Per capita income, human capital, and inequality convergence: A latent-variable approach

Journal of Agricultural and Applied Economics, 2003 by Deepak, Sri Devi, Seale, James L Jr, Moss, Charles B

The data on four indicators of human capital-per capita public expenditure on education as a percentage of per capita income (PE), per capita consumption of newsprint (CN), and the percentage of the population completing secondary school (ES) and university levels (ET)-are compiled from the two UNESCO series and span 36 years, 1955 to 1990. Though there are 24 countries in the OECD group, the data for Iceland and Luxembourg are insufficient for them to be included in the study. In total, the data set used in estimation of the latent-variable model has 36 observations for each of the 22 OECD countries (792 total observations) for each of the eight variables: Y, O, G, I, PE, CN, ES, and ET. The model estimates human capital (H) as a latent variable.

The Latent-Variable Model

The basic premises of the empirical model are derived from the national-income identity for an open economy and from recent developments in endogenous-growth models. The national-income identity states that national income is a function of consumption, investment expenditures, government expenditures, and the volume of exports and imports. International trade is one of the key determinants of economic interaction among countries, and countries gain from trading goods and services by taking advantage of the differences in their factor endowments and by achieving economies of scale in production. These gains are reflected in the growth of national income. Further, growth theorists (e.g., Barro; Lucas 1988, 1993; Mankiw, Romer, and Weil; Romer 1989, 1994; Tallman) have shown that accumulation of human capital is beneficial to the economy in terms of income growth.

Based on the above, real income is specified as a function of human capital, international openness, government expenditure, and investment expenditure. Human capital is an unobservable or latent variable, which makes it appropriate to estimate the model as a latent-variable model (Bollen). Although an unobservable variable, human capital has observable indicators from which one can construct an index of human capital. We postulate that the human-capital index can be measured from the common movements of per capita public expenditure on education as a percentage of per capita income (PE), per capita consumption of newsprint (CN), and the percentage of the population completing secondary school (ES) and university levels (ET).

The latent-variable framework as described by Bollen is written as

where [eta] is the latent variable measuring income (and in our case represents real per capita income [Y]), [Gamma] is a vector of estimated coefficients, [[gamma]^sub 1^, [gamma]^sub 2^, [gamma]^sub 3^, [gamma]^sub 4^], [xi] is a vector of exogenous variables (which may or may not be latent), and [zeta] is the error term. In the current formulation,

Openness, government expenditures, and investment expenditures are observable exogenous variables while human capital is a latent variable. The indicators or the elements of the [xi] vector are then quantified in the indicator equation,