INFLATION DYMAMICS IN BRAZIL AN EMPIRICAL APPROACH
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INFLATION DYMAMICS IN BRAZIL: AN EMPIRICALAPPROACHMauricio OrengProf. Marco A. BonomoThis Version: June, 25th 2003I.IntroductionCalvo’s model (1983) implied New Keynesian Phillips Curve (NKPC) addressed some of the unpleasant features of the New Classical version (NCPC), like the fact that only unanticipated variations in nominal spending could affect the real economic activity. Such result, if analyzed more thoroughly, would suggest that monetary policy could influence real GDP only through its immediate effects, affecting prices only in the medium / long run. This is, according to empirical evidence, highly counterfactual.By means of an optimal price setting model, using the hypothesis of staggered prices, Calvo addressed the issue, obtaining then a so called - by Roberts (1995) - New Keynesian Phillips Curve. Thereby, one could concluded that the impact of monetary policy on real economic activity may last until many periods ahead. In addition, this model had on its favor persuasive empirical evidence, as found by Sbordone (2000), when comparing actual inflation and its prediction by Calvo’s model.Nevertheless, according to some economists, we have some reasons one should not feel very comfortable with such model. There are supposedly two main problems with that specification of the Phillips Curve proposed by Calvo: (i) first: NKPC implies a negative relationship between inflation next period and today’s output gap, or, in particular, it predicts lower inflation following periods when real GDP is above its natural value. Second, such specification does not allow for any inflation inertia whatsoever, relying too much on agents’forward looking behavior, in spite of the fact that many central banks around the world use models incorporating persistence in price acceleration.With regard to the first issue, we observe that, in fact, most empirical work arrive at a positive correlation between output gap and inflation acceleration , which contrasts with the specification of the New Keynesian Curve. Nonetheless, Gali (1999) argues that this may be due to a methodological problem concerning the way one computes the smooth GDP, when calculating the output gap. The rationale is that the natural GDP is function of a vector of structural parameters, whose changes may account for disturbances in natural product measures. As a result, one could happen to find positive correlation between the current gap and inflation change next period, in empirical tests using plain measures of output gap. One solution proposed to address this sticky issue, is to look at the real labor unit cost (marginal cost equivalent), which, in Calvo´s model, is an increasing function of the output gap. This could bring us the possibility of using the real labor unit cost as a proxy for the income gap, amethodology that would allow us to test with more precision empirical evidence for Calvo’s Phillips Curve.On the second issue concerning the problems in NKPC specification, Christiano et al.(2001)’s VAR studies bring up some piece of evidence against the purely forward looking behavior hypothesis, suggested by Calvo’s NKPC. Examining the effects of monetary disturbances on inflation and output, Christiano found that inflation is affected by changes in monetary policy only after most of the output response (to the very same shock) has already occurred. However, as Calvo’s would preach by his model, inflation is determined solely by future expected output gaps, and thus, following a monetary shock, it should move before output. In addition those results, and unexpectedly in accordance with theory, Chistiano also found some high degree of persistence in inflation through this tests, which strengthened the will to try empirically variations on standard Calvo´s specification, now allowing for the possibility of existence of a backward looking component in inflation dynamics. The result then was a another NKPC, mixing agent’s backward and forward looking behavior, so called the Hybrid NKPC.Aiming at this discussion above on the NKPC’s problems, and using american data, Gali and Gertler (1999) tested models that incorporate the approach of using real marginal costs as a proxy for the (ad-hoc) output gap, and that allow for some degree of persistence in inflation as well. As one main result, for the US economy, they came up with the effectiveness of using marginal costs as a proxy to the output gap, yielding the model’s predicted negative relation between future gaps and inflation acceleration. They also found evidence of some mild degree of persistence in US economy’s inflation dynamics. In addition, Gali, Gertler and Salido (2001), performs tests of the same nature for the european economy, finding that NKPC fits the data very well (even better than in the US), what becomes another piece of evidence favoring such theory.How would those results turn out be for the brazilian economy? Our goal, in this current work, is simply to bring answers to such question. The idea is to perform empirical tests of the same nature as in Gali and Gertler (1999), always bearing in mind the need to adjust these experiments to brazilian reality. Hopefully, one will be able to obtain interesting conclusions about the brazilian inflation path within the Real era and to compare them with those obtained for the american economy. In addition, this may, in some cases, provide further robustness to empirical evidence favoring NKPC theorists, and specially in case of Gali and Gertler´s work.Having already motivated this work, now we briefly indicate the steps to be taken. In the next section, we provide methodological information, detailing the sample features,variables and proxies used, and providing some fast information on the econometric techniques. Later on, we stress, using both theoretical and empirical arguments (specificaly applied to the brazilian economy), on the advantages of using the marginal costs approach to estimate the NKPC, sustained by Gali and Gertler. The two sections that follow are dedicated to the estimations of, respectively, the purely NKPC and the hybrid one, always focusing to apply Gali and Gertler’s test to the brazilian economy. Then we conclude.II.Methodological ConsiderationsGiven the purpose of this current work - to perform, for the brazilian economy, the same type of tests Gali and Gertler have conduced for the US economy - our will here was: trying to perform, as closely as possible in a methodological sense, the very same procedures followed by the authors. So, it could be interesting to briefly highlight, at this point, some of the issues that came up whilst we took on the task of adapting the american research to brazilian reality.First of all, some problems involving data matters have appeared, which is quite not surprising, since there are major asymmetries in both availability and reliability of economic data when we compare Brazil and the US. It is already known to most researchers the scarcity of economic data faced in developing countries, Brazil in particular. Without a full nor broad mass of data in hands, there were times when we faced the need to adapt, to brazilian economy, concepts of economic data (variables and proxies) in the US, so as to reduce the presence of asymmetries in the tests ran for these economies, and to prevent the generation of unwanted noise or measurement errors as well. One standard result from econometrics is that the latter can potentially hurt consistency of OLS (and also GMM) estimates.To exemplify what we mean here, in the case of labor income data (used to obtain a measure of marginal costs), the US data comprises only the industrial and retail sectors (excluding agriculture), meanwhile, for Brazil, the unique of such measure available to us included the agricultural sector. We had some problems of the same nature with regard to variables like long term interest rates and broad-inflation. However, such data asymmetries are not expected to have huge impact on the estimates, for the proxies used herein were sought so as to maximize their co-movements with the original variables1. Thus, this problem1It might not be completely useless to remind the reader that OLS estimators - naturally GMM as well, being OLS’ generalization - are robust to linear transformations (like differences in levels between variables, which is commonly encountered when taking different proxies for a same economic variable).shall not hamper the comparability nor the quality of the results, despite the fact that some robustness tests (e.g. run the same tests with other proxies) should be performed in later versions.One additional issue is that, when it comes to perform the tests and to compare the results obtained for the different economies, it might not be wasteful to look at countries’historical differences in both economic and geo-political grounds. In particular, contrarily to the US, the brazilian economy had been facing in the past severe inflationary process, until the Real Plan - implemented in June 1994 - succeeded in bringing (relatively) price stabilization to the economy. In practical terms, this implies that, using time series comprising periods earlier and after the Real adoption, we are very likely to observe the presence of structural break(s) in our parameters estimates for Brazil.Bearing this in mind, we were left with two different alternatives: (1) to use a very broad sample period for consistency reasons (like Gali and Gertler), albeit generating somewhat distorted estimates as a result of the applicability of Lucas critique - see Lucas (1976); (2) or to reduce the sample used in the models’ tests, confining it to the Real period, loosing in terms of degree of convergence to the real parameter value (consistency), but reducing dramatically the probability of structural breaks within our dataset. We have found better to choose the second alternative.II.A - Observation Sampling WindowFollowing Gali and Gertler (1999), we chose a dataset of quarterly observations of brazilian data, covering the interval T = [1994:3, 2002:2]. One must notice that we are left with only 32 observations, roughly more than one fifth of Gali and Gertler’s dataset for the US economy, which comprises data across 37 years. Such choice of ours - to shrink the dataset - can be justified, though, for reasons already mentioned above: by reducing the sample window, we try to minimize the effects of Lucas’ critique onto the estimates herein obtained.One might know that, in brazilian economic history, one can easily divide the timeline in (at least) two very distinct moments: one phase earlier and another one after the Real implementation in 1994. The brazilian hyperinflationary process of the past was reversed by such major change in economic policy, which was crucial to bring yearly inflation down from figures around 2480% in 1993 to 22% in 19952. And intuitively, we know that higher inflation levels become more persistence (i.e. more dependent on the past),as a result of generalized price indexation. This allows us to conclude that the Real implementation brought not only a huge change in inflation level, but also affected the set of driving forces behind the inflation dynamics.One further argument is also applicable to justify the rejection of data prior to 1994:3: hyperinflationary processes are sometimes linked to trajectories associated with bubbles, which is hard to be modeled (and therefore estimated).Therefore, we realized (rather informally, we admit) that there can be little doubt about the existence of major structural changes in any inflation models’ parameters estimated with a sample beginning before 1994, as consequence of the Real Plan. In all, aware of the arguments above, it seemed very reasonable to us to avoid the greater costs of the existence of structural breaks by the compression of the sample window, even at a (smaller) loss in terms of convergence of parameters estimates.II.B - Database and conceptsBearing in mind the objective of being as close as possible to the methodology proposed by Gali and Gertler, and trying to minimize possible differences in concepts of data between the US and the brazilian economy, we set up the sample vector Q(T), for T established as above:Q(T) = [ π(T)´ R(T)´ Z(T)´ ]´,where π(T) is the dependent variable, that is, a broad measure of inflation for the observation period, and R(T), Z(T) are, respectively, a vector of regressors and a vector of instruments, i.e.,R(T) = [ s(T)´ x(T)´ ]´Z(T) = [ s(T)´ x(T)´ i*(T)´ πw(T)´ πc(T)´ πG(T)´ ]´.In Z(T), we used some lagged variables, as was the case of s t and x t.A rough characterization of the dataset can be seen below, for all t in T:2Data from IBGE’s IPCA, a nationwide consumer price index.(i): πt– Inflation will be represented by percent quarterly variation in FGV’s IGP-M (General Market Price Index), because of the unavailability (in such a frequency) in Brazil of a measure like US’ GDP Deflator, used by Gali and Gertler. Given that IGP-M is a linear combination of a consumer price index (IPC), a producer price index (IPA) and a real state price index (INCC), it is fairly broad measure and thus serve as a good proxy for inflation, given our purposes. In IGP-M, IPA has weight of 0.6, IPC 0.3, and naturally INCC’s share is 0.1.(ii): s t– Marginal cost is obtained from the following expression:s t = log[S t] – log[S*t],where S t = (W t N t)/ (GDP t n).W t is working people’s income (Rendimento Real das Pessoas Ocupadas –IBGE), N t is labor force (Ocupação - IBGE) and NGDP t is nominal gross domestic product (PIB Nominal –IBGE). So, s(t) represents deviation of labor income share from its steady state value, which we’ll assume here, as a proxy, to be its long term average. The idea of why one comes to use such a measure in our tests will be given in Section IV. (See Figure 1)(iii): x t is the detrended output gap:x t = y t – y*t,where, y t is the log of output (i.e., the log of the nominal GDP, released by IBGE, and deflated by FGV’s IGP-M). Meanwhile, y t* is the a long run trend for the real GDP, a proxy for the natural output, calculated using Hodrick-Prescott’s methodology (HP-Filter). (See Figure 2)(iv): i t* is interest rates term spread. It is an instrument, which captures the evolution of the difference between long run and short run interest rates. Such variable is heavily influenced by future expected inflation. In our tests, we use the difference between TJLP rate (% perannun) and 30 days CDB rate (bank deposit rates), with the first being a proxy for long run interest rates, and the latter playing the role of short term interests.(v): πw t and πc t are, respectively, percent change of labor income (a variable also used to calculate s(t)) and percent change of FIPE’s IPC index (consumer’s price index). The first plays the role of wage inflation, whilst the latter is just a standard consumer’s inflation measure.(vi): πG t is FGV’s IGP-DI index, another broad inflation measure, which comprises the same imput variables as IGP-M (with the same weights), differing only in the period of observation (difference of 10 days). It is used as instrument in most of our tests.The interested reader will find out that this sample specification is closely connected to the dataset used by Gali and Gertler, with marginal differences in interpretability, as in the case of IGP-M substituing a measure like GDP Deflator. Even the choice of the set of instruments used has respected the standards adopted in Gali and Gertler (1999).II.C – Econometric IssuesAs is commonly done across the literature, when it comes to estimate rational expectation models, we test models using the generalized method of moments (GMM), which also follows Gali and Gertler’s way. We shall estimate, for each model, both the reduced and structural forms (when possible), sometimes imposing restrictions in some parameters, in order to assess the robustness of results encountered, just like the original authors have done.The set of instruments utilized in GMM estimation will be the same for all tests conduced throughout this work. In this regard, the only diverging point from the original article is that we used up to 3 lags of each instruments, against 4 in Gali and Gerler (1999). This was motivated by problem we faced with lack of data - contrarily to what happened in the american research’s case - for the more lags we use, the less observations we have to estimate models’ parameters. Comfortably, following that methodological decision, one should expect no significant effect whatsoever in terms of parameters estimates, and results’comparability. The set of instruments used is constituted by: lag 3 of wage inflation; lag 3 of IPC; lag 2 of interest rate term spread; lag 2 of the output gap (HP-Filter); lags 0 until 3 of IGP-DI and, finally, lags 1 and 2 of marginal cost.For every model estimated, we used Heteroskedastic Autoregressive Consistent (HAC) Covariance Matrix, proposed by Newey & West (1987), which guarantees more precise standard error estimates, which are robust to both heteroskedasticity and serial correlation. This allows us to be more confident on the results generated by the t-statistics, which will be rejecting (or accepting) the null that the parameter equal zero with greater precision than otherwise.In case of models estimated by GMM (the vast majority in this work), we will perform tests on the overidentifying restrictions, the so called TJ test. Unwilling to go so much deep into econometric details, for this is not the scope here, the TJ statistic provide a test on the null hypothesis that the excessive number of moments condition (i.e. the number of instruments that exceeds the quantity of parameters estimated into the estimated equation) are indeed valid. One can prove that TJ statistic is distributed by a Chi-Square p.d.f., withw = r - a degrees of freedom, where r is the number of instruments and a the number of parameters to be estimated. More details on such test can be found in Hamilton (1994).III.The Problem of Estimating NKPC Using Output Gap III.A – Some Theory FirstOne arrives at the NKPC by solving the problem of a monopolistically competitive firm (or set of identical firms), which sets its (their) prices optimally, i.e., determining them such that profits are maximized, subject to the constraint of time-dependent price adjustment.Accordingly to Calvo, from the hypothesis of constant price elasticity of demand, we obtain an aggregate price level such as follows (p t is the log of price level, which for simplicity we name just price level):p t = θp t-1 + (1-θ) p t*(1),where θ is the probability that a firm will not change its prices in the current period. So, aggregate price level is a convex combination of last period’s price level and an optimal price set by firms (those able to change price in the current period).Letting mc t represents the deviation of a firm’s real marginal costs from its steady state, and βthe subjective discount rate, firms maximize their expected discounted profits (by an stochastic discount factor, which adjusts for the risk), subject to time-dependent price rules, determining their prices according to the expression below, for k between zero and infinity:p t* = (1-θ) Σk(βθ)k E t{mc t+k}(2).It is interesting to notice that, when θ = 0, we have the case of fully flexible prices, which in such case is to move accordingly to current marginal costs dynamics.Letting πt = p t – p t-1 denote the inflation rate in t th period, the two expressions above lead us to the following testable equation (for apropriate mc t):πt = λmc t + βE t{πt+1}(3),where λ = θ-1 (1 - θ) (1 - βθ).Using lead operators, we obtain, for k between zero and infinity:πt = λΣkβk E t{mc t+k}(4).III.B – The econometrics of the NKPC (Traditional Approach)In the past, researchers used the following relation to estimate expression (3):mc t = κx t(5),where x t = y t – y t*, being y t the log of the product, and y t* the log of the “natural” product, econometrically obtained through some smoothing methodology. Such hypothesis of linearmarginal cost (implicitly: quadratic cost function) yielded the following Phillips Curve, with κbeing marginal cost elasticity with respect to output:πt = λκx t + βE t{πt+1}(6).In consonance with our purposes, and similarly a s done by Gali and Gertler, we tested with brazilian data the following equation, lagging expression (6) by one period and also imposing β = 1 and α = -λk.πt = αx t-1 + πt-1 + εt(7).Using OLS method, we obtained the following results for (7):Table 1Parameter Estimate Std. Error t-Statistic Prob.α0.1520.067 2.2600.0312R-squared-0.803088 Mean dependent var0.025894Adjusted R-squared-0.803088 S.D. dependent var0.018792S.E. of regression0.025233 Akaike info criterion-4.489572Sum squared resid0.019102 Schwarz criterion-4.443315Log likelihood70.58837 Durbin-Watson stat 2.587593Notes: IGP-M used as the dependent variable. Exogenous variable is the log of the output gap, obtained by HP-Filter.IGP-M lagged by one period is another regressor in (7), however the test impose its coefficient to equal to one.OLS procedure used in estimation, with Newey & West HAC covariance matrix.Adjusted Sample: 1994:4 – 2002:2, with 31 observations.In the test shown above, we found a weakly significant (at 5% level, but not in a 1% sized test) and positive coefficient estimate, which comes relatively in synchrony with results obtained in the american study, where the authors yielded a significant positive value for α (trully, they got a equal to 0.081, rejecting the null on T-test at 1% level). The interpretation for such outcome is the same as in the original work, with this test above providing further evidence against the old fashioned way of estimating the New Keynesian Phillips Curve. In fact, such tests for both US and Brazil’s economy are more likely to support the old Phillips Curve (which uses E t-1{πt} instead of E t{πt+1}), rather than the one formulated by Calvo. Primarily, this would off course be viewed as a negative empirical result for Calvo’s model, had researchers not proven (with both american, and later on, with european data) thevalidity of the marginal cost approach to estimate parameters from the NKPC in Calvo’s fashion. We shall verify, in the sections that follow, if such results also hold true for the brazilian economy as well.IV.Marginal Costs Approach: The Purely Forward Looking NKPCIV.A – Motivating The New SpecificationThe poor empirical results obtained by Calvo’s NKPC, using data from both US and Brazil’s economy (the latter testified by the earlier section of this current work), when computing the output gap by some smooth technique, might not be a decisive evidence against Calvo’s model. In other words, these bad results should not lead to the rejection of its empirical validity, as some might conclude at a first glance. Gali and Gartler’s point is that such results are directly influenced by the methodology used to obtain the natural output, and the outcome of empirical tests on NKPC may be quite different conditional on the smoothing technique deployed. The authors claim that structural shocks, like change in tastes and variations in government spending may have an impact such that it offsets the forecasted negative relation between inflation acceleration today and the output gap last period. So it would be useful if we had a proxy for the output gap which did not suffer from this problem. The approach used here (for brazilian data), originally proposed in Gali and Gertler (1999), is to use marginal costs as a proxy to the output gap.Gali and Gertler sustain that an alternative way to test the NKPC model is, instead of estimating equation (6), estimating the expression (3), replacing therefore the output gap (x t) by the marginal costs (mc t). Since the latter are not directly observable, we must use theory to guide efforts on how to obtain such variable, so allowing us to go into estimation procedures. Section II.B of this current work shows details on how we obtained the measure of marginal costs (for the brazilian economy) which is deployed here. It is important to highlight here that the procedure used to get the marginal costs measure is meant to be as near as possible to the one proposed by the authors in this paper’s “original (american) version”.Let’s go straight to the point, now. Suppose a Cobb Douglas production function likeY t = A t K tαk N tαn(8).Real marginal costs can be expressed by the ratio of the real wage to the labor’s marginal product:MC t = (W t/P t)(?Y t/?N t)-1(9).Some algebraic manipulations, i.e., inserting using expression (8) and the partial derivative of Y t with respect to N t into (9), yields the following expression below:MC t = S tαn-1(10),where S t = W t N t(P t Y t)-1.From S t, the share of labor income, we obtain s t, which represents the percent deviations of S t from its steady state level (the latter is estimated by use of HP-Filter):s t = log[S t] – log[S t*](10*).Then, s t will then be used in the NKPC’s specifications that we test here, providing our measure of marginal cost that will replace (as a proxy for) the standard measure of the output gap.So, in the next section, we test the following version of Calvo’s NKPC:πt = λs t + βE t{πt+1}(11),whereλ = θ-1 (1 - θ) (1 - βθ).IV.B – Testing Calvo’s NKPC Using Marginal CostsIV.B.1 – Reduced Form EstimatesAs we have mentioned earlier, the estimation technique chosen to be applied to (11) is GMM, Generalized Method of Moments, very handy and widely deployed to test rational expectation models (as is the case now). One can show, by means of the iterated expectations law, that expression (11) implies the following moment condition, in the reduced form:E t{(πt - λs t - βπt+1)Z t } = 0(12).Here, Z t denotes the set of instruments defined in section II.B, the very same one that will be used in all tests henceforth.Table 2ParameterStd. Error t-Statistic Prob.Estimateλ0.1670.081 2.0610.0494β0.9470.04919.1480.0000S.E. of regression0.027701 Sum squared resid0.019950Durbin-Watson stat 2.846987 J-statistic0.145939Notes: IGP-M used as inflation measure. Marginal cost obtained by expression (10*). Instruments list can be viewed in Section II.B. GMM estimation procedure used, with Newey & West HAC covariance matrix estimationConvergence achieved after 54 iterations.Adjusted Sample: 1995:2 – 2002:1, with 28 observations.TJ test failed to reject the null hypothesis of validity of overidentifying restrictions at 10%, 5% and 1% levels - Chi-Square pdf at 8 d.f..For the american economy, Gali and Gertler (1999) had:πt = 0.023s t + 0.942E t{πt+1}(0.012) (0.045)And for the european economy, Gali, Gertler and Salido (2001) found:πt = 0.088s t + 0.914E t{πt+1}(0.041) (0.040)Thus, what we got a positive (and significant at 5%) value for λ, using marginal cost replacing as a proxy to the “actual” output gap. These results exposed in the table above are not so different to those obtained for the american economy (listed below). The great discrepancy concerns the estimates for λ, given that output elasticity obtained for brazilian data is 7 times as high as the one gotten in the american case, and almost the double of estimates from european economy. In addition, the significance of λ is rather weak in brazilian case, for we fail to reject the null at 1% level, contrarily to what happens for the Europe and US economies. Nevertheless, it is also interesting to notice the similar values obtained for the betas (not only coefficient estimates, but also standard deviations), implying impatience rates relatively consistent, and not very contradictory, across the three economies tested.It could also be worthwhile to provide, at this point, some information on the TJ test. In the test of (12), we failed to reject the null hypothesis about the validity of the (r – a) overidentifying restrictions, where r is the quantity of instruments (10) and a is the number of parameters estimated (2). At 5%, the critical value of Chi-Square at 8 degrees of freedom is 15.51, greater than the value of 4.09 obtained for the TJ statistic. In fact, the same will happen to all conditions tested henceforth, so we shall not waste time in detailing further TJ results on these tests.For symmetry ends, allowing us to compare this new approach to estimate the NKPC with the traditional one, we replaced s t for x t in (12), and estimated its parameters for the brazilian economy, yielding the following results:Table 3Std. Error t-Statistic Prob.ParameterEstimateλ-0.5430.076-7.1410.0000β 1.0880.1109.9290.0000S.E. of regression0.036116 Sum squared resid0.033913Durbin-Watson stat 1.877362 J-statistic0.164286Notes: IGP-M used as inflation measure. Log of the output gap used (HP-Filter). Instruments list can be viewed in Section II.B.GMM estimation procedure used, with Newey & West HAC covariance matrix estimationConvergence achieved after 500 iterations.Adjusted Sample: 1995:2 – 2002:1, with 28 observations.TJ test failed to reject the null hypothesis of validity of overidentifying restrictions at 10%, 5% and 1% levels - Chi-Square pdf at 8 d.f..。