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Aggregate consumption and the distribution of incomes
European
Review 6 (1975) 417-423. C North-Holland Publishing Company
Lonomic
AGGREGATE
CONSUMPTION AND THE DISTRIBUTlON OF INCOMES 3. VAN DOORN*
Unit~ersit.v of Durham, Dwham, DHl 3H Y, Engla~ul
Received June 1975 In this artaie an attempt is made to measure the effects of variations in the size distribution or inco:nes ori consumers spending. A critical suncy is given of some of the earlier attempts to und+:r?ake such an exercise. It is then shown under what conditions an empirical form caau be obtained which can be used to investigate the effects of variations in the distribution of incomes O/I dtffcrerrt commodity classes. Regional cross-section data were used for estimation purposes.
1IIIntroduction The purpose of this paper is to describe a simple method for analysing the effects of variations in the distribution of incomes on aggregate consumption. ‘First, however, a critical review will be presented of some of the earlier attempts t.o account for such effects, then an alternati*:e procedure will be developed and empirically tested. Many attempts that have been made to account for variations in the distribution of incomes in an aggregate consumption function refer to a statement by Keynes (1964, pp. 90-91) that: ‘The amount that the community spends on consumption depends partly on . . . the principles on which income is divided between them’ (the individuals). But the methods applied to quantify the possible effects differ widely. It may tncrefore prove worthwhile looking into these matters. 2. A short survey Two types of approach have bein pur .*led in attempts to incorporate the effects of income redistributions’ on segregate spending. One approach concentrates on variations in the functional distribution of incomes, the other on variations in the personal distribution. For this study the latter approach will form the m?in theme. *I would like to thank John Hey and John C *;cdy for their helpful comments on an earlier draft of this paper. IThe :erm redistribution refers to changes is the d;stribution either way. No normative connotations are intended.
418
J.c. Doom, Aggregoce conwnptiott
and income distribution
Total income is in the first approach partially disaggregated into two or more homogeneous income groups, usually labour and non-labour income,2 assuming for each group either insignificant internal redistributions or equal individual propensities to consume. A redistribution of national income between groups could then under certain conditions make a net addition to the explanation of cyclical variations in total consumption in a time-series analysis. Many econometric models !I:ereforc do to this extent indeed contain two explanatory income variables in a consumpaion function.3 Friedman (1957) too, emphasised the importance of a distinction between income from human and non-human wealth, but from a different angle. In his theory income inequality is thought to be attributable to differences in permanent income as well as to differences in transitory income. Insofar as inequality is caused by differences in permanent income it would not affect spending behaviour. Spending will only be affected if ;he source of inequality is attributable to digerences in transitory components: ‘. . . because inequality then means uncertainty about income prospects and hence increases the need for a reserve against emergencies’. [See riedman (1957, p. 235).] Hence it is uncertainty about income prospects rather than inequality in the distritsltion of inromes which may affect the propensity to consume. Consumption in his study was therefore not determined by permanent income alone, but also by the ratio of permanent income derived from non-human wealth. This was treated as an additional reserve to offset unexpected changes in labour income. Yet the empirical form employed by Friedman to test the validity of hi; hypothesis shows no explicit distinction between labour income and non-human wealth. This is quite different in :hc ll:ork by Ando and Modi@a% (1963) who intentionally and in contrast to Friedman separated Igbour it!come from non-human wealth {from which property income is derived), along with an expectations variable, in an attempt to test their ‘life-cycle hypothesis. The results of their tests were shown to be quite successful. The second approach to specify the effects of variations in the persona! distribution of incomes has mainly been pursued through the inclusion of higher sample moments about the mean, in particular the variance. A first attempt to undertake such an exercise was made by Staehle (1937). An index for the concentration of labour income’ explained 36.29 percent cf the 2This approach was already suggested in 1936 by Tinbergen (1959). jAmong the many econometric models, I would like to refer to the Klein-Goldberger (1955) model, and one of the models constructed by the Centraal Planbureau (1971) in Holland. “A traditional measure for the size distribution of incomes such as ‘Pareto’s -a* or ‘Gini’s -‘S’ was not used. Instead a new measure was designed showing no correlation with income changes : cumulative median income-ordinary median income B= cumulative median income which varies from zero, when all incomes are equal, to unity.
J.v. Doom, Aggwgatc- consumption and income distribution
419
variations in the proportion of retail sales to labour income. His conclusion not surprisingly read: ‘. . . it may be said that it is indispensable to take into account the variations in the distribution of incomes in constructing the propensity to consume ‘. However, R. and W.M. Stone (1938-1939) rejected, for statistical reasons, the idea of adding another measure for the distribution of income in a Keynesian consumptio I function. An earlier study by Johnson (1937) showed a great deal of inter-correlation between Pareto’s -cc and national income bata, Polak (1939) combined both approaches. In his statistical exercises not less than five income categories were used in addition to Pareto’s -a. The relations which included Pareto’s measure for income inequality were rejected since it was believed that the signs for the estimated parameters were incorrect.5 in none of these studies was the choice of an inequality index determined through consistent aggregation over the micro units. A first systematic critique of the ad-hocery in this type of approach was made by De Wolff (1940). This study was apparently overlooked by Ferber (1953), who raised no theoretical objections. Houthakker and Prais (1955) suggested another method of investigating the effects of Income redistribution on aggregate spending. Empirical tests were however not performed. To some extent the analysis as develol:cd in this Qaper will follow their suggestions.
3. Method and assumption Moments of the income distribution higher than the first will not enter an aggregate consumption function if the underlying micro equations are linear with constant, but positive, coefficients. The _Gze distribution of incomes is then completely characterised by total (average) income, whatever shape this distribution takes. Average income ceases to be the only determinant of constimption in two cases: (i) when the underlying micro functions are nvralinear in consumption and income, even if the individual propensities to consume are equal andl, (ii) when the irdividual propensities to consume are not constant, even if the micro fu;:ctL*. ,re linear. So let us assume a dou ti.: logarithmic micro relation, in which consumption per household (ci) is determined by household income (~2, and household size (zi>. The inclusion of the latter explanatory variable is justified by the assump: tion that consumption per person is related to income per person.
SMendershauscn(1936) pointed out later which factors could be made responsiblefor these results.
Js. Doom, Aggregate commmprio~~and kcome diwihutiorr
in which gi = CX, pi = p, yi = y and rj, /Yi,‘/i 2 0 for all i (i = 1, . . ., II). Summing over all households tion which reads as
dividing through by
Ii
gives a macro cqua-
where values in curly brackets stand for logarithms of geometric mean values
of ci, )‘i and zi. Eq. (2) cannot be used directly in an analysis of most data, since these do only include estimates of arithmetic mean variables and a bias in the specificatioI8 of eq. (2; might easily be incurred, see Cramer (I 969). Lnorder to transform eq. (2) into an eckat’at1 of more operational significance, we need rather more particularised assumptions, First i+ will be assumed ihat the distribution of all three variables concerned follow tLe log normal pattern.6 If a variable xi is log normally distributed as /i(-Ti 1n, CT’),where (( (- logarithm of geometric mean value) and cr* tire location and variance parameters respectively, then
d&i) - dx,
!
= Xib 2/(2n) exp
+-
, *
(log xj-jr)’
will be its density functzon, in which A(Xi) :,rands for N(log xi), and A for Xi s 0. A convenient propert:: is that
= 0
(arithmetic mean) 5 = exp {p + fa2), which shows how the arithmetic mean invo!ves both locatiun and dispersion ) parameters. Applying tlhe general result to all three variables it? eq. (2) wi!! give
Vor income and ho lsehold size, if measured on a scale where fractions are permitted, this assumption seems fairly wel; established. see Aitchison and Bnx+m(1966).
J.v.
Dawn,
Aggregate
consrrmption
ad
income
Data on o: are not avaiiabie but we can conveniently l-v assuming 0: = :a?.7 _ This will leave us with log L’ = a+p(logj+u;)+y
distributiotr
421
eliminate this statistic
log 2.
The variance of the logi,rithms to, the size distribution of incomes is monotonically related to the Lorentz index of concentration. In contrast to the Pareto index which concentrates on the higher income groups only, this index provides an overall measure for income inequality. Greater equality is indicated by a decrease in 0’ and will cause an increase in aggregate consumption. The effects of variations in the distribution of income may therefore show up if parameter estimates for eq. (4) which includes the variance term, are compared with estimates for eq. (5) which reads as log 2 = a+p logF+y and conforms to the conventional
log 2, log linear expenditure model.
4. Estimation and conclusion Data for ordinary Least-square analysis came from the 1970 and 1971 Family Expenditure Survey. The survey gives a bred.. -bdown of the data over the eleven U.K. standard regions. For one region a further breakdown was given. Twelve observations were available. Estimates were gi-:en for average household income and expenditure, average household size and the distribution of ncrconal incomes in each region. Regressions were carried out for total personal consumption in each region and for five major expenditure groups. Table I _
Parameter
____ ^_._ __..._ _ ____
Total Housing cons. __._-.._.-_.- _ . .._- 4.0134 - 0.3705 D (-0.8177) ( -- 2.435) 0.9297 1.8114 P (5.465) ( IO.20461 0.7029 - 0.8929 i’ (-1.003) (2.873 1) 0.9242 0.840 R1 __.-_. -.. -^ *f-values are presented in brackets.
estimates for eq. (bj.”
._ _.---._. Food
-.-. ..
- 0.3484 (-0.715) 0.4904 (5.606) 0.8281 (3.148) 0.741 _ _. _
_ .._ .
C!othing dnd footwear
.
-5.7136 (-2.915) 0.9868 (2.504) 3.8139 (3.6u4t 0.604
.-_. Transport and vehicles -._ _-._ -4.2713 (-2.503) 1.2131 (3.534) I .7865 (1.938) 0.582
_Services ___._ - 3.928 (-2.413)
1.4844 (4.536) -0.1135 (--0.129) 0.755 - --
‘It is important to realize that the relation log C/iz = a+Plog_F/Z as used, c.g.. by Stone (i954j implies, if :og normality is assumed, that oC2 = cry2 = uZ2 = 0 and moreover that /? ia order to eliminate multicollinearity between y, and zf. These ‘assumptions’ are ~:~~~ investigated in Van Dow-n (1973).
422
J.c. Doom, Ag[wqate consumption and income distribution Table 2
Parameter
2
B 7 RZ
Total cons.
Housing
-0.5703 (- 1.1342) 0.8964 (9.5494) 0.8247 (3.0914) 0.9145
- 4.2697 (- 2.325) 1.7194 (5.015) - 0.6959 (-0.714) 0.810
&mates
for eq. (5).
Food
Clothing and footwear
Transport and vehicles
Service
-0.5384 t- 1.164) 0.4901 (5.077: 0.9180 (3.742) 0.786
- 5.9098 ( - 2.869) 0.9482 (2.466) 3.9383 (3.614) 0.599
- 4.0922 ( - 2.080) 1.0799 (2.940) 1.8118 (I .736) 0.491
-4.5196 (-2.891) I .4868 (5.094) 0.1637 (0.197) 0.792
The results of the tests are slightly disappointing. However, it should be borne in mind that the range of income classes for each region is rather small. The difference between geometric and arithmetic means is correspondingly reduced. Estimates for the macro propensity to consume from geometric mean income (table 1) are, apart from those for Services, on average slightly higher and more stable than the estimates based on arithmetic mean income. Only the dik;ence in the estimates for the propensity t? consume on Transport and Vehicles is shown to be significant at the 5 percent Ieve:. For the other categories higher levels should have been accepted. The basic conclusion from this exercise merely seems to support the view that an increase in income inequality (dot > 0) will have a negative effect on consumer spending.’ For prediction purposes some preference for using geometric mean income can be claimed when significant income redistributions are expected, given thq: fact that under lognormal conditions geometric mean income stands as a better measure for the level of income than arithmetic mean income. Otherwise no particular preference for either statistic seems to exist. BThis conclusion finds support in a comment by Malinvaud (1970) that low values for the marginal propensity to consume, as computed from interwar data, may have been caused by a greater inequality in incomes.
References Aitchison, J. and J.A.C. IBrown, 1966, The lognormal distribution with special reference to its use in economics, (Cambridge University Press, Cambridge). Ando, A. and F. Modigliani, 1963, The life cycle hypothesis of saving, American Economic Review 53, no. 1.55-84. Centraal Planbureau 1971, Centraal Economisch Plan 1971 (Staatsuitgevery, Den Haag). Cramer, F.S., 1969, Empirical econometrics (North-Holland, Amsterdam). De Wolff, P., 1940, Income elasticity of drmand, A microeconomic and a macroeconomic interpretation, Economic Journal LI, 140-145. Ferber, R., 1953, A study of aggregate consumption functions, Technical Paper no. 8. (NBE.R., New York).
J.c. Doom, Aggregate consumption and income distribution
423
Friedman, M., 1957,A theory of the consumption function (N.B.E.R., New York). Johnson, NO., 1937,The Pareto law, Review of Economics and Statistics XIX, no. 1,20-26. Keynes, J.M., 1934, The general theory of employment, interest and money, 1964(Macmillan, London) 90-91. Klein, L.R. and A.S. Goldberger, 1955,An econometric model of the U.S., 1929-1952(NorthHolland, Amsterdam). Malinvaud, E., 1970, Statistical methods of econometrics, 2nd ed. (North-Holland, Amsterdam). Mendershausen, H., 1936, Changes in income distribution during the great depression (N.B.E.R., New York) 66, Polak, J.J., 1939,Fluctuations in United States consumption, 1919-1932,Review of Economics and Statist;,s XXI, no. 1, l-12. Prais, S.J. and H.S. Houthakker, 1955,The analysis of family budgets (Cambridge University Press, Cambridge). Staehle, H., 1937,Short-period variations in the distribution of incomes, Review of Economics and Statistics XIX, no. 3.133-143. See also the subsequent discussion between Staehle and Keynes in : 1939,Review of Economics and Statistics XXI, no. 3, 129-130. Stone, R. and W.M. Stone, 193&-1930.The marginal propensity to consume and the multiplier, A statistical investigation, Rc:iew of Economic Studies VI, l-24. Stone, R., 1954, The measurement of consumers* expenditure and behaviour in the United Kingdom, 1920-1938(NIESR, Cambridge). Tinhergeri, J., 1959, An economic policy for 1936, in: J. Tinbergen, selected papers (NorthHollar d, Amsterdam). Van Door& J., 1973, Aggregated consumption functions: A regional cross-section analysis, mimeo (University of Durham).
Review 6 (1975) 417-423. C North-Holland Publishing Company
Lonomic
AGGREGATE
CONSUMPTION AND THE DISTRIBUTlON OF INCOMES 3. VAN DOORN*
Unit~ersit.v of Durham, Dwham, DHl 3H Y, Engla~ul
Received June 1975 In this artaie an attempt is made to measure the effects of variations in the size distribution or inco:nes ori consumers spending. A critical suncy is given of some of the earlier attempts to und+:r?ake such an exercise. It is then shown under what conditions an empirical form caau be obtained which can be used to investigate the effects of variations in the distribution of incomes O/I dtffcrerrt commodity classes. Regional cross-section data were used for estimation purposes.
1IIIntroduction The purpose of this paper is to describe a simple method for analysing the effects of variations in the distribution of incomes on aggregate consumption. ‘First, however, a critical review will be presented of some of the earlier attempts t.o account for such effects, then an alternati*:e procedure will be developed and empirically tested. Many attempts that have been made to account for variations in the distribution of incomes in an aggregate consumption function refer to a statement by Keynes (1964, pp. 90-91) that: ‘The amount that the community spends on consumption depends partly on . . . the principles on which income is divided between them’ (the individuals). But the methods applied to quantify the possible effects differ widely. It may tncrefore prove worthwhile looking into these matters. 2. A short survey Two types of approach have bein pur .*led in attempts to incorporate the effects of income redistributions’ on segregate spending. One approach concentrates on variations in the functional distribution of incomes, the other on variations in the personal distribution. For this study the latter approach will form the m?in theme. *I would like to thank John Hey and John C *;cdy for their helpful comments on an earlier draft of this paper. IThe :erm redistribution refers to changes is the d;stribution either way. No normative connotations are intended.
418
J.c. Doom, Aggregoce conwnptiott
and income distribution
Total income is in the first approach partially disaggregated into two or more homogeneous income groups, usually labour and non-labour income,2 assuming for each group either insignificant internal redistributions or equal individual propensities to consume. A redistribution of national income between groups could then under certain conditions make a net addition to the explanation of cyclical variations in total consumption in a time-series analysis. Many econometric models !I:ereforc do to this extent indeed contain two explanatory income variables in a consumpaion function.3 Friedman (1957) too, emphasised the importance of a distinction between income from human and non-human wealth, but from a different angle. In his theory income inequality is thought to be attributable to differences in permanent income as well as to differences in transitory income. Insofar as inequality is caused by differences in permanent income it would not affect spending behaviour. Spending will only be affected if ;he source of inequality is attributable to digerences in transitory components: ‘. . . because inequality then means uncertainty about income prospects and hence increases the need for a reserve against emergencies’. [See riedman (1957, p. 235).] Hence it is uncertainty about income prospects rather than inequality in the distritsltion of inromes which may affect the propensity to consume. Consumption in his study was therefore not determined by permanent income alone, but also by the ratio of permanent income derived from non-human wealth. This was treated as an additional reserve to offset unexpected changes in labour income. Yet the empirical form employed by Friedman to test the validity of hi; hypothesis shows no explicit distinction between labour income and non-human wealth. This is quite different in :hc ll:ork by Ando and Modi@a% (1963) who intentionally and in contrast to Friedman separated Igbour it!come from non-human wealth {from which property income is derived), along with an expectations variable, in an attempt to test their ‘life-cycle hypothesis. The results of their tests were shown to be quite successful. The second approach to specify the effects of variations in the persona! distribution of incomes has mainly been pursued through the inclusion of higher sample moments about the mean, in particular the variance. A first attempt to undertake such an exercise was made by Staehle (1937). An index for the concentration of labour income’ explained 36.29 percent cf the 2This approach was already suggested in 1936 by Tinbergen (1959). jAmong the many econometric models, I would like to refer to the Klein-Goldberger (1955) model, and one of the models constructed by the Centraal Planbureau (1971) in Holland. “A traditional measure for the size distribution of incomes such as ‘Pareto’s -a* or ‘Gini’s -‘S’ was not used. Instead a new measure was designed showing no correlation with income changes : cumulative median income-ordinary median income B= cumulative median income which varies from zero, when all incomes are equal, to unity.
J.v. Doom, Aggwgatc- consumption and income distribution
419
variations in the proportion of retail sales to labour income. His conclusion not surprisingly read: ‘. . . it may be said that it is indispensable to take into account the variations in the distribution of incomes in constructing the propensity to consume ‘. However, R. and W.M. Stone (1938-1939) rejected, for statistical reasons, the idea of adding another measure for the distribution of income in a Keynesian consumptio I function. An earlier study by Johnson (1937) showed a great deal of inter-correlation between Pareto’s -cc and national income bata, Polak (1939) combined both approaches. In his statistical exercises not less than five income categories were used in addition to Pareto’s -a. The relations which included Pareto’s measure for income inequality were rejected since it was believed that the signs for the estimated parameters were incorrect.5 in none of these studies was the choice of an inequality index determined through consistent aggregation over the micro units. A first systematic critique of the ad-hocery in this type of approach was made by De Wolff (1940). This study was apparently overlooked by Ferber (1953), who raised no theoretical objections. Houthakker and Prais (1955) suggested another method of investigating the effects of Income redistribution on aggregate spending. Empirical tests were however not performed. To some extent the analysis as develol:cd in this Qaper will follow their suggestions.
3. Method and assumption Moments of the income distribution higher than the first will not enter an aggregate consumption function if the underlying micro equations are linear with constant, but positive, coefficients. The _Gze distribution of incomes is then completely characterised by total (average) income, whatever shape this distribution takes. Average income ceases to be the only determinant of constimption in two cases: (i) when the underlying micro functions are nvralinear in consumption and income, even if the individual propensities to consume are equal andl, (ii) when the irdividual propensities to consume are not constant, even if the micro fu;:ctL*. ,re linear. So let us assume a dou ti.: logarithmic micro relation, in which consumption per household (ci) is determined by household income (~2, and household size (zi>. The inclusion of the latter explanatory variable is justified by the assump: tion that consumption per person is related to income per person.
SMendershauscn(1936) pointed out later which factors could be made responsiblefor these results.
Js. Doom, Aggregate commmprio~~and kcome diwihutiorr
in which gi = CX, pi = p, yi = y and rj, /Yi,‘/i 2 0 for all i (i = 1, . . ., II). Summing over all households tion which reads as
dividing through by
Ii
gives a macro cqua-
where values in curly brackets stand for logarithms of geometric mean values
of ci, )‘i and zi. Eq. (2) cannot be used directly in an analysis of most data, since these do only include estimates of arithmetic mean variables and a bias in the specificatioI8 of eq. (2; might easily be incurred, see Cramer (I 969). Lnorder to transform eq. (2) into an eckat’at1 of more operational significance, we need rather more particularised assumptions, First i+ will be assumed ihat the distribution of all three variables concerned follow tLe log normal pattern.6 If a variable xi is log normally distributed as /i(-Ti 1n, CT’),where (( (- logarithm of geometric mean value) and cr* tire location and variance parameters respectively, then
d&i) - dx,
!
= Xib 2/(2n) exp
+-
, *
(log xj-jr)’
will be its density functzon, in which A(Xi) :,rands for N(log xi), and A for Xi s 0. A convenient propert:: is that
= 0
(arithmetic mean) 5 = exp {p + fa2), which shows how the arithmetic mean invo!ves both locatiun and dispersion ) parameters. Applying tlhe general result to all three variables it? eq. (2) wi!! give
Vor income and ho lsehold size, if measured on a scale where fractions are permitted, this assumption seems fairly wel; established. see Aitchison and Bnx+m(1966).
J.v.
Dawn,
Aggregate
consrrmption
ad
income
Data on o: are not avaiiabie but we can conveniently l-v assuming 0: = :a?.7 _ This will leave us with log L’ = a+p(logj+u;)+y
distributiotr
421
eliminate this statistic
log 2.
The variance of the logi,rithms to, the size distribution of incomes is monotonically related to the Lorentz index of concentration. In contrast to the Pareto index which concentrates on the higher income groups only, this index provides an overall measure for income inequality. Greater equality is indicated by a decrease in 0’ and will cause an increase in aggregate consumption. The effects of variations in the distribution of income may therefore show up if parameter estimates for eq. (4) which includes the variance term, are compared with estimates for eq. (5) which reads as log 2 = a+p logF+y and conforms to the conventional
log 2, log linear expenditure model.
4. Estimation and conclusion Data for ordinary Least-square analysis came from the 1970 and 1971 Family Expenditure Survey. The survey gives a bred.. -bdown of the data over the eleven U.K. standard regions. For one region a further breakdown was given. Twelve observations were available. Estimates were gi-:en for average household income and expenditure, average household size and the distribution of ncrconal incomes in each region. Regressions were carried out for total personal consumption in each region and for five major expenditure groups. Table I _
Parameter
____ ^_._ __..._ _ ____
Total Housing cons. __._-.._.-_.- _ . .._- 4.0134 - 0.3705 D (-0.8177) ( -- 2.435) 0.9297 1.8114 P (5.465) ( IO.20461 0.7029 - 0.8929 i’ (-1.003) (2.873 1) 0.9242 0.840 R1 __.-_. -.. -^ *f-values are presented in brackets.
estimates for eq. (bj.”
._ _.---._. Food
-.-. ..
- 0.3484 (-0.715) 0.4904 (5.606) 0.8281 (3.148) 0.741 _ _. _
_ .._ .
C!othing dnd footwear
.
-5.7136 (-2.915) 0.9868 (2.504) 3.8139 (3.6u4t 0.604
.-_. Transport and vehicles -._ _-._ -4.2713 (-2.503) 1.2131 (3.534) I .7865 (1.938) 0.582
_Services ___._ - 3.928 (-2.413)
1.4844 (4.536) -0.1135 (--0.129) 0.755 - --
‘It is important to realize that the relation log C/iz = a+Plog_F/Z as used, c.g.. by Stone (i954j implies, if :og normality is assumed, that oC2 = cry2 = uZ2 = 0 and moreover that /? ia order to eliminate multicollinearity between y, and zf. These ‘assumptions’ are ~:~~~ investigated in Van Dow-n (1973).
422
J.c. Doom, Ag[wqate consumption and income distribution Table 2
Parameter
2
B 7 RZ
Total cons.
Housing
-0.5703 (- 1.1342) 0.8964 (9.5494) 0.8247 (3.0914) 0.9145
- 4.2697 (- 2.325) 1.7194 (5.015) - 0.6959 (-0.714) 0.810
&mates
for eq. (5).
Food
Clothing and footwear
Transport and vehicles
Service
-0.5384 t- 1.164) 0.4901 (5.077: 0.9180 (3.742) 0.786
- 5.9098 ( - 2.869) 0.9482 (2.466) 3.9383 (3.614) 0.599
- 4.0922 ( - 2.080) 1.0799 (2.940) 1.8118 (I .736) 0.491
-4.5196 (-2.891) I .4868 (5.094) 0.1637 (0.197) 0.792
The results of the tests are slightly disappointing. However, it should be borne in mind that the range of income classes for each region is rather small. The difference between geometric and arithmetic means is correspondingly reduced. Estimates for the macro propensity to consume from geometric mean income (table 1) are, apart from those for Services, on average slightly higher and more stable than the estimates based on arithmetic mean income. Only the dik;ence in the estimates for the propensity t? consume on Transport and Vehicles is shown to be significant at the 5 percent Ieve:. For the other categories higher levels should have been accepted. The basic conclusion from this exercise merely seems to support the view that an increase in income inequality (dot > 0) will have a negative effect on consumer spending.’ For prediction purposes some preference for using geometric mean income can be claimed when significant income redistributions are expected, given thq: fact that under lognormal conditions geometric mean income stands as a better measure for the level of income than arithmetic mean income. Otherwise no particular preference for either statistic seems to exist. BThis conclusion finds support in a comment by Malinvaud (1970) that low values for the marginal propensity to consume, as computed from interwar data, may have been caused by a greater inequality in incomes.
References Aitchison, J. and J.A.C. IBrown, 1966, The lognormal distribution with special reference to its use in economics, (Cambridge University Press, Cambridge). Ando, A. and F. Modigliani, 1963, The life cycle hypothesis of saving, American Economic Review 53, no. 1.55-84. Centraal Planbureau 1971, Centraal Economisch Plan 1971 (Staatsuitgevery, Den Haag). Cramer, F.S., 1969, Empirical econometrics (North-Holland, Amsterdam). De Wolff, P., 1940, Income elasticity of drmand, A microeconomic and a macroeconomic interpretation, Economic Journal LI, 140-145. Ferber, R., 1953, A study of aggregate consumption functions, Technical Paper no. 8. (NBE.R., New York).
J.c. Doom, Aggregate consumption and income distribution
423
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