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Lawrence Christiano Objective Boom-bust Cycles and Estimate a - - PowerPoint PPT Presentation
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‘Normal’ technology shock: – Normal technology shock: – Shock considered here (J Davis):
at aat1 t
Shock considered here (J Davis):
‘recent information’
1 2 3 4
‘earlier information’
5 6 7 8 at aat1 t t1
1
t2
2
t3
3
t4
4
t5
5
t6
6
t7
7
t8
8
ti
i
ti
i
– Habit persistence in preferences Investment adjustment costs in change of – Investment adjustment costs in change of investment – Variable capital utilization – Calvo sticky (EHL) wages and prices Calvo sticky (EHL) wages and prices
Pit Pi,t1, Wj,t zWj,t1
Et
j l0
1.031/4
l preference shock
logCtl bCtl1 L ltl,j
2
2
l0
K 1 0 02K 1 S
marginal (in-) efficiency of investment
I Kt1 1 0.02Kt 1 S I,t It It1 It Yt
1
Yjt
1 f,t dj markup shock
, Yj,t zt exp
technology shock
Lj,t
1
utKj,t, zt expzt R R
1
1
a yt log Rt R log Rt1 R 1 1 R a log t1
4 log yt y t
M
markup markup log f,t f f log f,t1 f f,t discount rate logc,t c logc,t1 c,t efficiency of investment logI t logI t 1 t logI,t I logI,t1 I,t technology at aat1
iid
1
2
3
4
5
6
7
8
monetary policy t
M Mt1 M u,t.
Variance Decomposition, Technology Shocks variable t i1
8 ti i
t t i1
4 ti i
8 ti i
consumption growth 46.6 7.0 24.1 22.5 investment growth 16.1 2.3 8.2 7.9
45.4 6.2 23.1 22.3 log hours 45.3 5.5 20.0 25.3 inflation 49.0 7.0 23.8 25.2 interest rate 52.1 7.1 24.9 27.2
log, technology shock
aat1
‘recent information’
t t1
1
t2
2
t3
3
t4
4
t5
5
t6
6
t7
7
t8
8
Centered 5-quarter moving average of shocks Signals 5-8 quarters in past past NBER trough Current shock plus most recent Four quarters’ signals NBER peak
– positive signal induces expectation that consumption will be high in the future – Ramsey-efficient (‘natural’) real rate of interest jumps – Under Taylor rule, real rate not allowed to jump, so monetary policy is expansionary
p
rr 1 at t1p (natural (Ramsey) rate)
1 x
Etxt1 (intertemporal equation)
Response to signal that technology will expand 1% in period 1 Equilibrium Ramsey Equilibrium Ramsey Period Period Case Where Signal is False 1 2 3 0 1 2 3 4t
0 0 l A 0 0 logAt 0 0 loght 0.7 0 0 logyt 0.7 0 0 gy Case Where Signal is True 1 2 3 0 1 2 3
0.95, 1.5, x 0.5, 0.82
4t
0 0 logAt 1 .95 .9025 0 1 .95 .9025 loght 0 7 -0 04 -0 04 -0 04 0 0 loght 0.7 0.04 0.04 0.04 0 0 logyt 0.7 1.0 0.9 0.9 0 1 .95 .9025
Estimated a model in which agents receive advance information about technology shocks.
b i l d i p y p business cycle dynamics
– Important in variance decompositions – Boom-bust of late 1990s seems to correspond to a period in which there was a lot of initial optimism about technology, which later came to be seen as excessive
response to signal shocks
– Ramsey-efficient allocations require sharp rise in rate of interest, which `standard monetary policy does not deliver’. – Problem is most severe when wages are sticky relative to prices.