Research purpose: The aim of the article was to estimate and compute, (1) relative productivity contributions and (2) relative productivity contribution–employee remuneration cost levels for different age-skill categories.

Motivation for the study: The research was deemed necessary given the current debate on relative productivity levels and possible changes to the retirement age in the South African labour market. No real research in this regard has been published regarding the South African labour market situation.

Research design, approach and method: A less restrictive production function was used, allowing for the simultaneous estimation and final computation of relative labour contribution levels of different age-skill categories.

Main findings: The lower-skilled segment produced significantly smaller productivity contributions and the relative productivity contribution–employee remuneration cost ratios of the 55 years and older age group were superior in the higher-skilled segment but, at the same time, the lowest in the lower-skilled segment.

Practical/managerial implications: It is recommended that human resource practitioners (given the perceived rigidity of labour legislation) implement and maintain structures that promote higher productivity levels for all age-skill categories in the workplace.

Contribution/value-add: An estimation procedure, which can be applied to the measurement of the relative productivity contribution of different age-skill categories, has been established.

Over the past two decades, renewed research interest has focused on the relationship between the different employee age groups and labour productivity in the workplace. The increasing ageing profile of populations in developed economies (especially in Europe) and its impact on those economies has prompted more research (Colonia-Willner, 1998; Daveri & Maliranta, 2006; Dostie, 2006; Guest & Shacklock, 2005; Malmberg, Lindh & Halvarsson, 2005; Remery, Henkins, Schippers & Ekamper, 2003; Roger & Wasmer, 2009; Skirbekk, 2003; Vandenberghe & Waltenberg, 2010) on the age-productivity relationship. No real research has been conducted in this regard for developing economies, where the realities are (1) real positive population growth rates, (2) a greater number of younger people entering the job market and (3) a growing component of active employees at the higher end of the age groups.

General aspects on the age-labour productivity relationship, for which all the abovementioned studies are in agreement, are that:

• Employee remuneration differentials reflect actual differences in relative productivity contribution levels for the different age groups.

• Employee remuneration levels tend to vary far less than relative productivity levels.

• A definite inequality exists between relative productivity contributions and employee remuneration levels for all the different age groups (the argument is that employee remuneration differentials do reflect actual differences in employee productivity).

• Relative productivity contribution-levels tend to reach a maximum and then decline as employees become older.

• Employers are constantly trying to achieve an employee-age mix that would yield the highest possible relative productivity contribution levels.

In terms of the measurement of the productivity contribution of the different age-skill categories, the majority of the studies (Daveri & Maliranta, 2006; Dostie, 2006; Guest & Shacklock, 2005; Vandenberghe & Waltenberg, 2010) used a restrictive production function methodology. A less restrictive measurement methodology was developed by Roger and Wasmer (2009) in their extensive study on the actual profile of relative productivity contributions across the different age groups in the manufacturing, services and trade sectors of the French economy. These authors developed a unique and less restrictive production function in which the labour input was treated as a nested constant elasticity substitution (CES) model. In this particular model, (1) a smaller number of constraints were imposed on production technology and (2) the imperfect substitution between the different categories of employees was allowed for. The model also, (1) enabled the differentiation of employees simultaneously by age and skill level and (2) estimated the differences in the age-productivity and age-employee remuneration (in relative terms) separately within each skill level.

The methodology of the model of Roger and Wasmer (2009, pp. 10–12, 19, 27–35), as applied in this particular study, was explained in the following few paragraphs. In the model, the aggregate labour input (high-skilled and low-skilled employees) took the form of a nested CES function:

L = (Σδ_iL_i^pi)^1/p_i [Eqn 1]

where L = labour, i = skill category, δ_i = distribution parameter and p_i = substitution parameter.

In terms of the different age-skill categories, each skill category was treated as a CES function by itself:

L_i = (Σ_iδ_ijL_ij^pij)^1/p_ij [Eqn 2]

where i = skill category, j = age category, δ_ij = distribution parameter per age-skill category and p_ij = substitution parameter per age-skill category.

In the estimation process, the distribution- as well as the substitution parameters were estimated, followed by the estimation of the productivity differentials per age-skill category. In order to estimate the productivity contribution per employee category the marginal productivity (MP) for each employee category was computed (given the estimated values of the CES parameters). It is important to note that, (1) constant returns to scale was assumed and (2) that the Euler’s theorem was used in order to specify the labour function. This particular function is homogeneous to the degree of 1 and was presented as a sum of labour inputs times the marginal productivities:

f(L,L₂…..L_n) = L₁∂f/∂L₁ + L₂∂f/∂L₂ + …L_n∂f/∂L_n) [Eqn 3]

where f = the function of labour, L₁L₂L_n = labour inputs and ∂/L = marginal productivity per labour input.

In order to cater for skill differentiation the marginal product for each skill category was computed:

MP_i = ∂Y/∂L ∙ ∂L/∂L_i [Eqn 4]

where Y = output, L = labour input and L_i = different skill levels.

In terms of the nested CES function, the marginal productivity per skill category was presented as:

MP_i = AK^αβ(Σ_iδ_iL_i^pi)^{β/pi -1}δ_iL_i^pi-1 [Eqn 5]

where MP_i = marginal productivity per skill category,

K = capital input, α = marginal productivity of capital, δ_i = distribution per skill category, L_i = employee skill category and p_i = substitution parameter per skill category.

The ratio of the different skill levels was computed in order to determine the relative marginal productivity for the different employee skill categories:

MP₁/MP₂ = ∂L/∂L₁ ÷ ∂L/∂L₂ = λ = δ₁ / δ₂ (L₁/L₂)^pi-1 [Eqn 6]

where λ = ratio of the marginal productivities of the two skill categories 1 and 2 and δ₁ / δ₂ = ratio of the distribution parameters for skill categories 1 and 2.

A comparison of productivity contributions over different skill categories requires the estimation of the ratio between the marginal productivity of a skill category and the average marginal productivity of the total labour input:

MP₁/MP_av = L/L₁ + λ^-1L₂ and MP₂/MP_av = L/λL₁ + L₂ [Eqn 7]

where MP_av = average marginal productivity for the total labour input.

In terms of the impact of age differentiation on labour productivity, the marginal productivity per age-skill category is computed:

MP_ij = ∂Y/∂L ∙ ∂L/∂L_i ∙ ∂L_i/∂L_ij [Eqn 8]

where MP_ij = marginal productivity per age-skill category.

and

MP_i = AK^αβ(Σδ_i L_i^pi)^{β/pi - 1}δ_iLi^{pi/pj - 1}δ_ijL_ij^{pij -1} [Eqn 9]

where δ_ij = distribution parameter per age-skill category and p_ij = substitution parameter per age-skill category.

The relative marginal productivity of any two age groups of employees in a given skill category is:

MP_i1/MP_i2 = δ_i1/δ_i2(L_i1/L_i2)^pij-1 [Eqn 10]

The relative marginal productivities between the different age categories were:

• Relative marginal productivity for employees younger than 35 years versus employees older than 35 years but younger than 55 years of age, represented as:

MP_i35</MP_i35-55 = φ [Eqn 11]

• Relative marginal productivity for employees younger than 35 years versus employees 55 years and older, represented as:

MP_i35</MP_i55+ = γ [Eqn 12]

• Relative productivity for employees older than 35 years but younger than 55 years versus employees 55 years and older, represented as:

MP_i35-55/MP_i55+ = η [Eqn 13]

The productivity contribution of each age category was then given by the ratio of the marginal productivities of the respective age group over the average marginal productivity of a specific skill category:

MP_i35</MP_av = L_i/L_i35< + φ^-1L_i35-55 + γ^-1L_i55+ [Eqn 14]

MP_i35-55/MP_av = L_i/φL_i35< + L_i35-55 + η^-1L_i55+ [Eqn 15]

MP_i55+/MP_av = L_i/ γL_i35< + ηL_i35-55 + L_i55+ [Eqn 16]

In order to estimate the distribution and substitution parameters that are necessary to determine the productivity contributions of the different age-skill categories, the production function model (in which labour is differentiated simultaneously by the different age and skill categories) was estimated as:

Y = AK^α(γ(δ_L35<L_l35<^pl + δ_l35-55L_35-55l^pl + (1 – δ_l35< – δ_lm)L_lo^pl)

^ps/pl + (1 - γ) (δ_h35<L_h35<^ph + δ_h35-55L_h35-55^ph + (1 – δ_h35< – δ_h35-55)L_h55+^ph)^ps/ph)^β/ps [Eqn 17]

where γ = the ratio of the marginal productivities of the 35–55 years and the 55 years and older age groups,

δ_LY = distribution parameter of the lower skill 35 years and younger age category, δ_Lm = distribution parameter of the lower skill 35–55 years age category, δ_hy = distribution parameter of the higher skill 35 years and younger age category, δ_hm = distribution parameter of the higher skill 35–55 years age category, L_l35<^pl = substitution parameter of the lower skill 35 years and younger age category, L_l35-55l^pl = substitution parameter of the lower skill 35–55 years age category, L_l55+^pl = substitution parameter of the lower skill

55 years and older age category, L_h35<^ph = substitution parameter for the higher skill 35 years and younger age category and L_h55+^ph = substitution parameter for the higher skill 55 years and older age category.

The model also allowed for the computation of the total share of the different age-skill categories in terms of the total employee remuneration costs. These computations gave a clear indication of the relative employee remuneration–labour productivity levels per age-skill category.

Information on firms in the manufacturing, construction and the trade and accommodation industries was supplied by Construction Education and Training Authorities (CETA), Manufacturing Sector Education and Traing Authority (CATHSSETA), Service Sector Education and Training Authorities (SERVICES SETA), Manufacturing, Engineering and related service Sector Education and Training Authority (MERSET), Wholesale and Retail Sector Education Authority (W&RSETA), Food and Beverages Sector Education and Training Authority (FoodBevSETA), the Department of Labour, and Statistics South Africa (StastSA). It was also the aim of the data collection process to make sure that the spread of firms throughout the different industries was statistically significant. In the manufacturing and construction industries, only firms that have more than 80 employees were included in the sample groups. For the trade and accommodation industry, only firms that had more than 10 employees were included. Given the aforementioned constraint and statistical validation requirements, the sample response sizes (192 firms in the manufacturing industry, 96 firms in the construction industry and 89 firms in the trade and accommodation industry) were found to be statistically significant.

For each of the individual firms in the sample groups, data had to be collected on value added, value of the capital stock (including material stock), the hours worked per age group, the hours worked per age-skill category and the hourly earnings by age and by age-skill category. Monthly employee remuneration levels were transformed to hourly rates. Data on the different variables had to be standardised (values were divided by 100 000 and logarithms were then computed), in order to enable comparison and application of the data in the estimation process. The summary sample statistics are presented in Appendix A.

The data revealed interesting statistics for the different sample categories. Firstly, the individual percentage contribution of the different age groups to the total hours worked was relatively the same for all three industries. The 35–55 years age group was the biggest contributor (on average 45%), followed by the 35 years and younger age group (on average 33%) and, lastly, the 55 years and older age group (on average 21%). Secondly, in terms of the age-skill categories, the lower-skilled category contributed approximately 67% of the total hours worked (albeit a smaller contribution of 58% in the trade and accommodation industries), compared to the approximately 33% contribution of the higher-skilled category (except for the trade and accommodation industries where the contribution was higher at 42%). In the lower-skilled segment, the 35–55 years age group was the biggest contributor to the total hours worked, followed by the 35 years and younger age group. In the higher-skilled segment, the spread of the total number of hours worked per age group was more evenly in the case of the manufacturing and construction industries. In the trade and accommodation industry the contribution of the 35–55 years age group was much higher (47%). Thirdly, for both the lower-skilled and higher-skilled segments, the 35–55 years age groups had, by far, the greatest total employee remuneration capacity (in excess of 60%), whilst the total employee remuneration capacity of the 55 years and older age group exceeded that of the 35 years and younger age group.

Analysts should not only concern themselves with relative productivity contribution levels but should also consider the applicable employee remuneration cost aspect of a particular productivity contribution level. From a productivity contribution–employee remuneration cost perspective, it was deemed necessary to compute the marginal productivity contribution–marginal employee remuneration cost ratios for each of the age-skill categories in the different industries. This simply meant that the productivity contributions were matched with the employee remuneration costs. If the productivity contribution–employee remuneration cost ratio was greater than 1, the relative productivity contribution of a particular age-skill category exceeded the relative employee remuneration cost of that age-skill group and if the ratio was smaller than 1, the relative productivity contribution of a particular age-skill category was less than the relative employee remuneration cost of that age-skill group.

The computation of the marginal productivity–employee remuneration ratios also required the computation of the marginal employee remuneration cost ratios (i.e. average employee remuneration cost per age-skill category divided by average employee remuneration cost for the industry). If the relative employee remuneration cost ratio was greater than 1, the average employee remuneration cost of that particular age-skill category exceeded the average employee remuneration cost of the employers and if the ratio was less than 1, the average employee remuneration of that particular age-skill category was smaller than the average employee remuneration costs of the employers. The employee remuneration and the productivity contribution–employee remuneration cost ratios of all the different age-skill categories for the three industries are listed in Table 3.

The estimation results of the marginal ratios per age-skill category indicated that for the lower-skilled category, the 55 years and older age group had the lowest productivity contribution whilst the 35–55 years age group had the highest productivity contribution (the relative productivity contribution levels of this particular age group marginally exceeded the average industry productivity contribution levels for the three industries). It was also significant to note that for the 35 years and younger age group the productivity contribution was less than the average industry productivity contribution levels. These results are a confirmation of the general perception of low productivity levels for the lower-skilled employee component of the South African economy. The challenge for human resource practitioners (given the perceived rigidity of current labour legislation) is to (1) enhance a greater understanding of the importance of higher productivity levels in the workplace and (2) implement structures that would promote and monitor productivity levels more efficiently and to constantly improve work-based training.

The abovementioned findings are in contrast with the findings of the Roger and Wasmer (2009) study, which indicated a significant productivity contribution (exceeding the average industry productivity contribution) of the ‘younger’ age group (in those particular developed economies).

The results derived for the higher-skilled segment are in contrast with the results derived for the lower-skilled segment. The 55 years and older age group generated relative productivity contributions that significantly exceeded the average industry productivity levels. The same applies to the 35–55 years age group, but at a relative smaller magnitude. These results are similar to the findings of the Colonia-Willner (1998) and Roger and Wasmer (2009) studies, which indicated high productivity levels for the ‘older’ age group in the higher-skilled segment. A plausible explanation is that for certain higher-skilled occupations, a high level of longer job experience and ‘learning by doing’ effects are a necessity. Given the significant higher productivity contribution levels of the higher-skilled segment (in comparison with the lower-skilled segment) it is important that, (1) older highly-skilled employees are kept in the workplace for as long as possible and (2) that structures are put in place that could limit any outflow of high-skilled employees from the South African workplace. It is surprising to note that the relative productivity contribution of the 35 years and younger age group still remained lower than the average industry productivity contribution levels (albeit better than the lower-skilled segment). In this regard, it is felt that the productivity levels of this particular age-skill category can be improved by enhancing the quality and speed of learning and training and to rigorously keep track with technological progress.

The situation is totally reversed when the higher-skilled segment is considered. The productivity contribution–employee remuneration cost ratios of the 55 years and older age group (greater than 1) was greater than the other two age groups (in all three industries). This is a clear confirmation of the superior productivity contribution levels of this particular age-skill group. These results have been obtained even when the relative employee remuneration cost ratios were greater than 1 (for all three industries), which simply means that the relative productivity contributions of this particular age group exceeded the relative high employee remuneration costs. The productivity contribution–employee remuneration cost ratio for the 35–55 years age group was also greater than 1 (indicating high levels of relative productivity contributions). The younger than 35 years age group also presented better relative productivity contribution–employee remuneration cost ratios (compared to the lower-skilled segment). These ratios were slightly less than 1, indicating a situation where relative productivity contributions nearly match relative employee remuneration costs.

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