BI rate based on taylor rule
Figure 2. Impulse Response: Shock to entrepreneur's LTV ratio
Increase in LTV ratio requirement for entrepreneur will allow entrepreneur to have
more access to domestic and foreign financing and will result in an increase in investment,
22
consumption and the overall GDP. To accommodate increase in loan distributed to
entrepreneurs, bank diverts some of the risk free assets that they have and invest more in
loan to entrepreneurs. This will result in an increase in Loan to Deposit Ratio. Because the
increase in GDP is mostly comes from the higher growth of investment, inflationary
pressures is not as significant as in the previous case but central bank still need to respond
by increasing policy rate.
V.
CONCLUSION
We develop a small open economy DSGE model with financial frictions and banking
sector as in Gerali et al (2010). We modified the banking sector balance sheet from Gerali’s
model to include risk free assets and reserves, in addition to bank’s loan to households and
entrepreneur, as part of bank’s asset portfolio choices. This is in accordance to the current
condition of Indonesian (aggregate) bank’s balance sheet which includes a significant
amount of excess liquidity held in a form of risk free asset such as Bank Indonesia’s
Certificates (SBI) and Government’s Bonds (SBN). The main focus of the research is to
understand the transmission mechanism of LTV ratio requirement policy and how it will
interact with monetary policy.
Based on the model simulation, an increase in LTV ratio requirement for households’
lending will lead to an increase in consumption and housing asset accumulation of the
constrained households. This will lead to a higher growth of aggregate demand and inflation.
In order to increase households’ lending, the bank reduces the amount of risk free asset
from its portfolio and will cause an increase in its loan to deposit ratio (LDR). In addition,
allocating more assets with higher interest rate will also increase bank’s profit that will lead to
an increase in its capital. A higher growth in aggregate demand will increase inflationary
pressure and will prompt central bank to increase the policy rate. The same dynamics
applied to an increase in entrepreneur’s LTV ratio requirement. Entrepreneurs will increase
their consumption and investment because of the increase in funding they acquired from the
bank. This will lead to an increase in GDP. Because the increase in GDP is mostly comes
from the higher growth of investment, inflationary pressures is not as significant as in the
previous case but central bank still need to respond by increasing policy rate.
23
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Camilo E Tovar, 2008. "DSGE models and central banks," BIS Working Papers 258, Bank
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banking in a DSGE model of the euro area,"Temi di discussione (Economic working
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Catatan Riset No. 14/ 39 /DKM/BRE/CR, Bank Indonesia, Desember.
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Iacoviello, M. ,2005, “House Prices, Borrowing Constraints and Monetary Policy in the
Business Cycle" American Economic Review, Vol. 95(3), pp. 739-764.
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Vlcek,
Jan & Scott Roger, 2012. "Macrofinancial Modeling at Central Banks: Recent
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Zhang, X. & Verikios, G. ,2006, “Armington Parameter Estimation for a Computable General
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25
Appendix
Table A1. Steady State Values
Variables
Consumption to GDP ratio
Capital investment to GDP ratio
Housing investment to GDP ratio
Government expenditure to GDP ratio
Import to absorption ratio
Export to output ratio
Loan to HH to GDP ratio
Loan to entrepreneur to GDP ratio
Deposit to GDP ratio
Importer’s profit margin
Exporter’s profit margin
Domestic retailer’s profit margin
BI rate *
Rate on loan to HH*
Rate on loan to entrepreneur*
Rate on deposit*
Foreign interest rate*
CAR
Bank’s profit to total asset ratio
NPL ratio
Deposit to bank’s total asset ratio
Bank’s capital to total asset ratio
Loan to bank’s total asset ratio
Risk free asset to bank’s total asset
ratio**
Reserve to total asset ratio
Values
0.59
0.14
0.08
0.09
0.38
0.44
0.31
0.71
1.28
0.11
0.08
0.25
5.75%
13.65%
11.4%
4.5%
3%
0.14
0.2
0.3
0.9
0.1
0.7
0.2
0.1
Table A2. Calibrated Parameter
Parameters
Values
Mark-up parameter in labor market
𝜀𝑤
11
Depreciation rate of capital
𝛿𝑘
0.025
Depreciation rate of housing asset
𝛿𝜒
0.0125
Cost to managing bank’s capital
CAPU parameter 1
𝛿𝑏
𝜉1
0.1
0.08
CAPU parameter 2
𝜉2
0.008
Risk premium parameter
𝜌
𝑏
0.11
Capital share in production function
𝛼
0.54
Home bias parameter
𝜂
0.62
Elasticity of substitution between domestic and foreign goods
Elasticity of substitution for export goods
𝜇
𝜇𝐻∗
0.63
0.45
Labor income share of unconstrained household
𝜇𝐿
0.67
26
Parameters
Values
The probability of given labor (from patient and impatient HH) is selected not
to re-optimize its wage
Risky weight equation’s parameter 1
Risky weight equation’s parameter 2
𝜃𝑤𝑝 𝑎𝑛𝑑 𝜃𝑤𝑖
0.65
𝜌𝜔
𝛼𝑎
0.567
0.434
Risky weight equation’s parameter 3
𝛼𝑏
0.784
Reserve equation’s parameter
Excess reserve equation’s parameter
𝜌Γ
𝜌ε
0.197
0.632
Table A3. Estimated Parameters
Parameters
Distributions
Prior
Distribution
Posterior Distribution
Mean
Std.
Dev.
Mean
2.5%
97.5%
3.7737
Inverse of intertemporal elasticity of
substitution for housing
𝝈𝝌
Normal
2
0.5
3.6357
3.5297
Inverse of intertemporal elasticity of
substitution for consumption
𝝈𝒄
Normal
2
0.1
2.1950
1.0419
1.2683
Inverse of Frisch elasticity of labor
supply
𝝈𝒏
Normal
2
0.1
1.3663
1.3639
1.3694
Adjustment
deposit rate
parameter
for
𝜿𝒅
Gamma
3.25
0.2
3.2285
3.1799
3.2675
Adjustment cost parameter
entrepreneur loan rate
for
𝜿𝒃𝒆
Normal
3.5
0.2
3.6945
3.6299
3.7420
Adjustment cost parameter
household loan rate
for
𝜿𝒃𝒊
Normal
8
0.2
8.1280
8.0775
8.1676
Adjustment cost
capital investment
parameter
for
𝜿𝒌
Gamma
2
0.2
0.9811
0.9777
0.9855
Adjustment cost parameter
housing investment
for
𝜿𝝌
Normal
2
0.5
3.6510
3.5496
3.7510
Adjustment cost
bank’s CAR
for
𝜿𝒌𝒃
Beta
2
0.2
1.7823
Calvo parameter for import goods
𝜽𝒇
Beta
0.5
0.05
0.5707
Calvo parameter for domestic goods
𝜽𝐡
Beta
0.5
0.05
0.4996
Calvo parameter for export goods
𝜽𝐡∗
Beta
0.5
0.05
0.4149
0.4075
Interest rate smoothing parameter in
Taylor rule
𝝋𝒓
Beta
0.75
0.01
0.7412
0.7379
0.7436
Inflation weight parameter in Taylor
rule
𝝋𝝅
Gamma
1.9
0.01
1.8957
1.8929
1.8980
Output gap parameter in Taylor rule
𝝋𝒚
Normal
0.25
0.01
0.2548
0.2531
0.2562
Beta
0.6
0.05
0.4887
0.4770
cost
Habit persistence
consumption
parameter
parameter
in
𝝃
1.7208
0.5616
0.4890
1.8217
0.5776
0.5167
0.4264
0.5038
27