The impact of risk and mobility in dualistic models: Migration under random shocks/El impacto del riesgo y la movilidad en los modelos dualisticos: migration bajo shocks aleatorios.
| Autor | Martins, Ana Paula |
| Cargo | Article |
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Introduction
The aim of this research is to contrast the expected long-run impact of exogenous uncertainty on labor force flows and expected wages under alternative scenarios of institutional wage setting and barriers to mobility. The study of the matter would be a-temporally relevant; to the extent that migration issues are being discussed among the EU member states, and given the recent enlargement to new economies with different market rules on the one hand, and security profiles on the other, the layout of theoretical foundations for the understanding of those effects would appear as a timely exercise.
The basic structures chosen to replicate the effects of uncertainty were simple dualistic models in the tradition of Harris-Todaro (1970) rural-urban migration analysis. A good survey of theoretical literature can be found in Bhattacharya (1993). The principles behind its workings became widespread in the study of labor market regional as also sector--occupation, profession--allocation and under minimum or other wage legislation or restrictions. Examples of these can be found in Mincer (1976), McDonald and Solow (1985), Fields (1989), Brown, Gilroy and Kohen (1982). A survey of segmented labor markets can be seen in McNabb and Ryan (1990); and the applications of the theory with microfoundations for several dualistic structures can be found in Saint-Paul (1996).
We follow the cases contrasted in Martins (1996), inspecting the consequences of introducing a local stochastic noise of various nature in each of the scenarios, these differing according to the degree of mobility across the two sectors--of whether there is immediate access to the other region jobs or not--, and to whether any or both regions or sectors are subject to an (also exogenous) institutional wage floor.
Total--national, worldwide according to context we may wish to simulate--labor force supply is assumed perfectly inelastic. Workers choose location, or sector affiliation, maximizing the expected wage--risk-neutrality allows us to concentrate on how technology characteristics rather than risk-aversion of the individuals (the role of individual's risk-aversion on migration decisions has been studied before and was surveyed by Stark (1991). It was our purpose to generate, thus, other type of conclusions) of the population affect the market equilibrium responses--.
Exogenous uncertainty itself may interplay with the underlying local technologies in different ways. Two environments were always simulated: when uncertainty works as an (null expected mean) added noise to local labor demand--quantity uncertainty; and added to the inverse labor demand--that is, to labor productivity. For simplicity, such noise was modeled as a binary random shock--conclusions shouldn't change qualitatively if we assumed a general distribution--and we inspected the effect of an increase in its variance maintaining the mean constant. (That is a general conclusion in the inspection of the effects of uncertainty on the risk-premium (Martins, 2004)).
As the prototype economy has two regions or sectors, perfectly (positively and negatively) correlated increases in local risks were also simulated. Changes in uncertainty can also mimic changes in the degree of heterogeneity of the labor force--or local productive ability to cope with them--.
Being mobility of major concern in the analysis, two extreme cases of "barriers to adjustment" were also thought to be important in the inquiry: either adjustment to uncertainty is assumed to be immediate to the random shock. Then, the long-run equilibrium differs according to which, and is formed after the, exogenous impulse is observed--ex-post flexibility--. Or binding location/sector affiliation decisions are taken before the actual risk realization--ex-ante location choices--. (See Aiginger (1987) and Martins (2004a) for a survey and appraisal of the effects of uncertainty on production outcomes under the two contexts). Obviously, the latter stages wage dispersion more appropriately if the local wage is left as market determined rather than institutionally fixed.
After notation is briefly settled in Section II, we depart from the benchmark case--free market with perfect mobility across regions or sectors--, outlined in Section III. In Section IV, partial coverage with perfect mobility--i.e., people not employed in the primary sector can immediately get a job in the secondary sector and wait there for an opportunity to switch, and thus, there is (again) no unemployment generation--is introduced. In Section V, a version of the Harris-Todaro model--with imperfect mobility and institutionally fixed wage in one of the sectors--is inspected. In Section VII, the Bhagwati-Hamada economy--with two covered regions or sectors--is forwarded. The exposition ends with a concluding appraisal in Section VII.
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Notation
There are two regions--or two sectors--and a fixed exogenous labor supply, L;-.This total labor supply decides whether to locate in region (or affiliate to sector) 1 or 2. Denote by L;-i local/industry supply in region/sector i. Then:
[L;.sub.1]- +[L;.sub.2]- = [L;- (1)
In region i, the baseline deterministic aggregate demand function is given by:
[L.sub.i] = [L.sup.i]([W.sub.i]), i = 1, 2 (2)
A non-positive slope - that is, [dL.sub.i]/[dW.sub.i] = [L.sup.i]([W.sub.i])' [less than or equal to] 0 - is always assumed. Denote the corresponding inverse demand function by:
[W.sub.i] = [W.sub.i]([L.sub.i]), i = 1,2 (3)
There are no cross effects, i.e., [dL.sup.i]/[dW.sub.j] = 0 for i [not equal to] j. The wage elasticityofdemand ofregion i at a particular point oflabor demand will be denoted by
[[EPSILON].SUP.I] = [L.sup.i]([W.sub.i])'[W.sub.i]/[L.sup.i]([W.sub.i]) = [W.sup.i]([L.sub.i])/[[W.sup.i]([L.sub.i])'[L.sub.i]]. (4)
Let [Z.sub.i] be a Bernoulli lottery of null expected value: with probability [q.sub.i]; it takes value [s.sub.i]; with probability (1 - [q.sub.i]), it takes the value
[mathematical expression not reproducible] (5)
Var([Z.sub.i]) increases with [S.sub.I] if [S.sub.I] is positive, decreases if it is negative --a change in risk is modeled as a change in [S.sub.I], increasing with it if [S.sub.i] > 0, decreasing if [S.sub.i]
Two general risky environments are simulated: additive absolute uncertainty [Z.sub.i] is either added to local labor demand--and denoted by [X.sub.i]--quantity uncertainty:
[L.sub.i] = [L.sup.i]([W.sub.i]) + [X.sub.i]; and [W.sub.i] = [W.sub.i]([L.sup.i] - [X.sub.i], i = 1,2 (6)
Or to labor productivity - [Y.sub.i]:
[L.sub.i] = [L.sup.i]([W.sub.i] - [Y.sub.i]); and [W.sub.i] = [W.sub.i]([L.sup.i]) + [Y.sub.i], i = 1, 2 (7)
Then, meaningful effects are found - and, hence, inspected - for environments of:
1) Ex-post flexibility: the individuals make location choices after the observation of [Z.sub.i]. We will denote the equilibrium wage generated or labor force located in region i by:
[mathematical expression not reproducible] (8)
2) Ex-ante location arrangements. The population fixes itself or affiliates to a sector. Once there, if in a uncovered sector, it suffers random wage fluctuations; if in a covered sector, it is subject to employment availability uncertainty.
The background technology and preferences in the economy are anything but complex: an homogeneous good is produced and consumed in both regions. Identical workers as "land-owners" consume directly what they produce or receive as income: there is no (reason to), nor (need for) money. We allow for regional (sectoral) imbalances in terms of intrinsic resources: location in region 2 systematically provides a income-valued differential a in favor of each of its residents (a is allowed to be negative, though).
We will assume further through Sections II to V a subset of the following:
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individuals are risk neutral and maximize expected income.
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a. only region i is affected by risk--and [Z.sub.j] = 0.
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b. both regions are affected by perfectly positively correlated uncertainty--and [Z.sub.j] = [Z.sub.i] = Z.
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c. both regions are affected by perfectly negatively correlated uncertainty - and [Z.sub.j] = - [Z.sub.i] = - Z.
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a. there is perfect mobility across regions, alternatively.
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b.job rotation is only accomplished locally or within the industry.
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a. wage in region 1 is determined by market conditions, alternatively.
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b. wage in region 1 is institutionally determined.
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a. wage in region 2 is market determined, alternatively.
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b. wage in region 2 is institutionally determined.
Given assumption 1 - always assumed -, and the fact that a differential favors (for a > 0) region 2, an equilibrium will be such that (1):
[mathematical expression not reproducible] (9)
where (*) denotes an ex-ante decision context. Worker flows will exist till equalization of expected wage net of the compensation amount in the two regions.
Assumptions 2 stage different types of local risks. 2.a is useful to analyze the impact of unilateral risk level--inducing conclusions expected to be generalizable to situations where both regions are subject to uncertainty and the change in risk occurs in only one of them. 2.b and 2.c allow for a relation between uncertainty movements in the two regions--under ex-ante location commitments, the sign of the pertaining correlation becomes in some sense redundant to the determination of labor force flows.
Assumptions 3 to 5 characterize the mobility environment. Different combinations of alternatives a and b generate backgrounds of benchmark dualistic models that we shall stage. For instance, 3.a. insures that expected unemployment in the economy will be zero--provided that the wage is market determined in at least one of the regions--.
The fixed institutional wage mimicks a minimum wage in the region.
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Competitive labor markets under perfect mobility
Assume 3.a, 4.a and 5.a of the previous section. Then, under certainty equilibrium, labor flows will be expected between the two regions while equalization of...
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