Imperfect labor mobility and unemployment in LDCs: reply.

Beladi, Hamid

In a recent paper (Parai and Beladi 1997; PB hereafter), we have analyzed the implications of growth and trade policies for a small open economy facing imperfect labor mobility and unemployment of the Harris-Todaro variety. We have used the Casas (1984) specification of the labor immobility phenomenon for a Harris-Todaro type economy, and have shown that most of the results in Harris-Todaro framework remain unaltered even under imperfect labor mobility, provided that the elasticity of labor mobility parameter exceeds a critical minimum value. On the optimal tariff issue, Gilbert and Mikic (1997; GM hereafter) find our results counterconventional. In GM's view, the nonconventional result in PB is due to our simplification of the labor mobility specification given by Casas. In this note, we offer our response to GM's comments.

First of all, we appreciate GM's attention to our apparently counterconventional result about the positive optimal tariff because their comment has given us an opportunity to rectify a minor algebraic error in one of our results and clear up the confusions in its policy implications. But their conclusion that it is because of our simplification assumption of unitary values of the scale parameters a and b in Casas's specification is incorrect. Had we maintained the Casas specification intact, PB's equation 10 would become

[b/[(a).sup.1/[Epsilon]][([L.sub.1]/[L.sub.2]).sup.1/[Epsilon]] = [[L.sub.2]/([L.sub.2] + [L.sub.u])]. (1)

Logarithmic differentiation of Equation 1 would again yield equations 28 and 37 in PB. Consequently, the nonunitary values of a and b would leave all the comparative static results in PB unchanged.

On closer scrutiny of our algebra, however, we find an inadvertent error in the derivation of the optimal tariff, [Mathematical Expression Omitted]. The corrected expression reads

[Mathematical Expression Omitted],

where [Psi] [greater than] 1, [a.sub.s] [equivalent to] (d[X.sub.2]/dp)(p/[E.sub.2]) [greater than] 0, [a.sub.d] [equivalent to] - (d[D.sub.2]/dp)(p/[E.sub.2]) [greater than] 0, and G [equivalent to] [1/{1 - [[Lambda].sub.L1] (1 + [Epsilon])}] [less than] 0. Thus, the sign of [Mathematical Expression Omitted] becomes indeterminate as anticipated by GM.

As in Batra and Naqvi (1987), in PB as well, when labor mobility is perfect, a reduction of tariff will increase the social welfare of a Harris-Todaro economy. This can be verified from PB's equation 41. As [Epsilon] [approaches] [infinity], the third term within the bracket in the right-hand side of equation 41 disappears, and (dU/dt) [less than] 0. In a Harris-Todaro economy, rural-to-urban migration of labor causes a distortion in the output structure. Because of the migration, agricultural output is less than what would have been otherwise. Specifically, at the equilibrium production point, the social marginal cost of producing the industrial good becomes higher than its private marginal cost (for details, see Parai and Batra 1987, p. 316). Naturally, any policy that increases the output of agricultural sector would reduce the adverse effect of the production distortion and thereby increase welfare. A reduction of tariff on manufactured goods produced in the urban sector would be such a policy, and that is precisely the rationale behind the conventional argument against protection in the Harris-Todaro economy. In the literature, this point has been emphasized over and over again (see, e.g., Corden and Findlay 1975; Parai and Batra 1987; Batra and Naqvi 1987). Now why does this conventional result appear to be a paradox?

In the factor market distortions literature, the output structure is biased against the sector that pays the exogenously given higher wages to labor it employs (see, e.g., Batra 1973, chap. 10). Even in models where the wage differential is endogenous because of, say, imperfect mobility of labor, the same type of production bias is observed against the output of the sector that pays the wage differential (see, e.g., Casas 1984; Yu and Parai 1989). Consequently, any policy that increases the output of this sector will reduce the distortionary output effect and move the output structure closer to what would have been under nondistortionary situation. A tariff protection of, or a production subsidy to, the sector paying the wage differential thus becomes the second-best optimal policy. In the Harris-Todaro economy, there is an exogenous wage differential paid by the urban manufacturing sector. Then, following the policy recommendations of the factor market distortions literature, the manufacturing sector should be protected by a second-best tariff or production subsidy.

Thus, in the standard Harris-Todaro model, two apparently different distortions call for diametrically opposite policy recommendations. The antiprotectionist trade policy for a standard Harris-Todaro economy apparently signifies the dominance of the migration-related distortion over the wage differential-based distortion, and that shows the importance of the unique migration phenomenon, which happens to be the novelty of the Harris-Todaro model.

In PB's model, we distort the conventional Harris-Todaro economy even further by introducing imperfect labor mobility. The wage rate in the manufacturing sector is institutionally set at a higher rate than its counterpart in the rural sector. But workers in the agricultural sector do have a preference of living in rural areas over migrating to urban centers of glitter and glee. As a result, migration of labor toward the higher-wage sectors is limited. Because of the limited migration, the output of manufacturing (agricultural) sector would not increase (decrease) by as much as it would under perfect labor mobility. Thus, imperfect labor mobility dampens the strength of the migration-related distortion in Harris-Todaro and causes some indeterminate results.

GM raise questions about our use of the Casas (1984) specification in the context of Harris-Todaro unemployment. Specifically, in the presence of unemployment as labor mobility becomes perfect, the Casas specification yields

[Mathematical Expression Omitted].

This implies that with b [less than] 1, industrial employment ([L.sub.2]) becomes a constant fraction of the urban labor force ([L.sub.2] + [L.sub.u]) at the equilibrium when migration stops. This is no less "reasonable" an implication than a positive constant differential ([Rho]) between the expected urban and rural wage rates at the equilibrium in GM's alternative specification (eq. 5 in GM) of the Harris-Todaro model.

References

Batra, R. N. 1973. Studies in pure theory of international trade. New York: St. Martin's Press.

Batra, R. N., and N. Naqvi. 1987. Urban unemployment and gains from trade. Economica 54:381-95.

Casas, F. R. 1984. Imperfect factor mobility: A generalization and synthesis of two-sector models of international trade. Canadian Journal of Economics 17:747-61.

Corden, W. M., and R. Findlay. 1975. Urban unemployment, intersectoral capital mobility and development policy. Economica 42:59-78.

Gilbert, J., and M. Mikic. 1997. Imperfect labor mobility and unemployment in LDCs: Comment. Mimeograph.

Harris, J. R., and M.P. Todaro. 1970. Migration, unemployment and development: a two-sector analysis. American Economic Review 60:126-42.

Parai, A. K., and R. N. Batra. 1987. Customs union and unemployment in LDC's. Journal of Development Economies 26:311-9.

Parai, A. K., and H. Beladi. 1997. Imperfect labor mobility and unemployment in LDC's. Southern Economic Journal 64:180-90.

Yu, E. S. H., and A. K. Parai. 1989. Factor immobility and gains from trade. Southern Economic Journal 55:601-9.