aggregate supply and potential output assaf razin tel aviv university and cornell university
Post on 22-Dec-2015
220 Views
Preview:
TRANSCRIPT
Aggregate Supply and Potential Output
Assaf Razin
Tel Aviv University and Cornell University
Aggregate Supply and Potential Output
•The tradition in the monetary literature is that inflation is primarily affected by: (i) economic slack; (ii) expectations; (iii) supply shocks; and (iv) inflation persistence.
•The paper extends the standard New- Keynesian aggregate supply relationship to include also fluctuations in potential output, as an additional determinant of the relationship. It discusses whether potential output could be made a target for optimizing interest rules .
Aggregate Supply and Potential Output
The New-Keynesian aggregate supply derives from micro-foundations an inflation-dynamics model very much like the tradition in the monetary literature .
Inflation is primarily affected by: (i) economic slack; (ii) expectations; (iii) supply shocks; and (iv) inflation persistence .
This paper extends the New Keynesian aggregate supply relationship to include also fluctuations in potential output, as an additional determinant of the relationship.
Optimizing Monetary Rules Consider a micro-based loss function which is the discounted
value of a weighted sum of squared deviations of inflation from a zero level (so as to minimize distortion price dispersions among firms of identical technologies and demand schedules), the squared deviations in output from target output, and the level of the output target. The target output level is likely to be different from potential output under monopolistic competition because of the existence of a wedge between the marginal productivity of labor and the leisure/consumption marginal rate of substitution.A quadratic-linear optimal problem :
minimize a micro-based loss function, subject to the constraints: (1) Aggregate supply relationship; (2) Government debt dynamics, and 3) the dynamic low governing the potential accumulation of the stock of capital.
Conjecture: Optimizing interest rules would respond to potential output changes in addition to inflation surprise and output gap.
LiteratureUnderstanding why nominal changes have real consequences (why a short run aggregate supply relationship exists) has long been a central concern of macroeconomic research. Lucas (1973) proposes a model in which the effect arises because agents in the economy are unable to distinguish perfectly between aggregate and idiosyncratic shocks. He tests this model at the aggregate level by showing that the Phillips curve is steeper in countries with more variable aggregate maximal demand. Following Lucas, Ball, Mankiw, and Romer (1988) show that sticky-price Keynesian models predict that the Phillips curve should be steeper in countries with higher average rates of inflation and that this prediction too receives empirical support. Loungani, Razin, and Yuen (2001), and Razin and Yuen (2001) show that both Lucas’s and Ball-Mankiw-Romer’s estimates of the Phillips curve slope depend on the degree of capital account restrictions.
,111
0
djjcC tt
,1
1
11
0
djjpP tt
C is the Dixit-Stiglitz (1977) index of household consumption, P the Dixit-Stiglitz price index:
,)/();((; 10 PMdjjhvCuE sssss
ts
tst
Consumer’s Welfare
n
t
n
tttt
n
tt
n
ttt
tttt
t
n
tt
diidiihiwyP
diihiw
diiBi
MBMi
i
diicip
00
0
0
11
1
0
)()()(
)()(
)()1(
1
)()(
The Budget Constraint
t
t
ttc
tth
ttc
ttc
t
t
ttc
ttm
P
iw
cu
ihv
rcu
cu
i
i
cu
cu
)(
);(
));((
)1();(
);(
1);(
);(
11
First Order Conditions
))(()(
)()(
jhfAjy
P
jpCjc
ttt
t
ttt
,/1 jkjkjkIjI tttt
1,111
0
dijIjI itt
Consumption, Output, and Investment
Firm’s Optimization:
))(
(1
);(
);(
1)
)((
)()(
)))(
(('
1)
)((
1)
)(()()(
))(
()()()(
1
1
t
t
ttttc
tth
tt
t
t
tt
t
tt
t
tt
ttt
t
tttt
A
iy
ACu
hv
AA
iy
P
iwismc
Aiy
ffA
iy
AA
iyiwiSMC
A
iyfiwihiwVC
Nominal
Real
t
t
ttttt
t
t
tt
dt
tc
ht
ttttt
tt
p
p
ACysP
p
P
ipYy
AyfAfCu
AyfvACys
AjyffAP
jwjs
2
1
11
1
1~
1
1
11
),;,(
))(
(
));/((');(
));/((),;,(
));/)((('
)()(
Flexible prices
Set price one period in advance
Real Marginal Cost
Preset Nominal Prices
0)];;([);(
0)],;,((1
10
)(
)(1
1
)]()([1
1
][1
1
)(1
1
~1
1
22
11
2
11
1211
21
1
221
1
11
ttttttct
ttttt
ttt
tt
t
tt
t
t
ttttttt
tt
ttttt
t
tt
t
yysyyuE
ACysP
pPY
iE
ip
ii
E
A
pPYfwipPY
iMaxE
hwypi
MaxE
ii
MaxE
The Labor Market
Figure 1: Labor MarketEquilibrium
h
W/P
Marginal Factor CostLabor Supply
Marginal Productivity
MarkDown
Investment
)]}(/)([)](/)(['))(/)((
)({)1
1()](/)(['
121212
11
1
jkjkIjkjkIjkjk
jqP
P
iEjkjkI
tttttt
tt
t
tttt
)(/)(
)(/)()(/)()(/)(
jkjhAfA
jkjhAjkjhAjkjhAfjwjq
tttt
ttttttttttt
),;,(1
1
),;,(
),;,(
1
)1(])1([
)1/(11
)1/(11
1
1)1*(11
][
][
21
ttN
tN
t
ttN
tN
tt
Nt
Nt
ttNt
Nt
t
tt
AYKYs
n
AYYsnp
p
YC
ACYsnp
p
pnppnP
t
t
ttt
Potential Output
.,;,,1 tttn
tn
tt AIYYKs
x
xx
x
xx
CCppAAo
r
ttt
tttt
)log(
. , , ,
1)1(
Steady state:
Log-linearized Model
n
ttptntt
ntt
n
tt kkIyyyyss ˆˆˆˆˆ 11
pw
2,
f
f
v
vp
h
hhw
log-linearize the marginal cost function around the deterministic steady state equilibrium:
IYC
u
cu
c
cc
tp
tn
ttttt KIYYE ˆ1
ˆ1
ˆˆ11
11
1
tttttt PEPE loglog 11
nttpt
nttttt kkIYyPEP ˆˆˆˆˆloglog 2
12
112
nttpt
ntttt kkIYyPP ˆˆˆˆˆloglog 1
11
11
Log-linearizing the two price-setting equations, the investment rule, [equation (7)], and using equation (8), yields:
Aggregate Supply and Investment
nttpt
ntttt kkIYyPP ˆˆˆˆˆloglog 1
11
11
nttpt
nttttt kkIYyPEP ˆˆˆˆˆloglog 2
12
112
tttttt PEPE loglog 11
tp
tn
ttttt KIYYE ˆ1
ˆ1
ˆˆ11
11
1
1/ln ttt PP
tttn
tnt
nt AIYyks ,;,,1
Investment and Potential Output
tn
ttntp
nt uIKY
1
1111
ˆ1ˆ
tA
tt dAdu
tn
tnt
ntp uYIK
1
11
11
ˆ)(ˆ
Aggregate Supply and Potential Output
tn
tn
ttttt uYYYE ˆ1
ˆˆ11
11
1
,
pw
2,
f
f
v
vp
h
hhw
IYC
u
cu
c
cc
Conclusion
The paper demonstrates that potential output improves the inflation-output gap trade-off. My intuition is that the task of the monetary authority, which trades off inflation and output gaps is facilitated if they target potential output, as well as the inflation fluctuations and the output gaps.
In so doing the monetary authority should be independent, so as not to get trapped in Barro-Gordon dynamic inconsistencies. A Taylor-like rule makes interest rate respond not only to the fluctuations in inflation rates and output gaps, but also the fluctuations in potential output is bound to raise the measure of consumer.
The Open-EconomyPhillips Curve
c
cc
ph
hh
w
pw
N
tt
N
tt
N
tt
u
yu
fffA
yff
fvA
yv
CCYyss
(.)(.))('
)(.))(('',
'
)(
)()(
1
1
1
‘where
yA
y
yA
y
AA
yfv
yA
y
A
yfv
Ay
ffA
y
CCu
Cu
h
hh
cc
c
)(
)('
));((
)());((
))(('
1)(,
);(
);(
1
1
1
Elasticity of wage demands, wrt to output, holdingmarginal utility of incomeconstant
Elasticity of marginal product oflabor wrt output
Log-linearization of real mc:
n
tttt
ttssti
t
tttss
tit
tttss
tissii
ttttc
t
tt
t
th
ttt
yyiyis
AAA
F
sy
yyy
y
F
siy
iyiyiy
iy
F
sss
iyFyu
Aiy
Aiy
v
yys
)()()(
)(1
))(1
)(
)())()((
)(
1)log()log(
));(();(
))(
();)(
(
);;(
11
_
_
_
_
Partial-equilibrium relationship?
Aggregate Supply ttt
nt
nt
nt AIYyks ,;,,1
tn
ttntp
nt uIKY
1
1111
ˆ1ˆ
tA
tt dAdu
tn
tnt
ntp uYIK
1
11
11
ˆ)(ˆ
tn
tn
ttttt uYYYE ˆ1
ˆˆ11
11
1
n
ttttt YYE ˆˆ11
1
1
)log()log()1
1()
1(
))(1
())(1
)1(())(
1()
1()(
),log()log()(),log(
)log()1()]log()1()log([)log(
)]()()[log()log(
)()()log()log(
1
1
1
*
111
*21
1212
111
ttt
N
t
F
t
N
t
F
t
N
t
H
tttt
t
ttttttttt
t
tt
ttttt
N
tt
N
ttttt
N
tt
N
tttt
eEen
n
CCYYn
YYn
E
P
PePEPE
P
P
pnppnP
CCYyPEp
CCYyPp
)log()log()1
1()
1(
))(1
())(1
)1(())(
1()
1()(
),log()log()(),log(
)][log()log()1
1(
1)(
1
1)(
11)log()log(
)][log()log()1
1(
1)]log()[log(
1)log()log(
)]log()1()log()[log()1(
1)log(
)]log())[log(1()]log()log([
)]log())[log(1()]log()log([)log()log(
)log()1()]log()1()log([)log(
)log()log(
)](1
1)(
1)[log()log(
)(1
1)(
1)log()log(
)1(
)]log()[log(
)]()()[log()log(
)()()log()log(
1
1
1
111
11
1
*
111
*12
*1
*21
*1
*1111
*21
112
112
11
1212
111
ttt
N
t
F
t
N
t
F
t
N
t
H
tttt
ttttttt
tt
ttt
N
tt
N
t
W
tttt
t
ttt
tttttttt
ttttt
ttttttt
ttttttttttt
ttttt
ttt
N
tt
N
t
W
tttt
N
tt
N
t
W
ttt
F
t
H
t
W
t
tjt
W
tjt
N
tt
N
ttttt
N
tt
N
tttt
eEen
n
CCYYn
YYn
E
PEPEP
P
eEen
nCCYYPEP
P
Pe
eEen
nPpPEP
pnpnPn
p
pEpnppn
pEpnpEpnPEP
pnppnP
pEp
CCYYPEp
CCYYPp
YnYnY
PpYy
CCYyPEp
CCYyPp
Perfect Capital Mobility
)log()log()1
1()
1(
))(1
)1(())(
1()
1()(
0*)1(
1
1
ttt
N
t
F
t
N
t
H
tttt
Nt
eEen
n
YYn
YYn
E
CCrt
Closing the capital account:
)log()log()1
1()
1(
))(1
)1(())(
1()
1()(
,
1
11
1
ttt
N
t
F
t
N
t
H
tttt
N
t
N
t
H
tt
eEen
n
YYn
YYn
E
YCYC
Closing the trade account:
))(1
()1
()(
11
1
N
t
H
tttt YYE
n
Sacrifice Ratios in Closed vs. Open Economies: An Empirical
Test Prakash Loungani, Assaf Razin, and
Chi-Wa Yuen
BackgroundLucas (1973) proposed a model in which the effect arises because agents in the economy are unable to distinguish perfectly between aggregate and idiosyncratic shocks; he tested this model at the aggregate level by showing that the Phillips curve is steeper in countries with more variable aggregate demand. Ball, Mankiw and Romer (1988) showed that sticky price Keynesian models predict that the Phillips curve should be steeper in countries with higher average rates of inflation and that this prediction too receives empirical support
The data used in the regressions reported in this paper are taken from Ball (1993, 1994) and Quinn (1997). Sacrifice ratios and their determinants: Our regressions focus on explaining the determinants of sacrifice ratios as measured by Ball. He starts out by identifying disinflations, episodes in which the trend inflation rate fell substantially. Ball identifies 65 disinflation episodes in 19
DATA
OECD countries over the period 1960 to 1987. For each of these episodes he calculates the associated sacrifice ratio. The denominator of the sacrifice ratio is the change in trend inflation over an episode. The numerator is the sum of output losses, the deviations between output and its trend (“full employment”) level.
Sacrifice ratios and their determinants: Our regressions focus on explaining the determinants of sacrifice ratios as measured by Ball. He starts out by identifying disinflations, episodes in which the trend inflation rate fell substantially. Ball identifies 65 disinflation episodes in 19 OECD countries over the period 1960 to 1987. For each of these episodes he calculates the associated sacrifice ratio. The denominator of the sacrifice ratio is the change in trend inflation over an episode. The numerator is the sum of output losses, the deviations between output and its trend (“full employment”) level.
For each disinflation episode identified by Ball, we use as an independent variable the current account and capital account restrictions that were in place the year before the start of the episode. This at least makes the restrictions pre-determined with respect to the sacrifice ratios, though of course not necessarily exogenous.
Quinn (1997) takes the basic IMF qualitative descriptions on the presence of restrictions and translates them into a quantitative measure of restrictions using certain coding rules. This translation provides a measure of the intensity of restrictions on current account transactions on a (0,8) scale and restrictions on capital account transactions on a (0,4) scale; in both cases, a higher number indicates fewer restrictions. We use the Quinn measures, labeled CURRENT and CAPITAL, respectively, as our measures of restrictions.
Capital Flow Restrictions
Sacrifice ratios and Openness Restrictions
Independent variable)1()2()3()4(Constant-0.001
)0.012(
-0.059
)0.025(
-0.033
)0.022(
-0.058
)0/026(
Initial inflation0.002
)0.002(
0.003
)0.002(
0.003
)0.002(
0.003
)0.002(
Length of Disinflation0.004
)0.001(
0.004
)0.001(
0.004
)0.001(
0.004
)0.001(
Change of inflation during episode
-0.006
)0.003(
-0.007
)0.003(
-0.006
)0.003(
-0.007
)0.003(
CURRENT0.008
)0.003(
CAPITAL0.010
)0.006(
OPEN0.006
)0.002(
Adjusted R-Square0.160.230.190.23
Number of observations
65656565
NumbersIn paranthesesarestandarderrors
ConclusionIn our earlier work we showed that restrictions of capital account transactions were significant determinants of the slope of the Phillips curve, as measured in the studies of Lucas (1973), Ball-Mankiw-Romer (1998), and others. The findings of this note lend support to this line of work, in particular to the open economy new Keynesian Phillips curve developed in Razin and Yuen (2001). We find that sacrifice ratios measured from disinflation episodes depend on the degree on restrictions on the current account and capital account. Of course, to be more convincing this finding will have to survive a battery of robustness checks, such as sub-sample stability, inclusion of many other possible determinants (such as central bank independence) in the regressions, and using instruments to allow for the possible endogeneity of the measures of openness.
top related