LABOUR MOBILITY AND LABOUR UTILIZATION IN DEVELOPING COUNTRIES

OXFORD BULLETINof

ECONOMICS and STATISTICS

LABOUR MOBILITY AND LABOUR UTILIZATIONIN DEVELOPING COUNTRIES

By PAUL COLLIER

1 INTRODUCTION

There have been two separate debates concerned with labour utilization.Chronologically the first was that of rural surplus labour. The notion was that asubstantial proportion of agricultural labour could be withdrawn without reducingoutput and redeployed productively to generate capital formation. Recently,attention has shifted to the phenomena of rural-to-urban migration and urbanunemployment, the former apparently exacerbating the latter. If the empiricalassumptions of both these debates are correct then their conclusions concerninglabour utilization are both false. If there is surplus labour in each sector then therecannot be any sectoral mis-allocation of labour.

This paper is predicated upon the assumption that the rural surplus labourhypothesis is false. If the marginal product of labour in agriculture is positive thenthe efficient utilization of labour becomes a valid issue.

A necessary condition for efficient labour utilization is that the marginalproduct of homogeneous labour should be equated within and between all sectors.The issue we will consider is whether present patterns of labour mobility enable theachievement of this condition. This issue is a matter of some dispute. We brieflyreview current theories of labour allocation before setting out an alternativeapproach.

2 THEORIES OF INTER-SECFORAL LABOUR ALLOCATION

(a) Ideal-Typical Labour AllocationAssume:

perfect factor and commodity markets in each sector,the production of at least as many common commodities in both sectors as

there are common factors,identical production functions,

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absence of transport costs for commodities,no factor intensity reversals.

Then by the Factor Price Equalization theorem the marginal product of labourwill be the same in each sector without the need for labour mobility. It is notdifficult to find fault with these assumptions when applied to the rural and urbansectors of developing countries. In the absence of labour mobility marginalproducts are likely to diverge. Let us try a less restrictive package of assumptions.

perfect labour markets,no transport costs for labour.

Then, given perfect labour mobility, marginal products will be equated. lieseassumptions are obviously false. In particular wages in the urban manufacturingand government sector are above equilibrium level. However, the policy of wagesubsidy seemed the appropriate instrument to offset this distortion. Harris andTodaro [3] challenged this conclusion with a theory which has rapidly become thenew orthodoxy.

(b) The Harris-Todaro ModelThe Harris-Todaro theory explains urban unemployment as a voluntary queue

of rural migrants waiting for highly paid jobs in the modern urban sector. 1f theprobability of gaining such employment is 'p', and the modern sector wage is Wmthen the expected return from migration is p . wm. Ignoring transport costs thenmigration will occur until

PWmWA (1)

where wA = marginal income in agriculture. Thus p is a measure of the rural-urban wages cliff. We now introduce a probability function of the form

T

where J=jobsU = unemployed

Hence

Thus an extra job in the modem sector increases unemployment by (lip) 1.Migration to the city is the sum of the increase in J and the increase in U. Thusthe opportunity cost of the new job is the loss of the output of I/p rural workers,which equals wa/p. The shadow wage should be set equal to this opportunitycost. But since (from (1)) Wm= (wA/P) the shadow wage thus equals the actualwage.

The theory thus identifies a new problem, surplus urban labour, which cannotbe tackled by urban wage subsidies. One solution appears to be a reduction inmigration. Indeed since modem sector employment frequently expands no morerapidly than the natural rate of increase of urban population, it appears that ifmigration were stopped completely labour utilization would be improved. In this

LABOUR MOBILITY IN DEVELOPING COUNTRIES 171

second best situation, labour mobility worsens resource allocation whilst in ourearlier case it was a necessary and sufficient condition for efficiency.

We will argue that the HarrisTodaro model is itself an example of the secondbest paradox: whilst its assumptions represent a movement towards reality itsconclusions are less valid than those of our simple model.

The essence of the HarrisTodaro theory is that both migration and urbanunemployment can be explained by the term p. wmthe product of the wage inand the probability of attaining modem sector employment. The alternativetheory which we now introduce represents a substantial departure from thistheory. We argue that the HarrisTodaro explanatory variable in fact explainsneither migration nor unemployment, whilst their theory conflates distinctphenomena.

3 A TUEORY OF LABOUR ALLOCATION

A theory of labour allocation must supply answers to two distinct questions.First we need to know what determines the choice of sector for an individual agentand second, we must be able to predict the scale of such choices in the populationas a whole. The former requires a micro-theory which identifies explanatoryvariables. The latter requires a macro-theory which identifies selectivity variables.We start with the logically prior micro theory.

(a) Explanatory Variables in Labour AllocationWe will aggregate economic activity into four sectors between which each

agent must choose. Our four sectors will be, agriculture, urban modem, urbantraditional and urban unemployment. We assume that the wage in the urbanmodern sector is sufficiently high that an agent will always choose employment inthat sector in preference to the other sectors. However, agents do not enjoyperfect access to modern sector jobs. Hence some agents will be forced to choosebetween the remaining three sectors. We assume that all agents do enjoy perfectaccess to each of these sectors.

Three sets of explanatory variables can be distinguished in the allocativedecision between these three sectors.

(I) Objective Values: The most obvious independent variables influencing thedecision are income in the three sectors. The other objective variables (upon whichthe HarrisTodaro model focuses) are the differential probability of access to themodern sector whilst in the remaining sectors, and the modem sector wage.

The Utility Function: The Utility Function is important in two respects.Firstly, since we are concerned with probabilistic outcomes decisions will besensitive to our assumptions concerning diminishing marginal utility: the morerapidly utility diminishes the more risk averse decision makers will be. Secondly,allocative decisions will be sensitive to the valuation of future relative to presentconsumption. Hence, we must introduce an own discount rate.

The Perception Function: Whilst the decision maker definitionally has per-fect knowledge about his Utility Function this is not the case with respect to

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objective values. Decisions are based upon perceived values and are only affectedby objective values to the extent that the former are a function of the latter.

We now derive the conditions under which an agent will be indifferent betweenall three sectors. We will make the following assumptions about perceived andobjective values:

O=PA<PT<PU<PM=l; WU<WTWA<WM

where W =income P = probability of gaining modern sector employment du ringa specific time period and subscripts denote the sector in which the agent is en-gaged:

A=agricultureT =urban traditionalU urban unemployedM =urban modern

First we derive discounted future welfare in agriculture. This is simply:

U A U(WA) U(WA) U(WA)1+r +(1+)2+ +(1+)n

on the assumption that the perceived income is constant. It is convenient toassume that this stream is infinite for the net present value then reduces to:

U(A)= (5)

Discounted future welfare in the urban traditional sector is rather more c:m-plex. In the first time period the agent stands a chance T of gaining modernsector employment which, by assumption, he will then retain. The value of thisopportunity is

(4)

However, the agent stands a chance (1 - PT) of failing to secure a modern sectorjob in the first time period. He then receives U(WT)/(1 + r) and in addition has achance, PT, of achieving a modern sector job in the second time period. Thischance has a present value at time to of (7) minus the lost income in the first period,U(WM)/(l +r). By extension we have a series:

U T )U(WM)

1 P [U(WT)- T)(1+r)+(U(WM) U(WM)

Tr r 1+r

P 2- T) [U(WT) (U(WM) U(WM) U(WM)(1+r)2+ T

r 1+r (1+r)2

1 P- T)IU(WT) (U(WM) U(WM) U(WM) U(WM)

(+) + Tr 1+r (1+r)2 (1+r)3

1)T{U(WM)U(WM)

(6)1+r +(1+)2 (1+r) Iwhich reduces to

U(WM)T r (7)

which reduces to:

U(T)=IT(l +r)r(PT + r)

Analogously, the present value of unemployment is:

U(U)P(1 + r)

[U(WM) - U(W)]U(w)

r(P +r)Hence, the margin of indifference will be when:

U(A)=U(T)=U(U)

However, there is an important difference between unemployment and the tradi-tional sector in that the unemployed man is not working: all his receipts are byway of transfer payments. The significance of this is seen most clearly when weset P= P. In this case the agent will only be indifferent between the two sectorsif U(W) = U(W). However, this does not imply that monetary receipts must bethe same in the two sectors. The net welfare gain from working in the traditionalsector is

U(WT)U(L) (12)

where L is the labour input needed to earn the monetary income \VT; Hence, themargin of indifference will be when

U(WM)==U(WT) U(L) (13)

If the agent is free to choose the number of hours worked then the marginal hourwill yield no net welfare increase. If we assume that his supply curve of labour islinear and through the origin then the monetary cost of his effort for the averagehour will be half of his hourly earnings. Hence, (12) can be rewritten as:

U(WT) U(WT/2) (14)

and so (13) becomes:

U(W) =U(WT) U(WT/2) (15)

This gives us a critical relationship between WT and W which depends upon therate of decline of marginal utility. This relationship will be explored in a sub-sequent section.

The incomes and probabilities which appear in this expression are perceivedrather than objective values. To advance we must therefore postulate a specificperception function. We adopt the following specification: an agent in sector jwill perceive the objective variable in sector j to be

V = V (16)

where Vc = perceived valueV = objective value

a, ß = constants.

'Perfect knowledge' of objective values is thus represented by ß =1. As

knowledge becomes increasingly imperfect falls in value. In the limiting casewhen no information about objective values reaches the agent then = 0. Clearly


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the agent knows the income which he receives in the sector in which he is engaged,(so that when j = j then ß = 1) although his perception of employment probabilitiesmight still be false, for information on other sectors the agent has to rely upon asample of the total relevant population. The smaller is this sample then the lessconfidence the agents can place in its results: that is, his perception will be lesssensitive to objective values (a lower value of ß). As the sample gets very smail so

-* O and a takes over as the explanatory variable. When the quantity andquality of information is very poor the agent will base his estimate of objec:tivevariables upon some past history of information received. This might be repre-sented by a lag structure of past objective variables but the critical insensitivityto current objective values is more simply represented by the term a. A preferencefor the lifestyle of sector j will raise cc above zero even for ß =1 but there are otherimportant influences. Such information as the agent does receive might be biaseddepending upon its source. Further, differences in price levels might be in ade-quately recognizedthis can influence fi as well as a.

Finally, to complete our analysis at the micro-level, we investigate briefly theeffect of the objective variables. Clearly,

and

If

If P<l then

then

(i=A, T, U, M)

(j, =A, T, U, ij).

U(U) 8U(T)PU>PT then >UVVM

U(U) 8U(A)< and IfPT<l

SWM WA

SU(T) SU(A)and

UVYT OVVA

The effect of probabilities is equally straightforward:

(i=U,T)

and

(i=A,T,U,M; j=U,T,ij).

FurtherU(T) SU(U)

- 3PiJThe effect of the discount rate is:

U(i)<O (i=A,T,U,M)

U(T) SU(A)

WA WA


but8U(A) U(T) U(U)

8r &

Let us compare this microtheory with that specified in the HarrisTodaro model.Perhaps the most straightforward modification of the HarrisTodaro model is

the introduction of an urban traditional sector. The simple formulation of (1)could be altered to

WA=PWM+(lP)WT (17)

to allow for this. The introduction of WT has a considerable impact upon thecritical value of WA/WM at which equilibrium occurs. For example, let P = 0.25and WM/WT = 4. The critical value of WA/WM implied by (1) is 25% whilst thatimplied by (17) is 43.75%.

Our second correction is to take net present value of discounted future incomestreams. This also has an important quantitative effect. For example, using a20% discount rate and a linear utility function in (5) and (9) and the same objectivevalue as previously, the critical WA/WM rises to 75%, a very substantial differencefrom the prediction of (1).

Our third correction is the introduction of a utility function. The impact ofthis change depends upon the rate of decline of marginal utility. For example,if utility increases with the square root of income then the critical \VA/WM fallsfrom 75% to 59.3%.

Finally, the introduction of a perception function has an obvious impact uponthe critical value of objective incomes. Since W/W (OEA +PAWA)/(OEM +PMWM)and our above computations have been for critical values of perceived variables,the critical value of objective WA/WM can be derived as a function of OEA, M, PA'

ßM, W and W.Having identified as explanatory variables the utility function, the perception

function and the objective variables and having formalized these into specificequations we can now turn to the selectivity variables which determine the macro-aspects of labour allocation.

(b) SelecUvity Variables in Labour AllocationWe now introduce heterogeneity of agents. Each of the variables which we

have identified as important at the micro-level should now be seen as having afrequency distribution of values over the population of agents at the macro-level.The following explanatory variables must therefore be considered:

Objective values P' PTWa, WT, WM

(rUtility function

Perception function f °i

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Trivially, in the choice between sectors j and j those agents for whom PI/Pi, W1W,a/a and ß1/ß1 are atypically low and for whom r and U" are atypically close to zero(if W1 <Wi) will be atypically prone to select sector j rather than sector j. Theimportant stage is to find characteristics which correlate with such atypical values.

This stage must therefore be predominantly empirical, estimating, for ex-ample, the importance of age, sex and education. Here, however, we suggest akey selectivity variable is the sector in which the agent is located. That is, theexplanatory variables which determine sectoral allocation are themselves biasedbetween the various sectoral movements. This has quite far-reaching implicationsfor labour allocation; let us re-consider some fundamental issues.

(1) Who are the unemployed?The orthodox answer to this question which the HarrisTodaro theory pro-

vides is that those migrants who do not manage to get modern sector jobs form theunemployment queue. Migrants have the choice between unemployment and thetraditional sector. The problem is therefore:

max [U(T)

1U(U)

Our first counter-hypothesis is that migrants will allocate disproportionately inthe traditional sector. One reason for this is the relatively low objective probabil-ity of modem sector employment which migrants face. Given the ratio P./Pthe lower are employment probabilities then the higher is U(T)/U(U). Theobjective probability of employment depends upon the selection criteria adoptedby modern sector employers. Whilst generalization in this area is peculiarlydangerous two criteria appear common. Employers tend to favour the educatedover the uneducated and frequently rely upon senior workers to act as 'brokers'who find suitable candidates. Brokers tend to favour those within their own socialnetworks. On each of these criteria rural migrants tend to be disadvantaged;typically their educational attainment being low and their social contacts withthose in the modern sector being remote.

Secondly, migrants have relatively low objective receipts in unemployment(We). These receipts become of increasing importance the more rapidly marginalutility diminishes and the lower are employment possibilities. The source of thesereceipts will generally be transfer payments within the family. Whilst the ex-tended family is virtually open-ended it is plausible to assume that the moreperipheral the kinship connection the less generous will be the transfer paymentsboth in amount per time period and in duration. The payments to which anunemployed worker has access thus vary with the income of his close relations.Since rural incomes are relatively low and social connections with modern sectorworkers generally remote, once again migrants are relatively disadvantaged.

Direct evidence on receipts whilst in unemployment is available for a sampleof male migrants in Tanzania. Only 5% of receipts came from rural transferpayments. The remaining receipts divided equally between urban transfer pay-ments and the personal savings of the migrant. Whilst we are unable to test oura priori argument that migrants receive less generous urban transfer payments

(18)


because they are socially more peripheral, we see that rural transfer payments donot provide a substitute. The substitute which migrants do adopt appears to betheir own savings. However, dis-saving is not the welfare equivalent of transferreceipts since it has an opportunity cost in terms of future consumption foregonewhilst transfer receipts have no opportunity cost to the migrant. Further, dis-saving can provide only a temporary source of funds and it might be expected thatthose who rely most heavily on savings rather than transfers are forced into em-ployment at an earlier stage.

A simple methodology for testing our hypothesis empirically is as follows.Consider the urban labour force as being made up of a set of age cohorts, whereage is measured by the period of membership of the urban labour force. We focusupon the age cohorts of migrants, denoted by M, Me_1.. where subscriptsdenote the period of entry. The unemployment rate among migrants for whomU(U) >U(T) varies with age cohort. Those who have been in the city for oneperiod have an unemployment rate:

UM =Migrants who have been in the city for two periods have a lower unemploymentrate because they have had more opportunity to gain modern sector employment.Their rate of unemployment is:

UM = (lp)2 and generally, UM = (1 p)fl +1Our methodology is to estimate the value of p from data on the unemploymentrates of different age cohorts of migrants. That is, we estimate p as that valuewhich best predicts the structure of unemployment among age cohorts. Com-bining this with the observed unemployment rate among all migrants of the mostrecent cohort we can deduce that proportion of all migrants for whom U(U)exceeds U(T). The HarrisTodaro hypothesis assumes that this is the case for allmigrants, our hypothesis is that the proportion is low.

Using Kenyan data for an eight-year period the best estimate is p=O.23. TheHarrisTodaro hypothesis would thus predict an unemployment rate for the mostrecent cohort of 77% which compares with the observed rate of 24%. The pro-portion of migrants who conform to the HarrisTodaro model is the ratio of theobserved rate to the predicted rate and is thus 31 per cent. On this simple test itwould seem that even in Kenya the HarrisTodaro theory describes the behaviourof less than a third of all migrants. This simple test is subject to two omissions-its failure to allow for outmigration and temporary unemployment of very recentmigrants prior to entry into the traditional sector. Both of these bias our resultsin favour of the HarrisTodaro hypothesis.

Having queried the orthodox answer we must now suggest an alternativehypothesis about the composition of the urban unemployed. One important groupwill be those who have atypically high objective values of transfer payments andmodern sector job prospects. This group will in turn be dominated by the closerelatives of modern sector workers for they enjoy both close social contacts withthe modern sector and high family income.

Our hypothesis would suggest that households headed by a modern sector

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worker would support more dependents than those headed by a traditional sectorworker. Those members of the household who did gain employment would,however, earn more than their traditional sector counterparts since they wouldhave a greater tendency to be employed in the modern sector.

Data were available for Abidjan. Some 17 per cent of household heads wereclearly identifiable as modern sector workers being categorized as senior clericalworkers, skilled workers, and police. This group was compared with the 38 percent of household heads identifiable as having traditional sector occupations.These included service personnel, traditional traders and artisans and unskilledlabourers. The comparative data are set out below:

Activity of household head MODERN TRADITIONAL

Average earnings of other workers of household inemployment

Number of household members not in employment

13,000 10,100

4.0 2.5

These findings fully support our hypotheses. A lower proportion of the modernsector household members are in employment but those who are receive some30 per cent more than their traditional sector counterparts. That average earn-ings were still well below those of the household head might be explained by therelative positions of seniority scales. The employed members of the householdare likely to be junior to the head of the household [and hence on a lower positionon the earnings scale]. For example, junior clerical workers earn on average 57 percent of the salary of senior clerical workers. This compares with the 51 per centof the income of the household head which is earned by the average workingmember of the modern sector household.

(2) Does an increase in modern sector jobs or wages increase migration?The orthodox model is based on the premise that migration is a function of

(P . WM - WA). Therefore an increase in either P or WM must increase migration.There are two reasons why this is questionable. First, for most migrants the

objective probability of modern sector employment is likely to be low (at least forthe first few years in the city). Hence, U(T) will not be very sensitive to changes inPT or WM. An implication of this hypothesis would seem to be that as P -* Oso W - WA. The level of wages in the traditional sector, relative to rural m-comes could then be used as an estimator of PT. For example, in Tanzania sorneten per cent of the urban labour-force works for a lower income than could beachieved in agriculture. Hence, for the remainder of the labour force no expecta-tions term need be invoked to explain the allocative decision of migrants. How-ever, even for this ten per cent the expectation might not be of modern sectoremployment. Although our model has treated each sector as homogeneous in factthe traditional sector is typically highly heterogeneous with a larger Gini coefficient

Average earnings of household head (Francs per month) 25,700 11,100

Percentage of household members (other than head) inemployment 12.5 20


of income distribution than either agriculture or the modem sector. It is, therefore,quite possible to interpret the low income group in the traditional sector as holdingaspirations of advancement within the traditional sector. For example, in Tanzaniaself-employed recent migrants were found to be over-represented in the categoriesof porters and shamba cultivators where modal incomes are low compared withlonger stay migrants (over five years) who were disproportionately engaged ascontractors and keepers of shops, bars, and hotelsall activities where modal in-comes are high. Further, even within each category there are enormous variationsin income: for example the Gini coefficient of the distribution of income amongporters is 0.5.

If migrants accept initial incomes lower than those in agriculture because ofaspirations within the traditional sector then the rate of migration is unaffectedby opportunities in the modem sector.

The second reason why migration is unlikely to be sensitive to modem sectoropportunities is that potential migrants are only imperfectly aware of objectiveopportunities. Recall our specification of the perception function as

V = «u (16)

Our arguments about the determination of «u and Pu suggest that the rural sector,being the least informed about the modem sector, will have a high value of a anda low value of ß. But the lower the value of then the less responsive is the agri-cultural sector to the modern sector.

It might be argued that PAM is no lower than PATthis being rural perceptionsof the urban traditional sector. For much of the agricultural sector this may wellbe the case. However, typically some twenty per cent of the rural labour forceare engaged in non-farm activities, mainly trading and crafts. This group has themost direct contacts with the urban traditional sector and we would expect it tobe the most sensitive to objective change in the urban economy.

We are not claiming that modem sector employment prospects have no im-pact upon rural-to-urban migration, only that the responsiveness is likely to be aconsiderably more muted one than the orthodox theory suggests. The modifica-tion is, however, important because of its policy implications for the opportunitycost of modem sector expansion.

(3) Does an increase in modern sector jobs or wages increase unemployment?The Harris-Todaro theory predicts that unemployment is explained by reserva-

tion pricing of labour queuing for the modem sector. This we contest on two groundsFirst, once a traditional sector is introduced then a necessary condition for theorthodox explanation to remain valid is that P> PT. Yet this condition mustsurely be questionable. We have argued that modern sector recruiting practices-which determine the values of P and PTgenerally involve selection criteria whichlargely predetermine the probability of employment. Unlike much casual em-ployment in the traditional sector modem sector employment is not thereforesearch intensive. The task of awaiting employment need not be sufficiently timeconsuming to preclude other employment. Yet if this is the case no unemploy-

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ment should exist according to the HarrisTodaro theory. We need an alternativeexplanation which does not depend upon Pu> PT.

This explanation emerges from equation (15):

U(W) =U(WT) U(WT/2) (15)

which shows the margin of indifference between the traditional sector and une m-ployment when modern sector employment prospects are equal in the two sectors(PT= Pr). Our objective is to derive the critical relationship between traditionalsector earnings (WT) and transfer payments whilst unemployed (Wo) which

When the utility function is linear (x= 1) then the critical level of transfer pay-ments at which agents are indifferent between the two sectors is 50 per cent oftraditional sector income. The more rapidly marginal utility diminishes (x < 1)then the lower this critical percentage becomes. For example, when utility riseswith the square root of income (x = ) then the critical figure is approximatelyeight per cent.

Unfortunately, the value of x is not open to empirical investigation and wehave been unable to find reliable data on transfers received by the unemployed(Wc). Our counter-hypothesis cannot therefore be tested directly. However,the logic of the hypothesis is consistent. We have shown that if marginal utilitydiminishes then it is rational to choose unemployment rather than work in thetraditional sector even if monetary receipts are considerably lower. This argu-ment is equally valid when probabilities of modern sector employment differ(Pr> P) although the precise relationship of W to WT is more complex than thatof equation (22). The decision to be unemployed might still be explicable entirelyin terms of leisure preference with the different probabilistic outcome being slack.

Clearly, it would be extreme to claim that all unemployment could be ex-plained by transfer payments and leisure preference. However, we regard theorthodox hypothesis of differential employment probabilities as the explanationof unemployment as similarly extreme.

An indirect test of the rival hypotheses can, however, be constructed. Wehave earlier suggested that the availability of transfer payments will be a functionof modern sector earnings. We would therefore predict that unemployment wouldbe positively correlated with modern sector wages and employment. The Harris-Todaro hypothesis can be distinguished from this by its emphasis upon modernsector wages relative to rural incomes and upon employment opportunities ratherthan the stock of existing jobs. A plausible probability function would include

satisfies (12) for different utility functions. Let us specify the utility function as:U = W

where W = money income.(19)

Then (15) can be re-written as:-

so(:20)

W=(2x_ 1)(W/2)xand

(21)

W/W= (2x 1)hIx/2 :22)


both new jobs and the product of the quit rate and the stock of existing jobs.The theories would then be

U=U(WM, LM) (23)

U=U(WM/WA, qLM, ALM) (24)

However, in a linear regression q. LM would perform precisely as LM. Whereemployment is growing rapidly then new jobs will be a more important componentof employment opportunities than the existing job stock. This is especially thecase since quit rates tend to be very low. The HarrisTodaro hypothesis cantherefore be restated, replacing (24) by:

U=U(WM/WA, ALM) (25)

The probability function is thus changed from (2) to:

P = ALM/U (26)

From (1):P=WA/WM (27)

so

AL/U = WA/WM (28)

and hence,U = (WM/WA) ALM (29)

Because the income elasticity of supporting unemployed dependants need not beunity, equation (23) cannot be reduced to

U=WMLM (30)

To allow for non-unit elasticity (23) must take the logarithmic form:

log U = a log WM +ß log LM (31)

This transformation is not possible for (29) because some values of ALM are nega-tive. Instead, (25) is formulated both as (29) and as:

U=a(WM/WA)+fl ALM (32)

and is tested in each form.The alternative explanations offered by (28), (32) and (31) were tested on data

for Freetown, 1957-70. The urban wages series is for minimum wage rates. Thisis not an ideal measure of modern sector incomes. Whilst minimum legislation isgenerally evaded in the traditional sector, average incomes in the modern sectormight be considerably above minimum levels. However, average earnings willprobably be monotonic in minimum earnings. We would thus expect the co-efficient on WM to have the correct sign though its value would be less reliable.

This series and data on rural per capita incomes were both deflated by theirrespective price indices. Finally, the employment series included all non-agricul-tural establishments with six or more employees. This restriction combined witha known tendency to under-record the traditional sector should mean that thisseries is a reasonable proxy for the modem sector.

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The results are set out below:The test of the HarrisTodaro hypothesis in form (29) yielded:

U=10,988-361(WM/WA) LM r2=0.12(t=-1.69) D.W.=0.3

and in form (32) yielded:

U = 8,420 + 29,97G(WM/WA) 30.3 AiM r2 = 0.08

(t=0.34) (t=-1.6) D.W.=0.3

The test of our counter-hypothesis in form (31) yielded:

log U= 9.33+0.38 log WM+2.45 log LM r2=0.94

(t=2.02) (t=13.74) D.W.=l.4The HarrisTodaro hypothesis does not perform very well. In form (29) the

coefficient has the wrong sign whilst in form (32) the index of urbanrural incomedifferentials is not significant and the coefficient on new employment oppor-tunities has the wrong sign. The corrected coefficients of determination are 1)0thextremely low and the DurbinWatson statistic indicates a major misspecification.

The alternative hypothesis does rather better with a high corrected coefficientof determination and both variables significant. Because of our earlier qualifica-tions concerning the wage series the coefficient on the wage variable must betreated with caution. The Abidjan data yields an elasticity of non-employedhousehold members with respect to the income of the household head of 0.45.This compares with the elasticity of unemployment with respect to income of 0.38indicated by the Freetown data. However, the limitations of our data make thiscompatibility of results only mildly encouraging.

The coefficient on the labour force index implies that each additional house-hold head employed in the modem sector would on average establish a householdwhich included approximately 1.5 unemployed members. This is quite consistentwith the Abidjan data since not all of the non-employed members of the householdwill be potential members of the labour force.

This test is neither a conclusive refutation of the orthodox theory nor a proofof our theory. The HarrisTodaro hypothesis could perhaps be sophisticated,for example by the introduction of a lag structure, so as to be consistent with thedata, whilst our theory as represented in (22) cannot be tested directly. However,the difference in the performance of the two hypotheses is too striking to be dis-missed casually.

(4) The Monitoring of Inter-Sectoral MovementsSuppose that sector i becomes objectively more attractive relative to sector j.

This will induce an expansion of the labour force in j at the expense of j. The issuewe now raise is how this change in the size of the labour forces in the two sectorsis best monitored. The standard approach is to investigate the increase in thegross flow of labour from j to i. We argue that a priori this is likely to be an in-appropriate measure of intersectoral labour movements. Our argument is in twostages: first we suggest that gross flows will differ significantly from net flows.


Even when sector jis expanding there will be some movement of labour from j toj. Second, we argue that this outflow will be more sensitive to objective economicchange in sector j than the inflow from j to i.

Consider labour flows between the rural and urban sectors. Gross and netflows will diverge for three economic reasons. Urban-to-rural-migration will occurin part because the successful urban worker with rural origins may wish to retireor buy land in the country. In addition the unsuccessful may return because theyhave failed to gain urban employment which they regard as satisfactory and haveexhausted their savings. Finally, there will be those who return sadder and wiser.For most agents in the rural economy perceived urban economic values will differfrom objective values. Celeris paribus, those most prone to migrate will be thosewho most over-estimate these values. In our consideration of perception functionswe argued that an agent would have better knowledge about the sector in whichhe was located than about other sectors. Thus, the agent whose decision tomigrate is based upon a mistaken perception of urban values will gradually revisehis perceptions into line with objective values once he is a part of the urbaneconomy. On these revised perceptions the agent might decide to return to therural sector.

Even if the group of mistaken rural workers form a small segment of all ruralworkers they will form a significant segment of all rural-to-urban migrants pre-cisely because their mistake makes them most prone to migrate. Even whenthere is a major divergence between objective urban and rural values this neednot affect the proportion of all migrants who reverse their decision once in the city.There are two opposing factors. As objective urban opportunities improve so agreater proportion of the rural population should objectively migrate. Hence, thegreater is the proportion of those who overestimate objective values but whosedecision would be unchanged by a correct perception. Against this, given a con-stant coefficient of variation on the distribution of perceived relative to objectivevalues over the population, the greater is the proportion of those who choose tomigrate because of mistaken perceptions when objectively they should stay in therural sector. If these two forces cancel each other then urban-to-rural migrationdue to mistaken perceptions should be a constant (though lagged) proportion ofrural-to-urban migration regardless of objective relative economic values.

Our specification of the perception function as:

V = jj+ fi. V1

provides a theory of the relative sensitivity of rural-to-urban flows and urban-to-rural flows to changes in objective urban economic values. Given that the urbandwelling migrant has better knowledge of these changes than the rural dwellingpotential migrant he will have a higher value of fi. In the limiting case in whichurban dwellers have perfect knowledge (a = 0, fi =1) and rural dwellers have noknowledge (a >0, fi = 0) then all the re-allocation of labour between sectors willcome about due to the responsiveness of urban-to-rural migration. Whilst everurban dwellers have a higher value of fi then the elasticity of response of urban-to-rural migration will exceed the elasticity of response of rural-to-urban migration.

184 BULLETIN

Indeed the ratio of the elasticities will equal the ratio of the ß values. Since theabsolute size of rural-to-urban migration exceeds that of urban-to-rural migrationit is possible that that absolute response of the former exceeds that of the latter.However, a priori there is a strong case for arguing that neglect of urban-to-ruralmigration will involve a serious bias in estimates of inter-sectoral labour allocation.

It has not proved possible to test this hypothesis due to the lack of informationon urban-to-rural migration. Virtually all migration surveys to date have 'beenmade in the towns whilst this flow can only be monitored by rural surveys. Wehave, however, demonstrated that this is an important gap in our knowledge.

(5) The Social Marginal Product of MigrationThe private marginal product of migration is equal to income in agriculture.

The social marginal product can, however, diverge from this. That proportionof the inducement to migrate which is due to the opportunity of securing a modernsector job has no counterpart in output and hence is not part of the social product.Thus, the SMP of the unemployed is zero and in the simple HarrisTodaro niodelthis is also the SMP of migration.

We have argued that most migrants will work in the traditional sector, whilsttheir returns from the chance of modern sector employment are low. It mightappear that the SMP of migration would equal the wage in the traditional sectorand thus fall short of the SMP in agriculture by the value placed upon the chanceof modern sector opportunities. However, this would be to miss the generalequilibrium implications of our four sector model.

Our argument will be that migration reduces unemployment because it reducesthe probability of gaining modern sector employment. Hence, the true SNIP ofmigration must include the extra output generated by the transfer of workers fromunemployment into the traditional sector.

We will introduce our analysis by considering a simplified, though not im-plausible case. We have already suggested that indigenous urban job seekers willhave a higher probability of achieving a modern sector job than rural migrants.Letting:

the probability of an indigenous urban job seeker gaining a modernsector job whilst unemployed

P1=his probability of gaining a modern sector job whilst working in thetraditional sector

Pmt = the probability of a migrant gaining a modern sector job whilst in thetraditional sector

we will assume that P, >V> Pmt.To abstract from changes in the traditional sector wage we will at this stage assumethat the demand for labour is perfectly elastic in the traditional sector.

Now let:

P1/Pi=k 1mt/1=j and Lu/LT=Sso that S is the ratio of the unemployed labour force to the traditional sectorlabour force.


For simplicity we will assume that migrants choose to work in the traditionalsector rather than be unemployed:

U(U) <U(T)=U(A)

whilst that part of the indigenous labour force with better job prospects, equili-brates the unemployed and traditional sectors:

U(U)=U(T)>U(A)It is convenient to assume that initially this equilibrium occurs when all such jobseekers are unemployed, though neither this nor our previous assumption arenecessary for the validity of the analysis.

Now consider the effect of an inflow of migrants which increases the labourforce in the traditional sector by one per cent.

Each indigenous urban unemployed job seeker has the same chance of gainingone modern sector job as I /kj migrants. Hence, the pool of job seekers can beexpressed in units of indigenous unemployed job seekers as:

L(1+kj/S) (33)

A one per cent increase in the traditional sector labour force due to migrationincreases this pool by the percentage

Sfkj + 1I

(34)

and hence reduces the probability of each job seeker getting employment by thesame percentage. But this fall in the probability of employment reduces the valueof unemployment by more than the value of traditional sector work to the in-digenous job seeker. The value of unemployment falls by the same percentage asthe probability (if we ignore transfer payments for the moment). The value oftraditional sector work falls less because only a proportion k of private returnsaccrue from employment prospects. Hence, the value of traditional sector workfalls by the percentage-

kS/kj +1

and so the value of unemployment relative to traditional sector work falls by thepercentage-

1k

(35)

S/kj+1(3G)

This induces an equilibrating movement of labour out of unemployment intothe traditional sector. Each one per cent reduction in unemployment raises theoverall probability of employment by the percentage

1k1+kj/S

This raises the value of unemployment relative to the traditional sector by thepercentage-

(k-1)2l+kj/S

186 BULLETIN

Equilibrium is restored between the two sectors when unemployment hasfallen by a sufficient percentage (a) to offset the change expressed in (36). Since(38) expresses the effect of a one per cent fall in unemployment the equilibratingfall will be such that-

a(k-1)2 1k391+kjfSS/kj+1

so the equilibrating percentage fall in unemployment is:

1+kj/S 40(1+S/kj)(1k) (

This fall in unemployment represents a percentage increase in traditional sectoremployment of-

S + kj(1 +S/kj)(1 k)

Hence, the SMP of migration should include not just the output producedby the migrant, which is W, but the output resulting from the transfer of labourout of unemployment. The formula for the SMP is thus:

SMP=[1+(l+k)] WT (42)

The proportion of the Private marginal product of employment in the traditionalsector which is due to the wage earned (WT) is (from (9)):

WT 1

PMP [Pmt(1 +r)(C 1)]/(Pmt+r) + 1(where CWm/WT).Hence, the ratio of the social to the private marginal product of migration is:SMP I S+kj 1 1

Ï5M ,l+(1+S/ki)(1 k)] [Pmt(1+r)(C-1)]/(1nit+r)+144)

Before making the model more sophisticated it might be useful to work througha numerical example. We will specify the (hopefully plausible) parameter valuesas:

PmtO.05 S4r=0.3

k=! C=3A one per cent increase in traditional sector employment would in this case

lead to a reduction in unemployment of 3k per cent as labour moved into thetraditional sector. Each migrant induces a reduction in unemployment cf ofa man and his SMP is thus 1 times WT. The traditional sector wage represents73 per cent of the value to the migrant of traditional sector employment. Hence,the SMP of migration is 1.22 times the PMP. Restated social benefits of migrationexceed private benefits by 22 per cent. Market forces secure insufficient migration.

The analysis can now be extended to include diminishing marginal productivityof labour in the traditional sector and the receipt of gifts by those in unemploy-ment. The critical aspect of the analysis is that an increase in employment in thetraditional sector should reduce the value of unemployment by more than it

(41)

(43)


reduces the value of traditional sector employment. The former value falls by(34) whilst the latter value falls more slowly in our previous analysis since thatcomponent due to the wage is constant. Hence, the qualitative results will holdwhilst ever the wage falls by less than (34). The critical elasticity of demand fortraditional sector employment is thus:

EDS/kj+1 (45)

Letting gifts to the unemployed be a proportion B of the traditional sector wagethen the critical elasticity of demand becomes:

ED>S/kj- 1

(46)

For example, with B = the critical elasticity is 2.5. Since it is probable that thetraditional sector has a significant employment multiplier and that its output isincome elastic, the actual elasticity of demand might well be above this level.Further, once we allow for some price discrimination in the traditional sector thecritical elasticity of demand falls considerably. If marginal income can be re-duced without reducing intra-marginal income by the same proportion thenaverage earnings are less sensitive to employment levels. The heterogeneity oftraditional sector activity and the substantial proportion of the labour force whichis self-employed, both increase the extent of price discrimination. If, for example,two prices prevail which divide the market into two equal parts then the criticalelasticity of demand for labour would fall from 2.5 to unity, and yet this would onlyrepresent a very limited degree of price discrimination.

We have thus discovered that the general equilibrium properties of a foursector model differ considerably from those of a three sector model. Even if bothmigrants and the unemployed are motivated by the prospect of modern sectoremployment then migration can reduce unemployment and have a social valueabove its private value, these conclusions being precisely the opposite of those ofthe three sector model. The extent of this effect depends upon many parametersbut is particularly sensitive to the value of K. We have earlier suggested thatbecause the achievement of modern sector employment is not search-intensiveprospects of such employment are not greatly reduced by moving from unemploy-ment to the traditional sector. The smaller the difference in probabilities ofemployment between the two sectors then the larger the reduction in unemploy-ment which is secured by a given volume of migration. Indeed, Trade Theoristswill recognize in this a parallel with the scale of the Rybczynski Effect as afunction of the similarity of capital-labour ratios.

We have explicitly considered the effect of an exogenous increase in migration.However, it is apparent that the analysis is unchanged if the migration is anendogenous response to a change elsewhere in the system. In practice both migra-tion, which equilibrates agriculture and the traditional sector and the movementof indigenous labour between unemployment and the traditional sector should beseen as endogenous responses. However, when we introduce a perception functioninto the analysis the intra-urban labour movement should be more responsive toobjective economic change because information flows will be larger, more reliable

188 BULLETIN

and more rapid. It is because this sensitive intra-urban labour movement hasbeen ignored by the standard analyses of labour allocation that erroneous norma-tive conclusions have been reached about the social cost of migration and, by exten-sion, the social cost of modern sector employment.

(6) Policy Implications and ConclusionsSome Policy Implications

We conclude by considering some policy implications of our hypotheses. First,if the apparent link between migration and unemployment is questioned thensocial and private returns to migration might not be substantially divergent. Inthis case the curtailment of migration is not merely difficult, it is unnecessary.

Second, if the apparent link between new modern sector jobs and unemDloy-ment is questioned then the opportunity cost of labour, and hence the shadowwage, is reduced. We have suggested that any increase in unemployment is likelyto be due to the transfer payments made by modem sector workers rather than bythe impact on probabilities of employment. Since the establishment of a householdmight be a slow process the increase in unemployment might not occur for severalyears and is best predicted by examining dependency ratios of existing house-holds.

Finally, the importance of perceived as opposed to objective values should bestressed. This lack of information might well be a net social benefit, and certainlyprovides a potential additional instrument for the government in its labour alloca-tion policy. For example, education strongly affects the source upon whichmigrants rely for information. The tendency of the educated to migrate might beexplained more by the impact of education upon the perception function than byits impact upon objective values.

ConclusionThe core of this paper has been the attempt to create sound micro-foundations

for the theory of inter-sectoral labour allocation. This is in the spirit of the Harris-Todaro model. However, a micro-theory without a utility function, without time,and with perfect knowledge cannot be expected to provide secure foundations fora macro-theory.

We have attempted to demonstrate that the macro-implications of an accuratemicro-theory can differ considerably from those of the HarrisTodaro model.We have shown that each of the most fundamental postulates of their model canbe questioned at the a priori level and that in several cases such evidence as isavailable supports our alternative hypotheses.

The present data are insufficient for conclusions to be reached on most of theconflicting hypotheses. However, if we have re-opened issues which seemedsettled a priori, then our aim has been achieved. The need for empirical researchhas been increased and the direction which this research should take has becomemore specific.

Institute of Economics and Statistics,Oxford.


REFERENCESBienefeld, H. A. and Sabot, R. H., The National Urban Mobility Employ-

ment and Income Survey, Economic Research Bureau, Dar es Salaam, 1971.Joshi, H., Lubell, H. and Mouly, J., Urban Development and Employment

in Abidjan, International Labour Office, Geneva, 1974.Harris, J. and Todaro, M., 'Migration, Unemployment and Development:

A Two-Sector Analysis', American Economic Review, Vol. LX, 1970.Sabot, R. H., 'The Meaning and Measurement of Urban Surplus Labour

in an African Context', Mimeo, Oxford, 1974.

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LABOUR MOBILITY AND LABOUR UTILIZATION IN DEVELOPING COUNTRIES