Abstract
This fourth chapter “Labor Market Effects in (Neo)classical Models of Offshoring” evaluates the labor market and national welfare effects in existing classical and neoclassical theories. Section 4.1 studies offshoring of final goods in the Ricardian, Heckscher–Ohlin, and specific-factors model. We first study the welfare gains from trade in Samuelson's (2004) Ricardian model. The model also shows how technological progress in the foreign non-comparative advantage sector erodes all or at least some of the domestic country's previous gains from trade. Second, we evaluate the gains from trade in the basic Heckscher–Ohlin model, before presenting four theorems. Third, we analyze the effects of offshoring in the specific-factors model of Bhagwati et al. (2004). Generally, offshoring leads to social gains, but there are also scenarios where offshoring can generate welfare losses. Section 4.2 focuses on offshoring of intermediate goods. We use the Grossman and Rossi-Hansberg (2006a, b) general equilibrium model, which includes a set of intermediate tasks, to evaluate the wage effects of offshoring. Different scenarios are studied, namely the effects of offshoring low-skill-intensive tasks in a small and a large economy, the labor-supply effect and offshoring of skill-intensive tasks.
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Notes
- 1.
For a discussion of unemployment versus relative wages as labor market adjustments to globalization, see, e.g., Eckel (2003).
- 2.
Parts of this paragraph have been taken from Milberg and Schöller (2008).
- 3.
The real per capita income can also be obtained by calculating the geometric mean of \({\pi _A }\) and \({\pi _B }\), which is \({0.5\sqrt {2 \times 1/2} = 0.5}\). Since in equilibrium labor productivities correspond to real wages, 0.5 represents the real per capita income. The same holds for the foreign economy.
- 4.
Since in world equilibrium with total specialization \({w_A /P_A = \pi _A }\) and \({w_B^* /P_B^* = \pi _B^* }\), the ratio of domestic to foreign real wages yields: \({(w_A /P_A )/(w_B^* /P_B^* ) = \pi _A /\pi _B^* = (Y_A /\bar L)/(Y_B^* /\bar L^{{\rm{ }}*} )}\), which can be written as \({P_B^* /P_A = (Y_A /Y_B^* )(\bar L^{{\rm{ }}*} w_B^* /\bar Lw_A )}\). Under the assumption of zero profits, the countries' wage-bills equal their incomes, respectively, with \({\bar Lw_A = P_A Y_A }\) and \({\bar L^{{\rm{ }}*} w_B^* = P_B^* Y_B^* }\). Mill's assumption of equal income shares between both goods in a country has the following results. As the home country does not produce \({Y_B }\), it imports \({Y_B^* }\) from abroad and spends half of its income. Analogously, the foreign country spends half of its income on imported \({Y_A }\). Note that the import value must equal the export value of the foreign trading partner. Since the latter constitutes half of the trading partner's own income, the countries' total incomes must be equal. Thus, \({\bar L^{{\rm{ }}*} w_B^* = \bar Lw_A }\) and \({P_B^* /P_A = Y_A /Y_B^* }\) which corresponds to \({P_B^W /P_A^W = Y_A^W /Y_B^W }\).
- 5.
The unit cost minimization problem is specified by \({\min rK_i + wL_i }\) s.t. \({Y_i = Y(K_i ,L_i ) = 1}\), where \({Y_i }\) denotes the production function. This minimization problem can be solved using the Lagrange multiplier \({\lambda }\) and defining the Lagrangian \({\Gamma _i = rK_i + wL_i + \lambda ((K_i ,L_i ) - 1)}\). The two first order conditions (FOCs) \({\partial \Gamma _i /\partial K_i = \partial \Gamma _i /\partial L_i = 0}\) are given by: \({\partial \Gamma _i /\partial K_i = r + \lambda \partial F(K_i ,L_i )/\partial K_i = 0}\) and \({\partial \Gamma _i /\partial L_i = w + \lambda \partial (K_i ,L_i )/\partial L_i = 0}\). Thus, the optimal capital-to-labor ratio \({K_i /L_i }\) can be expressed as a positive function of the wage-rental ratio \({w/r}\).
- 6.
- 7.
Alternatively, this effect could have been modeled by shifting the \({{\rm{MPL}}_{HSA} \cdot P_A }\) curve to the left by the same amount.
- 8.
- 9.
- 10.
- 11.
The final version of this model was published in Grossman and Rossi-Hansberg (2008).
- 12.
The authors assume that there is no substitution between LS-tasks or between HS-tasks, so these tasks must be conducted the same number of times.
- 13.
Here, the authors assume implicitly that each LS-task (HS-task) is conducted the same number of times. The generality of increasing \({\tau (\iota )}\) is not lost, since each task which is repeated multiple times can be divided into multiple tasks, each of them having different indices. As long as the resulting tasks are characterized by slightly different trade costs, the model has no loss in generality.
- 14.
The factor intensities may be fixed due to technical restrictions or simply reflect the firms' optimal choices regarding current factor prices and substitution possibilities. As verbally explained above, sector Y A is relatively skill-intensive compared to sector \({Y_B }\), and thus \({a_{HSA} /a_{LSA} > a_{HSB} /a_{LSB} }\).
- 15.
The excess foreign labor requirement for the marginal task \({\tau ({\rm I})}\) is larger than the average excess foreign labor requirement \({T(I)/I}\), because the tasks with the least costs are relocated first (the marginal task has the highest costs among the offshorable tasks). This yields \({T(I)/I < \tau (I)}\) or \({T(I)/\tau (I) < I.}\)
- 16.
The productivity effect can also be derived as follows. Under the assumption that both goods \({Y_A }\) and \({Y_B }\) are produced in equilibrium, the zero-profit conditions imply:
$${1 = \Pi w_{LS} a_{LSA} (\Pi w_{LS} /w_{HS} ) + w_{HS} a_{HSA} (\Pi w_{LS} /w_{HS} )\ \rm and}$$(4.1)$${c = \Pi w_{LS} a_{LSB} (\Pi w_{LS} /w_{HS} ) + w_{HS} a_{HSB} (\Pi w_{LS} /w_{HS} ).}$$(4.2)It is evident that production technologies depend on the relative average factor costs \({\Pi w_{LS} /w_{HS} }\) when the profit-maximizing choice of offshoring is applied. Since the factor intensities \({a_{LSA} }\), \({a_{HSA} }\), \({a_{LSB} }\) and \({a_{HSB} }\) are all different, (4.1)' and (4.2)' determine \({\Pi w_{LS} }\) and \({w_{HS} }\) independently of \({\varphi }\). Consequently, as \({\varphi }\) falls, \({\hat w_{LS} = - \hat \Pi }\) and \({\hat w_{HS} = 0.}\)
- 17.
\({T{^*} > 1}\) designates the Hicks-neutral productivity inferiority of foreign firms in both sectors. In other words, if a foreign sector produces all tasks at the same factor intensities as the domestic sector, the output would only be \({1/T{^*} }\) as great. The zero-profit conditions for the foreign sectors imply:
$$1 = T{^*} w_{LS}{^*} a_{LSA} (w_{LS}{^*} /w_{HS}{^*} ) + T{^*} w_{HS} a_{HSA} (w_{LS}{^*} /w_{HS}{^*} ) {\rm and}$$(4.1)$$c = T{^*} w_{LS}{^*} a_{LSB} (w_{LS}{^*} /w_{HS}{^*} ) + T{^*} w_{HS} a_{HSB} (w_{LS}{^*} /w_{HS}{^*} ).$$(4.2)If one compares (4.1)'and (4.2)' with (4.1)” and (4.2)”, incomplete specialization in both countries implies “adjusted factor price equalization”, i.e. \({w_{LS} \Pi = w_{LS}{^*} T{^*} }\) and \({w_{HS} = w_{HS}{^*} T{^*} }\). The production techniques in the home country are based on the relative average factor costs \({w_{LS} \Pi /w_{HS} }\), whereas in the foreign economy they are based on factor prices \({w_{LS}{^*} /w_{HS}{^*} }\).
- 18.
Grossman and Rossi-Hansberg (2006b) derive this effect in detail (pp. 22–23).
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Winkler, D. (2009). Labor Market Effects in (Neo)Classical Models of Offshoring. In: Services Offshoring and its Impact on the Labor Market. Contributions to Economics. Physica-Verlag HD. https://doi.org/10.1007/978-3-7908-2199-4_4
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