貸款成數管制政策之實證意涵

科技部補助專題研究計畫報告

貸款成數管制政策之實證意涵(第2年)

報 告 類 別 ： 成果報告 計 畫 類 別 ： 個別型計畫

計 畫 編 號 ： MOST 107-2410-H-006-002-MY2 執 行 期 間 ： 108年04月01日至109年07月31日 執 行 單 位 ： 國立成功大學經濟學系

計 畫 主 持 人 ： 林姿妤

計畫參與人員： 碩士班研究生-兼任助理：謝乙慈 碩士班研究生-兼任助理：楊子慶 碩士班研究生-兼任助理：林佩蓉

本研究具有政策應用參考價值：■否　□是，建議提供機關

（勾選「是」者，請列舉建議可提供施政參考之業務主管機關）

本研究具影響公共利益之重大發現：□否　□是　

中　華　民　國　109　年　10　月　30　日

中 文 摘 要 ： 本計畫試圖檢視貸款成數限制對於總體經濟的影響，以 Gerali et al. (2010) 中帶有定價能力銀行部門的動態隨機一般均衡 (DSGE) 模型為基礎, 採用美國資料，使用貝氏方法估計，檢視當廠商貸款 成數限制變動，以及家計單位貸款成數限制變動時，對於總體經濟 的影響。分析結果顯示，廠商貸款成數受到衝擊時，對於產出、消 費、貸放款利率的影響，皆大於家計單位貸款成數衝擊的影響。

中 文 關 鍵 詞 ： 動態隨機一般均衡 (DSGE); 貸款成數

英 文 摘 要 ： This report relies on a dynamic stochastic general

equilibrium (DSGE) model developed by Gerali et al. (2010) to investigate the role of the loan-to value (LTV) ratio plays under the financial crisis which originated from banking system. Gerali et al. (2010) constructs and

estimates a DSGE model in which the financial frictions are enriched with an imperfectly competitive banking sector. In this report, the model is estimated with Bayesian

techniques using the US data. The analysis suggests that shock to LTV limit on firms and on households are

different. The effects of firm’s LTV ratio shock on

variables such output, consumption and investment are more profound while the effects of households' LTV ratio shock are relatively smaller.

英 文 關 鍵 詞 ： DSGE; loan-to-value ratio

The Empirical Implications of

the Loan-to-Value Ratio Policy

October 30, 2020

Abstract

This report relies on a dynamic stochastic general equilibrium (DSGE) model devel- oped by Gerali et al. (2010) to investigate the role of the loan-to value (LTV) ratio plays under the financial crisis which originated from banking system. Gerali et al. (2010) con- structs and estimates a DSGE model in which the financial frictions are enriched with an imperfectly competitive banking sector. In this report, the model is estimated with Bayesian techniques using the US data. The analysis suggests that shock to LTV limit on firms and on households are quite different. The effects of firm’s LTV ratio shock on variables such output, consumption and investment are more profound while the effects of households’

LTV ratio shock are relatively smaller.

1 Introduction

The financial crisis of 2007-2009, which is originated from the collapse of the housing market in the United States, devastatingly disrupted the financial system and dragged the economy into the Great Recession. We can see in Figure 1 that the US commercial and industrial loan in level and percentage change show a sharp decline during the crisis. At the same time, the US real GDP in level and percentage change presented in Figure 2 experience a subsequent economic slump. In both figures, the shaded areas indicate the recession period identified by the National Bureau of Economic Research (NBER).

This unprecedented crisis has ignited the discussion on a wide range of policy areas. The discussion about macroprudential regulation, which precedes the financial crisis by many years, attracted particular attention after the crisis.¹ Different from microprudential policies focusing on the soundness of individual financial institution, macroprudential approaches put emphasis on the interactions between financial intermediaries, markets and the wider economy. It aims at promoting financial stability and containing systemic risk and thus safeguard the financial sys- tem as a whole. Several policy tools are available in the macroprudential toolbox. Among them, the loan-to-value (LTV) ratio cap is identified by the Basel Committee on the Global Financial System as one of the macroprudential tools that may enhance financial system resilience and also act as an automatic stabilizer if adjusted around a pre-established cap in a countercyclical manner.²

According to a survey conducted using the IMF Global Macroprudential Policy Instruments (GMPI) database, 47 countries have introduced limits on the LTV ratio to mitigate boom-bust cycles of asset prices and build resilience against systemic risk.³ A more recent technical note

1See Evens et al. (2000), Borio et al. (2001), Borio (2003), Hanson et al. (2011), Angelini et al. (2012), Benigno et al. (2012), Bianchi et al. (2012), Lambertini et al. (2013), Claessens (2015)

2See BIS (2010).

3See Jácome and Mitra (2015).

Figure 1: Commercial and Industrial Loan

400 600 800 1,000 1,200 1,400 1,600 1,800 2,000

1988 1992 1996 2000 2004 2008 2012 2016

Level

-8 -6 -4 -2 0 2 4 6 8

1988 1992 1996 2000 2004 2008 2012 2016

% Change

Figure 2: Real Gross Domestic Product

6,000 8,000 10,000 12,000 14,000 16,000 18,000

1988 1992 1996 2000 2004 2008 2012 2016

Level

-12 -8 -4 0 4 8

1988 1992 1996 2000 2004 2008 2012 2016

% Change

reported by the IMF indicates that many countries have newly adopted LTV ratio as policy tool since the financial crisis. Among a sample of 28 countries, more than half impose a limit on LTV ratios below 80 percent.⁴

There is no official LTV policy being implemented in the US. However, a combined LTV data from the Urban Institute may give us a clue about an implicit LTV cap in the US. Figure 3 shows that the average LTV ratio at mortgage origination was less than 85% before the crisis, and climbed up to over 85% after the burst of the crisis.⁵ The figure seems to indicate a upward trend but the average ratio never attain 90%. This may suggest the existence of an implicit limit on the LTV ratio. Turning to the medium LTV ratio may also help shed light on the maximum LTV ratio (so-called LTV caps). An obvious bound on the medium LTV ratio can be observed, both before and after the crisis. The medium LTV ratio remained at 80% before the crisis, and became higher to 90% during the crisis and further increased to 95% after the crisis. This change of the LTV ratio to some extents corresponds to the objectives of a macroprudential tool articulated by the Basel Committee on the Global Financial System. On one hand, the implicit caps lasts for a while, contributing to enhance financial system’s resilience. And on the other hand, the cap is relaxed when the economic situation deteriorates, i.e., it is adjusted in a countercyclical manner.

To focus on the role of LTV ratio plays under the financial crisis which originated from banking system, this report relies on a DSGE model developed by Gerali et al. (2010). Gerali et al. (2010) constructs and estimates a DSGE model in which the financial frictions are enriched with an imperfectly competitive banking sector. In this model, banks collect deposits and issue collateralized loans to both households and firms, and accumulate capital out of retained earn- ings. Banks’ capital-to-assets ratio and the degree of interest rate stickiness determines loan

4See IMF (2017).

5Figure is downloaded from “US Mortgage Market Statistics: 2017” announced by the Magnify Money. Data sources include Corelogic, eMBS, HMDA, SIFMA and Urban Institute.

Figure 3: Loan-to-Value Ratio

margin. In this report, we estimate the model with Bayesian techniques using the US data. The analysis shows that when the LTV limit on firms is relaxed, loan obtained by impatient house- holds also increases. However, when the LTV limit on impatient households is relaxed, the loan to firms is crowded out and decreases. The effect of the firm’s LTV ratio shock on variables such output, consumption and investment is more profound while the effect of its counterpart is relatively smaller. Moreover, although the deposit increases in both case, shock to firm’s LTV ratio and shock to household’s LTV ratio, the deposit rate goes down in the former case while goes up in the later case. Similarly, the loan rates to firms and households fall when firms face more relaxed constraints and the loan rates increase when households’ borrowing constraints are loosen.

The rest of the report is organized as follows. Section 2 briefly presents the DSGE model.

Section 3 describes the data and the calibrated and estimated results. Section 4 discusses the

results and shows the impulse responses of monetary shocks. Section 5 concludes.

2 The Model

Gerali et al. (2010) constructs and estimates a DSGE model in which the financial frictions are enriched with an imperfectly competitive banking sector. A brief description of Gerali et al.

(2010)’s model is presented as follows.

There is a continuum of measure for three types of infinitely lived agents in the economy:

patient and impatient households, entrepreneurs, capital producers, retailers and bankers. The two types of households work and consume goods and housing. The difference between pa- tient and impatient households is that given the difference in their discount factors, the former saves and the latter borrows. Entrepreneurs also consume goods but not housing. Instead, entrepreneurs buy capital good and hire workers to produce intermediate goods. Like impa- tient households, the discount factor of entrepreneurs is lower than those of patient households.

Bankers provide two types of one-period financial instruments: saving contracts (deposits) and borrowing contracts (loans). To obtain a bank loan, agents face a borrowing constraint tied to the value of collateral holdings: households borrow against the value of their holding of houses, while entrepreneurs against the holding of physical capital. The positive financial flows in equi- librium is determined by heterogeneity in agents’ discount factors. As the discount factor of the patient households is the highest, they save by purchasing deposits, while impatient households and entrepreneurs whose discount factors are lower borrow a positive amount of loans. The banking sector is monopolistically competitive, allowing banks to set interest rates on deposits and on loans to maximize profits.

Except for entrepreneurs, two other producing sectors are considered, a monopolistically competitive retail sector and a capital goods producing sector. Retailers buy intermediate goods

from entrepreneurs in a competitive market, differentiate and price them subject to nominal rigidities. Capital goods producers are introduced in order to derive a market price for capital.

Households provide labor services which are differentiated through labor unions. Wages are thus set by labor unions to maximize members’ utility subject to adjustment costs.

2.1 Patient Households

Patient households maximizes the expected lifetime utility:

E₀

∞

X

t=0

β_P^t

"

(1 − a^P)ε^z_tlog c^P_t − a^Pc_t−1^P
+ ε^h_t log h^P_t − l_t^P1+φ 1 + φ

#

, (1)

where c^P_t, l_t^P, h^P_t denotes consumption, labor, and houses. Parameters βP, a^P, φ are discount factors, habit coefficient and inverse of the Frisch elasticity. ε^z_t, ε^h_t are the exogenous shocks on consumption and housing demand.

Patient households’s choices are subject to the budget constraint:

c^P_t + q_t^h∆h^P_t + d^P_t ≤ w^P_t l_t^P + 1 + r_t−1^d
d^P_t−1

π_t + t^P_t − Γ_t, (2)

where d^P_t, q_t^h, w_t^P, r_t^d, π_t ≡ P_t/P_t−1 are the deposit holdings, real house prices, real wages, nominal deposit rates and inflation. Last, t^P_t the lump-sum transfer including a labor union membership net fee and dividends from firms and banks, and Gamma_tis the lump-sum tax.

2.2 Impatient Households

Impatient households maximizes the expected lifetime utility:

E₀

∞

X

t=0

β_I^t

"

(1 − a^I)ε^z_tlog c^I_t − a^Ic_t−1^I
+ ε^h_t log h^I_t − l^I_t^1+φ 1 + φ

#

, (3)

where c^I_t, l^I_t, h^I_t denotes consumption, labor, and houses. Parameters βI, a^I, φ are discount fac- tors, habit coefficient and inverse of the Frisch elasticity. ε^z_t, ε^h_t are the exogenous shocks on consumption and housing demand.

As β_I < β_P, impatient households do not save but borrow from bank. Therefore, except for the budget constraint:

c^I_t + q^h_t∆h^I_t + 1 + r_t−1^bH
b^I_t−1 πt

≤ w_t^Il_t^I+ b^I_t + t^I_t, (4)

impatient households’s choices are also subject to a collateral constraint:

1 + r_t^bH
b^I_t ≤ m^I_tE_tq_t+1^h h^I_tπ_t+1 . (5)

Variables q^h_t, w^I_t, b^I_t−1, b^I_t, r^bH are the real house prices, real wages, gross reimbursement of borrowing, new loans and net interest rates. Last, t^I_t the lump-sum transfer is a labor union membership net fee, while dividends from firms and banks are not included. In the borrowing constraint, m^I_t is the LTV ratio for a collateral. The LTV ratios is first assumed to follow exogenous stochastic processes and later set to a fixed ratio.

2.3 Entrepreneurs

Entrepreneurs maximizes the expected lifetime utility:

E₀

∞

X

t=0

β_E^t(1 − a^E) log c^E_t − a^Ec^E_t−1
, (6)

where c^E_t denotes consumption and parameters a^E are the habit coefficient. Entrepreneurs’

choices are subject to the budget constraint:

c^E_t + w_t^Pl^E,P_t + w_t^Il_t^E,I+ 1 + r_t−1^bE

π_t b^E_t−1+ q_t^kk_t^E + ψ(u_t)k^E_t−1

= y_t^E

x_t + b^E_t + q_t^k(1 − δ)k_t−1^E , (7) where k_t^E, b^E_t , u_t, l^E,P_t , l^E,I_t , y_t^E are physical capital, loans from banks, the degree of capacity utilization, and the labor inputs from patient and impatient households, respectively. Above are variables to be chosen. Moreover, δ, q_t^k, ψ(u_t)k_t−1^E are the depreciation rate of capital, the price of capital in terms of consumption, the real cost of setting a level of utilization rate.

1/x_t= P_t^W/P_tis the relative competitive price of the wholesale good. The wholesale good y^E is produced by the following production function:

y_t^E = A_tk_t−1^E u_tαh

l_t^E,Pµl_t^E,I1−µi1−α

(8)

where A_tis the total factor of productivity.

Like impatient households, entrepreneur’s discount factor βE < βP make entrepreneurs borrowers instead of savers. Therefore, entrepreneurs are subject to a collateral constraint:

1 + r_t^bE
b^E_t ≤ m^E_tE_tq_t+1^k π_t+1(1 − δ)k_t^E

(9)

wher b^E_t is the bank loan, r_t^bEis the nominal interest rate and m^E_t the LTV ratio for entrepreneurs.

2.4 Banks

Banks conduct the intermediation activity and adjust interest rates both on loans and deposits in response to conditions of the economy. There are three branches in the banking sector:

wholesale, loan and deposit. The wholesale branch operates under perfect competition and manages the capital position of the group. In the contrary, the two retail branches set rates in monopolistically competitive markets. The loan branch differentiate loans to households and to entrepreneurs; the deposit branch obtain deposits and differentiate deposits.

Wholesale branch

The wholesale bank aim to maximize the discounted sum of real cash flows by choosing loans B_tand deposits Dt:

max

{Bt,Dt}E₀

∞

X

t=0

Λ^P_0,t

"

1 + R^b_t
B_t+ (1 + r_t) B_t− B_t+1π_t+1

+ D_t+1π_t+1− 1 + R_t^d
D_t+ K_t+1^b π_t+1− K_t^b
− κ_Kb 2

 K_t^b B_t − ν^b

2

K_t^b

#

= max

{Bt,Dt}R^b_tB_t+ r_tB_t− R^d_tD_t− κ_Kb 2

 K_t^b Bt

− ν^b

²

K_t^b, (10)

where R^d_t is the interest rate paid to the deposit branch for the deposit D_t, while R^b_t is the interest rate obtained from the loan branch for fund B_t. The maximization is subject to the balance-sheet constraint B_t = D_t+ K_t^b, where bank capital K_t^b is accumulated out of retained earnings. Moreover, the bank suffers a cost if the capital-to-assets ratio ^K_B^tb

t deviate from the target value ν^b.

The banks are assumed to have access to unlimited finance at the policy rate r_tprovide by the central bank. That is the wholesale deposit rate is equal to the policy rate according to no arbitrage condition and the optimal condition is

R^b_t− r_t= −κ_Kb K_t^b

B_t − ν^b  K_t^b B_t

2

(11)

Deposit branch

The retail deposit branch of bank decides interest rate r^d_t(j) and collects deposits d^P_t(i, j) from patient households and then brings the raised funds to the wholesale branch. The maximization problem for the deposit branch is

max

r^d_t(j) E₀

∞

X

t=0

Λ^P_0,t

"

r_td^P_t(j) − r_t^d(j)d^P_t (j) −κ_d 2

 r_t^d(j) r_t−1^d (j) − 1

² r_t^dd_t

#

, (12)

where κ_dmeasures the adjustment cost of interest rate.

Loan branch

Obtaining wholesale loans from wholesale branch, differentiating them costless and resell them to impatient households and firms. That is, the loan branch choose r^bH_t (j), r^bE_t (j) to maximize branch profits

r_t^bHmax(j),r^bE_t (j) E₀

∞

X

t=0

Λ^P_0,t

"

r_t^bH(j)b^I_t(j) + r_t^bE(j)b_t^E(j) − R^b_t b^I_t(j) + b^E_t(j)

− κ_bH 2

 r_t^bH(j) r_t−1^bH(j) − 1

2

r^bH_t b^I_t − κ_bE 2

 r_t^bE(j) r_t−1^bE (j)− 1

2

r_t^bEb^E_t

#

(13)

where κbH, κ_bE are parameters measuring adjustment costs.

Bank Profits

Sum up earnings from the wholesale branch, retail loan branch and retail deposit branch to obtain the bank total profits.

j_t^b = r^bH_t b^H_t + r^bE_t b_t^E + r_tη_tB_t− r_t^dd_t− κ_Kb 2

 K_t^b B_t − ν^b

²

K_t^b− Adj_t^B, (14)

The profits is then used to accumulate bank capital of which the accumulation follows

π_tK_t^b = (1 − δ^b)K_t−1^b + j_t−1^b , (15)

where δ^b measures bank capital management cost.

2.5 Monetary policy and market clearing

The monetary policy is set according to the Taylor rule

(1 + r_t) = (1 + r_t−1)^φR(1 + ¯r)^(1−φR)π_t π

φπ(1−φR) y_t y_t−1

φy(1−φR)

ε^r_t (16)

where r_tis the policy rate, ¯r is the steady state rate, φ_R, φ_π, φ_y are responding parameters, and ε^r_t denotes the monetary policy shock.

The good market clearing condition is

y_t = c^P_t + c^I_t + c^E_t + q_t^k[k_t− (1 − δ)k_t−1] + k_t−1ψ(u_t) + δ^bK_t−1^b

π_t + Adj_t+ G_t, (17) where the term Adjt includes all adjustment costs. Meanwhile, housing market, labor market and financial market all clear

¯h = h^P_t + h^I_t, (18)

l_t^E,P = l^P_t (19)

l^E,I_t = l^I_t (20)

Dt= dt (21)

B_t= b^I_t + b^E_t + η_tB_t (22)

2.6 Exogenous Process

Shocks considered in this framework includes technology shock, consumption preference shock, housing preference shock, goods market shock, labor supply shock, monetary policy shock and financial market shock such as LTV ratio shock, deposit rate shock, loan rate shock and capital- to-asset ratio shock. All exogenous shock are AR(1) process except monetary policy shock.

A_t = (1 − ρ_a) ¯A + ρ_aA_t−1+ e^a_t, (23) m^I_t = (1 − ρ_mI) ¯m^I+ ρ_mIm^I_t−1+ e^mI_t , (24) m^E_t = (1 − ρ_mE) ¯m^E + ρ_mEm^E_t−1+ e^mE_t , (25) ε^z_t = (1 − ρz)¯ε^z+ ρzε^z_t−1+ e^z_t, (26) ε^h_t = (1 − ρ_h)¯ε^h+ ρ_hε^h_t−1+ e^h_t, (27) ε^d_t = (1 − ρ_d)¯ε^d+ ρ_dε^d_t−1+ e^d_t, (28) ε^bE_t = (1 − ρ_bE)¯ε^bE+ ρ_bEε^bE_t−1+ e^bE_t , (29) ε^bH_t = (1 − ρ_bH)¯ε^bH + ρ_bHε^bH_t−1+ e^bH_t , (30) ε^y_t = (1 − ρy)¯ε^y + ρyε^y_t−1+ e^y_t, (31) ε^l_t = (1 − ρ_l)¯ε^l+ ρ_lε^l_t−1+ e^l_t, (32) ε^Kb_t = (1 − ρ_Kb)¯ε^Kb+ ρ_Kbε^Kb_t−1+ e^Kb_t , (33)

3 Data and Estimation

Bayesian methods is adopted to estimate the model. We use US data includes real consumption, real house prices, real deposits, real loans to households and firms, the overnight rate, interest rates on deposits, loans to firms and households, nominal wage, and inflation rates. The sample period is 1998Q1–2019Q4. Data with a trend are made stationary using the HP filter (smoothing parameter equal to 1,600), while all interest and inflation rates are demeaned. Figure 4 plots the transformed data. Values of the calibrated parameters are reported in Table 1. The calibrated parameters are set by following Gerali et al. (2010) and Roger and Vlˇcek (2011).

The prior distributions are set according to Gerali et al. (2010) and are listed in Tables 2 and 3. Summary statistics of the posterior distribution of the parameters are also reported in Tables

1990 2000 2010 2020 -0.2

0

0.2 Real loans to firms

1990 2000 2010 2020 -0.1

0

0.1 Real loans to HHs

1990 2000 2010 2020 -0.05

0

0.05 Real deposit

1990 2000 2010 2020 -2

-1 0

1Interest rate: loans to firms

1990 2000 2010 2020 -1

0

1Interest rate: loans to HHs

1990 2000 2010 2020 -2

-1 0

1 Deposit rate

1990 2000 2010 2020 -2

-1 0

1 Policy rate

1990 2000 2010 2020 -5

0

5 Inflation

1990 2000 2010 2020 -0.02

-0.01 0

0.01 Real wage

1990 2000 2010 2020 -0.02

0

0.02 Real consumption

1990 2000 2010 2020 -0.1

0 0.1

0.2 Real house prices

Figure 4: US data used in estimation

Table 1: Calibrated Parameters

Parameter Description Value

β_P Patient households’ discount factor 0.9925

β_I Impatient households’ discount factor 0.965

βE Entrepreneurs’ discount factor 0.965

¯

ε^h Weight of housing in households’ utility function 0.15

φ Inverse of the Frisch elasticity 1.0

µ Share of unconstrained households 0.75

α Capital share in the production function 0.35

δ Depreciation rate of physical capital 0.04

¯

ε^y _ε¯y^ε¯−1^y is the markup in the goods market 6

¯

ε^l _ε¯l^ε¯−1^l is the markup in the labor market 5

¯

m^I Households’ LTV ratio 0.7

¯

m^E Entrepreneurs’ LTV ratio 0.24

ν^b Target capital-to-loans ratio 0.08

δ^b Cost for managing the bank’s capital position 0.016

¯

ε^d _ε¯d^ε¯−1^d is the markdown on deposit rate -1.46

¯

ε^bH _ε¯bH^ε¯bH−1 is the markup on rate on loans to households 2.79

¯

ε^bE _ε¯bE^ε¯bE₋₁ is the markup on rate on loans to firms 3.12 ξ₁ Parameter of adjustment cost for capacity utilization 0.0478 ξ₂ Parameter of adjustment cost for capacity utilization 0.00478

2 and 3. Metropolis algorithm is adopted to obtain draws from the posterior distribution of the parameters. There are 10 chains and 100,000 draws for each chain. The degree of consumption habits a^H is estimated to be high at 0.85. The investment adjustment cost κ_i is around 9.6. For the monetary policy responding parameters, the estimation shows a relatively high responses to inflation, a relatively low response to output growth and a relatively high degree of policy rate inertia. The result also shows that wage stickiness is stronger than price stickiness as the previous studies suggest. As for the degree of stickiness in bank rates, the estimation suggests that deposit rates adjust more rapidly than the rates on loans to changes in the policy rate.

Overall, the characteristics of the estimation results are close to their counterpart in Gerali et al.

(2010).

All shocks except for consumption preference shock ρz and the price markup shock ρy are quite persistent. The standard deviations vary much more comparing to the persistency do. For example, the standard deviations of price markup shock and wage markup shock are ten times higher than the rest of shocks. The standard deviations of monetary policy shock, balance sheet shock and technology shock are relatively small.

4 Shocks to Loan-to-Ratio value

In this section, we study how the LTV ratio shocks change the constraints faced by impatient households and entrepreneurs and thus affect the model economy. First, we consider a positive shock to the LTV ratio a firm faces when trying to obtain loan from the bankers. Parameter values are set according to the estimated posterior median. Figure 5 shows the responses of selected variables such as loan rate, loans, output and consumption. Both loan to firms and households and deposit increase. Interest rat, no mater deposit rate or loan rates slightly go up at the beginning and then go down after a few quarters. Since firms are now loosely constrained,

Table 2: Prior and Posterior Distribution of the Structural Parameters

Prior distribution Posterior distribution Parameter Distribution Mean Std.dev. Mean 2.5% Median 97.5%

κ_p p stickiness Gamma 50.0 20.0 29.520 29.520 29.520 29.521

κ_w w stickiness Gamma 50.0 20.0 95.575 95.565 95.574 95.586

κ_i Invest.adj.cost Gamma 2.5 1.0 9.575 9.574 9.575 9.576

κ_d Dep.rate adj.cost Gamma 10.0 2.5 3.201 3.200 3.201 3.201

κbE Firms rate adj.cost Gamma 3.0 2.5 7.876 7.875 7.877 7.877

κbH HHs rate adj.cost Gamma 6.0 2.5 8.737 8.735 8.737 8.738

κ_Kb Leverage dev.cost Gamma 10.0 5.0 11.914 11.914 11.914 11.914

φ_π T.R.coeff.on π Gamma 2.0 0.5 2.118 2.118 2.118 2.119

φ_R T.R.coeff.on R Beta 0.75 0.10 0.606 0.606 0.606 0.606

φ_y T.R.coeff.on y Normal 0.10 0.15 0.423 0.423 0.423 0.423

ι_p p indexation Beta 0.50 0.15 0.090 0.090 0.090 0.090

ι_w w indexation Beta 0.50 0.15 0.187 0.186 0.187 0.187

a^H Habit coefficient Beta 0.50 0.10 0.846 0.846 0.846 0.846

a^P = a^I = a^E= a^H。

Table 3: Prior and Posterior Distribution of the Structural Parameters (exogenous process) Prior distribution Posterior distribution Parameter Distribution Mean Std.dev. Mean 2.5% Median 97.5%

AR coefficients

ρ_z Consumpt.prefer. Beta 0.8 0.10 0.382 0.382 0.382 0.382

ρh Housing prefer. Beta 0.8 0.10 1.000 1.000 1.000 1.000

ρ_mE Firms’ LTV Beta 0.8 0.10 0.814 0.813 0.814 0.814

ρ_mI HHs’ LTV Beta 0.8 0.10 0.930 0.930 0.930 0.930

ρ_d Dep.markdown Beta 0.8 0.10 0.818 0.818 0.818 0.818

ρ_bH HHs loans markup Beta 0.8 0.10 0.775 0.775 0.775 0.775

ρ_bE Firms loans markup Beta 0.8 0.10 0.840 0.840 0.840 0.840

ρ_a Technology Beta 0.8 0.10 0.957 0.957 0.957 0.957

ρ_y p mark-up Beta 0.8 0.10 0.318 0.318 0.318 0.318

ρ₁ w mark-up Beta 0.8 0.10 0.594 0.594 0.594 0.595

ρ_Kb Balance sheet Beta 0.8 0.10 0.761 0.761 0.761 0.761

Standard deviations

σ_z Consumpt.prefer. Inv. Gamma 0.01 0.05 0.075 0.075 0.075 0.075 σ_h Housing prefer. Inv. Gamma 0.01 0.05 0.055 0.055 0.055 0.055 σ_mE Firms’ LTV Inv. Gamma 0.01 0.05 0.072 0.072 0.072 0.072

σ_mI HHs’ LTV Inv. Gamma 0.01 0.05 0.044 0.044 0.044 0.044

σ_d Dep.markdown Inv. Gamma 0.01 0.05 0.117 0.117 0.117 0.117 σ_bH HHs loans markup Inv. Gamma 0.01 0.05 0.035 0.035 0.035 0.035 σ_bE Firms loans markup Inv. Gamma 0.01 0.05 0.076 0.076 0.076 0.076

σ_a Technology Inv. Gamma 0.01 0.05 0.016 0.016 0.016 0.016

σ_y p mark-up Inv. Gamma 0.01 0.05 0.673 0.672 0.673 0.673

σ_l w mark-up Inv. Gamma 0.01 0.05 0.589 0.589 0.589 0.589

σKb Balance sheet Inv. Gamma 0.01 0.05 0.013 0.013 0.013 0.013 σ_R Monetary policy Inv. Gamma 0.01 0.05 0.001 0.001 0.001 0.001

they are able to borrow more, buy more capital, hire more labor and thus produce more. Out- put, investment and consumption all increase. Bank capital also initially increases but it then decreases before reaching 10 quarters due the fall of interest rate spread.

Next, a positive shock to the LTV ratio an impatient household faces when borrowing is considered. Parameter values are set according to the estimated posterior median. Figure 6 shows the responses of selected variables such as loan rate, loans, output and consumption. In a stark contrast, the deposit and loan to households increase but loan to firms decrease. The relax of impatient households’ borrowing constraint crowds out the firm’s loan demand. As the loan tend to go to impatient households rather than firms, investment fall slightly but turns positive after around eight quarters. However, output and consumption increase. All interest rate raises.

In particular, deposit rate increases more than loan rates to households and firms do. The larger interest rate spread allows bank to earn more and accumulate bank capital more.

5 Conclusion

This report relies on a DSGE model developed by Gerali et al. (2010) to investigate the role of LTV ratio plays under the financial crisis which originated from banking system. Gerali et al.

(2010) constructs and estimates a DSGE model in which the financial frictions are enriched with an imperfectly competitive banking sector. In this model, banks collect deposits and issue collateralized loans to both households and firms, and accumulate capital out of retained earn- ings. Banks’ capital-to-assets ratio and the degree of interest rate stickiness determines loan margin. In this report, we estimate the model with Bayesian techniques using the US data. The analysis shows that when the LTV limit on firms is relaxed, loan obtained by impatient house- holds also increases. However, when the LTV limit on impatient households is relaxed, the loan to firms is crowded out and decreases. The effect of the firm’s LTV ratio shock on variables

0 10 20 -2

0

2 Policy rate

0 10 20

-2 -1 0

1 Interest rate: HHs

0 10 20

-2 -1 0

1 Interest rate: Firms

0 10 20

-0.1 -0.05 0

0.05 Inflation

0 10 20

0 2 4

6 Loan to HHs

0 10 20

-5 0 5

10 Loan to Firms

0 10 20

-2 0 2

4 Output

0 10 20

-1 0 1

2 Consumption

0 10 20

-10 -5 0

5 Investment

0 10 20

-5 0 5

10 Deposits

0 10 20

-1 -0.5 0

0.5 Deposit rate

0 10 20

-5 0

5 Bank capital

Figure 5: LTV ratio shock: Firms

All rates are shown as absolute deviations from steady state, expressed in percentage points. All other variables are percentage deviations from steady state.

0 10 20 -0.2

0 0.2

0.4 Policy rate

0 10 20

-0.2 0 0.2

0.4 Interest rate: HHs

0 10 20

-0.2 0 0.2

0.4 Interest rate: Firms

0 10 20

-0.02 0 0.02

0.04 Inflation

0 10 20

0 10 20

30 Loan to HHs

0 10 20

-0.2 0

0.2 Loan to Firms

0 10 20

0 0.02 0.04

0.06 Output

0 10 20

-0.05 0 0.05

0.1 Consumption

0 10 20

-0.5 0

0.5 Investment

0 10 20

0 5

10 Deposits

0 10 20

-0.1 0 0.1

0.2 Deposit rate

0 10 20

-5 0

5 Bank capital

Figure 6: LTV ratio shock: HHs

All rates are shown as absolute deviations from steady state, expressed in percentage points. All other variables are percentage deviations from steady state.

such output, consumption and investment is more profound while the effect of its counterpart is relatively smaller. Moreover, although the deposit increases in both case, shock to firm’s LTV ratio and shock to household’s LTV ratio, the deposit rate goes down in the former case while goes up in the later case. Similarly, the loan rates to firms and households fall when firms face more relaxed constraints and the loan rates increase when households’ borrowing constraints are loosen.

References

Angelini, Paolo, Stefano Neri, and Fabio Panetta (2012), Monetary and macroprudential poli- cies, Working Paper Series 1449, European Central Bank.

Benigno, Gianluca, Huigang Chen, Christopher Otrok, Alessandro Rebucci, and Eric R. Young (2012), Monetary and Macro-Prudential Policies: An Integrated Analysis, Working Papers 1208, Department of Economics, University of Missouri.

Bianchi, Javier, Emine Boz, and Enrique Gabriel Mendoza (2012), “Macroprudential Policy in a Fisherian Model of Financial Innovation,” IMF Economic Review, 60, 223–269.

BIS (2010), Macroprudential instruments and frameworks: a stocktaking of issues and experi- ences, CGFS Papers 38, Bank for International Settlements.

Borio, Claudio (2003), “Towards a Macroprudential Framework for Financial Supervision and Regulation?” CESifo Economic Studies, 49, 181–215.

Borio, Claudio, Craig Furfine, and Philip Lowe (2001), “Procyclicality of the financial sys- tem and financial stability: issues and policy options,” in, Marrying the macro- and micro- prudential dimensions of financial stability, vol. 1, BIS Papers chapters, Bank for Interna- tional Settlements, 1–57.

Claessens, Stijn (2015), “An Overview of Macroprudential Policy Tools,” Annual Review of Financial Economics, 7, 397–422.

Evens, Owen, Alfredo M. Leone, Mahinder Gill, and Paul Hilbers (2000), Macroprudential Indicators of Financial System Soundness, IMF Occasional Papers 192, International Mon- etary Fund.

Gerali, Andrea, Stefano Neri, Luca Sessa, and Federico M. Signoretti (2010), “Credit and Bank- ing in a DSGE Model of the Euro Area,” Journal of Money, Credit and Banking, 42, 107–

141.

Hanson, Samuel G., Anil K. Kashyap, and Jeremy C. Stein (2011), “A Macroprudential Ap- proach to Financial Regulation,” Journal of Economic Perspectives, 25, 3–28.

IMF (2017), Technial Note – Macroprudential Policy Framework, IMF Countery Report No.

17/93, International Monetary Fund.

Jácome, Luis I. and Srobona Mitra (2015), “LTV and DTI Limits–Going Granular,” IMF work- ing paper, No. 15/154.

Lambertini, Luisa, Caterina Mendicino, and Maria Teresa Punzi (2013), “Leaning against boom- bust cycles in credit and housing prices,” Journal of Economic Dynamics and Control, 37, 1500–1522.

Roger, Scott and Jan Vlˇcek (2011), “Macroeconomic Costs of Higher Bank Capital and Liquid- ity Requirements,” IMF Working Papers 11/103.

107年度專題研究計畫成果彙整表

計畫主持人：林姿妤 計畫編號：107-2410-H-006-002-MY2 計畫名稱：貸款成數管制政策之實證意涵

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