LA RESPONSABILIDAD CIVIL EN EL COMMON LAW

At the end of period t, each intermediate goods …rm f ₂ [0;1] produces a di¤erentiated intermediate good Yf;t, using physical capital Kef;t and labour services Nf;t. according to the following Cobb-Douglas technology:

Yf;t= t Kef;t (ztNf;t)1 zt (4.25)

1 4 9_{Coenen et al. (2013) assume that lump-sum taxes are levied on Ricardian households and a distribution}

of lump-sum transfers is favorable to non-Ricardian households. However, we adopt a di¤erent structure because an analysis of redistribution policy is not our objective. Cogan et al. (2013) stay in line with our model.

where t denotes transitory technology shock that a¤ects total factor productivity and

follows an AR(1) process:

ln t= ln t 1+ t;0< <1; t N(0; ) (4.26)

and the variableztdenotes a permanent technology shock that augments the productivity of labour permanently. The rate of labour-augmenting productivity gz;t = zt=zt 1 fol- lows a serially correlated process and determines the model’s balanced growth path. The

parameter is e¤ective capital share and the termzt is …xed costs of production. Physical capital Kef;t is a constant-returns-to-scale (CES) aggregate of private capital servicesKf;t and the public capital stockKG;t

e

Kf;t= ( 1= K

K (Kf;t)(1 1= K)+ (1 K)1= K(KG;t)(1 1= K)) K=( K 1) (4.27)

where Kis a share of private capital services, and the parameter K denotes the elasticity

of substitution between private capital services and the public capital stock.150

We adopt a time-to-build technology for public capital following Leeper et al. (2009), as

in Coenen et al. (2013). We, thus, assume that it takesLperiods to complete government investment and add the public capital stock. The law of motion for public capital is then

given by

KG;t+1 = (1 G)KG;t+AIG;t L+1 (4.28)

where G denotes the depreciation rate of the public capital stock. AIG;t L+1 is the autho-

rised budget for government investment in period t L+ 1. Government investment that

1 5 0

K ! 0 implies perfect complements, K ! 1 gives perfect substitutes, and K ! 1 yields the

is actually implemented is de…ned by IG;t = L 1 X n=0 bnAIG;t n (4.29) with L_P1 n=0

bn = 1, and enters the government budget constraint, as well as the economy’s aggregate resource constraint.

We assume that the domestic intermediate goods …rm charges di¤erent prices at home

and abroad, setting prices in domestic currency regardless of the market of destination. In

both markets, prices are adjusted following staggered price contracts of Calvo (1983).151

Therefore, the aggregate price index of product sold domestically PH;t is given by this equation: PH;t= (1 H) PeH;t 1=1 'H t + _H H H;t 1 1 H t PH;t 1 1=1 'H t 1 'H t (4.30)

Also the aggregate price index of product sold abroadPX;tis given by a similar equation:

PX;t= (1 X) PeX;t 1=1 'X t + _X X X;t 1 1 X t PX;t 1 1=1 'X t 1 ' X t (4.31)

Only a fraction 1 _H or 1 _X of the …rms are permitted to re-set their prices each

period. PeH;t and PeX;t are optimal prices in each market, respectively. 'Ht and 'Xt are price indexation parameters. We also assume that those …rms which are not permitted

to optimise its price can adjust their prices according to an average of past intermediate

goods in‡ation and the in‡ation target of the domestic monetary authority t. H and

X are indexation parameters determining the weight on past in‡ation.

4.3.3. Domestic …nal goods producers

1 5 1_{A detailed explanation of price setting is found in Appendix A.} 1 5 2

The …nal goods …rms produce three distinct non-tradable …nal goods by combining the

domestically-produced intermediate goods with the imported intermediate goods, namely

a private consumption good,QC_t , a private investment good,QI_t, and a public consumption good,QG_t .

The representative …rm producing the non-tradable …nal private consumption goods and

investment goods integrates a bundle of domestically-produced intermediate goods, H_tC, with a bundle of imported foreign intermediate goods,IM_tC, using the CES technology,

QX_t = [ 1= X X H X t 1 1= X + (1 X)1= X 1 IMX IM_tX=QX_t ; IM_t IM_tX 1 1= _X ] X= X 1 X _{2 f}C; I_g (4.32)

where _X denotes the intra-temporal elasticity of substitution between the distinct bundles

of domestic and foreign intermediate goods, while the parameter X indicates the home

bias in the production of the consumption goods and the investment goods. The …nal

goods producers is subject to a cost _IMX IM_tX=QX_t ; IM_t when varying the use of the bundle of imported goods in producing the consumption goods and the investment goods.

In contrast, the …nal public consumption good,QG_t , is produced by only using domestic intermediate goods; that is,QG_t =H_tG.