On the political economy of the informal sector and income redistribution

Abstract

In this paper we analyze a general equilibrium model in which agents choose to be employed in formal or in the informal sector. The formal sector is taxed to provide income subsidies and the level of redistribution is determined endogenously through majority voting. The model is simulated to produce qualitative results and to illustrate the differences between economies with different distributional features. We show that a distortion in the democratic rule in favor of the rich reduces transfers while the size of the informal sector may remain at high levels. Despite a greater demand for redistribution in societies where the majority has few resources (skills), we find that political systems which work in favor of a rich minority will produce little redistribution. Our results call for pro-poor measures such as free training and education programs that should be offered to those who cannot afford it.

Appendix

1.1 Regression analysis

We use Penn World Table 6.2 for GDP, IMF Government Finance Statistics Yearbook 2001 and 2003 for social security and welfare spending, and Schneider (2002) for data on informal sector size. We exclude the formerly communist countries from the sample set. We regress social welfare expenditures per capita on the informal sector size as a percentage of GDP using GDP per capita as the control variable. The coefficient of the informal sector size is −0.025 with a t-statistic of −2.60.

1.2 Proof of propositions in the text

Proof of Proposition 1 Assuming that t is exogenous, it is easy to see from (9) that an increase in taxes will correspond to an increase in ε*. In other words, the formal sector shrinks. To see how ε**, and therefore unemployment, is affected by an exogenous change in t, reconsider the formula for the leisure threshold.

$$ \varepsilon^{ * * } = {\tfrac{{at\bar{y}}}{(1 - a)(1 - t)G(K)}} $$

where $\bar{y} = G(K)\int_{{{\tfrac{{\bar{w}}}{1 - t}}}}^{\infty } {h^{f} \varepsilon f\left( \varepsilon \right){\text{d}}\varepsilon }$ and $h^{f} = (1 - a) - {\tfrac{as}{(1 - t)\varepsilon }}$ letting G(K) = 1 without loss of generality and rewriting ε**

$$ \varepsilon^{ * * } = {\tfrac{{at\int_{{{\tfrac{{\bar{w}}}{1 - t}}}}^{\infty } {\left[ {(1 - a) - {\tfrac{as}{(1 - t)\varepsilon }}} \right]\varepsilon f\left( \varepsilon \right){\text{d}}\varepsilon } }}{(1 - a)(1 - t)}} = {\tfrac{{at(1 - t)\int_{{{\tfrac{{\bar{w}}}{1 - t}}}}^{\infty } {(1 - a)\varepsilon f\left( \varepsilon \right){\text{d}}\varepsilon } - as\int_{{{\tfrac{{\bar{w}}}{1 - t}}}}^{\infty } {f\left( \varepsilon \right){\text{d}}\varepsilon } }}{{(1 - a)(1 - t)^{2} }}} $$

Since $s = t\bar{y}$ and $\bar{y}$ depends on s through (14), successive substitutions yield $\varepsilon^{ * * } = {\tfrac{{at\int_{{{\tfrac{{\bar{w}}}{1 - t}}}}^{\infty } {(1 - a)\varepsilon f\left( \varepsilon \right){\text{d}}\varepsilon } }}{(1 - a)(1 - t)}}.$ The sign of the derivative ${\tfrac{{\partial \varepsilon^{ * * } }}{\partial t}} > 0$ if ${\tfrac{{\partial \left( {at\int_{{{\tfrac{{\bar{w}}}{1 - t}}}}^{\infty } {(1 - a)\varepsilon f\left( \varepsilon \right){\text{d}}\varepsilon } } \right)}}{\partial t}} > 0$ which can be shown by the application of the Leibniz rule. $\square$

Proof of Proposition 2 To show that individual post-tax income can be ordered monotonically along the productivity dimension consider the after tax income of formal worker. $y_{\text{after}}^{f} = h^{f} w^{f} \varepsilon + as\quad \left( { 1 - t} \right)\left( { 1 - a} \right)G\left( K \right)\varepsilon \quad {\text{for}}\;\varepsilon > \varepsilon^{ * }$

Taking the derivative yields

$$ {\tfrac{\partial y}{\partial \varepsilon }} = (1 - t)(1 - a)G(K) > 0,\quad \forall (s,t) $$

All the individuals who would prefer to work informal sector when taxed would get the informal post-tax income $y_{\text{after}}^{i} = (1 - a)\bar{w}\varepsilon$ which is lower than their formal post-tax income but not lower than the existing informal post tax income therefore the monotonicity holds for all levels of productivity. Since individuals do not solve the problem of taxation and redistribution independently of each other, and informal wages are constant and lower than formal wages the choice of the tax rate is ordered by productivity, for all s and t.

Finally, we show that the subsidies are uniquely determined by the choice of tax rates. Plugging (14) back into the balanced budget equation in (13)

$$ s = t\int\limits_{{\varepsilon^{ * } }}^{\infty } {\left[ {\left( {1 - a} \right) - {\tfrac{as}{(1 - t)G(K)\varepsilon }}} \right]\varepsilon f(\varepsilon ){\text{d}}\varepsilon } $$

Rewrite the above equation as

$$ g(s(t)) = f(s(t),t) $$

Holding t fixed, ${\tfrac{\partial f(s(t),t)}{\partial s}} < 0$ and ${\tfrac{\partial g(s(t))}{\partial s}} > 0$ for all s and $g(s(t)) < f(s(t),t)$ for s = 0. Suppose now that s is not increasing in t for all t. Suppose there exists t _i and t _j such that t _i  < t _j , $g(s^{*} (t_{i} )) = f(s^{*} (t_{j} ),t_{j} )$ and $\left. {{\tfrac{\partial (s(t))}{\partial t}}} \right|_{{t = t_{i} }} > 0$ and $\left. {{\tfrac{\partial (s(t))}{\partial t}}} \right|_{{t = t_{j} }} < 0$ but then $\left. {{\tfrac{\partial g(s(t))}{\partial s}}} \right|_{{s = s^{ * } }} > 0$ and $\left. {{\tfrac{\partial f(s(t),t)}{\partial s}}} \right|_{{s = s^{ * } }} > 0$ which is a contradiction. $\square$