Fairness, Search Frictions, and Offshoring

Devashish Mitra; Priya Ranjan

doi:10.1515/bejeap-2012-0056

Article

Fairness, Search Frictions, and Offshoring

Devashish Mitra and Priya Ranjan

Published/Copyright: April 30, 2013

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From the journal The B.E. Journal of Economic Analysis & Policy Volume 13 Issue 1

Abstract: Fairness considerations are introduced into the determination of wages in a two factor Pissarides-style model of search unemployment to study its implications for the unemployment rates of unskilled and skilled workers in both the closed economy case and when the economy can offshore some inputs. Both fairness concerns and offshoring of jobs done by unskilled workers create the overhiring effect for skilled workers. An increase in the concern for fairness in the closed economy increases the cost of hiring unskilled workers and increases the unemployment rates of both types of workers; however, wage inequality decreases. In the open economy case, an increase in the concern for fairness leads to greater offshoring which prevents skilled unemployment from increasing, but the unemployment of unskilled workers increases. A reduction in the cost of offshoring also increases offshoring and increases the unemployment of unskilled workers, but has a positive effect on skilled workers. Due to the presence of an overhiring effect in the hiring of skilled workers for both offshoring and non-offshoring firms, skilled workers experience higher wages and lower unemployment. The opposite movements in skilled and unskilled unemployment render the net effect ambiguous. Even though wage inequality increases, the impact on the wages of unskilled workers is ambiguous.

Keywords: fair wages; unemployment; overhiring effect; offshoring

JEL Classification Codes: F16; F40; E24; J64

7 Appendix

7.1 Proof of Lemma 1

For eq. [10] can be written as

Note that the second equality above follows from the fact that where therefore, where

Following the same steps, eq. [11] can be written as

Again, the second equality follows from the fact that and hence,

7.2 Solution of the differential equation [26]

Re-write the differential equation [26] as

[45]

Next, note that the solution to the above differential equation is given by (see Chiang (1984, 488))

[46]

where A is a constant of to be determined.

For the integral above to converge, a sufficient condition is is continuous at zero. Finally, the assumption that pins down See Cahuc, Marque, and Wasmer (2008) for details.

7.3 Proof of Lemma 3

Proof of 3a: Differentiate both sides of [27] to obtain

[47]

Using integration by parts and after canceling terms out, obtain

[48]

Proof of 3b: Using [26] write Therefore,

Proof of 3c: First note that

[49]

Next, from [26] obtain

[50]

Use [50] in [49] to obtain

[51]

Proof of 3d: Immediately follows from [21] and [26].

7.4 Proof of lemma 7

Note from lemma 6b that therefore, [30] and [42] imply, obtain

[52]

Next, recall that and use from lemma 6a to write the above as

[53]

Totally differentiating above, with respect to , obtain (noting that

[54]

Next, using the definition of obtain

[55]

Upon using [54] in [55] verify that

Next, note that implies Therefore,

[56]

Since and remain unchanged in response to a change in we get

[57]

7.5 Proof of lemma 8

Recall from lemma 3c that the l.h.s of [30] is increasing in Therefore, a decrease in implies a decrease in Recall from lemma 6b that , therefore, . Since it implies This in turn implies from lemma 6a that Next, from [52] obtain

[58]

Totally differentiating [56] with respect to obtain

[59]

Finally,

[60]

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1
See Davidson and Matusz (2004) for an in-depth treatment (including their own pioneering work). Recent work on search unemployment in an open-economy also incoporates firm heterogeneity under monopolistic competition. See for instance important work by Davidson, Martin, and Matusz (1999), Helpman and Itskhoki (2010), Felbermayr, Larch and Lechthaler (2008) and Felbermayr, Prat, and Schmerer, (2011). An important paper, that further brings in worker heterogeneity into such a problem is Helpman, Itskhoki, and Redding (2010).
2
See for instance Akerlof and Yellen (1990), Bewley (2005) and Howitt (2005) for a survey of the evidence.
3
See the insightful paper of Cahuc, Marque and Wasmer (2008) which studies the overhiring effects in a very general model with multiple factors of production.
4
Alesina and Angeletos (2005) point to the fact that while the pre-tax inequality is much higher in the US than in Europe (Gini coefficient of 38.5 as opposed to 29.1), the redistributive policies are much more extensive, and the tax structure much more progressive in the latter. They argue that “the difference in political support for redistribution appears, rather, to reflect a difference in social perceptions regarding the fairness of market outcomes and the underlying sources of income inequality.”
5
A recent paper that looks at fairness considerations in wages (in both closed and open economy settings), but not within a search framework, is Grossman and Helpman (2008). In that paper, the utility derived by a worker is increasing in her own wage, but decreasing in the average wage of the firm. Because of this approach to modeling fair wages, there is no unemployment of any kind.
6
See also Egger and Kreickemeier (2009), where fairness is defined differently in terms of the relationship between wages and profits.
7
In a recent technical note, Helpman and Itskhoki (2009) develop a dynamic model along similar lines to show that its steady state looks similar to their static model. We have also worked through a dynamic version of our model and are able to confirm that the steady state results from such a model are no different from the results we obtain from the static model presented in this paper. The detailed analytics of the dynamic version are available from the authors upon request.
8
Pissarides (2000) describes the empirical support for a CRS matching function.
9
This can be done by imposing reasonable restrictions on the parameters of production and matching functions, and on the relative factor endowments of skilled and unskilled labor.
10
A special case of this, where the worker and employer have equal bargaining weights, exactly boils down to the Shapley value solution to a cooperative, multilateral bargaining problem.
11
The solution to this system of partial differential equations is very difficult to obtain, but thankfully is provided in Cahuc, Marque, and Wasmer (2008) in appendix B.4. The solution is given in eq. B.16 for the general case of N factors. Note that our wage equations in [8] and [9] are homogeneous differential equations (they do not have the constant term that the wage equation [8] in Cahuc, Marque, and Wasmer (2008) has). Therefore, the solution relevant for us is the second term on the r.h.s. of eq. B.16 which exactly corresponds to [10] and [11] above for the case of N = 2.
12
The proof is as follows. In Kreickemeier and Nelson, in a non-binding situation for unskilled workers, if there is one, the unskilled unemployment rate will be zero and in that situation the unskilled fair wage is , which will always be greater than , since skilled wage is always greater than the unskilled wage. Thus, there is a contradiction, and the unskilled fair wage will always bind.
13
If the fair wage was determined at the firm level, a case shown in an optional appendix (available from the authors upon request), then the overhiring effect would be even stronger. This happens because now when hiring an extra-skilled worker lowers the skilled wage, it also lowers the fair wage that firms have to pay to unskilled workers.
14
This assumption is reasonable if we believe that the South has large quantities of unskilled labor and that fixed labor productivity in a large subsistence, numeraire sector there fixes their unskilled wage.
15
The interesting and realistic case is that of a mixed equilibrium in which both offshoring and fully domestic firms exist side by side. The case where all firms in the economy offshore is not interesting, since in that case there will be an unskilled unemployment rate of 100%, a highly unrealistic situation. As long as is not extremely high and is not too low, we will have a mixed equilibrium since the recruitment cost per worker goes to zero as market tightness goes to zero (unemployment goes to 100%)

Published Online: 2013-04-30

Published in Print: 2013-07-01

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https://doi.org/10.1515/bejeap-2012-0056

Keywords for this article

fair wages; unemployment; overhiring effect; offshoring