Abstract
This paper addresses the dynamics of income inequality, both within and across countries, using an endogenous growth model with North–South trade and endogenous educational choice. The dynamics of income inequality is found to depend on the ability of workers to adapt to new technologies, captured by the quality of education. For developing countries with low quality of education, I find Southern trade liberalization leads to: (1) an overall decline in effective human capital; (2) an inverted U-shape transition of income inequality, where within-country inequality increases in the initial periods following a reduction in trade barriers; and (3) divergence in terms of average income in the short and long run. However, in cases where the South has a high quality of education, workers are better equipped to adapt to new technologies, and trade liberalization induces an U-shape dynamic transition of within-country income inequality, where income inequality can decline in the transition. This paper highlights the critical role the quality of education plays in explaining the variations in the observed dynamics of income inequality in developing countries.
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Notes
Uses inequality data from the University of Texas Inequality Project (available at http://utip.gov.utexas.edu/data.html) and SEDLAC (CEDLAS and The World Bank).
Data on GDP per capita is taken from Penn World Tables [Heston et al. 2006].
However, this finding is challenged in Duryea and Szekely [2000] and Behrman et al. [2000] where they show inequality fell within Brazil, Mexico, Venezuela, Argentina, and Bolivia, and was constant in Chile and Costa Rica during the 1980s and 1990s.
β-divergence in Barro and Sala-i-Martin [1992] terms.
σ-divergence in Barro and Sala-i-Martin [1992]. See the “twin peaks” literature following Quah [1993].
Introducing imperfect substitution between skilled and unskilled workers is possible, but the qualitative results would carry through and the analysis would be less transparent.
Within industries, different quality grades are perfect substitutes, however, weighted by their respective grades.
If this inequality does not hold, successful innovators charge monopoly prices and successful imitators engage in limit pricing strategies.
Intermediate producers in the South only face competition from the North. Bertrand price competition drives prices down to marginal costs, thus fellow intermediate firms in the South have no incentive to devote resources to imitate a good that has already been imitated.
The marginal cost of intermediate producers is equal to the price of the final good in that region. In the North, the price of the final good and therefore the marginal cost for intermediate firms in the North is unity, while the price of the Southern final good and marginal costs for Southern intermediate producers adjust to balance trade,
For more details on learning-to-learn effects refer to Connolly [2003] and Connolly and Valderrama [2007].
We assume trade is balanced at all times by the endogenous adjustment of the relative price of the Southern final good,
A lump sum transfer of tariff revenues does not change the dynamics of income inequality.
Code is available upon request.
Trade liberalization of a lesser or greater magnitude induces the same qualitative results.
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Appendix
Appendix
Detailed equations
Northern and southern average profits
This Appendix provides more details for equations (15) and (16). Firms located in the North whose closest competitor is a Northern firm obtain a flow sum of domestic and export profits:
where Λ
N
=A
N
1/(1−α)(α/q)1/(1−α), and 
is the average quality level on the frontier. Northern firms facing Southern competition, likewise, earn a sum of import and export profits:
where the size of the incremental quality increase, q, must be sufficiently large such the limit price exceeds the marginal cost of production. Average profits for intermediate firms in the North is:
where 
is the profits adjusted for the average quality level on the frontier. Trade barriers and the probability of innovation are embedded within 
A change in the rate of innovation and imitation, alter the effective levels of human capital (H
N
and H
S
), the equilibrium relative price of the Southern final good 
and the distribution of firms (n
NN
, n
NS
, and n
S
).
The partial effects of trade liberalization on the Northern average profits is given by:
Southern flow profits for intermediate producers are:
where Λ
S
=A
S
1/(1−α)(α/q)1/(1−α), and, as in the North, 
is the quality adjusted profits for Southern imitators. I assume the Northern tariff is sufficiently low such that the export profits for Southern firms, given the limit price, is positive. Since only the state-of-the-art technology is used, any good produced in the South will still have the same quality level as the lead Northern quality frontier.
The partial effects of trade liberalization on the Northern average profits is given by:
Resources allocated to R&D
Using the two world resource constraints, the expressions for Z N and Z S from equations (26) and (27) are, in the North:
where
and in the South:
where
where χ
N
=C
N
/Q
N
and χ
S
=C
S
/Q
N
. 
and 
are the quality adjusted expenditures on R&D.
Balanced trade condition
The relative price of the Southern final good adjusts at each point of time to balance trade between the North and South. Expanding equation (30), 
implicitly solves:
where the partial effects of trade liberalization is given by:
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Hall, J. Educational Quality Matters for Development: A Model of Trade, Inequality, and Endogenous Growth. Eastern Econ J 43, 128–154 (2017). https://doi.org/10.1057/eej.2015.40
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DOI: https://doi.org/10.1057/eej.2015.40