Skill Formation, Public Expenditure on Education and Wage Inequality: Theory and Evidence

Different facets of skill formation have been discussed in works like Autor (2014), Becker (1964), Brown et al. (2001), Crouch et al. (1999), Heckman and Krueger (2003), and Vanhuysse (2007).

There is no doubt that the study of the relationship between public spending on education and economic growth is equally important. However, we feel that the aspect of economic growth is a different issue which should be examined separately in a different work.

In this analysis the pattern of trade does not matter at all since commodity prices are taken to be internationally given and there are no commodity market distortions. So, no harm is done if one alternatively considers sector 1 (sector 2) to be the import-competing (exports) sector.

The issues like skill formation and skilled-unskilled wage inequality are extremely important not only in the context of the developing countries but also in the background of the developed economies (both small and large). Data from the World Bank indicate that developed countries spend high percentages of their GDP on education. For example, in 2011, the average percentages of GDP spent on education for high income, low income and OECD countries were 5,1, 3.9 and 5.2, respectively. The corresponding figure for the South Asian countries including India was 3.0%. (see http://​data.​worldbank.​org/​indicator/​SE.​XPD.​TOTL.​GD.​ZS). On the other hand, the problem of deteriorating skilled-unskilled wage inequality in the developed countries in the post-reform period has been indeed as per predictions of the standard Heckscher–Ohlin–Samuelson (HOS) model with Stolper-Samuelson theorem at its core. This has been confirmed by different empirical studies. For example, Chusseau and Dumont (2012) have found that the wage inequality has increased sharply in countries like US, UK and Germany although nations like Denmark, Finland, Norway, Sweden, and Netherlands have experienced a moderate increase in wage inequality. From these, we can conclude that issues like skill formation and wage inequality are not peculiar only to developing countries.

This structure is more applicable to a small developed country rather than to a developing country because factor market imperfections, presence of non-traded goods etc. are the salient features of the developing countries. See Chaudhuri and Mukhopadhyay (2014) for details.

One can introduce direct costs of acquiring skills which would not affect the basic results of the paper. See the concluding section of Chaudhuri (2014) in this context.

See Appendix 1 for its derivations.

This result also holds in period 2. See proposition 4.

Interested readers can easily check these results or can obtain the proofs from the authors on request.

This result also holds in period 2. See proposition 4 in this context.

See the verbal explanations provided for propositions 1 and 2.

The net demand for capital falls in period 2 in the case where \(\theta _{L1} \theta _{K2} <\theta _{K1} \theta _{S2}\) if the ratio \((\frac{W_S }{W}>1)\) is very low and close to unity. But, in the opposite case we always have \((\frac{a_{K2} }{a_{S2} })>(\frac{a_{K1} }{a_{L1} })\) since \(W_S >W\). So, the demand for capital cannot fall in this situation.

In ILOSTAT database this variable is defined as “This measure of earnings dispersion refers to the ratio of average earnings of employees in the ninth decile to those of employees in the first decile of the earnings”.

See footnote 5 in this context.

The conditions subject to which the wage inequality improves/deteriorates due to the education subsidy policy involve the distributive shares of different inputs of production in the low-skill and high-skill sectors of the model. It would be nice if one can find out any technique of empirically measuring the said shares of the stylised model that has been considered in this paper. This has, therefore, been left to future empirical research in this area.

In the WDI the ‘TOT index’ is defined as “Net barter terms of trade index is calculated as the percentage ratio of the exports unit value indexes to the imports unit value indexes, measured relative to the base year 2000. Unit value indexes are based on data reported by countries that demonstrate consistency under UNCTAD quality controls, supplemented by UNCTAD’s estimates using the previous year’s trade values at the Standard International Trade Classification three-digit level as weights. To improve data coverage, especially for the latest periods, UNCTAD constructs a set of average prices indexes at the three-digit product classification of the Standard International Trade Classification revision 3 using UNCTAD’s Commodity Price Statistics, interna-tional and national sources, and UNCTAD secretariat estimates and calculates unit value indexes at the country level using the current year’s trade values as weights.”

‘Openness’ in the WDI is mentioned as “The sum of exports and imports of goods and services measured as a share of gross domestic product.”

Following our theoretical consideration we also considered ‘gross capital formation (annual % growth)’ as another control variable. However, we noticed almost insignificant impact of this variable on wage inequality. Hence we have not included that variable in the empirical analysis.

The example of ‘India’ as a small open developing economy has often been cited in the trade and development literature. See Chaudhuri and Mukhopadhyay (2009, 2014) in this context.