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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