1A canonical Keynesian DSGE model Miller GR5215 A canonical Keynesian DSGE model: 2 We will describe a canonical Keynesian DSGE mode: Clarida, Gali and Gertler (2000), see Romer 7.8 Basic model is 3 equations: 1] the Calvo New Keynesian Phillips curve 2] the NK IS curve 3] a forward-looking interest rate rule as a behavioral model for central bank policy The three equations 3 The equations are linear, without intercepts: they should be regarded as local log-linear approximations around a steady state, thus all variables have the interpretation of deviations from steady state yt = Et[ yt+1]− 1θ rt +utIS π t = βEt[π t+1]+κ yt +utπ , 0< β <1, κ >0 rt =φπEt[π t+1]+φ yEt[ yt+1]+utMP , φπ >0, φ y ≥0 Model notes 4 The model is completely forward looking – the particular form of MP has been specified to make sure we don’t have a combination of forward looking and backward looking yt = Et[ yt+1]− 1θ rt +utIS π t = βEt[π t+1]+κ yt +utπ , 0< β <1, κ >0 rt =φπEt[π t+1]+φ yEt[ yt+1]+utMP , φπ >0, φ y ≥0 That’s also the reason for the Calvo model, even though there is strong evidence of backward- lookingness in inflation (inflation inertia – see Romer for discussion) Disturbances 5 Where the autoregressive parameters are all stable, that is lie on (-1,1) ut MP = ρMPut−1MP +etMP ut Is = ρISut−1IS +etIS ut π = ρπut−1π +etπ Express in terms of expectations and innovations 6 Use the monetary policy equation to substitute out the interest rate: yt = − φπ θ Et[π t+1]+(1−φ yθ )Et[ yt+1]+utIS − 1θ utMP π t = β − φπκ θ ⎛ ⎝⎜ ⎞ ⎠⎟ Et[π t+1]+(1−φ yθ )κEt[ yt+1]+κutIS +utπ −κθ utMP Special case: white noise disturbances 7 With white noise, there’s nothing backward looking in the model, so expectations will just be equal to the equilibrium results with no disturbances and will be the same every period – which is just zero for output and inflation, so: rt =ut MP So, like the basic RBC models, this model has no internal propagation mechanism; no serial correlation without serially correlated shocks yt =ut IS − 1 θ ut MP π t =κut IS +ut π −κ θ ut MP The general case 8 The model can be solved in a “straightforward” way using the method of undetermined coefficients …but it’s a mess and not very instructive – this is the kind of thing you want to use Matlab or similar on One approach is to pick some reasonable parameters and look at the impulse responses Shock impacts 9 See Romer for parameter values. If w.n. monetary shock: yt = −ut MP , π t = −0.13utMP , rt =utMP yt = −1.60utMP , π t = −0.40utMP , rt =0.80utMPIf autocorrelation of shock is 0.5: w.n. IS shock: yt =ut IS , π t =0.13utIS , rt =0 0.5 a.c. IS shock: yt =1.6utIS , π t =0.40utIS , rt =0.20utIS
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