The Australian Short-run Consumption Function

The Australian Short-run Consumption Function*

This paper provides an analysis of the quarterly behaviour of Australian consumption. After describing our data and our notation in Section 1, we start with a simple relationship between consumption and personal disposable income in Section 2, and analyse the effects of successive modifications in succeeding sections. Section 3 considers the effect of lagged consumption; Section 4 distinguishes between the marginal propensities to consume of farmers and non-farmers ; liquid assets are introduced in Section 5 ; in Section 6 the income and tax components of personal disposable income are separated out; and in Section 7 the significance of non-farm income before tax is analysed. The paper’s conclusions are presented in Section 8.

The analysis of the present paper differs in a number of ways from the recent quarterly consumption study by Norton and Broad- bent.l First, we use seasonally adjusted data whereas Korton and Broadbent use dummy variables to allow for seasonal variations. Secondly, we concentrate on aggregate consumption. Thirdly, we consider the effect on consumption of changes in the farm component of total income to allow for differences in the marginal propensities t o consume of farmers and non-farmers. Fourthly, we down-grade the importance of liquidity as a determinant of consumption. Finally, we disaggregate personal disposable income into two components, personal income before tax and income tax payable.

1. Data and Notation. Current price series, not seasonally adjusted, for consumption,

personal income, income tax payable, personal disposable income, farm income and non-farm income were all obtained from the Com- monwealth Statistician’s Quarterly E s t i m t e s of National Income and Expenditure. Our series for liquid assets, defined as notes and coin in the hands of the public, plus current and fixed deposits of the public with all trading banks, plus deposits with all savings banks,

*The authors are indebted to Mr M. Khan for research assistance, to Dr W. E. Norton and a referee for comments (though they should not be held re- sponsible for the final form of the paper), and to the State University of New York at Buffalo for financial support.

1W. E. Norton and J. R. Broadbent, Eqwtiotw f o r Personal Consumption Ezpenditure, Occasional Paper No. 38 (Reserve Bank of Australia, Sydney, March 1970).

220

JUNE, 1972 SHORT-RVN COXSUMPTION FUNCTIOOS 221 average of the weekly averages for the month preceding the current quarter, was obtained from the Reserve Bank of Australia’s monthly StatCstical Bulletin. The ‘All Groups’ consumer price index given in the Commonwealth Statistician’s Monthly Beview of Business Statistics was used as a deflator; all the series used are accordingly expressed in terms of $ million at 1952-53 prices. We then seasonally adjusted all the series using an additive method. The estimates in this study cover the period from the fourth quarter of 1958 t o the third quarter of 1968, inclusive.

Our notation is as follows: C = personal consumption expenditure, P = personal income, T = income tax payable, D = personal disposable income (= Y - 2’) , L = liquid assets for month preceding the current quarter, F = ratio of income of farm unincorporated enterprises t o personal income. The subscripts f and 7t indicate farm and non-farm respectkely, the subscript t relates to the marginal propensity t o consume out of income tax payable, and subscripts -1, -2, -3, . . , indicate 1, 2, 3, . . , periods before the current quarter. In the regressions the proportion of the variance of consumption explained is indicated by R2, the Durbin-Watson statistic by d, and the Durbin statistic by he2

2. Personal Dtkposable Income The obvious starting point in a short-run consumption study is

to make consumption a function of current disposable income. Thus we fit

C = a + b D . (1)

Because of the common time trend in consumption and personal disposable income we expect the correlation between the two to be high. The regression obtained is 1.1 in Table I.3 The constant term is significant at the 5 per cent level m d the marginal propensity to consume is highly significant. However, the Durbin-Watson statistic is 1.34 and this indicates serial correlation at the 5 per cent level. Regression 1.1 is therefore unsatisfactory.

3. Lagged Consumption We now introduce lagged consumption as an explanatory vari-

able, This may be justified by making consumption a distributed lag function of income, Suppose that consumption is a function not merely of income of the current quarter but also of income of previous quarters so that

C = a + b,,D + blD-l + b2D-2 + ... (2) 2 F o r a discussion of the applicability of the d and h statistics, see Section 3

below. 3 It is convenient to report the regression results in tabular form and re-

gressions are numbered by table and row in that table; for example, 2 . 3 indicates regression 3 in Table 11,

222 THE ECONOMIC RECORD JUNE

T~BLE I Australian 8hwt-vun Consumption Function Regressions

-- Regressi

no.

1.1

1.2

1.3

1.4

1.5

1.6

1-7

1.8

Constant

115.2 (50.5)

31.9 (28.6)

253.3 (30.3)

148.1 (38.8)

274.9 (41.4)

95.9 (48.6)

283.8 (30.2)

182.6 (48.6)

Coefficients and standard errors

D

0.848 (0.021)

0.186 (0.069)

0.854 (0.011)

0.492 (0.099)

0.352 (0.074)

0.174 (0.068)

0.653 (0.075)

0.466 (0.101)

C-1

0,786 (0.081)

0,427 (0,116)

0.626 (0.12 7)

0.345 (0.135) --

FD

-0’821 (0.083)

- 0.465 (0.12 1)

- 0.620 (0.107)

- 0.438 (0.122)

L

0.145 (0.021)

0.0428 (0.0265

0.0584 (0.0215

0.0274 (0.0234

R2

0,9775

0.9936

0.9938

0.9955

0.9900

0.9940

0.9948

0.9956

d , h

-I----- 1.34,

’ 0-50

1.78

0.35

0.83, 1 I

1.54

1.45

’ 1-31

---

and assume that the coefficients b4 in this general lag equation decline geometrically and are given by

( 3 ) Substituting for (3) in (2) yields

(4 ) Lagging (4) one period and multiplying by A gives

( 5 ) Subtracting ( 5 ) from (4) yields

( 6 ) that is,

(7) Equation (7) may be regarded as representing consumers’ habit

persistence-inertia or sluggishness in the adjustment of consumption to income.‘ Another interpretation of a consumption function includ-

4 The importance of habit persistence in the consumption function has been stressed by T. M. Brown, ‘Habit Persistence and Lags in Consumer Behaviour’, Econometrica, Vol. 20, July 1952, pp. 355-71; A Zellner, D. S. Huang, and L. C. Chau, ‘Further Analysis of the Short-run Consumption Function with Emphasis on the Role of Liquid Assets’, Econometrica, Vol. 33, July 1965, pp. 570-81 ; H. S. Houthakker and L. Taylor, Collsumer Demand in the United States 1929-1970 (Harvard University Press, Cambridge, Mass., 1966) ; and A. Zellner and M. S. Geisel, ‘Analysis of Distributed Lag Models with Applications to Consumption Function Estimation’, Econometrica, Vol. 38, November 1970, pp. 865-88.

bc = (1 - A ) X 4 b , where Of~<l.

c = a + (1 - A ) b D + (1 - A ) A b D - 1 + (1 - A)A%D-* + ... A C 4 = ax + (1 - h)AbD-1 + (1 - A)PbD-2 + ...

Ct - AC-1 = a( I - A ) + (I - A ) b D ,

C = a ( I - A ) + (1 - A)bD + AC-1.

1972 SHORT-RUN CONSCMPTION FUNCTION 223 ing lagged consumption is in terms of Friedman’s permanent income- consumption t h e ~ r y . ~ If it is assumed that permanent income is a weighted average of present and past values of measured income and that the weights decline geometrically, then a consumption function including current income and lagged consumption is obtained. A1- ternatively, a series for permanent income may be constructed from the measured income series using an arbitrary set of geometrically declining weights.6 This makes the inclusion of lagged consumption unnecessary.?

The inclusion of lagged consumption as an explanatory -variable raises statistical problems. When we include a disturbance term in ( 7 ) , in general this error term and lagged consumption are not independent (because lagged consumption is the dependent variable of the previous period and so affected by the disturbance term in that period) and hence the small-sample parameter estimates are biased and inconsistent. When a model such as that in equations (2) to (7) is used, even large-sample parameter estimates are biased. Suppose that the error term in (2) is u whicb is not serially correlated; then the composite error term in (7 ) is (u - hu-1) so that serial correlation is present ; and the combination of a lagged endogenous variable and serial correlation leads to asymptotic bias.

A further complication is that the standard tests of serial independence of the residuals from the regression equation, such as the Durbin-Watson test, are invalid when applied to models containing lagged dependent variables.8 Hovv-ever, DurbinQ has recently produced a test that may be applied in such circumstances. It involves comput- ing the quantity

n h = (1 - i d ) - ~

1 - nV(,i) J * , A

where d is the Durbin-Watson statistic, V(A) is the estimate of the variance of the lagged endogenous variable given by least-squares analysis, and n is the number of observations. h, may be tested for

5 M. Friedman, A Theory o,f the Consumption Function (Princeton Univer- sity Press, 1957).

6 Kote, however, that Holmes has demonstrated that there is theoretical in- consistency between the assumption that permanent and transistory components of income are independent and measuring permanent income with a geometrically declining set of weights (5. M. Hoimes, ‘A Condition for the Independence of Permanent and Transistory Components of a Series’, loi~rnal of the American Stafisfrcal Association, Vol. 66, March 1971, pp. 13-15.

7 Norton and Broadbent, op. cit., experimented with such measures of permanent income and reported markedly poorer results to regressions using personal disposable income.

8 J. Durbin and G. S. Watson, ‘Testing for Serial Correlation in Least Squares Regression’, Biometrika, Vol. 37, December 1950, pp. 409-28, and Vol. 38, June 1951, pp. 159-78. The Durbin-Watson statistic is biased towards 2 so that there is a tendency for the Durbin-Watson statistic to fail to indicate autocorrelation when it is in fact present.

J. Durbin, ‘Testing for Serial Correlation in Least Squares Regression when Some of the Regressors are Lagged Dependent Variables’, Econometrica, Vol. 38, May 1970, pp. 410-21.

224 THE ECOXOMIC RECORD J U N E

significance as a standard normal deviate. S o t e that it is a large- sample test.

The regression obtained when lagged consumption is included is reported as regression 1.2 . The R2 is raised significantly; the ratio of the mean square error in 1.2 to that in 1.1 is 3.44 which is significant a t the 1 per cent level. Durbin's h statistic is 0.50 and is clearly not significant so the introduction of lagged consumption has removed the serial correlation present in 1.1. If we may concentrate upon asymptotic properties, this suggests that no distributed lag bias exists in our estimates and that, if the consumption function process given by equations ( 2 ) t o ( 7 ) is correct, the assumption of no serial correlation in ( 2 ) must be rejected for otherwise the transformation from (2) to ( 7 ) would have introduced serial correlation and caused h t o be significant. The long-run marginal propensity to consume, b , is obtained by substituting A, the coe5cient of (2-1, into (1 - h ) b , the coefficient of D . A value of 0.870 is obtained.

4. Farm and Non-farm Income

There is some evidence f o r other countries that the marginal propensity t o consume of farmers is less than that for non-farmers,10 and in an important Australian study using annual data Arndt and Cameron found a better fit between consumption and non-farm disposable income than between consumption and disposable income.ll It would seem, therefore, that fluctuations in the share of personal disposable income going to farmers may be an important determinant of aggregate consumption and accordingly v e now investigate the possibility that there are significant differences in farm and non-farm marginal propensities to consume. X i t h different consumption functions €or farmers and non-farmers (denoted by the subscripts f and n, respectively) , we have

where

As

we may write (10) as

a = an + a,.

D = D, + Df

C = a + bn ( D - D,) + b,D, z u + b,D - ( b , - 6,) Dj . (12)

Unfortunately we do not know the share of personal disposable income accruing to farmers as we do not know the distribution of

10 See, for instance, the evidence pre:ented in Friedman, op. cit 11 H. \V. Arndt and B. Cameron, An Australian Consumption Function',

Economic Record, Vol. XXXIII, April 1957, pp, 105-15.

1972 SHORT-RUN CONSUMPTION FUNCTION 225

income tax payable between farmers and non-f armers. However, we do know the share of farm income in pre-tax income. This is given by

P = Y,/Y. (13) If we are prepared to assume that the farm share of income tax payable is the same as the farm share of income before tax, then we may write

and hence fit the regression 0, = PD (14)

(15) C = u + bnD - (bn - b , )FD.

We may incorporate a geometric lag pattern with equation (15). I n this case we have

C = (1 - X ) U + (1 - X ) b a - (1 - A) (6,s - b,)B'D + XC-1. (16)

The results obtained for equations (15) and (16) are given as regressions 1.3 and 1.4. It is clear that the FD term is highly sign%- cant in both regressions. In neither regression is there any evidence of serial correlation of residuals. When the coefficients of D and FD in both 1.3 and 1.4 are compared, it is apparent that they are very close to each other in magnitude but opposite in sign. Thus the coefficient of b, is not significantly different from zero.12 That is, the short- run marginal propensity t o consume of farmers is zero. This is consistent with the results of Arndt and Cameron.

Some problems associated with our approach must be noted. First, to the extent that Dt /D # Y,/Y, our estimates will be biased. Secondly, in the national accounts farm income is on a cash not an accrual basis, whereas non-farm income is essentially on an accrual basis. The extent that cash and accrual bases differ within a year is accounted for through our seasonal adjustment of the farm income series. Thirdly, we have assumed that A is the same for farm income and non-farm income but they may be quite different. As farm income vanes more than non-farm income, we anticipate that the X for farmers will be smaller than that for non-farmers. Also to the extent that our seasonal adjustment procedure has failed to remove entirely the cash-accrual effect, we expect farm A to be reduced. Finally, and fortunately, C-l is comprised of the lagged consumption of farmers as well as non-farmers. Thus to the extent that farm consumption is endogenous but not responsive to the short-run variables we have included, we shall pick up much of the effects in C-l. Thus we must be agnostic as to whether the long-run marginal propensity to consume of farmers is zero; we conclude only that there is no

We may test the significance of b, = b. - ( b . - bf) in 1.3 and (1 - h ) br = (1 - h)b. - (1 - A) (bn - b t ) in 1.4 by making use of the formulae var (br) = var (a) + var ( b , - b t ) - 2 COY (b", b, - b l ) ; and var (1 - h)bt = var ((1 - 1)bn) + y ({I - h}{b , - bf}) - 2 cov ({I - X}bn,{l - A> {b , - br ) ) . The respective t-values obtamed are 0.31 and 0.13. As (1 - X) is significant in (1.4) and as (1 - X)br is not significant, it follows that bt is not significant. C

22 6 THE ECONOMIC RECORD J G S E

evidence of a non-zero short-run marginal propensity t o consume on the part of farmers.

5. Liquid Assets lllany studies of the consumption function, including that of

ru’orton and Broadbent, give considerable emphasis t o liquid assets as a determinant of cor~sumption.~~ Insertion of liquid assets into the consumption function may be justified on two grounds-liquid assets may either be regarded as a proxy measure for wealth o r as providing a direct incentive to the consumer to spend.

T’he first view of liquidity is that apparently accepted by Sorton and Broadbent. They follow Tobin who regards Liquid assets as a prosy for net worth on the basis that ‘ for many households. liquid assets (bank deposits, savings accounts, savings bonds) are virtually the only assets held’.14 We reject this argument. Annual estimates of wealth are available for Australia. Over the period of o u r study liquid assets and vealth, both measured in terms of constant prices, rose. In order to remove the common time trends me correlated the first differences of liquid assets and wealth. The correlation coefficient is 0.236 if wealth is defined as private wealth; the correlation coeB- cient is 0 240 if wealth is d e h e d to include both private and public wealth. Xeither coeEcient is significant a t the 10 per cent level.lj bccordingly, there is no evidence that liquid assets act as a proxy for wealth. This should not surprise us. In Australia the holding of non- Liquid assets is widespread: home ownership is important even for relatively low income groups and so is the omership of automobiles and other consumer durables.

The second view of liquidity argues f o r the inclusion of Liquid assets on the basis that an increase in households’ liquid assets, other things being held constant, will cause households t o spend at least part of these on consumption goods rather than continuing to hold them as liquid assets or converting them into less liquid financial assets.

However, the direction of causation between liquid assets and consumption is unclear. Inserting liquid assets in the consumption function implies that the direction of causation is from liquid assets to consumption. We think i t is plausible that households accumulate liquid assets in order to undertake consumption expenditures on durables. T’he purchase of consumer durables requires the accumulation of liquid assets prior to the purchase because the pa-yment io-

13 Among others : Korton and Broadbent, op cit. ; Zellner, Huang, and Chau, op. cit. ; A. Zellner, ‘The Short-run Consumption Function’, Econornetrica, Vol. 25, October 1957, pp. 552-66; 2. Griliches, G. S. Maddala, R. Lucas, and N. \Tallace, ‘Sotes on Estimated Aggregate Quarterly Consumption Functions’, ECO~OmetrlCJ, Vol 30, July 1962, pp. 491-500; and Zellner and Geisel, op. cit.

14 J. Tobin, ‘Consumption Function’, in I n t e r m f i o d Ettcyclopedia of the Socml Sciences (Macmillan and the Free Press, New York, 1968), p. 366.

15 The constant-price wealth estimates are from C. Clark, Wet Capital Stock‘, Economic Record, Vol. 46, December 1970, Table 111, pp. 460-1. Liquid assets are as defined in Section 1 above and are from the Financial Supplement to the Re- serve Bank of Australia’s Statistical Bulletin, February 1966 and September 1969. The series was deflated by the consumer price index referred to in Section 1 a h e

1972 SEORT-RUN CONSUMPTION FUNCTION 227

volved is normally large relative to the current income flow. Such accumulation of liquid assets is necessary whether payment for the durable good is made in cash or whether the good is purchased on hire- purchase for in this case it is still necessary to accumulate sufficient liquidity to make the down-payment.16 On the other hand, purchases of non-durables are much more likely to be met out of the normal flow of income and thus not require prior accumulation of liquid assets.’?

Our hypothesis is supported by Norton and Broadbent’s results. They found liquid assets to be signacant in their regressions for purchases of motor vehicles and purchases of other consumer durables but insignificant in their regressions for non-durables.

Our own regressions gave little independent importance to liquidity as a determinant of consumption. Regressions 1.5 to 1.8 include the liquidity variable.18 In 1-5 the liquidity variable is significant at the 1 per cent level when included with just disposable income but the Durbin-Watson statistic is only 0.83, indicating marked serial correlation of residuals. When lagged consumption is included as well in regression 1.6, the liquidity variable is not significant at the 10 per cent level and the residuals are not serially correlated at the 10 per cent level. When the farm income variable is included but not lagged consumption, in regression 1 *7 the liquidity variable is significant at the 5 per cent level but, f o r the 5 per cent level of significance, the Durbin-Watson statistic is in the indeterminate region. When both lagged consumption and the farm income variable are included, in regression 1.8, liquidity is clearly insignificant, the coefficient of the liquidity variable being only slightly greater than the standard error. The residuals from the regression are not serially correlated at the 10 per cent level.

From these results it would seem clear that liquidity has no significant independent influence upon consumption and that its apparent significance in some regressions arises from incorrect speci-

16This argument is not vitiated by the tendency for many new-car buyers to have used cars which they trade-in and which form the down-payment as these cars are sold to used-car buyers some of whom are entering the market for motor vehicles for the first time and some of whom are in turn trading-in old used cars. These in turn use the cars they are trading-in as down payments but again some of these will be sold to new entrants to the motor vehicle market. So the process continues. Clearly there may be many links in this chain and time-lags may be involved. But unless there are buyers entering the market for motor vehicles for the first time, and who consequently need cash for down-payments, the price of used cars is depressed and this will discourage the purchase of new cars by present owners trading-in. This point, and the consequent transitory effect of changes in hire-purchase minimum down-payments and maximum repayment periods, have been discussed in D. J. Smyth, ‘A Quarterly Model of the Demand for Cars in the United Kingdom’, study paper prepared for the U.K. Department of Economic Affairs, July 1967.

17 Some non-durable consumption expenditures may be of such significant size as to require prior accumulation of liquid assets (such as expenditure on vacations) but these are likely to constitute a relatively small proportion of a household‘s non-durable consumption.

18 We do not experiment with alternative liquidity variables, as Norton and Broadbent’s results suggest that it makes little difference how the variables are defined or weighted.

22 8 THE ECONOXIC RECORD JUNE

fication of the consumption function, namely the omission of either the influence of farm income or lagged consumption or both.Ie

We conclude that there is is no causal relation from changes in liquidity t o changes in consumption. When consumption, especially consumption of durables, is about to rise (fall), liquidity rises (falls) ; but this change in liquidity is the result of the planned increase (decrease) in consumption rather than its cause. Thus while a change in liquidity may be a useful indicator of an impending consumption change, it would be unwise to rely on influencing consumption by changing liquidity.

6 . Income Tax Payable In the analysis so far, personal disposable income-that is, per-

sonal income minus income tax payable-has been used as the income variable. This assumes that the effect on consumption associated with a change in personal disposable income will be the same irrespective of whether the change in personal disposable income arose through a change in personal income or through a change, equal in magnitude but opposite in sign, in income tax payable. By disaggregating personal disposable income into its income and tax components, we may see if the coefEcients are of equal magnitude. We fit

(17) (18)

b t is the marginal propensity t o consume associated with tax changes. The fitted regressions are 2 . 1 and 2.2. It is apparent that the coefficient of tax revenues is not significant in either regression. In 2 .3 and 2 - 4 we drop the tax term without any apparent worsening of the fit.

C = a +- bY - btT C = (1 - A)a + (1 - A)bY + (1 - A)btT + AC-l.

TABLE I1 Australian Short-run Consumption Function Regressiom

I Coefficients and standard errors I

Regression no- j Constant

2.1 (41.6)

85.5 (3602)

285.8 (39.8)

(35.6)

R2 Y i c - ~ T !

~ - - - ~ 0.698 I -0,021 1 0.9833 (0.020) j (0~101) ,

~ I

0.181 ' 0.739 I 0.0256 1 0,9938 (0,068) j (0-095), (0,0627) , 0,696 (0.015)

j 0.9833 1

0-187 0.735 (0.065) 1 (0*093)!

19Exactly the same pattern emerges when liquidity is included with the regressions involving non-farm pre-tax income considered in Section 7. When lagged consumption is included, liquidity becomes insignificant and serial correlation is eliminated. W e do not tabulate these results.

1972 SHORT-RUN CONSUXPTION FUNCTION 229 aS we have income before tax disaggregated into farm and non-

farm components, we may use these directly. Accordingly we fit C = a + bnY, + blYl - btT C = (1 - A)a + (1 - A)bnYn + (1 7 A)blY, - (1 - A)b,T + AC-1.

(19)

(20) The fitted regressions are 3.1 and 3,2. Again it is apparent that the coefficient of tax revenues is not significant in either regression.20

TABLE I11 Australian dhort-ran Consumption Function Regressions

y.

0.700 (0.012) 0.377 (0.088) 0.701 (0.010) 0.383 (0.086) 0.700

0.364- (0.086)

(0.010)

Coef€iciente and standard errom I Regremion no. I Conetant Yt -~

0-123 (0.081) 0.070 (0.071) 0.124 (0.079) 0.076 (0,069)

3.1

3.2

3.3

3.4

3.6

3-8

3914 (30-8) 217.8 (64.1) 3908 (29.4) 216.7 (63.4) 4181 (24.3) 222.7 (63.3)

c-l

0.460 (0.126)

0.468 (0.123)

0.482 (0.121)

-- boo662 0.9932 0*00864) 0.0227 0,9961 0.0566)

0.9932

0.9961

0.9927

0,9949

We may explain the non-significance of the tax variables in terms of the permanent income hypothesis. Tax revenues change in part because, w i t h given tax rates, income changes lead to changes in tax revenues, and in part because tax rates have been changed, normally as part of an active stabilization policy. To the extent that changes in tax revenues are income induced, their effect on consumption will be picked up by pre-tax income. If changes in tax rates f o r stabilization purposes are regarded by households as transitory, then on Friedman’s hypothesis these rate changes would have no effect at all on consumption. It is plausible that these were regarded as transitory ; for during the period analysed the index of statutory rates on taxable personal income was changed five times but there is no apparent trend in the index.2I

Our results cast doubt on the effectiveness of one aspect of fiscal policy-tax rate changes-as a short-run stabilization device.22 Our

HIf we assume that income tax payable by farmers and non-farmers varies proportionately to their revenue before tax, the tax variables are still insignificant. Also it makes no difference whether we drop farmers’ pre-tax income or farmers’ income tax payable from the regressions-income tax payable is still not significant.

21 The index of statutory tax rates on taxable personal income is that given as series RPS in N. C. Mackrell, Equations for Tax Payments, Occasional Paper No. 3C (Reserve Bank of Australia, Sydney, April 1970)’ p. 25.

22In this they are consistent with the apparent ineffectiveness of the 10 per cent surtax in the United States in restraining inflation.

230 THE ECONOMIC RECORD J U N E

results do not imply merely a zero tax multiplier: when the money market is taken into account, a zero partial derivative between consumption and income tax payable implies a positive tax multiplier. Holmes and Smyth have shown that if households’ demand fo r money is a function of income after tax (and there are good theoretical reasons for supposing that income after tax, rather than income before tax, is the appropriate variable to use), then the tax multiplier is positive, zero, or negative according as I& 2 Ct (L4 - M;), where Lt and Ct are respectively the partial derivatives of the demand for money and consumption with respect to tax revenues, and Li, Mi and Id are respectively the partial derivatives of the demand for money, supply of money and investment with respect to the rate of interest.23 As we estimate Ct = 0, it follows that the tax multiplier will be positive providing I4 and Lt have their normal negative signs. It also follows that, compared to a proportional tax, a progressive income tax will act as a built-in destabilizer (when alternative equilibrium positions are compared), for the condition for this to occur is the same as for a positive tax multiplier.

7. Non-farm Income

In regressions 3.1 and 3.2 the farm income variable is not significant at the 10 per cent level. Regressions 3.3 and 3.4 drop the tax variable and again farm income is not significant at the 10 per cent level. Moreover, in both 3.3 and 3.4 the residuals are serially correlated at the 5 per cent level.

Regressions 3 - 5 and 3.6 drop the insignificant farm income variable. The residuals are still serially correlated at the 5 per cent level in the regression without lagged consumption, 3.5, but when lagged consumption is included, in 3.6, Durbin’s k-statistic does not indicate serial correlation at the 10 per cent level. This regression yields a long-run marginal propensity to consume out of pre-tax non-farm income of 0.703, while the short-run marginal propensity to consume (that for the current quarter) is 0,364. This indicates that consumption responds quite rapidly to short-run fluctuations as slightly more than half of the long-run response of consumption to income change occurs in the current quarter.

It is this final regression, 3.6, that we prefer. All non-significant variables have been eliminated. 3 .6 is simple, consumption being a function only of non-farm income before tax and lagged consumption.

23 J. M. Holmes and D. J. Smyth, ‘The Specification of the Demand for Money and the Tax Multiplier’, Journal of Politkal Economy, forthcoming. Briefly, a positive tax multiplier may occur because an increase in tax revenues will, for given national income, cause a fall in the transactions demand for money if this is a function of personal disposable income. With any given money supply, the amount of money available for holding as an asset is increased so that the equilibrium rate of interest in the money market, for any level of national income, is reduced. That is, the LM curve shifts to the right. If C1 is non-zero the IS curve shifts to the left. National income rises if the rightward shift of the L M curve is greater than the leftward shift of the IS curve. Here this is necessarily the case as Ct = 0 means that the IS curve does not shift.

1972 SHORT-RUN CONSUMPTION FUNCTION 231

Its simplicity make it valuable for forecasting purposes: there is no need to forecast farm income or income tax payable. The fit of 3.6 is good compared to the other regressions and the residuals are not serially correlated.

8. Conclusions

In this paper we have fitted alternative short-run consumption functions to Australian quarterly data. For the period covered by our study, ou r major conclusions are that :

(1) The short-run marginal propensity to consume of farmers

(2) Liquid assets have no independent effect on consumption. (3) Tax changes do not directly affect consumption. (4) Consumption is a function of lagged as well as current in-

come but more than half of the response of consumption t o income occurs in the current quarter.

( 5 ) TIe preferred consumption function is a simple one in which consumption is a function of current non-farm pre-tax income and lagged consumption.

is zero.

DAVEI J. SMYTH

PATRICK C. MCMAHON Ckemont Graduate School

University of Bimingham

!a For instance, the ratio of the mean square deviation of regression 1.4 to that of 3.6 is only 1.09 and this F-statistic is insignificant.

Documents

The Australian Short-run Consumption Function