A Model of Growth and Convergence in the Presence of Input-Enhancing Factors: An Empirical Study

Farhad Rassekh (*) I. INTRODUCTION The theoretical and empirical study of economic growth rests in part on the assumption of neutral technical change. This assumption maintains that the technical rate of substitution between inputs (say, capital and labor) is constant at each combination of labor and capital. In this article we ask: What if this substitution rate were variable at each factor input ratio? What would happen to the standard predictions of the neoclassical paradigm (e.g., convergence of output per worker across countries) in a growth model characterized with non-neutral technical progress? Would diminishing returns to capital still support the tendency toward convergence? Though we have no quarrel with growth models assuming neutral technical progress, we maintain that a model allowing for non-neutrality is worthy of exploration because it has the potential to offer new insights into the growth process. Moreover, recent empirical findings suggest that technical progress is not neutral but is biased in the labor-saving direction, as in Krugman (2000). To address the foregoing issues and questions, we introduce and estimate a model of non-neutral technical change for a cross-section of countries. The basic thrust of our model is that countries that have attained higher income per worker have benefited directly from factors enhancing the productivity of their labor and (particularly) capital. Thus to the extent that certain factors render a given amount of (for example) capital more potent in terms of its contribution to growth, investment becomes a necessary but not a sufficient condition for faster growth. This feature of our model allows for greater flexibility relative to growth models (e.g., neoclassical) in which, ceteris paribus, low-income countries are expected to grow faster. II. A MODEL OF GROWTH AND CONVERGENCE In what follows we employ a model of non-neutral technical change to explain differences in output per worker across a set of countries for the period 1960-1990. This procedure differs from previous attempts such as those in Mankiw et al. (1992), which invoke a production function exhibiting neutral technical change (typically labor augmenting under constant returns to scale). To this end, we assume that output is determined by a production function of the form (1) Q = [AL.sub.[alpha] ln H] [K.sub.[beta] ln J], (1) where: A, [alpha], and [beta] are positive constants; Q depicts a flow of output from flows of labor and capital inputs L and K, respectively; H serves to enhance or augment labor productivity; and J does likewise for capital productivity. In this specification changes in L and K would precipitate changes in output along a given production function, whereas changes in the H and J indices would shift the production function in a fashion that would reflect the relative impact of labor-versus capital-augmenting changes in technology. Choices for the variables H and J will be explained later in the empirical section of this article. From (1) it is easily seen that the marginal products of labor and capital are positive while diminishing returns to each input and the Inada conditions of the neoclassical production model hold if [alpha] ln H - 1 1, then the role of J is to eliminate (or at least moderate) the tendency for the occurrence of diminishing returns to capital. In fact, a similar statement regarding the labor input can be made if [alpha] ln H > 1. Moreover, both ([d.sup.2]/d[H.sup.2])([alpha] ln H) Because the exponents on L and K are not constant, this production model admits non-neutral technical progress. …