South Africa suffers from an unusually high unemployment rate – officially averaging 25% since 1999Q3. In addition, depending on whether one uses the official or broad definitions of unemployment, since 2008 there are on average between 2 and 3.3 times as many unemployed people as there are people in the informal sector. Hence the question: why do the unemployed not enter the informal sector to create a livelihood?

To fill this gap we propose a macro-economic framework that incorporates both formal (primary) and informal (secondary) sectors, as well as involuntary unemployment resulting from entry barriers to the labour market. We believe such a model provides a more suitable basis for macroeconomic policy analysis.

Standard macroeconomic theories at best provide a partial explanation for the South African unemployment problem, focusing mostly on the formal sector.

The article uses a theoretical analysis.

The article presents a macro-economic framework that incorporates both formal (primary) and informal (secondary) sectors, as well as involuntary unemployment resulting from entry barriers to the labour market.

If the assumptions on which the model draws hold in the South African reality, then a solution to the unem-ployment problem involve policies addressing product and labour market structures and behaviour in the primary sector, as well as policies addressing the numerous barriers to entry, such as borrowing constraints, that poten-tial entrants into the secondary sector face.

Few countries have as serious an unemployment problem as South Africa. In the pe-riod 2008Q1–2018Q2 the official unemployment rate averaged 25.1%, while the broad unemployment rate (which includes discouraged work-seekers) averaged 34.8% (StatsSA

The number of employed and unemployed workers (’000).

Composition of the employed (% of total employment).

Year | Shares | |||
---|---|---|---|---|

Formal sector (Non-agricultural) | Informal sector (Non-agricultural) | Agriculture | Private households | |

2000 | 58.8 | 19.7 | 11.0 | 10.5 |

2010 | 69.5 | 16.7 | 4.9 | 8.9 |

2017 | 70.3 | 16.6 | 5.0 | 8.1 |

Note: Data for 2000 from the Labour Force Survey. Data for 2010 and 2017 from the Quarterly Labour Force Survey. All data refer to September of the relevant year.

This raises the following question: if workers do not find employment in the formal sector, why do they become unemployed rather than enter the informal sector? Kingdon and Knight (

A characteristic of almost all the macroeconomic work on unemployment in SA is that it deals with the formal sector only (Fourie

The objective of this article is to start bridging the divide between the macroeconomic discourse and the labour and development discourses on unemployment by developing a model that includes labour market segmentation and entry barriers into a theoretical macroeconomic model. A major result of this model is that, given these incorporated fea-tures, it explains the existence of persistent high involuntary unemployment in equilibrium.

Modern macroeconomic theory largely focuses on the formal sector, ascribing unemployment mostly to product and labour market imperfections, as well as hysteresis (see Cahuc & Zylberberg

Discussing the informal sector draws segmented labour markets into the discussion. Agénor and Montiel (

Another branch of the literature represents the attempts by Layard, Nickell and Jackman (

Such a market-clearing secondary sector means that those who are not employed in either the primary or the secondary sectors are

This section develops a mathematical three-segment model for an economy such as that of South Africa (for more background and explanation, see Burger & Fourie

We derive a formal-sector job-offer relationship and an effort supply function.^{1}

In addition to these two relationships, the analysis below also presents wage-setting and price-setting relationships. These four relationships are then used to derive equilibrium condi-tions for the primary and secondary sectors.

At any given moment firms in the primary sector fill a number of positions (jobs). The total number of jobs available in the primary sector is _{p}. Those workers who do not obtain employ-ment in the primary sector are accommodated in the secondary sector (which is assumed to be without entry barriers). In the secondary sector there is equilibrium: the total number of jobs filled is _{s}. Thus, although there might be involuntary unemployment in the primary sector, there will not be involuntary unemployment at the aggregate level. The total number of filled positions in the economy (which in this case amounts to the entire labour force) is:

The allocation between the two sectors can be described in terms of the proportion of total positions filled by firms in the primary sector being _{p}/_{s}/

A worker who quits or is laid off in the primary sector, is assumed to move to the secondary sector. The quit rates in the primary and secondary sectors are _{p} and _{s;} _{2} represents the probabil-ity of the worker being laid off when caught shirking (or e.g. low productivity^{2}_{1} represents the probabil-ity of being laid off for shirking while not actually shirking (a false positive). Further-more, _{p} and _{s} represent the wage rates in the primary and secondary sectors. There-fore, _{p} _{1}_{p} represents the expected wage of those workers employed in the primary sector (i.e. who have not been laid off and have not quit the primary sector), while _{p} _{1}_{s} represents the expected wage of primary sector workers who are laid off in or quit from the primary sector and move to the secondary sector. (Shirkers are assumed to produce noth-ing, hence their _{s}_{s} represents the ex-pected wage of those workers in the secondary sector who remain in the secondary sector, while _{s}_{p} represents the expected wage of those workers who quit the secondary sector for the primary sector. Thus, the sum of the present value of expected primary and secondary sec-tor income in the economy is:^{3}

In equilibrium, labour flows into and out of the primary sector need to be equal. Thus _{p} _{1}_{s}_{p} _{1} = _{s}

Following Bulow and Summers (_{2} _{1}_{p} _{s}_{p} is the present value of primary sector work and _{s} the present value of secondary sector work (recall that non-effort is only possible in the primary sector, the sector that pays a wage premium over the secondary sector wage). This conditional expression shows the premium that firms pay (the right-hand side of

As mentioned above, the model in this article com-bines an efficiency wage model (with its non-shirking component) with a labour union model. As a result _{1}_{2}, where _{1} is the instantaneous gain in utility from not exert-ing effort (i.e. from shirking), and _{2} (which is ≥ ^{4}^{5}

The South African labour market is also characterised by significant spatial distortions result-ing from apartheid, where places of residence of black people very often were far removed from places of work (in the primary sector). These distances significantly raise travel costs, which need to be added to the premium that workers require before working in the primary sector. Therefore:
_{3} represents the cost per unit of distance:

Unions having more power implies a higher value of _{2} and therefore a higher value of

Similarly, the larger _{3} and _{3}

Rearranging

Using

Substituting _{p} yields:

Recalling that _{p} _{1} = _{s}

_{p} decreases. It also expresses the primary sector wage as the secondary sector wage plus a mark-up. (It still is an effort supply function: the mark-up or premium is what needs to be paid to primary sector workers to ensure effort.) Thus, the rela-tive proportion of positions allocated to primary sector jobs (

The relationship between primary and secondary sector wages.

Note that, as _{p} shifts and rotates from _{p1} to _{p2}).

To derive the price-setting relationship we use the standard textbook equation stating the relation-ship between wages, the marginal product of labour (and hence the level of employ-ment _{p}. Thus, holding

_{p} decreases as _{p} increases (but the wage cannot turn nega-tive).

The number of positions (_{p}) and hence also the proportion of jobs or positions offered by firms in the primary sector, ^{6}

Thus, at higher levels of _{p} the real wage is lower (because the marginal product of labour is lower), and hence so is the proportion of positions filled by firms in the primary sector,

Given the role of the marginal product of labour in

Note that in terms of _{p}, but a negative relationship between _{p} and _{p} increases, _{p} decreases, causing

Substituting

_{p} increases (and given that _{p} increases, simply because, as employment in the primary sector increases (and hence as employ-ers offer more jobs), workers can get work easier elsewhere in the primary sector (the probability of getting a job in the primary sector is larger if a larger proportion of total jobs are filled in the primary sector) – hence firms need to offer a higher wage to ensure that they stay, exert effort and do not strike.

Workers in the secondary sector are just paid their marginal product, which, for simplicity, is assumed to remain constant: with little capital and similar skills and each person more or less operating on their own, they are assumed to have the same marginal productivity.

The model can be summarised as follows.

First, in _{p} space there are two relationships (the [ ] indicates the sign of the _{p} relation-ship):

A job offer relationship:

An effort supply function:

Secondly, in _{p}_{p} space there are two relationships (with _{p}_{p} relationship):

A price-setting relationship:

A wage-setting relationship:

_{p}, and to calculate the equilibrium values of _{p} and

To calculate the equilibrium value of _{p} note that in equilibrium _{p}_{p} and that _{p}/_{p}:

Together with the effort supply function 8, the job offer relationship 11a then determines the equilibrium number of positions in the primary sector. Since the proportion of filled positions in the secondary sector is _{s}. (This assumption will be relaxed in the next section). Thus, in this model – as in the model of Bulow and Summers – there is no involuntary unemployment.

In this section the model is expanded to contain a third sector or segment that comprises the unem-ployed. The preference hierarchy follows the model above: workers in the secondary sector prefer the primary to the secondary sector; the unemployed would prefer secondary sector employment to unemployment and primary sector employment to secondary sector employment.

As in the previous section, we first consider the effort supply function. The effort supply func-tion introduces a role for entry barriers that imply that not all of those who are unable to find a job in the primary sector will be able to find one in the secondary sector.

The model makes a few simplifying assumptions. First, those quitting and being laid off in the primary sector (at rate _{p} _{1}), move to the secondary sector, while those quitting the secondary sector (at rate _{s}) move to unemployment (i.e. nobody moves from the secondary to the primary sector). Those of the unemployed who quit their unemployed status (at rate _{u}) move either into the primary or the secondary sector. The unemployed, of course, receive no wage.

As before, the proportion of filled positions (jobs) supplied in the primary sector is _{p}, while that of the secondary sector is _{s}. A critical difference is that, unlike the two-sector model with no unemployment (where everyone who is willing to work in the secondary sector for a wage equal to their marginal product, _{s}, finds employment), in this model the number of filled positions in the secondary sector, _{s}, is equal to or less than _{p}_{s} being smaller than _{p}

Grimm et al. (_{K}; there will be no profit left after paying the cost of capital. Hence, investment will not take place and the entrant will not enter the secondary sector. If, however, the minimum scale is lower than the borrowing constraint, investment will take place and returns to capital will exceed capital cost (this high return will of course fall to zero as the scale of capital is expanded and the marginal product falls with the expansion in scale). In their model (Grimm et al.

Subject to:

The capital stock is chosen so that

Note that in the two-sector model of the previous section all those workers who were unable to find jobs in the primary sector were able to find a job in the secondary sector if they were willing to work for a wage equal to the marginal product of their labour. However, in the three-segment model of this section, barriers to entry into the secondary sector means that only a fraction,

That fraction,

This implies that (_{p} _{s}) is the proportion of positions that the primary and secondary sectors would have supplied, _{p} and _{s} are expressed as ratios of _{p} + _{s}, +

With the above, and similar to

In equilibrium, outflows from the primary sector need to equal inflows into the primary sec-tor from the third segment (unemployed). Thus, _{p} _{1}_{p} = _{u}_{p}_{p} _{s}_{p} _{1}_{p} _{s}

In addition, the outflow from the secondary sector needs to equal inflow into the secondary sector from both the primary sector and the unemployed segment. Thus, _{s}_{s} = _{p} _{1}_{p} _{u}_{s}_{p} _{s}_{p} _{1}_{p} = _{s}_{s} _{u}_{s}_{p} _{s}_{u}_{p}_{p} _{s}

Assuming that the unemployed receive no income, it means that in this case too _{2} _{1}_{p} _{s}

Therefore:
_{p} yields:

Using the equilibrium condition that _{p} _{1}_{p} = _{u}_{p}_{p} _{s}_{u}_{p} _{1}_{p} _{s}

Now recall that _{s}= θ(1 – p_{p}

_{p} would cause _{p} to decrease and the slope of the effort supply function becomes flatter the larger _{p} becomes. Note that, unlike in ^{7}

Therefore, there is a positive relationship between _{p}, but a negative relationship (given that _{p} and _{p} (as _{p} increases, _{p} decreases, causing _{p} to also decrease).

Substituting

As _{p} increases (and given that _{p} increases.

The model can be summarised as follows.

First, in _{p} space there are two relationships (the sign within [ ] indicates the sign of the _{p} relationship):

A job offer relationship:

An effort supply function:

Secondly, in _{p}_{p} space there are two relationships (with _{p}_{p} relationship):

A price-setting relationship:

A wage-setting relationship:

In a similar fashion as in the previous section, _{p}, _{p} and _{p}:

Note that, unlike their two-sector equivalents (_{s}_{p}

In the three-segment model the unemployed are involuntarily unemployed. Those who end up in the third segment and who cannot re-enter either the primary or the secondary sectors, due to the presence of barriers to entry into both the primary and secondary labour markets, find themselves involuntarily unemployed.

Using _{p} _{s}), which equals the equilibrium level of positions filled, _{p} + _{s}. Hence:

The two-sector, three-segment model shows how the two-sector model can be expanded from a model that merely explains the allocation of labour between the primary and secondary sec-tors, to a model that caters for the possibility of involuntary unemployment on the aggregate level. The key difference centres on the following. In the two-sector model, workers who quit or lose a job in one of the sectors, circulate back to a job in the other sector. In the three-segment model, workers who quit or lose a job in one of the two employing sectors do not necessar-ily find a job again and may end up being unemployed. Some workers might also never have worked (and remain unemployed).

The main reason why workers end up unemployed is the existence of barriers to entry such as a lack of physical and human capital as discussed above. (If there are no barri-ers to entry into the secondary sector, the three-segment model reverts to the two-sector model.) To compare the two models, compare _{p} in the three-segment model’s _{p}, _{p} and _{p}.^{8}

In the literature (cf. Campbell & Orszag _{1}, i.e. the probability of being laid off for shirking while not actually shirking) do not affect _{p}, _{p} and _{p} because in equilibrium the flow into the primary sector equals the flow out of the primary sector – those who quit find jobs in the secondary sector and are replaced, in turn, by workers moving from the secondary to the primary sector.

However, because of entry barriers in the secondary sector in the three-segment model, the flows into and from the primary sector are not necessarily equal. This implies a relationship between quitting and _{p}, _{p} and _{p}. In the three-segment model, barriers to entry mean that _{p} in ^{9}_{p} would have no effect. Thus, in this model the presence of barriers to entry (which cause _{p} has an effect on _{p}, _{s} and _{p}. Higher levels of employment in the primary sector imply that should a worker quit, the probability of ultimately finding a job again in the primary sector is higher, which, in turn, may engender a greater willingness on the part of primary sector work-ers to quit. Hence the positive relationship between quit rates and _{p} and _{p}.

Unlike the two-sector model where all workers are employed either in the primary or the secon-dary sector, in the three-segment model _{p} _{s} ≤ _{p} _{s} will be, hence (using _{p} and _{p} will be.^{10}

Furthermore, note that the higher the quit rate _{s} from the secondary sector, the lower are _{p}, _{s} and _{p}. In the three-segment model, quitting from the secondary sector means that the worker moves towards unemployment, while in the two-sector model it means that the worker cir-culates back to the primary sector. For given quit rates from the primary and tertiary sec-tors (‘tertiary quitting’ being quitting from unemployment and thus moving back to either primary or secondary sector employment), a higher quit rate in the secondary sector means a higher probability of ending up without a job, even if one starts out in the primary sector. Thus, a higher quit rate from the secondary sector depresses wages, employment and the num-ber of jobs in the primary sector.

_{P}), while secondary sector employment is measured leftward from the vertical axis (_{S}). N_{N} represents the working-age population. Distance

Unemployment in the theoretical three-segment model.

Suppose, to start off, there is a perfectly competitive labour market with no market power and no efficiency wages. The wage paid in the primary and secondary sectors would be equal (i.e. there is no real distinction between the primary and secondary sectors). ^{11}_{PC} = _{SC}, with _{PC} and _{SC} being the corresponding employment levels in the primary and secon-dary sectors. The distance marked _{SC} (i.e. if they are will-ing to reduce their reservation wages).

Now suppose the economy is Neo-Keynesian, with market power and efficiency wages in the primary sector. This produces the two-sector Neo-Keynes-ian model (subscript K), still with no barriers to entry into the secondary sector. The wage-setting (_{P}) and price-setting (_{P}) relationships in the primary sector will, due to effort behaviour, establish a wage _{PK} that is higher than _{PC}. Employment in the primary sector, at _{PK}, will be lower compared to the perfectly competitive case, at E_{PC}. The difference in the num-ber of workers being employed in the primary sector equals distance _{PC} _{PK}. Workers who are not accommodated in the primary sector are diverted to and employed in the secondary sector. Thus, labour supply in the secondary sector is _{SC} should they wish to (i.e. if they lower their reservation wage); they are voluntarily unemployed.

Next we introduce barriers to entry into the secondary sector (for simplicity we ignore barri-ers to entry into the primary sector). Given the nature of ‘effort behaviour’ in the primary sec-tor, as before a quantity of workers equal to

Unlike the case of the perfectly competitive market where workers can simply offer their labour at a lower wage, in a market with efficiency wages (with firms paying a wage to ensure effort), firms in the primary sector set both wages and prices. Hence, workers cannot increase employment in the primary sector by offering to work for a lower wage. In addition, even if unemployed workers are willing to work in the secondary sector for a wage equal to the marginal product of labour, barriers to entry prevent them from doing so.

The workers represented by distance _{PC} = _{SC}, but are prevented from doing so due to the pay-ment of efficiency wages in the primary sector and the existence of barriers of entry in the secondary sector.

To create a theoretical model that explains the dual nature of the South African labour market (with its formal and informal sectors) and the simultaneous existence, indeed persistence, of very high unemployment, this paper draws on the dual labour market model of Bulow and Summers (

The model shows:

How a primary sector characterised by efficiency wage and labour union behaviour, as well as a mark-up due to high transport cost, can explain the dual nature of the labour mar-ket.

How barriers to entry faced by potential entrants into the secondary sector can prevent workers from entering the secondary sector. This constrains the effective supply of labour to the secondary sector.

How, as a result, these workers end up being (involuntarily) unemployed in a long-term macroeconomic equilibrium. The secondary sector does not simply absorb all those who cannot find employment in the primary sector.

From a policy point of view, the above suggests that there is no single or ‘silver bullet’ solution to address the unemployment problem. The solu-tion is not as easy as, for instance, simply decreasing wage levels to render labour cheaper. Indeed, if the assumptions on which the above model draws hold in the South African reality, then a solution to the unem-ployment problem involve policies addressing product and labour market structures and behaviour in the primary sector, as well as policies addressing the numerous barriers to entry, such as borrowing constraints, that poten-tial entrants into the secondary sector face.

The authors wish to thank REDI3x3 for the generous funding of this project, as reflected in Burger & Fourie (

The authors declare that they have no financial or personal relationships that may have inappropriately influenced them in writing this article.

Both authors contributed equally to the article.

Concerning the microfoundations of the model, the model assumes a simple utility function, resembling the specification by Bulow and Summers (_{t} = _{p}, _{s} + _{p}, λx_{s}_{p},_{s}

For simplicity, quitting and being laid off are modelled to depend on shirking (insufficient work effort or productivity); other factors that determine quitting or being laid off can be modelled analogously. The simplification is not central to the main result of involuntary unemployment present in the full model, but merely facilitates it – involuntary unemployment will depend on the presence of barriers to entry into the secondary sector. Nevertheless, because it is commonly used in international literature, the shirking model is used here.

For reasons of simplicity Equation 6 assumes infinitely lived workers and as such uses the simple formula for the calculation of the value of a consol to calculate the present value.

The premium rate is _{2}

.The South African labour market is also characterised by a clear skills-related stratification of the unemployed, with an oversupply of unskilled workers and a shortage of skilled workers: the unemployment rate among individuals holding post-school degree qualifications is approximately 5%, and among those who have not completed school just below 50% (CDE

Note that _{p} = _{p}_{p}), so dividing _{p}) by _{p}

That the first term containing _{p} would equal zero if _{p} _{1}_{p} = _{u}_{p}_{p} _{s}_{p} _{1}_{u}_{p} _{s}_{p} _{1}_{p}. If _{p} _{s} = _{u}_{p} _{s}_{p} _{1}

Why is this so? With _{p}_{p} (_{p} _{1}_{s}_{p}, for instance –(_{p} + _{1}_{s})^{2} in _{p}, the net effect of the three terms on the right-hand side containing _{p} will be positive, meaning higher equilibrium values for _{p}, _{p} and _{p}. (The only exception to this scenario would be the primary sector goods market approximates an almost perfectly competitive market, contrary to the assumptions of this model.)

Why the first two terms containing _{p} would equal zero if _{p} _{1}_{p} = _{u}_{p}_{p} _{s}_{p} _{1}_{u}_{p} _{s}_{p} _{1}_{p}. If _{p} _{s} = _{u}_{p} _{s}_{p} _{1}

The logic is as follows: Higher barriers mean a lower _{p}, _{p} and _{p} in a case of a lower _{p} and _{s} will also be lower.

Assuming a constant marginal product of labour for the secondary sector is not an altogether unrealistic assumption. Berry (