The post-crisis Phillips Curve and its policy implications
Liviu Voinea, Deputy Governor, National Bank of Romania
Keynote address to the National Asset- Liability Management Europe, 2019 Summit, London,
March 14th
Summary

The post-crisis Phillips curve makes 3 fundamental changes to the wage Philips curve: it
uses observable variables only; it changes the paradigm from flow to stock; and it allows
the curve to be non-stationary.
 -
We introduce the concept of a meaning the cumulative gap
cumulative wage gap
People relate to their
between current wage and a peak reference wage value in the past.
peak gains in the past rather than to uncertain future gains. They judge their consumption
decisions based on the relation between their current wages and their past wages, adjusted
for inflation.

The shape of the post-crisis Phillips Curve expresses the theoretical assumption that the
inflation rate stays below its target until the cumulative real wage gap closes, and that it
increases above its target when the cumulative real wage gap becomes positive.

We test our hypothesis using data for 35 OECD countries for the period 1990-2017. We
are able to confirm our hypothesis, as the coefficients have the expected sign and are
statistically significant for the OECD panel as well as for most of the individual
countries.

Bottom-line, inflation depends on the cumulative wage gap: it does not increase close to
or above its target level until the cumulative real wage gap is closed.

For Phillips Curve to work, the loss of welfare from a negative cumulative real wage gap
has to be fully compensated first - as a stock measure, not as a flow.

The policy implication from this finding is that, for those countries which have not closed
their cumulative real wage gap (most of the developed economies), inflation will remain
subdued until they close their cumulative wage gap.
Distinguished guests,
I would like to thank the organizers, Central Banking, for inviting me to speak about a
very topical issue: subdued inflation.
Inflation has been subdued in the post-crisis years, and the Phillips Curve has failed to
explain it. It is probably the greatest mystery of the economic science in the last decade: where
has the Phillips Curve gone? There are multiple references to the fact that the Phillips Curve has
flattened over the last decade, if not earlier (to mention just a few: Forder (2014), Leduc and
Wilson (2017), Borio (2017), Carney (2017), Cunliffe (2017), Praet (2016, 2018), Spencer
(2017), Murphy (2018), Bullard (2018)).
The flattened Phillips Curve and the lesser link between inflation and unemployment,
inflation and output gaps, or inflation and wages, have multiple explanations. As presented in
international literature, some of these explanations are: de-anchoring inflationary expectations,
the labor market slack, a lower natural rate of unemployment, changes in expectations regarding
the real pay growth, the decoupling between growth and inflation, the role of global value chains
in keeping prices down, the role of migration in keeping wages down in the countries of
destination, and others. While there is some truth in each and every of them, no alternative has
been successfully suggested so far.
I think that the Phillips Curve needs a reality-check. If we want to explain inflation, we
need to make some adjustments to the Phillips curve. The following presentation is based on two
working papers that I recently published with Center for European Policy Studies (CEPS)i,
respectively and Global Labor Organization (GLO)ii.
Three major changes are needed to the Phillips curve.
First, we should work with observable variables only. The problem with econometric models
which use non-observable variables is built-in: they tend to under-perform in bad times. Potential
GDP is revised retroactively. The output gap depends on potential GDP. Plus, an economy can
grow above its potential without being at its full employment (in particular, but not exclusively,
in catching-up economies).
Any measure of unemployment is controversial, given the impact of insufficiently accounted
factors such as the underground economy, migration, inactivity, part-time employment. A
nonobservable measure of unemployment, like NAIRU, is even more debatable. If Central Banks
rest their decisions solely on such non-observable variables, they are at risk of getting them
wrong. True, any non-observable variable becomes visible at some point in the form of a
disequilibrium in other observable variables, among which the twin deficits (budget deficit and
current account deficit). Yet, when this happens, it is usually too late for monetary policy.
Therefore, we drop the non-observable variables such as output gap, inflationary expectations
-
and NAIRU at least when the task at stake is to explain inflation in a post-crisis environment.
Instead, we choose to use observable variables only. Since wage is a measurable, reliable,
accounted for, and comparable indicator, we focus on a wage Phillips Curve where consumer
prices inflation rate is explained by the difference between past wages and current wages.
Second, we should make a fundamental change of paradigm from flow to stock. To
understand the consumers behavior, which in turn influences inflation,
we introduce the
-
concept of a cumulative wage gap meaning the cumulative gap between current wage and
a peak reference wage value in the past. The permanent income hypothesis is
fundamentally flawed in times of crisis, because of uncertainty of future income. The only
certain reference value lies in the past, not in the future: and that is why current
consumption is influenced by past income.
Third, we should allow for the Phillips Curve to be non-stationary: it moves over time, and it
is absolutely normal to do so. Reference wage values, social preferences, jobs' characteristics,
skills' endowments and even Central Banks' targets, they all change over time -
hence, the
impact of cumulative wage gaps on inflation cannot be the same in different time periods. In fact,
even Phillips (1958) mentioned that he ignored years in which import prices rise rapidly enough
to initiate a wage-price spiral. He stated that his hypothesis that the rate of change of money
wage rates can be explained by the level of unemployment is supported except in or immediately
after such years. In doing that, he effectively acknowledged the non-stationarity of his curve. He
referred to those years as events that occur very rarely except as a result of a war. Our approach
embraces these events, except that in modern times it is not war that makes the difference, but
recessions; and recessions happen more often than wars. We try to explain what happens during
and after recessions - which is exactly what is omitted by the original Phillips curve.
Wages, as the most important source of income for most households around the globe, stand at
the basis of any consumption theory.
The main problem with the prevailing consumption
consumption function (1936), Modigliani's
(Keynes' life-cycle hypothesis (1966) and
theories
Friedman's permanent income hypothesis (1957))
is their long-term approach. This puts them
at odds with our rather short and medium-term perspective on inflation, especially in times
of crisis.
Our approach is closer to Duesenberry (1952), who introduced relative income instead of the
rate of change of income as the explanation of the differences in saving at the same level of
income. He referred to the influence of past living standard on current consumption. Saving
depends, he wrote, on the level of current income relative to higher incomes in previous years.
However, he stopped short of calling a wage gap or of considering the influence his consumption
and saving theory may have on inflation.
What matters most for consumption during and after a crisis is not the unit change of income,
-
the savings for retirement, or the future income. A recession is a game changer. A global
financial crisis is a global game-changer. In a recession, the transitory component of income
becomes negative not only for one person or for a small group, but for the national or global
economy. This makes it very difficult to predict future income. When nothing is steady anymore,
the only valid reference remains the past income.
In a crisis, the reference is not ahead of us, but rather it is in the past. Retirement savings and
linear employment prospects are uncertain. People relate to their peak gains in the not so distant
past rather than to uncertain future gains.
Consumption does not depend only on current income and future expectations, but also
on past income.
Stock is more relevant than flow, because people have a strong reference which is their
People do not spend as much as before when their wage drops, and they
previous income levels.
spend more if they have higher wages. While this is intuitive and apparently well explained,
everything is related to wage flows and to wage dynamics. We hold that we should account the
stock as well, meaning the cumulative gap between current levels and past reference levels of
income.
Cumulative wage gap is a better predictor of inflation than output gap because it is
while output gap is
observable and it refers to past consumption and price levels;
nonobservable and it makes conservative assumptions for the future.
Past wages are the minimum potential wages in the mind of wage earners. We assume that
people judge their consumption decisions based on the relation between their current wages and
their past wages, adjusted for inflation.
The cumulative real wage gap, instead of nominal wage, is the explanatory variable in our
new Phillips Curve. The dependent variable is the inflation gap, which refers to the gap between
inflation and the inflation target (or, in the absence of a target, an average value of inflation over
a longer time-span).
Inflation gap is a more relevant variable for policy makers than the inflation rate because it
puts inflation in relation to a desired level. A negative inflation gap means more demand-side
measures are needed. A positive inflation gap means that the risk of overshooting is already
present and policy tightening is required.
-
For inflation, the reference point is not in the past but it is rather a normative value,
commonly agreed to be desirable for a given society at a given point in time.
Please bear with me for a short presentation of the cumulative wage gap model (please
see the attached slides).
We start by defining the wage gap:
= -
Wgap
Tn WTn WT0
where is the real wage gap at time Tn, is the real wage at time Tn, and is the real
Wgap
Tn WTn WT0
wage at time T0, the peak value of real wage in the reference period.
The cumulative real wage gap at time Tn is defined as:
N N
∑ ∑
= = -
cWgap n=1 Wgap n=1
TN Tn (WTn WT0)
A theoretical graphical representation of the real wage and the cumulative real wage gap for a
six-period model can be observed in the attached figures.
At time T0 real wage is at peak. Of course, wage earners are not aware of this peak until the
next year, when real wage drops.
Area A is the cumulative real wage gap between T1 and T0, area B is the cumulative real wage
T2 T3
gap between and T1, area C is the cumulative real wage gap between and T2, area D is the
cumulative real wage gap between T4 and T3, area E is the cumulative real wage gap between T5
and T4 and area F is the cumulative real wage gap between T6 and T5.
At time T1, when real wage W1 drops relative to the peak value W0, the cumulative real wage
gap is the area A (equal to the real wage gap). At time T2, when real wage drops even further, the
T3,
cumulative real wage gap is the sum of areas A and B. At time the real wage starts to
increase, but as it remains below the peak value, the cumulative real wage gap further deepens
(A+B+C). At time T4, when the real wage increases above the peak reference value, the
cumulative real wage gap starts to shrink (A+B+C+D). The growth of real wage makes the
cumulative real wage gap to close at time T5 (A+B+C+D+E) and to enter into the positive
T6
territory at time (A+B+C+D+E+F).
The cumulative real wage gap for the above 6-period model is described in the chart.
Therefore, equation (2) can be written as follows:
N N
∑ ∑
= - =
cWgap An
n=1 n=1
TN (WTn WT0)
where is the real wage gap between and expressed as area.
An Tn Tn-1,
If a new recession comes at T7 (not shown in the figures), the new peak value for the real
wage is the one recorded at T6.
is defined as the deviation from the central banks' target:
The inflation gap
∗
= -
Πgap
Tn ΠTn ΠTn
∗
where is the inflation gap at time Tn, is the inflation rate at time Tn, and is the
Πgap
Tn ΠTn
ΠTn
central banks' target at time Tn, or, in the absence of that, an average of long-time inflation.
A theoretical graphical representation of the inflation gap for a six-period model can be
observed in the attached figure.
At time T0, at the peak value of real wage, we assume that inflation rate is above the central
bank's inflation target,
given the inflationary pressures caused by high wages. Therefore,
inflation gap at time T0 is positive. However, the relationship is valid even when this assumption
does not hold. As wages enter an adjustment phase, inflationary pressures fade away and
inflation rate declines. Inflation gap turns negative and reaches a minimum at time T3, the same
as the cumulative real wage gap. In the next stage, as wages resume growth, inflation rate starts
rising, but it remains subdued, below the central bank's inflation
target, until time T5, when the
cumulative real wage gap is closed. Afterwards, wages continue to increase and the wage gap
widens in the positive territory. Consequently, inflationary pressures strengthen, pushing up the
inflation rate above the central bank's inflation target at time
T6.
The equation of the post-crisis Phillips Curve is written as follows:
= +
[Πgap f([cWgap
Tn]N Tn]N) [εTn]N
By introducing the equations for inflation gap and cumulative real wage gap into relation
(18), the post-crisis Phillips Curve becomes:
∗ N
- = f([∑ - +
]N n=1
[ΠTn ΠTn (WTn WT0)]N) [εTn]N
where N is the period of time for which the Phillips Curve is evaluated and is the residual,
εTn
which accounts for other variables influencing the inflation gap.
At time T0, cumulative real wage gap is considered zero, while inflation gap is considered
positive. This is one of the reasons why the curve does not cross exactly at the intersection of the
two axes. The other reason relates to the dynamic (non-stationary) feature of the curve,
expressing its different expected coefficients during different time periods.
The shape of the post-crisis Phillips Curve expresses the theoretical assumption that the
inflation rate stays below its target until the cumulative real wage gap closes, and that it
increases above its target when the cumulative real wage gap becomes positive.
The graphical representation assumes different slopes before and after closing the cumulative
real wage gap. A sharper slope after closing the cumulative real wage gap means that the same
amount of a cumulative real wage gap leads to less inflation as the cumulative gap is negative,
and to more inflation as the cumulative gap turns positive. We will test separately these two
assumptions: the shape of the curve and the break in the slopes.
In terms of methodology, the analysis covers the OECD countries over the period 1990-
-
2017, except for the United States where the data covers the period 1989 2017. Data sources
for wages and inflation are the OECD and the FRED databases (for US), annual data. The reason
for this selection is the availability of long-time data series on wages at OECD (they are only
available since 1990), while for US the FRED database allows us to start from a known peak
year, which was 1989. We used the following date: the average annual wage in 2017 constant
-
prices at 2017 USD PPPs, exchange rate (national currency units/US dollar) and inflation (CPI)
annual growth rate, from the OECD database, and the real median household income in the
United States, 2017 CPI-U-RS adjusted dollars, from the FRED database. We transformed the
average annual wage into local currency for ensuring comparability with the inflation rate, which
reflects changes in local prices.
Data sources for the inflation target of central banks are from the respective central banks'
websites. If a central bank targets a corridor rather than a level of the inflation rate, then the
midpoint of the target band is considered.
The year T0 is the peak year. We define a wage adjustment episode the adjustment in real
wages that follows after the peak year. For each wage adjustment episode in a country, the data
-
sample starts at year T0 (the peak year) and it ends when a new peak is detected (at year T0 new
1). We apply this only if the cumulative real wage gap has been closed before reaching the new
peak. If the cumulative wage gap has not been closed, then we continue to consider the new peak
as part of the same adjustment episode. A wage adjustment episode within a larger wage
adjustment episode is not considered. This approach prevents data overlapping and it secures
research consistency and integrity.
In the analysed period, there were three historical episodes of wage adjustments. Data shows
that the cumulative real wage gap was closed in all countries which experienced the first wage
adjustment episode, with the exception of two countries (Japan and Korea). In the case of the
second wage adjustment episode, the cumulative real wage gap has not yet been closed, with the
exception of other two countries (Mexico and Latvia). These latter two countries entered a new
wage adjustment episode, the third one.
For simplicity reasons, the wage adjustment episodes are numbered with reference to the time
periods and not to the country-specific episodes. We considered as the first wage adjustment
episode any episode which started in the last decade of last century (1990-1999) and the second
wage adjustment episode any episode which started after the year 2000. For example, Canada did
not have a wage adjustment during the first historical period, but it experienced one during the
second period. We refer to the latter as the second episode of wage adjustment in Canada.
Peak years are country-specific; hence they are not the same in all countries. This means that
the first wage adjustment episode, including the peak years, may have lasted, for example, 7
years in Italy, 8 years in Germany and France, 9 years in US, 20 years in Korea or 28 years (and
counting) in Japan.
Of the 35 countries analysed, 21 countries experienced the first historical episode of wage
adjustments, 33 countries experienced the second historical episode of wage adjustments and
only 2 countries experienced the third historical episode of wage adjustments.
This is why the total number of observations is much higher for the second wage adjustment
episode, compared against the first wage adjustment episode. In the case of the third wage
adjustment episode, the total number of observations is much lower.
And now we move to the juicy part. We present the graphical representation of our results for
all OECD countries which experienced wage adjustments (21 countries for the first wage
adjustment episode and 33 countries for the second wage adjustment episode).
The results are statistically significant and with the expected sign for the first two adjustment
episodes. For the third adjustment episode, the sign of the relationship is as predicted, but the
number of observations is too limited to have statistical significance.
The theoretical model is confirmed: the cumulative wage gap explains a significant part
of the deviation of inflation from its target: more than one third of the inflation gap in the
first wage adjustment episode and more than one fifth of it in the second adjustment
episode (which has not been closed yet). We also present graphical representations for selected
countries which have statistically significant coefficients.
For the first wage adjustment episode the cumulative wage gap explains more than 60%
of the inflation gap in Iceland, about two thirds of the inflation gap in the US and Ireland,
more than half the inflation gap in Finland and Switzerland, close to half of the inflation
gap in Netherlands. It even explains almost one quarter of the inflation gap in Korea,
despite the fact that this country has not closed the first wage adjustment episode yet.
For the second wage adjustment episode, the cumulative wage gap, which in most cases
has not been closed yet, explains more than 60% of the inflation gap in Slovenia and Slovak
Republic, between 40% and 60% of the inflation gap in Greece, Italy, Portugal, and Spain,
and between 20% and 40% of the inflation gap in Australia, Canada, Denmark, France,
Hungary, Ireland, Netherlands, New Zeeland, Switzerland and United States.
We checked the robustness of our results separately, in the standard method, as well as the
log-normalized method.
The results confirm the strong relation between cumulative real wage gap and inflation gap in
the OECD countries. Cumulative real wage gap explains a large share of the inflation gap, in
particular in the countries which experienced severe economic recessions and subsequent
material wage adjustments.
When aggregated for all OECD countries, having a large number of observations (197
for the first wage adjustment and 525 for the second one), the estimated slopes of the
postcrisis Phillips Curve are statistically significant at the 5% level, in case of the first wage
adjustment episode, and at the 1% level, in case of the second wage adjustment episode.
The coefficients' sign is positive, in line with the theoretical assumptions.
The individual results also confirm the strong and positive relation between cumulative
real wage gap and inflation gap. In the case of the first wage adjustment episode, out of 21
countries, 8 of them have positive and statistically significant coefficients; other 7 countries have
positive but not statistically significant coefficients, while the remaining 6 countries have
negative but not statistically significant coefficients. In the case of the second wage adjustment
episode, out of 33 countries, 16 of them have positive and statistically significant coefficients;
other 9 countries have positive but not statistically significant coefficients, while the remaining 8
countries have negative coefficients, out of which only 2 are statistically significant. Regarding
the third wage adjustment episode, out of 2 countries, one has positive and statistically
significant slopes and one has positive but not statistically significant slopes.
The minority negative or not statistically significant coefficients could be attributed to the low
number of observations, as well as to various specific factors that temporarily interrupted the
positive and strong relation between cumulative real wage gap and inflation gap.
The estimated coefficients of cumulative real wage gap using the log-normalized data point
to robust results and are more meaningful for policy makers. Results show that an
increase/decrease of cumulative real wage gap by 10% led inflation gap to rise/deepen by
0.561% during the first wage adjustment episode, by 0.846% during the second wage adjustment
episode and by 0.454% during the third wage adjustment episode.
We deepen the robustness check analysis and test if the inflation gap accelerates after the
cumulative real wage gap closes. In that respect, we estimated the slope of the post-crisis Phillips
Curve before and after the cumulative real wage gap was closed. The results in the standard
method, as well as the log-normalized method are presented attached.
The log-normalized results show that a fall of the cumulative real wage gap by 10%
corresponds to a decline of the inflation gap by 0.9%. On the other hand, a 10% increase of the
cumulative real wage gap after closes leads to an increased inflation gap by 2.2%.
This confirms the theoretical prediction that there a break in the slope of the curve, as the
coefficients are higher after the cumulative wage gap closes than before this happens.
Bottom-line, inflation depends on the cumulative wage gap: it does not increase close to
or above its target level until the cumulative real wage gap is closed. For Phillips Curve to
work, the loss of welfare from a negative cumulative real wage gap has to be fully compensated
-
first as a stock measure, not as a flow. The policy implication from our finding is that countries
which closed their cumulative real wage gap should be much more prudent in further wage
-
increases because they will be seen in inflation much faster and larger than in the recent past.
For countries which have not closed their cumulative real wage gap the implication is that
inflation will remain subdued until they close their cumulative wage gap.
Its efficiency is influenced by the fiscal policy,
Monetary policy cannot work in isolation.
by the wage policy in both the public and the private sector. Monetary policy is not a new-born.
It matters that we did not only last summer, but quite some time ago.
My two daughters, now 10 and 6 years of age, are still fascinated by the Disney's
animation "Frozen". In that movie, Princess Elsa convincingly sings that "Past is in the past".
However, fairytales do not apply in real life.
The past still influences our current consumption
choices, and therefore inflation and monetary policy decisions.
Moreover, monetary policy is less effective if it is done from an ivory tower.
Theoretical models, as captivating intellectual efforts as they are, need a reality check from time
to time. The signs are here for us all to see. In another fascinating Disney movie, "Tangled",
princess Rapunzel follow the signs she spots in the sky to beat its fears and escape from its ivory
tower. I think we should do the same.
Outside central banks, the greatest danger is populism.
The fact that in so many developed countries the cumulated wage gap has not been closed not
only subdues inflation, but it also fuels dissatisfaction of voters giving rise to populism. Inside
central banks, the greatest danger is dogmatism. We need to fight both with common sense,
with more data-dependent policies, and with a deeper understanding of the factors
influencing consumer choices and society as a whole.
i
Voinea, Liviu, 2018, Explaining the post-crisis Philips curve: Cumulated wage matters for inflation, No. 2018/05,
June 2018, CEPS Working Document
ii
Voinea, Liviu, 2019, The Post-Crisis Phillips Curve: A New Empirical Relationship between Wage and Inflation, GLO
Discussion paper Series 303