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Inflation and its variability
Economics Letters 1 (1978) 357-360 0 North-Holland Publishing Company
INFLATION AND ITS VARIABILITY Some Comments and the Dutch Case B.M. BALK Netherlands
Central Bureau of Statistics, Voorburg,
The Netherlands
Received January 1979
Some results concerning the rate and variability of inflation in the Netherlands during the period 1952-1975 are presented and contrasted with similar results for the U.S.A.
1. Introduction During the last few years some interest in the variability of inflation has been shown. This subject can be pursued in two directions. A representative of the first direction is Foster (1978), reviewing and extending earlier work. He clearly demonstrates the close connection between the average rate of inflation, measured by means of some aggregate price index, and the variability of this inflation, measured by the average change in the rate of inflation, which a country experiences during a certain period of time. Thus a higher average rate of inflation means more variability of this rate. An early representative of the second direction is Glejser (1965). He very clearly states the usual point of view on this subject: ‘Inflation is generally considered as a wave lifting the whole of prices to a higher level without altering significantly the respective position of each of them, at least in the long run.’ In his paper he presents evidence contradicting this usual point of view. His cross-country study reveals a positive correlation between the magnitude of average relative price variability and the average rate of inflation. Two more recent contributions however, deal with this subject by means of a time-series analysis. Vining and Elwertowski (1976) try to show that ‘the behavior of the general price level is related in a statistically systematic manner to the behavior of individual prices relative to each other’. They work at a very low level of aggregation using price indices from the U.S. Wholesale Price Index and Consumer Price Index at the item level. Let pit be the price (or price index) of commodity i in year t. For each of the years 1948 to 1974 inclusive, they calculate k
351
358
B.M. Balk /Inflation
and its vartibility
and
Yt =
i$@Pit- DPt)*
(2)
7
in which Dx, = logx, - logx,_r and k is the number of commodities. However, the authors are not clear about what has been proven by juxtaposing the timeseries of (1) and (2). On the one hand it seems that the relation between the general price change DPt and the dispersion of the relative price changes yr is at issue. The only evidence given consists in the visual inspection of their graphs (of which moreover the first one contains two mistakes). The product moment correlation of DPt and yt can be calculated from their tables. The values are 0.301 for the WPI and 0.223 for the CPI. On the other hand the authors talk about instability of the general price change and about changes in y* as well. However, they do not specify these notions precisely Now let us call the general price change stable if DPt = DP,_, . Then instability of the general price change means that (DP, - DPt_l ( # 0. From this point of view we have computed some product moment correlations from Vining and Elwertowski’s tables 1 and 2. (See our table 1.) In both cases there appears to be a close connection between yr, the relative price change dispersion, and lDPr - DP,_l I, measuring the instability of the general price change. Now, apart from a constant factor, lDPt - DP,_l( agrees with the socalled unanticipated rate of inflation defined by Parks (1978) who also noted the lack of precision in Vining and Elwertowski’s paper. Parks performed calculations on a very high level of aggregation, using price indices for 12 groups of commodities from the U.S. Personal Consumption Expenditure category of the National Accounts. From his table 3 I have calculated two product moment correlations for the period 1948-l 975. They have been included in table 1. Although the latter correlation is somewhat smaller than in the case of Vining and Elwertowski’s data it does confirm the conclusion of a connection between 7r and IDP, - DP,_l I. However, when we now consider the Dutch experience the picture changes. Table 1 Product moment
correlations:
USA. Vining and Elwertowski WPI
CPI
0.301
0.223
0.757
0.229
0.804
0.694
Parks
_ DP, and yt IDPr - DPt_l
I and Iyy - ~~-1 I
IDP, - DP,__II and yr
0.435
_
0.615
B.M. Balk /Inflation and its variability
359
2. The Dutch case The following forms part of a larger study of the Dutch inflation from 1952 to 1975 about which is reported in Balk, Van Driel and Van Ravenzwaaij (1978). The data consisted of 235 series of monthly commodity price index numbers from January 1952 to December 1975 inclusive, with base 1951 = 100. The group of 235 commodities contained 141 commodities from the Consumer Price Index and 94 commodities from the former Wholesale Price Index. They were selected because for them unbroken series of price index numbers were available. For each of these series and for each year a growth rate was computed by means of a linear regression of the natural logarithms of the price index numbers (December-December) on the time. These (monthly) growth rates were transformed to compound annual growth rates. In this way we obtained 24 distributions of 235 growth rates, viz. for each of the years 1952-1975. Table 2 summarizes these distributions by means of the average growth rate and the standard deviation of the growth rates. Unmistakably there is some connection between the average growth rate G,, measuring the general price change, and the standard deviation S, of the growth rates, measuring the dispersion of the relative price changes. Computation of the obvious, product moment correlations yields the following result: The product moment correlation between G, and S, is 0.62 while between lGt - G,__r I and S, it only amounts to 0.52. The difference between this result and the corresponding correlations in table 1 will be clear. The connection between the general price change and the dispersion
Table 2 Characteristics of distributions of price changes: The Netherlands. ___-
1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963
Average growth rate
Standard deviation
Average growth rate
Standard deviation
(%I
(%I
(%I
(%I
-1.2 -0.9 3.1 -1.4 3.7 2.7 0.2 1.9 -0.7 0.6 2.1 2.9
11.8 1.3 11.0 9.4 13.0 10.6 6.9 8.2 8.7 6.4 9.5 7.7
4.9 4.1 4.2 2.9 3.0 3.4 5.1 5.3 6.7 8.7 13.1 7.3
8.0 8.8 6.8 6.7 7.8 7.9 9.9 9.1 12.1 17.1 15.3 11.4
1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975
360
of the relative price changes is stronger than in the U.S. case. I have no explanation for this different behaviour. It would be useful to collect the same type of data for other countries and study the relationships. There is another point deserving some attention. Vining and Elwertowski remark that ‘the shape of the distribution of individual price changes .. . is in fact highly variable and almost never of normal and infrequently of even symmetrical form’. Now the use of only average growth rate and standard deviation as measures characterizing the subsequent distributions presupposes that the distributions are considered as belonging to one family and the relation between the corresponding stochastic variables as being a linear one. In the Dutch case this presupposition was tested by means of methods developed by Wilk and Gnanadesikan (1968). The presupposition appeared to be unwarranted, as could be expected. It is, however, reassuring to see that the use of more robust estimators for location and dispersion of the distributions of growth rates confirms the picture shown in the tables of the present section.
References Balk, B.M., G.J. van Driel and C. van Ravenzwaaij, 1978, Inflation in the Netherlands from 1952 to 1975 (Dutch with extensive English summary), Statistical Essays M4 (Staatsuitgeverij, The Hague). Foster, E., 1978, The variability of inflation, Review of Economics and Statistics LX, 346-350. Glejser, H., 1965, Inflation, productivity and relative prices - A statistical study, Review of Economics and Statistics XLVII, 76-80. Parks, R.W., 1978, Inflation and relative price variability, Journal of Political Economy 86, 79-95. Vining Jr., D.R. and Th.C. Elwertowski, 1976, The relationship between relative prices and the general price level, American Economic Review 66, 699-708. Wilk, M.B. and R. Gnanadesikan, 1968, Probability plotting methods for the analysis of data, Biometrika 55, 1-17.
INFLATION AND ITS VARIABILITY Some Comments and the Dutch Case B.M. BALK Netherlands
Central Bureau of Statistics, Voorburg,
The Netherlands
Received January 1979
Some results concerning the rate and variability of inflation in the Netherlands during the period 1952-1975 are presented and contrasted with similar results for the U.S.A.
1. Introduction During the last few years some interest in the variability of inflation has been shown. This subject can be pursued in two directions. A representative of the first direction is Foster (1978), reviewing and extending earlier work. He clearly demonstrates the close connection between the average rate of inflation, measured by means of some aggregate price index, and the variability of this inflation, measured by the average change in the rate of inflation, which a country experiences during a certain period of time. Thus a higher average rate of inflation means more variability of this rate. An early representative of the second direction is Glejser (1965). He very clearly states the usual point of view on this subject: ‘Inflation is generally considered as a wave lifting the whole of prices to a higher level without altering significantly the respective position of each of them, at least in the long run.’ In his paper he presents evidence contradicting this usual point of view. His cross-country study reveals a positive correlation between the magnitude of average relative price variability and the average rate of inflation. Two more recent contributions however, deal with this subject by means of a time-series analysis. Vining and Elwertowski (1976) try to show that ‘the behavior of the general price level is related in a statistically systematic manner to the behavior of individual prices relative to each other’. They work at a very low level of aggregation using price indices from the U.S. Wholesale Price Index and Consumer Price Index at the item level. Let pit be the price (or price index) of commodity i in year t. For each of the years 1948 to 1974 inclusive, they calculate k
351
358
B.M. Balk /Inflation
and its vartibility
and
Yt =
i$@Pit- DPt)*
(2)
7
in which Dx, = logx, - logx,_r and k is the number of commodities. However, the authors are not clear about what has been proven by juxtaposing the timeseries of (1) and (2). On the one hand it seems that the relation between the general price change DPt and the dispersion of the relative price changes yr is at issue. The only evidence given consists in the visual inspection of their graphs (of which moreover the first one contains two mistakes). The product moment correlation of DPt and yt can be calculated from their tables. The values are 0.301 for the WPI and 0.223 for the CPI. On the other hand the authors talk about instability of the general price change and about changes in y* as well. However, they do not specify these notions precisely Now let us call the general price change stable if DPt = DP,_, . Then instability of the general price change means that (DP, - DPt_l ( # 0. From this point of view we have computed some product moment correlations from Vining and Elwertowski’s tables 1 and 2. (See our table 1.) In both cases there appears to be a close connection between yr, the relative price change dispersion, and lDPr - DP,_l I, measuring the instability of the general price change. Now, apart from a constant factor, lDPt - DP,_l( agrees with the socalled unanticipated rate of inflation defined by Parks (1978) who also noted the lack of precision in Vining and Elwertowski’s paper. Parks performed calculations on a very high level of aggregation, using price indices for 12 groups of commodities from the U.S. Personal Consumption Expenditure category of the National Accounts. From his table 3 I have calculated two product moment correlations for the period 1948-l 975. They have been included in table 1. Although the latter correlation is somewhat smaller than in the case of Vining and Elwertowski’s data it does confirm the conclusion of a connection between 7r and IDP, - DP,_l I. However, when we now consider the Dutch experience the picture changes. Table 1 Product moment
correlations:
USA. Vining and Elwertowski WPI
CPI
0.301
0.223
0.757
0.229
0.804
0.694
Parks
_ DP, and yt IDPr - DPt_l
I and Iyy - ~~-1 I
IDP, - DP,__II and yr
0.435
_
0.615
B.M. Balk /Inflation and its variability
359
2. The Dutch case The following forms part of a larger study of the Dutch inflation from 1952 to 1975 about which is reported in Balk, Van Driel and Van Ravenzwaaij (1978). The data consisted of 235 series of monthly commodity price index numbers from January 1952 to December 1975 inclusive, with base 1951 = 100. The group of 235 commodities contained 141 commodities from the Consumer Price Index and 94 commodities from the former Wholesale Price Index. They were selected because for them unbroken series of price index numbers were available. For each of these series and for each year a growth rate was computed by means of a linear regression of the natural logarithms of the price index numbers (December-December) on the time. These (monthly) growth rates were transformed to compound annual growth rates. In this way we obtained 24 distributions of 235 growth rates, viz. for each of the years 1952-1975. Table 2 summarizes these distributions by means of the average growth rate and the standard deviation of the growth rates. Unmistakably there is some connection between the average growth rate G,, measuring the general price change, and the standard deviation S, of the growth rates, measuring the dispersion of the relative price changes. Computation of the obvious, product moment correlations yields the following result: The product moment correlation between G, and S, is 0.62 while between lGt - G,__r I and S, it only amounts to 0.52. The difference between this result and the corresponding correlations in table 1 will be clear. The connection between the general price change and the dispersion
Table 2 Characteristics of distributions of price changes: The Netherlands. ___-
1952 1953 1954 1955 1956 1957 1958 1959 1960 1961 1962 1963
Average growth rate
Standard deviation
Average growth rate
Standard deviation
(%I
(%I
(%I
(%I
-1.2 -0.9 3.1 -1.4 3.7 2.7 0.2 1.9 -0.7 0.6 2.1 2.9
11.8 1.3 11.0 9.4 13.0 10.6 6.9 8.2 8.7 6.4 9.5 7.7
4.9 4.1 4.2 2.9 3.0 3.4 5.1 5.3 6.7 8.7 13.1 7.3
8.0 8.8 6.8 6.7 7.8 7.9 9.9 9.1 12.1 17.1 15.3 11.4
1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975
360
of the relative price changes is stronger than in the U.S. case. I have no explanation for this different behaviour. It would be useful to collect the same type of data for other countries and study the relationships. There is another point deserving some attention. Vining and Elwertowski remark that ‘the shape of the distribution of individual price changes .. . is in fact highly variable and almost never of normal and infrequently of even symmetrical form’. Now the use of only average growth rate and standard deviation as measures characterizing the subsequent distributions presupposes that the distributions are considered as belonging to one family and the relation between the corresponding stochastic variables as being a linear one. In the Dutch case this presupposition was tested by means of methods developed by Wilk and Gnanadesikan (1968). The presupposition appeared to be unwarranted, as could be expected. It is, however, reassuring to see that the use of more robust estimators for location and dispersion of the distributions of growth rates confirms the picture shown in the tables of the present section.
References Balk, B.M., G.J. van Driel and C. van Ravenzwaaij, 1978, Inflation in the Netherlands from 1952 to 1975 (Dutch with extensive English summary), Statistical Essays M4 (Staatsuitgeverij, The Hague). Foster, E., 1978, The variability of inflation, Review of Economics and Statistics LX, 346-350. Glejser, H., 1965, Inflation, productivity and relative prices - A statistical study, Review of Economics and Statistics XLVII, 76-80. Parks, R.W., 1978, Inflation and relative price variability, Journal of Political Economy 86, 79-95. Vining Jr., D.R. and Th.C. Elwertowski, 1976, The relationship between relative prices and the general price level, American Economic Review 66, 699-708. Wilk, M.B. and R. Gnanadesikan, 1968, Probability plotting methods for the analysis of data, Biometrika 55, 1-17.