108 THE ECONOMIC ReCORD APRIL

ment; part of it is replacement. It seems to me quite natural to speak of the excess of replacement cost over historic cost of a piece of mec- can0 as “absorbing saving”, and I should regard the Wicksell effect as being measured by the excess of the wages cost of the replacement at the date when it is made over what it would have been if the wage rate were still the same as at the date when this particular piece of meccano was constructed.

In any case, i t is the actual replacement cost of capital goods that matters. A ‘‘revaluation of inventories’’ neither absorbs savings nor provides fmance for replacement.

When we have to get on without the idea of pieces of meccano this simple way of dealing with the problem will not work. My scheme of analysis is intended to make it possible to discuss accumulation in spite of the fact that capital cannot be measured in physical units, but it is evidently not very easy to follow and I feel that I owe Professor Swan (and any other readers I may have) an apology for causing so much trouble. I can only plead that I was doing my best. It is not really my fault that capital does not consist of pieces of meccano.

Jom ROBINSON Cambridge.

AN AUSTRALIAN CONSUMPTION FUNCTION’

The favourite child of Keynesian econometrics, the consumption function, has everywhere let down its admirers. In Australia, the ratio of consumption to personal disposable incomes (at current prices) has varied in the post-war years between 79 per cent and 90 per cent. The year-to-year variations have been much too large to make this func- tional relationship a reliable tool for forecasting. Conversion of the function into real terms, with all the price-index snags which this en: counters, does not appreciably improve the situation. Can anythmg be done about this?

It has frequently been noticed that the variations in the ratio of consumption to personal disposable incomes in Australia are closely related to year-to-year fluctuations in the incomes of farmers. This appears to reflect a tendency of farmers not to adjust their current consumption expenditure to the large short-term fluctuations in their incomes. Perhaps the simplest hypothesis on these lines is to assume that consumption ( C ) is related, not to total personal disposable in- comes (PDI) but to non-farm disposable incomes (WDI).’

We are indebted to Dr. C. E. V. Leser, who kindly carried out the statistical computations for this note.

1. In either case, disposable income is here obtained by subtracting from income the relevant personal income taxes (excluding estate and gift duties)-in the one case all personal income taxes are subtracted to obtain PDI, in the other personal income taxes paid by the non-farm sector are subtracted to obtain NFDI.

No breakdown of personal income tax between farmers and non-farmers is published. Non-farm income tax for the post-war years has been estimated from data published in the National Incomr White Paper, the Reports of the Commissioner of Taxation, and (for 1954/5 and 1955/6) from the Commonwealth Budget Papers. It has been assumed that the shares of the two sectors in total income tax paid in

1957 AN AUSTRALIAN CONSUMPTION FUNCTION 109

Table I compares the ratio of C to NFDI with the ratio of C to P D I fo r the post-war years. It appears that the ratio of C to NFDI not only is a good deal more stable but also happens to be very close to unity. We are tempted to proclaim, as an empirical law for the Aus- tralian economy, that conslimption equals no-farm dhposable incomes. More soberly, the regression line for the function (data from Table

C = 67.9 + 0.9598 (NFDI).

consumption function which suggest themselves :

I) is

The rest of this note deals briefly with five questions about this

(a ) How can we account for it? (b) How stable is it? (c) Does i t hold for the pre-war as well as for the post-mar yearst (d) What is its form in real terms? (e) Of what practical use is it T

(a ) A stable relationship between total consumption and non- farm disposable incomes can plausibly be rationalized by asking what determines consumption expenditure by farmers if i t is not governed by current farm incomes. It is not unreasonable t o suppose that farm- ers’ consumption levels are in various ways (such a s direct personal contacts, availability of goods and services, advertising) influenced by consumption levels in the rest of the community.2 If farm consumption is a function of non-farm consumption, which in turn is a function of non-farm disposable incomes, total consumption will be a function of non-farm disposable incomes.

It has sometimes been suggested that farm consumption follows farm incomes with a time lag. Various lags have been tested: that current farm consumption is a function of last year’s farm incomes, of the average of this year’s and last year’s farm incomes, or of the average of this year’s and the preceding two (or three) years’ farm incomes. Each of these gives, a distinctly less good fit than the thesis that farm consumption is a function of current non-farm disposable incomes. It seems not unlikely, however, (though the available data are inadequate to test this) that farm investment, including expendi- ture on durables such as cars, moves with current farm incomes, or follows them with a lag.

any year are proportionate to the ratio of the incomes of the two sectors in the pre. ceding year weighted by the average tax rates applied to each sector (in the pre- ceding year).

For the pre-war years, the data needed for this method of estimate are not available. Since income tax rates were lower and varied less, it has been thought sufficient to divide total income tax paid in the ratio of farm to non-farm incomes given by H. P. Brown, Economic Record, 1949.

2. Mr. J. G. Crawford has pointed out to us another possible influence of non- farm on farm consumption standards. Government measures of aid to farmers during the ’thirties were explicitly based on the principle that farqeFs were entitled to an income which would enable them to maintain a standard of .lmng (excluding luxury expenditure) comparable to standards prevailing among clty people. E

TA

BL

E I

1.34

6 16

4 1,

191

165

1.18

0 13

2 1,

048

1.06

9 -8

98

1-02

1. 2. 3.

4. 6. 6. 7. 8.

c

1.62

2 16

2 1,

460

261

1,36

1 13

1 1,

230

1.26

1 -8

64

1.02

5

fm.

Pers

onal

inc

ome

. . ..

..

..

Pe

rson

al in

com

e ta

x . .

..

..

Pers

onal

dis

posa

ble

inco

me

. . ..

In

com

e of

far

mer

s . .

..

..

.. N

on-f

arm

inco

mes

..

..

..

Pers

onal

non

-far

m in

com

e ta

x . .

..

Nan

-far

m d

ispo

sabl

e in

com

e . .

..

Pers

onal

con

sum

ptio

n . .

..

...

C +

PDI

.. ..

..

..

..

C

+ N

FD

I . .

..

..

..

..

1.90

0 19

8 ,7

02

323

,677

14

6 ,4

32

,464

-86

1-02

2

19

46

1

I 1941

-8

2,20

4 2.

897

194

351

2.01

0 2,

646

423

700

1,78

1 2,

197

128

164

1.66

3 2,

043

1,66

1 2,

018

*826

a7

93

1.00

5 -9

87

19-

1 1949

-SO

I 1

950-

1 19

51-2

3,21

4 39

9 2,

815

626

2,08

8 23

6 2,

462

2,38

0 ,8

46

47

1

I 19

54-5

3,82

7 36

1 3.

466

463

3.37

4 26

6 3.

119

3.07

9 -8

88

-087

4.07

9 38

7 3.

692

(406

) (3

.673

) 30

4 (3

.369

) (3

.324

) 4

-987

Figu

res

in g

ener

al a

re f

rom

the

Naf

ionu

l hco

rne

ond

Er)

endi

fure

Whi

te

Pape

r, 1

955-

6. H

owev

er,

data

for

194

6-7

and

1947

-8 a

re f

rom

th

e 19

54-5

Whi

te P

aper

. Per

sona

l co

nsum

ptio

n in

clud

es p

riva

te r

emitt

ance

s ov

erse

as.

Ref

er t

o fo

otno

te 1

.

1957 AN AUSTRALIAN CONSUMPTION FUNCTION 111

/450

(b) How good a fit does the proposed function give, compared with say the P D I function? Since each of the series C , NFDI and P D I rose rapidly after 1946/7, i t is clear that the correlation between any pair of them will be high. We can overcome this difficulty by tak- ing the regression of year-to-year changes in consumption on year-to- year changes in income. Here the relation between changes in C and changes in NFDI yields a correlation coefficient of 0.36 for the rela- tion between changes in C and changes in PDI.

5.000 -

/ CONSUMPTION

Srn.

-

3,000 - /

# 53

N.F.D.I. - P.D.I. ----

Em. INCOMES

1 coo I I 1,000 3,000 5,000

CHART I

The correlation of C with NFDI, though very good, is not perfect. As Chart I shows, consumption was relatively high in 1946/7, 1947/8 and 1948/9 and relatively low in 1951/2 and 1952/3. On the principle of econometric gamesmanship that one improves the fit of a curve by “explaining” the deviation^,^ one might point out that 1946/7, 1947/8 and 1948/9 were post-war years in which liqnid asset holdings were still abnormally high, while the low figures for 1951/2 and 1952/3 might be accounted for on the hypothesis that Australian consumers

3. Cf. R. Dorfrnan, “The Nature and Significance of Input-Output”, Review of Economics and Statistics, May 1954, p. 129.

112 THE ECONOMIC RECOaD APBIL

as a group spend less, out of a given income, if their income is falling than if it is rising.'

(c) The hypothesis that consumption in Australia is a function of non-farm disposable incomes fits the data for the pre-war decade (1928/9-1937/8) as well as for the post-war decade (Table 11, Chart 11). But the result is less impressive because, for the 'thirties, the conventional consumption function also works well. (The correlation

800

700

600

500

CONSUMPTION. fm. /

N.F.D.I. - P.D.I. -- - -

INCOMES fm.

400 500. 800 700

CHART I1

coefficients, even for the relation between year-to-year changes, are almost identical: 0.99 for changes in C on changes in NFDI; 0.97 for changes in C on changes in PDI.) The approximate post-war equality C = NFDI, however, does not hold for the pre-war decade, as the re- gression line of consumption on non-farm disposable income

C = 0.8 + 1.0473 (NFDI) 4. Such a hypothesis also fits the low red consumption levels of 1!X9/30 and

1930/1 (Chart 111). It is only fair to add, however. that the ob?emtions fpr 1951/2, 1929/30 and 1930/1 might also be explained by the hypothesis that the income of farmers docs exercise some influence on farm consumption-for farm incomes were falling in these years relatively to other incomes.

-

1.

2. 3.

4. 6.

6.

7.

8.

1930-1

667 19

63

8 30

627 18

60

0 62

2 43

70

1.02

6

fm.

Pers

onal

inc

ome

. .

..

..

Pers

onal

iuc

ome

tax

. .

..

Pers

onal

dis

posa

ble

inco

me

. .

Inco

me

of fa

rmer

s ..

..

N

on-f

arm

inc

omes

. .

..

..

Pers

onal

non

-far

m i

ncom

e ta

x . .

Non

-far

m d

koos

able

inco

me

. .

1931-2

-~

63

1

21

61

0 40

401 10

47

2 40

4 -0

60

1.04

7

Pers

onal

con

ium

ptio

n . .

..

Ci PD

I ..

..

..

..

C

-+ N

FD

I . .

..

..

..

748 12

73

6 00

640 10

630

667

~8

03

1.

028

191&9

I 1929-30

681 12

66

0 60

621 11

610

636

-861

1.

043

725 23

70

2 11

1 61

4 19

696

021

a893

1.

064

TA

BL

E I1

768 24

74

4 10

7 66

1 2

1

640

006

a805

1.

041

606

634

.932

1.

057

1932-s

622

644

-038

1.

042

642 22

62

0 46

407 20

47

1 60

0 4

62

1.

048

20

670 22

048 86

686 10

66

6 60

1

41

2

1.04

4

1936

-7

I 1937-8

Pers

onal

inc

omes

are

fro

m H

. P.

Bro

wn

in E

.R.

1949

, an

d pe

rson

al c

onsu

mpt

ion

is f

rom

an MS.

by H

. P.

Brown.

Inco

me

of f

arm

ers

is

obta

ined

by

usin

g %

fig

ures

in

H.

P. Brown

E.R

. 19

49 f

or f

arm

inc

ome.

Per

sona

l in

com

e ta

x is

obt

aine

d fr

om a

n an

alys

is o

f G

over

nmen

t ac

coun

ts.

Ref

er a

lso

to f

ootn

ote

1.

w

w

w

114 THE ECONOXIC RECORD APRIL

shows. The ratio of consumption to non-farm disposable incomes was stable a t about 1.05 rather than unity, suggesting that the function has since shifted downwards (or is curvilinear).

(d) I n order t o esplore this apparent downward shift further, it is necessary to convert the C = c (NFDI) function into real terms, since the slope of the function in money terms will have been distorted by the post-war ida t ion . Chart I11 shows the relation between con- sumption and non-fgrm disposable incomes, both deflated by the C-

3,a

2,N

1 .oo 1 .GQa

CONSUMPTION fm. 1953-4 PRICES

41

/ 38/

J NON-FARM DISPOSABLE INCOMES h. 1953-4 PRICES

3,000

series index. (There is no need to enter here upon the merits and de- merits of alternative deflators ; almost any alternative deflator avail- able will give a rather lower marginal propensity to consume since other indices, such as the wholesale price index, have risen more sharply than the C-series in the post-war period.) The pre-war decade gives a regression line of

The post-war period gives a regression line of C = -40.8 + 1.071 (NFDI).

C = 288.2 + 0.8875 (NFDI).

1957 AN AUSTRALIAN CONSUMPTION FUNCTION 115

By comparison, the regression line for the twenty years is C = 160.8 + 0.9342 ("FDI).6

These relations support the suggestion that the consumption function has shifted downward, a shift for which post-war pressures towards voluntary and involuntary personal saving may be the explanation.

(e) Of what practical use is an Australian consumption function of the form C = a + c (NFDI) (or, more boldly, C = NFDI) ? Con- sumption has hitherto. proved one of the most precarious components of market demand to forecast from year to year. The hypothesis here put forward does not solve the problem. Bu t if confirmed it would mean that, given an independent estimate of market supplies, and of gross private investment, government espenditure and exports, the large residual component of consumption (small errors in the forecast of which make a great deal of difference to the result) can be fairly accurately forecast provided we have a reasonable idea of non-farm incomes (from our estimate of domestic full employment output and wages rates) and of income tax on these non-farm incomes.

H. W. .ARNDT BURQZCS CAXERON.

5. The correlation coefficients for these three regression lines (not first differ- ences) are 0.9952, 0.9926 and 0.9988 respectively.