The model

2.1 The model

2.1.1 The goods market

Consider a small open economy operates under floating exchange rates and perfect capital mobility in a DSGE structure. There are households, firms, banks, and government. The typical household owns a monopolistically competitive firm and a perfectly competitive bank. All the goods are traded across countries by using capital and labor as inputs which are immobile across countries. The consumption bundle of the countries includes the domestic goods and imports.

The consumption bundle in the country consists of the domestic and imported goods:

t

( ) ( )

^{d 1 d ( 1)}

( ) ( )

^{1 m ( 1) ( )1}

The associated price index of the composite goods, and the associated demands for each type of goods are shown below: and each type of goods in the aggregate consumption. P is the price of goods _tⁱ associated with the firms of the country. The goods of type d and m present the domestic goods and imported goods respectively.

The consumption demand and the price index in the rest of the world follow the similar fashion:

( ) ( ( )

^/

)

^*,

Here, P_t^x is the home country’s export price index denominated in the foreign currency and P_t^* is the aggregate price index for the rest of the world. We assume that

the law of one price holds for the home goods and thus P_t^d =P e_t^x _t where e_t is the nominal exchange rate.

2.1.2 The representative household

The typical household’s preference is described by

0

( )

the labor supplied in the good production and banking sector separately. ψ characterizes the importance of the utility generated by consumption .

The typical household obtains income from the salary of working, revenue from production, receipt of financial assets, and net sales of capital goods. So the budget constraint can be written as

a It is a Dixit-Stiglitz consumption bundle, in advance for always lending to consume.

( ) ( )

real wage rate and is identical across sectors. l is the labor demanded by firms in the _t production sector, while n is the labor demand of banks. _t M is nominal holdings of _t high-powered money at the end of t . T stands for the real lump-sum tax payment in _t the period t .

1

Bt₊ is the bonds issued by the home government and R denotes the associated _t^B interest rate. We assume that the home bonds are circulated within the country only. On the world asset market, there is one internationally tradable bonds, B_t^*₊₁, with the

interest rate R . Following the specification in Kollmann (2002), we assume there is a _t^B* world interest rate that prevails on the global asset market and the relationship between the world interest rate and the bond rate paid by the individuals in the small open economy is stated as below:

(

^1+RtB*

)

^{= +}

⁽

^{1 Rt*}

^{) (}

^{-φ Bt*+1/Pt*}

⁾

^{/χ (4)}

Eq. (5) captures the friction in the global financial market with φ as the degree of capital mobility. Higher φ represents lower capital mobility and thus the bond rate faced by the home individual will be lower, closer to the world bond rate. χ is the steady-state value of exports

(

Pt^x/Pt^*

)

^−μ.

2.1.2 The goods market clearing condition

Goods are sold in the domestic market or are exported to the rest of the world. Under monopolistically competitive markets, output is determined by the demand. Therefore, the market clearing condition holds as follows:

( )

¹

^{( ) ( )}

* 0

To simplify the model, we will assume that the capital remains at its steady-state level all the time, following GM (2007). Therefore, in the following calibrations, the investment expenditure is completely reflected by the movements of the capital value,

qt.

2.1.3 Banks

Aside from the real sector, there is a banking sector in the economy to supply the liquidity services, including deposits and loans, to the market. If the typical household wants to consume goods, they need to hold money in the period t for the payment.

Therefore, the consumption is subject to the credit-in-advance constraint as follows:

t t t

c VD

= P (6)

where D_t is the nominal deposits, and V stands for the velocity of deposits.^a

The bank as the financial intermediary receives deposits and creates loans. Thus the bank’s asset is composed of the total reserves M_t and loans L_t, while the liability

a The concept comes from the equation of exchange

(

^{MV =PY}

)

, similar to the turnover rate of money per year.

consists of the demand deposit D_t. The balance sheet is shown below:

t t t

M +L =D (7)

where M_t =τD_t with τ as the bank’s reserve ratio^a.

To offer loans, the bank has to hire labor for the loan management (such as evaluating customers, monitoring loan repayments, and so on), as well as the acquisition of capital and the home government bonds as the collateral. The internationally traded bonds are not effective to serve as the collateral for loans. The loan production is assumed to follow the Cobb-Douglas form:

where Z is the constant measure of the loan production efficiency.

(

1 1

)

k

t t t t

b₊ +A q Kρ ₊

is the collateral with b_t+1=B_t+1/P_t

(

1+R_t^B

)

. A_t^k and A_tⁿare shocks to the efficiency of capital as the collateral and the effectiveness of monitoring respectively. The financial distress that originates from the credit market can be characterized by negative shocks to A_t^k and A_tⁿ. Θ is a constant which manifests the inferiority of capital than the government bonds for collateral uses.^b

2.2 First-order conditions

Before obtaining the first-order conditions, we let

(

^{1 1}

)

/ ^k

t αct bt₊ A Θq Kt t t₊

Ω = + (9)

Since all the agents are symmetric, prices of goods in the same category will be identical. The first-order conditions with respect to l l n K B_t^s, _t, , , , , _t^s _{t t+1} B_t^*₊₁ P_t are

a That is to say, τ is the reserve requirement plus excess reserves.

b Because capital requires higher monitoring cost and has lower liquidity.

listed as follows:

The difference between Eq. (15) and Eq. (16) is the liquidity service offered by the home bonds to serve as the collateral for loans. Therefore, the interest rate of foreign bonds has to be high enough to offset its failure to serve as the collateral for loans. Eq.

(20) is the law of one price condition and Eq. (21) is the government budget constraint.

The government does not hold any international traded bond, but finances its

expenditures by levying tax, issuing high-powered money and bonds. In the symmetric, flexible-price equilibrium, Eqs.(1), (2), (4) - (21) determine the values of twenty endogenous variables, , , , ,c l n w λ, , , , ,Ω L D q B B b e P, ^*, , , ,^* P^d, c^A, ,ξ T and R R^B, ^B* given the processes of exogenous variables and government policies M b, and g . For simplicity, we assume the government spending g_t equals to zero throughout.

2.3 Exogenous variables

Now we turn to the exogenous variables. There are the world’s price index, import good price, and world interest rate for the rest of the world which have to be specified exogenously, because the small open economy does not have the power to affect the rest of the world. Following Kollmann (2002), we assume all of these exogenous variables follow the AR (1) process:^a

* * * *

Moreover, the exogenous shocks also obey the AR(1) process:

(

¹

)

^{1 ε , 0 1}

a We accept the most standard formula; I think it is best to stay close to the mainstream of this theory.

In addition, we assume that the growth rate of high-powered money follows the similar evolution process:

h_t =ρ^hh_t−1+ε ,^h_t 0≤ρ^h < (28) 1

where h_t =logM_t−logM_t−1. By assuming the monetary policy as the control over the stock of high-powered money, instead of the interest rate rule, this model can generate the interest rates endogenously.

在文檔中 貨幣政策法則與匯率波動程度於大小型開放性經濟體系之差異---福利與景氣循環的數量分析 (頁 23-31)