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A model of embodied technical change and employment
TECHNOLOGICAL
FORECASTING
AND SOCIAL CHANGE
16.47-65
(1980)
A Model of Embodied Technical Change and Employment JOHN A. CLARK
ABSTRACT A “vintage” framework is described for studying the effects of technical change on economic development, particular attention being given to the level of employment. The framework is based on the notion that investment in new techniques is a major mechanism through which improvements in productivity are obtained. With the specification of demand and investment functions, a simple dynamic model is developed by means of which the effects of both continuous and discontinuous technical changes can be investigated, under various assumptions regarding the response of other economic variables to such changes. It is shown that a variety of behavioral characteristics are produced when technical change does not occur smoothly; in particular, it is suggested that variations in rates of technical change may act as a determinant of fluctuations in other economic variables.
Introduction The purpose of this article is to attempt to examine some of the economic effects of technical change, in particular its effect on employment. The choice of employment as an important topic for study in the current economic situation needs little justification; unemployment in Organization for Economic Cooperation and Development (OECD) countries is by any standards unacceptably high, and with the failure of conventional remedies there is increasing concern that the current situation is here to stay. Further, there is increasing interest in the possibility that technology may be an important influence in ameliorating or exacerbating the problem. The processes determining the rate and direction of technical change are, of course, poorly understood. As a result, technology is often incorporated in a very simple way in dynamic economic models, for example, as a time-dependent multiplier in a production function or, in econometric models, by trend terms representing extrapolations of past productivity patterns. Such treatment obscures some essential characteristics of technical change which, if incorporated, might be expected to suggest that this variable has more influence on the pattern of economic development than is often attributed to it. It is not suggested that technical change is the only factor of importance in the process of economic evolution. But it is clearly embedded in this process in many ways. What is argued here is that it should be regarded as an important, and frequently underestimated, component in the sequence of events which determine whether the economic
JOHN A. CLARK is a Fellow with the Science Policy Research Brighton, Sussex, England. @ Elsevier North Holland,
Inc., 1980
Unit, University
of Sussex,
Falmer,
0040-1625/80/01004719$02.25
JOHN A. CLARK
48
climate is good or bad. The degree to which technical change, investment, wages, demand, and other factors adapt to one another to yield harmonious (or unbalanced) economic development is of first importance. The model described later in this article is concerned principally with this question of adaptation. It is far less complex than national econometric models, simplicity carrying the major advantage that results can more readily be understood and interpreted. The model. represents only a single sector, so that Government policy instruments, for example, are not explicitly represented. The purpose is to examine the effects of technical change under various assumptions regarding demand and investment responses, whether these responses are prompted by Government stimuli or otherwise. The sector to which the concepts used in the model are most applicable is manufacturing, and the discussion will be carried out with that sector in mind. The question then arises of whether it is permissible to draw any conclusions from this about the behavior of the entire economy. While any such extension must necessarily be somewhat tentative, there is a good deal of evidence to suggest that the health of the manufacturing sector in industrialized countries is indicative of the well-being of the economy as a whole. Cornwall [I] cites several studies of postwar market economies in which the rate of growth of total output shows a high correlation with the rate of growth of manufacturing output. Further, the historical evidence quoted implies that when overall output is growing relatively rapidly, manufacturing output is growingrnore rapidly; conversely, slow overall growth is associated with even slower growth in manufacturing. This implies that manreflection of the level ufacturing acts as an “engine of growth," providing an exaggerated of overall economic activity. This behavior can be explained by the strong linkages which exist between manufacturing and other sectors of the economy. In the next section, the basic approach used to represent technical change is described. This is followed by a description of the model and the results obtained from it. Finally
the conclusions
of the analysis
are presented.
The Vintage Approach About twenty years ago. the idea of representing technical change as being related to successive generations, or “vintages,” of capital equipment, was proposed by Salter and others. A fundamental notion behind this approach is that a very important component of in, plant and equipment. Technitechnical change is that associated with, or “embodied” cal progress is linked very directly with the process of capital accumulation; each successive investment decision may involve the purchase of equipment of a type qualitatively different (presumably more productive) than those already in use, and hence any gross investment (even if purely to replace existing equipment) tends to raise productivity. This framework permits a representation of depreciation and the concept of an economic (as opposed to a physical) lifetime of capital goods. A plausible and widely used criterion for determining this lifetime is that equipment of a particular vintage becomes obsolete when its running costs exceed the running plus capital costs of the latest vintage. The emphasis, then, is on the factors determining the speed at which new techniques are absorbed into the production system. on the importance of the investment process in raising productivity, and on the fact that overall efficiency depends on the history of technical change, investment, etc. For example, for a given trend in “best practice” labor productivity, such as that shown in Figure I, there corresponds, at any point in time, a certain structure to the productivity of the capital stock, such as that shown in Figure 2 (these diagrams are similar to those presented by Salter [2].)
TECHNICAL
CHANGE
49
AND EMPLOYMENT c
labour/output ratio = 1 productivity
Fig. 1.
Each block in Figure 2 refers to capital of a particular vintage, associated with which is a particular labor productivity. The contribution to output of each vintage depends on past investment patterns. Over time, new blocks are added to the right-hand side of the diagram, those on the left-hand side disappearing as they become obsolete. Early economic models incorporating these or similar ideas (e.g., Solow [3], Kaldor and Mirrlees [4]) generally did not examine the question of unemployment, which was scarcely an issue at that time. In the Kaldor and Mirrlees model, for example, full employment is an explicit assumption, output being determined by the number of workers available to man each successive vintage. More recently, however, the vintage approach has been applied to the employment issue (e.g., Isard [51, van den Beld [61). Salter [l] discusses at some length the influences expected to govern both bestpractice productivity movements and the delay in the use of new techniques, but does not formalize his approach into a dynamic model. He presents data suggesting, among other things, that in the United Kingdom during the second quarter of this century very different rates of output per man between industries were recorded, but these were not reflected in significant differences in rates of increase of earnings per employee between industries; that “where little new equipment was installed output per man hour rose very little or even fell,” supporting the thesis that embodied technical change is of first importance; and that, in many industries, the difference in best-practice and average-practice labor productivity was very great, suggesting that delays in application of new methods can be very significant. The “vintage” formalism describes the process of diffusion of new techniques into the economic system, but not the generation of innovations. Hence, as Hahn and Matthews [7] point out: “The vintage approach does not as such involve necessarily any departure from the assumption that technical progress takes place at an externally even rate. The difference from the orthodox approach is merely that now the manna of technical progress falls only on the latest machines. This is not such a fundamental difference, so it
SO
JOHN
A.
CLARK
labour/outpu rat10
l
industry
average
t current
C
‘best’
L
technique
aVallabll?
output
Fig. 2.
is not surprising that vintage models can be made to yield results quite like orthodox ones.” In considering situations of steady-state growth, this observation is a fair one. While it is useful in providing a mechanism for determining the lifetime of machines and avoiding some of the problems of measuring aggregate capital, a vintage model in equilibrium seems unlikely to yield significantly more information than its conventional counterpart. If the rate of increase in “best practice” productivity is constant, the rate of increase of average productivity will be the same constant in equilibrium, and either factor may be regarded as providing the exogenous rate of technical progress. The main advantage of the method would therefore seem to lie in its ability to interpret the effects of discontinuous changes in rates of innovation. The mechanism of diffusion implicit within the framework then permits study of how such changes may be transmitted, and their implications for growth, employment, and other economic indicators. There is every reason to believe that rates of innovation are far from smooth. Schumpeter [8, 101 argued that radical technologies appeared every fifty years or so, and that these technologies were responsible for the long cycles in growth, prices, and employment suggested by Kondratiev [9]. l Freeman [ 1 1] has articulated Schumpeter’s ideas and extended them by suggesting that electronics-based technologies were to a great extent responsible for the boom following the Second World War, and the subsequent (current) recession.” Empirical work by Mensch [ 121 lends strong support to the notion of
’ Schumpeter steam
power. ‘Freeman
R and
D
technology relatively
suggested
the second [I I] argues
activity, thus
with ha5
specialized
that the first
(1843-1897) that a period
new
products
a significant sectors.
Later,
Kondratiev
with
cycle
railways.
of expansion having
positive however,
(1787-I
842)
and the third
with
is one in which
on the
it begins
economy.
to diffuse
power
the technology effect
a “demand-creating”
impact
was associated electric
but
and
at this
out to other
with
the introduction
and automobiles
leads
to a “bandwagon”
generating stage
economic
18,
employment.
of IO]. of The
is still
localized
within
wctors.
leading
in many
TECHNICAL
CHANGE
AND EMPLOYMENT
51
16161412106-
0.,
,
1740 60
Fig. 3. “Bunching”
I 1600
I 1650
of basic innovations
I 1900
I 1950
(reproduced from Mensch [121).
temporal “bunching” of innovations. Figure 3, reproduced from Mensch’s paper, implies a highly discontinuous occurrance of “basic” innovations, and it is noteworthy that the peaks in this figure are separated by a time span corresponding closely to that of a Kondratiev cycle. Mensch explicitly puts forward the proposition that the level of unemployment now being experienced is a direct consequence of the dearth of postwar radical innovations. In the next section of this paper a vintage model is proposed which allows for arbitrary changes in best-practice productivity (e.g., “radical,” or “incremental”) and in which full employment is not assumed. The model proposed is based on particular assumptions and has certain limitations which are common to this type of analysis. These limitations are discussed in detail by Salter [2] and Driehuis [ 131 and some are referred to in the description of the model. One obvious and important point is that not all technical change is embodied in plant and machinery-improvements in management technique and worker skills are examples of disembodied technical change. An attempt to assess the relative importance of the embodied and disembodied components of technical change is difficult, and such attempts have produced contradictory results. The distinction often appears very difficult to appreciate even conceptually. A change from the use of sickles to combine harvesters, for example, may appear to be a clear case of embodied technical change, except that a combine is useless unless someone has acquired the ability to operate it. It is assumed here that the skills required to operate any given machinery are available, and that disembodied progress involves an improvement over time in the efficiency with which the machinery is operated (by, for example, work study or “learning by doing”). Then it is argued that, in the majority of industries, over a time span of (say) a few decades, the disembodied component of technical change would be relatively small. No amount of acquired dexterity in using a sickle would allow one to compete with a combine. The importance of this limitation of the method, and the others mentioned above, is clearly dependent on industrial structure and on the sociopolitical environment in the country under consideration. Some of the more unrealistic assumptions may be relaxed, either within the model or in interpreting the results. With models of this type, the cases to radical changes in the means of production; this is a period characterized by “process” rather than “product” innovation. The period of recession begins; labor is displaced, competing industries producing equipment under the older processes decline, and stagnation results. On this view, the conflicting tendencies of labor absorption (through capital accumulation) and labor displacement operate in such a way that each is alternately predominant.
52
JOHN
A. CLARK
criterion for usefulness is whether new insights can be gained, either directly or indirectly, about certain aspects of the behavior of real economies.
The Model The variables introduced below represent aggregates over manufacturing industry. Let K, be the quantity of capital goods purchased during a year T, and let h, be the corresponding capital/output ratio. It is assumed that this capital retains constant efficiency during its service life; at any later time t, it is either fully operational or totally out of use, depending on whether the scrapping (profitability) criterion given below is satisfied. Thus at time t the output from this vintage is
Q(t,T)
K, -h s,(t)
=
(1)
T
where S,(t)
= 0 or K T. Then total output at time t is
Q(t) = T Q(t,T).
(2)
The labor required to produce this output is found by multiplying vintage by its corresponding labor/output ratio a T:
the contribution
of each
L(t) = $ Q(t,T) 0,
(3)
where it is assumed that, as with the capital/output ratio, the a ~ associated with a particular vintage remains constant. Although not a necessary assumption in this formulation, it is adopted here by virtue of its simplicity and the fact that, as argued previously, learning effects and other factors tending to change u, might be expected to be of secondary importance over long time periods and at relatively aggregate levels.:’ If P(t) and w(t), respectively, denote the price of one unit of output and the wage rate at time t, let diD
= :(6/w)
(4)
where w = w(t)/P(t) and D is demand. Then z gives the fractional increase in demand per unit fractional increase in w(t)lP(t). z is taken to be constant and, like w, is given exogenously; that wages are not determined internally to any particular sector follows Salter’s [2] observation of a lack of correlation between differences in wage rates and different rates of productivity growth between industries. Wage rates appear to be determined mainly by factors outside any given sector.” Solution of eq. (4) gives D(t)
= a [
“As Kaldor generation increased ‘An
w(t) p(t) 1
~
and Minks
of machinery maintenance alternative
[4] point out, the assumption
can be interpreted requirements
assumption
(5)
as implying
as the equipment
in which
wages
ages,
that the labor coefficient that increased leave overall
are determined
efficiency
0, is fixed for a particular acquired
labor efficiency
endogenously
is tested
through
use,
unchanged. in the next section.
and
TECHNICAL
53
CHANGE AND EMPLOYMENT
where (Yis a constant. Assuming that all output that can be profitably produced is immediately consumed, D(t) and Q(t) can be equated to yield the price P(t)
= w(t)
7
[ QL I'
(6)
and cr can be chosen to specify the initial price level. As with wages, it is assumed that the price of capital equipment Pk (t) is determined exogenously; writing P(t) as the sum of wage costs and profits when using the most recent generation of machinery, P(t) = a(t)w(t)
+ b(r)P,(t)r(r)
(7)
enables the rate of profit r(r) on the latest machine to be found given labor and capital output ratios U.(T = I) = a(t) and h,(r = t) = b(t), w(t) and P,<(t). Now, since at any given time P(t) and w(t) are the same for all vintages, it is clear that if wages are rising more quickly than prices (to be expected if a(t) is falling) there will come a time when, for a vintage T, P(t) s a,w(t)
(8)
at which point machines of vintage r and older are no longer able to produce at a profit, and are written off (the second term on the right-hand side of eq. (7) becomes negative). For all vintages satisfying this criterion at a given time t, S,(t) = K, in eq. (1). Several authors have pointed out that this treatment is analogous to Ricardian theory of rent on land. Capital of vintage r commands a “quasi-rent” r,(t) at any time t, which in general decreases with time. To quote Salter [2]: Capital goods in existence are equally as much a part of the economic environment as land or other natural resources. Both are gifts: natural resources are the gift of nature, capital goods are gifts of the past. The fertility of land corresponds to the level of technical knowledge embodied in capital equipment in both cases the margin of use is determined by the ability to show a surplus or rent; no-rent land corresponds to capital equipment that has just been abandoned.
Alternative scrapping criteria can be derived [ 13, 141, but the above fits easily into the current formulation. The simplifications incorporated in the analysis include an assumption of competitive markets (so that, for example, price regulations cannot be used to preserve the profitability of equipment), a neglect of the scrap value of obsolete equipment, and an association of a single “average” scrapping date with heterogeneous industrial systems. In the model, it is assumed that, provided markets are available, obsolete machinery is immediately replaced by capital of the latest vintage of equal productive capacity. In addition, some net investment I occurs, the magnitude of this depending on the “best practice” rate of profit and gross sector product, as follows:
f(t) = W(f)
[r(t)lr,,]*
(9)
where j3, r,,, and 6 are constants, and G(t) = P(t)Q(t). The gross (replacement plus net) investment so calculated gives the capital of latest vintage acquired, which enters eq. (1) in the next time step as a contribution to output. This completes the basic structure of the model. A number of interesting additional quantities can, however, be calculated from the results, for example, average productivity
54
JOHN A. CLARK
(to be compared with best-practice productivity), the average age of vintages in use and the age of the oldest surviving vintage. Since the purpose of this work is to consider in a general way the influence of technical change, no attempt is made here to calibrate the model. Several authors have pointed out that models of this kind are in general extremely difficult to estimate, and where attempts have been made in this direction account has generally not been taken of variations in the rate of technical change which is of prime interest for the purpose of this paper. It may well be useful however to consider the specific technical changes occurring within a given sector-especially one in which clear generations of techniques can be identified-and examine their implications via a vintage framework, as a tool for assessing the impact of particular technologies. The work of Simmonds [ 151 and Martin0 and Conver [16] lends support to this proposal. This idea will be examined further in later work; for current purposes a more macroscopic view is being taken.
Computer Implementation and Results Settling initial conditions for the model creates a slight problem in that it is not appropriate to allocate a quantity of capital in the base year to which much smaller incremental net additions are made via the net investment mechanism in subsequent years, since when the productivity associated with the initial block of capital satisfies the scrapping criterion it will become obsolete “en bloc,” creating unwanted discontinuities. To circumvent this problem annual investment (all of which is net of depreciation) is assumed to be constant for the first 15 years to build up a “history” of vintages. Also during this period the quantity LYin eq. (6) is set equal to Q/w to ensure that, with the elasticity z set equal to unity, P remains constant (and equal to unity). The end of this period is thus to be regarded as the start of the run, during which (Yretains a constant value and the net investment equation and the scrapping mechanism given in the previous section are in operation. The values of the other constants in the model were chosen as follows: Pk = 1, p = 0.06, r, = 0.1. With these values and with best-practice labor productivity Pa and wages w both increasing at 2% per annum, and with a constant capital/output ratio b of 3, the price P remained close to unity and the best-practice rate of profit close to 0.1. Such input data yielded apparently realistic values in other output variables; for example the lifetime of machines is about 18 years, and the ratio of best-practice to average labor productivity (pa/p) is about 1.2. Details are given below of the behavior of the model under various alternative assumptions.
SMOOTH CONTINUOUS
TECHNICAL
CHANGE
In the case of smooth variations in labor productivity and wages, some results can be derived immediately from the equations in the previous section. Following van den Beld [6], an expression can be derived for the time of introduction of the oldest machine still in use. From eq. (8), if machines purchased in year r are at the margin of obsolescence in year 1, P(t) = u(T)w(t). Thus if U(T) = a,,e- O7and w(t) = w,,e m’ where 19and 4 give the rates at growth of best-practice productivity and wages respectively, then In P(t) = In a,, + In w,, - BT + 4t
(10)
TECHNICAL
CHANGE
5.5
AND EMPLOYMENT
and 7 = [In a0 + In wO - In P(t) + @l/O. If price P(t) is constant (= P,,), then the age of the oldest surviving
(11) vintage of machinery
is
(12) Thus if wages are increasing more rapidly than best-practice productivity (4 > O), the lifetime of machinery declines over time; the quasi-rent on any given vintage of equipment is more quickly reduced to zero. If 4 = 8, the steady-state lifetime depends on this rate of growth and the share of income received by labor. Changes in employment in the model result from the net effect of the reduction in labor demand resulting from the replacement of obsolete machines by more labor-efficient new machines, and the increase in labor demand brought about by net investment in the latter. If 4 = 19,these effects cancel and employment remains constant. The model then describes an equilibrium growth path in which output increases at a steady rate 8. Computer runs with steady growth in wages and best-practice productivity gave the following effects. 1. Raising the demand elasticity z increases prices, employment, the rate of profit, and the lifetime of capital goods. This corresponds to a “demand-led boom.” 2. An increasing capital productivity (i.e., a declining capital/output ratio b) increases employment and output while reducing prices, the rate of profit and capital-good lifetime. In this case more output is obtained for a given net investment (thus increasing employment) and, from eq. (6), prices fall, and hence [eq. (7)] r(t) declines. The magnitude of these effects is reduced if a higher value of 6 in eq. (9) is chosen, i.e., if net investment is more responsive to fluctuations in r. 3. A declining price of capital goods leads to a lower output price and [from eq. (12)] a more rapid turnover of the capital stock. The next step is to consider the effects of modifying some of the assumptions and to consider, in particular, discontinuous technical change. DISCONTINUOUS
TECHNICAL
made above
CHANGE
In this section it will be assumed for convenience that the capital/output ratio is constant. The influence on employment and other model variables of stochastic fluctuations in best-practice labor productivity will be examined. In the absence of directly available empirical evidence on the extent of such fluctuations, recourse is made here to “plausibility” arguments and the fact that alternatives are examined to determine the importance of the particular assumptions made. A major purpose of this study is to examine whether, in terms of the model described above, variutions in best-practice productivity pa (which can be interpreted as variations in rates of innovation) are likely to be significant in changing employment levels; or, altematively, whether such variations may be “smoothed out” in the diffusion process, so that they may be ignored for present purposes and only overall trends considered. Three separate probability distributions are considered. These are shown in Table 1. In the first, the percentage change in any year may take any integer value from zero to 4, each of these five values being assigned equal probabilities. The second distribution is
56
JOHN
A. CLARK
broader and “skewed,” with a small probability of a large (19%) change; this distribution also includes the possibility of a negative (- 1%) improvement in productivity.” The third distribution consists of just two points; a high probability of a 1% (incremental) improvement, and a low probability of a very high (50%) improvement. In each of these distributions, the expectation (or “average”) value is 2%. In the simulations carried out, sampling takes place from these distributions using a pseudorandom-number generating package due to Neave [ 191. Each successive vintage of machinery is assigned the value of labor productivity resulting from amending that associated with the previous vintage by the randomly selected percentage change. Figure 4 shows the pattern of employment over an 85 year period for each of four different sequences of random numbers, using in each case the probability distribution of Table la. Employment is presented as a percentage deviation from the steady-state value obtained with a continuous increase in best-practice productivity of 2%; the dots in Figure 4a show the values obtained from a computer run with a steady increase of 2%, which indicate that the equilibrium value is not immediately attained; this is due to the presence of initial transient effects which decay with time. However, it is clear that the use of variable rates of innovation has induced substantial variations in employment. Figure 5 shows corresponding results obtained using distribution b in Table 1. As might be expected, this broader distribution gives rise to more extreme fluctuations in employment.
Fig. 4. Deviations in the level of employment tribution of Table la.
5Owing, the scrapping by Nelson
for example, mechanism,
and Winter
has been subject
value using the probability
to miscalculation of labor requirements. Such machinery will become before its immediate predecessors. The possibility of such regressions
[ 171;
to them.
from the “equilibrium”
the data of Solow
[ 181
cited by these authors
suggests
dis-
obsolete, via is suggested
that the American
economy
TECHNICAL
CHANGE
57
AND EMPLOYMENT
Fig. 5. Employment
deviations generated by the probability
distribution
of Table lb.
One notable feature of these results is that the curves are not continually crossing the horizontal axis (which represents the steady-state level of employment). If employment is at any time above (or below) “par, ” it appears probable that it will stay that way for some time in the future. This result derives from the features of random processes and the fact that it is the annual change in productivity which is assumed subject to random variations, best-practice productivity P,~ at any time reflecting the cumulative effect of such variations. In such a situation it can be shown that it is probable that P,~ will remain above (or below) the value expected on the basis of continuous change for some considerable time. This is illustrated by the fact that in the computer run on which Figure 4d is based, pa remains below the values obtained assuming continuous 2% growth for the entire period; even in the less extreme case of Figure 4a, it is consistently below the continuous-growth values for over 3/4 of the period. The statistical basis of this effect is discussed by Feller [20] and cited by David [21].6 The analysis of the section on Smooth Continuous Technical Change suggested that the relationship between wages and productivity has an important bearing on model “David comments as follows: “. anintriguing pair of theorems by William Feller. show that it is not at all unlikely that in a long coin-tossing experiment the cumulative number of heads (or tails) will hold the lead for practically the entire sequence of (2n) trials. Indeed, If n is large it can be computed that with a 0.20 probability heads (or tails) will be in the lead for 97.6% of the epochs!”
58
JOHN A. CLARK
TABLE 1 Probability Distributions for the Percentage Change in Best-Practice Productivity (For each distribution the expection value E(X) = X H’(X) = 2%) Percentage Increase in Best-PracticeProductivity X
Probability P(X)
(I 0
0.2 0.2 0.2 0.2 0.2
1
2 3 4 X
P(X) h
0.115 0.15 0.2 0.2 0.15 0.1
-1 0
0.05 0.025 0.01 c X
P(X) I
50
0.97959 0.02041
behavior. The results presented in Figures 4 and 5 incorporate the assumption that despite the extended deviations of pu discussed above, wages remain on a smooth 2% per annum growth path. As stated previously, this is not unreasonable given that a single sector is under consideration, and overall wage levels may be regarded as determined by factors in the economy as a whole. However, to consider the effects of this assumption of extreme wage rigidity, it was replaced by an assumption of extreme flexibility; the annual change in wages was set equal to the annual change in average productivity, i.e., an immediate response in wages to a change in the average state of technology. Figures 6a and 6b show results corresponding respectively to those of Figures 4a and 4b, i.e., the same frequency distribution and the same respective sequences of random numbers, were used. Thus the evolution of best-practice productivity used for Figure 6a is the same as that used for Figure 4a and similarly for Figures 6b and 4b. Although the amended assumption regarding wages clearly causes changes in detail, it does not appear to qualitatively change the nature or extent of the fluctuations in employment. Thus it appears to be a feature of the model that, despite the diffusion mechanism incorporated, fluctuations in rates of innovation are not damped out as the new techniques become absorbed into the economic system.
TECHNICAL CHANGE AND EMPLOYMENT
59
1
Fig. 6. Employment
deviations derived from Table la using alternative wages assumption.
Figure 7 shows a result obtained using the distribution shown in Table lc. In this particular example the higher change in productivity occurs just once in the period covered-curve 2 of Figure 7b illustrates the single step-function change in productivity. Figure 7a shows a dramatic decline in employment, but also, more interestingly, lesser declines some thirty and fifty years later, after recovery has taken place. Curve 4 in Figure 7b shows that average productivity responds rapidly to the sudden increase in best-practice productivity, and approaches it closely. This is because many earlier vintages of equipment suddenly became obsolete; the age of the oldest surviving machinery thus becomes very low, and the gap between average and best-practice becomes comparatively small. As pB resumes its slow continuous trend, average productivity p diverges from bestpractice; all functioning machinery is now of vintages subsequent to the date of the sudden productivity increase and no obsolescence occurs for some time. Eventually, however, the large quantity of equipment purchased at the time of the sudden increase (to replace the large quantity that became obsolete because of this increase) itself becomes obsolete; its replacement by new equipment causes a rapid increase in average productivity which gives rise to the indicated “secondary” decline in employment. Tinbergen and Polak [22] have pointed out that a specific attempt has been made by de Woolf [23] to explain the Kondratiev waves explicitly in terms of rebound effects of the type observed in the model. He argues that certain durable capital goods have a lifetime of
JOHN A. CLARK
60
Fig. 7. a. Employment deviation generated by the probability distribution of Table lc. b. Corresponding productivity movements compared with those obtained with steady growth: 1. best-practice productivity with continuous increase in pa; 2. best-practice productivity with step-function increase in pa; 3. average productivity with continuous increase in pa; 4. average productivity with stepfunction increase in pH.
about forty years,
and that the long waves
are reflections
of reinvestment
waves
of such
goods. In the model, cyclic effects become clearer if the not unreasonable assumption is added that if a particular change in pe is above (or below) the “average” (expectation) value, it is more likely than not that the succeeding change will also be above (or below) average. The sequence of changes then becomes a Markov chain. In the experiments carried out the possible values of the change in plr were taken to be the same as those in Table la (i.e., OS-4% per annum), the probabilities being derived from the transition matrix shown in Table 2. In this matrix any element Pii (i, j = 0, ,4) represents the probability that a given change 6p,, in pIS will be i%, given that the previous change was j%. Thus, if in a particular year the change is I%, the second column of the table indicates that in the following year the change is 0% with probability of 0.3, 17~ with probability 0.6, and 2% with probability of 0.2. Again the overall expectation value is 2%. This is an attempt to represent the possibility of bunching of innovations referred to in the section on the Vintage Approach. Figure 8 shows the evolution of employment using this matrix of conditional probabilities; the sequence of random numbers used in a and b are, respectively, the same sequences used in Figures 4a and 4b. The conditional probabilities make more probable and “small” productivity changes. The graphs than before strings of relatively “large” presented in Figure 8 suggest a clearer cyclic structure to employment. The initial decline and subsequent rise in employment in Figure 8a coincides roughly with periods in which &I,, is above and below its expectation value. The sharp decline in employment at point A occurs because equipment purchased in the period of lowlabor productivity growth becomes obsolete “en bloc”; these vintages have associated
TECHNICAL
CHANGE
AND EMPLOYMENT
61
TABLE 2 Conditional 0.6 0.2 0 0 0
0.3 0.6 0.2 0 0
0.1 0.2 0.6 0.2 0.1
Probability
Matrix 0
0
0 0.2 0.6 0.3
0 0 0.2 0.6
requirements very similar to one another, and hence from the scrapping criterion are scrapped at the same time, or in very rapid succession. This “bunching” of retirements gives rise to a corresponding bunching of replacement investment. Despite the fact that 6p, remains at a high level, there is a further rapid decline in employment at point B as this replacement investment becomes obsolete and is itself replaced “en bloc” by more productive equipment. The decline in employment at point C is similarly explained. As observed in Figure 7, “rebound” effects occur which do not, in this case, appear to be rapidly damped out. The above examples are based on the assumption that investment behavior is related to technical change through the rate of profit r [eq. (9)]. Relatively rapid productivity
Fig. 8. Employment
deviations using conditional
probability
matrix.
62
JOHN A. CLARK
changes tend to increase r, and hence to lead to higher investment and faster growth. But the availability of “radical” innovations might be expected to have a more direct influence on investment products for which
behavior, particularly if they encompass the development of new large markets are expected. Figure 9 illustrates the result of assuming if that p of eq. (9) varies in proportion to the change in p,,, with p = 0 (no net investment) Sp, = 0, and with the same average value as before. Comparing with Figure 8, it can be seen immediately
that fluctuations
in employment
are considerably
less severe,
although
traces of the previous cyclic structure appear to remain. The effect of this modification is that a relatively large change in ps leads to a relatively large change in output as well as in average productivity 6, and hence employment is subject to less dramatic change. However fluctuations are still in evidence, and it would be surprising if this were not so; the evolution of i, for example, depends in a complicated way on the history of productivity change and of obsolescence, which give rise to the particular structure of the capital stock in use at any time, and hence cannot be expected to follow precisely a pattern of incremental output change which is proportional to changes in best-practice productivity. Discussion and Conclusions The following points emerge
from the analysis
of this article:
1. Several researchers have concluded that current high levels of unemployment are caused by excessively high wage levels. Many vintage models, in fact, suggest just this: it is assumed that, because the lifetime of capital goods declines if wages increase more rapidly than productivity [(eq. (12)], employment also declines. However, the current model includes a demand side, through which net investment rises as wages rise. Hence with high wage rates, while the number of surviving vintages is reduced, more capital of any vintage is in operation. Given an overall tendency for wages to keep pace with productivity, the results of the section on Discontinuous Technical Change, suggest that the general results of the model are not sensitive to the precise relationship between these variables. 2. There is reason to believe that there are sharp fluctuations in the rate of generation of innovations; such fluctuations have been suggested from empirical evidence by Mensch [I21 and suggested earlier by Schumpeter [8]. These writers and others.
Fig. 9. Employment
deviations
with a variable investment
coefficient.
TECHNICAL
CHANGE
AND EMPLOYMENT
63
such as Rosenberg [24] and Nelson and Winter [25] also imply an internal momentum in the innovation process. “Natural trajectories,” to use the phrase of the latter authors, are argued to arise from the nature of technological change. A significant innovation, for example, may create new problems and bottlenecks which pave the way for further innovations. The model suggests that variations in rates of innovation, whether such variations are independent (“random walk”) or, as suggested above, nonindependent (the “Markov chain” case), can have a significant influence on employment. While the frequency distributions examined were hypothetical, the general result is that the maintenance of steady employment levels seems to depend on a “fine tuning” of investment activity which could scarcely be expected in the real world. 3. Oscillatory effects in the model occur through two mechanisms. First, the assumption that the rate of technical change is not independent between periods can give rise to cyclical trends in productivity growth which are relected in cyclical patterns in employment. Secondly, the scrapping criterion leads to rebound effects where employment is affected by earlier investment activity. Clearly the interaction of these two effects can produce quite complicated behavior. Both effects indicate that the influence of technical change on employment is essentially a historical process; they imply that it is not possible to ascribe unemployment to the fact that technical change is “too fast” or “too slow” over any particular short period of time, but that a rather long history of technological evolution, and the investment response in particular, needs to be taken into account. The effects of international competition and trade are not considered in the model. Preliminary experiments suggest that the current type of formulation may be very suitable for studying the effects of international competition on employment, particularly in that it captures the process of “induced” technical changes as domestic producers are “forced” to adopt more capital intensive techniques in response to competition from cheap imports. Further work will be carried out to examine this issue. Finally, what of the present unemployment situation in OECD countries? Obviously the actual level of unemployment depends on demographic factors as well as the demandside factors considered here, and the model has not been applied to any particular historical situation. But the implication of this work is that there is no reason to suppose that the current problem is short term, but equally there is no reason to assume that it is permanent. Lewis [26] notes that, historically, economic fluctuations have varied in length and severity, and comments as follows: Two groups of commentatorscontinue to ignore this point. One is the group of US economistsbroughtup on the National Bureau of Economic Research’s reference Kitchin cycles. They expect every recession to be over in eighteen months. and do not realize that it has been normal in the US economy for as many as six years to pass before the curve of production finally races to the next Kuznets peak. The other group are the children of the Apocalypse. Starting with Marx in 1848, every time there has been a recession critics have predicted the imminent collapse of capitalism, just as the early Christians expected the imminent arrival of Judgement Day.
Current technological developments-the microprocessor in particular-seem likely to play a very significant part in worsening or helping to resolve the current unemployment problem, depending on whether the labor-displacing effects are outweighed by
JOHN
64
A. CLARK
increases in labor-absorbing net investment [27]. Should the former effects prove to be predominant, they could be seen as presenting an opportunity (for reduced working hours and more leisure time) rather than the cause of an increasing split in society between those who have a job and those who do not. The latter development is not only highly undesirable in itself, but could lead to considerable problems when demand for labor is restored and there is a considerable proportion of the population which has never worked. In addition to policies designed to stimulate employment therefore, there is every incentive to devise social policies of redistributing the work available, should the need arise. There is a need to understand further the complex relationship between technical change and employment to help guide the formulation of such policies. The work reported Council. Thanks are due Ray, und Dr. R. E. Turner this article, and to Henry
was sponsored by UNITAR und by the U.K. Social Science to Professor Richard R. Nelson, Projessor H. Linstone, Dr. G. and other SPRU colleague.s,for comments on an earlier draji of Lucas jar computer programming advice. Acknowledgment is
also made to Messrs. George Allen Publishing Company,for permission
& Unwin (Publishers) Ltd. and to the North-Holland to reproduce e.xtracts from their publications.
References
I.
Cornwall.
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W.,
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laard,
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1965.
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and
Rev. Econ. Studies 29. June,
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1984: A New Push of Basic Innovatiom’?.
Unemployment,
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S.,
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Vandoome,
England
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Karlon,
1960.
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8. Schumpeter,
I I. Freeman.
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K. J.,
1977.
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10. Kuznets,
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Kondratiev,
Progress,
J. A., A New Model Impacts
C. A.,
to OECD,
Economic
1977.
Cambridge
in the Social Scirwcc~.\ , Stanford,
Methods
N. and Mirrlees,
presented
Robertson,
and Technical
P.. Employment
Rm.
Martin
Producfiviryund Tec~hnicul Chunge,
2. Salter,
Change
and the Aggregate
Number
of Geography.
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to Prohahility
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David,
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/mowtim
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( 1975).
TECHNICAL
CHANGE
65
AND EMPLOYMENT
22. Tinbergen, J. and Polak, J. J., The Dynamics oj’Business Cycles, Routledge (1950). 23. de Woolf, S., Het Economisch Getij, Emmering, Amsterdam (1929). 24. Rosenberg,
Change: Inducement Mechanisms and Focusing Devices, in University of Chicago Press, Chicago (1969). 25. Nelson, R. and Winter, S., In Search of a Useful Theory of Innovation, Research Policy 6, 3676 (1977). 26. Lewis, W. A., Growrh and Fluctuations 1870-1913, George Allen and Unwin, London (1978). 27. Freeman, C., Technical Change, Employment and Unemployment (unpublished 1978). Economic
N., The Direction of Technological
and Kegan Paul, London
Development
Received 22 September
1978;
md Cultural Change
revised 15 Januury
1979
FORECASTING
AND SOCIAL CHANGE
16.47-65
(1980)
A Model of Embodied Technical Change and Employment JOHN A. CLARK
ABSTRACT A “vintage” framework is described for studying the effects of technical change on economic development, particular attention being given to the level of employment. The framework is based on the notion that investment in new techniques is a major mechanism through which improvements in productivity are obtained. With the specification of demand and investment functions, a simple dynamic model is developed by means of which the effects of both continuous and discontinuous technical changes can be investigated, under various assumptions regarding the response of other economic variables to such changes. It is shown that a variety of behavioral characteristics are produced when technical change does not occur smoothly; in particular, it is suggested that variations in rates of technical change may act as a determinant of fluctuations in other economic variables.
Introduction The purpose of this article is to attempt to examine some of the economic effects of technical change, in particular its effect on employment. The choice of employment as an important topic for study in the current economic situation needs little justification; unemployment in Organization for Economic Cooperation and Development (OECD) countries is by any standards unacceptably high, and with the failure of conventional remedies there is increasing concern that the current situation is here to stay. Further, there is increasing interest in the possibility that technology may be an important influence in ameliorating or exacerbating the problem. The processes determining the rate and direction of technical change are, of course, poorly understood. As a result, technology is often incorporated in a very simple way in dynamic economic models, for example, as a time-dependent multiplier in a production function or, in econometric models, by trend terms representing extrapolations of past productivity patterns. Such treatment obscures some essential characteristics of technical change which, if incorporated, might be expected to suggest that this variable has more influence on the pattern of economic development than is often attributed to it. It is not suggested that technical change is the only factor of importance in the process of economic evolution. But it is clearly embedded in this process in many ways. What is argued here is that it should be regarded as an important, and frequently underestimated, component in the sequence of events which determine whether the economic
JOHN A. CLARK is a Fellow with the Science Policy Research Brighton, Sussex, England. @ Elsevier North Holland,
Inc., 1980
Unit, University
of Sussex,
Falmer,
0040-1625/80/01004719$02.25
JOHN A. CLARK
48
climate is good or bad. The degree to which technical change, investment, wages, demand, and other factors adapt to one another to yield harmonious (or unbalanced) economic development is of first importance. The model described later in this article is concerned principally with this question of adaptation. It is far less complex than national econometric models, simplicity carrying the major advantage that results can more readily be understood and interpreted. The model. represents only a single sector, so that Government policy instruments, for example, are not explicitly represented. The purpose is to examine the effects of technical change under various assumptions regarding demand and investment responses, whether these responses are prompted by Government stimuli or otherwise. The sector to which the concepts used in the model are most applicable is manufacturing, and the discussion will be carried out with that sector in mind. The question then arises of whether it is permissible to draw any conclusions from this about the behavior of the entire economy. While any such extension must necessarily be somewhat tentative, there is a good deal of evidence to suggest that the health of the manufacturing sector in industrialized countries is indicative of the well-being of the economy as a whole. Cornwall [I] cites several studies of postwar market economies in which the rate of growth of total output shows a high correlation with the rate of growth of manufacturing output. Further, the historical evidence quoted implies that when overall output is growing relatively rapidly, manufacturing output is growingrnore rapidly; conversely, slow overall growth is associated with even slower growth in manufacturing. This implies that manreflection of the level ufacturing acts as an “engine of growth," providing an exaggerated of overall economic activity. This behavior can be explained by the strong linkages which exist between manufacturing and other sectors of the economy. In the next section, the basic approach used to represent technical change is described. This is followed by a description of the model and the results obtained from it. Finally
the conclusions
of the analysis
are presented.
The Vintage Approach About twenty years ago. the idea of representing technical change as being related to successive generations, or “vintages,” of capital equipment, was proposed by Salter and others. A fundamental notion behind this approach is that a very important component of in, plant and equipment. Technitechnical change is that associated with, or “embodied” cal progress is linked very directly with the process of capital accumulation; each successive investment decision may involve the purchase of equipment of a type qualitatively different (presumably more productive) than those already in use, and hence any gross investment (even if purely to replace existing equipment) tends to raise productivity. This framework permits a representation of depreciation and the concept of an economic (as opposed to a physical) lifetime of capital goods. A plausible and widely used criterion for determining this lifetime is that equipment of a particular vintage becomes obsolete when its running costs exceed the running plus capital costs of the latest vintage. The emphasis, then, is on the factors determining the speed at which new techniques are absorbed into the production system. on the importance of the investment process in raising productivity, and on the fact that overall efficiency depends on the history of technical change, investment, etc. For example, for a given trend in “best practice” labor productivity, such as that shown in Figure I, there corresponds, at any point in time, a certain structure to the productivity of the capital stock, such as that shown in Figure 2 (these diagrams are similar to those presented by Salter [2].)
TECHNICAL
CHANGE
49
AND EMPLOYMENT c
labour/output ratio = 1 productivity
Fig. 1.
Each block in Figure 2 refers to capital of a particular vintage, associated with which is a particular labor productivity. The contribution to output of each vintage depends on past investment patterns. Over time, new blocks are added to the right-hand side of the diagram, those on the left-hand side disappearing as they become obsolete. Early economic models incorporating these or similar ideas (e.g., Solow [3], Kaldor and Mirrlees [4]) generally did not examine the question of unemployment, which was scarcely an issue at that time. In the Kaldor and Mirrlees model, for example, full employment is an explicit assumption, output being determined by the number of workers available to man each successive vintage. More recently, however, the vintage approach has been applied to the employment issue (e.g., Isard [51, van den Beld [61). Salter [l] discusses at some length the influences expected to govern both bestpractice productivity movements and the delay in the use of new techniques, but does not formalize his approach into a dynamic model. He presents data suggesting, among other things, that in the United Kingdom during the second quarter of this century very different rates of output per man between industries were recorded, but these were not reflected in significant differences in rates of increase of earnings per employee between industries; that “where little new equipment was installed output per man hour rose very little or even fell,” supporting the thesis that embodied technical change is of first importance; and that, in many industries, the difference in best-practice and average-practice labor productivity was very great, suggesting that delays in application of new methods can be very significant. The “vintage” formalism describes the process of diffusion of new techniques into the economic system, but not the generation of innovations. Hence, as Hahn and Matthews [7] point out: “The vintage approach does not as such involve necessarily any departure from the assumption that technical progress takes place at an externally even rate. The difference from the orthodox approach is merely that now the manna of technical progress falls only on the latest machines. This is not such a fundamental difference, so it
SO
JOHN
A.
CLARK
labour/outpu rat10
l
industry
average
t current
C
‘best’
L
technique
aVallabll?
output
Fig. 2.
is not surprising that vintage models can be made to yield results quite like orthodox ones.” In considering situations of steady-state growth, this observation is a fair one. While it is useful in providing a mechanism for determining the lifetime of machines and avoiding some of the problems of measuring aggregate capital, a vintage model in equilibrium seems unlikely to yield significantly more information than its conventional counterpart. If the rate of increase in “best practice” productivity is constant, the rate of increase of average productivity will be the same constant in equilibrium, and either factor may be regarded as providing the exogenous rate of technical progress. The main advantage of the method would therefore seem to lie in its ability to interpret the effects of discontinuous changes in rates of innovation. The mechanism of diffusion implicit within the framework then permits study of how such changes may be transmitted, and their implications for growth, employment, and other economic indicators. There is every reason to believe that rates of innovation are far from smooth. Schumpeter [8, 101 argued that radical technologies appeared every fifty years or so, and that these technologies were responsible for the long cycles in growth, prices, and employment suggested by Kondratiev [9]. l Freeman [ 1 1] has articulated Schumpeter’s ideas and extended them by suggesting that electronics-based technologies were to a great extent responsible for the boom following the Second World War, and the subsequent (current) recession.” Empirical work by Mensch [ 121 lends strong support to the notion of
’ Schumpeter steam
power. ‘Freeman
R and
D
technology relatively
suggested
the second [I I] argues
activity, thus
with ha5
specialized
that the first
(1843-1897) that a period
new
products
a significant sectors.
Later,
Kondratiev
with
cycle
railways.
of expansion having
positive however,
(1787-I
842)
and the third
with
is one in which
on the
it begins
economy.
to diffuse
power
the technology effect
a “demand-creating”
impact
was associated electric
but
and
at this
out to other
with
the introduction
and automobiles
leads
to a “bandwagon”
generating stage
economic
18,
employment.
of IO]. of The
is still
localized
within
wctors.
leading
in many
TECHNICAL
CHANGE
AND EMPLOYMENT
51
16161412106-
0.,
,
1740 60
Fig. 3. “Bunching”
I 1600
I 1650
of basic innovations
I 1900
I 1950
(reproduced from Mensch [121).
temporal “bunching” of innovations. Figure 3, reproduced from Mensch’s paper, implies a highly discontinuous occurrance of “basic” innovations, and it is noteworthy that the peaks in this figure are separated by a time span corresponding closely to that of a Kondratiev cycle. Mensch explicitly puts forward the proposition that the level of unemployment now being experienced is a direct consequence of the dearth of postwar radical innovations. In the next section of this paper a vintage model is proposed which allows for arbitrary changes in best-practice productivity (e.g., “radical,” or “incremental”) and in which full employment is not assumed. The model proposed is based on particular assumptions and has certain limitations which are common to this type of analysis. These limitations are discussed in detail by Salter [2] and Driehuis [ 131 and some are referred to in the description of the model. One obvious and important point is that not all technical change is embodied in plant and machinery-improvements in management technique and worker skills are examples of disembodied technical change. An attempt to assess the relative importance of the embodied and disembodied components of technical change is difficult, and such attempts have produced contradictory results. The distinction often appears very difficult to appreciate even conceptually. A change from the use of sickles to combine harvesters, for example, may appear to be a clear case of embodied technical change, except that a combine is useless unless someone has acquired the ability to operate it. It is assumed here that the skills required to operate any given machinery are available, and that disembodied progress involves an improvement over time in the efficiency with which the machinery is operated (by, for example, work study or “learning by doing”). Then it is argued that, in the majority of industries, over a time span of (say) a few decades, the disembodied component of technical change would be relatively small. No amount of acquired dexterity in using a sickle would allow one to compete with a combine. The importance of this limitation of the method, and the others mentioned above, is clearly dependent on industrial structure and on the sociopolitical environment in the country under consideration. Some of the more unrealistic assumptions may be relaxed, either within the model or in interpreting the results. With models of this type, the cases to radical changes in the means of production; this is a period characterized by “process” rather than “product” innovation. The period of recession begins; labor is displaced, competing industries producing equipment under the older processes decline, and stagnation results. On this view, the conflicting tendencies of labor absorption (through capital accumulation) and labor displacement operate in such a way that each is alternately predominant.
52
JOHN
A. CLARK
criterion for usefulness is whether new insights can be gained, either directly or indirectly, about certain aspects of the behavior of real economies.
The Model The variables introduced below represent aggregates over manufacturing industry. Let K, be the quantity of capital goods purchased during a year T, and let h, be the corresponding capital/output ratio. It is assumed that this capital retains constant efficiency during its service life; at any later time t, it is either fully operational or totally out of use, depending on whether the scrapping (profitability) criterion given below is satisfied. Thus at time t the output from this vintage is
Q(t,T)
K, -h s,(t)
=
(1)
T
where S,(t)
= 0 or K T. Then total output at time t is
Q(t) = T Q(t,T).
(2)
The labor required to produce this output is found by multiplying vintage by its corresponding labor/output ratio a T:
the contribution
of each
L(t) = $ Q(t,T) 0,
(3)
where it is assumed that, as with the capital/output ratio, the a ~ associated with a particular vintage remains constant. Although not a necessary assumption in this formulation, it is adopted here by virtue of its simplicity and the fact that, as argued previously, learning effects and other factors tending to change u, might be expected to be of secondary importance over long time periods and at relatively aggregate levels.:’ If P(t) and w(t), respectively, denote the price of one unit of output and the wage rate at time t, let diD
= :(6/w)
(4)
where w = w(t)/P(t) and D is demand. Then z gives the fractional increase in demand per unit fractional increase in w(t)lP(t). z is taken to be constant and, like w, is given exogenously; that wages are not determined internally to any particular sector follows Salter’s [2] observation of a lack of correlation between differences in wage rates and different rates of productivity growth between industries. Wage rates appear to be determined mainly by factors outside any given sector.” Solution of eq. (4) gives D(t)
= a [
“As Kaldor generation increased ‘An
w(t) p(t) 1
~
and Minks
of machinery maintenance alternative
[4] point out, the assumption
can be interpreted requirements
assumption
(5)
as implying
as the equipment
in which
wages
ages,
that the labor coefficient that increased leave overall
are determined
efficiency
0, is fixed for a particular acquired
labor efficiency
endogenously
is tested
through
use,
unchanged. in the next section.
and
TECHNICAL
53
CHANGE AND EMPLOYMENT
where (Yis a constant. Assuming that all output that can be profitably produced is immediately consumed, D(t) and Q(t) can be equated to yield the price P(t)
= w(t)
7
[ QL I'
(6)
and cr can be chosen to specify the initial price level. As with wages, it is assumed that the price of capital equipment Pk (t) is determined exogenously; writing P(t) as the sum of wage costs and profits when using the most recent generation of machinery, P(t) = a(t)w(t)
+ b(r)P,(t)r(r)
(7)
enables the rate of profit r(r) on the latest machine to be found given labor and capital output ratios U.(T = I) = a(t) and h,(r = t) = b(t), w(t) and P,<(t). Now, since at any given time P(t) and w(t) are the same for all vintages, it is clear that if wages are rising more quickly than prices (to be expected if a(t) is falling) there will come a time when, for a vintage T, P(t) s a,w(t)
(8)
at which point machines of vintage r and older are no longer able to produce at a profit, and are written off (the second term on the right-hand side of eq. (7) becomes negative). For all vintages satisfying this criterion at a given time t, S,(t) = K, in eq. (1). Several authors have pointed out that this treatment is analogous to Ricardian theory of rent on land. Capital of vintage r commands a “quasi-rent” r,(t) at any time t, which in general decreases with time. To quote Salter [2]: Capital goods in existence are equally as much a part of the economic environment as land or other natural resources. Both are gifts: natural resources are the gift of nature, capital goods are gifts of the past. The fertility of land corresponds to the level of technical knowledge embodied in capital equipment in both cases the margin of use is determined by the ability to show a surplus or rent; no-rent land corresponds to capital equipment that has just been abandoned.
Alternative scrapping criteria can be derived [ 13, 141, but the above fits easily into the current formulation. The simplifications incorporated in the analysis include an assumption of competitive markets (so that, for example, price regulations cannot be used to preserve the profitability of equipment), a neglect of the scrap value of obsolete equipment, and an association of a single “average” scrapping date with heterogeneous industrial systems. In the model, it is assumed that, provided markets are available, obsolete machinery is immediately replaced by capital of the latest vintage of equal productive capacity. In addition, some net investment I occurs, the magnitude of this depending on the “best practice” rate of profit and gross sector product, as follows:
f(t) = W(f)
[r(t)lr,,]*
(9)
where j3, r,,, and 6 are constants, and G(t) = P(t)Q(t). The gross (replacement plus net) investment so calculated gives the capital of latest vintage acquired, which enters eq. (1) in the next time step as a contribution to output. This completes the basic structure of the model. A number of interesting additional quantities can, however, be calculated from the results, for example, average productivity
54
JOHN A. CLARK
(to be compared with best-practice productivity), the average age of vintages in use and the age of the oldest surviving vintage. Since the purpose of this work is to consider in a general way the influence of technical change, no attempt is made here to calibrate the model. Several authors have pointed out that models of this kind are in general extremely difficult to estimate, and where attempts have been made in this direction account has generally not been taken of variations in the rate of technical change which is of prime interest for the purpose of this paper. It may well be useful however to consider the specific technical changes occurring within a given sector-especially one in which clear generations of techniques can be identified-and examine their implications via a vintage framework, as a tool for assessing the impact of particular technologies. The work of Simmonds [ 151 and Martin0 and Conver [16] lends support to this proposal. This idea will be examined further in later work; for current purposes a more macroscopic view is being taken.
Computer Implementation and Results Settling initial conditions for the model creates a slight problem in that it is not appropriate to allocate a quantity of capital in the base year to which much smaller incremental net additions are made via the net investment mechanism in subsequent years, since when the productivity associated with the initial block of capital satisfies the scrapping criterion it will become obsolete “en bloc,” creating unwanted discontinuities. To circumvent this problem annual investment (all of which is net of depreciation) is assumed to be constant for the first 15 years to build up a “history” of vintages. Also during this period the quantity LYin eq. (6) is set equal to Q/w to ensure that, with the elasticity z set equal to unity, P remains constant (and equal to unity). The end of this period is thus to be regarded as the start of the run, during which (Yretains a constant value and the net investment equation and the scrapping mechanism given in the previous section are in operation. The values of the other constants in the model were chosen as follows: Pk = 1, p = 0.06, r, = 0.1. With these values and with best-practice labor productivity Pa and wages w both increasing at 2% per annum, and with a constant capital/output ratio b of 3, the price P remained close to unity and the best-practice rate of profit close to 0.1. Such input data yielded apparently realistic values in other output variables; for example the lifetime of machines is about 18 years, and the ratio of best-practice to average labor productivity (pa/p) is about 1.2. Details are given below of the behavior of the model under various alternative assumptions.
SMOOTH CONTINUOUS
TECHNICAL
CHANGE
In the case of smooth variations in labor productivity and wages, some results can be derived immediately from the equations in the previous section. Following van den Beld [6], an expression can be derived for the time of introduction of the oldest machine still in use. From eq. (8), if machines purchased in year r are at the margin of obsolescence in year 1, P(t) = u(T)w(t). Thus if U(T) = a,,e- O7and w(t) = w,,e m’ where 19and 4 give the rates at growth of best-practice productivity and wages respectively, then In P(t) = In a,, + In w,, - BT + 4t
(10)
TECHNICAL
CHANGE
5.5
AND EMPLOYMENT
and 7 = [In a0 + In wO - In P(t) + @l/O. If price P(t) is constant (= P,,), then the age of the oldest surviving
(11) vintage of machinery
is
(12) Thus if wages are increasing more rapidly than best-practice productivity (4 > O), the lifetime of machinery declines over time; the quasi-rent on any given vintage of equipment is more quickly reduced to zero. If 4 = 8, the steady-state lifetime depends on this rate of growth and the share of income received by labor. Changes in employment in the model result from the net effect of the reduction in labor demand resulting from the replacement of obsolete machines by more labor-efficient new machines, and the increase in labor demand brought about by net investment in the latter. If 4 = 19,these effects cancel and employment remains constant. The model then describes an equilibrium growth path in which output increases at a steady rate 8. Computer runs with steady growth in wages and best-practice productivity gave the following effects. 1. Raising the demand elasticity z increases prices, employment, the rate of profit, and the lifetime of capital goods. This corresponds to a “demand-led boom.” 2. An increasing capital productivity (i.e., a declining capital/output ratio b) increases employment and output while reducing prices, the rate of profit and capital-good lifetime. In this case more output is obtained for a given net investment (thus increasing employment) and, from eq. (6), prices fall, and hence [eq. (7)] r(t) declines. The magnitude of these effects is reduced if a higher value of 6 in eq. (9) is chosen, i.e., if net investment is more responsive to fluctuations in r. 3. A declining price of capital goods leads to a lower output price and [from eq. (12)] a more rapid turnover of the capital stock. The next step is to consider the effects of modifying some of the assumptions and to consider, in particular, discontinuous technical change. DISCONTINUOUS
TECHNICAL
made above
CHANGE
In this section it will be assumed for convenience that the capital/output ratio is constant. The influence on employment and other model variables of stochastic fluctuations in best-practice labor productivity will be examined. In the absence of directly available empirical evidence on the extent of such fluctuations, recourse is made here to “plausibility” arguments and the fact that alternatives are examined to determine the importance of the particular assumptions made. A major purpose of this study is to examine whether, in terms of the model described above, variutions in best-practice productivity pa (which can be interpreted as variations in rates of innovation) are likely to be significant in changing employment levels; or, altematively, whether such variations may be “smoothed out” in the diffusion process, so that they may be ignored for present purposes and only overall trends considered. Three separate probability distributions are considered. These are shown in Table 1. In the first, the percentage change in any year may take any integer value from zero to 4, each of these five values being assigned equal probabilities. The second distribution is
56
JOHN
A. CLARK
broader and “skewed,” with a small probability of a large (19%) change; this distribution also includes the possibility of a negative (- 1%) improvement in productivity.” The third distribution consists of just two points; a high probability of a 1% (incremental) improvement, and a low probability of a very high (50%) improvement. In each of these distributions, the expectation (or “average”) value is 2%. In the simulations carried out, sampling takes place from these distributions using a pseudorandom-number generating package due to Neave [ 191. Each successive vintage of machinery is assigned the value of labor productivity resulting from amending that associated with the previous vintage by the randomly selected percentage change. Figure 4 shows the pattern of employment over an 85 year period for each of four different sequences of random numbers, using in each case the probability distribution of Table la. Employment is presented as a percentage deviation from the steady-state value obtained with a continuous increase in best-practice productivity of 2%; the dots in Figure 4a show the values obtained from a computer run with a steady increase of 2%, which indicate that the equilibrium value is not immediately attained; this is due to the presence of initial transient effects which decay with time. However, it is clear that the use of variable rates of innovation has induced substantial variations in employment. Figure 5 shows corresponding results obtained using distribution b in Table 1. As might be expected, this broader distribution gives rise to more extreme fluctuations in employment.
Fig. 4. Deviations in the level of employment tribution of Table la.
5Owing, the scrapping by Nelson
for example, mechanism,
and Winter
has been subject
value using the probability
to miscalculation of labor requirements. Such machinery will become before its immediate predecessors. The possibility of such regressions
[ 171;
to them.
from the “equilibrium”
the data of Solow
[ 181
cited by these authors
suggests
dis-
obsolete, via is suggested
that the American
economy
TECHNICAL
CHANGE
57
AND EMPLOYMENT
Fig. 5. Employment
deviations generated by the probability
distribution
of Table lb.
One notable feature of these results is that the curves are not continually crossing the horizontal axis (which represents the steady-state level of employment). If employment is at any time above (or below) “par, ” it appears probable that it will stay that way for some time in the future. This result derives from the features of random processes and the fact that it is the annual change in productivity which is assumed subject to random variations, best-practice productivity P,~ at any time reflecting the cumulative effect of such variations. In such a situation it can be shown that it is probable that P,~ will remain above (or below) the value expected on the basis of continuous change for some considerable time. This is illustrated by the fact that in the computer run on which Figure 4d is based, pa remains below the values obtained assuming continuous 2% growth for the entire period; even in the less extreme case of Figure 4a, it is consistently below the continuous-growth values for over 3/4 of the period. The statistical basis of this effect is discussed by Feller [20] and cited by David [21].6 The analysis of the section on Smooth Continuous Technical Change suggested that the relationship between wages and productivity has an important bearing on model “David comments as follows: “. anintriguing pair of theorems by William Feller. show that it is not at all unlikely that in a long coin-tossing experiment the cumulative number of heads (or tails) will hold the lead for practically the entire sequence of (2n) trials. Indeed, If n is large it can be computed that with a 0.20 probability heads (or tails) will be in the lead for 97.6% of the epochs!”
58
JOHN A. CLARK
TABLE 1 Probability Distributions for the Percentage Change in Best-Practice Productivity (For each distribution the expection value E(X) = X H’(X) = 2%) Percentage Increase in Best-PracticeProductivity X
Probability P(X)
(I 0
0.2 0.2 0.2 0.2 0.2
1
2 3 4 X
P(X) h
0.115 0.15 0.2 0.2 0.15 0.1
-1 0
0.05 0.025 0.01 c X
P(X) I
50
0.97959 0.02041
behavior. The results presented in Figures 4 and 5 incorporate the assumption that despite the extended deviations of pu discussed above, wages remain on a smooth 2% per annum growth path. As stated previously, this is not unreasonable given that a single sector is under consideration, and overall wage levels may be regarded as determined by factors in the economy as a whole. However, to consider the effects of this assumption of extreme wage rigidity, it was replaced by an assumption of extreme flexibility; the annual change in wages was set equal to the annual change in average productivity, i.e., an immediate response in wages to a change in the average state of technology. Figures 6a and 6b show results corresponding respectively to those of Figures 4a and 4b, i.e., the same frequency distribution and the same respective sequences of random numbers, were used. Thus the evolution of best-practice productivity used for Figure 6a is the same as that used for Figure 4a and similarly for Figures 6b and 4b. Although the amended assumption regarding wages clearly causes changes in detail, it does not appear to qualitatively change the nature or extent of the fluctuations in employment. Thus it appears to be a feature of the model that, despite the diffusion mechanism incorporated, fluctuations in rates of innovation are not damped out as the new techniques become absorbed into the economic system.
TECHNICAL CHANGE AND EMPLOYMENT
59
1
Fig. 6. Employment
deviations derived from Table la using alternative wages assumption.
Figure 7 shows a result obtained using the distribution shown in Table lc. In this particular example the higher change in productivity occurs just once in the period covered-curve 2 of Figure 7b illustrates the single step-function change in productivity. Figure 7a shows a dramatic decline in employment, but also, more interestingly, lesser declines some thirty and fifty years later, after recovery has taken place. Curve 4 in Figure 7b shows that average productivity responds rapidly to the sudden increase in best-practice productivity, and approaches it closely. This is because many earlier vintages of equipment suddenly became obsolete; the age of the oldest surviving machinery thus becomes very low, and the gap between average and best-practice becomes comparatively small. As pB resumes its slow continuous trend, average productivity p diverges from bestpractice; all functioning machinery is now of vintages subsequent to the date of the sudden productivity increase and no obsolescence occurs for some time. Eventually, however, the large quantity of equipment purchased at the time of the sudden increase (to replace the large quantity that became obsolete because of this increase) itself becomes obsolete; its replacement by new equipment causes a rapid increase in average productivity which gives rise to the indicated “secondary” decline in employment. Tinbergen and Polak [22] have pointed out that a specific attempt has been made by de Woolf [23] to explain the Kondratiev waves explicitly in terms of rebound effects of the type observed in the model. He argues that certain durable capital goods have a lifetime of
JOHN A. CLARK
60
Fig. 7. a. Employment deviation generated by the probability distribution of Table lc. b. Corresponding productivity movements compared with those obtained with steady growth: 1. best-practice productivity with continuous increase in pa; 2. best-practice productivity with step-function increase in pa; 3. average productivity with continuous increase in pa; 4. average productivity with stepfunction increase in pH.
about forty years,
and that the long waves
are reflections
of reinvestment
waves
of such
goods. In the model, cyclic effects become clearer if the not unreasonable assumption is added that if a particular change in pe is above (or below) the “average” (expectation) value, it is more likely than not that the succeeding change will also be above (or below) average. The sequence of changes then becomes a Markov chain. In the experiments carried out the possible values of the change in plr were taken to be the same as those in Table la (i.e., OS-4% per annum), the probabilities being derived from the transition matrix shown in Table 2. In this matrix any element Pii (i, j = 0, ,4) represents the probability that a given change 6p,, in pIS will be i%, given that the previous change was j%. Thus, if in a particular year the change is I%, the second column of the table indicates that in the following year the change is 0% with probability of 0.3, 17~ with probability 0.6, and 2% with probability of 0.2. Again the overall expectation value is 2%. This is an attempt to represent the possibility of bunching of innovations referred to in the section on the Vintage Approach. Figure 8 shows the evolution of employment using this matrix of conditional probabilities; the sequence of random numbers used in a and b are, respectively, the same sequences used in Figures 4a and 4b. The conditional probabilities make more probable and “small” productivity changes. The graphs than before strings of relatively “large” presented in Figure 8 suggest a clearer cyclic structure to employment. The initial decline and subsequent rise in employment in Figure 8a coincides roughly with periods in which &I,, is above and below its expectation value. The sharp decline in employment at point A occurs because equipment purchased in the period of lowlabor productivity growth becomes obsolete “en bloc”; these vintages have associated
TECHNICAL
CHANGE
AND EMPLOYMENT
61
TABLE 2 Conditional 0.6 0.2 0 0 0
0.3 0.6 0.2 0 0
0.1 0.2 0.6 0.2 0.1
Probability
Matrix 0
0
0 0.2 0.6 0.3
0 0 0.2 0.6
requirements very similar to one another, and hence from the scrapping criterion are scrapped at the same time, or in very rapid succession. This “bunching” of retirements gives rise to a corresponding bunching of replacement investment. Despite the fact that 6p, remains at a high level, there is a further rapid decline in employment at point B as this replacement investment becomes obsolete and is itself replaced “en bloc” by more productive equipment. The decline in employment at point C is similarly explained. As observed in Figure 7, “rebound” effects occur which do not, in this case, appear to be rapidly damped out. The above examples are based on the assumption that investment behavior is related to technical change through the rate of profit r [eq. (9)]. Relatively rapid productivity
Fig. 8. Employment
deviations using conditional
probability
matrix.
62
JOHN A. CLARK
changes tend to increase r, and hence to lead to higher investment and faster growth. But the availability of “radical” innovations might be expected to have a more direct influence on investment products for which
behavior, particularly if they encompass the development of new large markets are expected. Figure 9 illustrates the result of assuming if that p of eq. (9) varies in proportion to the change in p,,, with p = 0 (no net investment) Sp, = 0, and with the same average value as before. Comparing with Figure 8, it can be seen immediately
that fluctuations
in employment
are considerably
less severe,
although
traces of the previous cyclic structure appear to remain. The effect of this modification is that a relatively large change in ps leads to a relatively large change in output as well as in average productivity 6, and hence employment is subject to less dramatic change. However fluctuations are still in evidence, and it would be surprising if this were not so; the evolution of i, for example, depends in a complicated way on the history of productivity change and of obsolescence, which give rise to the particular structure of the capital stock in use at any time, and hence cannot be expected to follow precisely a pattern of incremental output change which is proportional to changes in best-practice productivity. Discussion and Conclusions The following points emerge
from the analysis
of this article:
1. Several researchers have concluded that current high levels of unemployment are caused by excessively high wage levels. Many vintage models, in fact, suggest just this: it is assumed that, because the lifetime of capital goods declines if wages increase more rapidly than productivity [(eq. (12)], employment also declines. However, the current model includes a demand side, through which net investment rises as wages rise. Hence with high wage rates, while the number of surviving vintages is reduced, more capital of any vintage is in operation. Given an overall tendency for wages to keep pace with productivity, the results of the section on Discontinuous Technical Change, suggest that the general results of the model are not sensitive to the precise relationship between these variables. 2. There is reason to believe that there are sharp fluctuations in the rate of generation of innovations; such fluctuations have been suggested from empirical evidence by Mensch [I21 and suggested earlier by Schumpeter [8]. These writers and others.
Fig. 9. Employment
deviations
with a variable investment
coefficient.
TECHNICAL
CHANGE
AND EMPLOYMENT
63
such as Rosenberg [24] and Nelson and Winter [25] also imply an internal momentum in the innovation process. “Natural trajectories,” to use the phrase of the latter authors, are argued to arise from the nature of technological change. A significant innovation, for example, may create new problems and bottlenecks which pave the way for further innovations. The model suggests that variations in rates of innovation, whether such variations are independent (“random walk”) or, as suggested above, nonindependent (the “Markov chain” case), can have a significant influence on employment. While the frequency distributions examined were hypothetical, the general result is that the maintenance of steady employment levels seems to depend on a “fine tuning” of investment activity which could scarcely be expected in the real world. 3. Oscillatory effects in the model occur through two mechanisms. First, the assumption that the rate of technical change is not independent between periods can give rise to cyclical trends in productivity growth which are relected in cyclical patterns in employment. Secondly, the scrapping criterion leads to rebound effects where employment is affected by earlier investment activity. Clearly the interaction of these two effects can produce quite complicated behavior. Both effects indicate that the influence of technical change on employment is essentially a historical process; they imply that it is not possible to ascribe unemployment to the fact that technical change is “too fast” or “too slow” over any particular short period of time, but that a rather long history of technological evolution, and the investment response in particular, needs to be taken into account. The effects of international competition and trade are not considered in the model. Preliminary experiments suggest that the current type of formulation may be very suitable for studying the effects of international competition on employment, particularly in that it captures the process of “induced” technical changes as domestic producers are “forced” to adopt more capital intensive techniques in response to competition from cheap imports. Further work will be carried out to examine this issue. Finally, what of the present unemployment situation in OECD countries? Obviously the actual level of unemployment depends on demographic factors as well as the demandside factors considered here, and the model has not been applied to any particular historical situation. But the implication of this work is that there is no reason to suppose that the current problem is short term, but equally there is no reason to assume that it is permanent. Lewis [26] notes that, historically, economic fluctuations have varied in length and severity, and comments as follows: Two groups of commentatorscontinue to ignore this point. One is the group of US economistsbroughtup on the National Bureau of Economic Research’s reference Kitchin cycles. They expect every recession to be over in eighteen months. and do not realize that it has been normal in the US economy for as many as six years to pass before the curve of production finally races to the next Kuznets peak. The other group are the children of the Apocalypse. Starting with Marx in 1848, every time there has been a recession critics have predicted the imminent collapse of capitalism, just as the early Christians expected the imminent arrival of Judgement Day.
Current technological developments-the microprocessor in particular-seem likely to play a very significant part in worsening or helping to resolve the current unemployment problem, depending on whether the labor-displacing effects are outweighed by
JOHN
64
A. CLARK
increases in labor-absorbing net investment [27]. Should the former effects prove to be predominant, they could be seen as presenting an opportunity (for reduced working hours and more leisure time) rather than the cause of an increasing split in society between those who have a job and those who do not. The latter development is not only highly undesirable in itself, but could lead to considerable problems when demand for labor is restored and there is a considerable proportion of the population which has never worked. In addition to policies designed to stimulate employment therefore, there is every incentive to devise social policies of redistributing the work available, should the need arise. There is a need to understand further the complex relationship between technical change and employment to help guide the formulation of such policies. The work reported Council. Thanks are due Ray, und Dr. R. E. Turner this article, and to Henry
was sponsored by UNITAR und by the U.K. Social Science to Professor Richard R. Nelson, Projessor H. Linstone, Dr. G. and other SPRU colleague.s,for comments on an earlier draji of Lucas jar computer programming advice. Acknowledgment is
also made to Messrs. George Allen Publishing Company,for permission
& Unwin (Publishers) Ltd. and to the North-Holland to reproduce e.xtracts from their publications.
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