Informal firms in developing countries: entrepreneurial stepping stone or consolation prize?

Abstract

The potential dynamic benefits of a firm having the option to adopt informal status are analysed. Informality may be a stepping stone, without which formality may never be achieved. This result is obtained for a broad range of realistic parameter values, suggesting a potential dynamic case for government support of informal firms. Informality may alternatively play a converse role as a consolation prize, with a firm only entering an industry (formally) because it recognizes that if profitability is disappointing, it can switch to informality. However, this result is obtained for a range of parameter values so narrow as to be of no practical significance.

Appendix

1.1 Derivation of expected profit at t = 2

X denotes exit, I denotes informal status, F denotes formal status and SO denotes staying out of the industry. Consider behaviour at t = 2. If F at t = 1, from (Eq. 3) and (Eq. 5) profits at t = 2 are θ − w if I is chosen, but $2(\beta \theta -\bar{w})$ if F chosen. Thus, if $w\geq \bar{w}/\beta ,$ I is not chosen at t = 2 for any θ: X is chosen if $\theta <\bar{w}/\beta ,$ but F if $\theta \geq \bar{w}/\beta .$ (Eq. 6) follows. But if (Eq. 8) holds, at t = 2, X is chosen if θ < w; I if $w\leq \theta <(\bar{w}+s)/(2\beta -1);$ F if $(\bar{w}+s)/(2\beta -1)\leq \theta \leq 2\Uptheta .$ (Eq. 9) follows.

If I at t = 1, then if ${\frac{1}{\beta}}\left( \bar{w}+{\frac{k} {2}}\right) \leq w,$ at t = 2 X (F) is chosen if $\theta <(\geq )(\bar{w}+{\frac{k}{2}} )/\beta .$ (Eq. 11) follows. But if (Eq. 13) holds, at t = 2 X is chosen if θ < w; I if $w\leq \theta <(\bar{w}+s+k)/(2\beta -1);$ F if $(\bar{w}+s+k)/(2\beta -1)\leq \theta .$ (Eq. 14) follows.

Lemma 1

From (Eq. 19), EV(f)−EV(i) = Δ₁ + Δ₂. From (Eq. 18), Δ₁ is increasing in Θ, and β, and decreasing in s, k and w, as in the lemma. Let us now focus on Δ₂. Since (Eq. 8) and (Eq. 13) each may or may not hold, and k > 0, three cases can be distinguished. First, if $\left( \bar{w}+{\frac{k}{2}}\right) \leq w$ then, using (Eq. 6) and (Eq. 11),

$$ \Updelta _{2}=k+{\frac{1}{2\Uptheta }}\left\{{\frac{1}{\beta }}\bar{w}^{2}-{\frac{ \left( k+4s+2w\right)}{4(2\beta -1)^{2}}}[(3\beta -2)(k+2w)+4(\beta -1)s]\right\} \hbox {.} $$

Using (Eq. 12), the lemma follows for this case. Second, if ${\frac{1}{\beta }}\bar{w}\leq w<{\frac{1}{\beta }}\left( \bar{w}+{\frac{k}{2}}\right)$ then, using (Eq. 6) and (Eq. 14),

$$ \Updelta _{2}=k+{\frac{1}{2\Uptheta }}\left[ {\frac{1}{\beta }}\bar{w}^{2}-{\frac{1}{ 2(2\beta -1)}}\left(2w^{2}\beta +4ks+2kw+4sw+k^{2}+4s^{2}\right) \right]. $$

Using (Eq. 15), the lemma follows for this case. Third, if $w<{\frac{1}{ \beta }}\bar{w},$ then using (Eq. 9) and (Eq. 14),

$$ \Updelta _{2}=k-{\frac{1}{4(2\beta -1)\Uptheta }}[2(\bar{w}+s)+k]k. $$

Using (Eq. 10) and (Eq. 15), the lemma follows for this case.