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# Inter-sector wage inequality and elasticity of substitution between skill-intensive products

Name
Shapoval
Surname
Alexander
Scientific organization
New Economic School
Doctor of Physical and Mathematical Sciences
Position
Leading Research fellow (NES CSDSI)
Scientific discipline
Humanities & Social sciences
Topic
Inter-sector wage inequality and elasticity of substitution between skill-intensive products
Abstract
We study the response of the inter-sector wage inequality to shocks in demand. The analysis is based on a general equilibrium model with monopolistic competition in skill-intensive sectors and perfect competition in a traditional sector. Motivated by higher wages, workers aims to employ in skill-intensive sectors but face a risk to be unemployed because of labor market frictions: rejected job market candidates fail to find a job immediately.
Keywords
monopolistic competition; labor market frictions
Summary

This paper examines the response of economies and, in particular, inter-sector wage inequality to shocks in demand. The analysis is performed by using a general equilibrium model with monopolistic competition in hi-tech sectors and perfect competition in a traditional sector. Hi-tech sectors are horizontally differentiated with respect to labor skills required by production technologies and to efficiency of these technologies. Motivated by larger wages, workers intend to work in hi-tech sectors but face a risk to be unemployed. Unemployment appears as a consequence of job market frictions: rejected skilled workers fail to find a new job immediately. The wages of employed workers are agreed through a bargaining mechanism.

As a result of monopolistic competition, the sector size is affected not only explicitly by consumers' distribution of spending but also implicitly by the elasticity of demand in the sector. Redistribution of spending from traditional to hi-tech goods underlies the expansion of hi-tech sectors. This attracts new workers but because of sectors' limited capacity, a part of job market candidates is rejected, and the number of unemployment agents increases. Variability of the elasticity of substitution (VES) between hi-tech goods implies that a demand shift in favor of a single differentiated product affects the production of all sectors. This influence is based on changes in the relative diveristy of the differentiated products, which is the number of the product's representatives normalized by the sector size measured with consumers' spending. We posit that the economy can respond in two alternative ways: the relative diveristy of the differentiated products either enlarges or shrinks. In the first case, the demand for specific representatives of expanding varieties goes down. Having a limited monopoly power, firms higher price their goods compensating the shift in demand. Whole sectors incur a negative scale effect: the redistribution of the output to larger amount of firms with a fall of individual productions reduces the sector output. Sector , which produces the favored differentiated product, overcomes this effect and increases its output because of a direct influence of increasing spending for its goods. Following the output, the labor increases (decreases) in sector  (respectively, in the other sectors) but the number of employees in each firm decreases. Hiring less workers, firms value each of them more and agree to increase their wages through the bargaining mechanism. Eventually, the inter-sector wage differential enlarges. In the second case, when the relative diveristy shrinks, we end up with the reverse prediction: the inter-sector wage differential decays.

The two responses of an economy are distinguished with consumers' elasticity of substitution $$\sigma$$ between hi-tech goods. A decreasing $$\sigma$$ leads to an increasing relative diveristy of the differentiated product, and vice versa. Intuition underlying this result is rather simple. We argue that spending additional money for specific goods, consumers exhibit a more elastic demand. The latter follows a growth/decline in demand for specific goods if $$\sigma$$ is increasing/decreasing.

In our model, changes in the wage inequality are explored as a size effect, which is washed out under preferences with constant elasticity of substitution. On the other hand, the existence of an equilibrium is proved under preferences with relatively small VES. Nevertheless, the response of the wage inequality to a shift in tastes can be distinguishable. To our knowledge, this is the first attempt to estimate quantitatively the effect of VES in structural models with monopolistic competition. The scale of the response positively correlates with the efficiency of technologies in the corresponding industries, whose model proxy is the ratio of fixed to variable costs faced by firms.