3 Production and Technology

3.1 Nontraded Services

The non-traded services is simply a function of labor L^h, intermediate goods M I and a technology shock Z_t^h

Y_t^h= Z_t^hM I_t^h L^h_t ^{1 h} (30) The coe¢ cient hrepresents the relative factor shares of intermediate goods, while the technology shock is given by Z_t.^hThis shock follows the autoregressive process:

ln(Z_t^h) = _Zhln(Z_{t 1}^h ) + ^h_t (31)

h

t N (0; ²_h ) (32)

The demand for the home services can be both for domestic consumption, as well for government services:

Y_t^h= C_t^h+ Gt (33)

We assume that the …rm faces a liquidity constraint. It must borrow an amount N_t^hfrom banks each quarter to pay a fraction _hof its wage bill, at the borrowing rate R_tⁿ:¹

N_t^h= _hWtL^h_t; (34)

The total pro…ts (or dividends) of the export …rm is given by the following identity:

h

t = P_t^hY_t^h (1 + _hRⁿ_t)WtL^h_t P_t^miM It (35) where P^mi is the price of intermediate goods. Maximizing pro…ts with respect to the use of labor and intermediate goods, we have the following …rst-order conditions for the …rm:

@Y_t^h

We assume intermediate goods M I are both domestically produced and imported from abroad, and that the price Pⁱ is the relevant price for these

1We assume that all these three sectors, non-traded, export and import, borrow from the domestic …nancial sector to …nance their wage or import spendings. The establishment of the

…nancial sector permits us to examine the …nancial shock same as the source of the current

…nancial crisis. The occurrence of …nancial shock leads to the rise in the …nancing costs of

…rms and thereby results in production contractions.

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goods. The investment variable is a CES aggregate of these two investment The parameters _mi and (1 _mi) are the relative shares of foreign and domestic goods in the overall investment index, while _miis the price elasticity of demand for each investment component.

The demand for each internediate-good component is a function of its relative price:

The index P_t^f is the price of imported goods, in domestic currency, while P_t^x is the price of domestic goods-producing forms (which can be exported, or used for domestic consumption and domestic investment). The overall price index for investment goods is given by the following equation:

P_t^mi= (1 _mi) (P_t^x)^{1 mi}+ _mi P_t^{f 1 mi}

1 1 mi

(41)

3.2 Export Goods

The …rm producing export goods, as well as traded goods for domestic con-sumption as well as domestically-produced investment and intermediate goods, face a Cobb-Douglas technology:

Y_t^x= Z_t^xK_t^x(L^x_t)^{1 x} (42) There is an export demand shock Z^xwhich follows the autoregressive process:

ln(Z_t^x) = _xln(Z_{t 1}^x ) + ^x_t (43)

x

t N (0; ²_x ) (44)

Foreign export demand X is also subject to a stochastic shock, _t at time t.

X_t = _X X_{t 1}+ (1 _X )X + _t (45)

t N (0; ²_X ) (46)

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Under a small open economy setting we also assume that the price of the ex-port good in domestic currency is simply equal to the exchange rate St multiplied by the world export price, P_t^x . We assume that the world export price follows the following exogenous stochastic process:

ln(P_t^x ) = _Px ln(P_{t 1}^x ) + (1 _Px ) ln(P^x_t ) + ^P_t^x (47)

P^x

t N (0; ²_Px ) (48)

Total demand for the export good is composed of the local demand (for consumption purposes and investment and intermediate goods) as well as the foreign demand:

Y_t^x= C_t^x+ X_t + I_t^d+ M I_t^d

These …rms face a liquidity constraint for meeting their wage bill:

N_t^x= _xWtL^x_t (49)

The pro…ts of the export-goods …rms are given by the following relation:

x

t = P_t^xY_t^x (1 + _xRⁿ_t)W_tL^x_t R^k_tK_t (50) Optimizing pro…ts implies the following …rst-order condition for cost mini-mization:

We assume that labor can move between the home-goods and export sectors.

This implies the following equality for real labor productivity in each sector:

@Y_t^x

Imported goods Y^f are used for both consumption C^f and for investment in the goods-producing …rms, I^f as well as intermediate goods M I^f :

Y_t^f = C_t^f + I_t^f+ M I_t^f (53)

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The importing …rms do not produce these goods. However, they have to borrow a fraction _f of the cost of these imported goods in order to bring them to the home market for domestic consumers and investors:

N_t^f = _f(S_tP_t^f Y_t^f) (54) where P_t^f is the world price of the import goods and S_tis the exchange rate.

The domestic marginal cost of the imported goods is given by:

AF_t= 1 + _fR_tⁿ S_tP_t^f (55)

3.5 Calvo Wage and Price Setting

The labor market does not clear, and wages are modelled as staggered contracts with a fraction (1 _w) renegotiated each period. Each household j chooses the optimal wage W_t^oby maximizing the expected discounted utility subject to the demand for its labor L^j_t = ^W_W^to

t

wL_t where _w is a parameter governing the degree of substitution.² This behavior is modelled in a similar manner to the Calvo sticky prices and the model is written in recursive form as:

W_t^num = (W_t) ^{w+ w$} L^1+$_t + _w :W_t+1^num (56) where, W_t^num and W_t^den are auxiliary variables in the formula.

We assume monopolistically competitive …rms in the non-traded services sector. Let the marginal cost at time t be given by the following expression:

At= P^{mi h}[(1 + ₁Rⁿ_t)Wt]^{1 h} Z_t^h

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( _h) ^h(1 _h)^{1 h} (60) In the Calvo price setting world, there are forward-looking price setters and backward looking setters. Assuming at time t a probability of persistence of the price at , with demand for the product from …rm j given by Y_t^h P_t^h , the expected marginal cost, in recursive formulation, is presented by the expression for A^num_t : The expected demand, for the given price, is given by the variable A^den_t :

2By using Bayesian estimation on Taiwan’s data, the posterior estimate of _wis 0.469 in Teo (2009). Although it is lower than the estimates of Smets and Wouters (2003) for the European countries, it still shows signi…cant wage stickiness in Taiwan.

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A^num_t = Y_t^h P_t^h A_t+ A^num_t+1 (61)

A^den_t = Y_t^h P_t^h + A^den_t+1 (62)

P_t^o = A^num_t

A^den_t + Z_t^P (63)

ln(Z_t^P) = _ZPln(Z_{t 1}^P ) + ^P_t (64)

P

t N (0; ²_P ) (65)

P_t^h;b = P_{t 1}^h (66)

P_t^h = P_t^{h;b 1} + (1 ) (P_t^o)¹

1 1

(67)

The stochastic term Z_t^P captures a mark-up pricing shock to the monopo-listic price-setting behavior. It follows, in logarithmic form, an autoregressive process with innovations have mean zero and standard deviation ²_P :

Calvo pricing for imported goods works in a similar way to Cavlo pricing for home goods. Given the marginal cost of imported goods, AFt; the following recursive setup gives us the price setting behavior for imported goods:

AF_t^num = Y_t^f P_t^t AFt+ AF_t+1^num (68)

AF_t^den = Y_t^f P_t^f + AF_t+1^den (69)

P_t^f;o = AF_t^num

AF_t^den (70)

P_t^f;b = P_{t 1}^f (71)

P_t^f = _i P_t^f;b

1

+ (1 _i) P_t^f;o

1 1¹

(72)