## 1. INTRODUCTION

The last decade has witnessed an increased interest by economists in the analysis of wage inequality. To a large extent, such interest arises from the fact that the tendency towards a reduction in wage inequality that had prevailed during the previous decades experienced a reversal during the 1980s. This is so not only for unconditional inequality, but also for wage inequality within groups defined based on education and experience (e.g. Juhn *et al.*, 1993). Although the original concern was documented for the United States (Levy and Murmane, 1992), increasing inequality is now well documented for almost all of the industrialized countries (Gottschalk and Smeeding, 1997).

A leading explanation for these changes in the structure of pay asserts that increases in wage inequality were caused by shifts in labour demand favouring high-skilled labour at the expense of low-skilled labour, primarily caused by changes in the technology, notably by the use of computers (Juhn *et al.*, 1993, Bound and Johnson, 1992, Autor *et al.*, 1998). The evidence supporting this hypothesis is rather indirect, and is based on the observation that despite the steady increase over time of the relative supply of high-skilled labour, conventional Mincerian wage equations indicate a rise in the returns to schooling. *Ceteris paribus*, increases in the number of college graduates would decrease the relative wage of college graduates, thereby decreasing inequality. To reconcile the increase in the skills of the labour force with increasing returns to education and wages inequality, one is naturally led to conclude that labour demand must have shifted to more than compensate the shifts in supply. The skill-biased technical change explanation was recently detailed by Bresnaham (1999), who stresses the organizational changes induced by the information and communication technologies and their direct impact on the relative demand for certain skills, namely ‘people’ and managerial skills.

The usual supply and demand framework typically employed to analyse changes in the structure of wages implicitly assumes that to each type of labour (say, skilled and unskilled), and after controlling for measured characteristics, there corresponds a single wage, as opposed to a distribution of wages. Perhaps more correctly, the conventional supply and demand analysis focuses only on the average wage. This is consistent with the conventional empirical approach of estimating Mincerian wage equations by least squares methods, which provide estimates of the effect of education (along with the effect of other attributes) upon the mean of the conditional wage distribution. Reasoning in the context of this framework, Topel (1997, p. 72) was led to assert that ‘[a] reason for interest in supply effects stems from the hope that human capital investment will mitigate future inequality’, while Johnson (1997, p. 53) suggested that ‘a long-term commitment to increasing greatly the fraction of individuals who go to college is the appropriate public policy response to the phenomenon of increasing inequality’.

However, recent research employing statistical methods other than the least squares regression (namely, quantile regression) has revealed that education has a greater effect upon the wages of individuals at the top of the wage distribution than upon wages of individuals at the bottom of that distribution.1 In other words, more educated individuals experience more unequal wage distributions, and this seems to have been exacerbated during the 1980s. These results suggest that education may have a second effect on wage inequality. By increasing the number of educated workers, a pressure is certainly exerted that decreases the wages of these workers. But, if more educated individuals experience greater wage spreads, increased educational levels may also contribute to an increase in wage inequality. The net result of these two effects is certainly an empirical question and constitutes the major motivation for this paper.

A full understanding of the changes that have occurred in wage schedules requires the disentanglement of the effect of changes in the stock of human capital in the working population from the effects of changes in returns to the components of human capital. We propose a method that extends the traditional Oaxaca decomposition of effects on mean wages (Oaxaca, 1973) to the entire wage distribution. The method is based on the estimation of the marginal density function of wages in a given year implied by counterfactual distributions of some or all the observed attributes. This methodology is applied to the analysis of the changes in the distribution of wages in Portugal from 1986 to 1995. For instance, we will estimate the wage density that would have prevailed in 1995 if education had been distributed as in 1986 and the other covariates as in 1995. By comparing it with the actual marginal distribution in 1995, we can isolate the contribution of changes in education to the observed changes in the distribution of wages.

The counterfactual nature of the exercise requires the estimation of the wage distribution conditional on the variables of interest. We accomplish this first step by means of quantile regressions, that is, by estimating models for the quantiles of the conditional wage distribution. Quantile regressions capture the impact of changes in covariates upon a conditional wage distribution, in very much the same way that mean regression measures the impact of changes in covariates upon the mean of the conditional wage distribution.

However, we wish to go beyond a mere conditional model. Indeed, a conditional distribution does not reflect the variability of the covariates in the population. In other words, it is the distribution that would prevail if all workers had the same observed characteristics. The second step of our approach, and its major methodological contribution, is thus to marginalize the conditional distribution estimated in the previous step using different scenarios for the distribution of workers' attributes. The basic gist of our approach resembles DiNardo *et al.* (1996) in that their methodology also estimates counterfactual densities and yields a decomposition of the factors that explain the changes in the marginal distribution of wages. However, as we shall see in Section 2 below, not only are the specifics of the two approaches quite distinct, but they also provide different insights into the factors behind observed changes in the distribution of wages.

The paper proceeds as follows. We present the methodology used to analyse the changes in wages in Section 2. Section 3 provides an application of the methodology to Portuguese wage data [Section 3.1 overviews the changes in the Portuguese labour market for the period 1986–1995, focusing on the changes in the wage distribution and in the characteristics of the labour force; we then proceed to present and discuss our empirical findings in Section 3.2]. Section 4 concludes.