The Impact of Ageing on Welfare and Labour Productivity: An Econometric Analysis for the Netherlands

Abstract

Ageing attracts ever-increasing attention because it has many implications for welfare and society and is an important subject for policymakers. This chapter focuses on ageing effects on welfare and labour supply. How can a falling labour supply be compensated for while welfare is maintained? In principle, there are five possible ways: (i) increase the retirement age; (ii) increase the annual number of working hours; (iii) increase labour productivity; (iv) increase net labour participation; and/or (v) optimise the spatial allocation of productive activities and jobs. This chapter focuses on growing labour productivity as a means to counteract the adverse effects of ageing using a new and unique micro-level dataset for the Netherlands.

Appendices

Appendix 1: Characteristics of the Data

The number of data points for all the firm variables, for each year between 1999 and 2005, is over 45,000. A summary of these data is provided in Tables 10.2 and 10.3. Table 10.2 provides an overview of the control variables in the database that are used when estimating Eq. (10.7), while Table 10.3 provides some descriptive statistics for the other variables used in the model. Table 10.2 reflects that each of the control variables (by industry, firm size and region) has sufficient observations for our analysis. Here, the ‘other services’ industry is the smallest with only 119 observations, which should be sufficient for estimation purposes.

Table 10.2 Distribution of data observations, 1999–2005

Table 10.3 Mean values of some plant-level variables, 1999–2005

Appendix 2: Calculation of Firm-Level Capital Stock

The database for 1999–2005 that we use in our empirical analysis of the level and growth of labour productivity lacks information about the capital stock of each firm and about the education or skill level of the individual workers. This means that the capital stock and worker skill level variables have to be approximated using variables that are available in our dataset.

It is generally accepted that, for productivity analyses, the productive capital stock of a firm is the best measure of capital input (OECD 2001). However, due to a lack of data, most studies use a proxy for productive capital stock. For example, Licht and Moch (1999) use the number of computers as a proxy for the computer capital stock. Book values of capital stock were used in Brynjolffson and Hitt (1996) and in Lichtenberg (1995), while Lehr and Lichtenberg (1999) used investment flows. Book values are imperfect measures of productive capital stocks as they are based on historic, rather than replacement, cost and on accounting rules rather than economic depreciation. Investment flows, as a proxy, are prone to be misleading if the investment growth rate is not constant, which is typically the case for computer investments.

An alternative approach is to derive productive capital stock using the Perpetual Inventory Method (PIM), which essentially sums past investment flows, correcting for reduction in productive capacity due to ageing. Assuming a geometric withdrawal pattern (see e.g. Jorgenson and Stiroh 2000), the capital stock is derived as follows:

$$ {K}_t={K}_{t-1}\left(1-\delta \right)+{I}_t $$

(10.10)

where K _t is the capital stock at year t, I _t the investment flow during year t, and δ the rate of economic depreciation.

The main problem with using this approach, especially in micro-level studies, is the lack of long series of investment flow data. Typically, micro-level data on investments are only available for a short time period. Standard methods to circumvent this problem in macro-analyses, such as the Harberger method, are nor appropriate and cannot be used. In the Harberger method, the initial year’s capital stock is estimated by dividing investment in the initial year by the sum of the growth rate of investment and the depreciation rate. This method is based on a steady-state assumption: and so investment flows must be smooth and grow at a constant rate. This might be an acceptable assumption for the total economy or the sectoral level, but it is not realistic at the firm level. Firm-level investment patterns are volatile: investments often occur in spikes. Here, we propose a new method to deal with this problem that uses information on depreciation reported by firms.

Most micro-production surveys that include investment variables also include depreciation recorded in the firms’ books. This reported (firm-level) depreciation, which is determined by accounting rules rather than technical factors, contains information on past firm-level investments. This information can be retrieved when the accounting practices of a firm is known using the so-called “booked depreciation method” (see Broersma et al. 2003). Linear depreciation is a standard accounting rule that is often used in practice. With this approach, an investment made in year t is written off in equal parts during the anticipated lifetime of the asset. If the lifetime L of an asset is say 15 year, each year one-fifteenth of the original investment value is recorded as depreciation. Hence, the booked depreciation in year t (i.e., D _t) is the summation of investments made in the period t–L to t, multiplied by 1/L:

$$ {D}_t=\sum_{k=1}^L\frac{1}{L}\cdot {I}_{t-k} $$

(10.11)

From this, one can deduce that:

$$ {D}_{t+1}-{D}_t=\frac{1}{L}{I}_t-\frac{1}{L}{I}_{t-L} $$

(10.12)

Rewriting gives:

$$ {I}_{t-L}={I}_t-L\left({D}_{t+1}-{D}_t\right). $$

(10.13)

This equation shows that past investment flows (made before time t) can be derived on the basis of investment and depreciation data at time t and later.

This “booked depreciation method” has been used to derive constant price investment flows for total capital before 1999 (see below for the formal derivation). For computer equipment, separate firm-level depreciation figures are not available. Therefore, we assumed that, prior to our first observation (1999), the capital stock of computer hardware for each firm was equal to its two-digit industry’s average proportion of computer capital in 1999 multiplied by the firm’s total capital stock in 1999, derived using the booked depreciation method.

Constant price investment flows were estimated by deflating firm-level investment flows by the price deflators (for the relevant two-digit industry) for total investment in fixed assets and in computing equipment, drawn from the EUKLEMS database (www.euklems.net). This deflator is also used to calculate firm-level constant price depreciations.

When using investment series in (10.10), stocks are derived using a depreciation rate for non-computer equipment of 0.067, based on an average lifespan of 15 years (δ = 1/L). The lifespan of buildings is much longer but we are only considering productive capital stocks and do not see buildings as falling within this category. When it comes to computer capital, we assume a lifetime of 5 years, and hence δ = 0.2. Finally, we estimate the real stock of non-computer capital simply by subtracting the computer stock from the total capital stock.

The specific application of the depreciation method outlined above to the current analysis requires further assumptions as depreciation and investment data are only available for the period 1999–2005. First, we split the 15-year period from 1984 to 1998 into two: 1984–1989 and 1990–1998 for reasons that will become apparent below. Based on a linear depreciation rule, and with K ₁₉₉₉ the real capital stock in 1999, we can state that:

$$ {K}_{1999}=\sum_{t=1984}^{1998}\frac{\left(t-1984+1\right)}{15}{I}_t=\sum_{t=1984}^{1989}\frac{\left(t-1984+1\right)}{15}{I}_t+\sum_{t=1990}^{1998}\frac{\left(t-1984+1\right)}{15}{I}_t $$

(10.14)

where I and D refer to the investment and depreciation flows in constant prices. The first term on the right hand can be derived using (10.13):

$$ {I}_t=15\left({D}_{t+15}-{D}_{t+16}\right)+{I}_{t+15},\operatorname{}t=1984\dots 1989 $$

(10.15)

From which we get:

$$ \sum_{t=1984}^{1989}{I}_t=\sum_{t=1984}^{1989}15\cdot \left({D}_{t+15}-{D}_{t+16}\right)+{I}_{t+15} $$

Then, substituting this in (10.14), we get:

$$ {\displaystyle \begin{array}{ll}\hfill & \sum \limits_{t=1984}^{1989}\frac{\left(t-1984+1\right)}{15}{I}_t\\ {}& =\sum \limits_{t=1984}^{1989}\left[\left(t-1984+1\right)\cdot \left({D}_{t+15}-{D}_{t+16}\right)+\frac{\left(t-1984+1\right)}{15}{I}_{t+15}\right]\hfill \\ {}& =\sum \limits_{t=1999}^{2004}\left[\left(t-1999+1\right)\cdot \left({D}_t-{D}_{t+1}\right)+\frac{\left(t-1999+1\right)}{15}{I}_t\right]\hfill \end{array}} $$

The second term on the right-hand side of (10.14) is unknown but can be approximated as follows:⁹

$$ \sum_{t=1990}^{1998}\frac{\left(t-1984+1\right)}{15}{I}_t\approx \frac{11}{15}\sum_{t=1990}^{1998}{I}_t $$

(10.16)

Using (11), the total depreciation over the period equals:

$$ \sum_{t=1999}^{2005}{D}_t=\frac{1}{15}\left(\sum_{t=1990}^{2004}{I}_t+\sum_{t=1989}^{2003}{I}_t+\dots +\sum_{t=1985}^{1999}{I}_t+\sum_{t=1984}^{1998}{I}_t\right) $$

(10.17)

which can be rewritten as the following three terms:

$$ \sum_{t=1999}^{2005}{D}_t=\frac{7}{15}\sum_{t=1990}^{1998}{I}_t+\sum_{t=1999}^{2004}\frac{\left(2004+1-t\right)}{15}{I}_t+\sum_{t=1984}^{1989}\frac{\left(t-1984+1\right)}{15}{I}_t. $$

(10.18)

Rearranging then gives:

$$ \sum_{t=1990}^{1998}{I}_t=\frac{15}{7}\sum_{t=1999}^{2005}{D}_t-\sum_{t=1999}^{2004}\frac{\left(2004+1-t\right)}{7}{I}_t-\sum_{t=1984}^{1989}\frac{\left(t-1984+1\right)}{7}{I}_t $$

(10.19)

The first and second terms can be simply found from the available data, and the third term can be derived from (10.15), i.e. I _t  = 15(D _t + 15 − D _t + 16) + I _t + 15, which yields I _1999–15 = I ₁₉₈₄ and so on. The third term then becomes:

$$ {\displaystyle \begin{array}{ll}\hfill & \sum \limits_{t=1984}^{1989}\frac{\left(t-1984+1\right)}{7}{I}_t\\ {}& =\sum \limits_{t=1984}^{1989}\left[\left(\frac{15\cdot \left(t-1984+1\right)}{7}\right)\cdot \left({D}_{t+15}-{D}_{t+16}\right)+\left(\frac{\left(t-1984+1\right)}{7}\right)\cdot {I}_{t+15}\right]\hfill \\ {}& =\sum \limits_{t=1999}^{2004}\left[\left(\frac{15\cdot \left(t-1999+1\right)}{7}\right)\cdot \left({D}_t-{D}_{t+1}\right)+\left(\frac{\left(t-1999+1\right)}{7}\right)\cdot {I}_t\right]\hfill \end{array}} $$

By combining information on $\sum_{t=1990}^{1998}{I}_t$ (from 10.19) with (10.16), we can obtain the second term in (10.14) as follows:

$$ {\displaystyle \begin{array}{l}\sum \limits_{t=1990}^{1998}\frac{\left(t-1984+1\right)}{15}{I}_t\approx \frac{11}{15}\sum \limits_{t=1990}^{1998}{I}_t=\left[\frac{11}{7}\sum \limits_{t=1999}^{2005}{D}_t\right] - \left[\sum \limits_{t=1999}^{2004}\frac{11\cdot \left(2004+1-t\right)}{105}{I}_t\right]\hfill - \sum \limits_{t=1999}^{2004}\left[\left(\frac{11\cdot \left(t-1999+1\right)}{7}\right)\cdot \left({D}_t-{D}_{t+1}\right)+\left(\frac{11\cdot \left(t-1999+1\right)}{105}\right)\cdot {I}_t\right]\hfill \end{array}} $$

As such, we now have an expression for the (constant price) capital stock in 1999. Using the perpetual inventory method (PIM), we can then easily construct the capital stocks for 2000 through 2005 as:

$$ {K}_t={K}_{t-1}\left(1-\delta \right)+{I}_t $$

where I _t is the investment (in constant prices) and δ the depreciation rate (δ = 1/L). For total capital we use L = 15 years, so δ = 0.067. The same methodology is applied to the computer capital stock, with the difference being that the depreciation period is now 5 years instead of 15 years, so δ = 0.2. The starting value for computer capital is determined, as outlined above, by simply assuming that, in 1999, the share of computer capital in total capital for a firm is equal to the computer share in total capital for the relevant industry. These are reported in the table below (Table 10.4). Since each firm has different starting values for K ₁₉₉₉ , each firm will also have different starting values for computer capital K _{IT, 1999}. Then, using PIM, for each firm we calculate the investment in computers in year t as I _IT,t , and, with δ = 0.2, we can then calculate the computer capital stocks for the years 2000 through 2005 for each firm.

Table 10.4 Share of computer capital by industry in 1999