Most people in the developing world derive all their income from employment (World Bank 2012). The structure of labor markets, and the policies enacted within them, therefore dramatically affect the lives of the poor. The multi-sector labor market model of Harris and Todaro (1970) (HT) remains the basic framework for a vast literature devoted to analyzing labor market policies in developing economies. These analyses primarily focus on wages and unemployment, while ignoring the welfare consequences of labor market policies. One reason for this oversight is that it is generally difficult, within such models, to draw robust welfare conclusions that do not critically depend on the specific welfare criterion adopted (Temple 2005). For example, in one of the few welfare economic analyses in this literature, Fields (2005) shows that the welfare consequences of various labor market policies are ambiguous even when restricting the analysis to abbreviated welfare functions.
In this article, I derive welfare conclusions that are both unambiguous and robust to alternative specifications of welfare criteria. I do so by exploiting the classic Atkinson (1970) welfare theorem, which specifies conditions under which one can make welfare statements for an extremely broad class of social welfare functions. The usefulness of this theorem is generally limited by its lack of applicability because its conditions are seldom satisfied in practice (Dutta 2002). Thus, the direct application of the Atkinson (1970) theorem can itself be considered an additional contribution of this article.
I consider the generalized HT framework of Fields (1989), which incorporates two of the more important subsequent extensions in the literature – informal sector dualism and on-the-job search. Within this framework, I analyze two labor market policies. The first, modern sector enlargement (MSENL), was the primary policy considered by HT and is now the benchmark policy for analyzing and comparing the structure of labor market models within the literature. The second, increasing the efficiency of on-the-job search from the urban informal sector (IEOS), is a novel policy enabled by informal sector dualism and on-the-job search.
I demonstrate that MSENL causes a Lorenz worsening of the income distribution and IEOS causes a Lorenz improvement. This is a novel result in itself given that policies within HT frameworks do not generally result in income distributions with non-intersecting Lorenz curves (Temple 2005). I also demonstrate that both MSENL and IEOS do not alter the mean of the income distribution. These properties satisfy the strict conditions of the Atkinson (1970) theorem, which I then invoke to conclude that MSENL reduces social welfare and IEOS improves social welfare for all anonymous, increasing and Schur-concave social welfare functions.
The article proceeds as follows. In Section 2, I describe the salient features of the extended Harris-Todaro model of Fields (1989). I conduct the welfare analysis in Section 3 and conclude in Section 4.
Fields (1989) defines three employment sectors – the urban modern sector (
The probability of finding a job using strategy
Denoting the number of workers electing search strategy
Total income in the economy is given by
3 Welfare Analysis
I evaluate the welfare effects of a policy of modern sector enlargement (MSENL) and a policy of increasing the efficiency of on-the-job search from the urban informal sector (IEOS) by comparing equilibrium income distributions before and after the application of each policy. MSENL is modeled as an increase in
In general, making unambiguous welfare comparisons depends critically on which specific welfare criterion is adopted. Thereom 1, proposed by Atkinson (1970) and later extended by Dasgupta, Sen, and Starrett (1973), states that under certain conditions, however, the welfare of one income distribution may be ranked relative to another for a broad range of social welfare functions.
Let X and Y be two income distributions with equal means. Let
Theorem 1 facilitates the welfare analysis in two ways. First, it reduces an analysis of welfare to one of inequality. If workers derive utility solely from income, which is implied by the search strategy behavior described by eq. , then an income distribution that Lorenz dominates another with the same mean is not only more equal, but better in terms of welfare. Thus, Theorem 1 ensures that the income distribution provides sufficient information to make welfare inferences.
Second, Theorem 1 ensures the robustness of any welfare implications, because the great majority of accepted social welfare functions are included within
MSENL and IEOS do not affect the mean of the income distribution.
The model emits explicit equations for labor allocations and earnings. I can therefore assess the impact of MSENL and IEOS by evaluating derivatives with respect to
Proposition 1 demonstrates that MSENL and IEOS reallocate workers and earnings across sectors in a manner that is neutral in terms of total income, thereby allowing Theorem 1 to be applied. It therefore remains to determine whether the labor market policies yield non-intersecting Lorenz curves.
MSENL causes a Lorenz worsening.
Workers fall into one of four employment categories. A Lorenz curve therefore consists of four piecewise linear segments, each characterized by the position of three kink points as shown in Figure 1. Without loss of generality, I normalize
IEOS causes a Lorenz improvement.
Propositions 2 and 3 demonstrate that both policies produce strict Lorenz orderings. In isolation, these results imply that MSENL increases inequality and IEOS decreases inequality. When combined with Theorem 1 and Proposition 1, however, the findings also have normative significance. Theorem 2, which is the main result of this article, follows directly from Theorem 1 and Propositions 1–3.
For all anonymous, increasing and Schur-concave social welfare functions, MSENL decreases social welfare and IEOS increases social welfare.
Within the context of the generalized Harris-Todaro model proposed by Fields (1989), I demonstrate that both MSENL and IEOS do not alter the mean of the income distribution. I then show that MSENL causes a Lorenz worsening and IEOS causes a Lorenz improvement. These properties allow me to draw robust welfare conclusions by exploiting Atkinson’s (1970) classic theorem, which demonstrates that Lorenz orderings coincide with welfare orderings for a very broad class of welfare functions. I conclude that a policy of MSENL therefore reduces social welfare while a policy of IEOS improves social welfare.
This article makes three contributions. First, it extends the work of Fields (2005), who performs welfare economic analyses within the basic HT framework, to the more complex multi-sector labor market model of Fields (1989). Second, it widens the scope of policy analysis to include welfare effects that are robust to all anonymous, increasing and Schur-concave social welfare functions. Third, and relatedly, it provides what is to my knowledge the first direct application of the Atkinson (1970) theorem within a multi-sector labor market model.
This work originated as a term paper for a Cornell University Development Economics course taught by Gary Fields. I would like to thank him for the inspiration. I am also grateful for the insightful comments provided by Kyle Rozema and two anonymous referees.
Derivation of Eqs –
Equation  implies that
The definition of
which is .
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The derivations can be found in the Appendix.