the chronic inflation process: a model and evidence from brazil and israel

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The chronic inflation process: a modeland evidence from Brazil and IsraelEmanuel Barnea a & Nissan Liviatan ba Research Department , Bank of Israel , Jerusalem, Israelb Department of Economics , Hebrew University, Jerusalem ,Research Department, Bank of Israel, Jerusalem, IsraelPublished online: 12 Aug 2008.

To cite this article: Emanuel Barnea & Nissan Liviatan (2008) The chronic inflation process: amodel and evidence from Brazil and Israel, Journal of Economic Policy Reform, 11:2, 151-162, DOI:10.1080/17487870802236192

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Journal of Economic Policy ReformVol. 11, No. 2, June 2008, 151–162

ISSN 1748-7870 print/ISSN 1748-7889 online© 2008 Taylor & FrancisDOI: 10.1080/17487870802236192http://www.informaworld.com

The chronic inflation process: a model and evidence fromBrazil and Israel

Emanuel Barneaa* and Nissan Liviatanb

aResearch Department, Bank of Israel, Jerusalem, Israel; bDepartment of Economics, Hebrew University, Jerusalem, and Research Department, Bank of Israel, Jerusalem, Israel

Taylor and FrancisGPRE_A_323786.sgm10.1080/17487870802236192Journal of Policy Reform1384-1289 (print)/1477-2736 (online)Original Article2008Taylor & Francis1120000002008Professor [email protected]

This paper challenges the dominant model which was used to explain the chronicinflation process, as in Latin America in the seventies and eighties. Unlike the usual longterm view we present a variant of the Barro and Gordon policy game model which isbased on short term considerations in the inflationary period. In the latter period themodel implies a random walk and after stabilization the model implies stationarity.The statistical tests, using data from Brazil and Israel, do not reject the implications ofthe model.

Keywords: chronic inflation process; persistence; unit root; nominal anchor

JEL Classification: E50, E52, E58

I. Introduction

The dominant model of long lasting (“chronic”) inflation processes, as in Latin America inthe 1970s and 1980s, was based on an infinitely lived representative agent who has fullinformation about the process and expects stabilization of the inflation path at some date inthe future. The expectation of eventual stabilization affects the path of inflation prior tostabilization. This is in the tradition of Sargent and Wallace (1981), Liviatan (1984) andDrazen and Helpman (1990) who consider a stabilization of the public debt along with infla-tion. This model leads under certain assumptions to a rising trend of inflation prior to stabi-lization.1 None of these models deals with the unemployment–inflation tradeoff. Chronicinflation was related to seigniorage and the fiscal motive. We shall refer to this class ofmodels as “long horizon models”.

However, we show that it is possible to formulate an alternative, and more realisticapproach to the rising inflation process that is based on policymakers with a short horizonwho do not care about the future and practically behave as if they do not internalize thefuture stabilization. These policymakers, who operate in an environment of political insta-bility, consider it very unlikely that the stabilization will occur in their term in office. Ourmodel is a variant of the Barro and Gordon (1983) policy game model, with the addition ofa term that expresses the aversion to a change in inflation (the motivation for this term willbe explained below). In our version inflation behaves like a random walk and leads to anever rising inflation and has therefore to be eventually terminated. After stabilization,following the change of the economic regime, inflation series has to be stationary andconsequently lends itself to an infinite horizon optimization. Naturally, the choice between

*Corresponding author. Email: [email protected] opinions expressed do not necessarily reflect those of the Bank of Israel or their staff.

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152 E. Barnea and N. Liviatan

these contrasting models can be decided only by turning to the facts. Formulating andexecuting the relevant tests is the main challenge of the present paper.

The paper is organized as follows. We first discuss the intuition of our approach and thecountries to which we apply it – Brazil and Israel. Next we formulate the model which isused in the analysis. We then present the empirical results for the inflationary period andafter stabilization, and conclude in the last section.

II. Preliminary considerations

The testable implications of the different approaches to the chronic inflation process

A basic characteristic of the short horizon policymakers is that they are willing to accept thecurrent state of the economy, but they are averse to changes that might “rock the boat”. Inthe context of the chronic inflation process we consider accordingly a short run policymakerwho relies on indexation mechanisms,2 which are common in inflationary economies, tohandle the level of inflation, but is concerned with rate of change of inflation, since this maydisrupt the indexation arrangements. The statistical implication is that inflation shall behavelike a random walk or a unit root (UR), since the concern of the short horizon policymakeris only with the rate of change in inflation. By contrast, after the change of regime that isrequired by stabilization, the policymaker is concerned with the level of inflation (as in theinflation-target regimes), and consequently the UR in inflation should be rejected. Themodel, after stabilization, should enable an extension to infinite horizon optimization, sincethis stage of the process is supposed to be permanent.

Brazil and Israel

We apply these tests to the experiences of Brazil and Israel, which represent chronic infla-tion processes, where inflation accelerated in the seventies and early eighties, in connectionwith the oil shocks, to triple digit levels, and was stabilized after many years. In addition thetwo countries shared some other features that are relevant to our problem. Since inflationlasted many years, both countries developed pervasive indexation mechanisms in both laborand capital markets as well as in the tax system in the course of the inflationary period.Thus, in contrast to hyperinflationary episodes,3 real wages and taxes were not erodedduring the inflationary process.

III. The model

A policy game model based on the change in inflation

We consider a policy game model in which the policymaker’s loss function is supposed toreflect her concern not only with the inflation plateau, but also with a change of this plateau.In the extreme case she is only concerned with preserving the existing inflation plateauwithout regard to its absolute level. Namely, her aversion to inflation takes the form of onlyan aversion to a change in the inflation plateau. In addition, the discretionary policymakermay benefit from a temporary unexpected inflation because it may enable her to erode thereal wage, to create a real devaluation or to make a fiscal gain (as in the Barro-Gordonmodels). This incentive is internalized by the public and is reflected in its expectations.After stabilization we show that the incentive to surprise vanishes if the level of inflationconverges to its target in the long run.

To realize the implications of the foregoing assumptions in a deterministic framework,consider the following one-period4 loss function

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Journal of Economic Policy Reform 153

where β0 > 0, β1, β2 ≥ 0, where πt, and denote actual, expected and target inflation(explicit or implicit) respectively in period t, and where (the expectations of the public)is determined before the realization of the inflation rate πt. is set according to a prede-termined path.5 The loss function reflects the policymaker’s aversion to the change in infla-tion in addition to its level.

Unemployment does not appear directly, but is assumed to be reduced by unanticipated(surprise) inflation (πt − ), as in the Barro-Gordon models. The unemployment orthe output gap can be brought in explicitly, for example, by using the Lucas supply functionyt − y* = β1 (πt − ), where (yt − y*, denotes the output gap (y* is the potential output).

In a discretionary model the policymaker takes πt−1 and as given and minimizes theloss function w.r.t. πt. In equilibrium the public equates the optimal πt of the policymakerwith . This yields the first order condition

It can be seen that the level of inflation has a steady state solution, where πt = πT (in (2)), ifβ1 = 0, i.e. if the policymaker abandons the option of surprising the public in terms of higherthan expected inflation. We assume this to be the case after stabilization. In the inflationaryperiod, however, we assume that β1 > 0, and hence there is no steady state for the level ofinflation.

In addition we assume that in the inflationary period β2 = 0. It means that the policymakeris concerned only with the change in inflation given its level. In this case condition (2) yields

Note that (3) implies that we have a constant rate of acceleration of inflation . Since

the rate of change in inflation is a positive constant then its level goes to infinity as long asβ2 = 0. This possibility is not specific to our system since it is present also in the Sargent-Wallace (1981) model prior to stabilization. Equation (3) remains valid, with minorchanges,6 for models with any finite number of periods. It cannot be extended though to aninfinite horizon because then inflation goes to infinity, which is unacceptable.

On the other hand, if 0 < β2 < ∞ and β1 = 0, as we assume after stabilization, where thepolicymaker is concerned only with the level of inflation and gives up the option of surpris-ing the public, then the optimal change in inflation is given by

The derivative of πt w.r.t. πt−1 is a positive fraction θ

Since this derivative is constant, the convergence to the steady state (πT) takes the form (πt

− πT)θi (i=1,2,…). In a fuller version of this paper (available from the authors upon request)

L t t t te

t tT= − +−

βπ π β π π

βπ π0

12

12 2

2 21( – ) ( – ) ( – ) ( )

π te π t

T

π te

π tT

π te

π te

π te

π te

β π π β β π π0 1 1 2 0 2( – ) ( – ) ( )t t t tT

− − + =

∆π π πββt t t ≡ − =−( ) ( )1

1

0

3

( )ββ

1

0

∆πβ

β βπ πt t

Tt= 2

0 +− −

21 4( ) ( )

∂∂

=+

≡π

πβ

β βθt

t –

( )1

0

0 2

5

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we show that the same formula remains valid for the infinite horizon optimization, so welimit ourselves to the simpler version of the one-period model.

Shocks

We assume that the incentive to surprise the private sector has a random component (vt)which is added to β1 in the loss function (1), so that the relevant term in the loss function is

now (β1 + vt)(πt − ). This incentive is more urgent in certain periods than in others. Forexample, in the event of a balance of payments crisis the incentive to erode the real wageand to create a real devaluation is stronger than in normal times. It is assumed that vt is astationary random variable with zero mean, and it appears only in the inflationary period;after stabilization it is identically zero. In the inflationary period vt is observed in period tby the policymaker before setting inflation, but not by the public at the time when it formsits expectations.7

In addition we allow for a random variation (εt) in the treatment of deviation of inflationfrom target. We consider the “policymaker” as a monetary committee which representsdifferent interest groups, so that the reaction to deviations from target is uncertain. Werepresent this uncertainty by the stationary random variable εt, so the last right hand side

term of the loss function is now (πt − − εt)2. We assume that εt (like vt) is observed in

period t only by the policymaker before setting πt, but not by the public when it forms itsexpectations. The loss function including shocks now looks as follows:

Define . We can further enrich the model by allowing for a change in the drift

over time, so we let C(t) be dependent on time. Next we define and

as before so that vt is relevant only for the inflationary period and εt is relevant

only after stabilization. Then in a discretionary optimum we can express the optimal changein inflation as

In the inflationary regime θ = 1 and hence (6) reduces to a UR system with a positivedrift. If C(t), the drift, is a positive constant, it means that the level of inflation series followsa positive linear stochastic trend. But if, say, the drift is increasing linearly over time (as aresult of improvements in the indexation mechanism), then we have a quadratic trend in theinflation series.

After stabilization 0 < θ < 1, and therefore the coefficient of πt−1 is a negative fraction,which implies stationarity [by the ADF (augmented Dickey-Fuller) criterion]. Explicitly,after stabilization we have, analogous to (4), the expression

π te

π tT

L t t t t te

t tT

t= − − + − + − −−β

π π β ν π πβ

π π ε01

21

2 2

2 21( ) ( )( ) ( ) ( ' )

C ≡+β

β β1

0 2

utt t≡

++

+ν

β ββ ε

β β0 2

2

0 2

θβ

β β=

+0

0 2

∆π θ π πt tT

t tC t u= + +−( ) ( – )( – ) ( )1 61

∆πββ

π π εt t tT

t= − −2

0

7( – ) ( )

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Condition (5) ensures the stationarity of the inflation path as represented by (7), assuming

is stationary. In the fuller version of the paper we show that the model can be extendedto an infinite horizon optimization and that condition (5) ensures the gradual convergenceof expected inflation to the steady-state (πT).8 As a linear approximation of (6) we have

In practice we use the ADF test equation (with k lags)

The possibility of switching between regimes

Evans and Wachtel (1993), Evans and Lewis (1995), and Ruge-Murcia (1995) model andestimate switching inflation regimes. To deal with this problem in our model, suppose that,contrary to our previous assumption, there is a certain probability of switching from theinflationary regime (where β2 = 0) to stabilization (where 0 < β2 < ∞) in period t. This willimply a rejection of the UR hypothesis in the inflationary period.

For suppose that the policymaker assumes that there is a positive probability λ that β2 =0 and (1 − λ) that β2 > 0 in period t. To simplify, suppose that this is the only kind of uncer-tainty and that the policymaker sets πt before the value of β2 is known. Then from (1) weget that the optimal value of inflation is

so that we do not have a unit root (by the ADF criterion), as the coefficient of πt−1 is betweenzero and one. It follows that if the data of the inflationary period do not reject the existenceof a UR, then it means that we cannot reject the hypothesis that in the inflationary regimethe public did not consider that a stabilization plan by the policymaker in the current periodis a real possibility. To put it differently, if there is a positive probability of stabilization,then our model implies a rejection of the unit root hypothesis. We note that all the long hori-zon models are based on the expectations of stabilization of the inflation process, and hencea rejection (in principle) of the unit root hypothesis. But as we shall demonstrate below thiswas not the case in the inflationary period, which implies in our model a rejection of thelong horizon models.9

An econometric consideration (ADF, KPSS)

A common criticism of the standard UR test (the ADF test), which has the UR as the nullhypothesis, implying that the series is a random walk, is that it has small power against thealternative hypothesis of the stationarity. In order to counter this criticism we want toincrease the power of the ADF test, which can be done only at the cost of increasing theprobability of its type one error.

In order to do this we supplement the ADF test with the KPSS test (of Kwiatkowski et al.1992) that has stationarity as the null hypothesis. As these tests do have different distribu-tions for stationarity (H1 in the ADF test and H0 in KPSS), there is a case for requiring thatthe ADF test should be consistent with KPSS. Specifically, if we do not reject a UR by the

π tT

∆π πt t tc c t b u= + + +−0 1 1 8( )

∆ ∆π π πt t j t j tj

k

c c t b b u= + + + +− −=

∑0 1 11

9( )

πβ

β λ ββ

β λ βπ

λ ββ λ β

πt t tT=

+ −+

+ −−

−+ −−

1

0 2

0

0 21

2

0 21 1

1

110

( ) ( )

( )

( )( ),

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ADF test (which means “accepting” the random walk), we require, for consistency, that theKPSS should reject the stationarity hypothesis at the required statistical significance level.

IV. Evidence from the inflationary period in Brazil and Israel

In the chronic inflation process we distinguish between two regimes: the inflationary oneand the post-stabilization one (where inflation was brought down on a permanent basis).The implications of the model are with respect to these regimes only. This rules out inBrazil certain years (1986–1994), between the Cruzado and the Real plans, where thereprevailed an intermediate regime based on repeated failed stabilization attempts (thoseyears are treated in the fuller version of the paper). Although the stabilization implementedin Israel in 1985 can be considered as the first phase on the road to price stability, it left theeconomy on a step of moderate inflation. The inflation target regime has been implementedin the beginning of 1992, and we confine our analysis accordingly to this period as thestabilization regime. So in all we have one inflationary and one stabilization regime foreach country.

The inflationary period

The inflationary period in Brazil is defined in this study from 1970:1 till 1985:4. It endswith the Cruzado plan which was implemented in 1986:1. Although inflation continued tobe very high till the mid-nineties, it was interrupted by a series of (failed) heterodox stabi-lization programs10 (see Kiguel and Liviatan 1991) and in this sense represented a differentkind of regime. So we include in the inflationary regime in Brazil only this phase. In Israelthe inflationary period is defined as extending from 1970:1 till 1985:2 when it was termi-nated by a major stabilization plan which was implemented in July 1985 (Bruno 1993), butannual inflation remained on the 15–20% step for more than five years.

The inflationary period in Israel was characterized by very large fiscal deficits and grow-ing debt. The operational deficit was more than 10% of GDP. But seigniorage was relativelylow (around 2% of GDP) and constant over time. The public debt more than doubled in thecourse of the process – from 80% to 170% of GDP (see Barkai and Liviatan 2007, ch. 1).

For Brazil we do not have reliable published records on the fiscal deficit for the seven-ties, but from the available data we learn that the deficits had been increasing – startingfrom around 1% of GDP in 1970 (Maddison and Associates 1992, p. 107) and ending in theearly eighties in 4–6%.11 Net public debt was increasing in the seventies and reached 24%of GDP in 1981, but then climbed to 50% with the beginning of the debt crisis in 1983(World Bank 1998, p. 17). Seigniorage was relatively low, as in Israel.

In the seventies all the oil-importing countries suffered two big shocks from the increasein oil prices. However, while in industrial countries the shock to inflation was temporary,the shock in the chronic inflation countries of the time was long term. After the second oilshock in 1979 Brazil and Israel implemented similar macroeconomic policies. The conser-vative policies of the two finance ministers –Mario Simonsen in Brazil and Yigael Hurwitzin Israel – were short lived, and were followed by a policy of a Tablita-type.12 The latterpolicy failed and gave rise to a higher inflation plateau in both countries.

Figure 1 shows the impact on the non-stationary inflation (in the past 12 months) processof various shocks including the oil crises in 1973 and 1979 in Brazil and in Israel in theseventies and the failure of the Tablita policies in the early eighties.Figure 1. Brazil and Israel inflation data: 1970.1–85.2 (rate of change of CPI in the last 4 quarters, %).It can be seen that the inflation path in both countries was surprisingly similar until 1983(also numerically!), and it indicates a long-lasting positive effect of the shocks. For example,

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following the first oil shock annual inflation jumped in both countries from around 15–20%to around 40% and stayed at this level for a number of years.

Since this figure suggests non-stationary behavior in the inflationary period, weperformed the UR tests for the inflationary period in both countries. We ran both tests (theADF and KPSS) for both countries, using quarterly data, for a few time intervals to verifythe robustness13 of the results for the entire inflationary period, as defined above (see resultsin Table 1). The data on quarterly inflation, on which these tables are based, were takenfrom IFS line 64 for each country.14

The test equation for the ADF was equation (9), with the null b=0 and that for KPSS wasπt = α0 + α1t with the null that w is stationary, where w is the least squares residual in πt =α0 + α1t + wt. All the tests were carried by Eviews5 software, allowing for a constant andlinear trend, and letting the number of lags be determined automatically by SIC (SchwarzInformation Criterion).

For Brazil, the ADF tests indicate that the UR cannot be rejected at the 5% level and thestationarity is rejected by the KPSS (see Table 1). In all these cases the results pass theconsistency criterion at the 5% level. The persistence parameter (which is defined as 1+b+b1

in (9)) is high but less than unity in all cases. In spite of the fact that the samples are over-lapping and hence not independent, these results lend strong support to the existence of aUR in the Brazilian inflation process.

In Israel the results are more variable but nevertheless are, in the fuller version of thepaper, in most cases supportive of a UR in the inflationary period. Generally, the ADF testscannot reject the UR at the 5% significance level, and the KPSS tests yield consistent results(of rejection of stationarity). The persistence parameter is more volatile by comparison withBrazil. It seems that the overall picture that emerges from Table 1 indicates that the two testsare supportive of a UR in both countries.

Our tests allow for a constant and a linear trend in the parameters of the estimating equa-tions, which are reported in the statistics in terms of the corresponding t-values. The results

0

100

200

300

400

500

70 70 71 72 73 73 74 75 76 76 77 78 79 79 80 81 82 82 83 84 85

Brazil Israel

Source: IMF, International Financial Statistics.

Figure 1. Brazil and Israel inflation data: 1970.1–85.2 (rate of change of CPI in the last 4 quarters, %).

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reported in Table 1 indicate, in the ADF tests, that the drift was increasing over time in bothcountries, which implies that the level of inflation might have followed a quadratic trend inthe inflationary period.

The major stabilizations

We turn now to the phase of the transition to price stability in both countries, whichmeans that they either implemented the inflation target regime, or were aiming at singledigit inflation. The basic stabilization plan in Brazil, known as the “Real (the name of thenew currency) Plan” was implemented in July 1994, which was until 1999 an exchange-rate-based stabilization (Cysne 2002). Quite contrary to popular wisdom the fiscal deficitrose with the implementation of the Real Plan and was cut only after 1999 with the float-ing of the currency. The inflation target regime was announced in 1999 in the wake ofmaxi devaluation which came along with fiscal tightening. This plan succeeded in reduc-ing inflation to single digits (Figure 2), which is consistent with the results of our modelin the case where β2 > 0.Figure 2. Brazil inflation: 1995.4–2006.1 (rate of change of CPI in the last 4 quarters, %).What was the reason for the success of the Real Plan in its early years, even without afiscal adjustment and an inflation target? We suggest that it was the world trend towardsprice stability that lent the plan the credibility that the fiscal adjustment will eventually

Table 1. ADF and KPSS tests results and sensitivity analysis of the existence of unit root anddeterministic trend in the Brazilian and Israeli quarterly inflation data: 1970.1–1985.4.

Sample From 70.1 To

ADFt-stat

critical value 5% P-value Persist-ence*

No. of lags (qtrs)

Const.t-value

Trendt-value

Adj. R2 D.W

ADF testBrazil85.4 −2.53 −3.48 0.31 0.77 0 −1.08 2.91 0.10 2.2085.2 −3.19 −3.49 0.10 0.73 0 −0.70 0.05 0.13 2.1484.4 −2.28 −3.49 0.44 0.79 0 −0.86 2.73 0.09 2.39

Israel85.2 −1.48 −3.48 0.83 0.56 5 −0.74 1.93 0.54 1.9684.4 −0.49 −3.49 0.98 0.60 4 −0.77 1.12 0.35 1.9284.2 −1.28 −3.49 0.88 0.42 1 −0.72 1.84 0.23 1.89

KPSS stat

critical value 5% Bandwidth

Const. t-value

Trend t-value

Adj. R2 D.W

KPSS testBrazil85.4 0.252 0.146 5 −1.72 17.07 0.82 0.4985.2 0.232 0.146 5 −1.28 16.44 0.82 0.4984.4 0.228 0.146 5 −0.94 15.76 0.81 0.45

Israel85.2 0.178 0.146 5 −2.24 11.51 0.68 1.0784.4 0.178 0.146 5 −2.15 10.86 0.66 0.6484.2 0.188 0.146 3 −1.62 11.29 0.69 0.96

* “Persistence” is the coefficient on lagged inflation in an inflation equation derived from the ADF UR test.

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materialize, as indeed was the case.15 A second reason may be related to the vast reformsthat Brazil implemented and might signal the introduction of a new regime (Baumann 2002).

Although the Real Plan was launched in July 1994, prior to the Mexican crisis ofDecember 1994, the stationarity of the inflation process took hold only towards the end of1995. The double tests of a UR starting in this period support the stationarity hypothesis inBrazil (see Table 2). The persistence parameter was reduced from 0.77 in the inflationaryperiod to 0.54 in post stabilization.

0

5

10

15

20

25

30

95 96 97 98 99 2000 2001 2002 2003 2004 2005


Figure 2. Brazil inflation: 1995.4–2006.1 (rate of change of CPI in the last 4 quarters, %).

Table 2. ADF and KPSS tests results and sensitivity analysis of the existence of unit root anddeterministic trend in the Brazilian quarterly inflation data: 1995.4–2006.2.

Sample: From95.4 To

ADFt-stat


No. of lags (qtrs)

Const.t-value

Trendt-value

Adj. R2 D.W

ADF test2006.2 −3.99 −3.52 0.02 0.54 0 1.87 0.17 0.26 1.792005.4 −3.98 −3.52 0.02 0.53 0 1.70 0.49 0.27 1.812005.2 −3.90 −3.53 0.02 0.53 0 1.54 0.74 0.27 1.81

Kpss stat


Const t-value

Trend t-value

Adj. R2 D.W

KPSS test2006.2 0.105 0.146 3 5.34 −0.36 −0.02 0.872005.4 0.111 0.146 2 4.96 −0.01 −0.03 0.892005.2 0.114 0.146 2 4.59 0.35 −0.02 0.88


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In Israel the drive towards price stability took place in early 1992 when an inflationtarget regime was put in place, and especially in late 1994 when the central bank embarkedon a tight monetary policy within the framework of that regime (Figure 3).Figure 3. Israel inflation: 1992.1–2006.1 (rate of change of CPI in the last 4 quarters, %).According to our model, in this phase inflation should be stationary since obviously thecountry was focusing on the level of inflation, and not only on its rate of change. This hypoth-esis is confirmed by the two-fold tests in Israel for the period starting in 1992:1, as Table 3shows. The persistence parameter was reduced drastically from 0.56 in the inflationaryperiod to 0.15 after stabilization.

-5

0

5

10

15

20

92 93 94 95 96 97 98 99 2000 2001 2002 2003 2004 2005 2006


Figure 3. Israel inflation: 1992.1–2006.1 (rate of change of CPI in the last 4 quarters, %).

Table 3. ADF and KPSS tests results and sensitivity analysis of the existence of unit root anddeterministic trend in the Israeli inflation data: 1992.1–2006.2.

Sample From 92.1 To

ADF t-stat


No. of lags (qtrs)

Const. t-value

Trend t-value

Adj. R2 D.W

ADF test2006.2 −6.27 −3.49 0.00 0.15 0 4.90 −3.84 0.40 1.982005.4 −6.23 −3.49 0.00 0.15 0 4.91 −3.87 0.40 1.992005.2 −6.36 −3.50 0.00 0.11 0 5.09 −4.10 0.42 1.98

Kpss stat


Const. t-value

Trend t-value

Adj. R2 D.W

KPSS test2006.2 0.100 0.146 1 9.71 −5.88 0.37 1.672005.4 0.079 0.146 2 9.70 −5.88 0.38 1.682005.2 0.069 0.146 3 9.90 −6.12 0.41 1.76


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These results confirm the implications of our short-horizon model that when the policy-makers care about the inflation level the existence of a UR is ruled out. Note that inflationin Brazil came down to single digits quicker than in Israel and this is reflected in constantsand trend coefficients in Tables 2 and 3. The reason is presumably that Brazil stabilized inthe nineties when it was clear that the world was becoming less inflationary, while Israelbegan stabilizing in the mid-eighties.

V. Concluding remarks

We have formulated a model that enables us to test the validity of the long horizonapproach to the inflation process against the alternative of the short term behavior in theinflationary period. The critical element of the test is the existence of a unit root in theinflation process and its absence after stabilization. We used data from Brazil and Israel toimplement the tests, and found that the results do not support the view that inflation can beexplained by the long horizon view. Quite the contrary – the results confirm the view thatthe inflation acceleration in these two countries can be better explained by short term opti-mization that does not take into account the eventual stabilization. For the post-stabilizationperiod we expect stationarity of the inflation series, and this hypothesis is indeed supportedby the data.

Notes1. A somewhat different model is the one by Bental and Eckstein (1990), which allows finite hori-

zons, but shares with the above models the assumption of perfect foresight and the expectation ofan eventual stabilization which affects the inflation process prior to stabilization.

2. An indexation mechanism is a set of arrangements that link nominal variables (e.g. wage, rent,interest, etc.) to the price level guaranteeing ex post real values.

3. Thus in 1990–1994, when inflation in Brazil reached hyperinflationary levels, real wages rose(Baumann 2002, p. 19). The taxes as percent of GDP did not show any trend in 1983–1993(World Bank 1994, p. 25). For Israel see Barkai and Liviatan (2007).

4. This model can be extended to an infinite number of periods if β1 = 0 and β2 > 0. In the oppositecase the model can be extended to any finite number of periods.

5. The inflation target is treated as exogenous in this study. In practice, it may be dictated by thegovernment to the central bank. It is assumed to be close to zero.

6. In the multiperiod case

7. As in Blanchard and Fischer 1989, p. 609.8. Intuitively, if expected future inflation converges gradually to the steady state (since there is a

cost of changing inflation) then the derivative of current w.r.t. to lagged inflation should be lessthan 1, as in (5).

9. It is possible that the tests fail to reject the UR because the probability of switching is negligible.This is in line with our view.

10. Crusado Plan, Bresser, Summer Plan, Color I, Color II.11. These estimates are based on Cardoso and Fishlow 1990, p. 323; and World Bank 1994, p. 70.12. See Cardoso and Fishlow (1990) for Brazil, and Barkai and Liviatan (2007) for Israel.13. There is considerable variability in the test statistics, so it would not be appropriate to rely on a

single sample. In the tables we present the results for the top three samples for each period andfor each country. In the fuller version of the paper we conducted similar computations for addi-tional samples, which did not affect the basic conclusions, despite some contradictory samples,as explained in that version.

14. The inflation data are not seasonally adjusted, because the adjustment itself depends on the infla-tion regime.

15. The primary deficit was raised to 5–6% of GDP in 2004–2005 and monetary policy was tightened(see United Nations, ECLAC 2005).

∆πββt > 1

0

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ReferencesBarkai, H. and Liviatan, N., 2007. The bank of Israel, volume 1, a monetary history. New York: Oxford

University Press.Barro, R.J. and Gordon, D.B., 1983. Rules, discretion and reputation in a model of monetary policy.

Journal of Monetary Economics, 12, 101–121.Baumann, R. ed., 2002. Brazil in the 1990s: an economy in transition. In: Brazil in the 1990s: An

economy in transition. Oxford: Palgrave, pp. 1–38.Bental, B. and Eckstein, Z., 1990. The dynamics of inflation with constant deficit under expected

regime change. The Economic Journal, 100, 1245–1260.Blanchard, O. and Fischer, S., 1989. Lectures in macroeconomics. London: MIT Press.Bruno, M., 1993. Crisis, stabilization and economic reform. Oxford: Clarendon Press.Cardoso, E.A. and Fishlow, A., 1990. The macroeconomics of the Brazilian external debt. In: J.D.

Sachs, ed. Developing country debt and economic performance. Chicago, IL: The University ofChicago Press, pp. 271–391.

Cysne, R.P., 2002. Macro and microeconomic of the reforms. In: Brazil in 1990s: an economy intransition. Palgrave.

Drazen, A. and Helpman, E., 1990. Inflationary consequences of anticipated economic policies.Review of Economic Studies, 57, 147–166.

Evans, M. and Wachtel, P., 1993. Inflation regimes and the sources of inflation uncertainty. Journalof Money Credit and Banking, 25, 475–511.

Evans, M.D.D. and Lewis, K.K., 1995. Do expected shifts in inflation affect estimates of the long-run Fisher relation? The Journal of Finance, 50, 225–253.

Kiguel, M.A. and Liviatan, N., 1991. The inflation-stabilization cycles in Argentina and Brazil. In:M. Bruno, S. Fischer, E. Helpman, N. Liviatan, and L. Meridor, eds. Lessons of economic stabi-lization and its aftermath. London: MIT Press, pp. 191–232.

Kwiatkowski, D., Phillips, P.C.B., Schmidt, P., and Shin, Y., 1992. Testing the null hypothesis ofstationarity against the alternative of a unit root. Journal of Econometrics, 54, 159–178.

Liviatan, N., 1984. Tight money and inflation. Journal of Monetary Economics, 13, 5–15.Maddison, A. and Associates, 1992. Brazil and Mexico. New York: Oxford University Press for the

World Bank.Ruge-Murcia, F.J., 1995. Credibility and changes in policy regime. Journal of Political Economy,

103, 176–208.Sargent, T. and Wallace, N., 1981. Some unpleasant monetarist arithmetic. Federal Reserve Bank of

Minneapolis Review, 5, 1–17.United Nations, ECLAC 2005. Preliminary overview of the economies of Latin America and the

Carribean. New York: United Nations.World Bank, 1994. Brazil, an agenda for stabilization. World Bank Report No. 13168-BR, October.World Bank, 1998. Brazil, from stability to growth through public employment reform. World Bank

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the chronic inflation process: a model and evidence from brazil and israel

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