An estimated dynamic stochastic general equilibrium model of the ...

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where β = 1/(1−τ+ r k ) . The current value of the capital stock depends negatively on the ex-antereal interest rate, and positively on its expected future value and the expected rental rate. TheQintroduction of a shock to the required rate of return on equity investment, η t , is meant as ashortcut to capture changes in the cost of capital that may be due to stochastic variations in theexternal finance premium. 16 We assume that this equity premium shock follows an IID-Normalprocess. In a fully-fledged model, the production of capital goods and the associated investmentprocess could be modelled in a separate sector. In such a case, imperfect information between thecapital producing borrowers and the financial intermediaries could give rise to a stochastic externalfinance premium. For example, in Bernanke, Gertler and Gilchrist (1998), the deviation from theperfect capital market assumptions generates deviations between the return on financial assets andequity that are related to the net worth position of the firms in their model. Here, we implicitlyassume that the deviation between the two returns can be captured by a stochastic shock, whereasthe steady-state distortion due to such informational frictions is zero. 17The capital accumulation equation is standard:(31) Kˆ(1 ) ˆ ˆt = − τ Kt− 1 + τIt−1With partial indexation, the inflation equation becomes a more general specification of the standardnew-Keynesian Phillips curve:(32)βpˆ t = Etπˆt+1+ πˆt−11+βγ p 1+βγ pπ11+βγp(1 − βξpξ)(1 −ξpγp)+ka p[ αrˆt + (1 −α)wˆt − εˆt + η ]Inflation depends on past and expected future inflation and the current marginal cost, which itself isa function of the rental rate on capital, the real wage and the productivity parameter. When γ p = 0 ,this equation reverts to the standard purely forward-looking Phillips curve. In other words, thedegree of indexation determines how backward looking the inflation process is. The elasticity ofinflation with respect to changes in the marginal cost depends mainly on the degree of pricestickiness. When all prices are flexible ( ξ p = 0) and the price-mark-up shock is zero, this equationreduces to the normal condition that in a flexible price economy the real marginal cost should equalone.Similarly, partial indexation of nominal wages results in the following real wage equation:t1617This is the only shock that is not directly related to the structure of the economy.This shock can also take up exogenous distortions or non-rational bubbles in asset prices. For such alternativeinterpretations of this equity premium shock and an analysis of optimal monetary policy in the presence of suchshocks, see Dupor (2001).12 NBB WORKING PAPER No.35 - October 2002
(33)wˆtβ1 β 1+βγ=+ +−w γE +−+wtwˆt 1 wˆt 1 Etπˆ−++ +t+πˆt πˆt1 β 1 β 1 β111+β 1+β1−1+β(1 − βξw)(1−ξw)⎡σL w⎤⎢wˆ− −c− − −+t σ LLˆt ( Cˆt hCˆt − ) εˆt η(1tλ ⎣−⎥+w)1σ L1 h(1) ξ⎦wλ wThe real wage is a function of expected and past real wages and the expected, current and pastinflation rate where the relative weight depends on the degree of indexation of the non-optimisedwages. Whenγ w= 0 , real wages do not depend on the lagged inflation rate. There is a negative effect of thedeviation of the actual real wage from the wage that would prevail in a flexible labour market. Thesize of this effect will be greater, the smaller the degree of wage rigidity, the lower the demandelasticity for labour and the lower the inverse elasticity of labour supply (the flatter the laboursupply curve).The equalisation of marginal cost implies that, for a given installed capital stock, labour demanddepends negatively on the real wage (with a unit elasticity) and positively on the rental rate ofcapital:(34) ˆkL = − ˆ + (1 + )ˆ + ˆt wtψ rtKt−1Ψ'( 1)where ψ = is the inverse of the elasticity of the capital utilisation cost function.Ψ" ( 1)The goods market equilibrium condition can be written as:G ak(35) Yˆt = (1 −τky − g y ) Cˆt + τkyIˆt + g yεt= φεˆt + φαKˆt rˆt (1 ) Lˆ− 1 + φαψ + φ −αt ,wherek y is the steady state capital-output ratio,g y the steady-state government spending-outputratio and φ is one plus the share of the fixed cost in production. We assume that the governmentspending shock follows a first-order autoregressive process with an IID-Normal error term:G G Gε t = ρGεt−1 + ηt.Finally, the model is closed by adding the following empirical monetary policy reaction function:(36)Rˆt= ρRˆr∆πt−1( πˆ+ ( 1 − ρ ){ πt− πˆt−1t) + r∆y+ r(Ŷπt( πˆ− Ŷt−1pt− π t ) + rY(Ŷ− (Ŷ − Ŷt−1pt−1t−1− Ŷ)) + ηThe monetary authorities follow a generalised Taylor rule by gradually responding to deviations oflagged inflation from an inflation objective (normalised to be zero) and the lagged output gapdefined as the difference between actual and potential output (Taylor, 1993). Consistently with theDSGE model, potential output is defined as the level of output that would prevail under flexiblept−1Rt)} +NBB WORKING PAPER No. 35 - October 2002 13
Page 3 and 4: AbstractThis paper develops and est
Page 5 and 6: TABLE OF CONTENTS:1. INTRODUCTION..
Page 7 and 8: 1. IntroductionIn this paper we pre
Page 9 and 10: shock leads to a gradual increase i
Page 12 and 13: 2.1.2 Labour supply decisions and t
Page 14 and 15: The first-order conditions result i
Page 16 and 17: jt⎛⎜ p− MCtt )⎜⎝Ptp,t(24)
Page 20: price and wages in the absence of t
Page 23 and 24: whereÊ t denotes the number of peo
Page 25 and 26: curve for a normal distribution wit
Page 27 and 28: where p(θ A ) is the prior density
Page 29 and 30: 3.3.2 Comparison of empirical and m
Page 31 and 32: the effects on marginal cost and in
Page 33 and 34: 4.3 Historical decompositionGraphs
Page 35 and 36: very much in response to the variou
Page 37 and 38: estimate of potential output should
Page 39 and 40: Table 1: Parameter estimatesPrior d
Page 41 and 42: Table 3: Variance decompositionC I
Page 43 and 44: 300020001000persistence productivit
Page 46 and 47: Graph 3: Productivity shock (1)0.50
Page 48 and 49: Graph 5: Wage mark-up shock0.050yc0
Page 50 and 51: Graph 7: Preference shock1.210.8yc0
Page 52 and 53: Graph 9: Equity premium shock0.30.2
Page 54 and 55: Graph 11: Monetary policy shock0-0.
Page 56 and 57: Graph 13: Inflation decomposition -
Page 58 and 59: Graph 16: Labour supply shock: flex
Page 60 and 61: Graph 18: Investment shock: flexibl
Page 62 and 63: Graph 20: Natural Output Gap105Natu
Page 64 and 65: ReferencesAbel A.D. (1990), “Asse
Page 66 and 67: Geweke J. (1999), “Computational
Page 68 and 69:
NATIONAL BANK OF BELGIUM - WORKING
Page 70 and 71:
24. "The impact of uncertainty on i
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