Australian Price Changes : Consumer and Capital Goods

I

Differential trends in the prices of products purchased by major sectors of the economy have important analytic implications as has been demonstrated by Professor Gordon1 using simple two-sector models. Empirical evidence for a number of economies, not including Australia, shows some divergence of experience in the period since World War 11, and it is desirable to examine the Australian case for which the necessary data may now be derived from the national accounts. Formal statistical tests of trend are the more essential because of the brevity of the series. Of the two types of test applied below, one is based upon the number of positive first differences and the other upon ranks of observations ; both are distribution-free tests of randomness. Since longer series can be constructed only by splicing together short series, it is of some interest to consider the effect of standard splicing techniques upon evidence of trend. One of the topics to be discussed, therefore, is the result of an experiment with splicing methods. More complex analytical models require the disaggregation of major sectors and, fo r this reason, it is worth exploring, to the extent of articulation feasible with the present form of the national accounts, what evidence exists of differential trends in subsectoral prices. In order to keep the study within reasonable bounds, questions relating to the structure of the derived price indices, the justification of the level of aggregation, o r the possibility of inherently time-related bias in the method of measurement of some prices, will not be discussed although such questions are relevant and important.

Before proceeding to the analysis of the Australian data it will be useful to summarize, very briefly, some of the main consequences of the explicit introduction of sectoral prices in two-sector models and the nature of available empirical evidence relating t o other economies. Let Pkn, P,, and P , denote, respectively, the price of capital goods, the price of consumption goods, and the general level of prices (a weighted average of the former two prices), measured for year TL relative to some base year. Adopting a simple Keynesian model with a linear real consumption function, constant over time, having

1 R. A. Gordon, ‘Differential Changes in the Prices of Consumers’ and Capital Goods’, American Economic Review, Vol. LI, December 1961.

412

SEPT., 1967 AUSTRALIAN PRICE CHANQES 413 the marginal real propensity to consume in the base year denoted by a, Gordon shows the investment multiplier in year n to be (Pkn/Pn) (I/ (1 - a ) ) . The government expenditure multiplier would require a similar adjustment if articulation of private and government sectors were adopted. Using a simple Harrod-Domar growth model with real base-year accelerator v and marginal propensity to save s, and assuming v independent of Pk/P, Gordon shows the equilibrium rate of growth for year n to be (pn/Pkn)(s /v) . With a two-input aggregate production function P, and a constant-price gross rental per capital unit r, he shows the necessary equilibrium condition with respect to capital stock, K, t o be L+B’/dIZ = r(Pkn/Pn). The policy implications are far-reaching: a secular rise in Pkn/P,, signifies a gradual erosion of the automatic stabilizers, the lowering of the equilibrium rate of growth of output, and a tendency to a falling capital-output ratio which may be effected by the adoption of capital- saving techniques. A full discussion of these and other implications is provided by Gordon.2

Professor Kuznets3 appears to have been the first to produce evidence of a secular rise in Pk/Po (and, hence, in Pk/P) in a number of countries. His data show such secular rise in the United States, Norway, Denmark, the United Eingdom, and Germany. The only country shown by his data t o have been an exception is Italy. Gordon4 extends the evidence of such secular rise in the United States, the United Kingdom, Canada, Sweden, and Denmark. In the last two countries the trend appears to die out in the 1930s. Gordon also examines O.E.E.C. evidence5 for a group of ten European countries in the post-war era; of these, in the period 1953-59, four displayed an upward trend in Pk/Pc, and a11 displayed an upward trend in P, /P , where P, denotes the price of government services. However, the only series f o r Pk/P, available in detail over a long period, namely that for the United States, exhibits, in addition t o the upward secular trend, a rather marked cycle of the Kuznets variety of about twenty years duration. This may be no more than a manifestation of the Slutsky effect, but since it appears, and there is some hint of it also in the Scandinavian data, the hypothesis that an upward trend in the relative price of capital goods has occurred in virtually all market economies during the post-war period cannot be dismissed with any degree of confidence without substantially more information.

2 Other writers who have considered changes in P,/P include : J. R. Hicks, A Contribution to the Theory of the Trade Cycle (Oxford University Press, London, 1950) ; W. E. G. Salter, Productivity and Technical Change (Cambridge University Press, London, 1960); J. E. Meade, A Neo-Classical Theory of Economic Growth (Allen and Unwin, London, 1960) ; H. A. J. Green, ‘Embodied Progress, Investment and Growth‘, American Economic Review, Vol. LVI, March 1966.

3 S. Kuznets, ‘Quantitative Aspects of the Economic Growth of Nations: VI. Long Term Trends in Capital Formation Proportions’, Economic Development and Cultural Change, Vol. IX, July 1961.

4 Op. cit. 5 W. Fellner et al., The Problem of Rising Prices (O.E.E.C., Paris, 1961).

414 THE ECONOMIC RECORD SEPT.

I I Current-price and constant-price series for expenditure by major

sectors of the Australian economy are now available for the period 1948-49 to 1964-65. From these may be derived the implicit price indices f o r gross national expenditure components on the base 1953-54 f o r the period 1948-49 to 1959-60, and on the base 1959-60 for the period 1953-54 to 196465. Annual estimates of the ratios Pk/P , and PB/Po may then be obtained in the form of two overlapping twelve- year series extending over a total of seventeen years; these implicit price indices and estimated ratios are shown in Table I. Seventeen

T~BLE I

Gross national

expenditure

ExpemcEn'ture Deflators for Major Sectors

Ratio of capital to

consumer goods prices

( P ~ / P , ) 1 0 0

Year

54.8 60.3 73.2 87.8

Personal consumption

pc

68.4 64.2 74.9 88.8

Financial enterprises and public authorities

current expenditure

pg

113.7

118.1 121.9 121.7 132.7

Gross fixed

capital

pk

108.2

112.8 114.8 116.4 119.0

76.6 78.9 86.7 88.6

90.7 91-6

100.0 103.7

108.3 108.2 114.3 119.5

1948-49 1949-50 1950-51 1951-62

1952-53

1954-56 1953-54

1955-56

1956-57 1957-58 1958-59 1959-60

83.6 86.2 90.5 93.3

96-4 97.7

100.0 103.3

105.7 106.6 108.7 112.5

60-4 65.4 74.4 89-6

97.6 100.0 101.7 106.2

112.2 113.7 115-6 118.2

1953-54 1954-56 1955-56 1956-57

1957-58 1958-69 1959-60 1960-61

1961-62

1963-64 1964-65

1962-63

83.4 86.2 89.1 94.0

96-4 97.3

100.0 104.1

104-9 105.6 108- 1 112.0

1953-54 = 100

59.3 65.0 74.5 89-2

9774 100.0 102.3 107.4

113.1 115.0 115.6 119.9

1959-60 = 100

96.7 98.1

100.6 99-1

99.6 100.0 101.2 101.9

100.4 101.0 100.8 100.7

82.6

89.0 93.2

95.0 96.6

100.0 103.8

105.3 106-0 109.0 112-8

84.8 100.3 101 * 1 101.6 99.2

101.0 100.4 100.0 99.3

100.8 101.1 100.6 100.6

Ratio of government to consumer goods

prices

90.8 92-2 98.4 98.0

99.6 100.0 103.4 107.1

105.2 107.2 105.4 112.3

90.7 92.6 96.2 94.1

95.0 94.1

100.0 99.6

101.3 102.6 105.8 106-7

Source: Commonwealth Statistician, Australian National Accounts, 1948-49 to 1964-66 (Canberra, 1966), Tables 10 and 11.

1967 AUSTRALIAN PRICE CHANQES 415 years of observations might provide a sufficiently long series to show trend, even if such trend is complicated by a Kuznets cycle, but in point of fact a series of seventeen directly comparable observations may be constructed only by splicing two shorter series and this is postponed for later discussion. Inspection reveals the appearance of a marked upward trend in the ratio €',/Po both in the earlier series and in the later. The rise, of the order of 18 per cent in the first ten years and of 11 per cent in the last ten years, seems very large compared with rises observed in the United States. It will be observed that the two series for P,/P, are perfectly consistent in showing the direction of change during the considerable period for which they overlap; it is this consistency which permits the treatment of the P,/P,, series as a single sequence of signs of first differences to which the Moore and Wallis sign test may be applied. The extent of variation from year to year seems sufficiently large at times to have fairly serious implications fo r short-term policy if the direction of change is unpredictable. The evidence of trend in the P J J P ~ series appears much slighter ; over the first ten years the ratio rose by about four per cent, and over the last ten years perhaps fell by one per cent. For this ratio also the two series are consistent in the period of overlap with regard to the direction of change ; the two series for Pk/P, may therefore be regarded as a single sequence of signs of first differences.

The data do not provide seventeen directly comparable estimates of the two ratios but do provide f o r each ratio a single sequence of signs of first differences for a series of seventeen observations. Consider now a series of m distinct observations; the total number of per- mutations is m ! and the number of theae permutations producing exactly d positive differences is a function of d, say fm(d). Hence, the probability of exactly d positive differences is fm(d)/m!. For m > 12 the distribution of d is approximately normal and a test of randomness in a time series based upon d, the number of positive differences, may be carried out by treating as a standard normal variate

F o r the ratio Pk/Pc, the number of positive differences is nine, and hence z = &0.41. As the probability of a value greater numerically than this is very large, the hypothesis of randomness is accepted. There is no evidence, as far as the sign test goes, of a trend in the relative price of capital goods. Applying the same procedure to the €',/Po series, the number of positive differences is found to be twelve and this gives z = k2.86. As the probability of a value numerically greater than this is less than one per cent, it may be concluded with a high degree of probability that there was an upward trend in the relative price of government services.s On the basis of the sign test

6 For an account of the Moore and Wallis sign test and further references, see E. S. Keeping, Introduction to Statistical Inference (Princeton University Press, Princeton, 1962).

z = 4[3 / (m+ 1)]1'2[[201- m f 11 - 11.

416 THE ECONOMIC RECORD SEPT.

i t may be concluded that the Australian economy shares with all other market economies thus far investigated a tendency fo r the relative price of government services to rise over time and that policy discussion could well profit from an explicit recognition of this tendency. On the other hand, as far as the sign test goes, Australia exhibits no significant tendency for the relative price of capital goods to rise over time.

It will be clear upon consideration that, despite the very small value of the standard normal variate obtained in testing Pk/P,, the result of the sign test in this case cannot be accepted as conclusive. A test based only upon the signs of first differences is not very sensitive in detecting trend where this is combined with a cycle. This is, of course, precisely the form of trend which the Kuznets-Gordon results suggest may pertain to the relative price of capital goods. Building up longer series of observations would not necessarily answer the case. However long the series, a cycle could result in a value of d close to E ( d ) in spite of a clear trend, although a sufficiently long series would have the advantage of permitting tests t o detect cycles. The alternative is to attempt a more sensitive test of trend.

A distribution-free test of randomness in a time series against a trend alternative is provided by Mann’s T-test based on the ranks of observations. Consider a time series (of distinct numbers) XI, Xz, . . . , XN. I f the series is random, all N ! permutations of the numbers are equally probable and the number of permutations containing exactly a given number of inequalities of the form X , < X , is count- able. Thus the probability that a sample contains a specified number of such inequalities can be determined. Mann therefore suggested a test for randomness in a time series against a downward trend alternative using

!r = s {&: i < j} +I, if X , < Xj, ( 0, otherwise,

and a critical region T < To such that P(T < To\ H,} = a, where Ho is the hypothesis of randomness, and a the size of the test. As Mann’s account‘ of the test for N 5 10 seems much the clearest avail- able, the test is reported below in its original form for such applica- tions. The test is more often applied to longer series where, since the distribution converges very rapidly to normality as N increases, a normal approximation may be used and this will be widely familiar in the form described by Kendall.8 In such applications below, the critical region of the test consists of values of Q exceeding

where htj =

Qo = N ( N - 1)/4 + z , (N(N - 1) ( 2 N + 5)/72)1/’

7 H. B. Mann, ‘Nonparametric Tests against Trend‘, Economctrica, Vol. XIII,

8 M. G. Kendall and A. Stuart, The Advulzccd Theory of Statistics (Griffin, July 1945.

London, 1961), Vol. 11, Ch. 31.

1967 AUSTRALIAN PRICE CHANGES 417

where z a i s the standardized normal variate appropriate for a test of size a and the sample statistic

Q = 8 {htj: i < j } +I, if x, > xj, ( 0, otherwise.

where htj =

The test is the same whether used in the Mann form or in the Kendall form. In the Mann form the decision that a significant down- ward trend exists is reached when it is found that there are too few upward movements from earlier years to later years to be attributable to pure chance, whereas in the Kendall form the decision that a significant downward trend exists is reached when it is found that there are too many downward movements from earlier years to later years to be attributable to pure chance. As all the numbers are assumed distinct, the two procedures are equivalent. In the account below, the notational difference will usefully distinguish applications of the exact form to short series (T) from applications of the normal approximation to longer series ( Q ) . Before proceeding to test, all ties were eliminated by carrying ratio estimates to one further decimal place than is shown in the tables. A test against an upward trend alternative is carried out by testing --XI, -Xz, . . . , -Xg against a downward trend alternative.

If splicing is not to be employed, some arbitrary selection of two consecutive series has to be made. In order to preserve the flavour of Kuznets’s methods, it was decided to treat the data in the form of two overlapping decades. Thus the series with base 1953-54 was used for the earlier decade running from 1948-49 to 1957-58 and the series with base 1959-60 was used for the later decade running from 1955-56 to 1964-65. Testing the Pk,/Pc series for the earlier decade against the alternative of upward trend, a value of T = 7 was obtained; as P{T 7) = 0.002 on the hypothesis of randomness, it may be con- cluded with a high degree of probability that the earlier decade shows a significant upward trend. Testing the Pk/Pc series for the later decade against the alternative of downward trend, the value of T = 22 is obtained. Since, under the hypothesis of randomness, E ( T ) = 22.5 for a series of ten observations, it may be concluded that in this series there is no evidence of trend. Accordingly it may be concluded from the Mann tests that, unless the change of weights associated with the change of base has considerably distorted the evidence, the Australian economy has experienced during the post-war years an upward trend in the relative price of capital goods, and conforms with the generaliza- tion that market economies are so characterized. On the other hand, the small magnitude of the rise and its association with the immediate post-war years give little support to the view that an explicit recog- nition of differential trends in the prices of capital and consumer goods would contribute much to the analysis of Australian growth and stabilization problems.

418 THE ECONOMIC RECORD SEPT.

I I I A natural next step in the inquiry, especially in view of the

deficiencies of sign tests, would be an attempt to construct a very much longer series of observations by the use of splicing. It is therefore relevant to inquire what effect standard splicing techniques may have upon evidence of trend. Different methods of splicing cannot affect the signs of first differences of the price indices spliced but may, none- the less, result in different sequences of signs of first differences in the Pk/P, ratio. A for t ior i , the ranking of observations will not remain invariant under different techniques of splicing. Two different tech- niques of splicing were adopted for the experiment; each of these methods is sufficiently standard to. be the only method described by an elementary text-the first method by Neter and Wasser- manQ and the second by Yarnane.lo Each of the differently based indices for Po, Pk, and P , was extended by use of the other by each of two methods of splicing and from these extended price indices eight different seventeen-year ratio series were constructed. The Mann test of randomness against an upward trend alternative was then applied to each of the extended ratio series. The results of the experiment are recorded in Table 11. It can be Seen that contradictory results are

TABLE I1 Results of M a m ’ s Test Applied to Extended Ratio Beries

Critical value for test of size 0.05 ( N = 17) Critical value for test of size 0.01 ( N = 17)

Q,, = 87.84 Q. = 96.19

Series extended Splicing method Q P, /P , base 1953-54 1 83

2 103 P , /P . base 1959-60 1 97

2 87 P, /Po base 1953-54 1 131

2 130 P,/P, base 1959-60 1 129

2 129

obtained in the case of the Pk/Pc series. If the 1953-54 base series is extended by the Neter-Wasserman method, there is no evidence of trend at the five per cent level of significance whereas if i t is extended by the Ya.mane method rather strong evidence of trend is obtained. On the other hand, if the 1959-60 base series is extended by the Neter- Wasserman method rather strong evidence of trend is obtained, whereas extension by the Yamane method leads to the conclusion of no significant trend at the five per cent level of significance. It is clear that ‘evidence of trend’ can be produced or suppressed a t will by

9 J. Neter and W. Wasserman, Fundamental Statistics for Business and Economics (Allyn and Bacon, New York, 1956).

1oT. Yamane, Statistics: A n Introductory Analysis (Harper and Row, New York, 1964).

1967 AUSTRALIAN PRICE CHANGES 419

appropriate choice of base and splicing method. In the case of the P,/P, series no such contradiction is obtained; where the sign test revealed evidence of trend, the choice of base and splicing method made little difference to the rank test result. Unless a genuine economic explanation fo r the apparent confusion could be found from a study of the change in weights, it would be preferable for further investigation to proceed in the direction of constructing a sufficiently long sign sequence for the Pk/P, series to permit both trend and cycle tests.

IT’ The disaggregation of the capital goods price index into separate

indices for producer durables and construction, which would allow interesting comparisons with the American economy, is unfortunately not permitted by the present form of the Australian accounts. The disaggregation that is possible is shown in Table I11 ; separate deflators

TABLE I11 Deflators f o r Xubsectors of Gross Fixed Capital Expenditure

Year

1948-49 1949-50 1950-51 195 1-52 1952-53

1953-54

1955-56

1957-58 1958-69 1959-60

1954-55

1956-57

1960-61 1961-62 1962-63

1964-65 1963-64

Public I Dwellings

953-54 = 101

59 64 74 87 96

100 103 109 112 113 115 118

84 87 91 92 96 97

100

104 108 110 113 118

67 64 76 88 96

100 105 112 117 118 118 121

359-60 - 10(

83 86 93 95 97 98

100

105 107 109 111 114

Other

>53-54 - lo( 58 64 76 91 99

100 102 107 112 115 117 119

959-60 - 100

84 85 89 93 97 98

100

103 103 104 105 108

Source: Commonwealth Statistician, Australian National Accounts, 1948-49

may be estimated for public gross fixed capital expenditure, dwellings, and ‘other’ gross fixed capital expenditure. Although the series on different bases are consistent in direction of change of sectoral prices in the period of overiap, a calculation of relative prices revealed the lack of consistency in direction of change of subsectoral relative prices. This means that the changes in weights associated with the change in base have more impact on the measurement of relative subsectoral prices than on the measurement of relative sector prices and this effect

to ,2964-65 (Canberra, 1966), Tables 10 and 11.

TDLE

IV

Def

lato

rs f

or

Con

sum

er G

oods

Tob

acco

R

ent

Oth

er

Food

C

loth

ing

Dur

able

s Y

ear

1953

-54

= 1

00

~

19

59

40

- 10

0 19

53-5

4 P

10

0 19

59-6

0 - 10

0 19

53-5

4 - 10

0 19

59-6

0 =

100

19

53-5

4 - 100

1959

-60

P 10

0 19

53-5

4 =

100

19

59-6

0 - 10

0 19

59-6

0 =

100

19

53-5

4 =

100

1948

-49

1949

-50

1950

-51

195 1

-52

1952

-53

1953

-54

1954

-55

1966

-66

1956

-57

1957

-58

1958

-59

1959

-60

1960

-61

1962

-63

1963

-64

19

66

65

19 6 1

-62

74

74

77

92

101

100

101

107

120

I21

122

123

58

67

77

93

99

100

100

101

103

106

107

108

63

68

79

94

98

100 99

104

107

110

108

110

73

76

79

83

93

100

112

120

129

137

147

156

53

58

69

89

97

100

101

106

110

108

110

113

61

66

75

88

97

100

102

106

113

115

116

119

kl a 0 3

82

5 93

z

95

0" 97

g

84

Q

87

100

88

89

93

97

95

97

100

107

104

103

105

111

92

93

94

95

98

99

100

102

103

103

104

106

80

82

87

97

98

99

100

101

103

103

103

108

90

89

93

96

97

97

100

101

102 99

100

100

66

73

78

84

89

95

100

110

117

125

133

139

103

105

105

108

112

Sour

ce:

Com

mon

wea

lth S

tatis

ticia

n, A

ustr

alia

% N

atio

nal

Acco

unts,

194

849

to 1

964-

65

(Can

berr

a, 1

966)

, Ta

ble

56.

1967 AUSTRALIAN PRICE CHANQES 421

might have been anticipated. The two differently based series of ratios cannot be treated as a single sequence of signs and it may be suffkient merely to inspect the index series. Inspection shows the rise in price in subsectors to be approximately the same, except perhaps for the final years when the price of publicly purchased fixed capital goods rose sharply compared with other capital goods. In all three sub- sectors, prices rose consistently throughout the period; there was no phase during which an absence of upward trend in the relative price of capital goods was associated with an absolute diminution in price of any category of fixed capital goods.

The consumer goods price index may be disaggregated as shown in Table IV. Unlike the separate categories of capital goods, the separate categories of consumer goods do show occasional absolute diminution of price and this is most marked in the case of household durables as would be expected. The major price ratios derived from the data of Table IV are shown in Table V. The ratio of rent to food

TABLE V Relative Prices of Ren t , Consumer Durables and Rood

Year

1948-49

Ratio of rent to food price

Ratio of consumer durables price to food price

1953-54- 100 1959-60 - 100 1953-54- 100 1959-60 = 100

138 118

1953-54 1954-55 1955-56 1956-57 1957-58 1958-69 1959-60

1949-50 1950-51 1951-52 1952-53

128 114 92 95

100 110 113 117 I 127

1960-6 1

1962-63 1963-64 196665

1961-62

133 138

I

75 82 84 87 93 97

100

103 113 122 127 126

I00 98 98 97

102 98 98

I

102 100 100 99 ..

102 100 100

96 98 96 95 90

price and the ratio of consumer durables price to food price exhibit that consistency between the differently based series which justifies the treatment of a relative price series as a single sign sequence. For the ratio of rent to food price, the number of positive differences is d = 12, giving z = 22.86, and it may be concluded with a high degree of probability that there was an upward trend in rent relative to food price over the post-war period. It may be observed that the immediate post-war years which showed a rise in the relative price of capital goods also show the only sustained fall in rent relative to

422 THE ECONOMIC RECORD SEPT., 1967

other prices. Thus the pattern of variation in the relative price of capital goods appears to have a close inverse association with the pattern of variation in rent relative to other consumer prices. A plausible explanation, therefore, why the upward trend in the relative price of capital goods is so much less pronounced than in other economies is that the Australian economy has experienced a much sharper and more persistent rise in rent relative to other prices. The ratio of consumer durables price to food price shows thirteen negative first differences (the tie being eliminated as before). This gives z = k3.68 , and it may be concluded with a high degree of probability that this series exhibits a downward trend. The contrast between the last two results strongly supports the view expressed above that a disaggregation among capital goods between construction and producer durables would be of considerable interest.

V It may be useful to summarize some of the main results of the

investigation. The treatment of the P,/P, series as a single sign sequence and the application of a simple sign test led to the con- clusion t,hat in the post-war period the Australian economy has experienced an upward trend in the relative price of government services. This confirms findings in other market economies and might usefully be taken into account in forward estimates of the government expenditure multiplier. The result of the application of the same procedure to the Pk/P , detected no trend but was held to be incon- clusive because of the suspicion that a cycle might be combined with the trend. The application of the Mann test to overlapping decades revealed the existence of an upward trend, provided it is assumed that the change of weights has not greatly distorted the evidence, but the rise was so slight and so much associated with immediately post-war years that explicit allowance for such trend is unlikely to contribute significantly to the analysis of Australian growth and stabilization problems. Subsectoral price indices revealed no markedly divergent trends in the relative prices of different capital goods; alternative forms of disaggregation are highly desirable. There was greater divergence in trends of prices of different consumer goods; the price of consumer durables showed a highly significant downward trend while rent showed a highly significant upward trend relative to food. This last result suggests a possible explanation why special features of Australian development should result in an upward trend in the relative price of capital goods being so much less obtrusive a tendency than in other market economies.

ESME PRESTON Monash University