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## Cuadernos de economía

*versión On-line* ISSN 0717-6821

### Cuad. econ. v.45 n.132 Santiago nov. 2008

#### http://dx.doi.org/10.4067/S0717-68212008000200004

Cuadernos de Economía, Vol. 45 (Noviembre), pp. 235-255, 2008
^{2} CONICET and Universidad Nacional del Sur, Argentina
Macroeconomic theory emphasizes the distorting impact of inflation on relative price variability (RPVI). In fact, a relevant function of the price system is the transmission of the information required by economic agents in order to allocate resources efficiently. Given that such information is contained in relative prices, the noise coming from inflation can make it difñcult to use the information optimally. The positive relationship between RPV and inflation has practically become a stylized fact in economics The rest of the paper is organized as follows. Section 2 summarizes the theories linking inflation and RPV and main empirical evidence, section 3 presents the data and variables. In section 4, we show the preliminary empirical evidence for the whole period under study, section 5 divides the period into inflation re-gimes using a Markov switching model and show the main determinants of RPV in each regime. Section 6 is focused on moderate inflation periods, and section 7 concludes.
Since the seminal papers of Vining and Elwertowski (1976) and Parks (1978), there is a vast literature showing a positive and strong relationship between inflation and RPV. The mechanisms underlying such correlation differ depending on the model used to explain it. The main theoretical approaches can be summarized as follows:
Table 1 summarizes the empirical evidence according to each model. In short, empirical evidence is mixed and there is no consensus about the mechanisms linking inflation and RPV. Although recent works like Dabús (2000) for Argentina, Caglayan and Filiztekin (2003) for Turkey and Caraballo
Price data series nave been extracted from the statistical bulletins of the Instituto Nacional de Estadísticas y Censos (INDEC), from January, 1960 to November, 1993. Individual price data conespond to the items of the national Wholesale Price índex (WPI), at the level of WPI groups
As it is common in this kind of literature, the RPVI index (RPVI) is measured as the standard deviation of the individual price changes around the average inflation rate. We introduce a slight variation because at high inflation the usual RPVI can be spuriously conelated with the mean of the distribution -the average inflation rate-. In order to avoid this problem, we define RPVI as a coefficient of variation, as follows: where i in the price index, INis the inflation rate of price _{it} i at month t and INis the inflation rate at period _{t} t.Inflation has been decomposed into expected, unexpected inflation and uncertainty where Equations (2) and (3) were estimated using the Marquardt algorithm. As the residu-als were not conditionally normally distributed, we compute the covariance matrix and standard errors using the methods proposed by Bollerslev and Wooldridge (1992). The Equation (3') is used to construct the series of uncertainty. Finally, we have distinguished volatility from uncertainty. Volatility is an As we are using monthly data, we define volatility as the absolute value of the difference between the current inflation rate and a moving average inflation rate of three, six and 12 months, respectively: The selection of the number of lags is arbitrary. Nevertheless, the idea of including a number of lags that span from 3 to 12 months is to capture the influ-ence of the inflationary environment on the current inflation rate in an economy of high and volatile inflation like Argentina. Intuitively, above 12 months, the values of volatility could be affected by far away high fluctuations that in fact would not be related to the period of time for which volatility is calculated, and therefore an overestimation error could arise. On the contrary, a number of lags under three can genérate an underestimation of the volatility, because movements of inflation trend, relatively closed to the current inflation, should be excluded from the measure.
This section presents the empirical results of the Inflation-RPVI rela-tionship for the period under study. The estimates were carried out following the main theoretical models developed in the literature -see Section 2-. Firstly, we estimate the effeets of the inflation rate on RPVI; secondly, we consider the role of expected and unexpected inflation, and ñnally we analyze the impact of uncertainty and volatility on RPVI. In first place, we regress RPVI on squared inflation -equation (5)- to capture non-linearities in such relation, and the absolute of inflation -equation (6)- to determine the effect of the magnitude of inflation on RPVI, independently of its sign. The lagged term of RPVI is included to capture the persistence of the variable. The estimated equations are: Our start point is to test if ß > 0 for both equations result that is in accordance with the four theories mentioned above and it is the first step in order to further analysis of the determinants of RPVI. Results are presented in Table 2, where we have also included the estimates with the lagged terms of inflation to reduce the problems associated with the simultaneous determination of both variables, as pointed out by Grier and Perry (1996). Along the paper, to test for autocorrelation we use the Breusch-Godfrey (BG) Lagrange multiplier test. Firstly, we estimate equations by Ordinary Least Squares (OLS), after that, we test for first and up to twelfth order autocorrelation in residuals. If no autocorrelation appears, we present the results of the OLS estimate. When autocorrelation is detected, we estimate by Non Linear Least Squares and, previously, we model the structure of the residuals attending to the autocorrelation properties shown by the residuals series. For all cases, residuals have been modeled using a moving average structure, its order depends on each case. Table 2 shows a positive and significant effect of current inflation on RPVI in both specifications: with squared and absolute values of inflation. Lagged absolute value of inflation is significant at 10% and lagged squared inflation is not significant. Henee, the main effect of inflation on relative prices is due to the contemporaneous relation between them, with decreasing impaets of past inflation. In second place, we estimate the effeets of inflation expectations on RPVI -equations (7) and (8)- and we test if the asymmetric response of RPVI to positive and negative unexpected inflation is significant. where UINdenote the positive and negative unexpected inflation, respectively. Recall that, on one hand, menu costs model predicts ß^{-}_{0} > 0 and, on the other hand, ß_{2} = ß_{3} > 0 can be considered as evidence in favor of the extended signal extraction model.Results are presented in Table 3. Both expected and unexpected inflation affect positively RPVI and Wald test shows that there are not asymmetric effects of unexpected inflation In order to analyze the role of uncertainty, we have considered firstly the models existing in the literature, focusing on Grier and Perry (1996). These aufhors propose a bivariate GARCH-M model of inflation and RPV to show that inflation uncertainty dominates trend inflation as predictor of RPV. We try to apply the same specification for RPVI in Argentina and, therefore, we have to test if the conditional variance of RPVI is constant. As first step, we have to model RPVI. The best fit is an ARMAX(1,5) with ^{6}: the Ljung-Box Q-Statistics adjusted for five ARMA terms is 116.31 and the Autoregressive Conditional Heteroskedasticity Lagrange Multiplier (ARCH-LM) statistics, which is asymptotically distributed as (1), is 52.25. Therefore, the two statistics lead us to reject the nuil at the 1%, which implies that the conditional variance of RPVI is not constant. Secondly, we have considered alternatives ways to model RPVI and we have chosen estimates IV and V in Table 2, where the absolute inflation and its lagged value appears to be significant at 1% and 10% respectively. For estimate IV, the Ljung-Box Q-Statistics adjusted for five ARMA terms is 44.36 and the ARCH-LM test statistics is 5.65; for estimate V, the Q-statistics is 67.72 and the ARCH-LM test statistics is 65.09. Therefore, for both cases we reject again the hypothesis of independence of the squared of the residuals at the 1%, so, as the conditional variance of RPVI is not constant, we have not applied the proposal of Grier and Perry. Instead, and in order to have a first overview of the role of uncertainty, we redeñne the above ARMAX(1,5) model including uncertainty as explanatory variable too, and given the structure of the residuals, we estimate equations (9) and (10):We use the Marquardt algorithm and the covariance matrix and standard errors are computed using Bollerslev and Wooldridge's method. The Analogously, we have used the same method for volatility, so we have estimated again equations (9) and (10) but including volatility instead of uncertainty, the three measures of volatility appear to be significant -see Appendix A for results-. In short, this preliminary analysis show that inflation rate, both the absolute and squared values, expected and unexpected inflation and volatility play a key role in explaining RPVI, while uncertainty has the expected sign but it is not significant, in contrast to results found by Grier and Perry (1996) and Aarstol (1999). Moreover, the relevance of squared inflation indicates a non-linear relation between inflation and RPVI. The intuition behind this result is such relation, and then the determinants of RPVI, changes across inflation regimes. This hypothesis is analyzed in next sections.
We determine the inflation regimes in Argentina applying the methodology based on Markov switching regression model -see Hamilton (1989,1994)-. Within this method, regimes are deñned using a model that endogenously shows the probabihty of being in a regime. We assume that a particular period can be included in a speciñc regime when the probabihty of being in such regime is above 0.5; and specify the Markov switching regression model as an autoregressive model of order one with three states of inflation -see Appendix B for details-. To estimate this model we used a reformulated version of the Hamilton's algorithm. Since the algorithm does not converge to any result for the whole series, the hyperinflation months were removed from the estimation. Henee, we obtained four regimes, one of hyperinflation, which includes the periods previously excluded from the sample, and three regimes (moderate, high and very high inflation) that were determined by the model. Using the maximum likelihood estimates for the transition probabilities matrix, the whole sample is divided into four different regimes, as it can be seen in Table 4. Moreover, such Table shows that the whole sample could be divided into a first period of moderate and stable inflation from January 1960 to May 1975, fol-lowed by a long period of changing inflation where, along 222 months, inflation goes from negative rates to hyperinflation and within this latter period, the four mentioned regimes can be distinguished. Once the inflation regimes were obtained, we include them in the estimates by means of the corresponding dummies to each regime and we carry out the basic regressions that appear in Table 5. Table 5 shows that results change when inflation regimes are included. On one hand, when we test if the coefficients are jointly equal, the (3) statistic leads us to reject the nuil. As far as significance of the variables is concerned, on one hand, squared inflation and unexpected inflation are significant at 5% or 1% in all regimes. On the other hand, expected inflation, uncertainty and volatility affect RPVI only beyond moderate inflation: they are significant at 5% or 10% for high and very high inflation (except uncertainty which is not significant in very high inflation) and at 1% for hyperinflation. In short, the results differ between moderate inflation and the other regimes. Thus, we carry out a deeper analysis of such regime. In order to do that, we have to take into account that we have two kind of moderate regime, the one in the first period of stable inflation, and the moderate inflation within a period of changing inflation. We consider both kinds of moderate inflation regimes separately.
This section analyses the determinants of RPVI in moderate inflation. Table 6 shows the results for the stable period, which spans from January 1960 to May 1975, and Table 7 presents the results for moderate inflation regime occurred along the unstable inflation period that goes from June 1975 to November 1993 As it can be seen from Tables 6 and 7, in both cases, the absolute inflation rate and the squared inflation are significant, and uncertainty and volatility are not significant. The main difference appears with expected and unexpected inflation, given that in a stable inflation period, expected inflation is significant and unexpected inflation is not significant at 5%, and the reverse is true for the moderate inflation regime in the changing inflation period. If we consider an asymmetric impact of unexpected inflation, results in Table 8 show that for stable period only positive unexpected inflation is significant, while in the changing inflation period the magnitude and not the sign is relevant. The (1) statistics implies that asymmetries appear in the stable period but not in the changing inflation period Finally, we check if the results are sensitive to changes in the forecast equation of inflation. When we consider the two periods separately, for the second period the best model to fit inflation is the ARMA(1,1)-GARCH(1,1) selected for the whole sample, but this does not hold for the stable period. Applying again the standard Box-Jenkin methodology, the best fit for inflation in the stable period is: As usual along the paper, we have applied the Marquardt algorithm and the p-value of the z-statistic computed using Bollerslev and Wooldridge's method is shown into brackets. From the above model, we obtain expected and unexpected inflation and we estimate equation (8) by means of OLS, given that residuals do not present autocorrelation: Equation (13) shows that both expected and positive unexpected inflation are significant while negative unexpected inflation is not. Moreover, the coefficients of positive and negative unexpected inflation are not statistically equal given that the value of the (1) is 14.61. Therefore, the above results hold. In short, for high inflation periods, volatility and all components of inflation are relevant in explaining RPVI, but for moderate regimes determinants of RPVI are quite different. More precisely, volatility and uncertainty are not significant, and the impact of expected and unexpected inflation depends on the inflationary context.
This paper analyses the relationship between inflation and RPVI in a high and volatile inflationary environment like the Argentinian economy in the period 1960-1993, focusing on the role of inflation regimes in explaining the changes in the determinants of RPVI. We have divided the whole sample into two main periods: the first one (1960-1975) characterized by a moderate and stable inflation, and the second one (1975-1993) characterized by a very changing inflation rate. We identify four inflation regimes: moderate, high, very high, and hyperinflation. We conclude that the determinants of RPVI changes not only with the regime but also with the inflationary context. In particular, the determinants of RPVI in moderate inflation change from the first period of stable inflation to the second period with a changing inflation environment. For high, very high, and hyperinflation regimes, volatility and all components of inflation (uncertainty, expected and unexpected inflation) are relevant in explaining RPVI but for the moderate regime, determinants of RPVI differ: volatility and uncertainty are not significant, and the impact of expected and unexpected inflation depends on the inflationary context. For the moderate regime in a stable inflation period, expected and positive unexpected inflation are significant while for moderate regime in a changing inflation period, expected inflation is not significant and the magnitude, and not the sign, of unexpected inflation is significant. Moreover, results are not sensitive to the forecast equation of inflation. These results show that, in all regimes, there is a welfare cost of inflation through its impact on RPVI, but there is not a unique theoretical model to explain how and why inflation affects RPVI. In fact, we have found evidence that favors the menu cost model (moderate regime in stable inflation period) and the extended signal extraction model (moderate regime in changing inflation period). These results are similar to those found by several authors for countries with a much lower inflation than the moderate inflation rate in Argentina -see Table 1-. The intuition behind our results is that the determinants of RPVI depend on the inflationary experience of the economy and not on the absolute value of the rate of inflation. In other words, the lowest inflation period in Argentina has not been even reached by U.S. or Germany in their periods of highest inflation, but theories like menu costs model or signal extraction model can explain the behavior of RPVI in the lowest inflation periods of different Economics, because what matters is the relative, and not the absolute, value of the inflation rate. The natural extension of this paper is to analyze the determinants of RPVI in countries with a similar inflationary experience like Argentina.
* We thank the financial support from Secretariado de Ciencia y Tecnología, Universidad Nacional del Sur (Argentina). Project PGI 24/E042. The assistance of Diego Caramuta is acknowledged.
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The following Markov-switching model with an where s* switches among the three states (moderate (m), high _{t})(h) and very high (vh) inflation regimes). In order to estimate de model, we define the variable st that characterizes the regime for date t as follows:And we denote And then The conditional density of where
And α is a vector of parameters characterising the conditional density: Moreover, it is assumed that Finally, the máximum likelihood estimates of parameters in a for our data are |