Luca Rebeggiani

Income Distribution and Growth -The Role of Demand Composition

Revised

Working Paper

May 2005

ISSN: 0949-9962

Chair for Economic Policy,Department of Economics,

University of Hanover.

Königsworther Platz 1, D-30167 Hannoverwww.wiwi.uni-hannover.de/konj/

- Preliminary version - Please do not quote -

ABSTRACT: This paper investigates the relationship between income distri-bution and growth through the demand composition channel within an endoge-nous growth model. Assuming non-homothetic preferences and non-homogeneousgoods, personal income distribution affects the patterns of demand of householdsand therefore the supply of firms, which in turn determines growth. It is shownthat high inequality is harmful for growth. The theoretical results are verified byusing data from the German EVS-Database. The results suggest that incomedistribution strongly affects households’ patterns of demand. Besides there issome evidence that demand composition influences factor returns and produc-tivity, which in turn determine income growth.

KEYWORDS: income distribution, growth, demand composition,non-homothetic preferences

JEL-CLASSIFICATION: D12, D31, E21, O15

1 IntroductionThe analysis of the relationship between personal income distribution and grow-th has experienced a sharp rise in academic attention since the early nineties,when endogenous growth models allowed integrating new determinants of grow-th in macroeconomic models. Although there is still some disagreement, mainchannels have been identified through which income distribution affects growth.The central ones are credit-market imperfections (see Galor/Zeira (1993) amongothers, and Galor/Moav (2004) for an extension), fiscal policy (Alesina/Rodrik(1994), Persson/Tabellini (1994), Benabou (1996)) and socio-political instability(Benhabib/Rustichini (1996), Carmignani (2003)). The main theoretical resultis that high inequality negatively influences growth, although some inequalitymay be needed at early stages of development (Galor/Moav (2004)) or from abehaviouristic point of view (as suggested by status-models like Corneo/Jeanne(2001)).

Another important link between income distribution and growth, which hasreceived less attention, is the role of demand structure. When households dif-fer in their incomes and wealth endowments, they develop different patterns ofdemand. So the aggregate structure of demand may change from one countryto another, or between stages of development of one country, due to a differentdistribution of income. The composition of aggregate demand influences heavilythe supply side by creating or enlarging markets for desired goods and shrin-king those for (relatively) undesired ones. This in turn affects factor incomesbecause of the different factor input requirements for the production of more orless sophisticated goods. These shifts in functional income distribution lead insubsequent periods to changes in personal income distribution, so that previousinterpersonal differences may be perpetuated, enlarged or reduced.

Studies of demand factors are traditionally underrepresented in neoclassicaleconomics. In the case of the inequality-growth relationship, numerous historical

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experiences and actual economic developments suggest that the problem of ag-gregate demand and of demand composition may be crucial. The different pathsadopted by the US-American and the British economy during the 19th centuryis an often cited historical example (e.g. Murphy/Shleifer/Vishny (1989)). Whi-le in the U.S. the internal demand was mainly constituted by a large middleclass of relative prosperous farmers, in Great Britain it was still relatively sharpdivided into a working class and an aristocratic upper class. The American far-mers demanded simple industrial goods in large amounts, whereas the Britishupper class preferred primarily expensive handcrafted products. This differentdemand conditions are regarded as one of the main causes of the astonishingtake-off of U.S. mass-production industries during the 19th century and of theirovertaking of the British ones (Rosenberg (1972)).

Different ’destinies’ due to diverging demand conditions were even experi-enced by several important developing countries (Brazil, Mexico, South Corea,Taiwan, Singapore, Hong Kong, Nigeria, to some extent the Philippines) in thelast decades of the 20th century, especially during the Sixties and Seventies.This period was characterized by high growth rates for all of them, but in somecountries it was accompanied by growing, in others by decreasing inequality.Only in those countries where the latter was the case (South Corea, Taiwan,Hong Kong, Singapore), this high-growth period led to a general and stabledevelopment process. In all the others, growth not only increased social diffe-rences, but also slowed down in the subsequent years, without providing thedesired ’big push’ that could lead to a stable developing path.

In recent times, the lack of internal demand is regarded as one of the maincauses of low growth in Germany during the last years, when the country hasexperienced a period of high unemployment and (like many other industrializedcountries) of growing inequality. It’s been argued that this lack is not ascribableto some forms of ’precautionary saving’, but that it is caused by the level anddistribution of income (Rees (2004), Rebeggiani (2005)).

These historical examples are taken as the starting point by this paper.Its aim is to develop a theoretical framework to study the inequality-growth-relationship through the demand composition channel, after providing an over-view over the existing literature (neoclassical and Keynesian). In the secondpart, the theoretical findings shall be verified using a large data set includingseveral waves of the German household survey ’Einkommens- und Verbrauchs-stichprobe’ (EVS) together with some aggregate data.

2 Theoretical Issues

2.1 Neoclassical vs. Keynesian ApproachesRelatively little theoretical work has been done in this field. This is mainly dueto the fact that the standard general equilibrium model is based on represen-tative agents, homothetic preferences and homogeneous goods, which do notallow addressing this topic. Preferences of individuals must be kept identical for

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reasons of formal tractability, but in order to investigate income distribution is-sues it’s necessary to provide them at least with different wealth and/or incomeendowments. The notion of hierarchical demand was introduced by the seminalworks of Ernst Engel (1857, 1881). It establishes that the consumption structureof an individual varies with the level of his income and that demand for somecategories of goods may be saturated after trespassing a certain level of income.This has been proved as one of the most stable empirical economic ’laws’ (seesection 3 below) and is quite common in microeconomic theory, whereas themost macro-models are still based on homothetic preferences, even those thatdeal with product innovation (e.g. Grossman/Helpman (1991)).

Besides, neoclassical economy is traditionally supply-side oriented. Say’s lawthat ’supply creates demand’ and that market clearing can be assumed for allproperly shaped commodity and labour markets is widely accepted, at least instandard neoclassical models. This goes that far, that N. Stern wrote in hissurvey article that growth theory is

about the accumulation of physical capital, the progress of skills,ideas and innovation, the growth of population, how factors are com-bined and managed and so on . . . (and) therefore, principally, aboutthe supply side. (Stern (1991), 123)

Keynesian economics, especially the ’pure’ or Post-Keynesian school, in con-trast puts its focus on the demand side and has in the last years insistentlyre-introduced the concept of ’demand-led growth’ (see e.g. Setterfield (2003)).For our purposes, the post-Keynesian sight is only in part useful, because it ismainly concentrated on investments and not on private consumption (e.g. Pal-ley (2002)). Besides, the often criticized micro-foundation of modern dynamicmacro-models turns out to be very useful, because it allows the modelling ofpersonal income distribution and the investigation of household consumptionbehaviour. For all this reasons, this paper will concentrate on neoclassical mo-dels, which are properly extended by assuming non-homothetic preferences andindividuals with different incomes or wealth endowments.

There is only a small amount of literature dealing with this topic. The firstformal analysis of the relationship between inequality and growth through thedemand composition channel has been performed by de Janvry and Sadoulet(1983) within a two-sector-model, which investigates the conditions for equita-ble growth. The authors establish the concept of ’key growth sectors’, whichare mainly responsible for the growth process of the economy. For them it iscrucial that their demand comes from large fractions of the society in order toensure equitable growth. Equitable growth means that the growth process goesalong with increasing equality. Otherwise, when e.g. the key growth sectors isconstituted by luxury goods consumed only by a small upper class, the growthprocess leads to widening inequality.

Another seminal work is been developed by Murphy, Shleifer and Vishny(1989), who analyze the relationship between income distribution, demand andindustrialization within a static model. Exogenous shocks like an export boom

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only lead to a general industrialization process when markets for industrial goodsare large enough. This depends on the size of the population and especially onthe distribution of income, because agents widen their range of demanded goodswith rising incomes. The level of demand determines in turn the profitability ofprogressive technologies. With a broad middle class, such an exogenous shockleads to an income increase, which is equally distributed, so that a large demandfor industrial goods in generated and a general take-off process is induced. Inthis model, as well as in de Janvry/Sadoulet (1983), high inequality is harmfulfor growth.

These theoretical insights were integrated in endogenous growth models star-ting from the mid-nineties by Falkinger (1994), Zweimüller (2000) and Foell-mi/Zweimüller (2002, 2004).1 They combine the analysis of product diversityand hierarchical demand with neoclassical innovation-driven growth models (e.g.Grossman/Helpman (1991)). The focus of these models are the R&D-activitiesof firms, which are the key determinant of growth. In this dynamic framework,the innovators can gain a limited monopoly through development of new or im-proved products and these R&D-activities in turn enhance global productivityand growth. Like in the Murphy/Shleifer/Vishy-model, the profitability of theseactivities crucially depends on the size of the market demand, which is determi-ned by the number of people who can afford the new developed products. Peopleare ranked by their income and hierarchical demand is assumed, so that onlyrich individuals will consume the latest innovations. In this way, income distri-bution determines the structure aggregate demand and this is a main factor forglobal productivity and so a key variable for growth. If inequality is beneficialfor growth or not depends upon several assumptions. A large market size, andthus an equal distribution, is positive for growth, but also the high mark-upsthat can be charged from rich individuals for innovative goods, so that evenscenarios where inequality affects positively growth are possible.

2.2 An endogenous growth modelAs starting point, this paper takes the theoretical framework developed in Ma-ni (2001) to investigate the relationship between income distribution, demandstructure and growth. It includes the requested features specified above andfurthermore the structure of models with credit-market imperfections like Ga-lor/Zeira (1993).

In an economy with non-homogeneous goods, which are produced by usinglabour of different skill intensity, unequal consumers widen with growing incometheir range of demanded products to such of higher quality. Different types ofproduction need workers with low or high skills, who are paid according to theirlevel of human capital. High-level human capital has to be accumulated by acostly education, which has to be financed out of bequests because of creditmarket imperfections. Education can therefore only be afforded by members ofrich dynasties.

1A similar approach have Chou and Talmain (1996) and Matsuyama (2002)

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In a situation of low income inequality, there is a broad middle class whichdemands goods of medium skill intensity, like simple manufactures. That meanshigh returns to medium-skilled labour and relatively high wages for medium-skilled workers. These workers may be able to bequeath enough for their childrento invest in higher education, so that the average educational level of the eco-nomy rises together with income. Inequality, on the contrary, falls. Under highinequality, the population is mainly divided into two groups: A large ’proletarianclass’, which can only afford basic needs, and a rich class, which buys sophisti-cated goods. The resulting lack of initial demand for medium skilled productioncauses low returns for this sector, so that neither the middle class, nor the poorcan afford high education for their children. Thus, inequality is perpetuated inthe future, and income growth is harmed by low accumulation of human capital.

Brief Outline of the modelIn the economy individuals i live for two periods, leaving one offspring. In

the first period they work according to their acquired skill, in the second theyconsume and bequeath a part of their wealth to their offspring. Agents are equalin preferences, but not in wealth endowments (and therefore neither in income,as will be showed below). They are ranked in increasing order over the interval[0,1].

The economy’s firm sector is structured into three classes: a sector thatserves basic needs (like food demand) B, a middle sector that produces simplemanufactures M and a skill-intensive sector H that supplies more sophisticatedgoods.2 An important general assumption is that B and H are traded goods,so that their prices are fixed internationally and only the one of good M isdeterminated endogenously in the model. Agents consume a certain amount ofthe basic good B and when this need is satisfied, they divide the rest of theirincome into demand of goods M and H and into bequest. Their total utility isgiven by:

U(c) = cB if cB ≤ cB

U(c, b) = cB + (V (cM , cH))α · (b)1−α otherwise.

The goods are produced with a linear production technology with labourinput only. The employed labour must be of a certain specialization: In SectorB (e.g. agriculture), no specific formation is needed, therefore every individualcould be employed. For the other two sectors a special schooling is needed, amiddle one for sector M and a high one for sector H. The workers are paidaccording to their specialization with wages wB , wM and wH .3 The education

2Good B is a basic good that will be consumed only until cB . Consumption of others,M and H, increases with income, whereas demand of good M is concave in income. Thus,its share in total budget shrinks with rising income, while that of good H, as a luxury good,increases.

3Because of the fixed commodity prices and the linear production technology, wH and wB

can be taken as parameters.

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has to be financed out of the bequests of the individuals, because no creditmarkets exist in this economy. The middle one requires an amount sM , higheducation costs sH . The intertemporal budget restriction of the individual i isgiven by

yt(i) = (1− α)yt−1(i) + (wt(i)− st(i)− cB)

where y(i) is the residual income net of education costs. We assume thatindividuals of the ’upper class’, who received their bequest from parents withincome wH , are always able to cover the high education costs sH :

sH <1− α

α(wH − sH − cB).

We assume further that all other agents, even those from the ’proletarianclass’, that inherit a bequest generated out of income wB , can afford the mediumeducation, but of course not the high one:

sH <1− α

α(wB − c̄B) ≥ sM

An intertemporal short-run equilibrium can be analyzed through the exami-nation of the labour market of sector M : In the other two sectors prices andwages are set by the world market and because of the linear production techno-logy labour demand and supply correspond to the supply and demand for thecommodity.

Labour supply LS of the households depends upon their wealth endowmentbecause of the required skill acquisition. The poorest agent that can afford higheducation will be denoted by i∗(y) ∈ [0, 1]. The fraction of the population thatcan finance sH is therefore given by (1 − i∗). Labour supply in sector M is afunction of the wage in this sector: If the wage wM is too low, workers willprefer to work in B, where every agent is entitled to work. If it is too high, thewhole population would be employed in M. Given equality, individuals wouldbe indifferent. Taking educational costs into account,4 labour supply in sectorM is given by:

Ls = 0 for wM < w

∈ (0, i∗] for w = w

= i∗ for w < wM < w

∈ [i∗, 1) for wM = w

= 1 for wM > w

Labour demand LD in sector M, which corresponds to the demand for goodM, is determined by the income earned in the previous period t − 1, becauseconsumption takes place only in the second period, and the current wage insector M, wM .

4In sector B they are equal to 0, so that the bequest can be saved: wB +sB = w . In sectorH holds: wH − (sH − sM ) = w

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w

w

w LD

LS

i*0 1

Figure 1: Short-run equilibrium

To obtain aggregate demand, individual demands can be integrated over thewhole population:

LDt (wt, yt−1) =

∫ 1

0

lD(wt, yt−1(i))di

Market clearing is provided at any time if wMt > w, so that

LDt (wt, yt) ≤ i∗(yt).

The labour supply curve is non-decreasing in wage, while a labour demandcurve that satisfies Inada-conditions is strictly decreasing in wage. Thus a uni-que market-clearing equilibrium is achieved in each period. The market clearingwage determines thereby the income distribution in the same period and thebequest distribution in the next one. At the same time, income distributiondetermines demand for good M and so labour demand, while the distributionof bequests determines labour supply by affecting the educational decision. The

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sequence of market clearing wages {wMt}∞t=0 is the requested dynamic link bet-

ween income distribution, demand composition and supply side. To investigatethe implication for growth, a long run analysis is needed. The starting point isconstituted by the case, when subsequent elements of the sequence are equal,that means of steady states.

In this model, a steady-state is characterized by a self-perpetuating distri-bution of incomes y. The latter takes the form of a two-point distribution: Insteady state, a fraction (1 − i∗) is employed in the high-skill sector, the other,i∗ does not:

y =wM − sM − cB

αfor fraction i∗

=wH − sH − cB

αfor fraction (1− i∗)

The second of these two income levels, the upper class income, is exogenous,the first is endogenously determined and depends upon the wage in the middlesector wM . In the labour market, this implies three possible steady states atthree different wage levels, already derived in the short-run analysis: w, w andan intermediate wage level w*.5 The first one is a low-wage equilibrium: in thissituation, demand for good M is low and at the same time labor supply is highbecause of the scarce possibility for workers to catch up to sector H due to theirlow wages. Thus, the low-income situation is perpetuated. When the wage isat the highest possible (w), demand for the middle good is large and workers’revenues are so high that they would all catch up to sector H. Wages in sectorM must therefore be at least as high as wH . Between these two solutions, thelabour force would be allocated into the two sectors H and M.6

These three steady states yield different implications for human capital ac-cumulation, level of per capita incomes, employment and inequality. In the firstcase, when wages in sector M are low, only a few people can afford high educa-tion, the individuals keep being employed in sectors B and M (between whichthey are indifferent due to equal wages), so that the economy-wide human capi-tal accumulation is low as well. This is associated with a low per capita income,because of the large fraction of agents employed in low-wage sectors, and highinequality due to the large gap between wM and wH . In the second setting, wa-ges in M are that high that all individuals can catch up with sector H. In this’Nirvana-case’, both human capital accumulation and income per capita wouldbe maximized and there would be no inequality at all. The most interesting case,

5At this steady state income level, individuals in sector M can afford high education. Fora detailed formal description of the steady states see Mani (2001), section III.

6No one would work in sector B, since the wage is lower than w* and everyone can byassumption afford middle education. The basic goods would have to be imported. This seemssomewhat confusing, but might reflect the situation of many industrialized countries, whereagriculture does not attract labour force anymore because of the low wages, so that a largepart of the consumed food is imported. In Germany, contribution of the agricultural sector toGDP has decreased down to 1,1% in 2003. In other European countries, wages in agricultureare kept artificially high by transfer payments and market protection of the EU.

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because closer to reality, is the intermediate one: at the income level w*, moreworkers would be employed in sector H and the others would move completelyto sector M. Human capital accumulation would therefore be higher as in thefirst case. and inequality lower, because of the smaller gap between wH and wM .Per capita income would rise as well.

As a first general result, the model yields that greater inequality goes alongwith lower human capital accumulation and lower per capita income. It canfurther be showed that, although wage movements are not fully predictable,the economy converges to one of the three steady states from every startingpoint. A positive income shock (increase of average income) leads to a rise ofwages in every subsequent period, until wM = w. Without such a shock, wageswill remain constant or decrease over time until they reach the lower bound w,so that convergence is always achieved. With wages in M, the distribution ofincome and that of bequests converge, too.7

To examine the long run effect of inequality on growth through the demandcomposition channel, a redistribution of income8 is considered and the conse-quent growth path is compared with the original one. The result is clear-cut: Theredistribution program leads to a higher long-run income level, a higher humancapital accumulation and a more equal distribution. A necessary condition isthat all individuals can afford the basic good. Given this, an increase in incomefor the poorer agents implies a rise in demand for goods and labour in sectorM.9 Labour supply remains equal in this first period, because no agent is drop-ped out of sector H. Therefore wages in M rise. This increase leads to a higherdemand for good M in the next period, too. Labour supply may in contrast fall,because some individuals may have caught up to sector H, so that wM growsagain, while overall inequality is reduced. A process is induced, which leads inthe long run to a higher growth path than without the initial redistribution.

These results hold for a ’normal’ situation, when the economy is not toopolarized. A very high initial inequality could implicate, that the redistributionfails to raise wages beyond w (when low and unskilled labour supply is too highbecause of a large fraction of poor) or that wages are not increased enough(because of a very high initial gap) to allow some dynasties to catch up in thelong run with the upper class.10 In both cases, the long run path would bethe same as the one without redistribution. This result is somewhat consistentwith older development theories which stated, that in very poor economies itwould be better to concentrate wealth among the few rich to allow take-offinvestments, especially those in physical capital, than to scatter it, dividing itinto too small fractions that would not help anyone. In general, the income levelis crucial for the country’s development in this model as well as its distribution:With a too low income level (or an extreme polarization), when some agentscan afford only good B, a redistribution from rich to poor would lead to lower

7A detailed derivation of this result is reported in Mani (2001).8Income is redistributed from rich to poor agents without altering the ranks and without

changing the size of M and H.9Demand increases because, as mentioned before, good M is concave in income.

10A proof is given in Mani (2001).

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growth rates, because it would not increase demand for good M from the poor,but reduce it from the rich.11 If the country is too rich (and very equal), thatmeans, when all agents can afford sH , inequality does not affect growth.

It should be remarked that the growth process is induced by a demand shift,which generates higher revenues for middle skilled workers, who in turn raisetheir demand in subsequent periods. In doing this, they induce general a higherhuman capital accumulation and long-run growth and lower inequality.12 Thistheoretical results shall be tested empirically.

3 Empirical evidence

3.1 Some general considerationsAn empirical analysis of this relationship has still not been performed in asatisfactory way. There does not even exist an agreement about the generalrelationship between inequality and growth, as one can see studying the maincontributions on this topic (see table 1). While older research seemed to find astable negative impact of inequality on growth, more recent studies, based ondata of better quality, give ambiguous answers.13

Table 1: Relationship between inequality and growth (empirics)

Positive impact ofinequality on grow-th

Negative impact No clear relation-ship

Forbes 2000 Persson/Tabellini 1994 Barro 2000 (whole sam-ple)

Barro 2000 (rich coun-tries)

Alesina/Rodrik 1994 Banerjee/Duflo 2003

Perotti 1996 Bleaney/Nishiyama2004

Falkinger/Zweimüller 1997Deininger/Squire 1998Barro 2000 (poor countries)Castelló/Domenech 2002 (hu-man capital inequality)

As far as the demand-structure-link is concerned, things turn out to be evenmore difficult. Only a few attempts have been made to test this link empiri-cally. There is the early work of de Janvry/Sadoulet (1983) and two papers ofFalkinger/Zweimüller (1996, 1997).

An empirical verification of the theory outlined above requires a two-stageanalysis: First, the impact of income distribution on demand composition and

11A similar result was obtained by Foellmi/Zweimüller (2002).12In a later version of this paper we aim to include physical capital in the model in order

to study the non-linear Galor/Moav (2004)-relationship described in the introduction.13In general, there seems to be no linear relationship between the two variables (Baner-

jee/Duflo (2003)

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second, an examination of the link between demand and factor returns or pro-ductivity as determinants of income growth. The first stage is similar to empiri-cal tests of the Engel curve. The second step was undertaken in a first attemptin Falkinger/Zweimüller (1997). The section below will present existing studieson this topic, divided by the two stages, and then show new empirical evidenceby using a large data set including three waves of the German household survey’Einkommens- und Verbrauchsstichprobe’ (1993, 1998, 2003).

3.2 The impact of income on consumption structureThe model predicts that individuals vary their demand with changing income. Itpredicts further that each category, especially the basic needs, is not faced withan infinite demand but with satiation at a certain level. Finally, it suggests thatindividuals widen their range of demanded products with growing income.14

We use the largest available data set for Germany, the household surveyEinkommens- und Verbrauchsstichprobe (EVS), to provide an empirical evi-dence for these theoretical results.15 The EVS is one of the largest householdsurveys in Europe and includes ca. 0,2% of the German households (ca. 60.000in 2003). The survey was run for the first time 1962 and since 1973 data arecollected in 5-years intervals. In our analysis, we include the last 3 waves (1993,1998, 2003)16 and selected published results from previous waves.

For a first assessment, one can analyze the structure of private consump-tion in the three years examined, as reported in figure 1. The development ofexpenditure shares for all EVS-waves is reported in the appendix (figure 3).17

As one can see, the structure of consumption has remained stable over thelast 10 years, with minimal shifts. Housing expenditures have increased theirshare at the expense of clothing and food, the other categories remain almostunchanged. Greater changes have occurred in the long run, as shown in figure 3.The share of food in total consumption has decreased from 37% in 1962 to 14%in 2003. Taking together the three categories of ’basic needs’, food, housing andclothing, the share has decreased from about two third of total consumptionto around the half, and the decrease would have been much stronger, if theexpenditure for housing would not have increased conspicuously. This is mainlyattributable to rising prices18 and to improvements in housing quality and size.Expenditure for leisure, entertainment and culture, typical luxury goods, havedoubled in the same time their budget share from 7% to 14%.

14This is the core of the Falkinger/Zweimüller/Foellmi-models, but holds even for the Mani-approach, although there are only three good categories.

15Data sets have been evidently improved over the last years. The EVS is one of the mostcomplete surveys, including a large sample of income and expenditure variables, and it isregarded as one of the statistically most reliable.

16Data for 1988 are also available but are left out of this version due to statistical problemswith the structural break of German unification 1990.

17Since distances between the single waves are too long, no time series analysis can beperformed, but only cross-section studies.

18The influence of prices on consumption structure is only in part eliminated by taking intoaccount expenditure shares and not expenditure amounts. Variation in price structure maybias the estimation of the impact of income on demand as well as preference shifts.

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Comparing these results with the growth path of GDP gives a first descriptivesupport for the Engel hypothesis. Real income per capita has grown from 9824EUR19 in 1962 (West Germany) to 23975 EUR20 in 2003. Households’ demandfor basic goods is likely to be satiated, so that the devoted budget share shrinks,and they can shift their demand to other goods and services.

Further evidence gives the comparison between consumption patterns of hou-seholds belonging to different classes, as shown in figure 2.

Again, food turns out to be a basic good, which occupies a larger share ofbudget in poorer households than in richer ones. This relationship is even clearerfor housing expenditures, which show a decrease of almost 10 percentage pointsfrom the poorest class to the richest.21 In contrast, ’transportation’ (where carpurchases are embodied, among others) seems to be a luxury good category,with a clear increasing share.

In a next step, an inductive statistic can be performed. The assumptionsderived from the model can be tested both with a conventional Engel curvestudy and with a specific Engel curve for variety. As already mentioned, empi-rical tests of the Engel relationship have a long tradition in economics and theresults are regarded as historically and geographically invariant. Table 2 showsa geographically and historically broad sample of Engel curve studies.

Table 2: Selected Engel curve studies

Author(s) Country Period Data Source Relationshipbetween in-come leveland con-sumptionstructure

Engel 1857/1881 Belgium,Kingdomof Saxony

1853 Ducpetiaux1855, ownsurveys

Yes

Deaton/Muellbauer1980 (p. 20)

UnitedKingdom

1974 British FamilyExpenditureSurvey

Yes

Missong 2002 Germany 1993 EVS 1993 YesCrawford 2002 Czech Re-

public1991-92 Czech Family

Budget SurveyYes

Battistin/Miniaci/Weber 2003

Italy 1995 Survey ofHouseholdIncome andWealth (Bancad´Italia), Sur-vey of FamilyBudgets (Istat)

Yes

Noll/Weick 2004 Germany 2003 EVS 2003 Yes

19In 1991 prices.20In 1995 prices.21A reason might be the higher percentage of house owners among rich households, so that

rent expenditure do not occur.

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Figure 2: Structure of private demand in 3 EVS waves

Figure 3: Expenditure patterns of different ’classes’ in 2003

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Engel curves for varieties estimate the relationship between an income in-equality measure and the variety of consumption structure. The latter can bemeasured by a simple count of the number of demanded products, or by aconcentration index like the Herfindahl-Index. Table 3 shows the main contri-butions. In this case as well, the existence of a strong influence of income onconsumption structure, here on consumption variety, can be seen as empiricallyproofed.

Table 3: Engel curves for variety

Author(s) Country Period Data Source Relationshipbetween in-come leveland con-sumptionvariety

Jackson 1984 USA 1972-73 Consumer Ex-penditure Sur-vey

Yes

Falkinger/Zweimüller1996

57 coun-tries

1980 UN Internatio-nal Compari-son Project

Yes

Falkinger/Zweimüller1997

27 coun-tries

1975 UN Internatio-nal Compari-son Project

Yes

We use EVS-data to provide further and recent empirical evidence. FollowingEngel’s hypothesis, a dependence of the budget share from income position canbe assumed. In it’s simplest form, an Engel curve for commodity j takes theshape of a linear function, with absolute expenditures as a dependent variable22

cj = Aj + Bj y.

Linear Engel curves are not consistent with the theory described aboveand mostly do not provide a good fit. They are commonly used as a refe-rence. Another popular form is the so called Working-Leser-Specification (Dea-ton/Muellbauer 1980, 19; Missong 2002, 29), which relates log-incomes withbudget shares of expenditures:

cj/y = Aj + Bj log y

Estimations of this model for a basic good (food, beverages and tobacco)and a luxury good (healthcare) are reported in the appendix (figures 6 and 7).The different relationships emerge, although the estimation results are not sa-tisfactory.23. Better results can be obtained controlling for additional variables,like the age of the main income recipient or the size of the household (table 4

22A linear Engel curve for food expenditure is reported in the appendix (figure 4).23In a later version of this paper, more advanced demand functions shall be tested, especially

quadratic and non-parametric ones.

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in the appendix). We still obtain a negative sign for income as determinant ofthe budget share of food expenditure. In contrast, the number of persons in anhousehold turns out to be a positive factor for the expenditure in basic goods.24

A simple method for including the non-linearity of the income-expenditurerelationship is constituted by a classification of the regressors in various classes(leaving one out as reference), by treating them as dummy variables and ob-serving the changes in the coefficients’ sign. We do this in figure 8. The outputshows the expected developing: For a basic good like food, the sign is positive forlow income classes and turns negative for high ones. The sign in the regressionfor a luxury good like leisure is directly opposed: it shows a negative correlationfor low incomes and a positive one for rich households. Again, the R-squared va-lues are not very satisfactory, especially for the category ’leisure’. This suggeststhat there are other main determinants of consumption beside income.

Nevertheless, our results with recent EVS-data confirm in general previousfindings about the Engel hypothesis, so that we can pass over to the next step.

3.3 Consumption Structure, Factor returns and GrowthEstablishing a link between demand structure, factor returns and growth turnsout to be the most challenging step. In their 1997 work, Falkinger and Zwei-müller found no significant relationship between product diversity and growth.In the older study of de Janvry and Sadoulet (1983), the key growth sectorsare identified by their high sectoral gross output rates25 and the link towardincome distribution is build up by measuring the share of demand of differentsocial groups. Comparing the U.S. with Brazil and Mexico, they find out thatespecially in Brazil demand for key growth sectors came in the Seventies almostexclusively from the upper class, while the poor were mainly cut out. This resultholds even if intermediate sector relationships are taken into account (with aninput-output matrix). In the U.S., participation in demand of key growth sec-tors was much more equal distributed.26 The authors argue that because of thislack of demand out of low wage income, growth of the key sectors leads to moreinequality. We could add that this particular type of growth, not supported by abroad inner demand, did not endure, but slowed down after 1978 and remainedunstable since today.

A complete test of the model presented in section 2 of this paper wouldrequire a very complex estimation of demand-induced factor returns within aninput-output matrix. These would then be related to growth rates to measurethe growth effects of demand shifts. To provide a first hint for this relationship,we take the aggregate wage share as a (very) crude measure for the middle sectorwage described in the theoretical section. The theory predicts that a increase

24This might be due to rising food expenditures in families with children.25These are directly related and easier to observe than the sectoral gross rates of capital

formation, which would be required by the model.26The main problem with this approach is that these ’key growth sectors’ change over the

years. In the Seventies they were constituted by the automobile and appliances industry, todaywe would probably think of the IT-sector and biotechnology. The automobile sector has yetbecome one of the most problematic ones.

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in demand pulls up workers wage and that this activates a virtuous process,which leads (by reinforcing itself and enhancing human capital accumulation)to a higher growth rate.

Without differentiating for sectoral demand and skill-specific returns to la-bour supply, we compile for Germany a time series, comparing aggregate privateconsumption, wage share and real GDP growth (figure 7). In a second step weuse 2-years lags, testing the hypothesis that demand (private consumption) in-fluences wages and the latter affects growth (figure 8). In both cases the theorywould implicate positive correlations and in the second case it would predicta precursory course of the private consumption curve compared to the wageshare curve and of the latter versus the GDP growth curve. Unfortunately, noneof these results arise. Correlation coefficients are always negative (around -0,5)and especially the wage share curve seems rather to follow GDP curve thanto precede it. This is a clear sign, that this simple empirical model does notcapture the theoretical link described above. We nevertheless believe that thislink can be identified and refer to the development experienced by Germany’seconomy during the last years, which could be a hint for not rejecting the theo-ry: The last decade was characterized by an increase in inequality and this wasassociated with a growth slowdown. One of the main causes of this slowdownis generally seen, even by supply-side oriented economists, in a lack of internaldemand (SVR (2003), Rees (2004)).

4 ConclusionWhile the evolution of income inequality and its impact of the development pro-cess have received great academic attention during the last years, the studies arealmost all directed toward the supply side. The role played by demand in growthprocess has been neglected especially by large parts of mainstream neoclassicaleconomics, while Keynesian approaches seem to be inadequate for modeling per-sonal income distribution. We based our analysis on the Mani (2001) model asthe most convincing way to illustrate the notion that income affects demandpatterns of individuals, so that the structure of aggregate demand is heavily in-fluenced by income distribution. This demand structure affects the supply side,by rising prices for more desired goods and input factors and vice versa, andhas therefore a large impact on factor returns. This factor returns are crucialfor subsequent human capital investment decisions and therefore for long-rungrowth. A relatively equal income distribution goes along with strong demandfor middle class products, like simple industrial goods, high returns to midd-le skilled labour and consequently higher educational spending for the middleclass workers’ offsprings. This general catching up process lowers inequality andenhances growth.

Using a large data set including three waves of the German household sur-vey Einkommens- und Verbrauchsstichprobe (1993, 1998, 2003), we find strongevidence for a link between household income and demand structure. Individu-als’ demand changes with growing income, so that the concept of hierarchical

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demand can be regarded as empirically proved. The share of expenditure forbasic goods shrinks with growing income, while the amount devoted to luxurygoods grows superproportionally.

The link between the demand structure and growth is still not completelyclear and much work has still to be done in this field. Further empirical studieswill also be directed toward more sophisticated demand function estimations.Finally, an international comparison of consumption patterns, factor returnsand growth shall be performed to prove the geographical independence of theresults.

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5 AppendixTable 4: Model

Model R R square Adj. R square Std. Error of the estimate1 0,426 0,182 0,181 0,06182

Table 5: Coefficients (dependent variable: budget share of food, beverages, tobacco)

Unstandardized coefficients Standardized coefficients t-valuesB Std. Error Beta

(constant) ,560 ,007 84,441Number of employees in the HH ,006 ,001 ,080 9,841Age of main income recipient ,002 ,000 ,110 15,607Log income -,054 ,001 -,485 -65,401Number of persons in the HH ,023 ,000 ,423 59,986

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Figure 4: Long-run structure of private demand. Source: Noll/Weick 2004

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Figure 5: Linear Engel curve for food, beverages, tobacco (2003)

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Figure 6: Working-Leser Engel curve for food, beverages, tobacco (2003)

21

Figure 7: Working-Leser Engel curve for healthcare expenditures (2003)

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Figure 8: Linear regression with dummy variables

Figure 9: Time series for aggregate private consumption, wage share and GDP growth

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Figure 10: Lagged time series for aggregate private consumption, wage share and GDPgrowth

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