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Further evidence on the variability of inflation and relative
price variability
a ,
*
bEric C. Chang
, Joseph W. Cheng
a
School of Business, The University of Hong Kong, Pokfulam Road, Hong Kong, Hong Kong
b
Department of Finance, The Chinese University of Hong Kong, Shatin, New Territories, Hong Kong, Hong Kong
Received 8 March 1999; accepted 13 July 1999
Abstract
Using a sample of monthly observations of both a 12-category group and a 203-category group of personal consumption expenditures, we furnish evidence that relative price variability is positively related to both the inflation rate and inflation variability. The relation is robust to oil-price shocks. 2000 Elsevier Science S.A. All rights reserved.
Keywords: Inflation variability; Relative price variability
JEL classification: E30; E31
The relationship between relative price variability (RPV) and inflation has been the subject of intensive investigation in recent years. Parks (1978) furnishes evidence of a significant relationship between RPV and the rate of inflation for the periods 1930–1941 and 1948–1975. Similar empirical
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evidence has also been documented in the literature for several foreign countries. One possible explanation for the relation is the imperfect information hypothesis which suggests that, since individuals do not have full information about the general price level, it is possible for them to confuse changes in the general price level with changes in relative prices (Hercowitz, 1981; Parks, 1978). Caporale and McKiernan (1997), for example, document that there is a positive and statistically significant relationship between the level and variability of inflation. Cukierman (1979, 1982) formally develops a theoretical model of relative and general price level behavior which implies a positive relationship between inflation variability and RPV.
*Corresponding author. Tel.: 1852-285-783-47.
E-mail address: [email protected] (E.C. Chang)
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Similar findings have been documented in an international context by Hercowitz (1981), Domberger (1987), and Lach and Tsiddon (1992, 1993).
On the empirical front, Marquez and Vining (1983) document a strong and positive relation between the variance of inflation and RPV for the US economy from 1948 to 1975. However, they also document that the relation has not remained stable over time. They attribute the instability to several factors including the imposition of price controls, the supply shocks of the seventies, and the
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linear approximation to a non-linear relation.
This paper provides further evidence on the variability of inflation and RPV. We extend Marquez and Vining’s (1983) study in two different ways. First, we use monthly observations of personal consumption expenditures for two levels of aggregation. We obtain monthly data on seasonally adjusted personal consumption expenditure in the US for the period 1959–1993 from the Bureau of Economic Analysis (BEA) of the US Department of Commerce. In the unpublished NIPA (National Income and Product Accounts) database compiled by the National Income and Wealth Division of the BEA, the 12 categories of personal consumption expenditures used in Parks (1978) have been further divided into 203 sub-categories. Earlier studies by Balk (1983) and Goel and Kam (1993) suggest that the level of commodity aggregation may have a nontrivial effect on the relationship. We re-estimate RPV and inflation rates based on this finer categorization. Second, monthly data provide us with many more observations than used in previous studies. It allows us to use a more sophisticated time series model to estimate a conditional inflation variability model and then relate the estimated inflation variability to RPV.
Our major finding is that, at both levels of commodity aggregation, RPV is positively related to
both the inflation rate and inflation variability. In addition, we show that the relations remain robust to
oil-price shocks. The evidence is consistent with the interpretation that RPV is related to the inability on the part of individuals to predict the general price level. However, since RPV relates to both inflation rate and the inflation variability, the positive relationship observed in Parks (1978) is not merely a proxy for the inflation variability effect.
1. Data and results
We obtain monthly data on seasonally adjusted personal consumption expenditure in the US for the period 1959–1993 from the Bureau of Economic Analysis (BEA) of the US Department of Commerce. Following Parks (1978), we first measure aggregate inflation and RPV based on a
12-category breakdown of annual personal consumption expenditures. Parks (1978) defines DP ,t
aggregate inflation, as the weighted average of the growth rates of the implicit price deflator for each of the 12 commodities (DP ). That is,it
12
DPt5
O
w DPit it (1)i51 2
Marquez and Vining’s (1983) study is based on Parks (1978) data which contain annual observations of 12 personal consumption expenditure groups. The inflation variability in year t is estimated by the standard deviation of K consecutive yearly inflation rates (years t2k to t), where K is the number of periods used in the estimation. It is recognized that the
where wit is the relative expenditure on category i in period t. To ensure that the source of cross-sectional dispersion is unambiguously coming from price changes, we instead use fixed weights to calculate both aggregate inflation and RPV. Following Blinder (1980), we apply a fixed weight for
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each component of the price deflator based on the 1972 relative expenditure on each category. Relative price variability (VP ) is defined as the weighted variance of deviations in inflation int individual categories from aggregate inflation as given by
12
2
VPt5
O
w DPis it2DPtd (2)i51
Since a fixed weight is used, we drop the time script t for each weight.
In the unpublished NIPA (National Income and Product Accounts) database compiled by the National Income and Wealth Division of the BEA, the 12 categories of personal consumption expenditures have been further divided into 203 sub-categories. We re-estimate DP and VP based ont t this finer categorization and re-examine their relationships.
Table 1 presents the summary statistics of the raw data. The annualized monthly mean rate of inflation over the sample period is about 4.40% (4.29%) for the 12 (203) categories. These numbers, by definition, are not sensitive to the level of commodity aggregation. However, the average relative price change variability based on 203 categories of consumption expenditures is substantially higher than that based on 12 categories. The former is 4.23 times of the latter (means, 0.020313 and 0.004801, respectively). The standard deviations of the relative price variabilities based on the two levels of aggregation also exhibit a similar pattern.
Table 1 also indicates a high first-order positive serial correlation for monthly inflation rates. The positive serial correlation remains significant even at lag 12, though it decreases with the number of lags. Table 1 also reports a positive first-order serial correlation for relative price variabilities. The serial correlations beyond lag 2 exhibit no particular patterns and are mostly insignificant.
Using monthly instead of annual data expands the number of observations for our analysis from 35 to 420. An advantage of using monthly observations is that a more sophisticated time series model can
Table 1
Summary statistics of annualized monthly rates of inflation (DP ) and variabilities of relative price changes (VP ):t t 1959–1993
Categories / variables Mean Standard Serial correlation at lag deviation
1 2 3 6 12
(I) 12 Categories
DPt 0.043969 0.029704 0.620 0.568 0.553 0.568 0.462
VPt 0.004801 0.012200 0.457 20.005 20.009 20.012 20.022
(II) 203 Categories
DPt 0.042876 0.028890 0.746 0.659 0.624 0.627 0.525
VPt 0.020313 0.026978 0.242 0.124 0.146 0.105 0.111
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be used to estimate inflation variability. We estimate inflation volatility by employing a variation of the time-series model developed in Schwert (1990) for estimating stock market volatility. In general, the model removes autoregressive and seasonal effects, if any, from monthly inflation rates to estimate unexpected inflation rates. The absolute values of the unexpected inflation rates are then used in an autoregressive and seasonal model to predict inflation volatility. The estimation procedure requires iteration between a pair of equations of the form
12 12
where DJan,t is a dummy variable having a value of 1 in January and 0 otherwise, u and v are,t t
respectively, the residuals from Eqs. (3) and (4), and u is the estimated inflation standard deviationu ut in month t. DJan,t is included to capture the possible existence of a seasonal inflation effect. The inclusion of DJan,t is warranted since Park and Reinganum (1986) document that there is a kink in the yield curve as it crosses calendar months and the kink is most pronounced as the yield curve crosses between calendar years.
In effect, Eq. (3) estimates monthly inflation, conditional on past inflation and past standard deviations of inflation. Eq. (4) then estimates monthly inflation variability, conditional on past unexpected inflation (ut2k) and past inflation variability to accommodate persistence in volatility. Following Davidian and Carroll (1987), we iterate between Eqs. (3) and (4) to calculate weighted
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least-squares estimates.
Table 2 contains estimates of Eq. (4) using monthly DP from January 1963 through Decembert
1993 for both levels of expenditure aggregation. In the 12-category panel, the estimate of the autoregressive coefficient is significantly positive at lag 1, showing moderate persistence in the movements of inflation variability. Most of the remaining estimates of autoregressive coefficients are of insignificant magnitude and have mixed signs. The only noticeable exceptions areg12 in A and r6, g9 andg10 in B, which are significant at the 10% level. The fitted values of Eq. (4) are our estimates of conditional inflation volatilities (VI ).t
We examine the relationship between the relative price variability and the variance of inflation rates and aggregate inflation by estimating the following model:
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VPt5a01a1D74,t1a2D80,t1a3DPt 1a4VIt1et (5)
where D74,t(D80,t) is a dummy variable having a value of 1 in year 1974 (1980) and 0 otherwise, and VI is the variance of the inflation rate which is equal to the square of the predicted value from Eq.t
5
(4). Bomberger and Makinen (1993) recently showed that the classic evidence in Parks (1978) is not robust. They document that when oil price shock years 1974 and 1980 are removed from the sample,
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Eq. (3) is initially estimated without lagged standard deviations on the right-hand side. Fitted standard deviations from Eq. (4) are included in Eq. (3) in subsequent iterations.
5
Specifically, D (D ) takes on a value of 1 from July 1973 (1979) to June 1974 (1980) and 0 otherwise. In one set of74 80
Table 2
Estimates of an autoregressive model for percentage monthly inflation variance, including effects of lagged unexpected inflation: 1959–1993 (using 12 lags and iterative weighted least squares)
Variable (A) Model based on 12 consumption (B) Model based on 203 consumption expenditure groups expenditure groups
Coefficient t-statistic Coefficient t-statistic
Intercept 0.011311 4.336 0.006618 3.178
Dummy-January 0.000527 0.159 0.002943 1.132
Lags of Uu t2ju
1 0.315169 5.883** 0.070881 1.316
2 20.017648 20.311 0.010890 0.200
3 20.033502 20.588 0.054776 1.010
4 0.026966 0.474 0.043642 0.823
5 20.009990 20.177 0.077672 1.469
6 0.035526 0.634 0.175487 3.313**
7 20.022059 20.396 0.079820 1.503
8 20.017459 20.313 0.031124 0.585
9 0.025897 0.464 20.041795 20.783
10 0.029210 0.523 20.006787 20.127
11 0.058674 1.047 0.084155 1.577
12 20.028588 20.542 0.008978 0.168
Lags of ut2k
1 20.170469 23.807** 20.001215 20.030
2 20.003644 20.080 20.024423 20.595
3 20.011708 20.256 20.016756 20.407
4 0.002025 0.044 0.009946 0.243
5 20.019186 20.424 0.016457 0.406
6 0.057922 1.281 0.060091 1.484
7 0.002972 0.066 0.054035 1.330
8 20.028824 20.639 20.020968 20.516
9 0.041462 0.919 0.088476 2.180*
10 20.046541 21.030 20.077338 21.888*
11 0.025524 0.565 20.003099 20.075
12 0.082768 1.849* 20.023337 20.577
2
Adj. R 0.0882 0.0705
Parks’ (1978) regressions reveal no strong relationships between inflation and RPV. This finding motivates us to include the oil price shock year dummies in the regressions. The results for two levels of aggregation are presented, respectively, in Panels A and B of Table 3.
Table 3 offers strong confirmation of the findings in Vining and Elwertowski (1976) and Marquez and Vining (1983). The variance of inflation provides substantial marginal explanatory power for the
movements of relative price variability. Without exception, all estimates of coefficients a4 are
Table 3
The relationship between the monthly rate of inflation (DP ), the variance of inflation (VI ) and the variability of relativet t
a
price changes (VP ): 1959–1993t
2
Regression a0 a1 a2 a3 a4 Adj-R
(A) Results based on 12 consumption expenditure groups:
(A1) 20.002878** 0.773972** 14.48635** 0.371
(23.67) (4.77) (12.65)
(A2) 20.002930** 20.002754 0.824978** 14.43979** 0.370
(23.73) (20.86) (4.78) (12.59)
(A3) 20.002903** 20.002138 0.815064** 14.39526** 0.370
(23.70) (20.67) (4.69) (12.47)
(A4) 20.002970** 20.003225 20.002705 0.885680** 14.31659** 0.370 (23.77) (21.00) (20.83) (4.72) (12.37)
(B) Results based on 203 consumption expenditure groups:
(B1) 0.005737* 1.973876** 31.60031** 0.125
(2.18) (4.58) (4.20)
(B2) 0.006812* 0.013570 1.751620** 28.77429** 0.129
(2.52) (1.60) (3.88) (3.73)
(B3) 0.005766* 20.003133 2.040327** 31.18562** 0.123
(2.19) (20.38) (4.38) (4.10)
(B4) 0.006808* 0.013402 20.001008 1.775748** 28.67578** 0.127
(2.51) (1.56) (20.12) (3.59) (3.70)
a 2
VPt5a 1a0 1D74,t1a2D80,t1a3DPt1a4VIt1et, where D74,t(D80,t) is a dummy variable having a value of 1 in year 1974 (1980) and 0 otherwise.
inflation (Caporale and McKiernan, 1997). If the demand and supply in each market react to the local perception of relative prices, the movements of relative price variability are expected to be associated with inflation variability.
In addition, results in Table 3 confirm the robustness of Parks’ findings. The estimates of a3 all remain positively significant even with the presence of two oil-shock dummy variables and the variance of inflation. Therefore, the positive relationship observed in Parks (1978) is not a proxy for the inflation variability effect. It is robust to oil-price shocks. The estimates of the coefficients on the two oil-shock dummy variables have mixed signs. None of them is statistically distinguishable from zero at any conventional significance level.
2. Conclusion
However, since RPV relates to both the inflation rate and inflation variability, the positive relationship observed in Parks (1978) is not merely a proxy for the inflation variability effect.
Acknowledgements
Eric C. Chang wishes to acknowledge financial support from the Center for Financial Innovation and Risk Management (CFIRM) of the University of Hong Kong and RGC Earmarked Research Grant 1999–2000 (HKU 7258 / 99H). Joseph Cheng wishes to acknowledge financial support from the Mainline Research Grant (BS95020) Council of the Chinese University of Hong Kong.
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