CENTRE FOR ECONOMIC REFORM AND TRANSFORMATION

School of Management and Languages, Heriot-Watt University, Edinburgh, EH14 4AS Tel: 0131 451 4202 Fax: 0131 451 3498 email: ecocert@hw.ac.uk

World-Wide Web: http://www.sml.hw.ac.uk/cert

Informal Sector, Income Inequality

and Economic Development

Prabir C. Bhattacharya‡

September 2007 Discussion Paper 2007/09

Abstract

This paper addresses – with the help of numerical simulation – some of the issues relating to income distribution in the context of development of an economy with an informal sector and migration of both low and high skilled workers from the rural to the urban area. A major aim has been to see under what conditions we do or do not get an inverted U-shaped curve of income distribution. The paper finds that the tendency always is for the Gini coefficient to rise and then decline. However, once it starts declining, it need not continuously decline; it may rise, then decline, then rise again and indeed rise above the previous peak before starting to decline again and may well end at the end of the simulation at a higher value than at the start. Any case for the redistribution of income is seen to be much stronger at later stages of development that at earlier stages, even though at later stages, Gini coefficient may be lower than at earlier stages. The policy implications of the findings are briefly considered.

Keywords: income inequality, Kuznets curve, informal sector, simulation JEL Classification: 011, 015, 017, 030, E17

‡ Department of Economics, School of Management and Languages, Heriot-Watt University, Edinburgh EH14 4AS, UK. Email: P.C.Bhattacharya@hw.ac.uk.

1. Introduction

We owe to the pioneer work of Kuznets (1955) the hypothesis that income inequality

first rises and then falls with development, tracing out an inverted U-shaped curve.

Kuznets argued that during the early stages of development, most of the population

will be in the agricultural sector, with low per capita income but low inequality,

incomes in the rural area being more equally distributed than in the urban area. As

people begin to migrate to the higher-income urban area, overall inequality will

increase. During the later stages of development, however, this force for inequality

would be more than offset by a decline in inequality within the urban area, owing to

the better adaptation of the children of rural-urban migrants to city life and “growing

political power of the urban lower-income groups” to enact “a variety of protective

and supportive legislation” (p. 17).

The empirical validity of the Kuznets curve continues to remain in question. Part

of the problem is methodological. Reliable time series data on the distribution of

income, over any substantial period, are not available for most developing countries.

Two approaches have therefore usually been taken by researchers to test the inverted–

U hypothesis. One is to make the heroic assumption that different countries observed

at different levels of development at a given point in time chart the path that a typical

country would follow over a long period of time. One then examines whether the

cross country data yield an inverted-U plot of inequality against level of development,

as measured by per capita income. The other approach is to examine changes in

inequality within countries over the short periods for which data are available, and see

whether inequality has risen in relatively less developed countries and declined in

more developed countries.

The Kuznets curve has received support in cross-sectional studies by Paukert

(1973), Cline (1975), Chenery and Syrquin (1975), Ahluwalia (1976) and Papanek

and Kyn (1986), among others. However, the findings of the cross-sectional studies

have been questioned, among others, by Anand and Kanbur (1993) who show that the

results are very sensitive to the choice of data set and that one can get U relationship,

inverted-U relationship or very little relationship at all by making different choices.

In a study exemplifying the second of the two approaches mentioned above, Fields

(1991) has shown that “inequality increases with growth as frequently in the low–

income countries as in the high-income countries. There is no tendency for inequality

to increase more in the early stages of economic development than in the later stages”

1

(p. 45). In a subsequent study, Fields (2001) found a substantial “Latin American

effect”: that the Kuznets curve that is observed in many cross-sectional data could

simply be a statistical fluke resulting from the fact that for specific historical reasons,

most Latin American countries happen to have both a middle level of income and a

high level of inequality.

There has also in recent years been the evidence of sharp rise in wage inequality in

most OECD countries since the early 1970s. Growth, it has been noted, has not

brought about a steady reduction in inequality. Various explanations have been

offered for this observed upsurge of inequality in developed countries, with a major

cause of the upsurge being attributed to a shift in the relative demands for skilled and

unskilled labour. Atkinson (1996), after reviewing the relevant evidence, concluded

that “there appears to be widespread agreement on the fact that there has been a shift

in demand away from unskilled labour in favour of skilled workers”, and that this

provides a straightforward explanation for rising earnings dispersion. Aghion and

Williamson (1998), in particular, have emphasised the role of skill-based

technological change in this context. Technological change, they argue, has been

biased towards certain skills and skilled workers and hence been an important source

of increasing inequality. As they write, “…technical progress stands as one important

source of increasing inequality. Given that it is also the major force of economic

growth, the Kuznets’ hypothesis appears to be strongly challenged” (p. 81). In this

view, there would be a spread of inequality in a high income region.1

There are others, however, who continue to hold that there is still good evidence

for the Kuznets curve. The difficulty, they argue, is that many other factors, in

addition to the level of development, affect a country’s level of inequality. Once the

analysis accounts for these factors, the Kuznets curve, as it were, “comes out of

hiding”. Barro (2000), in particular, has forcefully argued for this view.

Given the conflicting nature of the available empirical evidence, the scarcity of

reliable time series on income inequality spanning several decades, and the multitude

of factors likely to affect a country’s level of inequality, the use of numerical methods

would appear to be particularly appropriate here. It is, therefore, surprising that

numerical methods have so rarely been employed in this area. Such methods can

clearly complement both theoretical and empirical work. Numerical examples can

both illustrate the important results and show how sensitive they are to changes in key

2

parameters and initial conditions. The purpose of this paper is to use numerical

methods to address some of the issues surrounding income distribution and the

hypothesis of inverted-U curve. A major aim will be to highlight the key role that the

informal sector plays in the evolution of income distribution. The explanations offered

for the existence or non-existence of the inverted-U curve have not in general

incorporated the role of the informal sector in any systematic way.

In much of the theoretical literature, following Todaro (1969) and Harris-Todaro

(1970), the informal sector is viewed as being essentially a stagnant and unproductive

sector, serving merely as a refuge for the urban unemployed and as a receiving station

for newly arriving rural migrants on their way to the formal sector jobs.2 In sharp

contrast, the empirical literature increasingly sees the informal sector as dynamic,

efficient, contributing significantly to national output and capable of attracting and

sustaining labour in its own rights.3 Studies show that the share of the urban labour

force engaged in informal sector activities is growing and now ranges from 30 per

cent to 70 per cent, the average being around 50 per cent. Empirical findings also

show that many migrants from the rural to the urban area are attracted by income

earning opportunities in the informal sector itself; also that there is very little job

search activity by the workers in the informal sector.4

The present writer has elsewhere (Bhattacharya 1993a, 1994, 1998b) presented and

analysed a three-sector general equilibrium model of a developing economy which

systematically incorporates an informal sector and, in the dynamic version of the

model, presented alternative migration functions to those employed in the Todaro and

Harris-Todaro- type models. I now use this model as the base for the simulation

exercises to be performed here. In the simulation model, the aim, in particular, will be

to consider a number of different scenarios relating to the evolution of the primary or

formal sector wage and to study the implications of these for the evolution of income

distribution. We shall also examine the migration effects of both low and high skilled

workers from the rural to the urban area as also the effects of skill-biased

technological change. We shall also briefly study the effects of changes in the natural

1 In this context, see, however, the work of Galor and Zeira (1993). 2 For a review of this literature, see Bhattacharya (1993a) . 3 See, among others, ILO (1972), Sethuraman (1976), Bhattacharya (1996,1998a) and Gillis et al. (1992). 4 See, for example, Bhattacharya (1993b, 2002). See also Williamson (1988) for a review of some of the empirical evidence. As Williamson puts it “Todaro’s job-lottery and high unemployment view of urban labour markets in the Third World simply fails to pass the test of evidence”.

3

growth rates of different population segments in the economy. The focus will be on

Lorenz curves, the evolution of Gini coefficient and to see if and under what

conditions we do or do not get an inverted U-shaped curve of income distribution. We

shall also briefly consider the policy implications of the findings.

This paper is organised as follows. Section 2 presents a brief outline and then sets

out the final equations of the static model of the economy. Section 3 sets out the

dynamic model. The simulation model and the results of the numerical solution are

discussed in section 4. Section 5 concludes. Table 1 summarises the notation used in

the paper and is provided for convenient reference.

2. The Static Model: the Model Outline and the Final Equations

We have the following three sectors in our economy: the rural sector (R-sector)

which, as the name implies, is located in the rural area; and the formal and informal

sectors (F- and I- sectors, respectively), both located in the urban area. The people in

the rural sector are divided into two groups: those who own land and those who do

not. We call the former the rural hirers (RH) and the latter, the manual labourers (lm).

A rural hirer supervises agricultural operations in the land that he owns; he

“cultivates” this land by hiring landless labourers, i.e. by hiring lm. We assume that he

hires this labour at a market wage and not at a conventional wage. He also uses inputs

from the F-sector of the economy.5

In the urban area, the distinction between the formal and informal sectors is based

on the fact that due to the existence of the Minimum Wage Act, a firm in the urban

area which employs more than a specified number of workers, say l*, is required to

pay a wage which is “institutionally” determined and is above the free market wage:

the formal sector in this economy then consists of all such firms.6 The informal

sector, by contrast, consists of firms which obtain labour at the free market wage. The

informal sector is also characterised by ease of entry.

Within the informal sector itself, however, a distinction is made between two kinds

of unit and two kinds of output that they respectively produce. First, there is the

output produced by a group of I-sector workers which is directly consumed by the

people in the F-sector: the services of shoe-shine boys, domestic servants, etc., are

examples of this. We call this segment of the I-sector informal services (IS ) to

5 For example, fertilisers. 6 See also the discussion in the text on pp12-13 and footnote 15 below.

4

Table 1. Summary of notation

F the number of firms/owners of firms in the formal sector f the number of workers employed in the formal sector

Ff the number of workers employed in an -sector firm Fh the number of rural hirers i the number of firms in the -sector (each firm having an

owner/manager) MI

L the total labour in the urban area *l the maximum permissible size of firms beyond which the

“minimum” wage comes into operation/the number of workers employed in an firm MI

hl the amount of manual labourer employed by a rural hirer

ml manual labourer m the number of manual labourers p the price of the -sector output MIq the price of the -sector good R

HR rural hirer cFS , c

fS the amount of informal services consumed by an -sector employer and - sector employee, respectively

FF

v the wage in the informal sector *v the ‘minimum’ wage in the formal sector

w wage in the rural sector X the -sector output R

hX output produced by a rural hirer cFX , , ,

, ,

cfX c

hXcmX c

iX δciX

the amount of -sector goods consumed by an -sector employer, -sector employee, a rural hirer, a manual labourer, an informal sector worker, and the owner/manager of an informal sector firm, respectively

R FF

Y the -sector output FFY the output produced by an -sector firm F

hY the amount of -sector output used as input by a rural hirer Fc

FY , , cfY c

hY the amount of -sector goods consumed by an -sector employer, -sector employee and a rural hirer respectively

F FF

Z the -sector output MI

FZ the amount of -sector output used as input by an -sector firm MI Fα the fraction of their profit that is spent on consumption by an -

sector employer (F

)1( α− of profit, FΠ , being reinvested within the -sector) F

hβ the natural rate of increase of rural hirers

Lβ the natural rate of increase of urban labour

mβ the natural rate of increase of manual labourers δ the “reward demanded” by the entrepreneurs for the setting up of

firms MI

hΠ the profit of an HR

FΠ the profit of an -sector employer F

5

distinguish it from the other segment of the I-sector which we call informal

manufacturing (IM). Output of the firms in the IM segment is used by the F-sector as

input, with there often being a subcontracting relationship between the F-sector and

the IM -firms. People employed in the F-sector do not directly consume IM -goods as

they are perceived to be inferior; however, if the F-sector lends its “brand name” to IM

-goods, IM -goods are thereby transformed into F-goods and are consumed by such

people. In equilibrium, incomes of the workers in the IS and IM segments are equal.

There are thus four kinds of goods in our economy, namely, R-goods, F-goods, IM -

goods, and IS -goods. It is assumed that (a) the rural hirers consume R- and F-goods; (b)

the employers and the employees in the F-sector consume R-, F- and IS -goods; but that

(c) the lm and the workers in the I-sector cannot, due to their low earnings, consume

high-priced F-goods; and they consume only R-goods.

The economy just described has been modelled formally in Bhattacharya (1994) and

only the final equations of the model are therefore set out here7 (with Appendix I

providing brief interpretations of the labour market equilibrium equations of the model

for easy reference and ease of understanding):

The demand for and the supply of F-sector output is given by:

(1) ).*,(),(),(

*),,(),*,,,()]*,()[1(

PVYFwqYhwqYh

vvqYfpvvqYFpF

Fhc

h

cf

CFF

⋅=⋅+⋅+

⋅+⋅+Π⋅− ανα

The demand for and the supply of labour in the R-sector is given by:

. (2) mwqlh h =⋅ ),(

The demand for and the supply of R-sector output is given by:

(3) ).,(),,(),()(

),*,,,(*),,(),(),(

wqXhvqXivqXifL

pvvqXFvvqXfwqXmwqXh

hci

ci

cF

cf

cm

ch

⋅=⋅+−−+

⋅+⋅+⋅+⋅

δ

αδ

The demand for and the supply of IM output is given by:

*).()*,( lZipvZF iF ⋅=⋅ (4)

By the definition of δ , we have the following equilibrium condition:

).1(**)( δ+=−⋅ vvllZp i (5)

We state the conditions for labour market equilibrium in the urban area in the form of

two equations:

(6) ).,*,,,(*),,()1*( αpvvqSFvvqSflifL cF

cf ⋅+⋅+++=

7 In the formal model, the price of the F -sector output is taken as the numeraire of the system.

6

).*,( pvfFf F⋅= (7)

The endogenous variables of the model are: ; the exogenous variables

are: .

fvipwq ,,,,,

,,,*,*,,, αδFLlvmh

Eqs. (1), (2), (3), (4), (5) and (7) of the model are linearly dependent and for purposes

of carrying out comparative static exercises we can, therefore, drop one of the equations

from consideration and reduce the system to one of six equations in six unknowns. (The

unknowns are the price of the rural sector output, the wage in the rural sector, the price

of the IM -sector output, the number of firms in the IM -sector, the wage in the informal

sector, and employment in the formal sector.) The comparative static analysis of the

model has been carried out in Bhattacharya (1994) and the interested reader is referred

to that paper for a discussion of these results.8 Migration is introduced in the dynamic

version of the model and I now turn to outlining the dynamic model.

3. The Dynamic Model

3.1. The Model Outline and Rural-Urban Migration

Time enters in our model in three ways: through technical progress, through capital

accumulation in the formal sector, and through changes in the labour force. It is assumed

that technical progress occurs in the formal sector and in the rural sector, but not in the

informal sector. It is further assumed, in accord with wide empirical evidence, that

technical progress is labour-saving in the formal sector, but labour-using (and land-

augmenting) in the rural sector. In determining investment, we accept the spirit of the

capital stock adjustment model and write

),,( *1 ttttt kkkkI λ=−= +

where I = investment, is the optimal capital stock and the present capital stock.

We take the optimal capital stock as being some function of the expected profit and the

current profit as being a proxy for the expected profit. We can then write:

*k tk

8 The model, in particular, is seen to be block-recursive with changes in the rural sector, at any given time, having no effects on profit or employment creation in the urban area. The model, however, has a fundamental asymmetric feature in that while changes in the rural sector have no effects on the endogenous variables of the urban area, changes in the urban area do affect the endogenous variables of the rural sector, and these implications of the model, I have noted in Bhattacharya (1994), are in direct contrast to the fundamental implications of the Lewis (1954) -type models which suggest that agricultural development is a pre-requisite to industrial development and that it is agriculture which must necessarily provide resources for industrialisation. The model also questions the conventional wisdom that decreases in the formal sector “minimum” wage and increases in the maximum size of firm above which this minimum is enforced will help workers in the informal sector, the essential argument being that these policies may have adverse terms of trade effects on the informal sector that offset their favourable labour market effects.

7

Fttt knI Π⋅= )( .0,0 21 <> nn

In other words, of the total profit, Fttkn Π⋅− )](1[ is spent on consumption, while the

rest is reinvested. is the Fttkn Π⋅− )](1[ α of the static model.

The labour force in each of the three sectors changes due to population growth as

well as due to inter-sectoral movement of labour. We divided our people in the rural

sector into two groups, namely, and . Similarly, the people who look for jobs in

the urban area are divided into two categories: the H-type workers consisting of all those

who have friends and/or relatives working in the formal sector, and the L-type workers

consisting of those who have no such “contacts” in the formal sector. (The H-type

workers, in other words, consist of all those who have close “contacts” in and with the

formal sector: usually, though not necessarily, attainment of a certain level of formal

educational qualification can be take as a reasonably good proxy for “contacts” in the

formal sector). It is then assumed that those of the RH who search for jobs located in the

urban area form part of the H-type, while , if they migrate to the urban area, form part

of the L-type. If now the number of H-type workers exceeds the number of vacancies in

the formal sector, then a formal sector employer would not hire L-type workers until all

the H-type workers have been employed first; in which event the objective probability

of an migrant, an L-type worker, securing a formal sector job would be zero.

Migration flow is then modelled to consist of two distinct streams with two distinct

destinations – the manual labourers ( ) migrating to work in the informal sector in

response to higher wage in that sector compared to their rural wage, and the rural hirers

to the formal sector, with jobs mostly prearranged. (The model allows those of the rural

hirers who search for formal sector jobs to do so from either the rural or the urban area.

When search is from the urban area, search cost is borne by the hirers’ rural families.

The model also allows those of the hirers who go to the urban area to search for formal

sector jobs, but fail to obtain them, to return to the rural area). The migration function

for is given by the following expression:

HR ml

ml

ml

ml

ml

,)( tttm mwvF −

where is the total number of manual labourers ( ). That is, the proportion of who

migrate from the rural to the urban area is a function of the difference between the

informal sector wage, , and the rural sector wage, , and the greater the difference the

greater will be this proportion. There are both psychological and other costs involved in

m ml ml

v w

8

migration, and while some will migrate if is marginally higher than , others,

perhaps of less adventurous spirit or more attuned to the rural way of life, would be

motivated to migrate only if the difference between and is very much greater.

Potential migrants, in other words, have different levels of inertia in the face of a given

difference between and , so that the greater the difference between and the

greater will be the proportion of who would actually migrate.

ml v w

v w

v w v w

ml

The growth of in the rural area is, of course, given by the natural rate of increase

of minus the losses due to rural-urban migration, and can be expressed as:

ml

ml

))((1 ttmmttt wvFmmm −−=−+ β (9)

where mβ is the natural rate of increase of . ml

So far as the migration by the rural hirers (RH) is concerned, if the formal sector

wage, , is higher than their rural income, *v hΠ , then there is an incentive for an RH to

search for an F-sector job, and the greater the difference between and , the

greater will be the proportion of rural hirers who would search for such jobs. The actual

number of hirers who would search for F-sector jobs can then be expressed by the

following function:

*v hΠ

,)*( thH hvF Π−

where is the total number of hirers. Now, of course, only a fraction of these hirers

who search will in fact secure F-sector jobs since, quite apart from the fact that the

number of F-sector jobs available may be less than the number of RH searchers, there

will be other H-type candidates – the urban born H-types – who would also be searching

for F-sector jobs, and a proportion of the available jobs would go to these other

candidates. The share of RH searchers in the total number of H-type candidates would

therefore determine the proportion of the available F-sector jobs that would be secured

by the RH searchers. The actual number of RH searchers who secure F-sector jobs can

then be easily expressed by the following function:

h

),()*(

1 ttt

thH ffH

hvFg t −⎟⎟

⎠

⎞⎜⎜⎝

⎛ Π−+

9

where is the number of workers employed in the formal sector and H is the total

number of H-type candidates.

f9 And since the growth of RH is given by the natural rate of

increase of RH minus those RH who secure F-sector jobs and move permanently to the

urban area, we have

)()*(

11 ttt

thHthtt ff

HhvF

ghhh t −⎟⎟⎠

⎞⎜⎜⎝

⎛ Π−−⋅=− ++ β (8)

where hβ is the natural rate of increase of RH.

Given our migration functions, we can easily write the equation for the growth of

labour force in the urban area as follows:

)()*(

)( 11 ttt

thHtttmtLtt ff

HhvF

gmwvFLLL t −⎟⎟⎠

⎞⎜⎜⎝

⎛ Π−+−+⋅=− ++ β (10)

where is the total number of workers in the urban area and L Lβ is the natural rate of

increase of labour in the urban area.

3.2. The Model

We have now examined the avenues through which time, t, enters our model and we can

easily set out the dynamic version of the model. In the dynamic model set out below, we

omit, for the sake of convenience, the subscript t in all variables. (We also exclude

equation (1) because of linear dependency).

Equation (2): mtwqlh h =⋅ ),,(

Equation (3): ),*,,,(*),,(),(),,( tpvvqXFvvqXfwqXmtwqXh cF

cf

cm

ch ⋅+⋅+⋅+⋅

),,(),,(),()( twqXhvqXivqXifL hci

ci ⋅=⋅+−−+ δδ

Equation (4): *)(),*,( lZitpvZF iF ⋅=⋅

Equation (5): )1(**)( δ+=+⋅ vvllZp i

Equation (6): ),*,,,(*),,()1*( tpvvqSFvvqSflifL cF

cf ⋅+⋅+++=

Equation (7): ),*,( tpvfFf F⋅=

9 H, in other words, consists of all the urban-born H -type workers plus all the hirers who are searching for F -sector jobs. A numerical illustration may help clarify our discussion in the text. Suppose that initially there are 100 rural hirers in our economy. Further that, given the difference between and

, 20 of them are searching F -sector jobs. (As mentioned in the text, it does not matter whether they are searching from the rural area or from the urban area). Also suppose that in this economy there are 40 urban-born H -type workers. If now, say, 12 jobs become available in the F -sector, then (20/(20+40)). 12, i.e. 4 of the 12 jobs would go to the rural hirers, and these 4 hirers who secure F -

*vhΠ

10

Equation (8): dfHhvFgdthdh hHh ]/)*([ Π−−⋅⋅= β

Equation (9): dtmwvFdm mm ⋅−−= )]([β

Equation (10): dfHhvFgdtmwvFdtLdL hHmL ]/)*([)( Π−+⋅−+⋅⋅= β .

The endogenous variables of the model are: .,,,,,,,, Lmhfvipwq

It will be noted that in this dynamic counterpart of the static model of LDC, time, t,

enters in the production functions of the formal and the rural sectors to capture technical

progress in these sectors, but as there is no technical progress in the informal sector, t

does not enter in the production function of the IM -sector. In the formal sector, t also

additionally captures the impact of capital accumulation. And in the rural sector we also

let t incorporate the consequences of the fact that as time passes and the number of RH

increases, the given land gets subdivided amongst the increased number of hirers. The

consumption demand of both the rural hirers and the F -sector employers will also, it

will be noted, now depend additionally on t.

4. Numerical Solution

4.1. Setting the Scene

As already mentioned, the behaviour of the static model and the various dependencies

therein have been examined in detail in our earlier paper. To examine some of the

dynamic aspects of the model, I now specify explicitly the functions appearing in

equations (8) - (10) and carry out a numerical simulation. The equations of the static

model give the instantaneous values at time t of vipwq ,,,, and for the current value

of h, L, and . In the simulation, the functional forms and their dependencies are chosen

to reflect the analysis of the static model. Details are given in Appendix 2. It may be

useful, however, to summarise here the key initial conditions that describe our economy.

In choosing these initial conditions, our aim has been to reflect the situations in a fairly

“representative” LDC.

f

m

10 First, since most LDCs have a predominantly rural population

engaged in agriculture and a relatively small urban population, 30 per cent is taken as

the initial figure for the urban share in the total population. The manual labourers ( )

and rural hirers ( ) constitute 42 and 28 per cent, respectively, of the total population

ml

HR

sector jobs would then move permanently to the urban area and we will be left with 96 rural hirers in our economy. 10 For fuller justifications of the parameter values and the initial conditions used than provided here and in Appendix 2, the interested reader is referred to the analysis in Bhattacharya (1993b, 1996, 1998a). Many of the parameter values and initial conditions used here are also within the range of values used in previous simulation studies in the literature.

11

in the initial period.11 Second, the formal sector is taken to employ 40 per cent of the

urban workers initially. The fact that the informal sector provides employment to a very

large number of urban workers is now widely recognised12 and a share of 40 per cent for

formal sector employment would appear to be a reasonable figure to start with. Third, so

far as wages are concerned, we take the rural wage, w, to be a quarter and the informal

sector wage, v, to be a half of that in the formal sector in the initial period. I have

elsewhere provided some evidence on these wages in the Indian context13 and the initial

conditions used here are broadly in accord with this evidence. Gillis et al. (1987, pp.

191-93) also provide some observations on the wages in the three sectors as also a

discussion of the informal sector in Indonesia. So far as the rural hirer’s income, , is

concerned, a large number of rural hirers in our economy are likely to be those with

holdings of relatively small sizes,

hΠ

14 and it would seem reasonable to start with a value of

lower than the formal sector wage, v*, and accordingly we set the initial value of

at 0.6v*.

hΠ

hΠ

So far as the evolution of the formal sector wage, v*, is concerned, we shall consider

a number of different scenarios. While in the relevant literature, the formal sector wage

is commonly viewed as being the “minimum” wage, it can also, of course, be viewed as

being either a direct indicator of the union power or the efficiency wage.15 The formal

11 In other words, we take lm to constitute 60 per cent of the rural population. In determining which agrarian groups correspond to our RH and lm respectively, we recognise that our categories, like most used in social sciences, are not isomorphic. While they have strong empirical content, they are also ideal-typical, i.e., based on global qualitative characteristics. In most less developed countries (LDCs), landless and small holders, the two poorest groups in the rural sector, together constitute a majority of rural households (thus in India, in 1954-55, landless and those with holdings of up to 2.49 acres together accounted for about 56 per cent of agricultural households) and we take these two groups as broadly constituting our lm. Most small holders, of course, supplement their incomes by agricultural labour. 12 See, among others, Sethuraman (1981) and Bhattacharya (1996, 1998a) for evidence on the informal sector employment. 13 See Bhattacharya (1998a). 14 With holdings of between, say, 3 and 10 acres. See footnote 11 above. Also, and as Little (1982, p. 149) has noted, one of the views of LDC agriculture now widely accepted is that there is an active labour market in the rural areas of LDCs and that all but the smallest operators demand outside labour at times. 15 As is well know, the theoretical foundations of many dual labour market models are provided by the efficiency wage hypothesis, according to which labour productivity depends on the real wage paid by the firm, and employers have the incentive to offer wages in excess of workers’ reservation wage. The efficiency wage approach identifies four benefits of higher wage payments: reduced shirking by employees due to a higher cost of job loss; lower turnover; an improvement in the average quality of workforce employed by the firm, and improved morale. [Yellen (1984), Katz (1986) and Nickell (1990), provide good reviews of the relevant literature.] Dual labour markets are then explained by the assumption that the wage productivity nexus is important in the primary or formal sector of the economy and there is accordingly in that sector job rationing and voluntary payments by firms of wages in excess of market clearing. By contrast, in the secondary sector, the wage-productivity

12

sector wage can also be influenced by skill-biased technological change, with skill-

biased technological change leading to an increase in the wage gap between the formal

and informal sectors to reflect the skill differential. While the question of the skill-

biased technological change is addressed in Section 4.4 below, we mention this here to

make the point that the F-sector wage can be influenced by a number of different

factors. Against this backdrop, we, therefore, consider the following five cases to

examine the consequences of a change in the formal sector wage, v*, on the evolution of

our economy. First, in accord with the view of it being the fixed “minimum” wage, we

shall consider a case where v* is fixed (at 0.8; see Appendix 2). In practice, however,

the formal sector wage, v*, is likely to be determined in some relation to the market

determined wage in the informal sector, v. So we consider two cases where there are

fixed wage differentials between the formal and informal sectors. The cases are: v*=2v

and v*=4v. We then consider a case where we make v* time dependent: v*=2v+0.5.

sin(t/3). Finally, we consider a case where we fluctuate the formal sector wage in time

(with periodic oscillations): we set v*=2v for the first ten time periods, 4v for , 6v

for , and 4v for . Consideration of these five different cases will be seen to

bring some of the important results of the paper clearly to the fore.

30≤t

40≤t 40>t

Finally, so far as the natural rates of population growth are concerned, population

growth rates in urban areas of developing countries are generally lower than in rural

areas and in the simulation we set a natural growth rate of 2 per cent for urban workers,

3 per cent for manual labourers (lm) and, between these two, a rate of 2.5 per cent for

rural hirers.16

The time paths of the endogenous variables would of course be influenced by the

parameter values used. While the details of the parameter values and how these are

relationship is weak or non-existent and firms in this sector obtain labour at the free market wage. In that variant of the efficiency wage hypothesis known as the shirking model (Shapiro and Stiglitz, 1984; Calvo, 1985), it is assumed that the less observable is workers effort the more likely it is that they will shirk and hence the less productive they will be. By paying wages above the alternative rate, firms provide an incentive to workers not to shirk. A number of dual labour market models are then constructed on the assumption that effort is less observable in the formal than in the informal sector and a higher wage accordingly is paid for jobs in the formal than in the informal sector (in which shirking is difficult). See, for example, Bulow and Summers (1986) and Esfahani and Salehi-Isfahani (1989). See also Dickens and Lang (1988) for empirical foundations of dual labour market theory. Two-sector models can also of course be constructed on a distinction between an unionised and a non-unionised sector. For models along these lines, see Minford (1983) McDonald and Solow (1985) and Layard et al. (1991, ch. 2), among others. 16 Overall rates of population growth in the developing economies ranged from around 2 per cent a year in parts of Africa to over 3 per cent in much of Latin America and in major parts of Asia in the late 1950s and early 1960s. During the 1980s, they ranged from around 3 per cent a year in Africa to around 2 per cent in parts of Asia and Latin America. (Sources: UN Demographic Year Book 1962; and World Bank, World Development Report 1990).

13

incorporated in the simulation are given in Appendix 2, it may once again be useful,

before discussing the simulation results, to note here briefly the (proximate) influences

on the behaviour of some of the endogenous variables. Thus, the behaviour of the

informal sector wage, v, would ceteris paribus be influenced by changes in the labour

supply to the informal sector and changes in the demand for both the informal services

and the informal manufacturing output. The behaviour of the rural sector wage, w,

would be influenced by (i) technical progress in the rural sector, (ii) changes in the

number of hirers and of manual labourers in the rural sector, and (iii) changes in the

demand for the rural output X by the workers in the urban area.17 The rural hirer’s

income, , would be influenced by (i) technical progress in the rural sector, (ii)

changes in the number of hirers, and (iii) changes in the price, q, and the wage, w, in the

rural sector.

hΠ

In the simulation results to be presented below, the Lorenz curve has been calculated

for each time step of the simulation, based on the proportion of population and the

proportion of earnings, sorted in order to obtain the convex curve. Based on the Lorenz

curve, the Gini coefficient has been derived for each time step as a ratio of the area

between the line of equality and the Lorenz curve to the area of a totally unequal curve

(where one person earns all of the income in the economy). Lorenz curves have been

plotted at five different points, four of which – time periods 0, 8.135, 35.135 and 60 –

are common to all cases, and one is plotted at the maximum inequality (when the Gini

coefficient peaks) in each case.18 Therefore, one of the Lorenz curves is always plotted

at a different time in each of the diagrams below. 19

4.2. Different Cases Relating to the Formal Sector Wage and the Simulation Results

The results of the simulation for different cases relating to the formal sector wage, v*,

are presented in Figures 1–4. As the figures show, for the specified parameter values and

[Figures 1-4 here]

17 In our model, when the demand for the rural output X increases, the price of X, q, rises when q rises, the rural hirers ceteris paribus demand more labour, and w, the wage in the rural sector, increases as a result. See the discussion in Appendix 2. 18 Lorenz curves have been evaluated at the start of the simulation, at the first point on or after the time period 8, at the maximum of Gini coefficient, at the first point on or after the time period 35 and at the end of the simulation. The points have fractions because of the step size chosen by the solver of the differential equation in Matlab. 19 For readers interested in intra and intersectoral inequalities in a generic form, graphs for logarithmic variances are available on request from the author.

14

the initial conditions, the number of manual labourers in the rural sector, m, as a fraction

of total population, T, decreases in all cases. The number of urban labourers, L, as a

proportion of total population, T, on the other hand, increases in all cases. The number

of rural hirers, h, as a fraction of total population remains more or less unchanged.

Employment in the formal sector, f, increases absolutely, but as a fraction of urban

labour, L, it increases slightly for a brief period of time before declining steadily.20 The

informal sector wage, v, on the other hand, rises steadily over time. The rural sector

wage, w, too rises, but rises very slowly and the gap between v and w widens over time.

The income of rural hirers, , also rises but v rises faster than hΠ hΠ .

An intuitive explanation of the behaviour of v in the model can be offered as follows.

An increase in the labour supply in the urban area will of course ceteris paribus tend to

decrease the informal sector wage, v. As against this, however, when capital

accumulation in the formal sector leads to an increase in employment in that sector,

some of the workers in the urban area – some of the urban-born H-type workers – find

employment in the formal sector and this tends to decrease the labour supply to the

informal sector and so increase v. The demand for informal sector output also increases

over time and this too tends to increase v. As investment in the formal sector increases,

the demand for the IM -sector output (i.e., the demand for Z input) by the F-sector firms

increases. Further, as employment in the formal sector increases due to capital

accumulation in that sector, the demand for informal services also increases as a result:

the informal services, it will be recalled, are consumed by F-sector employers and

employees, and an increase in the number of F-sector employees, therefore, ceteris

paribus, leads to an increase in the demand for such services. (The F-sector employers’

demand for such services can also be expected to increase over time, though given their

relatively small number, it is unlikely that their increased demand for such services can

have a significant impact on v). The net effect of these tendencies is then a steady rise in

v.21 By contrast, changes influencing the behaviour of the rural sector wage, w, in the

20 In absolute terms, the number of manual labourers first rises, then declines in all cases, while the number of rural hirers, total urban labour and employees in the F-sector all increase in all cases. Graphs showing the behaviour of different population segments in absolute terms are not presented here to save space, but are available on request from the author. 21 So far as the effect of an increase in the formal sector wage, v*, on v is concerned, this was found to be ambiguous in the static model. An increase in v*, on the one hand, leads to a decrease in the number of people employed in the formal sector and this tends to decrease the demand for informal services and so tend to decrease v. As against this, however, an increase in v* means that employees in the F -sector , whose wages have increased, will now demand more informal services and this would tend to increase in v. Also, an increase in v* may lead to F-sector employers sub-contracting out more to IM

15

model generate a number of conflicting tendencies (see discussion in Appendix 2) such

that w rises only very modestly and the gap between v and w widens over time.

It will be noted that what the particular value of the formal sector wage, v*, is (i.e.,

whether v*=0.8 or 2v or 4v or time dependent) does not make much of a difference to

the evolution of the gap between the informal sector wage, v, and the rural sector wage,

w, in the model. The gap between v and w w

idens over time (Fig. 2). Also, the fractional

distributions of population are not significantly affected by these changes in v*, with a

higher value of v* relative to v leading to a slightly higher level of urbanisation – i.e.,

the proportion of urban to total labour (L/T) – at the end of the simulation, but not by

very much so (Fig. 1). Even when we fluctuate the formal sector wage in time with

periodic oscillations (case 5), this stimuli does not affect significantly either the

fractional distributions of population or the wages in other sectors (including the rural

hirer’s income).

However, changes in the formal sector wage, v*, have major effects on Lorenz

curves and the evolution of the Gini coefficient. One can observe that the number of

employees in the formal sector, f, as a proportion of urban labour, L, – i.e., f/L – grows

for the first 10 - 15 time periods of the evolution of the system (Fig. 1). After this time,

this fraction decreases in time in all cases, with varying speed. Therefore, depending on

the behaviour of v*, two types of Gini coefficient evolution can be observed:

1. When v* is fixed, the income of the group earning the most in the early stage of the

evolution (i.e., the income of F -sector workers) quickly becomes equal with the

incomes of other groups, due to the lack of growth of v*; and the Gini coefficient

declines over time (Fig. 4). However, the case of v* being permanently fixed is, of

course, an unrealistic one. It is unlikely that v* would remain unchanged as v grows.

Instead, v* will also grow in time.

2. When v* grows, Gini coefficient will increase in the beginning, since the smallest

group – the workers in the formal sector, f – earns the most, with their wages also

increasing; but in time, the fraction “f” starts to decline and other groups earn more,

as the wages and income of other groups also grow in time.

So except when the formal sector wage, v*, is fixed, we do get an inverted U-shaped

curve of income distribution. With a higher value of v* relative to the informal sector

wage, v, Gini coefficient rises higher, peaks later and ends at a higher value at the end of

firms to save on labour costs and this too would tend to increase v. The net effect of an increase in v* on v is therefore not unambiguous and is likely to be relatively small.

16

the simulation. Thus, in the case of v*=2v, Gini coefficient peaks at the time period

14.135 and ends with a value of 0.23 at the end of the simulation; in the case of v*=4v,

Gini coefficient peaks at the time period 23.135 and ends with a value of 0.3 at the end

of the simulation. In the case where we fluctuate the formal sector wage in time (case 5),

Gini coefficient peaks at the time period 30.635 and ends with a value of 0.3 at the end

of the simulation, with the tendency always for the Gini coefficient eventually to

decline. Of course, the Gini coefficient need not necessarily decline continuously after

reaching a peak; it may decline for a while, then rise again to another peak, higher than

the previous peak, due to a renewed widening of the gap between v and v*, but the

tendency always is for the inverted U-shaped curve to reassert itself. So the observation

of a rise in Gini coefficient after a decline in it will not necessarily imply that there is no

underlying inverted U-shaped curve. We shall comment more on this aspect of the

inverted-U hypothesis when we come to discuss the skill-biased technological change in

Section 4.4 below.

It may also be noted that our results for Lorenz curves and Gini coefficient do not

imply that the poorest group of the population (lm) are necessarily worst off – in terms of

their share in total income – at the period when the Gini coefficient is at its peak. For

example, in the case of v*=2v, Gini coefficient peaks at the time period 14.135, but the

Lorenz curve for that period lies above that, for example, for the period 35.135 towards

the bottom left corner of the diagram (case 2, Fig. 3). In this case, at the time period

35.135, bottom 25 per cent of the population has about 8 per cent of the total income,

whereas at the time period 14.135 – when the Gini coefficient is at its peak – they have

about 9 per cent of the total income. Similarly, at the time period 60, bottom 15 per cent

of the population has about 5 per cent of the income, whereas at the time period 14.135,

they have about 6 per cent of the income. While in absolute terms, the poorest are better-

off at time periods 35.135 and 60 than at 14.135, in relative terms they are clearly

worse-off in these later time periods, even though Gini coefficient is lower at these later

time periods that at 14.135.

Note, however, that it is only in time periods after the period when the Gini

coefficient is at its peak that the poorest are relatively worse-off (in terms of their share

in total income) compared with the period when the Gini coefficient is at its peak. In

earlier periods – periods before the period when Gini coefficient is at its peak – the

poorest are relatively better-off (in terms of their share in total income) compared with

the period when the Gini coefficient is at its peak. In later periods of the evolution of the

17

economy, income of other groups increase by very much more than that of lm income.

The case for redistribution of income would thus appear to be much stronger at later

stages of development than at earlier stages in our model.

4.3. Effects of a Change in the Migration Sensitivity Parameters

Having considered the effects of a change in the formal sector wage, v*, we now

consider the effects of a change in the responsiveness of potential migrants to rural-

urban income differences. Am is the parameter that measures the responsiveness of

potential lm migrants – the low skilled workers – to differences between the informal

sector wage, v, and their rural sector wage, w (see Appendix 2). In the simulation so far,

we have assumed Am=0.05. We now speed this up and set Am=0.05+0.0008t, while

keeping all other parameter values and initial conditions unchanged. And we consider

here only the case of v*=2v. Results are presented in Figure 5. The graphs in Figure 5

are to be compared with those for the case of v*=2v (i.e., case 2) presented in Figures 1-

4.

[Figure 5 here]

Comparing the graphs, one can see that a change in Am has significant effects on the

evolution of the rural sector wage, w, the gap between the informal sector wage, v, and

the rural sector wage, w, and on the fractional distributions of population. When Am

increases, w rises, the gap between v and w becomes smaller, and urban labour as a

proportion of total labour – i.e., L/T – increases. A change in the migration sensitivity

parameter Am, in other words, has greater effects on the evolution of these variables than

does a change in the formal sector wage , v*, which, as we have seen, has relatively little

effects on the evolution of these variables.

An increase in Am also leads to Gini coefficient peaking earlier: while in the case of

v*=2v and Am=0.05, Gini coefficient peaks at the time period 14.135, in the case of

v*=2v and Am=0.05+0.0008t, it peaks at the time period 11.135. Also, in this latter case,

the Gini coefficient ends much lower at the end of the simulation. An increase in the

responsiveness of lm to differences between their rural and the informal sector wage, in

other words, would lead to an improvement in income distribution in this model.

By contrast, a change in the migration sensitivity parameter for the rural hirers, Ah,

has very little effects on the evolution of our economy. Ah is the parameter that measures

the responsiveness of rural hirers – the high skilled workers – in looking for F-sector

jobs in the face of differences between the formal sector wage, v*, and their rural

18

income, (see Appendix 2). In the simulation of the paper, we have set Ah=0.1.

However, we also carried out a simulation for the case of v*=2v with Ah=0.1+0.0016t,

while keeping all other parameter values and initial conditions unchanged. Nothing

significantly different was seen to happen as a result of this change. These graphs with

Ah=0.1+0.0016t are not presented here to save space, but are available on request from

the author. So while a change in the migration sensitivity parameter for lm, Am, has

significant effects on the behaviour of our economy, a change in the migration

sensitivity parameter for the rural hirers, Ah, has no such effects.

hΠ

4.4. Effects of Skill-Biased Technological Change

As noted in the introduction, Aghion and Williamson (1998) have emphasised the role

of skill-biased technological change in the observed upsurge of inequality in most

OECD countries since the early 1970s. In this view, as a result of skill-biased

technological change, there would be a spread of inequality in a high income region. It

would clearly be interesting to try to capture some of the effects of skill-biased

technological change in our model.

F-sector is the sector which would be subject to skill-biased technological change in

the model, with RH migrants and urban-born H-type workers being the skilled workers.

If there is a skill-biased technological change, employment in the F-sector will increase

as a result, the skilled workers to be employed in the sector coming from the ranks of the

urban-born H-type workers working in the I-sector and from RH migrants.

Subcontracting relationships between the F-sector and the I-sector will probably

weaken: more skill intensive F-sector will demand less IM output to be used as input.

Further, the wage gap between the formal and informal sectors will widen to reflect the

increased skill differential.

We can change the values of two of the parameters in our model to incorporate these

features of skill-biased technological change. We have so far assumed the technical

progress in the formal sector to be labour saving. The parameter tγ has captured the

contrasting effects of capital accumulation and of the labour saving technical progress in

the formal sector on the number of people employed in the formal sector, f (see

Appendix 2). In the simulation so far we have set tγ =0.0075. We now change this to

tγ =0.0095 to reflect the impact of skill-biased technological change, which, as we just

noted, would lead to an increase in employment in the formal sector, f. The other value

19

we change is that of the parameter tζ . tζ captures the effects of capital accumulation

and technical progress in the formal sector on the demand for IM output by the F-sector

firms. We have so far set tζ =0.0075. We now change this to tζ =0.005 to reflect the fall

in the demand for IM output by the F-sector firms following the skill-biased

technological change.

We can now carry out the following simulation to try to capture some of the effects

of the skill-biased technological change in the model: we set v*=2v, tγ =0.0075 and

tζ =0.0075 for the first 40 time periods of the simulation, then for the rest of the

simulation we set v*=4v,22 tγ =0.0095 and tζ =0.005 (i.e., we allow the skill-biased

technological change to impinge on our system after 40 time periods). All other

parameter values and initial conditions remain unchanged, i.e., are those as set out in

Appendix 2. The results of the simulation are presented in Figure 6. The graphs in

Figure 6 are to be compared with those for the case 2 presented in Figures 1–4 (i.e., the

case where we set v*=2v, tγ and tζ =0.0075 all through).

[Figure 6 here]

The results show that while the number of employees in the formal sector, f, as a

proportion of urban labour, L, – i.e., f/L – temporarily rises as a result of skill-biased

technological change, the fraction soon begins to decline again, though compared with

the case 2, it ends at a higher value at the end of the simulation. Urban labour as a

proportion of total labour (L/T), however, ends lower at the end of the simulation in this

case compared with the case 2. Skill-biased technological change, in other words, leads

to a higher share of F-sector employees in the total urban labour force, but to a lower

level of urbanisation.

Rural wage, w, is not significantly affected by skill-biased technological change, but

the informal sector wage, v, declines due to the reduction in the demand for IM output by

the F-sector firms following the skill-biased technological change. So while

employment in the formal sector increases as a result of skill-biased technological

change, the wage in the informal sector decreases as a result of such change.

So far as the evolution of the Gini coefficient is concerned, it now peaks at the time

period 41. Before the introduction of the skill-biased technological change, Gini

coefficient was already on the decline, but the wage premium associated with the

20

increased skill differential now leads to an increase in Gini coefficient, but after this

increase, the tendency again is for the Gini coefficient to decline, though, in this case, at

the end of the simulation it ends at a higher value than at the start.

4.5. Effects of a Change in the Natural Growth Rates of Population

In the simulation so far, we have assumed the natural growth rate of population for

manual labourers, mβ , to be 0.03; that for rural hirers, hβ , to be 0.025; and that for

urban labourers, Lβ , to be 0.02. To examine the consequences of a change in the

natural growth rates of population of manual labourers and rural hirers, however, we

also carried out a simulation with 02.0=== Lmh βββ , while keeping all other

parameter values and initial conditions unchanged. Locus of Gini coefficients over time

again traced out an inverted U-shaped curve. The results showed the rural wage, w, to

rise ever so slightly higher and the gap between v and w to be ever so slightly smaller in

this case compared with the case of mβ =0.03, hβ =0.025 and Lβ =0.02. The results also

showed Gini coefficient peaking earlier23 and ending lower at the end of the simulation

in this case compared with the case of mβ =0.03, hβ =0.025 and Lβ =0.02. Reducing the

natural growth rates of population of RH and lm and bringing these in line with the

natural growth rate of population in the urban area, in other words, would improve

income distribution in this economy. Graphs of simulations with 02.0=== Lmh βββ

are not presented here to save space, but are available on request from the author.

5. Concluding Remarks

The aim of this paper has been to address – with the help of numerical simulation –

some of the issues relating to income distribution in the context of development of an

economy with an informal sector and migration of both low and high skilled workers

from the rural to the urban area. In particular, we wanted to see under what conditions

we do or do not get an inverted U-shaped curve of income distribution.

22 The gap between v* and v widens to reflect the skill differential. 23 Thus while in the case of v*=2v and mβ =0.03, hβ =0.025 and Lβ =0.02, Gini coefficient peaks at

the time period 14.135, in the case of v*=2v and 02.0=== Lmh βββ , Gini coefficient peaks at the time period 9.635.

21

The gap between the informal and the rural sector wage is in general seen to widen

over time in our model.24 Changes in the formal sector wage have relatively little effects

on the evolution of this gap or on the proportion of urban to total population in the

economy.25 A change in the responsiveness of potential lm migrants – the low skilled

workers – to differences between the informal and their rural sector wage has much

greater impact on these.26 Skill-biased technological change has little effects on the

evolution of the rural sector wage, but it leads to a lowering of the informal sector wage.

It also leads to an increase in the share of formal sector workers in total urban workers

but to a lower level of urbanisation at the end of the simulation.

We found the tendency always is for the Gini coefficient to rise and then decline.27

However, once it starts declining, it need not continuously decline; it may rise, then

decline, then rise again and indeed rise above the previous peak before starting to

decline again and may well end at the end of the simulation at a higher value than at the

start. How exactly the Gini coefficient moves over time depends crucially on the

evolution of the gap between the formal and the informal sector wage. And this gap can,

of course, be influenced by a number of different factors such as changes in the forces

emphasised in efficiency wage theories,28 insider power, government policies, trade

union pressure, skill-biased technological change, and so on.

So far as the policy implications of the paper are concerned, it is clear that the

expansion of the informal sector and migration by manual labourers (lm) to the informal

sector play vital role in reducing income inequality in the model. Policies designed to

strengthen sub-contracting relationship between the formal and informal sectors may be

particularly important in this context (especially if there is skill-biased technological

change tending to weaken this relationship). Also, it is clear that owing to the slow

growth of their wage in the rural sector, the manual labourers (lm) in the rural area will

continue to remain poor even at later stages of development. There is, therefore, a case

for redistribution of income. However, we found the case for redistribution to be

24 Except in the case of skill-biased technological change (case 7) where, as we saw, following the introduction of skill-biased technological change, the informal sector wage, v, declines due to a reduction in the demand for IM output by the F-sector firms. 25 These results, it will be noted, are very different from those obtained in the Todaro (1969) and Harris-Todaro (1970) -type models. 26 A change in the responsiveness of potential RH migrants – the high skilled workers – to differences between their rural income and the formal sector wage, by contrast, was seen to have very little effects on the evolution of the economy. 27 Except in the case where the formal sector wage, v*, is kept fixed (case 1). But that, as we noted, is an unrealistic case. 28 See footnote 15 on p13 above.

22

stronger at later stages of development than at earlier stages, even though at later stages,

Gini coefficient may be lower than at earlier stages. We also examined the effects of

reducing the natural growth rates of population of rural hirers and manual labourers and

found that bringing these in line with the natural growth rate of population in the urban

area would improve income distribution in the economy.

Finally, while ours has been a simulation exercise, nevertheless the empirical

evidence regarding the dynamic nature of the informal sector, the wage gap between the

informal and rural sectors, the dual migration streams and the conflicting evidence on

the inverted-U hypothesis would all seem to suggest that our analysis very probably

does capture some important aspects of income distribution and growth in many

developing countries.

Appendix 1. The Labour Market Equilibrium Equations

This appendix provides interpretations of the labour market equilibrium equations of the

static model. As mentioned in the text, the full derivation of the static model has been

provided in Bhattacharya (1994). In the model, the price of the F -sector output is taken

as the numeraire of the system.

The rural sector

The demand for and the supply of labour in the rural sector is given by mwqlh h =⋅ ),( .

The equation is derived as follows.

(a) We assume that all rural hirers are identical. A rural hirer’s production function is

given by

),,( hhhhh YlnXX = ,

where

= output produced by a rural hirer (RH); hX

= amount of land owned by an RH, assumed fixed in the short run; hn

= amount of manual labourers (lm) employed by an RH; and hl

= amount of F-sector output used as input by an RH. hY

As a producer, a rural hirer’s problem is to choose and to maximise hl hY

23

hhhhhh YwlYlnXq −−⋅ ),,( ,

where

q = the price of R-sector goods, and

w = the wage in the R-sector.

The solution to this maximisation problem yields the following demand function for

inputs:

),( wqll hh =

),( wqYY hh = .

(b) A manual labourer (lm) in our model is characterised by a labour supply function:

mm ll = . We assume that an lm supplies ml units of labour inelastically ( 1=ml ).

The equilibrium condition for the rural labour market is then easily written as:

mwqlh h =⋅ ),( , (2)

where

h = the number of rural hirers, and

m = the number of manual labourers.

The urban area

The conditions for labour market equilibrium in the urban area are stated in the form of

two equations:

).,*,,,(*),,()1*( αpvvqSFvvqSflifL cF

cf ⋅+⋅+++= (6)

).*,( pvfFf F⋅= (7)

The total demand for labour in the urban area consists of (i) the demand for labour in

the F-sector, (ii) the demand for labour in the IM segment of the I-sector, and (iii) the

demand for labour in the IS segment of the I -sector.

The formal sector

We assume that the number of firms, F, is fixed in the F-sector, that they are all

identical, and that each firm has a single owner. The production function of a firm in the

F-sector is given by

),,( FFFFF ZKfYY = ,

24

where

YF = output of an F-sector firm;

fF = amount of labour employed in an F-sector firm;

KF = amount of capital employed in an F-sector firm, assumed fixed in the short

run; and

ZF = amount of IM -output used as input by an F-sector firm.

The firms in this sector face a constraint in the form of a “minimum” wage = v*. We

assume that there is an abundance of labour for the F-sector, so that the constraint is

binding. A profit-maximising firm’s problem then is to choose fF and ZF to maximise

FFFFFF pZfvZKfY −− *),,( ,

where p = the price of the IM -good. The solution to this maximisation problem yields

the following demand functions for inputs:

)*,( pvff FF =

)*,( pvZZ FF = .

It is assumed that the profit, )*,( pvFΠ , earned by the firm is distributed between

consumption and investment: a fraction ( )α−1 of )*,( pvFΠ is reinvested within the F-

sector, while the remainder is consumed. As a consumer, the problem of the owner of a

firm is to maximise his utility function subject to his budget constraint, i.e., to maximise

),,( CF

CF

CFF SYXU ..ts )*,( pvSvYXq F

CF

CF

CF Π=⋅++⋅ α ,

where

= The IS -good consumed, and CFS

= The wage in the I-sector. v

The solution yields the following demand functions for the good he consumes:

),*,,,( αpvvqXX CF

CF =

),*,,,( αpvvqYY CF

CF =

),*,,,( αpvvqSS CF

CF = .

The informal sector

The production function of a firm in the IM segment of the I-sector is given by

)( iii lZZ = ,

where

25

li = amount of labour employed in an IM –firm .

The firms in this sector face a constraint on size: beyond l* they have to pay the

“minimum” wage. A firm’s problem, then, is to choose li to maximise

,)( iii lvlZp ⋅−⋅ s.t . *lli ≤

We assume that the solution of this maximisation problem is li = l*. This implies that

Profit = **)( lvlZp i ⋅−⋅ .

The alternative for an organiser of an informal firm is a wage salary and we next

assume that firms will continue to be set up in the informal sector so long as profit

exceeds )1( δ+v , where δ may be interpreted as a measure of the entrepreneurial zeal.

This means, in other words, that in equilibrium we will have

).1(**)( δ+=⋅−⋅ vlvlZp i (5)

This of course helps us determine the number of firms in the IM sector in equilibrium.

The supply of IM -output is then given by *)(lZi i⋅ , where i is the number of firms in the

IM -sector.

The demand for labour in the urban area

We can now easily write the total demand for labour in the urban area;

(i) The demand for labour in the F -sector is given by

).*,( pvfF F⋅

(ii) The demand for labour in the IM segment of the I-sector is given by:

)1*( +li , where the one is added to account for the

owner/manager of an IM firm.

(iii) The demand for labour and the supply of output in the IS segment of the I-sector

is given by

, ),*,,,(*),,( αpvvqSFvvqSf CF

cf ⋅+⋅

where

f = the number of workers in the F-sector;

= the consumption of informal services by an F-sector worker (which cfS

in the model is seen to depend on q,v,and v*; see Bhattacharya

(1994)); and

F = the number of employers in the F-sector.

26

The equilibrium condition for the urban labour market is then easily written as:

),*,,,(*),,()1*()*,( αpvvqSFvvqSflipvfFL CF

cfF ⋅+⋅++⋅+⋅= ,

where L is the total labour in the urban area.

Appendix 2. The Simulation Model

Equation 8: dtdf

HhvF

ghdtdh hH

h ⎥⎦

⎤⎢⎣

⎡ Π−−=

)*(β

Equation 9: mwvFmdtdm

mm )( −−= β

Equation 10: dtdf

HhvF

gmwvFLdtdL hH

mL ⎥⎦

⎤⎢⎣

⎡ Π−+−+=

)*()(β .

A far as is reasonable we choose all functions to be linear functions. The etas, zetas and

Ds mentioned below can be related to partial derivative terms of the static model and are

expanded in due course.

)*( hhH vAF Π−=

)*( thmLvA thmLhh oηηηη −−−−Π−= ;

hFLH H+= 0α ,

where 0α is the fraction of L that is H-type workers; g has been scaled into 0α and Ah;

0*ft

vL

f tL ++= γ

γ

(L enters this equation to capture the effects of a change in p on f. The static model has

and hence, . An increase in v* also leads unambiguously to a

decrease in f in the static model. Changes in h and m, however, have no effect on f in the

static model.

0/ <∂∂ Lp 0/ >∂∂ Lf

ttγ captures the contrasting effects of capital accumulation and of the

labour-saving technical progress in the formal sector on f).

)( wvAF mm −=

tfLvv tfL ξξξ +++= 0

tDfDLDhDmDww tfLhm +++++= 0 .

27

The expressions of Ds, zetas and etas mentioned above are as follows:

0: >∂∂

=LwDDs L , 0>

∂∂

=fwD f ,

mwDm ∂∂

= , hwDh ∂∂

= ;

Dtt captures the effects of technical progress in the rural sector on w. (In the static model

an increase in L leads to an increase in w. When L (and also f) increases, the demand for

the rural output X by the workers in the urban area increases. As a result, the price of X,

q, rises and when q rises, the rural hirers demand more labour and w, the wage in the

rural sector, increases as a result. The effects on w via these changes, however, are likely

to be relatively small and for purposes of simulation we set both DL and Df at 0.0001.

The effects of changes in m and h on w are seen to be ambiguous in the static model. An

increase in the number of manual labourers, m, on the one hand, leads to an increase in

the supply of labour in the rural sector and so tends to decrease w, but, on the other

hand, the consumption of X by manual labours also increases following an increase in

their number and this tends to increase q and hence w. On balance, however, the former

effect is likely to be stronger than the latter and for the simulation we set Dm=-0.1. An

increase in the number of rural hirers, h, similarly, leads to an increase in the amount of

the rural sector output produced and so tends to decrease q and w, but, on the other hand,

an increase in h also leads to an increase in the demand for labour in the rural sector and

this tends to increase w. For the simulation we set Dh=0.0001. Finally, so far as the

effects of technical progress in the rural sector on w are concerned, this technical

progress will, on the one hand, tend to increases the amount of the rural sector output X

and so tend to decreases q and therefore w; on the other hand, however, due to its

labour-using characteristic, this technical progress will also tend to increase the demand

for labour in the rural sector and this would tend to increase w. The net effect on w of

technical progress in the rural sector is therefore not unambiguous and we set Dt =

0.001).

zetas:

0<∂∂

=Lv

Lξ , 0>∂∂

=fv

fξ ;

ttξ captures the effects of capital accumulation and technical progress in the formal

sector on the demand for IM output by the F-sector firms. (In the static model, an

increase in L leads to a decrease in the informal sector wage, v. An increase in f – i.e., an

increase in employment in the formal sector – increases v both by reducing the labour

28

supply to the informal sector and by increasing the demand for informal services.

Changes in h and m, however, have no effects on v in the static model. For the

simulation we set ,0045.0−=Lξ 0045.0=fξ and 0075.0=tξ ).

etas: Lη =

0>⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂Π∂

+∂∂

∂Π∂

Lw

wLq

qhh , h

hhm m

wwm

qq

ηη ,0>⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂Π∂

+∂∂

∂Π∂

=

= 0<⎟⎟⎠

⎞⎜⎜⎝

⎛∂∂

∂Π∂

+∂∂

∂Π∂

hw

whq

qhh ;

ttη captures the effects on of both the (land-augmenting) technical progress in the

rural sector and the subdivision/consolidation of land following a change in the number

of hirers. ( depends on q, w, and on technical progress. The effects on via

hΠ

hΠ hΠ Lη

and hη are likely to be smaller than those via mη and for the simulation we set

mη =0.003, Lη =0.0025, hη = -0.0025, and tη =0.0055).

Summary of parameter values and initial conditions:

h(0) = 0.28 v* = 0.8 DL = 0.0001 Lη = 0.0025

L(0) = 0.3 = 0.6v* Dh = 0.0001 0hΠ mη = 0.003

m(0) = 0.42 v0 = 0.5v* Dm = -0.1 hη = -0.0025

f0 = 0.4L(0) w0 = 0.25v* Df = 0.0001 tη = 0.0055

hβ = 0.025 Ah = 0.1 Dt = 0.001 Lξ = -0.0045

mβ = 0.03 Am = 0.05 Lγ = 0.0001/v* fξ = 0.0045

Lβ = 0.02 0α = 0.3 tγ = 0.0075 tξ = 0.0075.

References Aghion, P. and Williamson, G. (1998), Growth, Inequality and Globalisation –

Theory, History and Policy, Cambridge: Cambridge University Press.

Ahluwalia, M. S. (1976), “Inequality, poverty and development”, Journal of Development Economics, Vol. 3, pp. 307-312.

Anand, S. and Kanbur, S. M. R. (1993), “The Kuznets process and the inequality-development relationship”, Journal of Development Economics, Vol. 40, pp 25-42.

Atkinson, A. (1996), “Bringing income distribution from the cold”, Presidential address to the Royal Economic Society, Swansea.

29

Benabou, R. (1996), “Inequality and growth”, NBER Macroeconomics Annual 11, Boston: MIT Press.

Barro, R. J. (2000), “Inequality and growth in a panel of countries”, Journal of Economic Growth, Vol. 5, No 1, pp. 87-120.

Bhattacharya, P. C. (1993a), “Rural-urban migration in economic development”, Journal of Economic Surveys, Vol. 7, No. 3, pp. 243-81.

(1993b), “The role of the informal sector in structural transformation: a framework and some Indian evidence”, Heriot-Watt University Discussion Paper in Economics, No. 21.

(1994), “A multi-sector model of LDC”, Scottish Journal of Political Economy, Vol. 41, No. 3, pp. 225-255.

(1996), “The role of the informal sector in structural transformation: some Indian evidence”, Journal of International Development, Vol. 8, No. 1, pp. 83-94.

(1998a), “The informal sector and rural-to-urban migration: some Indian evidence”, Economic and Political Weekly, Vol. 33, No. 21, pp. 1255-1262.

(1998b), “Migration, employment and development: a three-sector analysis”, Journal of International Development, Vol. 10, No. 7, pp. 899-921.

(2001), “Aspects of employment and unemployment in a model of the developed and the less developed economies”, Economic Modelling, Vol. 18, No. 2, pp. 297-311.

(2002), “Rural-to-urban migration in LDCs: a test of two rival models”, Journal of International Development, Vol. 14, No. 7, pp. 951-972.

Bulow, J. I. and Summers, L. H. (1986), “A theory of dual labour markets with application to industrial policy, discrimination and Keynesian unemployment”, Journal of Labour Economics, Vol. 4, No. 3, pp. 376-414.

Calvo, G. A. (1985), “The inefficiency of unemployment: the supervision perspective”, Quarterly Journal of Economics, May, pp. 373-387.

Chenery, H. and Syrquin, M. (1975), Patterns of Development, 1950-1970, New York: Oxford University Press.

Cline, W. (1975), “Distribution and devleopment: a survey of the literature”, Journal of Development Economics, Vol. 2, pp. 25-42.

Dickens, W. T. and Lang, K. (1988), “The reemergence of segmented labour market theory”, American Economic Review Proceedings, May, pp.129-34.

Esfahani, H. S. and Salehi–Isfahani (1989), “Effort observability and worker productivity; towards an explaination of economic dualism”, Economic Journal, September, pp. 818-836.

Fields, G. S. (1991), “Growth and income distribution” in G. Psacharopoulos (ed.), Essays on Poverty, Equity and Growth, Oxford: Pergamon Press.

(2001), Distribution and Development: A New Look at the Developing World, Cambridge, Mass.:MIT Press.

Galor, O. and Zeira, J. (1993), “Income distribution and macroeconomics”, Review of Economic Studies, Vol. 60, No. 1, pp. 35-52.

30

Gillis, M., Perkins, D. H., Roemer, M. and Snodgross, D. R. (1987), Economics of Development, New York, Norton.

Harris, J. R. and Todaro, M. P. (1970), “Migration, unemployment and development; a two-sector analysis”, American Economic Review, Vol. 60, pp. 126-42.

International Labour Office (1972), Employment, Incomes and Equality: A Strategy for Increasing Productive Employment in Kenya, Geneva: ILO.

Katz, L. F. (1986), “Efficiency wage theories: a partial explaination”, NBER Macroeconomic Annual, pp. 235-276.

Kuznets, S. (1955), “Economic growth and income inequality”, American Economic Review, Vol. 45, pp. 1-28.

Layard, R. G., Nickell, S. J. and Jackman, R. A. (1991), Unemployment: Macroeconomic Performance and the Labour Market, Oxford: Oxford University Press.

Lewis, W. A. (1954), “Economic development with unlimited supplies of labour”, The Manchester School, Vol. 22, May, pp. 139-91.

Little, I. M. D. (1982), Economic Development, New York: Basic Books.

McDonald, I. M. and Solow, R. (1985), “Wages and employment in a segmented labour market”, Quarterly Journal of Economics, C, pp. 1115-1141.

Minford, P. (1983), “Labour market equilibruim in an open economy”, Oxford Economic Papers, November, pp. 207-244.

Nickell, S. (1990), “Unemployment: a survey”, Economic Journal, Vol. 100, June, pp. 391-439.

Papanek, G. F. and Kyn, O. (1986), “The effect on income distribution of development, the growth rate, and economic strategy”, Journal of Development Economics, Vol. 23, pp. 55-65.

Paukert, F. (1973), “Income distribution at different levels of development: a survey of evidence”, International Labour Review, Vol. 108, pp. 97-125.

Sethuraman, S. V. (1976), The Urban Informal Sector in Developing Countries, Geneva: ILO.

Shapiro, C. and Stiglitz, J. E. (1984), “Equilibruim unemployment rate as a worker discipline device”, American Economic Review, Vol. 74, June, pp. 433-444.

Todaro, M. P. (1969), “A model of labour migration and urban unemployment in less developed countries”, American Economic Review, Vol. 59, pp. 134-148.

Williamson, J. G. (1988), “Migration and urbanization” in Chenery, H. and Srinivasan, T. N. (eds.), Handbook of Development Economics, Vol. 1, Amsterdam: North-Holland, pp. 424-465.

Yellen, J. (1984), “Efficiency wage models of unemployment”, American Economic Review Proceedings, Vol. 74, pp. 202-205.

31

0 10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

time

Case 1: v*=0.8

h/Tm/TL/Tf/L

0 10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

time

Case 2: v*=2 v

h/Tm/TL/Tf/L

h, L

, m, f

(fra

ctio

nal)

h, L

, m, f

(fra

ctio

nal)

0 10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

time

Case 3: v*=4 v

h/Tm/TL/Tf/L

0 10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

time

Case 4: v*=2 v + 0.5 sin(t/3)

h/Tm/TL/Tf/L

h, L

, m, f

(fra

ctio

nal)

h, L

, m, f

(fra

ctio

nal)

0 10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

time

Case 5: v*=2v : t≤10, 4v : t≤30, 6v : t≤40, 4v : t>40

h/Tm/TL/Tf/L

h, L

, m, f

(fra

ctio

nal)

Figure 1. The number of rural hirers (h), manual labourers (m), total urban labour (L) as fractions of total population (T), and employees in the formal sector (f) as fractions of urban labour (L).

32

0 10 20 30 40 50 60

0.5

1

1.5

2

2.5

3

time

Case 1: v*=0.8

Πhwvv*

0 10 20 30 40 50 60

0.5

1

1.5

2

2.5

3

time

Case 2: v*=2 v

Πhwvv*

w, v

, v*,

Πh

w, v

, v*,

Πh

0 10 20 30 40 50 60

0.5

1

1.5

2

2.5

3

time

Case 3: v*=4 v

Πhwvv*

0 10 20 30 40 50 60

0.5

1

1.5

2

2.5

3

time

Case 4: v*=2 v + 0.5 sin(t/3)

Πhwvv*

w, v

, v*,

Πh

w, v

, v*,

Πh

0 10 20 30 40 50 60

0.5

1

1.5

2

2.5

3

time

Case 5: v*=2v : t≤10, 4v : t≤30, 6v : t≤40, 4v : t>40

Πhwvv*

w, v

, v*,

Πh

Figure 2. The rural sector wage (w), the formal sector wage (v*), the informal sector wage (v) and the rural hirers income (Πh).

33

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Percentage of population

Case 1: v*=0.8

0yr8.1349yr0yr35.1349yr60yrequality

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Percentage of population

Case 2: v*=2 v

0yr8.135yr14.135yr35.135yr60yrequality

Per

cent

age

of in

com

e

Per

cent

age

of in

com

e

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Percentage of population

Case 3: v*=4 v

0yr8.135yr23.135yr35.135yr60yrequality

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Percentage of population

Case 4: v*=2 v + 0.5 sin(t/3)

0yr8.135yr6.635yr35.135yr60yrequality

Per

cent

age

of in

com

e

Per

cent

age

of in

com

e

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Percentage of population

Case 5: v*=2v : t≤10, 4v : t≤30, 6v : t≤40, 4v : t>40

0yr8.135yr30.635yr35.135yr60yrequality

Per

cent

age

of in

com

e

Figure 3. Lorenz curves (plotted at time periods 0, 8.135, 35.135 and 60 for all cases and one plotted additionally for each case at the point of maximum inequality (when the Gini coefficient peaks)).

34

0 10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

time

Case 1: v*=0.8

gini coeff

0 10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

time

Case 2: v*=2 v

gini coeff

Gin

i coe

ffici

ent

Gin

i coe

ffici

ent

0 10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

time

Case 3: v*=4 v

gini coeff

0 10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

time

Case 4: v*=2 v + 0.5 sin(t/3)

gini coeff

Gin

i coe

ffici

ent

Gin

i coe

ffici

ent

0 10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

time

Case 5: v*=2v : t≤10, 4v : t≤30, 6v : t≤40, 4v : t>40

gini coeff

Gin

i coe

ffici

ent

Figure 4. Locus of Gini coefficients over time.

35

Case 6. v*=2v, Am=0.05+0.0008t

0 10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

time

h/Tm/TL/Tf/L

0 10 20 30 40 50 60

0.5

1

1.5

2

2.5

3

time

Πhwvv*

h, L

, m, f

(fra

ctio

nal)

w, v

, v*,

Πh

Figure 5a. See Figure 1 for notes. Figure 5b. See Figure 2 for notes.

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Percentage of population

0yr8.135yr11.135yr35.135yr60yrequality

0 10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

time

gini coeff

Per

cent

age

of In

com

e

Gin

i coe

ffici

ent

Figure 5c. See Figure 3 for notes. Figure 5d. See Figure 4 for notes. Figure 5. Effects of a change in the migration sensitivity parameter for the manual labourers (lm), Am (from Am=0.05 to Am=0.05+0.0008t).

36

Case 7. v*=2v for t≤40, 4v for t>40; γt=0.0075 for t≤40, 0.0095 for t>40; ζt=0.0075 for t≤40, 0.0050 for t>40

0 10 20 30 40 50 60

0.2

0.4

0.6

0.8

1

time

h/Tm/TL/Tf/L

0 10 20 30 40 50 60

0.5

1

1.5

2

2.5

3

time

Πhwvv*

h, L

, m, f

(fra

ctio

nal)

w, v

, v*,

Πh

Figure 6a. See Figure 1 for notes. Figure 6b. See Figure 2 for notes.

0 0.2 0.4 0.6 0.8 1

0.2

0.4

0.6

0.8

1

Percentage of population

0yr8.135yr41.1028yr35.135yr60yrequality

0 10 20 30 40 50 60

0.1

0.2

0.3

0.4

0.5

time

gini coeff

Per

cent

age

of In

com

e

Gin

i coe

ffici

ent

Figure 6c. See Figure 3 for notes. Figure 6d. See Figure 4 for notes. Figure 6. Effects of skill-biased technological change

37