Implementation and Interpretation of Model

To implement the decomposition described above the first step is to estimate the distributions of F^ and F^ in 1980 and 1990. Once these distributions are estimated one can calculate the dispersion of each distribution in each year. Juhn et al choose the wage differential between the 90*’’ and 1 0*’’ percentile worker as their measure of wage dispersion but this is not necessary, one could use other measures of dispersion such as the variance of the distributions Y^, Y^ and F^ in each year. Changes in the dispersion of F^ are attributed to changes in the distribution of the quantity of observable characteristics. Changes in the dispersion of F^ are put down to changes in the quantity of observable characteristics and their prices. Hence changes in the dispersion of F^ over and above F^ are ascribed to changes in the dispersion of the price of observable characteristics. Changes in the dispersion of F^ over and above F^ are ascribed to changes in the distribution of unobservable earnings.

These distributions can be viewed as having two parts an observable part and an unobservable part. The process for calculating the observed and unobserved wage components is identical: multiply the quantity by the market premia. For wage distribution F^ the observable part for each

worker in each period t based on characteristics and the average coefficients p , i.e. predicted

wage. Added on to this is an unobserved component. This is obtained by assigning to each individual a residual based on his actual percentile in the distribution of unobservable wages each

— 1 year and multiplying it by the average price (for both years) of unobservables, C . For distribution F^ the observed characteristics X a r e multiplied by the prices p , that differ by year.

^^The distribution of allows for complete flexibility and therefore mirrors the tme distribution of wages Yit.

The unobservable component is computed by the same method described above which takes — 2

account of the fixed price of unobservables

a

In each case the unobservable component of wages for each person is determined as follows. First for each earnings equation the residual earnings for individual i in time t is given by:

e!,=Y.;-Ÿ^

[3.3.7]

[3.3.8]

where the standard deviations of e * and are interpreted as the average price of unobservable skill or the market rate of return to unobservable skill. Secondly from each residual a standardised residual is calculated which preserves the individuals percentile ranking^^ (since ranking the quantities of unobserved skill held by each individual is of greatest importance such a transformation will suffice). This proxy of the percentile ranking is a convenient way of measuring the quantity of unseen skills individuals possess in relation to the rest of the population. Third, multiplying such a quantity by the price of unobserved skill averaged over the two years impart the residual component of earnings.

So far a discussion regarding the interpretation of the three components has not been addressed. Each components contribution is closely linked to how the earnings equation has been specified. Here four separate earnings equation specifications are used (See Appendix A). First of all a simple human capital earnings equation is used. It includes age, age squared, race and dummy variables for levels of education. Component one of the decomposition, i.e. the contribution of changes in the distribution of observable quantities given this specification will isolate the effects

^^Positive residuals will indicate large amounts of unobservable qualities and a percentile ranking greater than 50, negative residuals will correspond to small amounts of unobservable qualities and a percentile ranking of below 50. The average unobservable quality however will be zero and is possessed by the median worker.

of changes in the age structure, changes in the distribution of qualifications and changes in the proportion of non-whites between 1980 and 1990. Component two of the decomposition will consist of the changes in the premia to education, labour market experience and racial discrimination. The third component of the decomposition will contain changes in the quantities and returns to factors not included in the earnings equation. These factors include observable characteristics which are thought not to influence earnings levels, job characteristics like industry and occupation (these will be sequentially included to the other three specifications) and unobservable qualities such as communication and organisational skills.

The three other specifications build on this human capital specification. In the second case dummy variables for 13 occupational classes are appended, in the third dummies for 10 industry classes and in the fourth, most general specification, both occupation and industry dummies are included. Interpretation of each components of the IM P decomposition will be contingent on what specification is used. In the most general case (specification four), the first component wiU measure the contribution of changes in the structure of industry and occupation as well as the contribution of changes in age structure, the distribution of qualifications and the proportion of non-whites. The change incurred by the first two components relative to the human capital specification indicates the relative importance of industrial and occupation structure between 1980 and 1990.

3.3 Results

Juhn, Murphy and Pierce (1993) develop a structure (explained in section 3) in which to analyse the trends in hourly wage inequality in the United States. This structure is used to decompose the observed trend in weekly earnings inequality in Great Britain. In this section results for the inequality trend between 1980 and 1990 are presented and in section 3.5. these are compared to the changes taking place between 1979 and 1989 and 1981 and 1991. The objective of the present analysis is to understand why the dispersion of earnings increased and how this increase relates to

distributional changes in observable characteristics, their prices and changes in the dispersion of residual earnings. Since changes in each of these components may differ across region, a decomposition of regional trends are given in section 3.3.2