Master Thesis - Humboldt-UniversitÃ¤t zu Berlin

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4.7 Market equilibrium The final good market is in equilibrium if the production equals the demand by domestic consumers and investors plus exportation to the US and the Rest of the World economies: F t = C t + I t + X t (28) Government spending is assumed to be realized exclusively in domestic goods so aggregate demand for the intermediate good is given by: D t = D p t + D f t + G t (29) The equilibrium of the trade bock imposes the equalisation of imports and exports M T t = X t (30) The capital rental market is in equilibrium if the demand for capital expressed by the intermediate goods domestic producer equals the supply by the households. Equilibrium on the labour market is realized if the firm’s labour demand equals the labor supply at the wage set by the households. The interest rate is determined by an empirical reaction function describing monetary policy decisions. These are governed by a Taylor type reaction rule. The specific form of the monetary policy reaction function will be introduced in log-linearized version in the next section. 18
5 Model analysis We find it more convenient to treat the first order conditions, steady state and log-linearized equations together. For the purpose of the paper, we need to write the model in log-linearized form. This emerges from the first order condition equations and linearizing the equations around the steady state. 5.1 Households: Optimization problem Write the Lagrange function: H = E 0 ∞ ∑ t=0 + λ t ( 1 R e t β t 1 [( (Ct τ − H t )) 1−σc · exp( σ c − 1 (lt τ ) 1+σ l ) 1 − σ c 1 + σ l B τ t P C t + 1 Bt τ∗ − Bτ t−1 Rt e∗ Pt C S t Pt C − Bτ∗ t−1 P C t S t + (1 + τ c t )C τ t + I τ t − (1 − τt)w l t τ lt τ − ((1 − τt k )(rt k − δ)zt τ Kt−1) τ − δz t Kt−1 τ + Ψ(zt τ )Kt−1 τ − Divt τ − T Rt τ ) ( ) ɛ I + µ t (K t − K t−1 (1 − δ) − (1 − S t I t )I t )] I t−1 where λ t is the marginal value in utils of one real domestic currency’s worth of bonds and µ t is the marginal value of a unit of capital in utils (as defined in Kimball (1995)). The marginal value of capital Q t is: Q t = µ t λ t (31) Given the Ricardian equivalence implied by the model, it is not necessary to keep track of the household stock of bonds or the government’s budget constraint. Deriving the Lagrangian function with respect to holdings of domestic and foreign bonds, capital, investment, capital utilization, labor yields the following FOCs: 19
Page 1 and 2: Master Thesis: Monetary and Fiscal
Page 3 and 4: 6.9 ROW demand shock . . . . . . .
Page 5 and 6: Preference shocks, inflation object
Page 7 and 8: the households behavior with respec
Page 9 and 10: 4 The Model Our model consists of t
Page 11 and 12: The effective returns on domestic a
Page 13 and 14: y j t = min { } (1 − ω − ζ)
Page 15 and 16: M T t = M t + O t (17) Non-oil impo
Page 17: 4.5 Government For simplicity, we a
Page 21 and 22: with RP positive. The risk premium
Page 23 and 24: Î t = 1 1 + β (Ît−1 + βÎt+1
Page 25 and 26: W τ t = −Pt C 1 + τt c (1 + λ
Page 27 and 28: an exogenoeus ARMA(1,1) process aro
Page 29 and 30: Households use the following rule f
Page 31 and 32: 5.4 Final goods sector: Optimizatio
Page 33 and 34: ¯M d Ȳ = χ ¯C (1 − θ)( ν Ȳ
Page 35 and 36: P ˆ M d t Pt D − ˆ P M d t−1
Page 37 and 38: In the paper most of the shocks are
Page 39 and 40: 6.7 Capital tax shock Responses of
Page 41 and 42: 7 Conclusions In this model we have
Page 43 and 44: (AWM) for the Euro Area”, ECB Wor
Page 45 and 46: 9 Appendixes 9.1 Appendix 1 Data de
Page 47 and 48: Y: Real GDP (YER) W: Nominal wages
Page 49 and 50: Figure 3: Impulse-response analysis
Page 51 and 52: Figure 7: Impulse-response analysis
Page 53 and 54: Figure 11: Impulse-response analysi
Page 55 and 56: Figure 14: Impulse-response analysi
Page 57 and 58: Figure 16: Dynare code 57
Page 69:
Figure 28: Dynare code 69
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Master Thesis - Humboldt-UniversitÃ¤t zu Berlin

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