5 Wage Predictions
5.1 Derivation of the predicted wage
This section describes how a wage rate may be assigned to unemployed individuals. In the simple case where the selection and wage equations contain a common set of variables, consider first the conditional mean log-wage rate, for an individual with given characteristics. For those who are employed, this is given by:
(8) 
Imputed wage rates for those who are unemployed can be obtained using the expression:
(9) 
The use of the conditional mean log-wage is perhaps the most obvious choice for the predicted wage. It is also possible, for example, to take a random draw, for each individual, from the relevant conditional distribution. Indeed, in labour supply analyses there is no necessity to be restricted to using observed wage rates for those employed in the sample period: it would also be possible to take random draws from the relevant conditional distributions.
In the present context, the expression in (9) cannot be used without modification because some variables used in the estimation of the wage functions are not available for non-workers. In addition to the wage rate, neither the occupation nor the industry of non-workers is known. Although these variables could not be included in the selection equations, they were included in the wage equations because of their demonstrated importance in wage determination. An alternative predictor for non-workers is simply (9) with the dummy variables for occupation and industry replaced by the sample proportions in the different categories. Since it is likely, that the distribution across occupations differs between the employed and the unemployed workers, extraneous information on unemployment rates within the various occupation and industry groups are used to assign proportions within occupation and industry groups to the non-workers (see Table A.3). For a complete discussion of this approach see Creedy et al. (2001).
