Searching for the Natural Rate of Unemployment in a Large Relative Price Shocks' Economy: the Brazilian Case

Searching for the Natural Rate of Unemployment in a Large
Relative Price Shocks’ Economy: the Brazilian Case*



T
†
ITO NÍCIAS TEIXEIRA DA SILVA FILHO




Abstract

This paper contributes to fill the huge existing gap in the literature on the
Brazilian natural rate of unemployment. It reveals not only that the
Brazilian Phillips curve (PC) has broken down since the stabilisation of
the economy but, more surprisingly, that in the recent past it has a
positive slope. In other words, there has been no unconditional trade-off
between inflation and unemployment. This fact highlights the paramount
importance of supply shocks in recent inflation dynamics in Brazil. The
paper shows that the exchange rate has been a major source of shocks to
inflation, even though it is not enough to explain the magnitude and
persistence of those shocks. The missing element comes from the large
effects produced by privatisation on the price mechanism in Brazil. The
evidence suggests that the Brazilian natural rate has been constant since
1996, and despite the high degree of uncertainty involved in estimations,
it seems to lie somewhere in the 7.4%–8.5% range. Finally, the paper
also provides important insights on the transmission mechanism of
monetary policy and sheds crucial light on why real interest rates have
been so high for extended periods of time in Brazil. It also shows that
one widely used core inflation measure in Brazil has important
shortcomings and, therefore, is misleading.













Keywords: Natural rate of unemployment, NAIRU, Unemployment Gap, Phillips Curve,
inflation, supply shocks, relative prices.
JEL Classification: C22, C51, E24, E31, E32, E52

* The author would like to thanks Fernando de Holanda Barbosa, Nelson Sobrinho and participants of
the “Investigación Conjunta Sobre Variables No Observables - Reunión de Coordinación” held at
Buenos Ayres.
† Central Bank of Brazil. E-mail: tito.nicias@bcb.gov.br

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“Economists are a long way from having a good
quantitative understating of the determinants of the
natural rate, either across time or across countries”

(Blanchard and Katz, 1997)


1 – Introduction


Among the variables that are part of the selected menu of economic indicators followed
closely by central banks those aimed at measuring the degree of slackness in the economy
stand out. Among them a key variable is the natural rate of unemployment or, more precisely,
the unemployment gap. The natural rate is crucial to monetary policy and plays a central role
in two key economic concepts: money neutrality and potential output. Moreover, despite
some controversy the Phillips Curve (PC) is considered by many economists a valuable tool
for predicting inflation. Blinder (1997), for example, has praised the reliability of the PC
framework by stating that it is ‘[…] the “clean little secret” of macroeconometrics’. However,
surprisingly, despite its theoretical and empirical relevance, there is virtually no work done on
the natural rate of unemployment in Brazil.

This empirical vacuum is similar to the one found at the beginning of the century regarding
potential output estimates, a situation called to attention by da Silva Filho (2001). At the time
he argued that the macroeconomic instability and the inflation disarray that Brazil had faced
for so many years had turned the economic debate away from long term issues and focused it
on daily matters. Indeed, when one is unable to assess with reasonable accuracy how much a
country’s currency will be worth in a few months time, Cagan’s model seems much more
relevant than Solow’s. Nevertheless, since then macroeconomic stability has built up, and
after much time the long run finally entered economists` agenda. Indeed, growth prospects
were a major subject in the 2006 presidential election. Hence, the lack of studies on the
natural rate of unemployment is even more puzzling given that in recent years there has been
a growing interest on potential output estimation. So how could one reconcile these two facts?

Although a fully satisfactory answer seems unavailable, some factors could help explaining
this empirical vacuum. For example, in recent years unemployment rates have been well
above their historical average, so that agents might have taken for granted the existence of a
comfortable slack on the labour market. Moreover, this assessment might have been
strengthened since 2002, when the main unemployment survey went through a major
methodological review, which caused measured unemployment to rise sharply. In such a
situation the natural rate becomes less relevant. Even so, potential output estimates usually
require estimates of the natural rate of unemployment, so where do they have been coming
from? Mostly due to its simplicity (it is just a matter of pressing a button!), that need has been
fulfilled by applying the widely known HP filter to the unemployment series. However, the
HP filter has frequently been much more of a curse than a solution to the profession, often
preventing economists to delve into the subject at hand.

This paper has accepted the challenge and estimates the natural rate of unemployment for
Brazil using the Phillips curve framework. Among the several methods available in literature
the Phillips curve framework seems to provide the right balance between a-theoretical setups,
like univariate filters, and more structural approaches. Moreover, it can be obtained as the
reduced form of several types of structural models.1 Another appealing feature is that it takes

1 Note, however, that there is no agreement on the “true” structural labour market model. Moreover,
several known key natural rate determinants, such as institutional factors and labour regulations, are
very hard to be properly measured and inserted in those models.

2

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explicitly into account the link between unemployment and inflation. Finally, the PC
framework is quite flexible and can be used jointly with the unobserved components (UC)
technology, opening the possibility of estimating a time-varying natural rate of
unemployment. Indeed, the PC framework has been widely used and is the preferred method
of the OECD (see Richardson et al., 2000).

This paper shares the unbending belief that an essential part of any successful empirical
modelling strategy is a deep understanding of the economic phenomenon under analysis.
Therefore, the “search for robustness” here does not come from applying several
methodologies and comparing their results – a common procedure – but rather from analysing
and understanding what seems to have driven unemployment in Brazil, and confronting those
findings with the empirical results. A “side-effect” or “by-product” of such a strategy was that
while investigating the Brazilian natural rate of unemployment crucial light was shed on
several related subjects. For example, it was found that one very popular core inflation
measure in Brazil has important shortcomings and, therefore, is misleading. The paper also
provides valuable evidence on why real interest rates have been so high for so many years in
Brazil, a feature that has puzzled many economists. In addition it offers interesting insights on
the transmission mechanism of monetary policy, especially regarding the asymmetric effects
on inflation of changes in the exchange rate.

Like many others (e.g. Gordon, 1997; Staiger et al., 1997; Stiglitz, 1997; Mankiw, 2001; Ball
and Mankiw, 2002) this paper considers the terms natural rate of unemployment and NAIRU
as synonyms and, therefore, both are used interchangeably throughout. The paper is organised
as follows. Section 2 examines the behaviour of inflation and unemployment in recent
decades in search for stylised facts, and tries to uncover the reasons behind the sharp increase
in unemployment since the 1990s. Section 3 carries out a preliminary analysis on the
inflation-unemployment link and reveals the unexpected absence of trade-off between
inflation and unemployment in the recent past in Brazil. Section 4 investigates the main
reasons behind that finding. Section 5 provides estimates of the natural rate of unemployment
in Brazil. The following section concludes the paper.


2 – A First Look at the Data


The first major challenge one faces when investigating the NAIRU in Brazil is how to cope
with the major methodological break that took place in 2002 within the Monthly
Unemployment Survey (PME), rendering the new and old surveys incompatible.2 The new
PME survey has changed in several ways. The working-age population now includes those
aged ten or older, instead of fifteen or older as before. Also, the geographic area covered by
the survey was broadened, with the inclusion of several municipalities, even though the six
metropolitan regions surveyed remained the same. Finally, several changes were implemented
in order to better capture employment features and unemployment conditions, such as
conceptual changes in work definition and in the way information is gathered and classified
(see IBGE, 2002). As a result unemployment rates faced a big jump in the new survey,
increasing more than 50% when compared to the old series. Indeed, attempts to make the new
survey comparable with the old one by correcting it both in terms of geographic and age
coverage were unsuccessful, producing only marginal changes. Hence some assumption,
hoped to be relatively harmless, had to be made in order to create a longer unemployment
series, enabling research about the NAIRU and other related subjects.

Since both surveys overlap during some period one “solution” is to calculate the difference in

2 The PME is a household survey carried out by the Brazilian Institute of Geography and Statistics
(IBGE), which investigates unemployment in the urban areas of six metropolitan regions.

3

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average unemployment level between them, and use the resulting level factor to extend the
new survey backwards. In doing so the underlying assumption is that both surveys differ
essentially in their levels, but not in their dynamics. Unfortunately, they were published
simultaneously for a very short period of time, which makes this “solution” much less reliable
than one would hope. Even so, such a procedure was carried out and one long unemployment
series going back to 1985 was obtained (named UN1).3 Another “solution” is to apply the
same procedure but now with the survey carried out jointly by the SEADE Foundation and
Dieese, which measures unemployment in the metropolitan area of São Paulo only. In this
case besides the crucial assumption that the level gap between both surveys remained
relatively constant through time, one also assumes that unemployment changes in São Paulo
reflect accurately “national” developments. Even though this last assumption was not needed
in the first procedure, note that both the new PME and the Dieese surveys have been
overlapping since the first was implemented making the level shift factor much more reliable.
More importantly, when one compares both series since 2003 not only they almost coincide in
levels but their difference seems to be quite stable.4 Hence another long unemployment series
was constructed going back to 1985 (named UN2), and both series are used in Section 5
together with the Dieese unemployment series itself (named UND) in order to check which
one produce the best models.5

Figure 1 plots the UN2 series together with the old PME survey series, and some stylised
facts emerge.6 First, both series show unemployment rising since 1990, although it seems to
be down trending since 2004. Second, there are two important breaks in average
unemployment during this period: one around 1990 and another about 1996. Hence one can
divides unemployment dynamics into three (approximate) periods. In the first (1985.4–
1990.1) average unemployment was 5.9%. In the second period (1990.2–1995.3) it increased
to 8.1%, and in the last one (1995.4–2006.4) average unemployment jumped to 10.7%.
Although not shown in the graph, according to the old PME, unemployment rates were much
higher in the beginning of the 1980s than in the first period (i.e. 1985.4–1990.1), with rates
similar to those observed in the 1998.1–2002.4 period. From that perspective, recent rates are
not unusually high on historical grounds.

Figure 2 plots CPI inflation according to the IPCA, the official inflation targeting index in
Brazil, since 1980, when inflation began to rise very rapidly. Due to the high figures involved,
monthly rates are shown to better visualisation. It shows how chaotic has historically been
inflation in Brazil, and highlights the several structural breaks caused by stabilisation plans.
Figure 2 also shows the huge success of the Real Plan in curbing inflation. In its turn, Figure 3
shows quarterly inflation rates since 1994.3, when the Real Plan was implemented.

Comparing Figures 1 and 2 it becomes evident that after the Real Plan unemployment rates
rose sharply while inflation rates plunged. So, before estimating the NAIRU one would like to
get some intuition on what is behind those dramatic changes in unemployment dynamics,
especially from the second to the third, more recent, period, when average unemployment
jumped almost three percentage points. More specifically, was there any apparent structural
reason behind those movements (i.e. an increase in the NAIRU), or are they largely due to
policy, shocks or cyclical factors? More broadly, do increases in average unemployment

3 The average level shift was calculated using data from January 2002 to December 2002.
4 Comparing the old PME and Dieese surveys, which overlapped for eighteen years, one finds a
growing level difference along time, what makes one conclude that had it been possible to compare the
new and old PME for a longer period the difference would not have been stable. Such evidence
suggests that the first “solution” is inappropriate.
5 The average level shift between the new PME and Dieese surveys was calculated using data from
January 2003 to December 2006.
6 Note that, by construction, the UN2 and the Dieese unemployment series are very similar before
2003.

4

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necessarily mean that the natural rate has also increased, as implicitly assumed by many
economists when, for example, the widely known HP filter is used to obtain the NAIRU, or
persistent and large deviations are feasible?7
Figure 1
Quarterly Unemployment Series
14%
12%
10.7%
10%
8.1%
8%
5.9%
6%
4%
2%
0%
1985
1986
1987
1988
1989
1990
1991
1992
1993
1994
1995
1996
1997
1998
1999
2000
2001
2002
2003
2004
2005
2006
Constructed Series (UN2)
Old PME


Figure 2
Monthly IPCA Inflation and Stabilisation Plans
90%
80%
Collor I
Plan
70%
(18/03/90)
Real
Plan
60%
Verão
(01/07/94)
Plan
Collor II
(16/01/89)
Plan
50%
(31/01/91)
Bresser
Plan
40%
(13/06/87)
Cruzado I
Plan
30%
(28/02/86)
20%
10%
0%
jan/80
jan/81
jan/82
jan/83
jan/84
jan/85
jan/86
jan/87
jan/88
jan/89
jan/90
jan/91
jan/92
jan/93
jan/94
jan/95
jan/96
jan/97
jan/98
jan/99
jan/00
jan/01
jan/02
jan/03
jan/04
jan/05
jan/06


The first jump in average unemployment took place in 1990, and is unambiguously linked to
the implementation of the Collor Plan I, which produced a huge recession. In a nutshell: ¾ of

7 Of course, in this case one is implicitly assuming that unemployment suffers from hysteresis.

5

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M4 was confiscated overnight disrupting the economy and causing GDP to fell 4.35% in
1990, the biggest documented recession in Brazil. Given the failure of the Collor Plan I, in the
following year another stabilisation plan, the Collor Plan II, was implemented and failed as
well. As a result, during the 1990–1992 period GDP fell 3.9% in Brazil, and the strong growth
in the following two years (4.9% in 1993 and 5.9% in 1994) meant basically a cyclical
recovery from the previous recession. Indeed, in the four-year period from 1990 to 1993 while
the Brazilian economy grew just 0.8% the labour force increased almost 7%, a fact that
largely explains the jump in unemployment.

Figure 3
Quarterly IPCA Inflation
11%
10%
9%
8%
7%
6%
5%
4%
3%
2%
1%
0%
-1%
3
3
3
3
3
3
3
3
3
3
3
3
3
94.
95.
96.
97.
98.
99.
00.
01.
02.
03.
04.
05.
06.
19
19
19
19
19
19
20
20
20
20
20
20
20

Figure 4
Quarterly Real Interest Rates (Deflated by the IPCA)
20%
15%
10%
5%
0%
(5%)
(10%)
(15%)
(20%)
(25%)
5
6
7
8
9
0
1
2
3
4
5
6
7
8
9
0
1
2
3
4
5
6
198
198
198
198
198
199
199
199
199
199
199
199
199
199
199
200
200
200
200
200
200
200


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Although it is easy to see why average unemployment soared and remained high in the first
half of the 1990s, it is less evident why there was another jump as of 1996. A major part of
the reason seems to lie in the characteristics of the Real Plan, which was an exchange-rate-
based stabilisation plan and, in contrast to money-based stabilisation plans, initially produces
an expansionary effect on the economy while inflation falls (i.e. do not induce the usual
Phillips curve trade-off) and postpones the recessionary costs.8 The latter effect arises due to
the stylised fact that exchange-rate-based stabilisation plans produce real exchange-rate
overvaluation leading to trade and current account deficits, requiring restrictive monetary
policy. Indeed, while inflation fell from 2,477% in 1993 to 22% in 1995, GDP growth
increased from 4.9% in 1993 to 5.9% in 1994, and remained high in 1995, at 4.2%. However,
along with reducing inflation the Real Plan also produced, in a very short period of time, a
large current account deficit that required high real interest rates, as shows Figure 4, to both
attract foreign capital and slow down the economy. Indeed, by early 1996 the exchange rate
overvaluation had already reached its peak.

The large current account deficit was one key ingredient behind two speculative attacks that
took place in October 1997 and September 1998 in Brazil, and forced the Central Bank to
sharply raise interest rates as high as 46% p.a. to defend the parity. As a result, average GDP
growth fell from 5.0% in 1994–1995 to just 1.4% in the 1996–1999 period, a pace clearly
well below the one required to prevent unemployment from rising. Hence during the 1990s
the Brazilian economy was characterized by erratic growth due to stop and go policies, and
needed high real interest rates to cope with recurrent imbalances. High unemployment was
just the reflection of that environment of both low growth and high uncertainty.

Nonetheless, given that the exchange rate floated in early 1999 one might ask why
unemployment did not fall consistently afterwards. This may come as a surprise, but a major
part of the answer hinges, once again, on the behaviour of real interest rates, which have
remained too high after the floating, although they do began to slowly fall subsequently.
Initially, high rates were necessary to prevent devaluation from turning into inflation and,
later on, to cope with the large and persistent supply shocks that hit the Brazilian economy
during the 1999–2004 period, as will become clear in Section 4. Hence, a major factor that
seems to explain the jump in unemployment since 1996, as well as its persistency, is
monetary policy, which had to react to macroeconomic imbalances and shocks. This felling
gets stronger as we note that since 2004, when fundamentals began to improve and the
Brazilian economy to grow faster, unemployment appears to be trending downwards, while
inflation is falling.

Whether and to what extent the increase in unemployment since 1990 and, more specifically,
since 1996, also reflected an increase in the natural rate of unemployment requires a more
detailed analysis, however some remarks are useful at this point. First, it seems unequivocal
that the increase in unemployment in the first half of the 1990s is much more linked to the
1990–1992 recession than to increases in the natural rate. Nonetheless, it should be called to
attention that the Brazilian economy was overheated during most of the 1985–1989 period –
as the negative real interest rates shown in Figure 4 suggests – experiencing unsustainably
low unemployment rates, so that an increase in average unemployment was to be expected
afterwards. This fact is likely to partially explain the rise in unemployment in the first half of
the 1990s. Second, one must recognize that regardless of whether the natural rate increased or
not the labour market did went through important structural changes in the first half of the
1990s, such as the steep rise in informality and changes in sectoral employment, with jobs
moving from the industrial to the service sector, a phenomenon that has also been witnessed
worldwide. Behind those changes lay not only the effects of the 1990–1992 recession but also

8 See Kiguel & Liviatan (1992) on the stylised facts associated with exchange rate-based and money-
based stabilisation plans.

7

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the process of trade liberalisation that began in 1990, which exposed inefficient domestic
firms to foreign competition.9 Whether those events changed the natural rate is unclear,
however, note that heightened globalisation has been cited elsewhere as one of the reasons
behind the decrease in the natural rate of unemployment.10 One might also argue that a higher
degree of informality could change the reservation wage, thus affecting the natural rate of
unemployment.11 In such a case, however, the reservation wage is likely to reduce, since not
only informal workers have lower wages than formal ones but they are likely to pay a
premium for joining the formal market again, hence decreasing rather than increasing the
natural rate of unemployment. Finally, although controversial, another factor that has been
cited elsewhere as to why the natural rate decreased during the 1990s in the U.S. is
productivity gains.12 Since there was a clear productivity increase in Brazil as of early 1990s
this factor would, once more, act to decrease the natural rate.13

Apparently, possible structural – labour market-related – reasons for changes in the natural
rate of unemployment during the 1990s could only have stemmed from changes in labour
regulations made by the 1988 constitution. The main amendments were:14 a) the maximum
number of weekly working hours was reduced from 48 to 44; b) the maximum daily journey
for continuous work shift decreased from 8 to 6 hours; c) the price of overtime hours was
raised from 1.2 to 1.5 times the normal wage rate; d) paid vacations were raised from the
normal monthly wage to 1.33 that rate; e) the fine for non-justified dismissal was raised from
10% to 40% of the FGTS.15 f) The creation of unions was made easier and they became more
autonomous.

The 1988 changes in labour regulations had basically two direct effects: a) an increase, ceteris
paribus, in the relative price of labour;16 b) (non-justified) lay offs became more costly to
firms. Hence it is tempting to claim a link between the 1988 constitutional changes and the
increase in average unemployment during the 1990s. However, some caution is clearly
needed at this stage, for several reasons. First, the increase in labour costs seems too small to
explain such a large jump in average unemployment during the 1990s. Second, for many
firms some of those changes were probably not binding. For example, Gonzaga et al. (2002)
claim that almost half of the workers already worked less than 48 hours per week in 1988.
Also, more expensive overtime matter the most when the economy is growing fast, but
growth was dismal during the 1990s. Third, the effects of some changes were relatively
simple to be offset. Since what really matters to firms is the overall hourly labour cost the
increase, for example, in paid vacations, could easily be offset by a tiny reduction in monthly
real wages. Fourth, the change that seems to be the most biding is the increase in the cost of
dismissal, which certainly affected all firms. However, it seems more likely to affect the
volatility of unemployment and, possibly, of the natural rate, than their levels. More
importantly, it is highly unlikely that changes occurred back in 1988 are actually behind
increases in unemployment that took place eight years or more later. Furthermore, as calls to
attention da Silva Filho (2006c), in contrast to the international experience, the relative price
of capital has been increasing in recent years in Brazil. Finally, and most importantly, the
above analysis is only partial. Besides changes in labour regulations the literature also points

9 See da Silva Filho (2006b) for a detailed analysis of the Brazilian labour market during the 1990s.
10 For example, see Weiner (1995), Stiglitz (1997) and Ball and Mankiw (2002) for the U.S. case. The
former has a critical view on this argument.
11 Note that PME’s unemployment rate encompasses both formal and informal workers.
12 Even if productivity does not affect the natural rate in the long run, it is very likely to affect it in the
short term.
13 See Ball and Mankiw (2002) for a discussion on the U.S. case.
14 For more details see Barros et al. (1999).
15 The FGTS is an individual fund on behalf of the employee (not related to social security) created in
1966 that obliges firms to deposit each month in the fund 8% of the employee monthly wage. The
FGTS can only be withdrawn by the employee upon unjustified dismissal or in a couple of other cases.
16 An increase in the relative price of labour will lead firms to substitute capital for labour.

8

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to changes in socio-demographic factors as the main determinants of the natural rate of
unemployment. However, demography has almost certainly acted to decrease the natural rate
in recent decades, as the Brazilian population is getting older. So together with more
openness, higher informality, and higher productivity gains demography points to the other
direction (i.e. a decrease on the natural rate). And since what we are looking for is the net
effect of all those changes, large increases in the natural rate seem very unlikely. As a matter
of fact, even the sign of all those changes looks difficult to establish.

Given the absence of any obvious structural factors behind the rise in unemployment, mainly
after 1996, one would wonder whether the sole fact that unemployment remained high for
such an extended period could have caused the natural rate to rise. In other words: were there
any hysteresis effects upon the natural rate of unemployment that accounts for the high
unemployment rates, and if so to what degree? Despite being a very popular hypothesis in
explaining high and persistent unemployment rates, the empirical evidence regarding
hysteresis effects is actually weak. Indeed, not only such reasoning seems to be largely a
rationalisation in face of the difficulties in explaining the persistency of high unemployment
rates, but its rationale faces serious difficulties when the opposite holds (i.e. unemployment is
decreasing). In fact, as call to attention Blanchard and Katz (1997), hysteresis is far from
enough in explaining the magnitude of changes in European unemployment. In their words:
“The empirical case for hysteresis is far from tight, however. […] But the evidence on the
relative and absolute importance of the specific channels for hysteresis is weaker”. This
assessment should not come as a surprise since at closer scrutiny the alleged channels through
which hysteresis operate are not very convincing.

For example, the loss of skills argument is very popular but hardly convincing enough. While
it is certainly true that a worker unemployed for a long time can become “obsolete”, this can
usually be sorted out in a short period of time with on-the-job training or career recycling
programs. If one could graduate in 4 years, or do an MBA in just one, how much time does
one need to do a career update or recycling? Explaining high unemployment rates that
sometimes last more than one decade based on such reasoning is hard to accept. Note that this
channel is very similar to another one that has gained popularity since the 1990’s: skill
mismatch. The argument runs as follows: in a world of fast technological change and jobs
displacement from the industrial to the service sector, many workers would lack the required
skills to find a job, either because they changed sectors or because newer skills are required.
Although apparently compelling, the evidence on this seems weak as well. For example,
during the high tech 1990s unemployment rates have plunged in both the US and the UK.

To conclude, unemployment rates have increased substantially since 1990 in Brazil.
Nonetheless, as argued above and discussed further in Section 4, the reasons behind that seem
clear and do not appear to be related to increases in the natural rate of unemployment, mainly
after 1995.


3 – The Inflation-Unemployment Trade-off: An Exploratory Analysis


The main implication of the natural rate theory is the prediction that conditional on the
slackness of the labour market – given by the unemployment gap – one should at least be able
to forecast the direction of change of inflation. In other words, the natural rate theory should
be good at making qualitative forecasts. So, Table 1 answers the following simple question:
assuming a constant NAIRU during 1996–2006, how often next year’s inflation increased
(decreased) given that in the previous year the unemployment gap was negative (positive), for
different NAIRU levels? Hence, it provides an assessment of the natural rate theory’s
qualitative forecast accuracy. It also shows for those years in which the forecast was wrong

9

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what type of error was committed: under-prediction (+) or over-prediction (–). The analysis is
carried out for the 1996–2006 period since the results from the previous period are highly
affected by the several interventions caused by stabilisation plans (see Figure 2).
Table 1
Qualitative Accuracy and Errors Type (1996–2006)
Nairu
5%
6%
7%
8%
9%
10%
HP

72.7%
72.7%
72.7%
72.7%
63.6%
36.4%
54.7%
Error (+)
100.0%
100.0%
100.0%
100.0%
100.0%
75.0%
20.0%
Error (–)
0.0%
0.0%
0.0%
0.0%
0.0%
25.0%
80.0%

Some interesting evidence emerges from this simple non-parametric exercise. First, based
solely on the bivariate inflation-unemployment link, there seems to be an upper bound of
around 8% for the Brazilian NAIRU during the 1996–2006 period, a much lower figure than
the average unemployment for that period (see Figure 1). Note, however, that the same
forecast accuracy of around 73% was obtained using several assumptions regarding the
NAIRU.17 More precisely, NAIRU figures equal or below 8% produce the same qualitative
results, since unemployment rates were above that level during the sample. Such a result
suggests a large degree of uncertainty regarding the precise value of the NAIRU, evidence
that has been widely found elsewhere.18 For example, Staiger et al. (1997) found that a 95%
confidence interval for the U.S. NAIRU in 1994 spanned almost four percentage points
(3.9%–7.6%) when inflation was measured by the CPI and nearly two and a half points
(4.5%–6.9%) when the core CPI was used.

However, it might actually have been the case that the NAIRU was not constant during the
above period, and allowing for that possibility could have produced more precise forecasts. In
order to get some idea on that the same exercise was made using the unemployment gap
obtained by applying the HP filter, which is widely used by economists with that precise aim.
However, as Table 1 shows, in that case the accuracy would have been much worse than
under the constant NAIRU assumption. Finally, note that in the constant NAIRU case all the
errors were under-predictions, meaning that although the unemployment gap was positive
inflation actually increased, suggesting the occurrence of important supply shocks in those
specific years. This result is in sharp contrast with that from the HP case, when only 20% of
the errors came from under predictions, suggesting that supply shocks played only a minor
role on forecasting errors, evidence that is highly at odds with the recent Brazilian experience.
This is a pretty worrisome performance for such a widely used method.

Indeed, the three forecasting mistakes in the constant NAIRU case occurred in the years 1999,
2001 and 2002. In early 1999 the fixed exchange rate regime collapsed and the Brazilian
currency depreciated sizable 60% in the first three quarters of that year, increasing inflation.
And, during 2001 and 2002, there was a big election-related scare in Brazil (see Figure 6). As
a result, the exchange rate began to depreciate in early 2001 when the market began to take
seriously the possibility that a leftist could win the presidency in the following year’s election.
After the confirmation of the Labour Party’s victory depreciation intensified even further, and
reached 100% between the first quarter of 2001 and the third quarter of 2002, adding
significant pressure on prices. Indeed, those shocks meant large forecasting errors by both the
Central Bank of Brazil and private agents.19


17 Fisher et al. (2002) claim a success rate between 60% and 70% for the U.S. Analysing this link on a
quarterly basis Stiglitz (1997) argues for an 80% success rate in the U.S.
18 This is hardly surprising since inflation is a much more complex phenomenon than the simple
bivariate relation implied by the Phillips Curve.
19 Da Silva Filho (2006a) provides evidence on the forecasting performance of both the Central Bank of
Brazil Inflation Report forecasts and market forecasts.
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