Abstract
Recent empirical studies, e.g. by Amiti and Davis (2012) and Goldberg and Pavcnik (2007), confirm that trade liberalization is attended by rising income inequality. Scheve and Slaughter (2007) as well as the OECD (2008) argue that these distributional issues are critical because they raise resistance to free trade and so policy makers might be forced to increase the degree of protectionism.
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- 1.
In general, our paper can also be classified among the large body of literature concerning the redistribution of trade gains in the absence of firm heterogeneity (see, for instance, Brecher and Choudhri, 1994; Davidson and Matusz, 2006) To the best of our knowledge, however, none of these studies incorporates income inequality into the welfare function and they are thus unable to derive an optimal RS in our sense.
- 2.
Notably, our interpretation of the parameter ϕ is slightly different to that of Melitz (2003). We prefer the term entrepreneurial (instead of firm) productivity, in order to distinguish between the quality of the management and originality of the business idea, on the one hand, and a firm’s total productivity, which also depends on the quality of its employed workers, on the other.
- 3.
Helpman et al. (2010a,b) introduced this concept in order to allow for worker heterogeneity. However, in their model, abilities are match-specific and independently distributed. Hence, a worker’s ability for a given match does not convey any information about his or her ability for other (future) matches. The ability of an individual worker is unobservable, even if the worker has an “employment history”.
- 4.
Note that this approach is a short-cut for different profit tax rates for firms with different productivities. To keep our analysis as simple as possible, we set the profit tax rate for non-exporting firms at zero while assuming a positive value for exporting firms.
- 5.
The minimum quality requirement assumption can be motivated from both an empirical and a theoretical point of view. For a detailed discussion, see de Pinto and Michaelis (2011).
- 6.
In our model, this outcome is, however, not trivial. A wage hike swells the firm-specific interval of abilities, \({\overline{a}}_{i}\) and thus the marginal revenue rise. Consequently, there are two effects operating in opposite directions in response to a wage increase: marginal costs and marginal revenues both shift up. The strength of the latter effect can be measured by the wage elasticity of average abilities \({\epsilon }_{{\overline{a}}_{i},{w}_{i}}\). As shown in detail by de Pinto and Michaelis (2011), \({\epsilon }_{{\overline{a}}_{i},{w}_{i}}\) is equal across all firms and (for reasonable parameter settings) smaller than one. Then, the derivation of (4.6) with respect to w i proves that \(\partial {h}_{i}/\partial {w}_{i} < 0\) holds for \({\epsilon }_{{\overline{a}}_{i},{w}_{i}} < 1\). Increasing marginal revenue does not compensate for rising marginal costs, but it mitigates the employment reduction.
- 7.
Recall that the labor demand curve becomes steeper if the wage rate increases because of rising average abilities. Consequently, the monopoly union also anticipates the positive effect of a higher wage rate, but, as shown above, employment nevertheless decreases.
- 8.
One might argue that high-skilled workers with a reservation wage above the wage paid by the representative firm are not affected by \(w(\widetilde{{\phi }}_{t})\). Consequently, \(w(\widetilde{{\phi }}_{t})\) should not be part of their outside option. However, in a Melitz world with Pareto-distributed productivities, the aggregate variables have the property that they are identical to what they would be if the economy were endowed with M t identical firms with productivity \(\widetilde{{\phi }}_{t}\). Therefore, \(w(\widetilde{{\phi }}_{t})\) is only a shortcut for the “true” distribution of wages in the economy. A shift in \(w(\widetilde{{\phi }}_{t})\) should thus be interpreted as a proxy for a shift in the whole wage distribution, thus affecting all wages irrespective of skill level.
- 9.
Note that the wage w i is increasing in the entrepreneurial productivity ϕ i . High-productivity firms have to pay higher wages than low-productivity firms, since the ability and thus the fallback income of the median member of the corresponding trade union is higher. The empirical literature supports this result (see, for instance, Munch and Skaksen, 2008).
- 10.
Clearly, the inclusion of \({t}_{\pi }{\pi }_{i}\) into the export profit function is unconventional. We can justify this approach with an economic and a formal argument. First, \({t}_{\pi }{\pi }_{i}\) are costs connected to the export decision. If firms export, market shares increase: there are some gains of trade. In this case only, the government redistributes a fraction of the trade gains by imposing the profit tax. Thus, it is plausible to assume that the costs of the profit tax are paid from the additional export profits. By analogy, firms also bear the payment of the (variable and fixed) trade costs from π ix . Second, we avoid a discontinuity in the export profit function. If \({t}_{\pi }{\pi }_{i}\) disappears, firms with a positive export profit up to a certain threshold have no incentive to export because of the profit tax on domestic profits. Note again that the profit tax base is the exporter’s total profit. Consequently, not only \({t}_{\pi }{\pi }_{i}\) but also \({t}_{\pi }{\pi }_{ix}\) has to be considered for the definition of net export profit.
- 11.
“Active” means that these workers have a positive employment probability. Nevertheless, at any point in time a fraction of active workers is unemployed.
- 12.
Notably, entrepreneurial productivity and workers’ abilities are both Pareto-distributed with identical lower bounds and shape parameter k. These characteristics, combined with the assumption of random matching, imply that the ratio of employed workers with ability j, H j , to the number of all workers with ability j, L j , is equal for all j. As a result, the unemployment rate is identical across all abilities:\(u = {u}_{j} = 1 -\frac{{H}_{j}} {{L}_{j}} \,\forall j\).
- 13.
Notably, (4.26) implies \({\phi }^{{_\ast}} < {\phi }_{x}^{{_\ast}}\). Thus, the marginal firm only produces for the domestic market, concluding \({\pi }^{net}({\phi }^{{_\ast}}) = \pi ({\phi }^{{_\ast}}) = \frac{1} {\sigma }r({\phi }^{{_\ast}}) - f\).
- 14.
Note that if all firms pay the profit tax, the export decision is independent of t π and we obtain \(r\left ({\phi }_{x}^{{_\ast}}\right ) = \sigma f{\tau }^{\sigma -1}\).
- 15.
The stability of the general equilibrium turns out to be critical in one way. Theoretically, the marginal firm has an incentive to deviate from the (monopoly union) wage setting in order to increase its profit. As explored in detail by de Pinto and Michaelis (2011), however, we can avoid this behavior by assuming a further labor market friction, i.e. efficiency wages. Clearly, extending the model in that way has a value added. But, balancing this value added with the loss of analytical tractability, we decided to postpone this issue to further research and to refrain from giving marginal firms additional latitude.
- 16.
Note that we abstain from mixing the three sources of income in order to consider the diverging effects of the differential taxes separately.
- 17.
For a general equilibrium model with ex post revenue-neutrality, i.e. one in which the budget is neutral after the consideration of all possible adjustments in the economy, see Michaelis and Pflüger (2000).
- 18.
For instance, Jin et al. (2011) show in an empirical analysis for China that decreasing income inequality positively affects the marginal propensity to consume and thus c.p. overall consumption.
- 19.
The welfare function is rather unconventional. For a detailed motivation for it and a discussion of its properties see Lommerud et al. (2004).
- 20.
For a similar problem, see Egger and Kreickemeier (2009a).
- 21.
One important remark: Given the standard parameter setting, trade liberalization, e.g. a reduction of variable trade costs from τ0 = 1. 6 to τ0 = 1. 3, unambiguously increases aggregate income in our model (see de Pinto, 2012 for evidence) because of the well-known FS effect. Furthermore, it increases income inequality because of both the increasing number of exporters who pay higher wages to a higher share of workers and the increasing unemployment rate. Both increasing aggregate income and a more unequal distribution of income motivate the government’s redistribution aims.
- 22.
Notably, this finding strongly depends on the assumption of using the net outside wage in the computation of UB (see (4.12)). If instead \({B}_{j} = s{\overline{w}}_{j}\) is applied, the decline in fallback income becomes smaller and thus it does not compensate the increasing wage claim – w would be a positive function of t w . However, simulations show that a variation in the wage tax rate has an extremely low influence on w. Thus, we ignore this effect in the following. The corresponding simulation results are available upon request.
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de Pinto, M. (2013). An Optimal Redistribution Scheme for Trade Gains. In: International Trade and Unemployment. Contributions to Economics. Physica, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33236-4_4
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