ARTICLES
Estimating the sacrifice ratio
for the euro area
Jérôme Coffinet
Julien Matheron
Céline Poilly
Research Directorate
Monetary Policy Analysis
and Research Division
Research Directorate
Economic and Financial
Research Division
Research Directorate
Economic and Financial
Research Division
and University of
Cergy-Pontoise – THEMA
In this article, we use three methods to estimate the sacrifice ratio, which corresponds
to the short-term cost of disinflation in terms of output loss: an ad hoc method,
a structural VAR approach and a general equilibrium model.
Estimates are based on euro area data from the first quarter of 1985 to the
fourth quarter of 2004. According to these three methods, the sacrifice ratio is estimated
at between 1.2 and 1.4%. In other words, the short-term cost of a 1 percentage point
permanent decline in inflation would be over 1 GDP point. Given the long-term cost
of inflation, this result highlights the importance of price stability.
A series of counterfactual exercises is carried out to measure the sensitivity of the result
to different degrees of labour market rigidity. In the neighbourhood of the estimated
values, two important results are brought to light:
• a decline in wage indexation to past inflation and wage stickiness results in a
proportionate fall in the sacrifice ratio;
• however, the impact of a decline in nominal wage stickiness is limited; conversely,
greater wage stickiness leads to a rise in the sacrifice ratio. In addition, the impact of a
change in wage stickiness is asymmetrical, as an increase in stickiness has a particularly
negative effect on the sacrifice ratio.
Key words: sacrifice ratio, labour market flexibility, disinflation
JEL codes: E502, E58
NB:This study is part of a project “Labour market flexibility and monetary policy effectiveness”.This article presents the main results of a previous
study carried out by Coffinet, Matheron and Poilly (2007).The authors would like to thank Thomas Heckel for his remarks on a previous version
of this article.
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Estimating the sacrifice ratio for the euro area
1| The sacrifice ratio, a tool for analysing
monetary policy
1|1 Definition and relevance of the sacrifice ratio
for monetary policy
In the 1980s, developed countries set price stability as the primary objective
of their monetary policy. Indeed, price stability contributes to raising
the growth potential of an economy, by making relative prices more
transparent, lowering the risk premium on inflation and preventing the
arbitrary redistribution of wealth and income (ECB, 2004). Numerous
studies confirm the positive effect on long-term growth of containing
inflation (Barro, 1996; Feldstein, 1999). However, in the short run, the
recessionary effects brought about by a disinflationary policy are likely
to constrain growth.
This is why the sacrifice ratio, defined as the cumulative output loss
resulting from a permanent 1 percentage point decrease in inflation,1 has
attracted so much attention from central bankers. Indeed, the objective,
i.e. price stability, having been established, it is important to understand
its mechanisms, advantages and possible costs.
1|2 The sacrifice ratio and the labour market
In the literature, the sacrifice ratio is often linked to price and wage
stickiness.
From a theoretical point of view, two types of arguments are usually
brought forward. On the one hand, wage stickiness resulting from the
wage setting mechanisms (frequency of changes, degree of indexation),
which reflects a lesser degree of labour market flexibility, is likely to weigh
on the adjustment of the economy in a disinflationary period and thus
increase the sacrifice ratio. Gordon (1982) uses this argument to explain
the fact that the sacrifice ratios are higher in the United States than in
Japan over the 1960-1980 period. On the other hand, according to the
New Keynesian view, the non-neutrality of money in the short term is
attributable to producer prices rather than wages (Mankiw, 1990). Wage
setting institutions could thus only play a secondary role as regards the
level of the sacrifice ratio.
1 For a detailed presentation of the concept of the sacrifice ratio, see Coffinet (2006).
2
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Estimating the sacrifice ratio for the euro area
From an empirical point of view, labour market rigidities are generally
control variables of the estimates and not a subject of research as such.
Indeed, analysing the link between labour market rigidities and sacrifice
ratios comes up against some difficulties. First, the studies on the subject
are all conducted under partial equilibrium, which limits the understanding
of the mechanisms at the root of the sacrifice ratio. Second, estimating
the sacrifice ratio itself is based on two different methodologies, which
have sometimes yielded divergent results: an approach based on an
ad hoc identification of disinflationary periods (Ball, 1994; Zhang, 2005)
on the one hand, and a structural VAR methodology (Cecchetti and Rich,
2001) on the other.
1|3 Objectives of the study
This study aims to estimate the sacrifice ratio for the euro area since the
1980s using an ad hoc method, a structural VAR representation and a general
equilibrium model, then on the basis of the latter to analyse the interactions
with the labour market. In Part 2, we estimate the sacrifice ratio for the euro
area using two traditional methods (ad hoc and structural VAR). In Part 3,
it is estimated using a general equilibrium model. Counterfactual exercises
and sensitivity analyses are then carried out to clarify the mechanisms
whereby disinflation is likely to lead to a loss of output in the short term.
For the sake of consistency, all of the data used directly2 in this study
are taken from the Area-Wide Model (AWM) database (Fagan, Henry and
Mestre, 2005) for the period from Q1 1985 to Q4 2004.
2| Traditional estimates of the sacrifice ratio
for the euro area
2|1 Ad hoc method
The approach developed by Ball (1994) consists in identifying the disinflation
episodes ex ante, then calculating the sacrifice ratio for each episode. The
loss in terms of output is equal to the cumulative sum over the entire
disinflationary period of the difference between output and potential
output. The sacrifice ratio is then defined as the ratio of output loss to the
change in trend inflation over the period under review.3
2 This is not the case for the structural VAR.
3 For an explanation of this method see Coffinet (2006).
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Estimating the sacrifice ratio for the euro area
Table 1 Sacrifice ratios for the euro area according to the Ball method
Variable
Initial level of inflation
Final level of inflation
Start of the disinflation episode
End of the disinflation episode
Sacrifice ratio
Value
5.10%
1.38%
Q2 1991
Q4 1998
1.37%
The period 1985-2004 shows only one episode of disinflation (see Table 1).
It starts in the second quarter of 1991 and ends in the fourth quarter
of 1998. The decline in underlying inflation amounts to 3.72% and the
sacrifice ratio 1.37%.
These results seem to be consistent with those of Coffinet (2006), according
to which the sacrifice ratio for Germany and France during the same period
stands at roughly 2% compared with 0.7% in Italy.
2|2 Structural VAR representation4
The use of a structural VAR representation to estimate sacrifice ratios was
first introduced by Cecchetti (1994) then taken up by Cecchetti and Rich
(2001). This approach first consists in estimating a two-variable structural VAR
model (including output and inflation) or three-variable model (including
output, inflation and real interest rates), taking account of possible identifying
restrictions.5 The impulse response functions of the variables are then
written as a weighted sum of the different shocks. Lastly, the sacrifice ratio is
calculated as the ratio of cumulative output loss due to a monetary shock over
the cumulative effect of this same monetary shock on the inflation rate.
According to Durand, Huchet-Boudon and Licheron (2005), the average
sacrifice ratio for the euro area is around 1.19% for the period from
Q1 1994 to Q4 2003.
2|3 Limitations of these approaches
Although the ad hoc method provides a precise analysis of the link between
the estimated sacrifice ratios and indicators of labour market rigidity, it
4 In the VAR representation, all of the selected variables from the theoretical model have the same status.The relations are thus purely statistical.
5 The structural VAR models incorporate some information from the economic literature to identify the structural VAR shocks (for example, the
fact that aggregate demand shocks do not have a permanent effect on the level of real GDP).
4
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Estimating the sacrifice ratio for the euro area
is nevertheless open to criticism. First, the calculation of the sacrifice
ratios is highly sensitive to the identification of the start and end of the
disinflation episodes. Second, the numerous methodologies put forward
to estimate the potential output specific to each episode have yielded
mixed results. Finally, these methods are not able to isolate the monetary
shocks. In other words, the disinflation episode is entirely and arbitrarily
attributed to a monetary shock, without taking account of other possible
supply and demand shocks.
Under the structural VAR approach, it is easier to distinguish structural
supply and demand shocks and monetary policy may be broken down
between systematic components (reaction function of the monetary
authorities) and stochastic components (monetary policy shocks).
However, two criticisms may be made. First, the results are sensitive to the
specification of the model. This is partly due to the difficulty of identifying
the shocks. Second, VAR models are not associated with enough theoretical
constraints to be really structural. They are therefore open to the Lucas
criticism and cannot be used to analyse the economic mechanisms that
underpin the sacrifice ratio.
3| Estimating the sacrifice ratio
in the framework of a general equilibrium model
3|1 Presentation of the model
This third part features a small microfounded dynamic stochastic general
equilibrium model likely to explain the dynamic behaviour of the variables
following a shock. According to this methodology, it is not only possible
to calculate the sacrifice ratio and test its significance, but also to study
the mechanisms at work during a disinflation episode. In addition, this
approach enables us to assess the sensitivity of the sacrifice ratio to the
various labour market rigidities. The model used, where prices and wages
are sticky and indexed to past inflation, fits into the New Keynesian school
of thought.
The model in equilibrium can be synthesized by 6 behavioural equations
(Box 1).6
6 More precisely, we derived the optimisation programme for each agent (household, firm) and imposed an ad hoc monetary policy rule.We then
represented each solution in loglinear form. Each variable is therefore expressed as the deviation of its logarithmic value from its stationary
value. See Coffinet, Matheron et Poilly (2007) for a more detailed presentation of the model and the underlying assumptions.
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Estimating the sacrifice ratio for the euro area
BOX 1
Equations of the theoretical model
(1)
Euler equation: yt = βηEt {yt + 1} + yt - 1 – (1 – (η(1 + β))) λt + gt – ηζt
(2)
Risk-free bonds equation: λt = it + Et {λt + 1 – πt + 1}
(3)
Price-setting equation: πt – γp πt - 1 = κp (wt + ϖp yt) + βEt {πt + 1 – γp πt},
where κp = ƒ(αp) with ƒ(.) decreasing function
(4)
Wage-setting equation: πwt – γw πt - 1 = κw (ϖw ϕyt – λt – wt) + βEt {πwt + 1 – γw πt} + χt
where κw = g(αw) with g(.) decreasing function
(5)
Accounting equality: πwt = πt + wt – wt - 1 + ζt
(6)
Monetary policy rule: it = ρti it-1 + (1 – ρi)[ap πt - 1 + ay yt - 1] + εt
yt is output, λt is the Lagrange multiplier, interpreted as a cumulative long-term real
interest rate, πt is the inflation rate, πwt is the wage inflation rate, wt is the real wage
and it is the nominal interest rate. As this model does not include capital, consumption
is equal to output. All of the non-stationary variables are expressed as a deviation
from their stochastic trend.
In addition, ζt, gt, χt and εt are random (productivity, preference, labour supply and
monetary) shocks. Except for ζ, which is iid, all of these shocks are supposed to follow
an autoregressive process of order 1.
The parameters are 0 < β < 1, η > 0, 0 < γp ≤1, κp > 0, ωp > 0, 0 < γw ≤1, κw > 0,
ϖw > 0, ϕ > 0, ρi > 0, ay > 0, 1 < ap .
The Euler equation (1) reflects the consumption behaviour of the
representative household, which depends on past consumption, expectations
of future consumption and λt, the marginal utility of wealth. This variable
may be interpreted as the cumulative long-term real interest rate.
Equation (2) is the risk-free bonds pricing equation. It links the return on
these assets to the expected growth rate of the marginal utility of wealth.
The price-setting equation (3) is the new Phillips curve. It links the rate
of inflation to the real marginal cost and expectations of future inflation.
Parameters αp and γp measure the degree of product market rigidity: the
higher the values of the parameters, the stickier the prices. αp is the
probability of a firm not being able to reoptimise its price at a given date
(Calvo, 1983). γp is the degree of price indexation to past inflation.7
7 Symmetrically, 1 – γp measures the degree of price indexation to the inflation target.
6
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The wage-setting equation (4) is the wage Phillips curve. It stems from
the assumption of labour market rigidities via the wage setting process.
Thus, wage inflation is linked to expectations of future wage inflation. The
parameters αw and γw are respectively the probability of a household not
being able to reoptimise its wage at a given date and the degree of wage
indexation to past inflation.8
In addition, wage inflation and inflation are linked through equation (5).
Lastly, according to the monetary policy rule (6), the central bank sets
nominal interest rates on the basis of past inflation and output (Taylor,
1993). Coefficients ap and ay measure respectively the degrees of reaction
to past inflation and past consumption. In addition, in the tradition of
Clarida, Gali and Gertler (2001), nominal interest rates show inertia,
measured by ρi.
3|2 Estimation of the model and the sacrifice ratio
BOX 2
Method for estimating the parameters of the model
We first define θT as the vector stacking the autocovariances of order 0 to 6 of the
variables of interest (output, inflation, wage inflation and nominal interest rate). This
vector is estimated using a VAR model of order 2.
We then calculate h(ψ), the vector of the theoretical counterparts of θT . More precisely,
for a given value of the parameters ψ, the resolved theoretical model is written in the
form of a VAR model, for which we deduce the value of the moments of these same
variables. Thus, the vector of theoretical moments h(ψ) is a function of the value of
the parameters of the model, contained in the vector ψ.
Lastly, we estimate the value of the parameters which minimise the quadratic
distance between the vector of empirical moments θT., and its theoretical counterpart.
Formally, the vector of the estimated parameters ψT , is chosen such that:
ψT = Argmin (h(ψ) – θT)’WT (h(ψ) – θT), where WT is a weighting matrix.
The standard deviations of the estimated parameters are obtained by direct numerical
integration.
8 Like in the case of the product market, 1 – γw measures the degree of wage indexation to the inflation target.
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Table 2 Results of the estimation of the model
Parameter
αp
αw
γp
γw
b
ay
ap
ρi
Interpretation
Degree of nominal price stickiness
Degree of nominal wage stickiness
Price indexation
Wage indexation
Habit persistence
Elasticity of i relative to y
Elasticity of i relative to p
Degree of smoothing of i
Value
0.84***
0.67***
0.47***
1.00
0.86***
0.10***
1.44***
0.07
In this Table, the symbol *** denotes a significiance threshold of 1%
The parameters of the model are obtained by matching the autocovariances
of the series under consideration (Box 2).9 For the sake of clarity, only the
estimated values of the parameters essential for the study of the sacrifice
ratio and its sensitivity to labour and product market rigidities are presented
(Table 2).10 For the set of estimated parameters, the model is capable of
correctly replicating the empirical moments.11
As regards the nominal rigidities, it appears that on average
households’ wages do not change for roughly three quarters (which
corresponds to a value of αw equal to 0.67). In addition, wages are entirely
indexed to past inflation (γw = 1), which is characteristic of the euro area
(Avouyi-Dovi and Matheron, 2005).12 Furthermore, the degree of price
stickiness is relatively higher than that of wages (αp = 0.84), which means
that on average firms do not alter their prices during one year and three
quarters. Finally, the degree of indexation of prices to past inflation is 0.47,
in accordance with Smets and Wouters (2003).
As regards the monetary policy rule, it appears that the degree of smoothing
of the interest rate is very low and non significant, while the weights of
inflation and output in the rule (1.44 and 0.10 respectively) correspond
on the whole to the standard values.
9 All of the parameters of the model have not been estimated; some are calibrated either because their value may be deduced from the large
ratios or because they are not identifiable.
10 All of the results of the estimation are available in the working paper. All of the estimated values of the parameters are consistent with the
existing literature.
11 This result is described in the working paper. In addition, we are able to carry out a more in depth assessment of the quality of the estimated
model through a series of exercises on the theoretical impulse response functions and the forecast error variance decomposition.
12 The estimated value of this parameter, for euro area data, tended to be very high. In order to remain within a reasonable framework, we decided
to limit it to its upper bound.
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Estimating the sacrifice ratio for the euro area
Chart 1 Cumulative output loss following a 1 percentage point disinflation
(relative deviation in %, quarterly data)
0.0
-0.2
-0.4
-0.6
-0.8
-1.0
-1.2
-1.4
-1.6
0
10
20
30
40
50
60
70
Source: AWM database – Estimates by authors.
Chart 1 shows the cumulative output loss over a horizon of 70 quarters
following a 1 percentage point permanent decline in inflation (the estimation
method is explained in Box 3). The shaded area corresponds to the 95%
confidence interval. By construction, once the disinflationary shock has been
absorbed, the cumulative output loss stabilises at the level of the sacrifice
ratio, i.e. 1.28% (this value is significantly different from zero). This result
is close to that obtained using the ad hoc method and consistent with the
existing literature (Durand, Huchet-Bourdon and Licheron, 2005).
BOX 3
Estimating the sacrifice ratio
The sacrifice ratio is usually defined as the cumulative output loss arising from a
1 percentage point permanent decrease in inflation. In the framework of the estimated
model, the sacrifice ratio is calculated as follows. At t = 0, the inflation target
(i.e. long-term inflation) goes from π1 to π2 < π1 . Consequently, at t = 0, the relative
deviation of inflation compared to the new steady-state is π-1 ≈ π1 – π2 > 0. In addition,
wage inflation and the nominal interest rate, in a steady state, are linked to inflation.
Consequently, the initial values of the variables are all set at 0, except those for inflation,
wage inflation and the nominal interest rate, which are set at π-1.The sacrifice ratio Rt
is thus defined as Rt = (∑t=0…T yt) / |π1 – π2|.
Subsequently, the disinflation episode corresponds to a 1 percentage point decrease in
inflation, such that |π2 – π1| = 1. A negative value for Rt denotes an output loss.
Contrary to the ad hoc approach, the value of the sacrifice ratio depends on the
estimated parameters of the model. It is then possible to calculate the confidence
interval according to the estimated parameters.
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3|3 Wage stickiness and the sacrifice ratio
Unlike the ad hoc method, the structural model enables us to interpret with
precision the economic mechanisms that occur following a disinflationary
period. In particular, Chart 2 shows the pattern of output (yt), real wages
(wt), wage inflation (πwt), inflation (πt), the nominal interest rate (it) and the
cumulative long-term real interest rate (λt) following a permanent decline
in inflation in the framework of this model.
On this chart, the episode under consideration corresponds to a 1 percentage
point disinflation, so the relative deviations of inflation, wage inflation and
the nominal interest rate are equal to 1% before the start of the disinflation
episode.
The value of the sacrifice ratio is measured as the area between the x-axis
and the output curve. The size of this area depends on the amplitude and
the persistence of the change in output. The latter, in turn, depend on the
dynamics of the cumulative real interest rate, as shown by equation (1).
In the case studied here, the disinflation mechanism may be described as
follows: given the central bank’s reaction function, expressed by equation (6),
relatively aggressive in response to inflation (ap = 1.44), nominal interest
rates rise by a greater amount than inflation. Furthermore, monetary policy
is hardly sensitive to output changes (ay = 0.10). This results, at least in
the short run, in a rise in real interest rates. Provided that this is a lasting
rise, economic agents will also expect an increase in cumulative long-term
interest rates. Via the behavioural equations (1) and (2), this leads to a drop
Chart 2 Transitional dynamics following a 1 percentage point disinflation
(relative deviation in %, quarterly data)
2.5
2.0
1.5
1.0
0.5
0.0
-0.5
0
2
y
w
4
6
8
πw
π
10
12
14
16
18
20
i
λ
Source: AWM database – Estimates by authors.
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Estimating the sacrifice ratio for the euro area
in output on impact, which is itself linked to the scope and persistence of
the rise in cumulative long-term real interest rates.
The scope and persistence of this rise depend on the degrees of nominal
wage stickiness and indexation. Indeed, Chart 2 shows that wage inflation
is initially higher than inflation. This results from the strong indexation of
nominal wages to past inflation (γw = 1 in equation (4)). Consequently, real
wages rise and prevent inflation from adjusting to its new long-term target.
The stronger the inflationary pressures, the firmer the response required
by the central bank, resulting in a further rise in real interest rates.
In addition, inflation dynamics in the model are more inertial when the
elasticity of inflation relative to the real marginal cost is low (αp large).
This specificity contributes to increasing the real interest rate.
The structural model gives us a more detailed picture of the effect on the
sacrifice ratio of the different degrees of nominal wage stickiness and
indexation. We re-estimate the sacrifice ratio by varying the parameters αw
and γw in the neighbourhood of their estimated value, the other coefficients
remaining unchanged. It should be stressed that the monetary policy
remained unchanged throughout the exercise. Table 3 shows the results,
with for each pair (αw, γw) the corresponding sacrifice ratio.
Relative to its estimated value (αw = 0.67), setting αw at 0.72 means
that wages cannot be reoptimised during approximately one additional
half-quarter,13 which reflects a small increase in the degree of nominal
wage stickiness.
It appears that a decline in wage indexation to past inflation results in
a fall in the sacrifice ratio. Indeed, when γw decreases, wage inflation
adjusts more rapidly to its long-term target, which contributes to easing
the inflationary pressures generated by wage stickiness.
Table 3 The sacrifice ratio and degrees of nominal wage stickiness (αw)
and indexation to past inflation (γw)
αw
γw
0.90
0.95
1.00
0.62
0.67
0.72
-0.89%
-0.98%
-1.07%
-1.01%
-1.14%
-1.28%
-1.18%
-1.37%
-1.57%
13 The average length of time during which wages are unchanged in quarters, denoted D, is defined using the following equation: D = 1/(1– αw).
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In addition, a fall in labour market rigidity results in a decline in the
sacrifice ratio, all the more so as wages are indexed. Indeed, all other
things being equal, a 5% increase in γw brings about a 0.14 point rise in the
sacrifice ratio with αw set at its estimated value. In the neighbourhood of
the estimated values, a decline in wage stickiness αw, leads to a relatively
small drop in the sacrifice ratio. Conversely, an increase in αw has more
negative consequences for the sacrifice ratio (a 5% rise in αw leads to 0.29
percentage point fall in the sacrifice ratio, all other things being equal).
This result reflects the non-linear effect of nominal wage stickiness (αw)
and the average length of time during which wages remain unchanged on
the economy’s dynamics generated by a disinflationary shock. In particular,
the higher the parameter αw , the more inertial the economy.
This structural approach corroborates the assumption that labour market
rigidities have a clear impact on the output loss arising from a disinflationary
shock. However, it moderates this impact insofar as the size of the variations
in the sacrifice ratio according to the degree of wage stickiness seems
relatively small.
This article presents a structural estimation of the sacrifice ratio for the euro area
that is consistent with the other estimation methods available (ad hoc method and
structural VAR representation). The value of the sacrifice ratio for the euro area over
the period under review is estimated at between 1.2% and 1.4%.
A series of counterfactual exercices is carried out to gauge the impact of wage stickiness
on the sacrifice ratio. It shows that:
• a decline in nominal wage indexation and stickiness results in a fall in the sacrifice
ratio;
• however, in the neighbourhood of the estimated values, a decline in wage stickiness
has a limited impact on the sacrifice ratio; conversely, greater wage stickiness leads
to a rise in the sacrifice ratio. In addition, the impact of a change in wage stickiness
is asymmetrical, as an increase in stickiness has a particularly negative effect on the
sacrifice ratio. This asymmetry results from the non-linear influence of nominal wage
stickiness on the model’s persistence properties.
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