f. Occupational mobility

B1

D2 - D

1

; (61)

Application of this new additional investment rate normally gives an overall labour balance close to zero, i.e, full employment at the end of the projection period. Investment across sectors is allocated as before – equations 15 to 19. There will, nevertheless, exist labour imbalances by education level. Thus, "full employment" could, for example, hide significant educated unemployment. The projection period should not be too short to allow the changed economic growth to have its full impact. At least 5 years are needed, and the larger the employment im-balance is, the longer is the projection period required.

2.3f. Occupational mobility

This section describes the technique used for simulating dynamic labour movements between oc-cupations. This is the first time, to my knowledge, that these considerations have been included in a manpower model of the type specified here. It assumes that wage differentials give the incentive to move between them. The time needed to acquire the appropriate skills for a new occupation constrains the movements.

Labour movements between occupations take place from those in supply excess to those in supply deficit, if the movement yields a gain in wage – based upon relative wages entered exogoneously..

The mobility depends on the training period required to take on the new occupation. If potential supply from excess occupations is larger than the deficit of the target occupation, a problem arises about which excess levels shall make good the deficit. The solution adopted is to make the recruit-ment of labour proportional to the difference between the wage in the supplying occupation and that of the target occupation, giving priority to the labour gaining most in wage -–the idea being that labour will move to the occupation providing the highest wage gain when there are choices to be made. Of course, this over-simplifies some of the theoretical notions discussed in Chapter II – efficiency wage ideas are ignored for instance. If an occupation remains in surplus at the end of a year of labour movements, the surplus labour loses one year of training knowledge and moves to a correspondingly lower occupation.

The basic projections, referred to in the preceding section, give for each occupation k and year t an unadjusted labour supply Sk,t and demand Dk,t. As these change between years, one can for each year define the net new entries DSk affecting the supply and the net new needs DDk changing the demand for labour: Dropping the time subscript, the demand for labour in occupation k is denoted by Dk, the supply by Sk and the wage by wk. There are n occupations in total, each with a supply excess Ek that may be positive, negative or zero:

By summing over all occupations, a supply excess E. is obtained:

D. = ∑

If the supply excess is positive (there is an overall unemployment), it is assumed that the labour market is in equilibrium when no occupation is in deficit. Conversely, if the excess is negative (there is labour shortage), equilibrium is reached when no occupation is in surplus.

The transfer of a supply excess from occupation i to occupation j in deficit takes place with a time delay yi,j determined by the length of the training period. Two parts compose this delay:

1) the period required to become competent to move from one occupation ki to another kj at the same education level, ψ_ki,kj;

2) the period of training for moving from the education level mi required for the occu-pation kj to the education level mj needed for occuoccu-pation kj, λ_mi,mj (which has a positive value only if mi>mj). The education levels are those that are dominant for the occupations in question according to the statistics.

The time delay is defined by:

yi,j = ψ ki,k

j

+λ_m

i,m_j where λ_m

i,m_j = ∑

m=mi m_j-1

λm,m+1 ; (65)

For a time delay of more than one year, transfers to other occupations may meanwhile reduce the supply excess existing in an earlier period. Hence, the potential transfer, Ti,j, is determined by the conditions:

Ti,j= 0 if yi,j> the number of projection years, else

Ti,j=minimum of current year's Ei and the Ej existing yi,j years earlier. (66) Summing the potential transfers over the occupations j fulfilling the wage and supply excess conditions gives a total to be compared with the deficit of the target occupation i. If the total is less than or equal to the deficit, all the potential transfers are made. However, if the total is larger than the deficit, a priority problem arises. The solution derives from the following technique:

It is assumed that priority pj is a linear function of the wage ratio between the target and the supplying occupations, ai,j = wi/wj. The potential transfer from the occupation j with the highest ai,j is fully used, i.e., pj = 1, whereas the transfer from the other occupations j is given a lower pj.

The linear function can be expressed as follows:

pj = α + β a

i,j ; (67)

Denoting the highest wage ratio by âi , it can be stated:

1 = α + β a^∧

i ; (68)

Substituting (68) into (67) gives:

pj = 1 + β (a

i,j - a^∧

i) ; (69)

This means that the priority becomes a linear function of the difference between the wage ratio observed for occupation j and the highest wage ratio observed for any occupation in the set of occu-pations potentially providing labour to occupation i. The coefficient ß is found by summing up the potential transfers multiplied by the priority rates and setting this sum equal to the supply deficit to be filled:

∑

j=1 n

Ti,j [1 + β (a

i,j - a^∧

i)] = E

i ; (70)

Solving for ß gives:

β =

Ei -

∑

j=1 n

Ti,j

∑

j=1 n

Ti,j (a

i,j - a^∧

i)

; (71)

This means that the coefficient ß is equal to the difference between the demand for transfer from occupation i and the potential supply of transfers from occupations j divided by the weighted sum of differences between the wage ratio for occupation j and the highest one observed in relation to occupation i, the weights being the potential transfers.

By the end of the year, all remaining labour surpluses lose one year of training, as they could not take on the tasks for which they had received training. Hence, for each surplus is searched an occupation that fulfils the conditions that:

- its wage is lower than the one for the surplus occupation, and - the training delay to reach the latter occupation is one year.

The first one found receives the whole surplus in question irrespective of its own excess situation.

The search process starts from the occupation with the lowest wage.

2.3g. Education and cost implications of occupational mobility

From a planning point of view, it is important to know the impact on the educational system of the training needed to make the labour force competent to move from one occupation to another.

Training consists of two components:

- vocational training for moving between occupations requiring the same formal school education;

- additional formal training, if the occupations have different requirements in this respect.

A procedure computes the number of students that, each year of the projection period, must attend training at a certain education level to make them competent for the move. Using data from the module on Educational costs (note that relative prices are not determined endogoneously), the implications of the training are estimated in terms of number of teachers and costs. To simplify matters, averages by education level are used rather than figures by grade. The same conditions apply to vocational training as to tertiary education.

The basis for the procedure is the information about the number of potentially realized labour force transfers, Ti,j, from one occupation (j) to another (i) over the time span yi,j that is determined by the total period of training. In each year t of this time span a number of students Sm,t, equal to Ti,j (not adjusted for death rate), attend training at the education level m, determined by equation (65) above. As each Ti,j creates its own stream of students at different education levels, the student numbers are cumulated over time and education levels.

The information in the Education cost module is used to obtain unit figures on number of teachers and education costs per student, by year and education level. These unit figures are applied to the cumulative number of students (cum Sm,t) to get the volume and costs of the training required for