## Abstract

This paper formalizes the dynamics of the informal sector with a special emphasis on the levels of labor market competitiveness in the formal and informal sectors. Specifically, it analyzes the effects of improved productivity and higher entry costs into the formal sector on the size of the informal sector for different degrees of competitiveness in the labor markets. We show that when the informal labor market is competitive while the formal labor market is not, lower production technology in the formal sector or a higher entry cost *reduces* the size of the informal sector in the long run.

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## Notes

Kingdon and Knight (2004) suggest that entry barriers also exist in the informal sector in South Africa. In contrast, Amaral and Quintin (2006) propose a theoretical possibility that such phenomena occur even in a perfectly competitive labor market with no entry barriers so long as informal managers, facing limited financial access, substitute low-skilled labor for physical capital.

As an anonymous referee correctly pointed out, one of the most relevant differences between Dessy and Pallage (2003) and our paper is that we consider the case in which entry fees collected from formal sector firms by the government are not used to finance the provision of public goods. Therefore, entry costs in our model include bribes paid by formal sector firms to corrupt public officials. Our theoretical predictions match the empirical evidence provided by Dreher et al. (2009) and Virta (2010).

The productivity of formal firms is higher than that of informal firms due to, say, a higher capital-labor ratio.

An individual that continues to work in the same sector is also randomly relocated on that circle in the second period.

Kats (1995) establishes that the ‘equal distance’ location pattern is an equilibrium of the two-stage location-price game, where firms simultaneously choose locations in the first stage and prices in the second stage.

Consider the net income of a worker located at distance

*x*from firm*i*, and distance \(\left(\frac{1}{n_0}-x\right)\) from firm*j*. His net income is*y*_{ F }(*x*,*w*_{ i }) =*w*_{ i }−*sx*if he works for firm*i*, \(y_F\left(\frac{1}{n_0}-x,w_j\right) = w_j - s\left(\frac{1}{n_0}-x\right)\) if he works for firm*j*, and zero if he is unemployed. Therefore, he works for firm*i*if and only if \(y_F(x,w_i)\geq\max\left\{0, y_F\left(\frac{1}{n_0}-x,w_j\right)\right\}\), which can be rewritten as \(x\leq\hat{x} \equiv \min\left\{\frac{w_i}{s}, \frac{1}{2s}\left(\frac{s}{n_0} + w_i - w_j\right)\right\}\) as it appears in the text. Moreover, provided that*w*_{ i }≥ 0 as usual, condition \(|w_i - w_j| \leq \frac{s}{n_0}\) guarantees that distance \(\hat{x}\) is non-negative. In other words, a firm never employs workers located on the other side of its adjacent firms.We ignore old formal workers here. This does not affect the following analysis.

Since there does not exist a rational expectation concerning competition between firms when \(n_0\in\left(s/b,\,3s/2b\right]\), symmetric equilibria do not exist in such cases. Put differently, if the firm sets a wage expecting, for example, that it does not need to compete for workers with the adjacent firms, it turns out that the firm in fact needs to compete with the adjacent firms in order to employ the intended amount of labor when \(n_0\in\left(s/b,\,3s/2b\right]\).

In other words, we restrict attention to the values of the parameters \(\hat{y}\),

*C*_{ I },*C*_{ F },*a*,*b*,*r*,*s*,*n*_{0}and*m*_{0}such that*n*_{ t }and*m*_{ t }, which are respectively given by Eqs. 4 and 5, satisfy*n*_{ t }≤*s*/*b*and*m*_{ t }> 3*r*/2*a*for all*t*≥ 0, respectively, assuming that such sequences \(\{n_t\}_{t=0}^\infty\) and \(\{m_t\}_{t=0}^\infty\) exist. It follows from Eq. 1 that \(w_{F,t} = b/2 > \hat{y}\) and \(w_{I,t} = a - r/m_t > \hat{y}~(\Leftrightarrow m_t > \max\{3r/2a,r/(a-\hat{y})\})\) must be satisfied for all*t*≥ 0.The opposite case, in which the formal sector is relatively competitive \(\left(n_t > \frac{3s}{2b}\right)\) and the informal sector is relatively less competitive \(\left(m_t \leq \frac{r}{a}\right)\), is analyzed in the Appendix.

In other words, these young individuals are located within distance (

*w*_{ F, t − 1}−*C*_{ F })/*s*from the closest firms.Since the expected income of formal workers is higher than the profit of an informal-firm owner (\(\bar{y}_{F,t} > \pi_{I,t}\)), young formal workers in period

*t*− 1 who could set up an informal firm in period*t*will not choose to do so.It should be noted that (

*w*_{ F }= )*b*/2 >*C*_{ F }by assumption.The number of firms in the informal sector is larger in the new steady state. To see this, plug the steady state values,

*m*_{ t }=*m*_{ t − 1}=*m*, \(\hat{G}_{t-1}=\hat{G}\), and*w*_{ I }=*a*−*r*/*m*, into Eq. 5, and obtain$$ m=\frac{2rG}{2G\left(a-C_I\right)-r}. $$Clearly, the steady-state number of firms in the informal sector rises with

*C*_{ I }.

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## Acknowledgements

The authors wish to thank the responsible editor, Alessandro Cigno, and two anonymous referees for their very useful comments and suggestions. Thanks are also due to Yoko Asuyama and Paul Kandasamy for their helpful comments.

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*Responsible editor:* Alessandro Cigno

## Appendix: The case in which formal firms compete for workers whereas informal firms do not

### Appendix: The case in which formal firms compete for workers whereas informal firms do not

In this appendix, we consider the case in which *n* > 3*s*/2*b* and *m* ≤ *r*/*a*. In this case, the wage in the formal sector increases as the number of formal firms rises (*w*
_{
F
} = *b* − *s*/*n*), while the wage in the informal sector is independent of the number of informal firms (*w*
_{
I
} = *a*/2). From these wages and the steady-state conditions, we obtain

Thus, the size of the informal sector in the steady state is expressed as

where \(P_I^* > 0\) because *w*
_{
I
} = *a*/2 > *C*
_{
I
}. From this expression, we can see that the steady-state size of the informal sector is increasing in the transaction cost in its labor market (*r*) and the setup cost of an informal firm (*C*
_{
I
}), and is decreasing in the productivity in the informal sector (*a*).

Suppose that *C*
_{
I
} increases for example. In the short run, the number of firms decreases and unemployment increases in the informal sector. As a result, fewer young individuals receive education, and thus more individuals enter the informal labor market. Given the same number of formal firms, the population size of the informal sector increases while that of the formal sector declines. In the next period, the number of formal firms decreases and that of informal firms increases. Since the labor market in the formal sector is more competitive than that in the informal sector, the wage and employment in the formal sector is more responsive to changes in the number of firms than those in the informal sector. Hence, the net worker inflow into the informal labor market increases. Therefore, the informal sector expands as the setup cost of an informal firm rises. The effects on the size of the informal sector of changes in the production technology and transaction costs in the informal sector can be understood in a similar way.

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Goto, H., Mano, Y. Labor market competitiveness and the size of the informal sector.
*J Popul Econ* **25**, 495–509 (2012). https://doi.org/10.1007/s00148-011-0360-1

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DOI: https://doi.org/10.1007/s00148-011-0360-1

### Keywords

- Informal sector
- Imperfect labor market
- Entry costs

### JEL Classification

- O17
- J42
- L13