4.1 The Financial Sector
Banks lend to all three types of …rms:
Nt= Ntx+ Nth+ Ntf (73) In addition to these …rms, the banks lend to the government Btg and receive a risk-free interest rate Rt.
They borrow from foreign …nancial centers the amount Bf and pay a risk premium above the domestic interest rate when such foreign debt exceeds a steady-state level Bf :
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t= maxn 0; 'h
e(jBtf 1 Bfj) 1i Bt 1f o
(74) The banks thus pay a gross interest rate Rt+ ton their outstanding dollar-denominated debt Bt 1f to foreign …nancial centers.
In addition to paying deposits the interest rate Rmt we assume that banks are also required to set aside a required ratio of reserves on outstanding deposits,
MMt. The relevant opportunity cost of holding these reserves is of course the amount the banks can earn by holding risk-free government bonds, MRtMt:
In addition, banks are required to set aside a fraction of capital against their outstanding loans, N;tNt:: As in the case of the required reserves against deposits, the opportunity cost is given by N;tRtNt:
The parameter N;t is time-varying, and captures a stochastic uncertainty component in the costs of bank lending to all types of …rms. The parameter is the autoregressive parameter while N is the steady-state capital/asset ratio for banks.
N;t = N;t 1+ (1 ) N+ ;t
;t~N (0; 2)
The gross pro…t of the banking sector is given by the following balance-sheet identity:
B
t = (1 + Rt 1)Bgt 1+ (1 + Rnt 1)Nt 1+ StBtf+ Mt (75) (1 + Rt 1+ t 1)Bt 1f St (1 + Rmt 1)Mt 1
Btg Nt MRt 1Mt 1 NRt 1Nt 1
The bank maximizes its present discounted value of its pro…ts, given by VtB, with respect to its portfolio of assets (loans to the government and …rms, Bgt and Nt ) and liabilities (deposits from households and borrowing from foreign
…nancial centers Mtand Btf).
M ax
fBgt;Nt;Mt;Bftg
VtB = Bt + Vt+1B
This set of …rst-order conditions leads to the familiar set of spreads for interest rates, as well as the interest-parity equation:
Rt = Rnt N (76)
Rt = Rmt + M (77)
(1 + Rt)St = (1 + Rt + t+ 0tBtf)St+1 (78) The foreign interest rate evolves according to the following law of motion:
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Rt = R Rt 1+ (1 R )R + R ;t R ~N (0; 2R )
4.2 The Monetary Policy
We assume that the liquidity provision to the banking sector, which causes the change in the reserve of the banking sector RES; adjusts to the target for the rate of growth of deposits in the banking sector.3
RESt = RES RESt 1 (1 RES) M[ Mt ] + M;t
M;t~N (0; 2M)
where is the target rate of deposit growth, RES is the smoothing parameter and M is the reaction coe¢ cient, with M > 1: There is also a shock to monetary policy, M;t, normally distributed with variance 2M:
The interest rate adjusts in this case to equilibrate the balance sheet of the
…nancial sector.
Rt=
Nt+ Bt+ (1 + Rt+ t 1)Bft 1St 1+ (1 M)Mt 1 RESt Mt BftSt (1 N)Nt 1 Bt 1
Bt 1+ Nt 1(1 N) Mt 1(1 M)
Basically this equation states that the ‡ow returns to the system from gov-ernment bonds and loans to …rms, less interest payments on deposits, should be su¢ cient to …nance new loans to …rms and the government, as well as payments on foreign debt, net of new deposits and reserve injections by the central bank..
Thus, ceteris paribus, an increase in bond issues or loan demand by …rms, or foreign interest rates would increase the domestic interest rate, while an increase in deposits or reserves would decrease the interest rate.
In the counterfactual scenario of an in‡ation targeting Taylor rule, the in-terest rate adjusts in the following way:
Rt= rRt 1+ (1 ) bt+ (1 r)R (79) The coe¢ cients r and are the smoothing parameter and in‡ation
coef-…cient, with 0 < r < 1 and > 1:R is the steady state interest rate, equal to the steady state foreign interest rate R and bt is the deviation of actual in‡ation from the target rate of in‡ation. Given that the central bank sets the interest rate, it provides reserves (or takes out reserves) to the banking sector through open market operations to insure a balance-sheet equilibrium:
3In the absence of currency, Mtis equivalent to the measure of broad money in this model.
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RESt = Nt+ Bt+ (1 + Rt+ t 1)Bt 1f St 1 +(1 + Rt M MRt)Mt 1 BtfSt
(1 + Rt+ N NRt)Nt 1 Mt (1 + Rt)Bt 1 (80) In the counterfactual cases of the …xed exchange-rate case or exchange-rate mangement, the domestic interest rate follows the foreign interest rate plus the risk premium, while the central bank adjusts reserves to the banking sector to assure balance-sheet equiibrium
For the in‡ation-targeting exchange-rate rule, the following formula holds:
st= s st 1 (1 s) s bt+ (1 r) s (81) This rule shows that the monetary authority adjusts depreciation of the nom-inal exhange rate relative to the long-run depreciation rate s with a smoothing coe¢ cient s; with 0 < s< 1: When in‡ation is above its target rate, withbt
> 0; the monetary authority will allow the nominal rate to appreciate. As in the Taylor rule, we assume s > 1:
4.3 Fiscal Policy
The government takes in taxes from the households and engages in spending on non-traded services. . We assume that spending may be either pro-cyclical or counter-cyclical, depending on the value of GY, that there is smoothing in government consumption, and there is a stochastic component to spending:
Gt = (1 G)G + GGt 1+ (1 G) GY(Yt 1 Y ) + G;t (82)
G;t~N (0; 2G) (83)
Given its source of labor and consumption tax revenue, the …scal borrowing requirement is given by the following identities:
T AXt = WtLt+ cPtCt (84)
Btg = (1 + Rt 1)Bgt 1+ PthGt T AXt (85)
4.4 Foreign Assets
The aggregate foreign borrowing or asset accumulation evolves through the fol-lowing identity:
StBtf = [1 + Rt 1+ t 1]StBt 1f + Ptf(Ctf+ Itf) Ptx(Ct) (86) It should be noted that the risk premium embedded in the accumulation of foreign debt e¤ected closes this open economy model, so that the domestic
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consumption and foreign debt levels do not become indeterminate. There are other ways to close the open economy model, such as adjustment costs on foreign debt accumulation, or an endogenous discount factor [see Schmitt-Grohé and Uribe (2003)] We think that the incorporation of a time-varying endogenous risk premium is a more intuitive way to close this model.
5 Calibration
5.1 Calibrated Parameters a¤ecting Steady State
We calibrate the parameters in accordance with the steady state by using the Taiwan’s quarterly data from the beginning of 1998 through the end of 2007, before the outbreak of the subprime crisis, for the characterization of the macro-economic fundamentals in Taiwan.
The discount parameter follows the value used by most conventional mod-els. The habit persistence parameter % is consistent with most of the empirical estimations.4 1 > 2 is assumed to indicate a higher intratemporal elasticity between consumption of home and foreign goods in the total consumption index than the elasticity of intratemporal substitution between consumption of export and home goods in the domestic consumption index.
For investment, we assume an equal share of domestic and imported goods, with i = :5: The elasticity parameter i is set at 2.5, equal to the elasticity parameter for home and foreign goods.
The ratios of consumption of foreign goods in the aggregate consumption,
1and the share of export-goods consumption in the total domestic consump-tion basket, 2, are assumed to be 0.3 and 0.2 respectively, for an approximated characterization of Taiwan’s consumption pattern. In this model, the steady-state values are quite sensitive to the tax rates. The income and consumption tax rates , C are assumed to be slightly higher than the applicable tax rates in Taiwan, which can be approximately 0.15 on average for the income tax and 0.05 for consumption tax respectively. The parameters are speci…ed to generate the steady-state government expenditure share in GDP to be 0.24 close to 0.2 that the data indicate.
Since the …nancial system is well established in Taiwan, thus we assume rela-tively low …nancial friction parameters. The parameters i, i = 1; ::3;which rep-resenting the borrowing needs of the export, home-goods and importing …rms, were all set equal at a value of .5. The capital coe¢ cient in the export produc-tion funcproduc-tion, x, is set to to replicate the shares of capital and labor in the economy. Finally the banking reserve and lending cost parameters M; N, are set to replicate observed low spreads in the …nancial sector.
4According to Teo (2009), the estimated habit persistence parameter of Taiwan is approx-imately 0.8.
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Table 2: Calibrated Parameters
1Symbol De…nition Values
discount factor 0.99
% habit parameter 0.8
capital depreciation 0.06
adjustment cost 0.005
1 foreign cons. in total cons. index 0.3
2 share of export good in dom.cons. index 0.2
i share. of export good in investment index 0.5
relative risk aversion parameter 3.0
$ labor supply elasticity 5
L disutility of labor 1
C consumption in CES utility 0.9
{ CES utility coe¢ cient -0.1
1 intratemporal substitution elasticity, total cons 2.5
2 intratemporal substitution elasticity, domestic cons 1.5
i intratemporal substitution elasticity, investment 2.5
; C tax rates on labor income and consumption 0.2, 0.2
h; x; f …nancial friction parameters 0.5
; w substitution elasticity for di¤erentiated goods and labor 6
x capital coe¢ cient in traded goods 0.33
h intermediate coe¢ cient in non-traded production 0.33
M; N deposit and lending costs for banks 0.1, 0.2
5.2 Calibrated Parameters for Dynamics and Volatilites
Table 2 shows the calibrated values for the volatilities and the dynamic adjust-ment parameters for the shock processes and the Calvo pricing. Since this is a a simulation, we specify the shocks volatilities at .01 for separate simulations.
We make use of Bayesian estimation resutls by Teo for most of the parameters governing the dynamics of the shocks and the Calvo pricing.
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Table 3:
Parameters and Std Deviations for Dynamic Processes
Volatility Name Values
Zx Traded Goods Prod .5
Calvo Pricing-Home Goods .5
w Calvo Wage Setting .5
I Calvo Pricing-Imported Goods .5