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LTV Policy Simulation in DSGE Model Iskandar SimorangkirNur 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 ([email protected]) and Nur M. Adhi Purwato ([email protected]) 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.
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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
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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.
II. LITERATURE REVIEW
II.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
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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 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
2 See Roger and Vleck (2011)
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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.
II.2 Indonesia’s Commercial Bank Characteristics
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
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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.
-.8
-.4
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1 2 3 4 5 6 7 8 9 10
Response of D(BI_RATE) to D(BI_RATE)
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1 2 3 4 5 6 7 8 9 10
Response of D(R_PINJAMAN_CONS) to D(BI_RATE)
Response to Cholesky One S.D. Innovations ± 2 S.E.
-0.50
-0.25
0.00
0.25
0.50
0.75
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1 2 3 4 5 6 7 8 9 10
Response of D(BI_RATE) to D(BI_RATE)
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1 2 3 4 5 6 7 8 9 10
Response of D(R_DPK) to D(BI_RATE)
Response to Cholesky One S.D. Innovations ± 2 S.E.
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.
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-.8
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1 2 3 4 5 6 7 8 9 10
Response of D(BI_RATE) to D(BI_RATE)
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1 2 3 4 5 6 7 8 9 10
Response of D(R_PINJAMAN_ENT) to D(BI_RATE)
Response to Cholesky One S.D. Innovations ± 2 S.E.
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. 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.
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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 consumptionc t
P, the amount of leisure time ntP and the amount of housing assets
they acquired χ tP .
maxc tP (i ), χ t
P (i ), ntP (i)∑t=0
∞
(βP ) t εu ,t [ (c tP ( i )−ξ c t−1
P )1−σ c
1−σ c+ε χ ,t
χ tP (i )1−σ χ
1−σ χ−εn ,t
ntP ( i )1+ σn
1+σn] ... (3.1)
The parameter ξ determines the level of external habit formation and ε u ,t , ε χ ,t , εn , t are intertemporal, housing preference and labor preference shocks that have an AR(1) dynamics with an iid errors.
Patient households revenue comes from labor income W t ntP, interest
income from deposit (1+rt−1D )d t−1
❑ , and dividend Π tP (they are the owner of banks
and retailers). They spend their income to pay taxes to governmentT tP, consume,
acquire housing assets and save the remaining in the form of bank’s depositd t. The following is patient households’ budget constraint:
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Pt c tP ( i )+P χ , t ( χ t
P (i )−(1−δ χ ) χ t−1P ( i ) )+d t
❑ ( i )=W tn tP (i )+ (1+r t−1D ) dt−1
❑ ( i )−T tP ( i )+Π t
P ( i ) ... (3.2)
In the budget constraint equation, consumption and housing asset are multiplied by their prices to get their nominal values. Parameter δ χ is the depreciation level of the housing assets own by the households.
Utility function for impatient households is very similar to the patient households’:
maxc tI (i) , χ t
I ( i) ,ntI (i ) ,bt
I (i)∑t=0
∞
(βI )t εu , t[ (c t
I ( i )−ξ c t−1I )1−σ c
1−σ c+ε χ ,t
χ tI ( i )1−σ χ
1−σ χ−εn ,t
ntI (i )1+ σn
1+σn] ... (3.3)
To finance their expenditures, besides having revenue from labor income W t ntI,
impatient household also borrow from the bank the amount of b tI ( i ). Because of
this, impatient household also have obligation to pay the previous period loan along with the interest ((1+rt−1
BI )bt−1I ) as part of their expenditures.
Pt c tI (i )+P χ , t ( χ t
I (i )−(1−δ χ ) χ t−1I ( i ) )+(1+r t−1
BI )bt−1I ( i )=W t nt
I (i )+btI ( i)−T t
I (i) ... (3.4)
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 mt
I.
(1+rtBI )bt
I (i )≤mtI Et [P χ , t+1 (1−δ χ) χ t
I (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 mt
Idetermine 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,c t
E:
9
E0∑s=0
∞
(β E )s(εu ,t+ s(c t+ s
E ( i )−ξ c t+s−1E )1−σ c
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 ) k t−1 (i ) ]α nt ( i )1−α ... (3.7)
WhereAt is the total factor productivity, ut ϵ [0 , ∞ ) is the capital utilization rate, k t 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 (b t
E ¿and from foreign financial entities (b t
¿¿.
Pt c tE (i )+W P , tnP ,t (i )+W I ,t nI ,t (i )+Pk ,t (k t ( i )− (1−δ k )k t−1 ( i ) )+Ptψ (ut (i ) )k t−1 ( i )+(1+r B,t−1
E )bt−1E (i )+et
❑ (1+ρt−1) (1+rB , t−1¿ )bt−1
¿ (i )=PW , t A t [ut (i ) k t−1 ( i ) ]α [n t (i ) ]1−α+b t
E ( i )+e t❑b t
¿(i)
... (3.8)
Where Pk , t is the price of the capital goods, PW , t is the price of the intermediate goods, δ k is the depreciation rate of capital goods, ρt is the risk premium, b t
E is the amount of domestic loan (from the banks), b t
¿ is the amount of foreign loan, e t
❑ 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:
Et [ et+1❑ (1+ρt ) (1+rB, t¿ )bt
¿ ( i ) ]+(1+rB, tE )b t
E ( i )≤mtE E t [Pk ,t+1 (1−δ k )k t ( 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.
Producers10
There are three producers in the model: capital goods producers, housing producers, and final (consumption) goods producers.
Capital good producers operate in a perfectly competitive market and use consumption goods to produce capital goods. Capital goods are produced from un-depreciated previous period capital ((1−δ k) k t−1 ) and transformation of consumption goods (ik ,t ¿ with the following production function:
k t=(1−δ )k t−1+εi , t(1−12 κk ( ik , tik ,t−1
−1)2
)ik ,t ... (3.10)
Where ε i ,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:
maxk t
∑s=0
∞
(β p )s (Pk ,t+ sk t+ s−(P k ,t+s (1−δ ) k t+s−1+Pt+s ik ,t+s ) ) ... (3.12)
Housing producers have similar characteristics with capital goods producers with also a similar production function:
χ t=(1−δ χ ) χ t−1+εiχ ,t (1−12 κ χ ( i χ , ti χ ,t−1
−1)2
) i χ ,t ... (3.13)
κ χ>0 ... (3.14)
The utility function is as follows:
maxχ t
∑s=0
∞
(β p )s (Pχ , t χ t−(Pχ ,t (1−δ χ ) χ t−1+Pt i χ ,t )) ... (3.15)
Final good producer is the agent that combines goods from domestic retailers yH ,t( jH ) and importing retailers y F,t ( jF) to produce final goods to be sold in a perfectly competitive market. The production function of the agent is as follows:
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y t=[η μ1+ μ yH ,t
11+μ+(1−η )
μ1+μ y F,t
11+μ ]
1+ μ
... (3.16)
Where η is the home bias parameter, and μ the parameter that determines elasticity of substitution between domestic and foreign goods.
Optimization of the utility function will result in imported goods ( yH ,t) and domestic goods (y F,t) demand equation, and also the price for the final (consumption) goods (Pt ¿:
yH ,t=η( PH , t
Pt)−1+μ
μ ... (3.17)
y F,t=(1−η )( PF ,t
Pt)−1+ μ
μ y t ... (3.18)
Pt
−1μ =η (PH , t )
−1μ +(1−η ) (PF ,t )
−1μ ... (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−1π t−1. This will result in the following aggregate price at time t:
4 θ∈ [0,1 ]
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PH ,t=(θH (PH , t−1πH ,t−1 )1− εH+(1−θH ) (PH ,t ( i ) )1−ε H)1
1−ε H ... (3.20)
Log linearization of the first order condition of domestic retailer’s utility function will result in the following equation:
πH , t=1
(1+βP )πH , t−1+
βP
(1+ βP )( πH ,t+1 )+
(1−βPθH ) (1−θH )(1+βP )θH
( PW ,t−PH ,t ) ... (3.21)
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−1π t−1. The aggregate price level of goods sold by importing retailers at time t is:
PF,t=(θF (PF ,t−1πF ,t−1)1−εF+(1−θF ) (PF ,t (i ) )1−ε F )
11−ε F ... (3.22)
The log linearization of the FOC of importing retailer’s utility function is the following equation:
πF ,t=1
(1+βP )π F, t−1+
βP
(1+ βP )( π F, t+1 )+
(1−βPθF ) (1−θF )(1+βP )θF
( st−PF, t ) ...(3.23)
Exporting retailer buy domestic undifferentiated goods differentiate them at no cost and sell them to the foreign market with a price ofPH ,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
¿
PH , t¿ )
−(1+ μH ¿)μH ¿ yH ,t
¿ ... (3.24)
Where yH¿ the output of exporting retailers where:
yH ,t¿ =(∫
0
1
yH ,t¿ ( jH¿ )
11+μH ¿ d jH
¿ )1+μH ¿
... (3.25)
And PH ,t¿ is
PH ,t¿ =(∫
0
1
PH ,t¿ ( jH¿ )
−1μH ¿ d jH
¿ )−μH ¿
... (3.26)
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Moreover, it is assumed that foreign demand is given by the following equation:
yH ,t¿ =(1−η¿ )(PH ,t
¿
P t¿ )
−(1+μH ¿)μH¿ y t
¿ ... (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¿ π t−1
¿ . The aggregate price at time t is:
PH ,t¿ =(θH
¿ (PH , t−1¿ πH ,t−1
¿ )1−εH¿
+(1−θH¿ ) (PH ,t
¿ (i ) )1−ε H¿
)1
1−εH¿ ...(3.28)
The log linearization of the FOC of the utility function of exporting retailers will result in the following equation:
πH , t¿ = 1
(1+βP )πH , t−1
¿ +βP
(1+ βP )( πH ,t+1
¿ )+ (1−β PθH¿ ) (1−θH
¿ )(1+βP )θH
¿ ( PW , t− st+ PH ,t¿ ) ... (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
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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+B t=(1−Γ t )Dt+K tb ... (3.30)
Where RFt (Risk free Asset), Bt(Total loan) and Dt (Deposit) are the choice variables of the wholesale unit. Γ t is the reserve ratio and K t
b 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:
K tb=(1−δ b ) K t−1
b +wb jt−1b ... (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 }
E0∑s=0
∞
(βP )sλt+ sP
λtP [Γ t+ sDt+s−Γ t+s+1Dt+ s+1+(1+r t+s ) RFt+ s−RFt+ s+1+(1+Rt+ s
b )Bt+ s−Bt+s+1+D t+ s+1−(1+Rt+sd )Dt+s+ ΔK t+s+1
b −κKb
2 ( K t+ sb
ωt+ sb Bt+s
−vb ,t+s)2
K t+ sb ]
... (3.32)
s.t. RFt+B t=(1−Γ t )Dt+K tb ... (3.33)
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Where λt+sP
λtP is the stochastic discount factor, Rt
b 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−r t=−(ωt
b )κKb ( K tb
ωtb Bt
−vb ,t)( K tb
ωtbBt
)2
... (3.34)
rt (1−Γ t )=Rtd ... (3.35)
When the Capital Adequacy Ratio (CAR=K t
b
ωtb Bt
¿is equal to the minimum
level ( vb ,t), then wholesale loan rate wil be equal to plicy rate ( Rtb=r t). 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 Rt
b), 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 (Γ t=0), then the ratio of the ratio of wholesale unit’s deposit rate to
policy rate will be equal to 1( R td
r t=1), While in the condition of reserve
requirement greater than zero (Γ t ¿0), bank is facing an increase in opportunity cost and will react by lowering the cost by by lowering the deposit rate (Rt
d) to decrease the amount of deposit acquired.
Following modification done by Angelini et al (2011), we also include the risky asset weight variable (ωt
b) 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 bank’s
loan composition (btE
btI ) and the default risk (nplt).
16
ωtb=ρωωt−1
b +(1− ρω )αabtE
btI +(1−ρω )α bnplt ... (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 (Γ t
r) set by the central bank as follows (after log linearization):
Γ tr=ρΓ Γ t−1
r +e Γr, t ... (3.37)
This reserve requirement ratio then will influence the amount of excess reserve (ε tΓ) held by the bank:
ε tΓ=ρε εt−1
Γ +(1−ρε) Γ tr+eΓ ,t ... (3.38)
And the dynamic of the bank’s reserve ratio is as follows:
Γ t=λΓ Γ tr+(1− λΓ) ε t
Γ ... (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 the following variables ε t
bH, ε tbE . The same mechanism is also assumed for deposit with
variable ε td 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. 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.
17
The following are equations for loan demand by entrepreneur (b tE) and
impatient households (b tI):
b tI ( j )=( r t
bH ( j )r tbH )
−ε tbH
btI ... (3.40)
b tE ( j )=( r t
bE ( j )r tbE )
−εtbE
btE ... (3.41)
Patient household’s demand for deposit’s (d t) equation is:
d t ( j )=( rtd ( j )r td )
− εtd
d t ... (3.42)
Loan branch received loans (Bt) from wholesale unit with interest rate equal to Rt
b, 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:
max{rtbH ( j ) ,rt
bE ( j) }E0∑
s=0
∞
(β P )sλt+sP
λ tP [rt+sbH ( j )bt+s
I ( j )+r t+ sbE ( j )b t+s
E ( j )−Rt+ sb Bt+s ( j )−
κbH
2 ( r t+sbH ( j )
r t+ s−1bH ( j )
−1)2
rt+sbH bt+s
I −κbE
2 ( r t+ sbE ( j )
r t+s−1bE ( j )
−1)2
rt+sbE b t+ s
E ] ... (3.43)
Subject to
b tI ( j )=( r t
bH ( j )r tbH )
−ε tbH
btI ... (3.44)
b tE ( j )=( r t
bE ( j )r tbE )
−εtbE
btE ... (3.45)
Bt ( j )=bt ( j )=btI ( j )+bt
E ( j ) ... (3.46)
18
Similar to loan branch, deposit branch collects deposit (d t) from households and forward them to the wholesale unit and set the deposit rate rtd. Utility function of the deposit branch is as follows:
max{rtd ( j )}
E0∑s=0
∞
(β P )sλt+sP
λ tP [R t+s
D D t+ s ( j )−r t+ sd ( j )d t+ s ( j )−
κd
2 ( r t+sd ( j )
rt+ s−1d ( j )
−1)2
r t+sd d t+ s] ... (3.47)
subject to
d t ( j )=( rtd ( j )r td )
− εtd
d t ... (3.48)
Dt ( j )=d t ( 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¿ )e tbG ,t−1
¿ +(1+r t−1❑ )bG ,t−1
❑ =(T tP+T t
I )+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 T t
I 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+r t−11+r❑
)ϕR(( π t
π t)ϕπ (~y t
~y )ϕ y)1−ϕR
εr ,t ... (3.51)
Where ϕ π and ϕ y are weight for inflation and output stabilization, r❑ nominal steady state interest rate and ε t
r is the i.i.d. shock to monetary policy with normal distribution and standard deviation σ r.
19
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 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 Schmitt-Grohe and Uribe (2003), the risk premium is defined as a function of total foreign loan to GDP ratio.
Final Goods Producers Output
y t=c t+ik .t+i χ ,t+g t+ψ (ut ) k t−1 ... (3.52)
c t=γ I c tI+γPc t
P+γE c tE ... (3.53)
Intermediate Homogenous Goods Market
∫0
1
yH ,t ( j )dj+∫0
1
yH ,t¿ ( j )dj= yW ,t ... (3.54)
Housing Market
γP χ tP+γ I χ t
I= χ t ... (3.55)
Balance of Payment
PF,t y F, t+e t (1+rt−1¿ ) ρt−1btot ,t−1¿ =e t PH , t
¿ yH ,t¿ +e t btot ,t
¿ ... (3.56)
Where
b tot , t¿ =bt
¿+bG, t¿ ... (3.57)
GDP
Pt~y t=Pt y t+et PH ,t
¿ yH ,t¿ −PF ,t
❑ y F,t❑ ... (3.58)
20
Risk Premium
(1+ρt )=exp (−ϱe t b tot , t
¿
P t~y t )ε ρ , t ... (3.59)
IV. ESTIMATION AND SIMULATION
IV.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 non-performing 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
21
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 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 (φ r , φπ and φ y ), 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).
IV.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.
5 We use the CES based estimation that is in accordance with the assumption of the model used in this research.
22
10 20 30 40-0.5
0
0.5
1BI Rate
10 20 30 40-0.2
0
0.2Loan Rate to Household
10 20 30 40-0.5
0
0.5Loan Rate to Firm
10 20 30 40-0.5
0
0.5Deposit Rate
10 20 30 40-1
0
1Deposit
10 20 30 40-0.5
0
0.5Bank Capital
10 20 30 40-2
-1
0
1Total Loan
10 20 30 40-5
0
5Loan to Household
10 20 30 40-0.5
0
0.5Loan to Firm
10 20 30 40-2
0
2
4Risk Free
10 20 30 40-1
-0.5
0
0.5LDR
10 20 30 40-1
-0.5
0
0.5Spread Loan rate to HH
10 20 30 40-0.5
0
0.5Spread Loan rate to firm
10 20 30 40-0.5
0
0.5Spread deposit rate
10 20 30 40-1
-0.5
0
0.5CAR
10 20 30 40-0.5
0
0.5CPI Inflation YoY
10 20 30 40-0.5
0
0.5Exchange Rate
10 20 30 40-1
0
1Output
10 20 30 40-0.2
0
0.2Consumption
10 20 30 40-1
0
1Total Invesment
10 20 30 40-2
-1
0
1Housing Investment
10 20 30 40-0.5
0
0.5Capital Investment
10 20 30 40-1
-0.5
0
0.5Export
10 20 30 40-0.5
0
0.5Import
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 mark-down 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 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).
23
BI rate fixed for 4 quarters
BI rate based on taylor rule
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.
10 20 30 40-0.2
0
0.2BI Rate
10 20 30 40-0.2
0
0.2Loan Rate to Household
10 20 30 40-0.2
0
0.2Loan Rate to Firm
10 20 30 40-0.1
0
0.1Deposit Rate
10 20 30 40-2
0
2Deposit
10 20 30 40-0.2
0
0.2Bank Capital
10 20 30 400
1
2Total Loan
10 20 30 40-5
0
5Loan to Household
10 20 30 40-1
0
1Loan to Firm
10 20 30 40-4
-2
0Risk Free
10 20 30 400
0.5
1LDR
10 20 30 40-0.1
0
0.1Spread Loan rate to HH
10 20 30 40-0.05
0
0.05Spread Loan rate to firm
10 20 30 40-0.05
0
0.05Spread deposit rate
10 20 30 40-2
0
2CAR
10 20 30 40-0.2
0
0.2Output
10 20 30 40-0.2
0
0.2CPI Inflation YoY
10 20 30 40-0.2
0
0.2Exchange Rate
10 20 30 40-1
0
1Impatient HH Consumption
10 20 30 40-5
0
5Impatient HH Stock of Housing
10 20 30 400
1
2LTV for HH
Shock mi
Figure 4.2. Impulse Response: Shock to household's LTV ratio
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
24
BI rate fixed for 4 quarters
BI rate based on taylor rule
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.
10 20 30 40-0.1
0
0.1BI Rate
10 20 30 40-0.05
0
0.05Loan Rate to Household
10 20 30 40-0.05
0
0.05Loan Rate to Firm
10 20 30 40-0.05
0
0.05Deposit Rate
10 20 30 40-0.5
0
0.5Deposit
10 20 30 40-0.2
0
0.2Bank Capital
10 20 30 40-1
0
1Total Loan
10 20 30 40-1
0
1Loan to Household
10 20 30 40-1
0
1Loan to Firm
10 20 30 40-2
0
2Risk Free
10 20 30 40-0.5
0
0.5LDR
10 20 30 40-0.05
0
0.05Spread Loan rate to HH
10 20 30 40-0.05
0
0.05Spread Loan rate to firm
10 20 30 40-0.05
0
0.05Spread deposit rate
10 20 30 40-1
0
1CAR
10 20 30 40-0.5
0
0.5Output
10 20 30 40-0.1
0
0.1CPI Inflation YoY
10 20 30 40-0.05
0
0.05Exchange Rate
10 20 30 40-0.2
0
0.2Entrepreneur Consumption
10 20 30 40-0.01
0
0.01Intermediate Good Price
10 20 30 40-2
0
2Capital Investment
10 20 30 400
1
2LTV for Entrepreneur
Shock me
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, 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.
25
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.
26
REFERENCES
Adolfson, Malin & Laséen, Stefan & Lindé, Jesper & Villani, Mattias, 2005. "Bayesian Estimation of an Open Economy DSGE Model with Incomplete Pass-Through," Working Paper Series 179, Sveriges Riksbank (Central Bank of Sweden).
Agung, Juda ,2010.”Mengintegrasikan Kebijakan Moneter dan Makroprudential: Menuju Paradigma Baru Kebijakan Moneter di Indonesia Pasca Krisis Global”. Bank Indonesia Working Paper No.WP/07/2010.
Angelini, Paolo & Andrea Enria & Stefano Neri & Fabio Panetta & Mario Quagliariello, 2010. "Pro-cyclicality of capital regulation: is it a problem? How to fix it?", Questioni di Economia e Finanza (Occasional Papers) 74, Bank of Italy, Economic Research and International Relations Area.
Angelini, Paolo & Stefano Neri & Fabio Panetta, 2011."Monetary and macroprudential policies", Temi di discussione (Economic working papers) 801, Bank of Italy, Economic Research and International Relations Area.
Bank Indonesia, 2006, “General Equilibrium Model Bank Indonesia 2006,” Bank Indonesia Working Paper.
Bank Indonesia .2009, “Bank Indonesia Structural Macromodel” Bank Indonesia Working Paper.
BIS, 2010. “Macroprudential instruments and frameworks: A stocktaking of issues and experiences. Committee on The Global Financial System.
Brzoza-Brzezina, Michał & Krzysztof Makarski, 2011, "Credit crunch in a small open economy," Journal of International Money and Finance, Elsevier, vol. 30(7), pages 1406-1428.
Camilo E Tovar, 2008. "DSGE models and central banks," BIS Working Papers 258, Bank for International Settlements.
Gerali, Andrea & Stefano Neri & Luca Sessa & Federico M. Signoretti, 2010,"Credit and banking in a DSGE model of the euro area,"Temi di discussione (Economic working papers) 740, Bank of Italy, Economic Research and International Relations Area.
Gunadi, Iman & Advis Budiman ,2011, “Optimalisasi Komposisi Portfolio Bank di Indonesia”, Kajian Stabilitas Keuangan No. 17, September.
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Harmanta & Nur Purwanto, 2012, “Stickiness Suku Bunga Retail Perbankan di Indonesia “, Catatan Riset No. 14/ 39 /DKM/BRE/CR, Bank Indonesia, Desember.
Iacoviello, M. ,2005, “House Prices, Borrowing Constraints and Monetary Policy in the Business Cycle" American Economic Review, Vol. 95(3), pp. 739-764.
Lawrence J. Christiano & Martin Eichenbaum & Charles L. Evans, 2005. "Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy," Journal of Political Economy, University of Chicago Press, vol. 113(1), pages 1-45, February.
Liu, Zheng & Pengfei Wang & Tao Zha, 2010. "Do credit constraints amplify macroeconomic fluctuations?", Working Paper 2010-01, Federal Reserve Bank of Atlanta.
Vlcek, Jan & Scott Roger, 2012. "Macrofinancial Modeling at Central Banks: Recent Developments and Future Directions," IMF Working Papers 12/21, International Monetary Fund.
Zhang, X. & Verikios, G. ,2006, “Armington Parameter Estimation for a Computable General Equilibrium Model: A Database Consistent Approach”, Economics Discussion Working Papers No. 06–10, The University of Western Australia, Department of Economics. Zhang and Verikios (2006)
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AppendixTable A1. Steady State Values
Variables ValuesConsumption to GDP ratio 0.59Capital investment to GDP ratio 0.14Housing investment to GDP ratio 0.08Government expenditure to GDP ratio 0.09Import to absorption ratio 0.38Export to output ratio 0.44Loan to HH to GDP ratio 0.31Loan to entrepreneur to GDP ratio 0.71Deposit to GDP ratio 1.28Importer’s profit margin 0.11Exporter’s profit margin 0.08Domestic retailer’s profit margin 0.25BI rate * 5.75%Rate on loan to HH* 13.65%Rate on loan to entrepreneur* 11.4%Rate on deposit* 4.5%Foreign interest rate* 3%CAR 0.14Bank’s profit to total asset ratio 0.2NPL ratio 0.3Deposit to bank’s total asset ratio 0.9Bank’s capital to total asset ratio 0.1Loan to bank’s total asset ratio 0.7Risk free asset to bank’s total asset ratio** 0.2Reserve to total asset ratio 0.1
Table A2. Calibrated Parameter
Parameters Values
Mark-up parameter in labor market εw 11 Depreciation rate of capital δ k 0.025 Depreciation rate of housing asset δ χ
0.0125
29
Parameters Values
Cost to managing bank’s capital δ b 0.1 CAPU parameter 1 ξ1 0.08 CAPU parameter 2 ξ2 0.008 Risk premium parameter ρb 0.11 Capital share in production function α 0.54 Home bias parameter η 0.62 Elasticity of substitution between domestic and foreign goods μ 0.63 Elasticity of substitution for export goods μH∗¿¿ 0.45Labor income share of unconstrained household μL 0.67 The probability of given labor (from patient and impatient HH) is selected not to re-optimize its wage θ℘∧θwi 0.65 Risky weight equation’s parameter 1 ρω 0.567Risky weight equation’s parameter 2 α a 0.434Risky weight equation’s parameter 3 α b 0.784Reserve equation’s parameter ρΓ 0.197Excess reserve equation’s parameter ρε 0.632
Table A3. Estimated Parameters
Parameters Distributions
Prior Distribution
Posterior Distribution
Mean
Std. Dev.
Mean 2.5% 97.5%
Inverse of intertemporal elasticity of substitution for housing
σ χNormal 2 0.5 3.635
7 3.5297 3.773
7
Inverse of intertemporal elasticity of substitution for consumption
σ cNormal 2 0.1 2.195
0 1.0419 1.268
3
Inverse of Frisch elasticity of labor supply σ n
Normal 2 0.1 1.3663
1.3639 1.3694
Adjustment cost parameter for deposit rate κd
Gamma 3.25 0.2 3.2285 3.1799 3.2675
Adjustment cost parameter for entrepreneur loan rate κbe
Normal 3.5 0.2 3.6945 3.6299 3.7420
Adjustment cost parameter for household loan rate κbi
Normal 8 0.2 8.1280 8.0775 8.1676
Adjustment cost parameter for capital investment κ k
Gamma 2 0.2 0.9811 0.9777 0.9855
Adjustment cost parameter for housing investment κ χ
Normal 2 0.5 3.6510 3.5496 3.7510
Adjustment cost parameter for bank’s CAR κ kb
Beta 2 0.2 1.7823
1.7208 1.8217
Calvo parameter for import goods θ f
Beta 0.5 0.05 0.5707
0.5616 0.5776
Calvo parameter for domestic goods θh
Beta 0.5 0.05 0.4996
0.4890 0.5167
Calvo parameter for export goods θh∗¿¿
Beta 0.5 0.05 0.4149
0.4075 0.4264
Interest rate smoothing parameter in Taylor rule φ r
Beta 0.75 0.01 0.7412
0.7379 0.7436
30
Parameters Distributions
Prior Distribution
Posterior Distribution
Mean
Std. Dev.
Mean 2.5% 97.5%
Inflation weight parameter in Taylor rule φπ
Gamma 1.9 0.01 1.8957
1.8929 1.8980
Output gap parameter in Taylor rule φ y
Normal 0.25 0.01 0.2548
0.2531 0.2562
Habit persistence parameter in consumption ξ Beta 0.6 0.05 0.488
7 0.4770 0.503
8
31
