On applications of duality to the study of immigration

Economic Papers (Economic Society of Australia), March, 2003 by Christis Tombazos, Jaai Parasnis

1 Introduction

The fear that immigrants to Australia induce a nontrivial level of downward pressure on the demand for native (1) labour has been a subject of considerable policy debate during the last few federal elections. Interest in this issue is likely to have been fuelled by the large percentage of foreign born labour in the Australian workforce which has almost reached 25% in recent years, a figure which is considerably higher than those corresponding to other "immigrant nations". In the case of the United States, for example, the relevant figure is only 11.7%. (2)

Ensuing academic interest in the economics of immigration is reflected in a number of recent articles that examine this issue. Some of the most prominent examples of relevant research include the contributions of Chapman and Cobb-Clark (1999), and Addison and Worswick (2002). (3) These and similar studies provide important perspectives on the role of immigration in the Australian labour market, and generate useful results with policy relevant implications. However, a shared deficit of the preponderance of such research is that it appears to rely excessively on behavioural characterisations that are essentially ad hoc (and, as such, do not derive explicitly from a well specified optimisation framework).

Aside from inherent methodological shortcomings of ad hoc specifications, their lack of structure undermines efforts to isolate (or investigate simultaneously) a host of important variables that are likely to exert a nontrivial influence on endogenous arguments of interest (such as wages, employment and so on). For example, capital accumulation, international trade, as well as technology, represent key relevant dimensions that have, for the most part, eluded research in this area. Yet, such elements interact directly and explicitly with all factors of production, including immigrant labour, in generating market outcomes. (See Kohli, 1983 and Tombazos, 1999 for the role of capital accumulation, international trade, and technical change in the Australian labour market).

The objective of this paper is to submit a research program that ameliorates aforementioned deficits of mainstream, largely ad hoc, methodologies. The proposed approach relies on the microeconomic foundations of production and duality theory in the context of recent developments in this field. Though the application of duality to the study of immigration is hardly a recent development, it has been grossly underutilised in relevant research -- and, as far as we know, it has not been employed at all in the case of Australia. We suspect that, at least in part, this may relate to a host of technical complexities associated with this approach.

In what follows we provide a brief general outline of duality theory, with particular emphasis on the flexibility of this approach as well as the technical difficulties that discourage the use of this methodology in empirical research on immigration. As such, this paper may be viewed as a guide to the empiricist who may not have had extensive training in econometric applications of duality theory, but who wishes to extend the scope of inquiry in the study of the economic impact of immigration along a production theory frontier.

Production theory is briefly, alas superficially, canvassed in the following section. Section 3 outlines various behavioural specifications and the choice of an appropriate functional demarcation between endogenous and exogenous variables. Elasticities that derive from each of the examined analytical frameworks are discussed in Section 4. Section 5 guides the selection of a flexible functional form and examines the issue of regularity conditions. Concluding remarks are reserved for Section 6.

2 A Production Theory Approach

Since Baldwin Grossman's pioneering study (1982), the production theory approach to the study of immigration has been extensively employed in the case of the United States (Greenwood and Hunt, 1995; Greenwood, Hunt et al, 1996), and more recently Canada (Akbari and Devoretz, 1992) and Switzerland (Kohli, 1999). In the context of this methodology, immigrant, along with native labour, as well as physical capital and imported intermediate goods are all treated symmetrically as inputs to production. This simple approach readily facilitates a framework of analysis that enables the study of substitution possibilities that may exist between immigrants and other factors of production, including native labour.

Using parsimonious notation, the prevailing production technology may be characterised as follows

Y = f(x) (1)

where y is the quantity of gross output and x [[x.sub.j]] is the vector of input quantities.

In addition to capital, labour, and imports, the empiricist may include in this vector a range of additional factors that may be of interest. (4) Consistent with the usual requirements of economic theory, the employed production function is generally considered to be well defined for all non-negative input quantities and assumed to be linearly homogeneous, nondecreasing, concave, and twice continuously differentiable.