Durevall (1998)

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The Dynamics of Chronic Inflation in Brazil, 1968-1985Author(s): Dick DurevallSource: Journal of Business & Economic Statistics, Vol. 16, No. 4, (Oct., 1998), pp. 423-432Published by: American Statistical AssociationStable URL: http://www.jstor.org/stable/1392611Accessed: 11/04/2008 12:51

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The Dynamics of Chronic Inflation in Brazil, 1968-1985

Dick DUREVALL Department of Economics, School of Economics and Commercial Law, G6teborg University, Box 640, SE-40 530 Gothenburg, Sweden ([email protected])

This article develops an error-correction model with the aim of analyzing the behavior of prices during a period of chronic inflation in Brazil. The degree of inflationary inertia is estimated, and tests for the importance of disequilibria in the domestic-money, foreign-goods, labor, and domestic- goods markets on inflation are carried out.

KEY WORDS: Cointegration; Error-correction model; Inertial inflation.

The purpose of this article is to analyze the inflationary process in Brazil over 1968-1985. During this period, the yearly rate of inflation varied from somewhat below 20% in the years prior to the first oil shock to almost 250% at the end of 1985. High and persistent inflation of this kind is labeled chronic inflation (Beckerman 1992, p. 1).

I start by specifying long-run equilibria in the monetary and foreign sectors, from which inflation is usually assumed to originate in an open economy. Then I develop an error-correction model (ECM) to analyze the dynamics and long-run determinants of chronic inflation. In estimat- ing the model, I first test for cointegration in the money and foreign-exchange markets using the Johansen procedure. The cointegration vectors are included in an autoregressive distributed-lag model, which is tested to make *sure that the assumptions regarding its stochastic proper- ties are fulfilled. Next, this overparameterized model is reduced to obtain a parsimonious representation. I then test for (and find insignificant) omitted variables such as wages, the output gap, alternative measures of money, and so forth. Finally, the stability of the model is investigated using recursive estimation. Domestic inflation appears to be determined by foreign prices and the exchange rate in the long run, with dynamic effects from money, output, the interest rate, and oil prices.

The period covered by the study is based on my interest in chronic inflation and is more or less the same sample that has been used in several other studies (see Barbosa and Mc- Nelis 1990; Parkin 1991; Novaes 1993). The analysis begins in 1968 because indexation, which is one of the main characteristics of chronic inflation, became widespread in Brazil in the mid-1960s. Indexation included wages, rents, govern- ment bonds, taxes, deposit rates, and so forth. Moreover, beginning in 1968, a policy of gradual foreign-exchange adjustment was adopted, which implied that the exchange rate became indexed as well.

The study ends in 1985 because the second half of the 1980s and the beginning of the 1990s are better described as a period of mega-inflation or hyperinflation rather than chronic inflation. There was a sharp decrease in price stability, and yearly inflation rates reached four-digit levels (see Cardoso 1991). The change began with the Cruzado Plan, launched in February 1986. The plan consisted of price,

wage, and exchange-rate freezes and a virtual elimination of indexation. After the plan collapsed in late 1986, inflation- and-stabilization cycles occurred time and again, with price freezes, relaxation of price controls, and expectations of new price freezes (Kiguel and Liviatan 1991). From 1992 to June 1994, inflation rose from about 20% per month to 40% per month, and then it was stopped abruptly by the Real Plan, launched in July 1994.

Section 1 provides theoretical and historical background. In Section 2 I briefly review the data and use the Johansen procedure to test for (and find) the cointegrating vectors. The ECM of inflation is estimated and analyzed in Section 3, and Section 4 concludes.

1. ECONOMIC THEORY AND HISTORICAL BACKGROUND

I shall, in this section, first outline the theoretical models used in accounting for the long-run relations in my data. Then I present the ECM and discuss how it is related to other models that have been used to analyze chronic inflation in Brazil.

Two dominant theories for price formation in an open economy act through purchasing power parity (PPP) and money demand. The long-run relationships are

p = ble + b2p* (1)

and

m - p = b3y + b4R + b5Ap, (2)

where p and p* are the logs of the domestic and foreign price levels, respectively, e is the log of the exchange rate, m is the log of the money stock, y is the log of real output, R is the interest rate, and A is the first-difference operator.

Ideally, I would analyze (p, e, p*, m, y, R) as a single system and proceed from there. Because of the shortness of the sample, however, I adopt an alternative strategy, which is in the spirit of Juselius (1992). I first estimate the preced- ing equations separately via cointegration analysis. Then,

? 1998 American Statistical Association Journal of Business & Economic Statistics

October 1998, Vol. 16, No. 4

423

424 Journal of Business & Economic Statistics, October 1998

12

8-

6-

4-

1979 1975 1989 1985 1998

a - . .--.:--.--.. . ..---.- -. ... .. . ................

1979 1975 1988 1985 1998

Figure 1. Upper Panel: the Log of the Price Level p ( ) and the Log of the Exchange Rate e (.. ); Lower Panel: the Growth Rates for the Price Index Ap (-) and the Exchange Rate Ae (. .).

to examine the relative importance of these relationships in determining Brazilian prices, I develop a single-equation ECM for inflation that incorporates feedback from both relationships. The ECM is thus of the form

k-1 k-1

Apt = c + E riiApt-i + Z wr2i4et-i i=1 i=O

k-1 k-1 k-1

+ S 3iAp*i + 5 4iAmt-i + 5riAlyt-i i=O i=O i=O

k-1

+ E 7r6iARt-i + al[p - bie - b2p*]t-1 i=O

+ a2[m - p - b3Y- b4R - b5Ap]t-1 + vt. (3)

Equation (3) can be viewed as a general model of inflation that embeds several other models relevant for the period of chronic inflation in Brazil. One important model comes from the inflation-inertia hypothesis, which was developed after the failure of stabilization programs in the early 1980s. According to this hypothesis, backward indexation of wages and accommodating monetary policy made inflation insensitive to demand policies and mainly determined by its own history (Arida and Lara-Resende 1985; Lopes 1986). The inertia was considered so large that negative shocks to inflation, such as the oil-price hikes in the 1970s, were believed to shift inflation to a new level, where it would stay until a new shock occurred. Empirical studies of the Phillips curve and the finding of a random-walk component in the inflation rate supported the hypothesis of inertial inflation (Lara-Resende and Lopes 1981; Lopes 1982; Cardoso 1983a). The inertia approach would thus predict that the coefficients on lagged inflation in (3) sum to unity, that the variables related to demand are insignificant

15 -

14.8

14.6

14.4

14. 2

14

13.8

13.6 1978 1975 1988 1985 1998

Figure 2. The Log of the Price Level Minus the Log of the Exchange Rate p - e ( ) and the Log of the Foreign Price Level p* ( - (.).

or very small, and that the other variables only affect the rate of change of inflation.

The failure in 1986 of the Cruzado Plan, which was based on the idea that inflation was basically inertial, however, indicated that demand does play a role in the determina- tion of inflation in Brazil (Cardoso 1991). Relatedly, several models in the monetarist tradition of Harberger (1963) have been applied to Brazil with some success (Cline 1981; Hanson 1985; Barbosa and McNelis 1990). In these models, excess money supply is the measure of excess demand. In the pure monetarist models, only variables entering the money-demand relation should be significant, but other ver-

.33

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.24

.21

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.15

.63

1978 1975 1988 1985 1998

Figure 3. The Inflation Rate Ap (--- ) and the Real Exchange Rate e - p + p* (.. ).

Durevall: The Dynamics of Chronic Inflation in Brazil, 1968-1985 425

Table 1. Cointegration Analysis of the Foreign Sector

Eigenvalue .398 .089 .045 Null hypothesis rank = 0 rank < 1 rank < 2 Atrace 44.6** 9.6 2.8 95% critical value 29.7 15.4 3.8

Standardized cointegration vector and adjustment coefficients

Variable Ap e- p p* Cointegration vector 0 1.00 -.23 -.29 Adjustment coeff. a -1.12 .57 -.11

Tests of the significance of a given variable and of weak exogeneitya

Variable Ap e- p p* Exclusion X2(1) 28.5** 26.7** 28.2** Weak exogeneity X2(1) 27.1** 7.05* 1.78

Test of cointegration between real exchange rate and inflation: X2(1) = 22.61 [.00]

Misspecification testsb

Equation Ap e - p p* Joint test AR: F(5, 45) 1.70 [.15] 1.54 [.20] .65 [.66] F(45, 98) = 1.11 [.33] Normality X2(2) 1.40 [.50] 1.11 [.57] 4.55 [.10] X2(6) = 8.32 [.22] Hetero F(18, 31) .83 [.65] 1.04 [.44] .55 [.91] F(108, 156) = .90 [.72]

F tests for simplification from 5 to 3 lags

F tests 5 to 4: F(9, 102) = 1.19, 4 to 3: F(9, 109) = 1.14, 5 to 3: F(18, 109) = 1.17

p value [.31] [.34] [.30]

NOTE: The vector autoregression includes three lags in each equation, an unrestricted constant term and centered seasonal dummies, two impulse dummies, which take the value of 1 for the devaluations in 1979:4 and 1983:1, and four impulse dummies in the equation for p* that remove outliers in 1973:1, 1974:1, 1974:3, and 1975:1. The estimation period is 1968:4-1985:4. Atrace is Johansen's trace

eigenvalue statistic for testing cointegration. The null hypothesis is in terms of the cointegration rank, such that rejection of rank = 0 is evidence of at least one cointegrating vector. Critical values are taken from Osterwald-Lenum (1992, table 1). The asterisks indicate

significance at the 95% (*) and 99% (**) level, respectively, where the statistics have been adjusted for degrees of freedom lost in estimation.

a Exclusion and exogeneity tests are carried out under the assumption of rank = 1. b The misspecification tests are against the alternative hypotheses-residual autocorrelation (AR), skewness and kurtosis (normality),

and heteroscedasticity (hetero). Hendry (1995) provided a description of the tests. The p values are given in brackets.

sions would predict that imported inflation influences domestic inflation. In any case, a reasonable requirement for the monetarist model to be valid empirically is that the error-correction term for money demand enter significantly in (3).

A related issue regards the fundamental, or long-run, causes of inflation in an open economy. Blejer and Leider- man (1981) incorporated a real-exchange-rate policy rule in a model based on the monetary approach to the balance of

payments and applied it to Brazilian data. They claimed that the authorities can control the rate of inflation in the long run by adjusting domestic credit; that is, money serves as a nominal anchor. In contrast, Adams and Gros (1986) argued in a theoretical study that the adoption of a real-exchange- rate rule leads to the loss of the nominal anchor and that current inflation then becomes equal to lagged inflation, just like in the model of inertial inflation.

These two hypotheses are related to (3) in the following way. If money is the long-run determinant of inflation, the error-correction term for the money market should be significant. If there is no nominal anchor, however, the parameters on lagged inflation should sum to unity, and neither of the error-correction terms should be significant. These hypotheses can be tested empirically.

2. THE DATA AND COINTEGRATION ANALYSIS

In this section I use graphs to show some characteristics of the data and give some intuition as to why cointegration holds. I then test for cointegration between variables using the Johansen (1988) procedure. All numerical results are from PcGive 8.1; see Doornik and Hendry (1994).

The data used are quarterly for 1967:1-1985:4, and the estimation period is 1968:4-1985:4 unless otherwise noted. The analysis begins in 1968:4 because of a major devaluation in 1968:3 before the adoption of real-exchange-rate targeting. The main variables are the general price index, P; money plus quasi money, M, as defined in the International Financial Statistics database; the interest rate on bills of exchange, R, expressed as In[l+ (% interest rate/100)]; real output, Y; the exchange rate, E, in cruzados per U.S. dollar; and world prices, P*, represented by the U.S. wholesale price index. Details appear in the Appendix.

As reported in several studies, nominal variables such as the price level can be described as 1(2) processes (see Novaes 1993; Rossi 1993). Because cointegration analysis with the Johansen method at the 1(2) level is still being developed and is rather complex, I prefer to transform the 1(2) variables to I(1) (see Johansen 1995). For the foreign sector, I thus get e - p, p*, and Ap as the relevant variables, and for the money market, m - p, y, R, and Ap. I have in


.3

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* 12 "" :i

.99-

1970 1975 1988 1985 1999

Figure 4. The Inflation Rate Ap ( ) and the Velocity of Money

Ae), with the log-levels adjusted to have equal means. The log-levels and the growth rates follow each other closely, and their shapes suggest I(2)-ness. Figure 2 (p. 424) depicts both the price minus the exchange rate (p - e) and the mean adjusted logarithm of world prices (p*). Apparently PPP holds well to 1979, when it breaks down. Figure 3 (p. 424) graphs inflation (Ap) and the scale-adjusted real exchange rate (e+p* -p). This figure indicates that dynamics, through the steady-state solution, recover PPP as a long-run solution for the whole sample.

Table 1 (p. 425) reports results from the application of the Johansen procedure to the foreign-exchange sector, involv- ing (Ap, e - p, p*). The vector autoregression (VAR) contains three lags, an unrestricted constant and centered seasonal dummies, impulse dummies for the maxi-devaluations in 1979:4 and 1983:1, and four impulse dummies to improve the specification of the regression on world prices (1973:1, 1974:1, 1974:3, and 1975:1). The last four dummies do not alter the overall results of the analysis, but they make all the misspecification tests insignificant, as shown in Table 1. The number of lags was determined with F tests, simplifying from a VAR(S) to a VAR(3).

The trace statistic for rank = 0 is significant, but not for rank s 1, so there appears to be one cointegrating vector. All the variables are statistically significant in the cointegrating vector, as shown by the significance of the exclusion tests, and only the world price level is weakly exogenous, according to the tests for weak exogeneity (see Johansen and Juselius 1990 on these tests). All the signs of the coefficients are as anticipated, and the values of coefficients for e - p and p* are very similar. A formal test, however,

rejects the imposition of equal coefficients. This is probably an issue of high power from the high variation in the data.

The variables used in money-demand analysis are de- picted in Figures 4 and 5. Figure 4 shows that inflation and the logs of velocity (p + y - m), scale adjusted, are likely to form a cointegrating vector. Figure 5 demonstrates that the interest rate and inflation follow each other over time. Table 2 presents the formal tests for these relationships.

A VAR for (m - p, y, Ap, R) was estimated with four lags, an unrestricted constant and centered seasonal dummies, and two impulse dummies (1984:4 and 1985:3) capturing policy-induced shocks to the interest rate. There appear to be two cointegrating vectors, as expected. The first one looks like a money-demand relation; that is, the coefficients of m - p and y are almost equal but with opposite signs, the coefficient of inflation is positive, and the adjustment parameter (a) for m - p is negative. In the second vector, as well as in the first, the coefficients of the interest rate and inflation have similar values but opposite signs. More- over, according to the exclusion tests, which are all significant, each variable enters one or two of the cointegrating relations. The misspecification tests for the individual equations are insignificant, except for the interest-rate equation, in which the normality test is significant. The test for residual autocorrelation is significant at the 5% level but not at the 1% level. Joint distribution tests also indicate some nonnormality, but the test statistic for autocorrelation is not significant at the 5% level.

To test whether the two cointegration vectors can be expressed as a money-demand relation and the real interest rate (a Fisher relation), I carried out a likelihood ratio test. As reported in Table 2, the restrictions are accepted. I also tested for weak exogeneity and, somewhat surprisingly, the only weakly exogenous variable was inflation. This test is

.3-

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.18 ::

.15

.12

?03- .63

1978 1975 1988 1985 1998

Figure 5. The Interest Rate R ( - ) and The Inflation Rate Ap (- .).


Table 2. Cointegration Analysis of the Monetary Sector

Eigenvalue .370 .360 .091 .088 Null hypothesis rank = 0 rank < 1 rank < 2 rank < 3 Atrace 75.6** 43.7** 12.9 6.3* 95% critical value 47.2 29.7 15.4 3.8

Standardized cointegrating vector and adjustment coefficients

Variable m- p y Ap R Cointegrating vectors 3 1.00 -1.15 7.84 -6.66

-1.19 1.00 4.58 -5.28 Adjustment coefficient a -.18 .06 -.01 -.01

-.80 -.05 -.01 -.01

Tests of the significance of a given variable and of weak exogeneity

Variable m- p y Ap R Exclusion X2(2) 15.39** 16.20** 25.35** 19.25** Weak exogeneity X2(2) 18.18** 9.64** .83 10.93**

Restricted cointegrating vectors and adjustment coefficients

Variable m - p y Ap R Cointegrating vectors 3 1.00 -1.00 .96

6.92 -6.92 Adjustment coefficient a -.09 .11 -.02

.01 -.00 Test for restricted cointegrating vectors: X2(2) = 4.44 [.11].

Misspecification tests

Equation m - p y Ap R Joint test AR: F(5, 42) 1.01 [.42] 2.08 [.09] .75 [.59] 3.80 [.01] F(80, 97) = 1.41 [.053] Normality X2(2) 2.45 [.29] .60 [74] .05 [.98] 29.40 [.00] X2(8) = 21.64 [.006] Hetero F(32, 14) .63 [.86] .29 [.99] .58 [.90] ,93 [.58] F(320, 75) = .39 [1.00] F tests for simplification from 5 to 4 lags: F(16, 122) = .620 [.862].

NOTE: The VAR was estimated with four lags, an unrestricted constant and centered seasonal dummies, and two impulse dummies (for 1984:4 and 1985:3), capturing shocks to the interest rate. See Table 1 for more notes.

not invariant to inclusion of I(0) variables, however. Like- wise, weak exogeneity in the full system (p, e, p*, m, y, R) may differ from weak exogeneity in the two subsystems examined.

3. A DYNAMIC MODEL OF INFLATION

In Section 3.1 I develop an ECM of inflation using the general-to-specific modeling approach, and in Section 3.2 I discuss the economic interpretation of the preferred model. In Section 3.3 diagnostic tests are used to check for omitted variables. Finally, Section 3.4 analyzes the model's empirical constancy.

3.1 Development of the Empirical Model

I begin by specifying a general unrestricted ECM and test for whether it is well specified, with white noise, normally distributed residuals, and so forth. The variables entering the model are the second differences of the price level, the exchange rate and the money stock, the first difference of output and the interest rate, and the variables entering the cointegrating vectors, lagged one period. Moreover, I in- clude the second difference of the log of the oil price in U.S. dollars, op*, to account for the oil-price shocks in the 1970s. All regressions reported have a constant and centered seasonal dummies.

The estimated parameters and the misspecification tests of the model are reported in Table 3. To start with, five lags were used, but F tests indicated that the model could be simplified to three lags. When the model was estimated with ordinary least squares (OLS), the parameter of A2mt was negative and significant. Because this could be due to simultaneity bias, the model was reestimated with instrumental variables for A2mt, where the added instruments were A2mt_4 and lags 1 to 4 of the second difference of the log of high-powered money, A2hpm. The result was a small increase in the t value, making the estimated coefficient of A2mt insignificant. That model was also estimated assuming that A2et was endogenous, but there was little change in the parameter estimates. As reported, the specification test for the validity of the instrumental variables is insignificant, and there is no evidence of misspecification of the model. Most of the individual coefficients are of little interest in themselves. Those of the lagged levels of the variables of the foreign sector are clearly significant, however, but those belonging to money demand are insignificant.

Next, the number of parameters in the general model was reduced to obtain a parsimonious model. The strategy followed was to delete insignificant parameters in steps starting with those that are obviously 0, and to test both for the specification of the model and for whether


Table 3. General Error-Correction Model for Inflation

Lag i

Variable 0 1 2 3

A2pti --1 -.112 -.174 -.137 (-) (.239) (.169) (.152)

A2et-i .252 .132 .079 .042 (.044) (.053) (.047) (.041)

AP* i .276 -.021 -.237 -.189 (.280) (.239) (.238) (.202)

A2mt_i -.154 -.179 -.084 .006 (.074) (.076) (.082) (.071)

Ayt-i -.142 .040 -.110 -.010 (.108) (.102) (.092) (.109)

ARt-i .165 .400 -.192 1.357 (.174) (.195) (.264) (.378)

A2oP?_i .008 .034 .020 .011 (.015) (.015) (.017) (.020)

Apt-i -.472 (.235)

e - pt-i .191 (.038)

pt-i .200 (.054)

m - pt-i .028 (.041)

yt-i .016 (.071)

Rt-i -.247 (.159)

Sit 1.819 -.020 -.008 -.013 (.504) (.021) (.017) (.015)

NOTE: The dependent variable is A2pt, Sot is the constant term, and Sit, S2t and S3t are centered seasonal dummies. Standard errors are given in parentheses. The tests reported, apart from those listed in Table 1, are tests for residual autocorrelation (dw), autoregressive conditional heteroscedasticity (ARCH), nonlinearity (RESET), and specification test for the validity of the instruments used for the IV estimation (IV specification test). Method OLS, T = 69 [1968:4- 1985:4]; R2 = .90; standard error = .0127; F test for simplifying from 5 to 3 lags: F(14, 18) = 1.13 [.40]; AR; F(5, 27) = .48 [.78], dw = 2.14; ARCH: F(4, 24) = .64 [.64]; normality: X2 (2) = 1.85 [.39]; RESET: F(1, 31) = 1.73 [.20], IV specification test: X2(4) = 1.41 [.84] (additional instruments used are A2mt-4, and lags 1 to 4 of A2hpm).

any of the excluded variables are different from 0. Er- icsson, Campos, and Tran (1990) gave a good description of this modeling strategy. In simplifying, three trans- formations were made: Current and lagged exchange-rate variables were aggregated with relative weights of 2 to 1 (a simple Almon polynomial); an error-correction term was formed with Aptl,,e - pt-1, and p* 1; and ARt-3 was subtracted from ARt-2. The following highly parsimonious and statistically acceptable ECM was finally obtained:

A2p, = .281 (2A2t + 2et-1) + .058A2mt-3 (.043) (.023)

- .080Ayt_2 - .567A2Rt2 + .032A20p_1l (.053) (.108) (.010)

- .594(Ap - .257(e - p) - .308p*)t-I + 1.499 (.088) (.222)

+ .003Slt + .002S2t - .002S3t (.008) (.006) (.009) (4)

where T = 69 [1968:4-1985:4], R2 = .81, standard error = .0131, AR: F(5, 54) = .95, dw = 1.90, normality:

X2(2) = .63, ARCH: F(4, 51) = .65, RESET: F(1, 58) =

1.12, hetero: F(15, 43) = .53, Chow test of parameter constancy 1982:1-1985:4: F(16,42) = 1.55, F test for simplification from three lags: F(27, 32) = 1.15, and F test for adding (m - p - y + .96Ap)t_- and (R - Ap)t_l: F(2, 57) = .015[.9853].

Apart from the seasonals and the constant, (4) contains only six explanatory variables relative to the 33 that entered the general ECM in Table 3, and the standard error is only .04% higher. Moreover, the regressors are relatively orthog- onal. The highest correlation coefficient is .58 in absolute value, and there are only two other correlations above .20. All the estimates are clearly significant at the 5% level, except the one for output growth, whose t value is somewhat below 2. Output growth was kept in the model because it affects the model's stability. Surprisingly, neither cointegration vector from the monetary sector appears significant: F(2, 57) = .015[.9853].

3.2 Economic Interpretation To facilitate the interpretation of my model, I can rewrite

it by adding and subtracting inflation lagged one period to get

Apt= .41Apt1 + .28 (2A2et + A2et-1

+ .06A2mt-3 - .08Ayt-2 - .57A2Rt_2

+ .03A22op*t1 - .15(p - e - 1.2p*)t-i, (5)

where for simplicity I leave out the deterministic variables and the error term. Equation (5) refutes the inertial hypothesis that the inflationary process is best described by a random-walk model. The coefficient on lagged inflation is only .41, and the price level enters with a negative coefficient. Moreover, lagged inflation is likely to capture the effects of expectations and other indexation schemes as well as wage indexation. Thus, in Section 3.3 I test directly for whether wages contributed to inflation.

Money only enters the model in second differences. A 1% increase in the rate of change of the money supply increases inflation by about .06%. Money influences inflation only in the short run, and consequently, there is no support for the view that excess supply of money is the basic driving force of inflation.

The rate of devaluation, oil-price shocks, output growth, and the second difference of the interest rate also influ- ence the short-run movements in inflation. All four variables have coefficients with the expected signs. Thus, the short-run effect of a one percentage point increase in the rate of devaluation is a rise in inflation of .28%. A one percentage point increase in the growth rate of oil-price inflation increases general inflation by .03%, and a 1% higher output growth lowers inflation by .08%. The impact of a unit change in the second difference of the interest rate is .57%. This value is only valid for the final year of the sample, however, as shown in Section 3.4.

The most interesting variable in the equation is the error- correction term, which is associated with the PPP relation. Although there are different ways of interpreting error-


Table 4. Diagnostic Tests for Omitted Variables

Sample Variables F test

68:4-85:4 (hpm - p)t-1 Yt-1 Rt-1 APt-1 Ahpmt-1 F(10, 49) = .858 A2hpmt A2hpmt_ A2hpmt-2 A2hpmt-3 A2 hpmt-4 [.578]

71:3-85:4 (m3 - p)t Yt-1 Rt-1 Apt-1 Am3t-1 F(10, 38) = 1.146 A2m3t A2m3t_-1 A2in3t2 A2m3t_3 A2m3t-4 [.356]

72:3-85.4 (w - p)t-1 prodt awt-1 Apt-1 A2wt F(12, 32) = .941 A2 Wt-1 A2 Wt-2 A2 Wt-3 A2Wt-4 SWO-2t [.520]

71:1-85:4 A2apt A2apt-i A2apt-2 A2aPt_3 A2 aPt-4 F(5, 45) = 1.988 [.092]

68:4-85:4 (y-trend)t (y-trend)t-1 (y-trend)t-2 F(3, 56) = .505 [.680]

68:4-85:4 (y-strend)t (y-strend)t-1 (y-strend)t-2 F(3, 56) = .523 [.668]

68:4-85:4 (y-hptrend)t (y-hptrend)t-1 (y-hptrend)t-2 F(3, 56) = .774 [.513]

NOTE: SWo_2t is a seasonal dummy intended to capture the change in seasonality in the wage series. It is 0 up to 1977:4. prod is a proxy for productivity, y-trend is output detrended with a linear trend; y-strend is output detrended with a segmented trend, where the breaks are in 1974:2, 1979:4, and 1983:3; and y-hptrend is output detrended with the Hodrick-Prescott filter.

correction terms, the most straightforward is as an approx- imation to the deviation around the long-run real exchange rate. Accordingly, when the real exchange rate is underval- ued, inflation goes up, and when it is overvalued, inflation goes down.

The feedback parameter is relatively small, -.15, which shows that the adjustment is slow toward static-state equilibrium-that is, when all prices are constant. By com- parison, the adjustment to a steady state-that is, where all prices grow at a constant rate-is relatively fast because the value of the feedback parameter is -.59, as shown in Equation (4). A similar result is obtained by de Brouwer and Ericsson (1998, in this issue) in a study of Australian inflation.

3.3 Diagnostic Tests

In this subsection I test for omitted variables, including other measures of money, wages, the output gap, and price

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. ......... ..... . ...................

-.3 /

-..4

1975 1989 1985 1999

Figure 6. The Log of the Real Wage Level w - p ( ) and the Trend of the Log of Output Calculated With the Hodrick-Prescott Filter prod (.-.).

shocks in agriculture. Omitted-variable tests are calculated on subsets of variables: Degrees of freedom prevent us from looking at all these variables jointly.

Because the definition of money might be important for the results, Table 4 reports F tests for adding the log of either high-powered money (hpm) or of M3 (m3) to Equa- tion (4). Instead of going through the Johansen procedure again, I entered the variables directly into (4). To allow for multicointegration-that is, cointegration between a linear combination of 1(2) variables that form an I(1) variable and the first difference of these variables-I also added the rate of change of hpm and m3. Moreover, to capture short-run effects, four lags of the second difference were included. The F tests are insignificant in both cases.

Wages and wage indexation have played a central role in the discussion of inflation in Brazil, so I tested whether wages enter (4). Data for the labor market poses a problem, however. Quarterly wage data do not exist for the whole estimation period, so the longest series available was used. It starts in 1971:1 and covers the manufacturing industry. Data on the level of productivity are not available, so as a proxy I used the trend of output obtained with the Hodrick- Prescott filter. It captures the trend in the real wage quite well, as shown in Figure 6. Thus, to test for an effect from the labor market, I included the real wage level, w - p, the proxy for productivity, prod, wage and price inflation, four lags of the second difference of the wage level, and subsample seasonal dummies to capture the change in seasonality in the wage series in 1978 (see Fig. 6). As reported in Ta- ble 4, the F test for these variables is not significant. This result is surprising, considering the large number of theoretical studies on wage-price dynamics in a setting of wage indexation. Several attempts were therefore made to find a significant effect from wages, going through the general-to- specific procedure again for the subsample. The result was the same, however, which supports Baer's claim that wage policy was not a strong inflation-propagating mechanism (Baer 1989, p. 148). It should be remembered, though, that there might be large measurement errors because the series for the wage level and productivity are really both proxies.

Earlier studies of the Phillips curve failed to find a clear effect of excess demand on inflation. This might be caused


4 " Constant - t_ A2Rt.2 = .3 ..., -. P 3........ .. .. ... -.

1978 1982 1986 1978 1982 1986 1978 1982 1986 1.2 et eop .04 One-step residuals =

.04 0 V- 4VV_

o z~1------ ---- - ----------_____

1978 1982 1986 1978 1982 1986 1978 1982 1986

16 WOne-step Chows =

.08, 0

0 ..--------.IZL Z~ 4 L 0 -..

1978 1982 1988 1978 1982 1986 1978 Break-point Chows = 1986

.2 .28

1978 1982 1986 1978 1982 1986 1978 1982 1986

Figure 7. Recursive Estimates of the Coefficients of the Parsimonious ECM Model With + 2 Estimated Standard Errors (. .), One-Step Residuals With Corresponding Standard Errors ( - .), and One-Step-Ahead Chow Statistics and Breakpoint Chow Statistics Scaled With Their 1% Critical Values. The straight lines at unity show the 1% critical level

by using deviations of output from a linear trend as the measure of the output gap. Tombini and Newbold (1992), for instance, argued that the Brazilian gross domestic product (GDP) contains structural breaks. To investigate whether an augmented Phillips curve can be obtained for Brazil, I used three different measures of the output gap as proxies for excess demand-the deviations of the log of output from a linear trend, y-trend; the deviations from a segmented trend, y-strend, as in Gordon (1988); and the deviations from a trend obtained with the Hodrick-Prescott filter, y-hptrend, used by Chadha, Masson, and Meredith (1992). Current values and two lags of each of the three proxies for excess demand were added to (4). None of the variables have significant coefficients (Table 4).

Finally I checked whether agricultural price-shocks af- fected inflation, as argued by Marques (1985). Four lags of the second difference of the log of the price of agricultural products (A2ap) were entered. As in the previous cases, the F test is insignificant.

3.4 Parameter Constancy In this subsection, I investigate the stability of the model

using recursive estimation. The volume of output is large, but it can be efficiently summarized in graphs. Details about recursive estimation and stability tests were given by Hendry (1995).

Figure 7 plots the recursive estimates of the coefficients in Equation (4) and ?2 estimated standard errors. Most of the parameters are reasonably stable. The exception is the coefficient of the interest rate, which oscillates around 0 until the end of the sample in spite of having a t value of -5 over the whole sample. This is broadly consistent, however, with the view that the interest rate first becomes important for the dynamics of inflation after the debt crisis

(Cardoso 1991). In practice, it works like a dummy for a few observations in our model, and it is a good example of the risk associated with relying exclusively on t values without first checking the stability of the parameters.

Further information on the stability of the model can be obtained from the three last plots in the right column in Figure 7. The first one shows the one-step residuals and the corresponding calculated standard errors for (4). All residuals are within the confidence intervals, thus showing no evidence of coefficient changes or outliers. The two final graphs present the sequentially estimated one-period- ahead Chow test statistics and breakpoint Chow test statistics, scaled by their 1% critical values. The 1% level was chosen rather than the 5% level to help control overall size, noting that these are sequential tests over roughly 40 observations. In no case are the tests significant at the 1% level. Hence, I conclude that the overall stability of the model is fairly good.

4. SUMMARY AND CONCLUSIONS

This study investigated the inflationary process in Brazil for the period 1968:4-1985:4. The model should not be viewed as a final product but as part of what Hendry (1995, p. 550) called a progressive research strategy, in which new models improve and encompass old ones. Nonetheless, the model does convey interesting information. Our key find- ings are as follows.

The degree of inflationary inertia, as indicated by the coefficient value of lagged inflation, is only .41. This is much less than that obtained from other studies and much less than what is assumed in many theoretical models. More- over, the price level enters the error-correction term with a positive coefficient, which implies that less than 40% of an increase in inflation is transmitted to the next period's infla-


tion. The actual size of inertia thus depends on the time it takes the exchange rate to adjust to an increase in inflation. According to Blejer and Leiderman (1981), it took as long as a year during the 1970s.

Inflation is driven by the error-correction term, consist- ing of the price level, the exchange rate, and world prices. This relation can be interpreted as showing deviations from the equilibrium real exchange rate. Thus, in the long run, domestic prices are determined by the exchange rate and world prices. Moreover, there is no evidence that excess money supply is the direct cause of inflation nor that money is a nominal anchor. The importance of the foreign sector for the rate of inflation is surprising, considering the size of the Brazilian economy and that the import share of GDP was below 10% during most of the years in the sample.

It was not possible to detect any effects on inflation from the three measures of excess demand in the goods market that I constructed. Moreover, I failed to find any direct effect on inflation from wages. The quality of the wage and productivity variables used, however, calls for caution regarding these results.

In terms of dynamics, an increase in money growth or oil-price inflation increases overall inflation. Moreover, as expected, inflation increases when the rate of devaluation of the exchange rate increases, and inflation decreases when output growth goes up. There seems to be no effect on inflation from changes in the interest rate until the mid-1980s, when it had a strong negative impact, albeit while not having any long-run effects.

ACKNOWLEDGMENTS

I thank the associate editor, Neil R. Ericsson, for very useful comments. I am also grateful to two anonymous ref- erees, Arne Bigsten, Steve Kayizzi-Mugerwa, and Boo Sjoo for helpful suggestions. I retain responsibility for any re- maining errors, however. Financial support was provided by the Swedish Council for Research in the Humanities and Social Sciences (HSFR).

APPENDIX: DATA DESCRIPTION

Price Index. The general price index (P) is the price index mostly used in studies on Brazilian inflation. The source is Fundaqao Getulio Vargas. It is defined as the weighted average of the wholesale price index, the consumer price index for Rio de Janeiro, and an index for construction costs, with the weights .6, .3, and .1, respectively.

Monetary Aggregates. The monetary aggregate used in the analysis is money plus quasi money (M). It was chosen because it had a clearly significant effect on inflation in Granger-causality tests by Durevall (1993). In the diagnostic tests, high-powered money (hpm) and a measure of broad money (M3) were used. The variables were taken from International Financial Statistics (IFS) database, lines 34 + 35, 14, and 59mc, respectively.

Exchange Rates and World Prices. The exchange rate (E) is cruzados per U.S. dollar, IFS line ae, and the foreign price (P*) is the U.S. wholesale price index, IFS line 63.

I also tried the parallel exchange rate and trade-weighted exchange rates and foreign prices, but the results were less satisfactory, though not substantially different.

Oil Price. The oil-price index (OP*) is for Kuwait crude, IFS line 44376aad.

Interest Rate. The interest rate (R) is on three-month bills of exchange, taken from Rossi (1988).

Real Output. The index for real output (Y) was com- puted by Cardoso (1983b) up to 1979 from quarterly data on cement production, industrial electricity consumption, motor-vehicle production, and the real revenue of the Na- tional Treasury. From 1980, the series is the official GDP published by Fundaqio Instituto Brasilero de Geografia e Estatistica (IBGE).

Wages. The wage series (W) is taken from Estatisticas Historicas do Brasil (1988), published by IBGE. It covers the manufacturing industry. Comparisons with other shorter wage series that have a wider coverage show little difference between the series.

Agricultural Prices. The price index for agricultural products (AP) was supplied by Fundaqao Getulio Vargas.

[Received December 1994. Revised December 1997.]

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Cover PageArticle Contentsp. 423p. 424p. 425p. 426p. 427p. 428p. 429p. 430p. 431p. 432

Issue Table of ContentsJournal of Business & Economic Statistics, Vol. 16, No. 4, Oct., 1998Volume Information [pp. 509 - 510]Front MatterSpecial Section on Exogeneity, Cointegration, and Economic Policy AnalysisAssociate Editor's Introduction [p. 369]Exogeneity, Cointegration, and Economic Policy Analysis [pp. 370 - 387]Asymptotic Inference on Cointegrating Rank in Partial Systems [pp. 388 - 399]A Structured VAR for Denmark under Changing Monetary Regimes [pp. 400 - 411]The Relationship between Inflation and the Budget Deficit in Turkey [pp. 412 - 422]The Dynamics of Chronic Inflation in Brazil, 1968-1985 [pp. 423 - 432]Modeling Inflation in Australia [pp. 433 - 449]

Cointegration and Long-Horizon Forecasting [pp. 450 - 458]Outlier Detection in Cointegration Analysis [pp. 459 - 468]Prior Density-Ratio Class Robustness in Econometrics [pp. 469 - 478]Why Do Investment Euler Equations Fail? [pp. 479 - 488]Measuring Intervention Effects on Multiple Time Series Subjected to Linear Restrictions: A Banking Example [pp. 489 - 497]The Risk Premium of Volatility Implicit in Currency Options [pp. 498 - 507]Back Matter [pp. 508 - 508]

Durevall (1998)

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