Download Sacrifice Ratio or Welfare Gain Ratio? Disinflation in a DGSE monetary model C

CENTRE FOR DYNAMIC MACROECONOMIC ANALYSIS
CONFERENCE PAPERS 2008
CDMC08/06
Sacrifice Ratio or Welfare Gain Ratio?
Disinflation
in a DGSE monetary model
*
Tiziano Ropele
Bank of Italy
Guido Ascari
University of Pavia
MAY 30, 2008
PRELIMINARY AND INCOMPLETE -PLEASE DO NOT
CIRCULATE
ABSTRACT
PRELIMINARY AND INCOMPLETE -PLEASE DO NOT CIRCULATE
* Address: Department of Economics and Quantitative Methods, University of Pavia, Via San Felice
5, 27100 PAVIA, Italy. Tel: +39 0382 986211; e-mail: [email protected]
CASTLECLIFFE, SCHOOL OF ECONOMICS & FINANCE, UNIVERSITY OF ST ANDREWS, KY16 9AL
TEL: +44 (0)1334 462445 FAX: +44 (0)1334 462444 EMAIL: [email protected]
www.st-andrews.ac.uk/cdma
2
Empirical evidence on disin‡ations
This section brie‡y reviews the empirical evidence to illustrate the basic facts characterizing a disin‡ation. Most of the empirical literature on disin‡ations focused on the
so-called sacri…ce ratio (SR), de…ned as the ratio of the total cumulative percentage
output loss following a disin‡ation to the size of the disin‡ation. For a given disin‡ation
episode, thus, the SR measures the output costs per unit of decrease in trend in‡ation.
Simplifying, the literature used three alternative approaches to estimate the SR. The
…rst one is based on Phillips curve estimates. Using this methodology, Gordon and King
(1982) obtained a wide range of estimates from 0 to 8, while more recently Andersen
and Wascher (1999) provided a comprehensive analysis for 19 industrialized countries,
showing that the estimate are subject to a great deal of variation across time periods and
model speci…cation. Moreover, Andersen and Wascher (1999) showed that the average
sacri…ce ratio has increased from 1.5 to about 2.5 as the average rate of in‡ation has
decreased from the ’80s to the ’90s, because lower rates of in‡ation cause a ‡attening of
the aggregate supply curve. A result, which is similar in spirit, is contained in J.Filardo
(1998), that highlights the importance of non-linearities in the estimation of SRs, since
the estimates of the slope of the Phillips curve are quite di¤erent between periods when
the economy is booming and periods when the economy is weak.
A second type of approach is based, instead, on the analysis of the single disin‡ation
episodes. This method to estimate the SR was popularized by Ball (1994), that applied
it to 65 episodes in 19 moderate-in‡ation OECD countries from 1960 to 1991. The
estimates of Ball (1994) vary from 1.8 to 3.3. Analyzing the Volcker disin‡ation in the
years 1982-1985 in US, Mankiw (1999) arrived at an estimate of 2.8, higher than the one
of 1.8 by Ball (1994), that in turn is anyway very close to the more recent estimate of 1.7
by Erceg and Levin (2003). Ball (1994) also showed that the SR is negatively related
to the speed of disin‡ation. Zhang (2005) generalized Ball (1994) approach showing
that the estimates of the SR are larger when long-lived e¤ects on output are taken into
account. Moreover, Zhang (2005) presented evidence for a negative relationship between
SR and the level of in‡ation at the beginning of the disin‡ation, and between SR and the
2
speed of the disin‡ation. Quite interestingly, the signi…cance of these two relationships
disappears when the regression features both the initial in‡ation level and the speed of
the disin‡ation. This results suggests that the data are not able to distinguish between
the two competing e¤ects, because of collinearity.
This second approach has been criticized by Andersen and Wascher (1999) and Cecchetti and Rich (2001), that advocates the use of more structural models. Andersen and
Wascher (1999) used structural wage and price equations in one of their model speci…cations. Cecchetti and Rich (2001) employed a structural VAR methodology on quarterly
US data for the period 1959-1997, using three di¤erent identi…cation models and estimating the SR over a one-to-…ve-year horizon. The estimates varying considerably from
1 to nearly 10 and are quite imprecise.1 Similarly Collard, Fève, and Matheron (2006)
and Fève, Matheron, and Sahuc (2007) used SVAR analysis, and Fève, Matheron, and
Sahuc (2007) provided an estimate of SR for the Eurozone of 4.26.
This third approach based on structural estimation and SVAR methodology provides
also a description of the dynamic e¤ects of a disin‡ation. The impulse responses in Cecchetti and Rich (2001), Collard, Fève, and Matheron (2006) and Fève, Matheron, and
Sahuc (2007) undoubtedly show that after a disin‡ation output declines and eventually
turns back, while in‡ation decreases permanently. There are, however, di¤erences in the
size and the timing of the e¤ects of a disin‡ation across model speci…cations, identi…cation assumptions and data sets. In particular, two di¤erent cases seem to emerge. In the
…rst one, in‡ation is quite sticky, and it actually increases on impact, before declining
sluggishly afterwards to its permanently lower value. In this case output enters a deep
and very protracted (more than 5 years) recession. This kind of impulse responses is
identi…ed by Cecchetti and Rich (2001) (in one of their model speci…cation) and by Collard, Fève, and Matheron (2006), both for US data. The second case, instead, exhibits
a quick fall in in‡ation, that declines abruptly on impact, then surges mildly (since the
adjustment path is oscillatory) and eventually converges to its lower new long-run value.
1
A striking results that conveys an idea of the large con…dence bands is that a 90% con…dence
interval foir teh sacri…ce ratio includes 0 for all the three models estimated by Cecchetti and Rich
(2001).
3
The response of output is similar to the previous case, but the recession is smaller in size
and less prolonged. Also for output the adjustment exhibits small damped oscillations.
This kind of impulse responses is shown by Cecchetti and Rich (2001) in their benchmark
model speci…cation for US data, and by Fève, Matheron, and Sahuc (2007) for Eurozone data. It is important to note that in all cases the paths of consumption and hours
worked qualitatively follow the one of output (see Collard, Fève, and Matheron (2006)
and Fève, Matheron, and Sahuc (2007)).2 Finally, it is di¢ cult to assess superneutrality
from this literature, that is, the long-run e¤ects on output of a permanent reduction in
in‡ation. As often in the literature, Cecchetti and Rich (2001) employs Blanchard and
Quah (1989) typical identifying restriction of no long-run e¤ects of aggregate demand
shock on output. However, when this restriction is not imposed, it is not granted that
output goes back exactly to its initial level (see Collard, Fève, and Matheron (2006) and
Fève, Matheron, and Sahuc (2007)).
The two cases of disin‡ation dynamics described above can be easily reconciled by
appealing to imperfect credibility (see Erceg and Levin (2003)). Under imperfect credibility expected in‡ation adjust sluggishly and therefore, given some version of the New
Keynesian Phillips Curve, also in‡ation is persistent and the disin‡ation e¤ects are more
long-lasting. Recall that SVAR analysis necessary implies taking an average across disin‡ation episodes. Hence, it simply may be that di¤erent data sets hide di¤erent degrees
of credibility, and di¤erent identi…cation schemes weights them di¤erently, generating
biased results through one of the two possibilities.
The aim of this paper is to see how successful the current workhorse DSGE model
of business cycle ‡uctuations can be in replicating the stylized facts above, without
resorting to any kind of irrationality or imperfect credibility/information. We will see
that: (i) the SR resulting from the model simulations are well within the range of the
estimated SRs in the literature; (ii) the second kind of dynamic adjustment path is
perfectly coherent with the CEE model of the business cycle. Finally, we perform a
rigorous welfare evaluation of the costs of a disin‡ation, constructing a welfare based
2
Both Collard, Fève, and Matheron (2006) and Fève, Matheron, and Sahuc (2007) performed a
comprehensive robustness analysis to establish the robustness of these impulse response paths.
4
SR.
3
A medium-scale NK-DSGE model: a brief overview
Brief presentation of the main features of the Schmiit-Grohè-Uribe (2004a,b) mediumscale model version of Christiano et al. (1995), see Appendix.
The basic setup is a medium-scale macroeconomic model, obtained by augmenting
the standard New Keynesian model with nominal and real frictions that are proved to
be crucial in replicating the dynamics of US business cycle. Since the model is exactly
the one described in many papers such as SGU and CEE3 , we will brie‡y introduce here
the key elements, leaving to Appendix all the details about the model and calibration.
The model displays both real and nominal frictions. The real features of the model
are monopolistic competition, habit persistence in consumption, …xed cost in an otherwise standard Cobb-Douglas production function that generates increasing return to
scale and guarantees zero pro…t in equilibrium, variable capacity utilization and adjustment costs in investment. Money is introduced into the model via real balances in the
utility function and cash-in-advance constraint on wage payments of …rms. Wages and
prices are sticky à la Calvo-Yun. Furthermore, as in CEE, prices and wages, that are
not reoptimized each period, are indexed to past in‡ation. CEE argues that all these
frictions appear to be crucial in replicating the dynamics of macroeconomic variables
along the business cycle.
3.1
Long-run E¤ects
The model calibration assumes full past indexation of prices and wages. Nonetheless,
the CEE model implies non-superneutrality of money because of the cash-in-advance
constraint on the …rms payment of the wage bill. As explained by CEE, this assumption
makes the marginal cost to depend on the nominal interest rate, and this is crucial for
the model to match the empirical impulse response function. The fact that …rms need
3
Other empirical papers use analogous set-up such as Smets and Wouters (2003) and Schmitt-Grohé
and Uribe (2005).
5
to pay the wage in advance, however, does not only a¤ect the short run dynamics, but
it also has long run implications: it causes real cost of in‡ation.4 The higher the steady
state in‡ation level, the higher the cost of labor for the …rms, and hence, ceteris paribus,
the lower the wage paid to the worker. Households would then reduce their labor supply,
so that employment falls. Firms in turn decreases their capital stock, because labor and
capital are complements in the production function. As a consequence, real output falls.
In particular, the steady state real wage is equal to:
mc (1
w=
)z
1+
Rt
Rt
ut k t
hdt
1
(1)
:
It is easy to show that the full indexation assumptions implies that the steady state real
marginal cost (i.e., mc equals to the inverse of the mark-up) depends only the elasticity
of substitution between goods in the usual CES consumption aggregator in the utility
function. In other words, the marginal cost is independent from the rate of steady state
in‡ation. It follows that also the capital-labor ratio is independent from the rate of
in‡ation, since so are both the marginal cost and the cost of capital. (1) shows that the
steady state cost of labor, instead, is a function of the nominal interest rate, given the
cash in advance constraint on …rms. The wage is decreasing in R, and hence in ; since
R = = and
Rt 1
Rt
=1
= : However, w [(1
1=R) + 1] does not depend on ; as
also the relative cost of the two productive inputs (and indeed the capital-labor ratio is
constant): wt [(1
1=R) + 1] =rtk : It is also easy to show that the steady state labor
supply equals to
hd =
b+
p
b2 + 4a~
cw
;c =
2a
b+
p
b2 + 4a~
cw
; y = zt
2
k
hd
hdt
where a; b; c~ are terms independent from the steady state in‡ation rate, while only w
depends on the rate of in‡ation as in (1). Steady state employment, consumption and
output are therefore all decreasing in the rate of in‡ation. Note that without the cash
in advance on …rms, i.e.,
= 0, money would be superneutral.
Even assuming full prices and wages indexation, therefore, the long-run Phillips
Curve is not vertical, meaning that a disin‡ation would produce a long-run increase in
4
Obviously, in steady state the rate of in‡ation is equal to the rate of growth of money supply.
6
output. Given CEE calibration these e¤ects are rather minor: a permanent 1% reduction
in in‡ation implies roughly a 0,1% increase in steady state output.5
The fact that the rate of growth of money has real e¤ects in the long-run implies
that it will also a¤ects the long-run welfare level of the representative household. In
particular, the household’s utility function is the sum of three components: consumption,
employment and real money balances. The steady state values of all the three arguments
of the utility function decreases with long-run in‡ation. The e¤ects on welfare is thus
ambiguous. Given our calibration, positive long-run in‡ation would entail welfare costs,
since the decrease in consumption a¤ects utility more than the decrease in employment
(while the real money balances e¤ect is only marginal). This model thus implies longrun welfare gains from a disin‡ation. These e¤ects are also quite small: a permanent
reduction in in‡ation implies roughly a 0,07% increase in steady state consumption for
each point of in‡ation.
It is important to stress that assuming full indexation in prices and wages we are
cancelling possible real e¤ects arising from the nominal rigidities. It is well-known that
a positive steady state in‡ation rate increases steady state price and wage dispersion in
the absence of full indexation and that price or wage dispersion causes an ine¢ ciency
loss on aggregate production, due to the non-linearity of the CES aggregators (e.g.,
Ascari, 2004, SGU). In other words, with partial wage and/or price indexation the real
e¤ects of long-run in‡ation, and thus also the e¤ects on welfare, would be much larger.
4
Cold-turkey disin‡ationary monetary policies
In this section we study the e¤ects of disin‡ationary monetary policies through the
lenses of the non linear version of Christiano, Eichenbaum and Evans (2005) model.
The type of disin‡ation experiments we look at can be described as follows. Suppose
the economy is in a steady in‡ation regime, characterized by a positive in‡ation target
H,
5
which is believed to last forever. All nominal variables, thus, grow at the rate
H,
Moreover, these e¤ects are approximately linear, in the sense that the output gains are insensitive
to the starting in‡ation level.
7
whereas, without loss of generality, real variables are constant. At time t = 0, the central
bank unanticipatedly, credibly, permanently and without further surprises implements
a cold-turkey disin‡ation, i.e., it immediately lowers the in‡ation target from
with 0 6
L
<
H.
H
to
L,
A disin‡ationary monetary policy of this kind can be realised in
accordance with two di¤erent operative strategies: either by way of a money supply
rule or by way of an interest rate rule. In the former case, the central bank in order
to achieve a sustained reduction of in‡ation appopriately changes the growth rate of
nominal money supply
that enters the rule
) Mt 1 .
Mt = (1 +
(2)
A cold-turkey disin‡ation then calls for an immediate step reduction of
from
H
to
L.
In the former case, i.e., under the interest rate targeting rule, the central bank
disin‡ates by changing the time path of the in‡ation target
that enters the simple
feedback rule, given by
1 + it =
where 0 <
1+
1+
1+
t
< 1 is the subjective discount factor and
,
(3)
is a constant strictly greater
than one. Again, in the case of a cold turkey disin‡ation, the path for the in‡ation
target takes the form of a step reduction from
H
to
L.
Using in turn each of the two operative strategies described above, we address four
issues closely related to the short-term e¤ects of disin‡ations:
1. does the cold turkey disin‡ation entails recessionary e¤ects?
2. if so, how large are the disin‡ation costs?
3. does the disin‡ation size, i.e.,
H,L
H
L,
plays any role?
4. do initial and …nal values of steady state in‡ation matter?
Explain here why these questions are relevant.
8
To answer questions 2), 3) and 4), we consider two customary measures, largely
used in the empirical literature: the sacri…ce ratio (henceforth, SR) and the discounted
sacri…ce ratio (henceforth, -SR).6
The sacri…ce ratio. The SR, which has been popularised by Ball (1994) and then
commonly used in the empirical literature, is de…ned as the cumulative output loss that
the economy has to bear to achieve a sustained reduction of in‡ation. Analytically, the
SR over a time horizon of T quarters is calculated as
SR =
T
X
1
Yt
YL
H,L t=0
where
H,L
H
L
YL
,
(4)
represents the disin‡ation size and YL is the steady state level
of output in the new regime (notice that
L
<
H
implies YL > YH ). A value of 2
for the SR means that in order to achieve a permanent reduction of in‡ation rate of 2
percentage points the economy has to “sacri…ce”a cumulative output loss of 6 per cent
(relative to steady state).
The discounted sacri…ce ratio. Following Gordon and King (1982), the discounted
sacri…ce ratio, discounts at the rate
-SR =
the future output deviations from YL ,
1
T
X
H,L t=0
t
Yt
YL
YL
.
(5)
By construction, the -SR tends to deliver larger values as it attaches greater weight
to short run recessions and relatively less weight to future output expansions. [to be
checked and completed].
4.1
Cold turkey disin‡ation under money targeting rule
Figure 1 illustrates the dynamic adjustment of some key variables after a cold-turkey
disin‡ation under the money targeting rule, as in equation (2). Each panel reports transition paths for di¤erent initial steady in‡ation regimes, namely,
6
H
= f2%; 4%; 6%; 8%g.7
....and propose a new welfare-based indicator. Generally speaking, the SR and the
-SR can be
viewed as measures of the short-(medium) term disin‡ation costs, while the welfare-based indicator is
meant to be a synthetic index for both the transitional e¤ects and the steady state e¤ects...
7
Throughout, transition paths of variables reported in …gures are expressed in percentage deviations
from the new steady state.
9
Does the cold turkey disin‡ation entails recessionary e¤ects? No matter the initial
steady in‡ation rate, cold turkey disin‡ation under money targeting rule comes with a
notable recession. There is an initial hump-shaped output downturn followed thereafter
by a small boom. Eventually, output converges to the new steady state through dying
oscillations. Regarding other key variables, in‡ation abruptly drops …rst giving rise to
a long-lasting de‡ation. Real money balances gradually build up while the nominal
interest rate decreases. The ex ante real interest rate increases at the beginning and
then reverts towards steady state.
To understand the adjustment paths depicted in Figure 1 and the e¤ects of varying
H,
it is useful to focus …rst on the disin‡ation from 2% to zero.
At time zero, when the central bank halts the nominal money supply, only a fraction
of intermediate …rms receives the Calvo signal to re-optimise prices. Acknowledging the
new in‡ation regime and the forthcoming output contraction (necessary to bring down
the in‡ation rate), optimising intermediate …rms lower prices. Those …rms that instead
do not receive the Calvo signal mechanically raise prices as for full indexation to previous
period’s in‡ation rate, i.e.,
H.
As shown in …gure 1, of these two opposing pricing
decisions the former dominates, causing the aggregate price index to decrease relatively
to previous period’s. In‡ation rate overshoots the zero target, unexpectedly boosting
real money balances while pushing downwards the nominal interest rate. However, the
ex-ante real interest rate rises considerably re‡ecting the deep expected de‡ation in place
in the next period.8 Consequently, households postpone consumption and investment
spending. The economy then enters a recession.
In the following period, both optimizing and non-optimising intermediate …rms lower
prices. The former do so because of the weakening aggregate demand: habit in consumption and investment adjustment costs indeed make households to respond only gradually
to the rise of the real interest rate. The latter lower prices as for the full indexation
to the de‡ation rate occurred in the previous period. Thus, the de‡ation exacerbates,
the ex-ante real interest rate peaks up and output reaches the bottom. In the following
8
In the following period, also non optimising intermediete …rms will lower their prices because of
past in‡ation indexation.
10
periods, the real interest rate slowly reverts its path and as soon as it goes below its
long-run equilibrium level the economy enters a temporary boom. The dynamic pattern
of in‡ation qualitatively mirrors that of output and at last reaches the new steady state
after about 28 periods.
As already mentioned, neither the overall transmission mechanism nor the timing
of recession and boom alternation are a¤ected by higher initial steady in‡ation rates.
Interestingly enough, however, the initial steady in‡ation rate remarkably a¤ects the
amplitude of ‡uctuations of key variables during the transition towards
L
= 0. In
general, higher initial steady in‡ation rates yields substantially more macroeconomic
volatility. Table 2 reports output and in‡ation variances, computed during the transition
period.9 Output variance substantially increases from 0:52 for
and 4:92 for
1:08 for
H
H
H
= 2% to 1:66, 3:15
= 4%, 6%, 8%, respectively. Similarly, in‡ation variance moves from
= 2% to 8:74 for
H
= 8%. Thus, output and in‡ation variances tend
to linearly rise with the initial steady in‡ation rate. Intuitively, higher values of
H
urge optimising intermediate …rms to lower prices more, thus yielding a larger drop of
in‡ation10 and a more pronounced rise of the ex-ante real interest rate.
How costly is the cold turkey disin‡ation under money targeting rule? Table 1 reports
the theoretical values of SR and -SR calculated for T = 28, i.e., the number of periods
in‡ation takes to converge to the new in‡ation target. Interestingly, the values of SR and
-SR are approximately equal to 2.8, a value fairly close to the empirical estimates.11
Accordingly, to permanently lower the steady in‡ation rate (equivalently, the in‡ation
target), say, from 2% to zero the economy has to sacri…ce a cumulative output loss (in
deviation from the new steady state) of 5:6%.
9
10
Formule here
Notice that not in all case the price reduction operated by optimising …rms is enough to lower the
aggregate price index and lead to a de‡ation. For instance, this happens for
H
= 6% and
H
= 8%.
And in this cases, one can also see that after the disin‡ation, real money balances decrease.
11
Using quarterly data for the United States, Mankiw (1991) examines the Volcker disin‡ation in the
early 1980s and estimates a sacri…ce ratio of 2.8. More recently, Ball (1994) examine various disin‡ation
episodes from 1960 to 1991 in moderate in‡ation countries of the OECD and obtain estimates that vary
from 1.8 to 3.3.
11
Does the size of disin‡ation matter? Ball et al. (1988) argue that initial values
of trend in‡ation do in‡uence the value of the sacri…ce ratio: at higher level of trend
in‡ation, in particular, …rms adjust prices more forcefully, leading to a smaller sacri…ce
ratio. Referring back to Table 1, the disin‡ation size marginally a¤ects the values of the
sacri…ce ratios. There is indeed a negative relation between the initial steady in‡ation
rate and the values of the sacri…ce ratios, but however is quantitatively negligible. For
di¤erent values of
H,
the values of SR and
-SR lie in the range 2.9-2.7. Hence,
varying the initial steady in‡ation rate produces a constant rescaling of the output
transition paths, also present in terms of output (and in‡ation) variability which then
leaves essentially unchanged the sacri…ce ratios.
Finally, do initial and …nal values of in‡ation target matter? To study the e¤ects,
if any, of varying the initial and …nal values of steady in‡ation rate, namely, the pair
(
H;
L ),
we experiment cold turkey disin‡ations of …xed size. For
we thus investigate disin‡ationary policies aimed at achieving
L
H
= f4%; 6%; 8%g
H
2%. The
bottom (left) panel of Table 1 reports the sacri…ce ratios. Whereas in the previous
discussion we saw remarkable similarities across the values of the sacri…ce ratios, here
there are interesting di¤erences. Lowering the in‡ation target from 4% to 2% entails
a sacri…ce ratio of 2.2, that is 0.8 points lower than the value reported for the cold
turkey disin‡ation from 2% to zero. The values of the sacri…ce ratios further decrease
when the initial steady in‡ation rate rises: the SR, for example, drops to 1:8 and 1:6
for
H
= 6% and
H
= 8%, respectively. The same is true for the -SR. In sum, cold
turkey disin‡ation of …xed size under money supply targeting rule has non trivial (or
asymmetric) e¤ects on the sacri…ce ratio.
What then drives these …nding? Everything rests on the optimal behaviour of price
setters …rms. When the central banks reduces the growth rate of money from 2 per cent
to zero, we have seen, optimising intermediate …rms lower prices, anticipating the future
path of money supply; the in‡ation rate falls, the ex-ante real interest rate increases and
output drops. When the central bank disin‡ates from 4% to 2% there are two important
e¤ects to take track of. Firstly, optimising intermediate …rms cut prices by a smaller
amount, when compared the disin‡ation from 2% to zero. They do so because, among
12
other things, the real marginal costs does not decrease as much. On this regard, recall
that in the CEE model, the real marginal costs positively depend on the nominal interest
rate, which in the long run moves one to one with trend in‡ation. Secondly, As a result,
in‡ation reduces less while the ex-ante real interest rate increases more moderately. The
recession turns out thus to be less severe giving rise to a less costly disin‡ation. Needless
to say, that with higher the initial level of steady in‡ation, the e¤ects just described
are substantially strenghted, then resulting in lower sacri…ce ratios.
Note that this
story is exactly the opposite of the common view. The literature (Ball &Romer, Akerlof
& Perry) often rationalizes higher sacri…ce ratios for lower starting in‡ation level, by
suggesting that nominal rigidities are stronger at lower level of average in‡ation. Hence,
at low level of initial in‡ation, the adjustment of nominal variables would be smaller
on impact and slower in speed, explaining higher sacri…ce ratios. Here, instead, the
path of in‡ation is exactly the opposite: the higher the initial in‡ation level, the lower
and smoother the in‡ation. However, this makes the real interest rate to fall less, thus
making the recession less severe and having a positive e¤ect on the sacri…ce ratio.
4.2
Cold-turkey disin‡ation under interest rate targeting rule
We now turn to analyse the e¤ects of cold turkey disin‡ations under the interest rate
targeting rule, as in equation (3). Figure 3 illustrates dynamic adjustment paths of some
key variables for di¤erent initial steady in‡ation rates, namely,
H
= f2%; 4%; 6%; 8%g.
Is the cold-turkey disin‡ation recessionary? Also under the postulated contemporaneous interest rate rule cold turkey disin‡ation comes with a notable recession, the
intensity of which worsens as the initial steady in‡ation rate increases. Although the
transmission mechanism is for many aspects similar to the one at work under money supply targeting rule, see Figure 1, there however a number of qualitative and quantitative
di¤erences worthy to emphasize.12
Qualitatively, the key things to notice regard the dynamic adjustment path of nom12
These results are somewhat sensitive to the speci…cation of the Taylor rule. In particular, letting
the central bank to also care about the output gap may yield de‡ation and overall more volatility in
the adjustment of the economy.
13
inal interest rate and in‡ation. Firstly, the cold turkey disin‡ation under interest rate
targeting rule involves an immediate rise of nominal interest rate.13 As one might expect, the disin‡ation is initiated by a monetary policy contraction. Even though the
new steady state equilibrium level of nominal interest rate is lower (Fisher equation),
the central bank increases the nominal interest rate to raise the real interest rate, which
then leads to lower aggregate demand and lower in‡ation rate. As consumption and
investment adjust only gradually following a hump-shaped path, the central bank already in the …rst period cuts the nominal interest rate. Nonetheless, the ex-ante real
interest rate remains above steady state for several periods, ensuring the endurance of
the recession. Secondly, under the interest rate targeting rule in‡ation rate converges
to steady state following a gradual and largely monotonic path. There is a de‡ationary
spell between the sixth and tenth period, but it is quantitatively negligible. This is in
stark contrast to what is shown in Figure 1, in which the transition to the zero steady
in‡ation rate occurs through a notable and long-lasting de‡ation.
Quantitatively, there are two aspects to notice. Firstly, cold turkey disin‡ation under
the interest rate yields, generally speaking, less macroeconomic volatility than under the
money supply targeting rule. This is visually evident for output when comparing …gures
1 and 3; indeed, the bottom values of output during the initial recession under money
supply targeting are roughly three times larger than under interest rate targeting. This
is largely con…rmed in Table 1, where output volatility under interest rate targeting not
only is remarkably lower than under money supply targeting but is also less sensitive
to the initial steady in‡ation rate. Secondly, cold turkey disin‡ation under interest rate
targeting is accomplished in 15 periods. This is approximately half of the time taken
under money supply targeting.
Finally, …gure 2 also shows the growth rate of money supply implied by the interest
rate rule. The growth rate of money supply (
13
t)
is retrieved using the transformation
To see this, note …rst before the disin‡ation takes place the nominal interest rate is given by
1 + i = (1 +
H) =
. At time zero, when the disin‡ation is actually implemented (
interest rate is given by 1 + i1 = (1 +
1)
= . So, provided that
1
> (1 +
1=
H)
because there is not de‡ation, the central bank raises the nominal interest rate.
14
L
= 0), the nominal
1, and this is true
t
=
mt
mt 1
t,
where mt denotes real money balances while
in‡ation rate at time t. As illustrated, the path of
t
t
Pt =Pt
1
is the (gross)
is somewhat unusual. At time
zero the growth rate of nominal money supply suddenly falls and then right away rises
overshooting the initial steady level. Only afterwards, the growth rate of money supply
gradually decreases towards equilibrium through dying oscillations. Notice that the
earliest behaviour of
t
is due to the initial rise of the nominal interest rate, which
temporarily depresses real money balances.
How costly is the cold turkey disin‡ation under the interest rate targeting? Table 1
reports the values of sacri…ce ratios calculated for T = 15. Not surprisingly, the costs of
disin‡ation are signi…cantly lower, perhaps too low, than under money supply targeting.
Both the values of SR and -SR are equal to one. Thus, for each percentage point of
reduction of trend in‡ation, the cumulative output loss to be sustained is 1%.
Does the size of disin‡ation matter? Paralleling the case under money supply targeting, the disin‡ation size seems irrelevant for the values of the sacri…ce ratios. Also in
this case, higher initial steady in‡ation rates tend to re-scale the dynamic adjustment
path output leaving the sacri…ce ratio essentially unchanged.
Finally, do initial and …nal values of trend in‡ation matter? As it has been done in
the previous section, to address this question we run cold-turkey disin‡ations of …xed
size. The bottom right panel of Table 1 shows that the values of the sacri…ce ratios do
not change much, and remain close to one.
What then drives these results? The answer is as follows. Everything rests on
the non linear optimal price (wage) setting equation. We have shown?? that when
trend in‡ation reduces from 2 per cent to zero, the time pro…le of the e¤ective discount
factor shift downwards and slightly tilts clockwise. Ceteris paribus, adjusting …rms
(households) set lower prices (wages). The in‡ation rate falls, the (ex-ante) real interest
rate increases and output contracts. So, what happens when disin‡ating from 4 to 2 per
cent? Firstly, the adjustment in the e¤ective discount factor is more muted. The new
e¤ective discount factor will still tend to discount more the future economic conditions.
As intermediate …rms reckons that the permanent reduction does not imply any level
e¤ects on output, they will more heavily discount the long-term economic condition and
15
less the short-run recession. Together these two e¤ects make …rms (and wage setters) to
adjust less prices and wages (perhaps there is also another result - …rms reckon that with
positive trend in‡ation they relative ). In‡ation will drop less and the real interest rate
will more moderately increase. Consequently the recession will be less severe. As we
experiment with higher initial trend in‡ation these two e¤ects just described strenghted
and therefore we will observe less output loss. Trivially it follows that the sacri…ce ratio
will re‡ect these results.
5
Disin‡ation timing
We now relax some of the assumptions underlying the mechanics of the cold-turkey
disin‡ation. In particular, we look at two cases: gradualism and anticipations. In the
former case, the central bank implements a gradual reduction of the in‡ation target
towards the new in‡ation target over a certain time window. In the latter case, instead,
the central bank announces today a cold-turkey disin‡ation forthcoming in a given future
date.
5.1
Cold-turkey vs. gradual disin‡ation
At time zero the central bank implements a gradual reduction of the in‡ation target
to be completely accomplished in k periods. In particular, the central bank sets the
time-varying in‡ation target path to ful…ll the following stair function,
t
for t = 0; 1; :::; k
=
H
t 1
1 and given that
L
k
1
=
, with k > 1,
H.
(6)
Notice that k can be thought as the
disin‡ation speed: the lower k, the faster the reduction of in‡ation target. Clearly, the
cold-turkey disin‡ation attains for k = 1.
Figures 4 and 5 illustrate dynamic adjustment paths of output and in‡ation for
di¤erent disin‡ation speed, i.e., k = f0; 4; 8; 12g and di¤erent initial level of steady
in‡ation, i.e.,
H
= f2%; 4%; 8%g.
16
Is the gradual disin‡ation recessionary? Both under money supply and interest
rate targeting rule, gradual disin‡ation leads to an initial hump-shaped recession, then
followed by a small, but persistent, expansion of output. While it is true that for a
given k, higher initial steady in‡ation rate of in‡ation increases output volatility, more
gradual disin‡ationary policy schemes yields the opposite e¤ect. Table 2 shows, in fact,
that for k = 4, 8, 12 output variability decreases to a larger extent under the money
supply targeting and to a lesser extent under interest rate targeting. In the former case,
it must be said, that output variability, in absolute terms, is already much smaller.
These results hinge on the fact that operating a gradual disin‡ation makes optimising
intermediate …rms to lower prices less. (On this see the previous discussion on the
…xed-size cold-turkey disin‡ation - gradual disin‡ation can be thought as a mixture of
an initial cold-turkey disin‡ation and the announcement of future C-D disin‡ations).
Consequently, in‡ation adjusts more gradually, the ex ante real interest rate increases
more moderately and the contraction of output follows less severe.
Interestingly, the e¤ects of gradualism has ambiguous e¤ects on in‡ation variability.
Under money supply targeting, more gradual disin‡ation distinctly dampens the variance of in‡ation. Under interest rate targeting, however, in‡ation variability is lowest
for k = 4, taking into account also k = 0, and remarkably increases for k = 8, 12.
How costly is the gradual disin‡ation? As we have just seen, gradual disin‡ation
both under money supply and interest rate targeting entail output costs, however, these
are remarkably smaller than under cold turkey disin‡ations. Two results are worth
stressing. Firstly, under money supply targeting for a given disin‡ation size more gradual
disin‡ation monotonically reduces the sacri…ce ratios. Table 3 shows that moving from
cold turkey to 1-year gradual disin‡ation both SR and -SR decrease by roughly 0.6,
regardless of the disin‡ation size. A further 0.6 reduction of sacri…ce ratios is gained
when moving from 1-year to 2-year gradual disin‡ation, while it becomes 0.2 from 2year to 3-year. Secondly, under interest rate targeting the reduction of the values of the
sacri…ce ratios are not monotonic in k. Referring back to Table 3, the sacri…ce ratios
decrease up until k = 8, and then start rising.
Does the size of disin‡ation matter? As shown in Table 3, with gradual disin‡ation17
ary monetary policies the size of disin‡ation does matter for the sacri…ce ratio. Quite
interestingly, for a given k the values of the sacri…ce ratios are negatively correlated
with the size of disin‡ation. To say, it is less costly to gradually disin‡ate the economy
starting o¤ from relatively higher initial steady in‡ation rates. From a quantitative
standpoint, these e¤ects are more noticeable under money supply targeting rule.
5.2
Unanticipated versus anticipated cold-turkey disin‡ation
Another practical case to look at is the anticipated cold-turkey disin‡ation: the central
bank in this instance announces at time t = 0, and it is perfectly believed, a cold-turkey
disin‡ation plan that will take place only after k periods ahead. We consider cold-turkey
disin‡ations implemented after 1, 2 and 3 years from the announcement period.
The adjustment paths under money targeting rule and interest rate rule are illustrated in Figures 6 and 10, respectively. Under money targeting rule, the e¤ects of
announcing the future intension to disin‡ate the economy has considerable e¤ects both
qualitatively and quantitatively. It holds true, and it is quite robust, that there is an
initial recession, followed then by a boom. The main e¤ect of delaying the implementation of the cold-turkey is mainly re‡ected in the intensity of the recession and boom.
Indeed, the more delayed is the disin‡ation the smaller are the ‡uctuations of output.
These results hold true for all the disin‡ation size taken into account, but the scale
e¤ects already mentioned in previous analysis. Even more remarkable, when compared
to Figure 1, are the e¤ects of the adjustment path of in‡ation. In this case, delaying the
implementation of the disin‡ation greatly reduces the de‡ation and in the case of 2- and
3-year announcement the de‡ation basically disappears. It is indeed the intermediate
…rms’behaviour of slowly adjusting their prices that results in a gradual reduction of
in‡ation, a more muted response of the ex-ante real interest rate and thus a milder
recession. Table 2, however, highlights the fact that delaying the implementation of the
cold-turkey disin‡ation does not result in a monotonic reduction of the sacri…ce ratios.
As a matter of fact, although announcing in advance the disin‡ation considerably reduces both the SR and the
-SR compared to the unanticipated case, the bene…t of
18
delaying are relative stronger in the case of the 2-year announcement. After that both
the sacri…ce ratios increase. As illustrated in Table 2, these e¤ects carry on also for
relatively larger disin‡ation size.
Turning to the interest rate rule, the e¤ects of announcing a future cold-turkey
disin‡ation are for several reasons more surprising. Indeed, delaying the cold-turkey
disin‡ation by one year has more stabilizing e¤ects compared to the unanticipated policy. The intensity of the recession and the following boom are considerably decreased.
Announcing a cold-turkey disin‡ation that will be implemented after two years or even
worse after three years has profound destabilising e¤ects this is due to the intrinsic
destabilising e¤ects of the interest rate rule that in the period between the announcement and the implementation. In this period, indeed, the central bank seeks to stabilise
the economy around a target values of in‡ation and the nominal interest rate that are
di¤erent from the steady state ones.[... to be …nished ....]
The results in Table 2 and 3 seem to suggest that an announced disin‡ation policy
might perform better relative to a gradual disin‡ation.
6
6.1
A welfare based measure of the cost of disin‡ation
A microfounded SR
As already noted in Gordon and King (1982), the output loss from disin‡ation does not
by itself contain policy implications. A careful assessment must be made of the welfare
cost of lost output and the welfare bene…ts of lower in‡ation. On this latter point,
the recent monetary policy literature has abundantly and convincingly emphasized the
reasons why achieving full price stability is desirable (see Woodford, 2003 and the references therein). One notable advantage of working with structural model is that they
provide a natural metric to evaluate the overall welfare implication of disin‡ation. Our
welfare-based indicator relies on the representative household’s value function. Since
we are dealing with a DSGE model, we can easily calculate a welfare based measure
of the cost of disin‡ation, rather than an empirical based one, as the sacri…ce ratio.
19
Paralleling the way SR is built, the numerator of this welfare based measure would just
be the di¤erence between the level of the value function in period 1 and the level of the
value function if the policy was not implemented, that is, the old steady state value.
(V1
VH ) measure indeed the loss in welfare caused by the implementation of the policy.
So a possible microfounded sacri…ce ratio could be
1
M SR =
(V1
(7)
VH )
H,L
where VH = starting steady state value function, and V1 = value function the …rst period
after the implementation of the disin‡ationary policy. Note that, as in the standard
sacri…ce ratio de…nition, if V1
VH < 0, that is disin‡ation brings about a welfare
loss, then M SR > 0; and vice versa It is important to note that V1 includes both the
transition dynamics and the long-run e¤ects.
The consumption equivalent measure
A policy maker is interested in the welfare cost of implementing a disin‡ationary
policy, but given that the utility function is not cardinal, a measure based on V is
not very revealing. The di¤erence (V1
VH ) can, as usual, be expressed in terms of
consumption equivalent units. The consumption equivalent measure is then de…ned as
that constant fraction of consumption that households should give away in each period
in the starting steady state in order to obtain the same level of value function that
households would get if the disin‡ationary policy is implemented. Note that this is a
true measure of the costs of disin‡ation in terms of consumption: indeed it measures
how much households have to su¤er in terms of consumption loss, in order to reduce
the in‡ation rate permanently of a certain amount.
Finally, this measure is very easy to get. The starting initial value function is
VH = E0
1
X
t
t=0
"
ln(ct
bct 1 )
mh
0 2
ht + t
2
1
1
m
m
#
(8)
;
that in steady state this reduces to
VH = Vss0 =
1
1
"
ln ((1
20
b)c)
mh
0 2
h +
2
1
1
m
m
#
:
(9)
Given the value of V1 from our simulations, then we just need to solve for what constant
fraction of steady state consumption households should give away in each period in
the starting steady state to obtain the same level of value function at the moment the
disin‡ationary policy is implemented. This is a very simple problem, since it ends up to
…nd the solution for
in the following equation
"
1
V1 =
ln ((1 b)c(1
))
1
where
mh
0 2
h +
2
1
1
m
m
#
;
(10)
measure exactly that constant fraction. The consumption equivalent measure
is simply given by
=1
exp [(1
)(V1
VH )] :
(11)
Finally, the proposed welfare based sacri…ce ratio measure is14
W SR =
(12)
H,L
The last columns of Table XXX reports W SR in the case of CD disin‡ations under
both a money targeting and an interest rate targeting rule. W SR is negative: the
disin‡ation is welfare improving.15 Therefore, we should not speak, as the empirical literature, of sacri…ce ratio, but of welfare gain ratio. The long-run gain therefore
prevails on the short run costs. We think this is an interesting result: the empirical
literature focuses only on the short-run cost of a disin‡ation in terms of output, but it
neglects (or denies) any long-run e¤ect (gain or loss). We demonstrate that in a medium
scale DSGE monetary model of the business cycle, instead, a disin‡ationary policy is
welfare improving. The size of W SR; however, is small: under both polices the welfare
gain is equivalent to an extra 0.06% of consumption each period.
Actually, the results are possibly even more striking, if we disentangle the short-run
costs of a disin‡ation during the adjustment dynamics and the long-run gains due to price
14
V1
15
Note that there is no minus in front of
1
H ,L
to mantain a positive sign for a loss. Indeed, if
Vss < 0, that is disin‡ation brings about a welfare loss, then > 0; and vice versa.
Note that this qualitative result does not depend on the inclusion of real money balances in the
utility function. We can also calculate a similar measure without taking into account the gain in utility
coming from an increase in real money balances in the new steady state. The measure would then
around 2/3 of the one reported.
21
stability. In a standard medium scale DSGE macro model, considered as a benchmark
model in the literature, a cold-turkey disin‡ation entails a large and prolonged recession,
as basic intuition would predict. The sacri…ce ratio, moreover, are in line with the
empirical evidence. The short-run costs of such a painful adjustment path are, however,
insigni…cant. The order of magnitude must be given by the di¤erence between W SR
and the long-run gains, that is, roughly about 0.01% of initial consumption.
Table XXX,indeed, shows the long-run gains and the short-run costs of a cold-turkey
disin‡ation under the two policies. Following the same reasoning above:
(i) the consumption equivalent long-run costs are equal to16
LR
=1
exp [(1
)(VL
(13)
VH )]
where VH (VL ) is the value function in the high (low) in‡ation steady state, and the
same costs or gains can be expressed per unit of diminished in‡ation to yield a long-run
welfare based sacri…ce ratio
W SR_LR =
LR
(14)
;
H,L
(ii) a short-run welfare based sacri…ce ratio is then given by
W SR_SR =
=
LR
=
H,L
exp [(1
)(VL
VH )]
exp [(1
)(V1
VH )]
;
(15)
H,L
Table XXX shows the di¤erent W SR for di¤erent experiment and monetary policy
rules. Obviously, the long-run gains, i.e., W SR_LR; do not depend on the monetary
policy strategy. The analysis of the short-run costs, instead, show that disin‡ating
through an interest rate targeting rule is always less costly, for any kind of experiment
considered in Table XXX. The di¤erence is anyway very tiny, relatively insensitive to
the kind of experiment, and it approximately amounts to a 0.002% of consumption in
16
Note that if Vss2
Vss < 0 (that is if disin‡ation brings about a welfare loss) then
versa.
22
> 0; and vice
each period.. Regarding cold turkey disin‡ation, the size of the disin‡ation matters only
for the long-run gains, while short-run costs seems insensitive to it. Moreover, there are
"decreasing returns to scale to disin‡ating", in the sense that , W SR_LR; i.e., the
long-run gains per percentage point of diminished in‡ation, decreases, almost linearly,
with the size of the disin‡ation. Both long-run gains and short-run costs are, instead,
decreasing with respect to the initial level of in‡ation, for a given size of disin‡ation. The
long-run e¤ects, however, quantitatively dominates, such that the gains from disin‡ating
decreases with the starting level of in‡ation.17
As in Table XXX, Table XXX looks at the e¤ects of anticipated and gradualist
policies on our welfare based measure of the sacri…ce ratio. As for the case of output
based sacri…ce ratios, the bene…ts of a gradual disin‡ation are monotonic in the case
of a monetary rule, while they are not monotonic in the case of an interest rate rule.
Furthermore, anticipation increases the gains from disin‡ating only up to a point, which
is two year in the case of a monetary rule and one year in the case of an interest rate rule.
In any case, these e¤ects are really marginal. The main message from the two Tables is
that a disin‡ation is going to be welfare improving of the order of an increase of initial
consumption of 0.06-0.07% each period per point of diminished in‡ation, no matter
how the disin‡ation is implemented (monetary policy strategy, gradualism,
anticipation).
This stands in sharp contrast with the common wisdom view about the e¤ects of
a credible disin‡ation. What is the intuition for these results? To illustrate it, let’s
take the case of a cold turkey disin‡ation implemented through a monetary rule. Figure
XXX displays the path of consumption and employment, expressed in deviation from
…nal steady state, together with value of the utility function. The cold-turkey disin‡ation induces a prolonged recession that cause both consumption and employment to be
below their new (and higher) steady state value for some periods. Consumption and
employment, however, has opposite e¤ects on the utility function of the representative
agent. It follows, therefore, that the net e¤ects of the recession on the utility of the
17
Disin‡ation from 8% to 6% exhibits a higher (more costs) W SR than disin‡ating from 6% to 4%.
In a sense, there are "increasing marginal returns to scale to disin‡ating".
23
representative agent is ambiguous. Indeed, the decrease in consumption dominates in
the impact period, dragging the utility function down, but then already in the second
period the e¤ects of the dynamics of employment takes over, and the utility function is
above its new higher long-run value. Moreover, it will stay there for all the periods of
the recession. This is because the drop in employment is bigger in percentage terms, and
slightly more sluggish. It follows that the positive e¤ect of employment is quite e¤ective
in counterbalancing the negative e¤ect of lower consumption. Overall the transition,
thus, entails a short-run cost, as shown above, but of a negligible order of magnitude.
Finally, also the value of the utility function without counting the real money balances
term is visualized in Figure XXX, so to make clear that the role of the real money
balances term in the utility function in the above results is nil.
This result obviously should not be taken as face value. Indeed, in the dynamics of
the "average" representative consumer are hidden very di¤erent situations. In particular,
as known, a representative agent framework can not be taken into account the fact that
some people may su¤er a very big drop in utility during recession because they loose
their jobs: such a composition e¤ect is missing by construction. We believe, however,
our results show two important points. On the one hand, they cast shadow on using
these DSGE models for welfare evaluation without "inspecting the mechanism". In
particular, the ranking between di¤erent monetary policy rules or the optimal policy
problems are bound to be based on mechanism similar to ours. On the other hand,
recall that if there are complete markets (and agents are the same ex-ante), then all the
agents will have the same marginal utility from consumption. Hence, our results simply
show once again that, if the economy could provide an e¢ cient risk-sharing between
the agents (either through good capital markets, or some public welfare system), then
disin‡ation, in particular, and recession, in general, are less a problem than we normally
think.
7
Conclusions
[to be done]
24
8
References
References
Andersen, P. S. and W. L. Wascher (1999). Sacri…ce ratios and the conduct of monetary policy in conditions of low in‡ation. Technical Report BIS Working Paper
82, Bank of International Settlements.
Ascari, G. (2004). Staggered prices and trend in‡ation: Some nuisances. Review of
Economic Dynamics 7, 642–667.
Ball, L. (1994). What determines the sacrifcie ratio? In N. G. Mankiw (Ed.), Monetary
Policy, pp. 155–182. University of Chicago Press, Chicago.
Cecchetti, S. G. and R. W. Rich (2001). Structural estimates of the U.S. sacri…ce
ratio. Journal of Business Economic Statistics 19, 416–427.
Christiano, L. J., M. Eichenbaum, and C. L. Evans (2005). Nominal rigidities and
the dynamic e¤ects of a shock to monetary policy. Journal of Political Economy 113 (1), 1–45.
Collard, F., P. Fève, and J. Matheron (2006). What happens after a disin‡ation policy
shock. Technical report, University of Toulouse. mimeo.
Erceg, C. J. and A. T. Levin (2003). Imperfect credibility and in‡ation persistence.
Journal of Monetary Economics 50, 915–944.
Fève, P., J. Matheron, and J.-G. Sahuc (2007). Disin‡ation shocks in the eurozone:
A DSGE perspective. Technical report, University of Toulouse. mimeo.
J.Filardo, A. (1998). New evidence on the output cost of …ghting in‡ation. Federal
Reserve Bank of Kansas City Economic Review 3rd quarter, 33–61.
Schmitt-Grohé, S. and M. Uribe (2004). Optimal operational monetary policy in the
Christiano-Eichenbaum-Evans model of the U.S. business cycle. NBER wp No.
10724.
25
Woodford, M. (2003). Interest and Prices: Foundations of a Theory of Monetary
Policy. Princeton University Press.
Zhang, L. H. (2005). Sacri…ce ratios with long-lived e¤ects. International Finance 8,
231–262.
26
9
Tables
Calibration
1:03
0:25
Time discount rate
0:36
Share of capital
0:5827
Fixed cost (guarantee zero pro…ts in steady state)
0:025
Depreciation of capital
1
Elasticity of substitution of di¤erent varieties of goods
6
Elasticity of substitution of labour services
21
Probability of not setting a new price each period
~
0:6
Probability of not setting a new wage each period
b
0:64
Degree of habit persistence
0
1:1196
Preference parameter
1
0:5393
Preference parameter
m
10:62
Intertemporal elasticity of money
2:48
Investment adjustment cost parameter
1
Price indexation
1
Wage indexation
1
0:0324
Capital utilization cost function parameter
2
0:000324
Capital utilization cost function parameter
1
Steady state value of technology shock
z
0:979
Serial correlation of technology shock (in log-levels)
z
0:0072
Standard deviation of technology shock
g
0:96
Serial correlation of demand shock (in log-levels)
g
0:02
Standard deviation of demand shock
0:18
Parameter scaling all exogenous shocks
~
~
z
Table 1. Calibration
27
Money supply rule
Interest rate rule
(T=15)
(T=28)
SR
-SR
W-SR
SR
-SR
W-SR
0%
2.94
2.96
-6.40
1.06
1.04
-6.59
4%
0%
2.85
2.85
-6.29
1.05
1.03
-6.49
6%
0%
2.78
2.77
-6.20
1.04
1.02
-6.39
8%
0%
2.73
2.72
-6.12
1.03
1.01
-6.31
4%
2%
2.22
2.23
-6.26
1.03
1.02
-6.39
6%
4%
1.89
1.90
-6.12
1.01
1.00
-6.23
8%
6%
1.69
1.71
-5.99
0.99
0.98
-6.08
H
L
2%
Table 1: Costs of cold turkey disin‡ation
10
Figures
28
29
1.08
0.32
0.17
0.10
0.67
0.33
0.20
0.18
0.04
0.02
0.38
0.25
0.66
2
2
Y
2
Y
2
Y
2
2
2
2
Y
2
Y
2
Y
2
2
2
k=4
k=8
k=12
k=4
k=8
k=12
k=4
k=8
k=12
k=4
k=8
k=12
disin‡ation
Anticipation
Gradualism
0.52
2
Y
Cold turkey
2!0
8.18
3.51
2.19
0.19
0.14
0.77
2.06
1.96
3.46
0.40
0.73
1.68
5.79
3.15
6!0
15.59
7.02
3.58
0.34
0.20
1.05
4.04
3.33
5.24
0.54
0.99
2.45
8.74
4.92
8!0
0.93
0.41
0.22
0.02
0.01
0.07
0.22
0.21
0.35
0.04
0.07
0.16
0.61
0.29
4!2
1.02
0.50
0.20
0.02
0.01
0.03
0.27
0.20
0.26
0.03
0.04
0.10
0.45
0.21
6 !4
1.04
0.54
0.20
0.02
0.01
0.02
0.30
0.20
0.22
0.02
0.03
0.07
0.36
0.17
8 !6
2.78
1.35
0.52
0.06
0.01
0.023
0.98
0.66
0.50
0.02
0.02
0.04
0.51
0.05
2!0
11.04
5.39
2.09
0.24
0.07
0.09
3.89
2.64
2.01
0.10
0.08
0.15
2.05
0.22
4 !0
24.17
11.92
4.70
0.52
0.16
0.20
8.79
5.91
4.49
0.22
0.19
0.34
4.59
0.48
6 !0
42.22
20.96
8.32
0.90
0.29
0.35
15.60
10.50
7.97
0.38
0.33
0.58
8.12
0.84
8 !0
2.74
1.32
0.50
0.05
0.01
0.02
0.95
0.64
0.48
0.02
0.02
0.03
0.49
0.05
4!2
2.52
1.23
0.48
0.05
0.01
0.02
0.96
0.63
0.46
0.02
0.02
0.03
0.47
0.05
6 !4
Interest rate targeting rule (T=15)
Table 2: Measures of output and in‡ation volatility.
3.25
1.31
1.14
0.09
0.09
0.47
0.83
0.99
1.92
0.26
0.45
0.96
3.20
1.66
4!0
Money suppy targeting rule (T=28)
2.29
1.14
0.46
0.04
0.01
0.02
0.89
0.60
0.45
0.02
0.01
0.03
0.45
0.04
8!6
30
Anticipation
Gradualism
-SR
-SR
k=8
k=12
SR
k=12
-SR
SR
k=8
k=4
SR
-SR
k=12
k=4
-SR
k=8
SR
k=12
-SR
SR
k=8
k=4
SR
k=4
1.25
0.94
1.52
1.28
0.94
1.51
1.31
1.53
2.13
1.32
1.52
2.12
4!0
1.24
0.83
1.34
1.28
0.84
1.33
1.16
1.35
1.96
1.16
1.34
1.96
6 !0
1.25
0.78
1.21
1.29
0.78
1.20
1.05
1.21
1.84
1.06
1.21
1.83
8 !0
1.31
0.87
1.18
1.36
0.87
1.17
1.16
1.23
1.65
1.16
1.22
1.63
4!2
1.34
0.79
0.93
1.39
0.80
0.92
1.05
1.04
1.36
1.06
1.03
1.35
6!4
1.36
0.77
0.79
1.41
0.78
0.79
0.99
0.93
1.20
1.00
0.93
1.19
8!6
1.72
0.86
0.77
1.80
0.90
0.79
1.01
0.84
0.93
1.05
0.86
0.95
2!0
1.69
0.86
0.76
1.77
0.90
0.78
1.00
0.83
0.92
1.04
0.85
0.93
4 !0
1.66
0.86
0.76
1.74
0.90
0.78
0.99
0.82
0.91
1.03
0.84
0.92
6 !0
1.64
0.86
0.75
1.72
0.90
0.77
0.99
0.81
0.89
1.02
0.83
0.91
8!0
1.68
0.84
0.76
1.76
0.88
0.77
0.98
0.80
0.91
1.02
0.83
0.91
4!2
1.60
0.82
0.75
1.68
0.85
0.76
0.98
0.80
0.89
1.01
0.82
0.90
6 !4
Interest rate targeting rule (T=15)
Table 3: Sacri…ce ratios: gradual and anticipated disin‡ations
1.31
1.13
1.77
1.35
1.13
1.76
1.55
1.79
2.33
1.55
1.78
2.32
2!0
Money suppy targeting rule (T=28)
1.54
0.81
0.75
1.61
0.84
0.76
0.97
0.79
0.87
1.00
0.81
0.88
8 !6
Long-Run
H
L
2%
0%
4%
6%
8%
4%
6%
8%
0%
0%
0%
2%
4%
6%
2
Monetary Rule
Welfare Gain (10 )
Short-Run
2
W -SR (10 2 )
Welfare Cost (10 )
-7.40
-7.30
-7.20
-7.11
-7.18
-7.00
-6.82
MS
1.00
-6.40
IR
0.81
-6.59
MS
1.00
-6.29
IR
0.81
-6.49
MS
1.00
-6.20
IR
0.81
-6.39
MS
1.00
-6.12
IR
0.80
-6.31
MS
0.91
-6.26
IR
0.79
-6.39
MS
0.87
-6.12
IR
0.76
-6.23
MS
0.83
-5.99
IR
0.74
-6.08
Table 4: Costs of cold turkey disin‡ation
31
32
Anticipation
Gradualism
6!4
8!6
-6.62 -6.51 -6.42 -6.34 -6.42 -6.25 -6.11
-6.57 -6.46 -6.37 -6.29 -6.37 -6.21 -6.06
-6.57 -6.48 -6.40 -6.32 -6.39 -6.23 -6.08
-6.57 -6.47 -6.38 -6.30 -6.37 -6.20 -6.05
W -SR
W -SR
k=8
k=12
Table 5: Sacri…ce ratios and welfare gains:gradual and anticipated disin‡ations
-6.63 -6.52 -6.43 -6.35 -6.43 -6.26 -6.11
-6.51 -6.42 -6.35 -6.27 -6.37 -6.22 -6.08
W -SR
k=4
-6.61 -6.50 -6.41 -6.33 -6.41 -6.24 -6.09
4!2
-6.53 -6.45 -6.37 -6.30 -6.37 -6.21 -6.07
8!0
W -SR
6!0
k=12
4!0
-6.62 -6.51 -6.42 -6.34 -6.42 -6.25 -6.10
2!0
-6.51 -6.42 -6.35 -6.27 -6.36 -6.21 -6.07
8!6
W -SR
6!4
k=8
4!2
-6.61 -6.50 -6.41 -6.33 -6.41 -6.24 -6.09
8!0
-6.42 -6.36 -6.28 -6.20 -6.32 -6.18 -6.04
6!0
W -SR
4!0
Interest rate targeting rule (10 2 ) (T=15)
k=4
2!0
Money suppy targeting rule (10 2 ) (T=28)
OUTPUT
INFLATION RATE (ANNUALIZED)
5
10
5
0
0
-5
-5
-10
0
5
10
15
20
-10
quarters
REAL MONEY BALANCES
0
5
10
15
20
quarters
GROWTH RATE OF MONEY SUPPLY
5
8
From 8%
From 6%
From 4%
From 2%
6
0
4
to 0%
to 0%
to 0%
to 0%
-5
2
-10
0
5
10
15
0
20
quarters
NOMINAL INTEREST RATE
2
1
1
0
0
0
5
10
15
5
10
15
20
quarters
EX-ANTE REAL INTEREST RATE
2
-1
0
-1
20
0
5
quarters
10
15
20
quarters
Figure 1: Cold-turkey disin‡ation under money supply rule. Transition paths are expressed in percentage deviations from the new steady state.
33
OUTP UT
INFLATION RATE (ANNUALIZED)
1
8
6
0
4
-1
2
0
-2
From
From
From
From
-3
-4
0
5
10
8%
6%
4%
2%
15
to
to
to
to
0%
0%
0%
0%
-2
-4
-6
20
0
5
quarters
10
15
20
quarters
REAL MONEY BALANCES
GROWTH RATE OF MONEY SUP P LY
1
8
0
6
-1
-2
4
-3
2
-4
-5
0
5
10
15
0
20
0
5
quarters
10
15
20
quarters
NOMINAL INTEREST RATE
EX-ANTE REAL INTEREST RATE
0.6
1.5
0.5
1
0.4
0.3
0.5
0.2
0.1
0
0
-0.1
0
5
10
15
-0.5
20
quarters
0
5
10
15
20
quarters
Figure 2: Cold-turkey disin‡ation under money supply rule for a …xed 2% disin‡ation
size. Transition paths are expressed in percentage deviations from the new steady state.
34
OUTPUT
INFLATION RATE (ANNUALIZED)
1
10
0
5
-1
0
-2
0
5
10
15
-5
20
quarters
REAL MONEY BALANCES
10
0
5
-5
0
0
5
10
15
0
5
10
to 0%
to 0%
to 0%
to 0%
15
20
quarters
GROWTH RATE OF MONEY SUPPLY
5
-10
From 8%
From 6%
From 4%
From 2%
-5
20
quarters
NOMINAL INTEREST RATE
0
5
10
15
20
quarters
EX-ANTE REAL INTEREST RATE
3
1.5
1
2
0.5
1
0
0
0
5
10
15
20
-0.5
quarters
0
5
10
15
20
quarters
Figure 3: Disin‡ation policies implemented via a Taylor rule. Transition paths are
expressed in percentage deviations from the new steady state.
35
OUTPUT GAP
INFLATION RATE (ANNUALIZED)
0.5
3
0
2
-0.5
1
-1
0
-1.5
-1
-2
0
5
10
15
20
-2
25
OUTPUT
4
0
2
-1
0
-2
-2
0
5
10
5
10
15
20
25
(INFLATION RATE (ANNUALIZED)
1
-3
0
15
20
-4
25
0
OUTPUT
5
10
15
20
25
INFLATION RATE (ANNUALIZED)
2
10
0
5
-2
0
-4
-6
0
5
10
15
1-year gradualism
20
-5
25
0
2-year gradualism
5
10
15
20
25
3-year gradualism
Figure 4: Gradual disin‡ation under money supply rule. Transition paths are expressed
in percentage deviations from the new steady state.
36
OUTPUT
INFLATION RATE (ANNUALIZED)
0.1
3
0
2
-0.1
1
-0.2
0
-0.3
-0.4
0
5
10
15
20
-1
25
OUTPUT
4
0
3
-0.2
2
-0.4
1
-0.6
0
0
5
10
5
10
15
20
25
INFLATION RATE (ANNUALIZED)
0.2
-0.8
0
15
20
-1
25
OUTPUT
0
5
10
15
20
25
INFLATION RATE (ANNUALIZED)
0.5
8
6
0
4
-0.5
2
-1
-1.5
0
0
5
10
15
20
1-year gradualism
-2
25
0
5
2-year gradualism
10
15
20
25
3-year gradualism
Figure 5: Gradual disin‡ation under interest rate targeting rule. Transition paths are
expressed in percentage deviations from the new steady state.
37
OUTPUT
INFLATION RATE (ANNUALIZED)
0.5
3
2
0
1
-0.5
0
-1
-1.5
-1
0
5
10
15
20
-2
25
OUTPUT
0
5
10
15
20
25
INFLATION RATE (ANNUALIZED)
0.5
4
0
3
2
-0.5
1
-1
0
-1.5
-2
-1
0
5
10
15
20
-2
25
OUTPUT
0
5
10
15
20
25
INFLATION RATE (ANNUALIZED)
1
10
0
5
-1
0
-2
-3
0
5
10
15
1-year annauncement
20
-5
25
0
5
2-year annauncement
10
15
20
25
3-year annauncement
Figure 6: Anticipated disin‡ation under money supply rule. Transition paths are expressed in percentage deviations from the new steady state.
38
OUTPUT GAP (% DEVIATION)
ANNUALIZED INFLATION RATE
0.1
3
0
2
-0.1
1
-0.2
0
-0.3
-0.4
0
5
10
15
20
-1
25
0
OUTPUT GAP (% DEVIATION)
5
10
15
20
25
ANNUALIZED INFLATION RATE
0.2
6
0
4
-0.2
2
-0.4
0
-0.6
-0.8
0
5
10
15
20
-2
25
0
OUTPUT GAP (% DEVIATION)
5
10
15
20
25
ANNUALIZED INFLATION RATE
0.5
10
0
5
-0.5
0
-1
-1.5
0
5
10
15
20
1-year anticipated
-5
25
0
2-year anticipated
39
5
10
15
3-year anticipated
20
25
CONSUMP TION
EMP LOYMENT
1
1
0.5
0
0
-1
-0.5
-1
-2
-1.5
-3
-2
From
From
From
From
-2.5
-3
0
5
10
8%
6%
4%
2%
to 0%
to 0%
to 0%
to 0%
15
-4
-5
-2
20
0
2
4
6
UTILITY FUNCTION
-1.11
-1.12
-1.12
-1.13
-1.13
-1.14
-1.14
-1.15
-1.15
-1.16
-1.16
0
2
4
6
8
10
10
12
14
16
18
20
UTILITY FUNCTION WITHOUT REAL MONEY BALANCES
-1.11
-2
8
quarters
quarters
12
14
16
18
20
-2
quarters
0
2
4
6
8
10
12
14
16
18
20
quarters
Figure 7: Cold-turkey disin‡ation under money supply rule. Consumption and employment paths are expressed in percentage deviations from the new steady state. Utilty
function are expressed in levels.
40
www.st-and.ac.uk/cdma
ABOUT THE CDMA
The Centre for Dynamic Macroeconomic Analysis was established by a direct grant from
the University of St Andrews in 2003. The Centre funds PhD students and facilitates a programme
of research centred on macroeconomic theory and policy. The Centre has research interests in areas
such as: characterising the key stylised facts of the business cycle; constructing theoretical models
that can match these business cycles; using theoretical models to understand the normative and
positive aspects of the macroeconomic policymakers' stabilisation problem, in both open and
closed economies; understanding the conduct of monetary/macroeconomic policy in the UK and
other countries; analyzing the impact of globalization and policy reform on the macroeconomy;
and analyzing the impact of financial factors on the long-run growth of the UK economy, from
both an historical and a theoretical perspective. The Centre also has interests in developing
numerical techniques for analyzing dynamic stochastic general equilibrium models. Its affiliated
members are Faculty members at St Andrews and elsewhere with interests in the broad area of
dynamic macroeconomics. Its international Advisory Board comprises a group of leading
macroeconomists and, ex officio, the University's Principal.
Affiliated Members of the School
Dr Fabio Aricò.
Dr Arnab Bhattacharjee.
Dr Tatiana Damjanovic.
Dr Vladislav Damjanovic.
Prof George Evans.
Dr Gonzalo Forgue-Puccio.
Dr Laurence Lasselle.
Dr Peter Macmillan.
Prof Rod McCrorie.
Prof Kaushik Mitra.
Prof Charles Nolan (Director).
Dr Geetha Selvaretnam.
Dr Ozge Senay.
Dr Gary Shea.
Prof Alan Sutherland.
Dr Kannika Thampanishvong.
Dr Christoph Thoenissen.
Dr Alex Trew.
Senior Research Fellow
Prof Andrew Hughes Hallett, Professor of
Economics, Vanderbilt University.
Research Affiliates
Prof Keith Blackburn, Manchester University.
Prof David Cobham, Heriot-Watt University.
Dr Luisa Corrado, Università degli Studi di Roma.
Prof Huw Dixon, Cardiff University.
Dr Anthony Garratt, Birkbeck College London.
Dr Sugata Ghosh, Brunel University.
Dr Aditya Goenka, Essex University.
Prof Campbell Leith, Glasgow University.
Dr Richard Mash, New College, Oxford.
Prof Patrick Minford, Cardiff Business School.
Dr Gulcin Ozkan, York University.
Prof Joe Pearlman, London Metropolitan
University.
Prof Neil Rankin, Warwick University.
Prof Lucio Sarno, Warwick University.
Prof Eric Schaling, Rand Afrikaans University.
Prof Peter N. Smith, York University.
Dr Frank Smets, European Central Bank.
Prof Robert Sollis, Newcastle University.
Prof Peter Tinsley, Birkbeck College, London.
Dr Mark Weder, University of Adelaide.
Research Associates
Mr Farid Boumediene.
Mr Johannes Geissler.
Mr Ansgar Rannenberg.
Mr Qi Sun.
Advisory Board
Prof Sumru Altug, Koç University.
Prof V V Chari, Minnesota University.
Prof John Driffill, Birkbeck College London.
Dr Sean Holly, Director of the Department of
Applied Economics, Cambridge University.
Prof Seppo Honkapohja, Cambridge University.
Dr Brian Lang, Principal of St Andrews University.
Prof Anton Muscatelli, Heriot-Watt University.
Prof Charles Nolan, St Andrews University.
Prof Peter Sinclair, Birmingham University and
Bank of England.
Prof Stephen J Turnovsky, Washington University.
Dr Martin Weale, CBE, Director of the National
Institute of Economic and Social Research.
Prof Michael Wickens, York University.
Prof Simon Wren-Lewis, Oxford University.
www.st-and.ac.uk/cdma
THE CDMA CONFERENCE 2008, held in St. Andrews, 3th to the 5th of September
2008.
PAPERS PRESENTED AT THE CONFERENCE, IN ORDER OF PRESENTATION:
Title
Author(s) (presenter(s) in bold)
Robust Learning Stability with Operational
Monetary Policy Rules
George Evans (Oregon and St Andrews) coauthored with Seppo Honkapohja
Who pays for job training?
Parantap Basu (Durham)
Electoral Uncertainty and the Deficit Bias in a
New Keynesian Economy
Campbell Leith (Glasgow)
Sacrifice Ratio or Welfare Gain Ratio?
Disinflation in a DGSE monetary model
Guido Ascari (Pavia)
Estimating insurance and incentive effects of
labour market reforms
Klaus Waelde (Glasgow)
Using time-varying VARs to diagnose the source
of 'Great Moderations': a Monte Carlo analysis
Tony Yates (Bank of England)
The Optimum Quantity of Money with Gold
Reserves
Max Gillman (Cardiff)
Managing Disinflation Under Uncertainty
Eric Schaling (Pretoria)
Factor demand linkages and the business cycle:
interpreting aggregate fluctuations as sectoral
fluctuations
Sean Holly (Cambridge)
Monetary and Fiscal Rules in an Emerging
Small Open Economy
Paul Levine (Surrey) with joint with Nicoletta
Batini (IMF and Surrey) Joe Pearlman (London
Met)
Can a pure Real Business Cycle Model explain
the real exchange rate?
Patrick Minford (Cardiff)
Macroeconomic Implications of a Key Currency
Matthew Canzoneri (Georgetown)
How we can model the credit crunch
Sticky information versus efficient indexation
Peter Sinclair (Birmingham)
Richard Mash (New College, Oxford
See also the CDMA Working Paper series at www.st-andrews.ac.uk/cdma/papers.html.