# Productivity growth in manufacturing, 1963-85: the roles of new investment and scrapping.

PRODUCTIVITY GROWTH IN MANUFACTURING, 1963-85: THE ROLES OF NEW
INVESTMENT AND SCRAPPING The twin forces of investment in new and
scrapping of old equipment are traditionally supposed to play a large
part in explaining productivity growth. Scrapping cannot in practice be
observed directly but can be inferred by estimating a vintage capital
model. When this is done it is found that these forces do indeed have a
substantial role to play in explaining differences between industries in
productivity growth rates in the 1960s and 1970s, but not in the 1980s.
The productivity improvement observed in most industries in the 1980s
must therefore be ascribed largely to forces other than new investment
and scrapping.

1. Introduction To what extent is the rate of growth of labour productivity explained by the twin forces of investment in new and scrapping of old equipment? This article seeks to answer this question for manufacturing, making use of a vintage capital model. The results to be discussed are for both total manufacturing and a large sample of manufacturing industries, from the 1960s to the 1980s. We shall be particularly concerned to see to what extent the improvement in productivity growth which has occurred in most industries in the 1980s can be explained by the forces under investigation.

Up to the mid 1960s, output, employment and productivity (output per person employed) in manufacturing displayed a simple pattern of business cycle fluctuations superimposed on a strong upward trend. After 1966, however, employment began to decline and has continued to do so, particularly in the 1980s. Output also fell after 1973 and particularly after 1979; despite some recovery since 1982 it has not regained the 1973 level. The growth rate of labour productivity tended to rise in each successive cycle, until 1973. There then followed a marked slowdown in the 1970s, followed by a recovery in the last sub-period (though the rate during 1979-86 is still less than that of the much despised Wilson--Heath era).

A number of writers (including Muellbauer, 1986) have suggested that the slowdown in the 1970s and the recovery in the 1980s can both be explained (at least in part) by a vintage capital approach. The vintage model sees new capital investment as the prime source of productivity growth in the long run: new technology must be embodied in new equipment. At any one time, there exists a stock of capital equipment of different ages. The productivity of labour on older, less technically advanced equipment is lower than that on newer equipment. In the event of an unexpected rise in demand older equipment will be retained in use for longer than anticipated; in extreme cases `mothballed' equipment may be brought back into use. The average age of the capital stock in use will rise and the observed growth of labour productivity, which is an average across all vintages of capital in use, will fall.(1) In the longer run, if the rise in demand persists, there will be more investment in new equipment and the growth rate of labour productivity will rise again. Conversely, if there is an unexpected fall in demand, older vintages of equipment may be scrapped prematurely. In this case the average age of capital equipment in use will fall and the growth rate of labour productivity will be observed to rise, as a higher proportion of the surviving labour force becomes concentrated on newer, more productive equipment. Note that according to the vintage capital model, it is always the oldest equipment which is scrapped first. In summary then, the growth of labour productivity is the result of the balance between two forces--first the rate at which new technology is introduced, measured by gross investment, and second, the rate at which older equipment, embodying inferior technology, is scrapped.

A possible explanation of the 1970s slowdown is that investment slowed down during this period, thus lowering the rate of introduction of new technology. The 1980s recovery in productivity could be explained by exceptionally heavy scrapping of old equipment. (The period 1973-9 was also a period of above-average scrapping in the view of many, which would have tended to raise the productivity growth rate; if the vintage model is correct, this effect must have been outweighed by low investment.) An extreme version of this thesis would assert that there has been no change in the underlying growth rate of productivity (the rate which would be observed in a hypothetical steady state) and that all changes in observed productivity are due either to variations in the rate of gross investment or to variations in the rate of scrapping.

Both the total and split into two components: plant and machinery (IP) and new buildings (IB). The third, much smaller component, is vehicles, ships and aircraft. Investment in new buildings fell heavily after 1969. Investment in plant and machinery, apart from cyclical fluctuations, shows no absolute decline, but its growth rate clearly flattens off in the 1970s. So the evidence on investment is at least weakly consistent with the vintage model. For scrapping, however, there is no direct evidence at all, though estimates have been made, on quite different bases, by Wadhwani and Wall (1986) and Oulton (1987).

The vintage model is set out formally.

2. The vintage capital model The vintage capital approach was popularised by Salter (1960). The approach was formalised as a model by Solow et al. (1966). Further theoretical development is in Johansen (1972). A simple exposition of the model is provided by Solow (1969). In what follows a highly simplified (technically a `clay-clay') version of the vintage model will be analysed. No substitution between capital and other inputs, either ex ante or ex post, will be allowed. A little will be said later on the effect of relaxing this assumption of no substitutability, which is made purely because of the difficulties of estimating the parameters of a more general vintage production function.

Capacity output (Y) is related to past (gross) investment (I) as follows: (Mathematical Expressions Omitted) Here m=m(t) is the age of the oldest plant still in use at time t, which may in general vary with time. The parameter a is capacity output per unit of investment. Labour (L) required to produce capacity output is given by: (Mathematical Expressions Omitted) where it is assumed that labour required per unit of capacity output declines exponentially at rate b from the level required in the base year ([b.sub.0]), that is, labour required on vintage v is [b.sub.0e.sup.-bv]. Labour productivity (Q) is

Q(t) = Y(t)/L(t) (3)

The above relations hold in or out of the steady state. If a steady state is assumed in which output grows at rate g and a constant proportion of output, s, is invested per period, then putting [Y.sub.0] = Y(0) and [I.sub.0] = I(0), (1) and (2) become: [Mathematical Expressions Omitted] where [mu] is the steady state life of plant (m(t) = [mu], all t). Setting t = 0 in (4) and using the fact that s = [I.sub.0]/[Y.sub.0], we find

a = g/s(1-[e.sup.-g [mu]). (6)

Given therefore three out of the four quantities s, g, a and [mu], we can find the remaining one.

Labour productivity in the steady state, from (4) and (5), is given by: [Mathematical Expressions Omitted] Hence, in the steady state,

b = dlog Q(t)/dlog t. (8) that is, the steady state growth rate of productivity is b. Also, by setting t = 0 in (7), we can find an expression for [b.sub.0]: [Mathematical Expressions Omitted] putting [Q.sub.0] = Q(0).

In summary, if we could observe the economy in a steady state, we could readily estimate the unknown parameters of the vintage capital model (a, [b.sub.0] and b). The observed growth rate of productivity would give us b (equation (8)); a and [b.sub.0] would come from (6) and (9) respectively, since the saving ratio(s), the output growth rate (g) and the age of the oldest equipment still in use (mu) would all be in principle observable. Alternatively, without assuming a steady state, if m(t) were known for some t, we could find the parameter a from (1). If in addition b were known, then [b.sub.0] could be found from (2), again without assuming a steady state.

3. Estimating the effect of premature scrapping. Suppose that we wish to estimate the impact of premature scrapping between two date, say S and T (T [greater than] S). It is convenient now to switch to a discrete-time representation of the vintage model, since the data themselves are inevitably discrete. Consider the labour required at T to man the new equipment installed between S and T, [L.sup.N] (T): [Mathematical Expressions Omitted] where c is the rate at which labour requirements are declining on equipment installed after S (c need not equal b, the rate assumed for equipment installed up to S). It is assumed that the interval (T-S) is short enough so that no new capital installed between these dates has been scrapped before T.

Labour required at T on plant installed up to S, and which is still in use at T, [L.sup.0] (T), is: [Mathematical Expressions Omitted] The quantity [Alpha] is a slight complication induced by discrete-time analysis. The point is that the oldest vintage in existence might not represent all the investment done during that year; it is possible that part only of the oldest vintage has been scrapped. The age of the oldest plant in existence at T, n(T), can therefore be defined as

n(T) = m(T) - 1 + [Alpha] (12)

Total labour requirements at T are:

L(T) = [L.sup.0] (T) + [L.sup.N] (T) (13)

Next we calculate the output producible on the capacity available at T: [Mathematical Expressions Omitted] where the `[caret]' over Y is added to indicate that this output level is the one predicted by the vintage model. The model of the preceding section has been generalised slightly by the introduction of the parameter [Delta] which measures the physical rate of depreciation (physical decline in output-producing capacity of capital equipment). We can also define the predicted productivity level as:

[caret] Q(T) = [caret] Y(T)/L(T) (15)

Suppose that we know the parameters a, [b.sub.0], b, c and [Delta] and that we have data on labour, output and investment for as far back as necessary. Then we can solve for the remaining unknowns in the following way. First, observations on investment enable us to solve for [L.sup.N] (T) from (10). Knowing [L.sup.N] (T), we can then find [L.sup.0] (T) from (13). Plugging the newly-found value for [L.sup.0] (T) into (11), we can solve for m(T) and [Delta] by a simple iterative process. Finally, (14) and (15) can be solved to find the output and productivity predicted by the vintage model.(2)

An alternative approach is to assume that the vintage model predicts productivity growth exactly. One of the five parameters now becomes free, to be determined by the data; it is most natural to let c, the rate at which labour requirements on new equipment are falling during the period under analysis, be the free parameter. Under this alternative approach, since [caret] Y(T) = Y(T) by assumption now, we can solve (14) for m(T) and [Delta] by a simple iterative process. [L.sup.0] (T) can now be found from (11) and hence [L.sup.N] (T) from (13). Plugging this value for [L.sup.N] (T) into (10), we can solve for c.

Turning now to the parameters, as we have seen, by assuming a steady state all the parameters required for the calculations (except c) can be estimated from equations (6), (8) and (9), provided that the age of the oldest vintage in the steady state is known (mu). An alternative course, which minimises reliance on the assumption of a steady state, is to estimate b from equation (8) and then to estimate a and [b.sub.0] from equations (1) and (2). This was the course actually adopted. It was assumed that manufacturing was approximately in a steady state over the period 1960--4; b was then set equal to the observed growth rate of productivity over this period, 3.12 per cent. a and [b.sub.0] were then found from discrete versions of equations (1) and (2), with t = 1964 and three alternative values for m (1964), namely 15, 30 and 45 years.(3) The wide span assumed for m seems justified by the intrinsic uncertainty about this parameter. The evidence presented in Griffin suggests that 30 years is a reasonable central value, contrary to most people's intuition. Finally, under the first approach where a value for c must be fixed in advance, it was assumed that c = b.

To summarise, the steps required for calculating the productivity growth rate predicted by the vintage capital model for a particular period are as follows: (1) Estimate the basic parameters, using data from a

period preceding the one under analysis. (2) Calculate the labour required to operate

equipment installed during the period under analysis

(investment during the period being known); this

quantity is called [L.sup.N] (T) above. (3) Subtracting [L.sup.N] (T) from the (known) total labour

force at the end of the period under study, we can

derive the labour required to operate the rest of

the equipment still in use at the end of the period,

that is, the labour required for that part of the total

equipment still in use which was installed before

the start of the period; this quantity is called [L.sup.0] (T)

above. (4) Given knowledge of investment prior to the period

under analysis and knowing now the labour force

employed on old equipment, we can calculate

how much of that investment has actually

survived to the end of the period, that is, the age of

the oldest equipment still in use. (5) Knowing the age of the oldest equipment still in

use, we can calculate the output producible on

the entire stock of equipment which has survived

to the end of the period under study and hence the

productivity predicted by the vintage model.

4. Results for total manufacturing As already noted, the CSO distinguishes three types of investment--plant and machinery; buildings; and vehicles, ships and aircraft. Investment in plant and machinery would seem to correspond best with the vintage model. By contrast, buildings have a long life (on average 60 years, according to the CSO;), are frequently malleable (as exemplified by 18th century warehouses in the Docklands) and so are infrequently subject to scrapping due to obsolescence. Vehicles have a short life (about 10 years, according to the CSO, but in practice probably considerably less) but this is probably due in the main to declining physical efficiency and rising maintenance costs, rather than obsolescence. The calculations to be reported therefore employ gross investment in plant and machinery by manufacturing as a whole.

The results of these calculations, for successive sub-periods. The periods chosen are business cycle peaks (except for 1986), in order that the observed labour force should correspond fairly well to that required for full capacity working. The calculations are based on data for output, employment and gross investment in plant and machinery in manufacturing as a whole.(4) Full details of the data are in the appendix. In these calculations c in each sub-period is assumed to equal b (which in turn is assumed to equal 0.0312 or 3.12 per cent); [Delta] is assumed to be zero.

For 1964--8 and 1968--73, with the age of oldest plant assumed to be 30 years, the vintage model does a reasonable job of predicting productivity growth. But it also predicts a substantial shortening of plant life, while what direct evidence there is indicates constancy of plant life (Griffin, 1979). The model really goes wrong in trying to explain 1973--9, where, regardless of the assumed plant life, the productivity growth rate is grossly over-predicted. There is a further substantial over-prediction in the final period. With the oldest plant in 1964 assumed to be 30 years, the model predicts that the age of the oldest plant in 1986 is less than 17 years, quite out of line with CSO estimates (CSO, 1985).

The reason for this poor performance is clear. Since output actually fell after 1973, there must, according to the vintage model, have been large scale scrapping, which should have led to a big increase in productivity growth. The greater is the age assumed for the oldest plant in 1964, the greater the amount of low productivity plant in existence and so the greater the scope for productivity gains from scrapping. Similarly, if the vintage model were correct, productivity growth in the 1980s should have been higher than observed, because of the large scale scrapping which the model predicts.

A number of variations on the methods were tried. For example, (1) steady state values for all the parameters were used; (2) different values for b were tried; (3) [Delta] was set equal to 0.02; (4) total investment rather than plant and machinery only was tried; but without any appreciable change in the results.

The hypothesis that the underlying productivity growth rate has been the same throughout the whole 22 year period (the hypothesis that b = c) has thus been decisively rejected. It is possible, however, that the vintage model may still be found to fit the facts, if the underlying productivity growth rate (c) is allowed to vary in each subperiod. Reports results based on finding the values of c and n in each subperiod which reproduce exactly the observed productivity growth. Clearly, these results are unbelievable. Making the central assumption that the age of the oldest plant in 1964 was 30 years, the model predicts that productivity on new equipment was falling during 1979--86 at the rate of 8.6 per cent and that by 1986 the oldest surviving plant was only 13 years old. The basic problem for the vintage model is again that, given the large labour force reductions which have occurred, the observed rate of productivity growth should have been much higher than was actually the case; this can only be `explained' by `predicting' that productivity growth on new investment was very low (in fact, negative). But even in the 1960s this version of the vintage model produces implausible results in trying to explain the modest increases in productivity growth observed then.(5)

Another, more positive, view might be taken of these results. It could be argued in favour of the vintage model that it demonstrates how large changes in productivity growth rates can be generated by the observed changes in labour, output and investment. Furthermore, the predicted changes in productivity growth are in the right direction. Thus the model predicts a slowdown in productivity growth in the 1970s and a speed-up in the 1980s. The fact that growth is over-predicted in 1973--9 could be explained by the presence of special factors during this period. The implausible results for the age of capital equipment could be avoided by stressing the difference between the age of the oldest equipment in existence and the age of the oldest equipment in use (which may be less and anyway is much harder to measure). Above all, a larger role could be allotted to factor substitution.(6) But rather than pursue the approach of refining the model, it was decided instead to see how far a simple model could take us in explaining the inter-industry differences in productivity growth rates.

5. Cross section results for manufacturing In this section the results of testing the vintage capital model on a cross section of 60 industries are reported. These 60 industries, which accounted for about half of total manufacturing output in 1985, were selected as follows. First of all, as part of a wider study of industrial productivity, 141 industries covering the whole of the production sector of the economy were selected. These industries, classified in accordance with the 1968 Standard Industrial Classification (SIC), were chosen in such a way as to maximise the chance of getting consistent data back to the 1950s. In all but a couple of cases, the industries are either Minimum List Headings (MLH) or subsections of MLH. No MLH covered by the Census of Production was excluded. Second, the MLH which are not counted as part of manufacturing under the 1980 (not 1968) SIC's definition were excluded. Third, industries for which an output price index was not available back to the 1950s were excluded. This last step is in practice the most significant one. A list and description of the 60 industries finally selected is in Oulton (1988, Appendix B).

The data on output and employment were drawn from the Census of Production. The availability of the Census determines the periods which can be studied, which are consequently somewhat different from those used in studying total manufacturing. The periods were 1954--63 for estimating the basic parameters a, [b.sub.0] and b for each industry, and 1963--8, 1968--73, 1973--9 and 1979--85 for testing the predictions of the model. Productivity is defined as net output divided by total employment, where net output is as defined in the Census except that a rough correction has been made for stock appreciation. Net output was deflated to a constant price basis using each industry's producer price index (formerly wholesale price index) for home sales. Investment in plant and machinery from 1948 onwards also comes from the Census. However, the Census has only been annual since 1970, so between then and 1948 interpolation was necessary for some years using annual investment data on industry groups within manufacturing (from the CSO) as a control. The current price investment data were deflated using the appropriate CSO deflators for plant and machinery and then adjusted for financial leasing.

The major problem in calculating consistent series from the 1950s to the present is the change from the 1968 SIC to the 1980 SIC. Until 1979 the Census of Production was produced on the 1968 basis; from 1980 it has been produced on the 1980 basis. The problem of reclassifying data on the new basis back to the old one has been analysed by Oulton (1988, appendix C) and the methods described there were used to reclassify the investment, net output, employment and price data. A fuller description of the data sources and the methods employed is in the appendix. In what follows the empirical results will be summarised; more detail can be found in Oulton (1988).

Statistics of the growth rates of productivity experienced by the sample of 60 industries over the 31 years from 1954 to 1985, broken down into five periods. Not surprisingly, the average performance of these industries mimics the performance of manufacturing as a whole. On average, productivity growth accelerated in 1963--8 and again in 1968--73, fell heavily in 1973--9 and recovered in 1979--85. Nevertheless there is a considerable diversity of experience; in fact, as measured by the standard deviation of growth rates, diversity has tended to rise over time. 11 industries bucked the trend by showing higher rates of productivity growth in 1973--9 than in the previous period and 10 showed lower rates in 1979--85 than in 1973--9. The standard deviation of the change in growth rates between 1968--73 and 1973--9 was 5.62 per cent and that of the change in growth rates between the last two periods was 6.08 per cent. It is also noteworthy that negative rates of productivity growth occurred in 1 industry in 1963--8, in 3 industries in 1968--73, in no less than 24 industries in 1973--9 and in 1 industry in 1979--85.(7)

Though it is a digression from the main theme of this paper, it is interesting to consider the correlation between output growth and productivity growth. The correlation coefficients in our sample were as follows:

Thus the Verdoorn Law, though somewhat weaker in the last period, is still far from dead.

Summary statistics of the vintage capital model's predictions for plant life which assumes a 30 year life in 1963. In these and later estimates, the parameters a, [b.sub.0] and b have been estimated separately for each industry, using industry data, by the same method as for total manufacturing; [Delta] is set to 0. The underlying productivity growth rate is assumed not to have changed after 1963 (that is, b = c for each industry in every subsequent time period). On average, plant life is predicted to decline substantially to only 17.3 years in 1985. Whatever the value assumed for plant life in 1963, it turns out that the model predicts a decline in plant life after that date--to 10.9 years in 1985 if the 1963 value is 15 years and to 28.1 years if the 1963 value is 45 years. This predicted decline is at variance with what little direct evidence we have; it is far greater than that which the CSO assumes to have occurred after 1970 (CSO, 1985), which in any case has been questioned by Prais (1986).

Within the overall pattern of declining plant life, there are a considerable number of exceptions. Thus, in the four time periods, the number of industries in which plant life is predicted to have increased is successively 20, 20, 17 and 4. In 1985 there are 8 industries with predicted plant lives greater than 30 years. In some industries the increase in plant life is so great that it can only have occurred if (implausibly) some earlier vintages, instead of being scrapped, were first mothballed and then brought back into use.

The model's predictions for productivity growth rates which again assumes a 1963 plant life of 30 years, and the predictive accuracy of the model is for three different values of 1963 plant life. It can be seen that the model's performance is insensitive to the plant life assumption. On the root mean square error (RMSE) criterion, no one assumption dominates the rest. A life of 15 years might be preferred on purely statistical grounds, though there is little difference in RMSE between this and a 30 year life. On any assumption about plant life, the vintage capital model tends to over-predict productivity growth in both the last two periods, as it does at the aggregate level; furthermore, the accuracy of its predictions diminish substantially with each successive period.

The results of regressing actual on predicted productivity growth for each period. If the vintage model were to be a fully satisfactory explanation of productivity growth then we would expect that (1) the constant term would be insignificantly different from zero; (2) the coefficient on predicted productivity growth would be insignificantly different from one; and (3) [R.sup.2] would be high. None of these hopes are satisfied. In terms of explanatory power, the period 1968--73 is the best for the model and next is 1973--9. However, the constant is always significantly different from zero, indicating that the model's predictions are biased. Most important, the coefficient on expected productivity growth is always significantly different from one. Nevertheless, the latter variable is highly significant in three out of the four periods, though not at all in the last. This suggests pooling the observations in the first three periods, to produce the following regression results (180 observations, t ratios in parentheses):

h = 1.68 + 0.46h[carets] (15)

(4.59) (6.69)

[R.sup.2] = 0.2008

[R.sup.2] = 0.4437 Here h and h[carets] are actual and predicted productivity growth; D68 and D73 are period dummies taking the value 1 in 1968-73 and 1973-9 respectively and 0 at other times. The first of these regressions suggests that vintage effects alone can account for about 20 per cent of the interindustry variation in productivity growth over the period 1963-79. Adding a dummy for 1973-9 raises the proportion explained to about 44 per cent. In conclusion then, the vintage capital model does seem to have a role to play in explaining productivity growth over 1963-79. In addition, there is some evidence for a common factor depressing all growth rates in 1973-9.(8) However, the results also indicate that vintage effects have no role to play in explaining productivity growth differences after 1979.

How sensitive are these conclusions to the particular sample and to the particular assumptions used? The estimates of b vary widely across industries. This may be because the assumption of an approximately steady state during 1954-63 was far from the truth for many industries. The calculations were therefore rerun assuming the same value of b for all industries, namely the sample average over 1954-63 of 0.038. We can see that, on the RMSE criterion, assuming the same b for all industries gives better results. However, the regression analysis leads to conclusions similar to those of the earlier one. Once again, the coefficient on the predicted growth rate is insignificant for the 1979-85 period.

A second sensitivity test was to enlarge the sample of industries. Price data is available for many more industries from the 1970s. These can be brought into the sample if ways can be found of estimating the parameters. The method adopted was first, to assume b to be the same for all industries, equal to the value used in the preceding section for total manufacturing (0.0312), and second, to estimate a and [b.sub.0] using 1973, rather than 1963, in equations (1) and (2). The results, which are for 94 industries covering most of manufacturing, are in table 10.(9) The RMSE is now a bit lower for 1973-9 than in the 60 industry sample but much higher for 1979-85. The regression results for the full sample show at first sight a rather puzzling pattern in that the predicted growth rate is insignificant in 1973-9 but highly significant in 1979-85, the reverse of the finding for the 60 industry sample. Inspection of the scatterplot, however, suggests that the results are being distorted by a single outlier, MLH 311 (iron and steel). When this industry is omitted, the predicted growth rate becomes insignificant again in 1979-85.

6. Concluding remarks In an earlier note (Oulton, 1987), some doubt was cast on the proposition that premature scrapping can explain the improved productivity performance of the 1980s. The present article reinforces these doubts. As we have seen, our (admittedly simple) version of the vintage model tends to overpredict productivity growth in both the 1970s and in the 1980s. Moreover, though the model has some success in explaining the inter-industry variation in productivity growth in the 1970s, it has much less success (by itself) in explaining the pattern in the 1980s. These results might be considered surprising, given the stress traditionally laid by economists on the importance of capital accumulation and the substantial degree of subsidy accorded until recently to investment, particularly to investment in plant and machinery. It may be that the comparative lack of success of our version of the vintage model is due to its restrictive assumptions; if these were relaxed, no doubt more could be explained. However, although the vintage capital model, in its general form, is widely considered to be more realistic than its neo-classical rival, it is worth considering the possibility that two of its key assumptions may turn out on reflection to be suspect empirically, at least when applied at the industry level. These are firstly that it is always the oldest, least productive plant which is the first to be scrapped and secondly that all technical progress must be embodied in new equipment.

The first of these assumptions clearly need not hold at the macro level. For example, demand might decline particularly sharply in industries whose equipment happened to be relatively new. Premature scrapping in these industries might then remove equipment which was relatively young compared to equipment elsewhere. But the assumption need not hold at the micro level either. Consider an industry which is divided into two parts--one part making luxury products by traditional methods and another part making mass-produced, standardised goods. Perhaps under government prodding, the mass-production part of the industry has re-equipped itself with modern plant to face the foreign competition. In the event the foreign competition proves too strong and much of the modern equipment is scrapped; meanwhile the more traditional sector of the industry survives. This little parable might apply to the textile industry.

The second key assumption, that all technical progress must be embodied in new equipment, is clearly extreme. There are a number of ways in which productivity can be raised without investing in new equipment. These include: (1) the elimination of previously hoarded labour; (2) changes in working practices leading to better use of existing equipment; (3) increased work intensity; (4) a more skilled labour force; (5) the development of higher quality products (higher value added). No direct evidence exists of which I am aware bearing on the last of these five possibilities. However, a higher quality product probably requires a more highly skilled workforce (see, for example, Steedman and Wagner, 1987) and there is much evidence to suggest that skill levels have not improved in recent years, thus eliminating the fourth possibility as well. The evidence set out in earlier sections suggests that the first three routes to higher productivity may have been more important for productivity growth than were investment and scrapping, the factors stressed by the vintage model, at least in the 1980s.(10) APPENDIX: DATA SOURCES

In the description of the sources the following abbreviations have been used:

A. Total manufacturing

Output, employment and productivity were converted from index numbers (1980 = 100) to respectively million pounds at 1980 prices, thousands and pounds at 1980 prices per person employed, by using the 1980 values of these variables, from MDS (December, 1987). The output figure was calculated as 26.6 per cent of GDP at factor cost.

The investment data for 1948-54 is in current prices and was deflated to 1980 prices using unpublished CSO deflators. I am grateful to R.J. Allard for supplying me with these, as also with the unpublished investment data for years prior to 1948. The latter derive ultimately from the CSO and are used in their perpetual inventory model of the capital stock. From 1968 onwards, investment includes leasing, assumed to be wholly of plant and machinery. Leasing comes from the NIESR data bank for 1968-79 and from MDS (December, 1987) for 1980-6. B. Industry data (a) Sources

(b) Reclassification from 1980 SIC to 1968 SIC From 1948 up to 1979 Census of Production data is available under the 1968 SIC. From 1980 on, Census data has been published according to the 1980 SIC. The 1980 SIC is more detailed than the 1968 one; there are some 206 Activity Headings (AH) in manufacturing in the former, compared with some 137 Minimum List Headings (MLH) or sub-sections of MLH for which data is available more or less consistently back to 1948 under the 1968 SIC (though the definitions of the manufacturing sector differ somewhat). Hence it was decided to reclassify data on the 1980 SIC basis back to the 1968 one rather than the other way round.

The CSO has published a `reconciliation' between the two classification (CSO, 1980) which shows for each AH the one or more MLH or sub-sections of MLH to which it corresponds. The problem of reclassification is to decide in what proportions an AH must be divided on the numerous occasions when it has to be split between two or more MLH. It is important note that these unknown proportions will in general be different for different variables, for example net output, employment or investment. A solution is possible since the 1979 Census was published on the basis of both SIC. With the aid of the two Census reports and the `reconciliation', computer programs were written which can calculate the unknown proportions for any Census variable and then using these proportions reclassify data on an AH basis back to an MLH basis. The reclassification problem and the solution proposed are more fully discussed in Oulton (1988, Appendix C). By these means the post-1979 data on net output, employment and investment were made comparable with data for earlier years. For producer prices, the AH level indexes were aggregated using gross output weights (derived from the reclassification procedure) to arrive at MLH level indexes. (c) Adjustment for stock appreciation The Census of Production concept of net output is gross of stock appreciation. An adjustment conceptually identical to the one in the national accounts which turns the increase in the value of stocks into what is called `Value of the physical increase in stocks at current prices' is required also at the industry level. The Census distinguishes three kinds of stocks--materials and fuel, work in progress and goods on hand for sale (the last two usually being aggregated) and records both the value of the stocks at a reference date and the increase in value over the preceding year. For most, though not all, respondents the reference date is the end of the Census year. Ideally, separate price indexes should be used for each stock. Also, while net output is deflated by an index which is an annual average, calculating stock appreciation requires an end-of-year index. In practice, partly owing to the absence of adequate price indexes for materials and fuel in the earlier years, a much rougher method of adjustment was employed. The same price index was used for all three stocks and for all industries, namely the price index for aggregate manufacturing output. Using this method, stock appreciation as a percentage of unadjusted net output was on average about 6 per cent in 1973 and 1979 and considerably less in other years. (d) Interpolation and extrapolation of Census investment data Since 1948, questions about capital expenditure have been included in the Census. However, prior to 1970 the Census was not annual so there are missing values (the number varies between industries--nearly all industries have data for 1948, 1954, 1958, 1963 and 1968; some have more). The missing values between 1948 and 1970 were filled in by interpolation, using annual investment series on 25 industry groups in manufacturing (1968 SIC) as a control. For years prior to 1948 annual investment series on 11 industry groups were available and these were disaggregated to the MLH level using the average share of each industry in total investment by the group over the period 1948-54. Obviously, this extrapolation procedure can produce at best a reasonable guess for an industry's investment prior to 1948. However the main use for investment in the distant past is in estimating the constants a and [b.sub.0], to which the results of the vintage capital model are unlikely to be sensitive. Two of the 25 post-1948 annual series were for single MLH, 370 (Shipbuilding) and 383 (Aerospace), and these were taken from various issues of the Blue Book. The remaining 23 post-1948 annual series and the 11 pre-1948 series are unpublished CSO material which was used in their perpetual inventory model of the capital stock before they switched their estimates to a 1980 SIC basis. I am very grateful to R.J. Allard for making these data available to me. The procedures for interpolating and extrapolating the Census data on investment are more fully explained in O'Mahony and Oulton (1989). (e) Adjustment for financial leasing The basis for the adjustment for financial leasing is an unpublished CSO series giving gross investment in plant and machinery by financial institutions for the purpose of leasing, 1980 prices, 1967-85. Prior to 1967 financial leasing is generally agreed to have been negligible. I am grateful to my colleague Tony Smith for making this series available to me. It was assumed that one half of this investment was for leasing to manufacturing, a `guesstimate' derived from table 1 of Penneck and Woods (1982). The total amount was then apportioned among the industries using the share of each industry in `Hire of plant, machinery and vehicles' recorded in the 1979 RCP (SIC 1980 version). This is the only year in which payments for hiring plant and machinery are shown separately from rents of building and land. NOTES (1)In the short run there are other, cyclical influences on the observed growth rate of labour productivity. Typically, the labour force is adjusted more slowly than output, so that productivity growth falls during a recession and rises during a recovery. (2)There have been a number of attempts, such as Mizon and Nickell (1983) and Ingham et al. (1987), to estimate vintage models econometrically. These often require elaborate estimation methods which it would be impractical to use at the industry level. Also, they assume the underlying productivity growth rate to be constant, while it is one of the purposes of the present paper to test whether in fact it is. (3)The equations were: [Mathematical Expression Omitted] (4)The use of cyclical peaks means that measuring productivity in terms of employment rather than hours worked, which are anyway only available for operatives, is likely to have very little effect on the results, except perhaps for the 1960s. To illustrate, the index of hours worked per operative for selected years is as follows (1980=100):

(5)Table 3 might be criticised as logically inconsistent, since for each sub-period it is assumed the vintage model, with given, constant value of b, is correct up to the start of that sub-period. However the table itself refutes this assumption. An alternative is, when calculating c and n for a given sub-period, to employ the values of c and n calculated for the preceding sub-periods. This has been done, but produces results which are even more implausible than those of table 3. (6)A more complex vintage model for total manufacturing is described in Wren-Lewis (1988). (7)Some of these extreme values can probably be explained by labour hoarding, contrary to the model's assumptions. The clearest example of this probably MLH 311 (Iron and steel), where there was a huge fall in output between 1973 and 1979 but a much smaller fall in the labour force. Between 1979 and 1985, output rose but the labour force more than halved. Most likely, labour was being hoarded in 1979 but was subsequently dishoarded. The role of labour hoarding is examined in Oulton (1989). (8)This is, of course, not a new conclusion. Candidates for this common factor include the first oil price shock, inflation and over-optimistic expectations of future output, leading to labour hoarding in 1979 (Wren-Lewis, 1986). If the oil price shock were the culprit, this would work by inducing substitution of labour for energy and capital (if energy and capital are complements), thus reducing the growth rate of labour productivity, a possibility ruled out in the present model by the `clay-clay' assumption (Ingham et al., 1987). The oil price hypothesis has recently come under attack from Hulten et al. (1987) who find that the relative prices of second-hand, energy-intensive capital goods in the US did not fall after 1973, as one might have expected if there had been accelerated scrapping of such equipment. (9)The 94 industries can be identified from the list of 96 industries given in Oulton (1988, Appendix B), except that MLH 262 and 263 have been excluded in the present paper since they are no longer part of the 1980 definition of manufacturing. (10)Some other explanations of the experience of the 1980s, in particular the roles of labour shakeout and of the shock of the 1980--1 recession, are explored in Oulton (1989); see also Layard and Nickell (1988) and Metcalf (1988). REFERENCES Central Statistical Office (1980), Standard Industrial Classification Revised 1980: reconciliation with Standard Industrial Classification 1968, London, HMSO. Central Statistical Office (1985), United Kingdom national account: sources and methods, 3rd edition, London, HMSO. Griffin, T. (1979), `The stock of fixed assets in the United Kingdom: how to make best use of the statistics', in Patterson, K.D. and Schott, K. (eds.) The measurement of capital: theory and practice, Macmillan, London. Hulten, C.R., Robertson, J.W. and Wykoff, F.C. (1987), `Energy, obsolescence and the productivity slowdown', NBER Working Paper No. 2404. Ingham, A., Ulph, A., and Toker, M. (1987), `A vintage model of scrapping and investment', University of Southampton, mimeo. Johansen, L. (1972), Production functions: an integration of micro and macro, short-and long-run aspects, North-Holland, Amsterdam. Layard, R. and Nickell, S. (1988), `The Thatcher miracle?', Centre for Labour Economics, mimeo. Metcalf, D. (1988), `Water notes dry up', London School of Economics, Centre for Labour Economics, Discussion Paper No. 320. Mizon, G. and Nickell, S.J. (1983), `Vintage production models of UK manufacturing industry', Scandinavian Journal of Economics, vol. 85, no. 2, pp. 295-310. Muellbauer, J. (1986), `Productivity and competitiveness in British manufacturing', Oxford Review of Economic Policy, vol. 2, no. 3, Autumn, pp. i-xxv. O'Mahony, M. and Oulton, N. (1989), `Industry-level estimates of the capital stock in UK manufacturing, 1948-85', mimeo. Oulton, N. (1987), `Plant closures and the productivity `miracle' in manufacturing', National Institute Economic Review, no. 121, August, pp. 53-o. Oulton, N. (1988), `Productivity, investment and scrapping in UK manufacturing: a vintage capital approach', National Institute of Economic and Social Research Discussion Paper 148, November, London. Oulton, N. (1989), `The productivity improvement of the 1980s: tests of some alternative hypotheses', National Institute of Economic and Social Research, mimeo. Penneck, S. and Woods, R. (1982), `Effects of leasing on statistics of manufacturing capital expenditure', Economic Trends, February, pp. 97-104. Prais, S.J. (1986), `Some international comparisons of the age of the machine stock', Journal of Industrial Economics, vol. 34, no. 3, pp. 261-77. Salter, W.E.G. (1960), `Productivity and technical change', Cambridge University Press, Cambridge. Solow, R.M. (1969), Growth theory: an exposition, Clarendon Press, Oxford. Solow, R.M., Tobin, J., von Weizsacker, C.C. and Yaari, M. (1966), `Neoclassical growth with fixed factor proportions', Review of Economic Studies', vol. 33, pp. 79-115. Steedman, H. and Wagner, K. (1987), `A second look at productivity, machinery and skills in Britain and Germany', National Institute Economic Review, no. 122, November, pp. 84-95. Wadhwani, S. and Wall, M. (1986), `The UK capital stock--new estimates of premature scrapping', Oxford Review of Economic Policy, vol. 2, no. 3, pp. 44-55. Wren-Lewis, S. (1986), `An econometric model of UK manufacturing employment using survey data on expected output', Journal of Applied Econometrics, vol. 1, pp. 297-316. Wren-Lewis, S. (1988), `Supply, liquidity and credit: a new version of the Institute's domestic econometric macromodel', National Institute Economic Review, no. 126, November, pp. 32-43. ACKNOWLEDGEMENTS I should like to thank Bart van Ark, Mary O'Mahony, Sig Prais, Hilary Steedman, Simon Wren-Lewis and a referee for helpful comments on an earlier draft. Some of the results reported here draw on joint work with Mary O'Mahony. Darinka Martin provided research assistance. I am very grateful to Dick Allard and Tony Smith for generously making data on investment available to me. This research was made possible by a grant from the Leverhulme Trust.

1. Introduction To what extent is the rate of growth of labour productivity explained by the twin forces of investment in new and scrapping of old equipment? This article seeks to answer this question for manufacturing, making use of a vintage capital model. The results to be discussed are for both total manufacturing and a large sample of manufacturing industries, from the 1960s to the 1980s. We shall be particularly concerned to see to what extent the improvement in productivity growth which has occurred in most industries in the 1980s can be explained by the forces under investigation.

Up to the mid 1960s, output, employment and productivity (output per person employed) in manufacturing displayed a simple pattern of business cycle fluctuations superimposed on a strong upward trend. After 1966, however, employment began to decline and has continued to do so, particularly in the 1980s. Output also fell after 1973 and particularly after 1979; despite some recovery since 1982 it has not regained the 1973 level. The growth rate of labour productivity tended to rise in each successive cycle, until 1973. There then followed a marked slowdown in the 1970s, followed by a recovery in the last sub-period (though the rate during 1979-86 is still less than that of the much despised Wilson--Heath era).

A number of writers (including Muellbauer, 1986) have suggested that the slowdown in the 1970s and the recovery in the 1980s can both be explained (at least in part) by a vintage capital approach. The vintage model sees new capital investment as the prime source of productivity growth in the long run: new technology must be embodied in new equipment. At any one time, there exists a stock of capital equipment of different ages. The productivity of labour on older, less technically advanced equipment is lower than that on newer equipment. In the event of an unexpected rise in demand older equipment will be retained in use for longer than anticipated; in extreme cases `mothballed' equipment may be brought back into use. The average age of the capital stock in use will rise and the observed growth of labour productivity, which is an average across all vintages of capital in use, will fall.(1) In the longer run, if the rise in demand persists, there will be more investment in new equipment and the growth rate of labour productivity will rise again. Conversely, if there is an unexpected fall in demand, older vintages of equipment may be scrapped prematurely. In this case the average age of capital equipment in use will fall and the growth rate of labour productivity will be observed to rise, as a higher proportion of the surviving labour force becomes concentrated on newer, more productive equipment. Note that according to the vintage capital model, it is always the oldest equipment which is scrapped first. In summary then, the growth of labour productivity is the result of the balance between two forces--first the rate at which new technology is introduced, measured by gross investment, and second, the rate at which older equipment, embodying inferior technology, is scrapped.

A possible explanation of the 1970s slowdown is that investment slowed down during this period, thus lowering the rate of introduction of new technology. The 1980s recovery in productivity could be explained by exceptionally heavy scrapping of old equipment. (The period 1973-9 was also a period of above-average scrapping in the view of many, which would have tended to raise the productivity growth rate; if the vintage model is correct, this effect must have been outweighed by low investment.) An extreme version of this thesis would assert that there has been no change in the underlying growth rate of productivity (the rate which would be observed in a hypothetical steady state) and that all changes in observed productivity are due either to variations in the rate of gross investment or to variations in the rate of scrapping.

Both the total and split into two components: plant and machinery (IP) and new buildings (IB). The third, much smaller component, is vehicles, ships and aircraft. Investment in new buildings fell heavily after 1969. Investment in plant and machinery, apart from cyclical fluctuations, shows no absolute decline, but its growth rate clearly flattens off in the 1970s. So the evidence on investment is at least weakly consistent with the vintage model. For scrapping, however, there is no direct evidence at all, though estimates have been made, on quite different bases, by Wadhwani and Wall (1986) and Oulton (1987).

The vintage model is set out formally.

2. The vintage capital model The vintage capital approach was popularised by Salter (1960). The approach was formalised as a model by Solow et al. (1966). Further theoretical development is in Johansen (1972). A simple exposition of the model is provided by Solow (1969). In what follows a highly simplified (technically a `clay-clay') version of the vintage model will be analysed. No substitution between capital and other inputs, either ex ante or ex post, will be allowed. A little will be said later on the effect of relaxing this assumption of no substitutability, which is made purely because of the difficulties of estimating the parameters of a more general vintage production function.

Capacity output (Y) is related to past (gross) investment (I) as follows: (Mathematical Expressions Omitted) Here m=m(t) is the age of the oldest plant still in use at time t, which may in general vary with time. The parameter a is capacity output per unit of investment. Labour (L) required to produce capacity output is given by: (Mathematical Expressions Omitted) where it is assumed that labour required per unit of capacity output declines exponentially at rate b from the level required in the base year ([b.sub.0]), that is, labour required on vintage v is [b.sub.0e.sup.-bv]. Labour productivity (Q) is

Q(t) = Y(t)/L(t) (3)

The above relations hold in or out of the steady state. If a steady state is assumed in which output grows at rate g and a constant proportion of output, s, is invested per period, then putting [Y.sub.0] = Y(0) and [I.sub.0] = I(0), (1) and (2) become: [Mathematical Expressions Omitted] where [mu] is the steady state life of plant (m(t) = [mu], all t). Setting t = 0 in (4) and using the fact that s = [I.sub.0]/[Y.sub.0], we find

a = g/s(1-[e.sup.-g [mu]). (6)

Given therefore three out of the four quantities s, g, a and [mu], we can find the remaining one.

Labour productivity in the steady state, from (4) and (5), is given by: [Mathematical Expressions Omitted] Hence, in the steady state,

b = dlog Q(t)/dlog t. (8) that is, the steady state growth rate of productivity is b. Also, by setting t = 0 in (7), we can find an expression for [b.sub.0]: [Mathematical Expressions Omitted] putting [Q.sub.0] = Q(0).

In summary, if we could observe the economy in a steady state, we could readily estimate the unknown parameters of the vintage capital model (a, [b.sub.0] and b). The observed growth rate of productivity would give us b (equation (8)); a and [b.sub.0] would come from (6) and (9) respectively, since the saving ratio(s), the output growth rate (g) and the age of the oldest equipment still in use (mu) would all be in principle observable. Alternatively, without assuming a steady state, if m(t) were known for some t, we could find the parameter a from (1). If in addition b were known, then [b.sub.0] could be found from (2), again without assuming a steady state.

3. Estimating the effect of premature scrapping. Suppose that we wish to estimate the impact of premature scrapping between two date, say S and T (T [greater than] S). It is convenient now to switch to a discrete-time representation of the vintage model, since the data themselves are inevitably discrete. Consider the labour required at T to man the new equipment installed between S and T, [L.sup.N] (T): [Mathematical Expressions Omitted] where c is the rate at which labour requirements are declining on equipment installed after S (c need not equal b, the rate assumed for equipment installed up to S). It is assumed that the interval (T-S) is short enough so that no new capital installed between these dates has been scrapped before T.

Labour required at T on plant installed up to S, and which is still in use at T, [L.sup.0] (T), is: [Mathematical Expressions Omitted] The quantity [Alpha] is a slight complication induced by discrete-time analysis. The point is that the oldest vintage in existence might not represent all the investment done during that year; it is possible that part only of the oldest vintage has been scrapped. The age of the oldest plant in existence at T, n(T), can therefore be defined as

n(T) = m(T) - 1 + [Alpha] (12)

Total labour requirements at T are:

L(T) = [L.sup.0] (T) + [L.sup.N] (T) (13)

Next we calculate the output producible on the capacity available at T: [Mathematical Expressions Omitted] where the `[caret]' over Y is added to indicate that this output level is the one predicted by the vintage model. The model of the preceding section has been generalised slightly by the introduction of the parameter [Delta] which measures the physical rate of depreciation (physical decline in output-producing capacity of capital equipment). We can also define the predicted productivity level as:

[caret] Q(T) = [caret] Y(T)/L(T) (15)

Suppose that we know the parameters a, [b.sub.0], b, c and [Delta] and that we have data on labour, output and investment for as far back as necessary. Then we can solve for the remaining unknowns in the following way. First, observations on investment enable us to solve for [L.sup.N] (T) from (10). Knowing [L.sup.N] (T), we can then find [L.sup.0] (T) from (13). Plugging the newly-found value for [L.sup.0] (T) into (11), we can solve for m(T) and [Delta] by a simple iterative process. Finally, (14) and (15) can be solved to find the output and productivity predicted by the vintage model.(2)

An alternative approach is to assume that the vintage model predicts productivity growth exactly. One of the five parameters now becomes free, to be determined by the data; it is most natural to let c, the rate at which labour requirements on new equipment are falling during the period under analysis, be the free parameter. Under this alternative approach, since [caret] Y(T) = Y(T) by assumption now, we can solve (14) for m(T) and [Delta] by a simple iterative process. [L.sup.0] (T) can now be found from (11) and hence [L.sup.N] (T) from (13). Plugging this value for [L.sup.N] (T) into (10), we can solve for c.

Turning now to the parameters, as we have seen, by assuming a steady state all the parameters required for the calculations (except c) can be estimated from equations (6), (8) and (9), provided that the age of the oldest vintage in the steady state is known (mu). An alternative course, which minimises reliance on the assumption of a steady state, is to estimate b from equation (8) and then to estimate a and [b.sub.0] from equations (1) and (2). This was the course actually adopted. It was assumed that manufacturing was approximately in a steady state over the period 1960--4; b was then set equal to the observed growth rate of productivity over this period, 3.12 per cent. a and [b.sub.0] were then found from discrete versions of equations (1) and (2), with t = 1964 and three alternative values for m (1964), namely 15, 30 and 45 years.(3) The wide span assumed for m seems justified by the intrinsic uncertainty about this parameter. The evidence presented in Griffin suggests that 30 years is a reasonable central value, contrary to most people's intuition. Finally, under the first approach where a value for c must be fixed in advance, it was assumed that c = b.

To summarise, the steps required for calculating the productivity growth rate predicted by the vintage capital model for a particular period are as follows: (1) Estimate the basic parameters, using data from a

period preceding the one under analysis. (2) Calculate the labour required to operate

equipment installed during the period under analysis

(investment during the period being known); this

quantity is called [L.sup.N] (T) above. (3) Subtracting [L.sup.N] (T) from the (known) total labour

force at the end of the period under study, we can

derive the labour required to operate the rest of

the equipment still in use at the end of the period,

that is, the labour required for that part of the total

equipment still in use which was installed before

the start of the period; this quantity is called [L.sup.0] (T)

above. (4) Given knowledge of investment prior to the period

under analysis and knowing now the labour force

employed on old equipment, we can calculate

how much of that investment has actually

survived to the end of the period, that is, the age of

the oldest equipment still in use. (5) Knowing the age of the oldest equipment still in

use, we can calculate the output producible on

the entire stock of equipment which has survived

to the end of the period under study and hence the

productivity predicted by the vintage model.

4. Results for total manufacturing As already noted, the CSO distinguishes three types of investment--plant and machinery; buildings; and vehicles, ships and aircraft. Investment in plant and machinery would seem to correspond best with the vintage model. By contrast, buildings have a long life (on average 60 years, according to the CSO;), are frequently malleable (as exemplified by 18th century warehouses in the Docklands) and so are infrequently subject to scrapping due to obsolescence. Vehicles have a short life (about 10 years, according to the CSO, but in practice probably considerably less) but this is probably due in the main to declining physical efficiency and rising maintenance costs, rather than obsolescence. The calculations to be reported therefore employ gross investment in plant and machinery by manufacturing as a whole.

The results of these calculations, for successive sub-periods. The periods chosen are business cycle peaks (except for 1986), in order that the observed labour force should correspond fairly well to that required for full capacity working. The calculations are based on data for output, employment and gross investment in plant and machinery in manufacturing as a whole.(4) Full details of the data are in the appendix. In these calculations c in each sub-period is assumed to equal b (which in turn is assumed to equal 0.0312 or 3.12 per cent); [Delta] is assumed to be zero.

For 1964--8 and 1968--73, with the age of oldest plant assumed to be 30 years, the vintage model does a reasonable job of predicting productivity growth. But it also predicts a substantial shortening of plant life, while what direct evidence there is indicates constancy of plant life (Griffin, 1979). The model really goes wrong in trying to explain 1973--9, where, regardless of the assumed plant life, the productivity growth rate is grossly over-predicted. There is a further substantial over-prediction in the final period. With the oldest plant in 1964 assumed to be 30 years, the model predicts that the age of the oldest plant in 1986 is less than 17 years, quite out of line with CSO estimates (CSO, 1985).

The reason for this poor performance is clear. Since output actually fell after 1973, there must, according to the vintage model, have been large scale scrapping, which should have led to a big increase in productivity growth. The greater is the age assumed for the oldest plant in 1964, the greater the amount of low productivity plant in existence and so the greater the scope for productivity gains from scrapping. Similarly, if the vintage model were correct, productivity growth in the 1980s should have been higher than observed, because of the large scale scrapping which the model predicts.

A number of variations on the methods were tried. For example, (1) steady state values for all the parameters were used; (2) different values for b were tried; (3) [Delta] was set equal to 0.02; (4) total investment rather than plant and machinery only was tried; but without any appreciable change in the results.

The hypothesis that the underlying productivity growth rate has been the same throughout the whole 22 year period (the hypothesis that b = c) has thus been decisively rejected. It is possible, however, that the vintage model may still be found to fit the facts, if the underlying productivity growth rate (c) is allowed to vary in each subperiod. Reports results based on finding the values of c and n in each subperiod which reproduce exactly the observed productivity growth. Clearly, these results are unbelievable. Making the central assumption that the age of the oldest plant in 1964 was 30 years, the model predicts that productivity on new equipment was falling during 1979--86 at the rate of 8.6 per cent and that by 1986 the oldest surviving plant was only 13 years old. The basic problem for the vintage model is again that, given the large labour force reductions which have occurred, the observed rate of productivity growth should have been much higher than was actually the case; this can only be `explained' by `predicting' that productivity growth on new investment was very low (in fact, negative). But even in the 1960s this version of the vintage model produces implausible results in trying to explain the modest increases in productivity growth observed then.(5)

Another, more positive, view might be taken of these results. It could be argued in favour of the vintage model that it demonstrates how large changes in productivity growth rates can be generated by the observed changes in labour, output and investment. Furthermore, the predicted changes in productivity growth are in the right direction. Thus the model predicts a slowdown in productivity growth in the 1970s and a speed-up in the 1980s. The fact that growth is over-predicted in 1973--9 could be explained by the presence of special factors during this period. The implausible results for the age of capital equipment could be avoided by stressing the difference between the age of the oldest equipment in existence and the age of the oldest equipment in use (which may be less and anyway is much harder to measure). Above all, a larger role could be allotted to factor substitution.(6) But rather than pursue the approach of refining the model, it was decided instead to see how far a simple model could take us in explaining the inter-industry differences in productivity growth rates.

5. Cross section results for manufacturing In this section the results of testing the vintage capital model on a cross section of 60 industries are reported. These 60 industries, which accounted for about half of total manufacturing output in 1985, were selected as follows. First of all, as part of a wider study of industrial productivity, 141 industries covering the whole of the production sector of the economy were selected. These industries, classified in accordance with the 1968 Standard Industrial Classification (SIC), were chosen in such a way as to maximise the chance of getting consistent data back to the 1950s. In all but a couple of cases, the industries are either Minimum List Headings (MLH) or subsections of MLH. No MLH covered by the Census of Production was excluded. Second, the MLH which are not counted as part of manufacturing under the 1980 (not 1968) SIC's definition were excluded. Third, industries for which an output price index was not available back to the 1950s were excluded. This last step is in practice the most significant one. A list and description of the 60 industries finally selected is in Oulton (1988, Appendix B).

The data on output and employment were drawn from the Census of Production. The availability of the Census determines the periods which can be studied, which are consequently somewhat different from those used in studying total manufacturing. The periods were 1954--63 for estimating the basic parameters a, [b.sub.0] and b for each industry, and 1963--8, 1968--73, 1973--9 and 1979--85 for testing the predictions of the model. Productivity is defined as net output divided by total employment, where net output is as defined in the Census except that a rough correction has been made for stock appreciation. Net output was deflated to a constant price basis using each industry's producer price index (formerly wholesale price index) for home sales. Investment in plant and machinery from 1948 onwards also comes from the Census. However, the Census has only been annual since 1970, so between then and 1948 interpolation was necessary for some years using annual investment data on industry groups within manufacturing (from the CSO) as a control. The current price investment data were deflated using the appropriate CSO deflators for plant and machinery and then adjusted for financial leasing.

The major problem in calculating consistent series from the 1950s to the present is the change from the 1968 SIC to the 1980 SIC. Until 1979 the Census of Production was produced on the 1968 basis; from 1980 it has been produced on the 1980 basis. The problem of reclassifying data on the new basis back to the old one has been analysed by Oulton (1988, appendix C) and the methods described there were used to reclassify the investment, net output, employment and price data. A fuller description of the data sources and the methods employed is in the appendix. In what follows the empirical results will be summarised; more detail can be found in Oulton (1988).

Statistics of the growth rates of productivity experienced by the sample of 60 industries over the 31 years from 1954 to 1985, broken down into five periods. Not surprisingly, the average performance of these industries mimics the performance of manufacturing as a whole. On average, productivity growth accelerated in 1963--8 and again in 1968--73, fell heavily in 1973--9 and recovered in 1979--85. Nevertheless there is a considerable diversity of experience; in fact, as measured by the standard deviation of growth rates, diversity has tended to rise over time. 11 industries bucked the trend by showing higher rates of productivity growth in 1973--9 than in the previous period and 10 showed lower rates in 1979--85 than in 1973--9. The standard deviation of the change in growth rates between 1968--73 and 1973--9 was 5.62 per cent and that of the change in growth rates between the last two periods was 6.08 per cent. It is also noteworthy that negative rates of productivity growth occurred in 1 industry in 1963--8, in 3 industries in 1968--73, in no less than 24 industries in 1973--9 and in 1 industry in 1979--85.(7)

Though it is a digression from the main theme of this paper, it is interesting to consider the correlation between output growth and productivity growth. The correlation coefficients in our sample were as follows:

1963--8 0.59 1968--73 0.76 1973--9 0.80 1979--85 0.55

Thus the Verdoorn Law, though somewhat weaker in the last period, is still far from dead.

Summary statistics of the vintage capital model's predictions for plant life which assumes a 30 year life in 1963. In these and later estimates, the parameters a, [b.sub.0] and b have been estimated separately for each industry, using industry data, by the same method as for total manufacturing; [Delta] is set to 0. The underlying productivity growth rate is assumed not to have changed after 1963 (that is, b = c for each industry in every subsequent time period). On average, plant life is predicted to decline substantially to only 17.3 years in 1985. Whatever the value assumed for plant life in 1963, it turns out that the model predicts a decline in plant life after that date--to 10.9 years in 1985 if the 1963 value is 15 years and to 28.1 years if the 1963 value is 45 years. This predicted decline is at variance with what little direct evidence we have; it is far greater than that which the CSO assumes to have occurred after 1970 (CSO, 1985), which in any case has been questioned by Prais (1986).

Within the overall pattern of declining plant life, there are a considerable number of exceptions. Thus, in the four time periods, the number of industries in which plant life is predicted to have increased is successively 20, 20, 17 and 4. In 1985 there are 8 industries with predicted plant lives greater than 30 years. In some industries the increase in plant life is so great that it can only have occurred if (implausibly) some earlier vintages, instead of being scrapped, were first mothballed and then brought back into use.

The model's predictions for productivity growth rates which again assumes a 1963 plant life of 30 years, and the predictive accuracy of the model is for three different values of 1963 plant life. It can be seen that the model's performance is insensitive to the plant life assumption. On the root mean square error (RMSE) criterion, no one assumption dominates the rest. A life of 15 years might be preferred on purely statistical grounds, though there is little difference in RMSE between this and a 30 year life. On any assumption about plant life, the vintage capital model tends to over-predict productivity growth in both the last two periods, as it does at the aggregate level; furthermore, the accuracy of its predictions diminish substantially with each successive period.

The results of regressing actual on predicted productivity growth for each period. If the vintage model were to be a fully satisfactory explanation of productivity growth then we would expect that (1) the constant term would be insignificantly different from zero; (2) the coefficient on predicted productivity growth would be insignificantly different from one; and (3) [R.sup.2] would be high. None of these hopes are satisfied. In terms of explanatory power, the period 1968--73 is the best for the model and next is 1973--9. However, the constant is always significantly different from zero, indicating that the model's predictions are biased. Most important, the coefficient on expected productivity growth is always significantly different from one. Nevertheless, the latter variable is highly significant in three out of the four periods, though not at all in the last. This suggests pooling the observations in the first three periods, to produce the following regression results (180 observations, t ratios in parentheses):

h = 1.68 + 0.46h[carets] (15)

(4.59) (6.69)

[R.sup.2] = 0.2008

and h = 3.03 + 0.37h[carets] + 0.64D68 - 3.67D73 (16) (6.63) (6.34) (1.22) (-6.90)

[R.sup.2] = 0.4437 Here h and h[carets] are actual and predicted productivity growth; D68 and D73 are period dummies taking the value 1 in 1968-73 and 1973-9 respectively and 0 at other times. The first of these regressions suggests that vintage effects alone can account for about 20 per cent of the interindustry variation in productivity growth over the period 1963-79. Adding a dummy for 1973-9 raises the proportion explained to about 44 per cent. In conclusion then, the vintage capital model does seem to have a role to play in explaining productivity growth over 1963-79. In addition, there is some evidence for a common factor depressing all growth rates in 1973-9.(8) However, the results also indicate that vintage effects have no role to play in explaining productivity growth differences after 1979.

How sensitive are these conclusions to the particular sample and to the particular assumptions used? The estimates of b vary widely across industries. This may be because the assumption of an approximately steady state during 1954-63 was far from the truth for many industries. The calculations were therefore rerun assuming the same value of b for all industries, namely the sample average over 1954-63 of 0.038. We can see that, on the RMSE criterion, assuming the same b for all industries gives better results. However, the regression analysis leads to conclusions similar to those of the earlier one. Once again, the coefficient on the predicted growth rate is insignificant for the 1979-85 period.

A second sensitivity test was to enlarge the sample of industries. Price data is available for many more industries from the 1970s. These can be brought into the sample if ways can be found of estimating the parameters. The method adopted was first, to assume b to be the same for all industries, equal to the value used in the preceding section for total manufacturing (0.0312), and second, to estimate a and [b.sub.0] using 1973, rather than 1963, in equations (1) and (2). The results, which are for 94 industries covering most of manufacturing, are in table 10.(9) The RMSE is now a bit lower for 1973-9 than in the 60 industry sample but much higher for 1979-85. The regression results for the full sample show at first sight a rather puzzling pattern in that the predicted growth rate is insignificant in 1973-9 but highly significant in 1979-85, the reverse of the finding for the 60 industry sample. Inspection of the scatterplot, however, suggests that the results are being distorted by a single outlier, MLH 311 (iron and steel). When this industry is omitted, the predicted growth rate becomes insignificant again in 1979-85.

6. Concluding remarks In an earlier note (Oulton, 1987), some doubt was cast on the proposition that premature scrapping can explain the improved productivity performance of the 1980s. The present article reinforces these doubts. As we have seen, our (admittedly simple) version of the vintage model tends to overpredict productivity growth in both the 1970s and in the 1980s. Moreover, though the model has some success in explaining the inter-industry variation in productivity growth in the 1970s, it has much less success (by itself) in explaining the pattern in the 1980s. These results might be considered surprising, given the stress traditionally laid by economists on the importance of capital accumulation and the substantial degree of subsidy accorded until recently to investment, particularly to investment in plant and machinery. It may be that the comparative lack of success of our version of the vintage model is due to its restrictive assumptions; if these were relaxed, no doubt more could be explained. However, although the vintage capital model, in its general form, is widely considered to be more realistic than its neo-classical rival, it is worth considering the possibility that two of its key assumptions may turn out on reflection to be suspect empirically, at least when applied at the industry level. These are firstly that it is always the oldest, least productive plant which is the first to be scrapped and secondly that all technical progress must be embodied in new equipment.

The first of these assumptions clearly need not hold at the macro level. For example, demand might decline particularly sharply in industries whose equipment happened to be relatively new. Premature scrapping in these industries might then remove equipment which was relatively young compared to equipment elsewhere. But the assumption need not hold at the micro level either. Consider an industry which is divided into two parts--one part making luxury products by traditional methods and another part making mass-produced, standardised goods. Perhaps under government prodding, the mass-production part of the industry has re-equipped itself with modern plant to face the foreign competition. In the event the foreign competition proves too strong and much of the modern equipment is scrapped; meanwhile the more traditional sector of the industry survives. This little parable might apply to the textile industry.

The second key assumption, that all technical progress must be embodied in new equipment, is clearly extreme. There are a number of ways in which productivity can be raised without investing in new equipment. These include: (1) the elimination of previously hoarded labour; (2) changes in working practices leading to better use of existing equipment; (3) increased work intensity; (4) a more skilled labour force; (5) the development of higher quality products (higher value added). No direct evidence exists of which I am aware bearing on the last of these five possibilities. However, a higher quality product probably requires a more highly skilled workforce (see, for example, Steedman and Wagner, 1987) and there is much evidence to suggest that skill levels have not improved in recent years, thus eliminating the fourth possibility as well. The evidence set out in earlier sections suggests that the first three routes to higher productivity may have been more important for productivity growth than were investment and scrapping, the factors stressed by the vintage model, at least in the 1980s.(10) APPENDIX: DATA SOURCES

In the description of the sources the following abbreviations have been used:

BB Blue Book BrBu British Business BLSHA British Labour Statistics: Historical Abstract 1886--1968, Department o f employment and productivity, (HMSO, London, 1971). ETAS87 Economic Trends Annual Supplement 1987 (CSO, 1987) MDS Monthly Digest of Statistics HRCP Historical Record of the Census of Production 1907 to 1970 (Business St atistics Office, 1978) RCP Report on the Census of Production: summary tables, PA1002 (BSO, variou s years)

A. Total manufacturing

Output 1980-86 MDS (December, 1987), table 7.1 1948-79 ETAS87, p.80 Employment and 1980-86 MDS (December, 1987), table 7.2 productivity 1960-79 ETAS87, p.108 1950-59 BLSHA, table 104 Investment (plant 1980-86 MDS (December, 1987), table 1.8 & machinery; 1955-79 ETAS87, p.56 buildings; total) 1951-54 BB, 1962, table 58 1948-50 BB, 1956, table 50 1900-47 CSO,unpublished material

Output, employment and productivity were converted from index numbers (1980 = 100) to respectively million pounds at 1980 prices, thousands and pounds at 1980 prices per person employed, by using the 1980 values of these variables, from MDS (December, 1987). The output figure was calculated as 26.6 per cent of GDP at factor cost.

The investment data for 1948-54 is in current prices and was deflated to 1980 prices using unpublished CSO deflators. I am grateful to R.J. Allard for supplying me with these, as also with the unpublished investment data for years prior to 1948. The latter derive ultimately from the CSO and are used in their perpetual inventory model of the capital stock. From 1968 onwards, investment includes leasing, assumed to be wholly of plant and machinery. Leasing comes from the NIESR data bank for 1968-79 and from MDS (December, 1987) for 1980-6. B. Industry data (a) Sources

Net output 1954, 1958, 1963, 1968 HRCP (current prices) 1973 RCP 1973 (BSO, 1978) and employment 1979 RCP 1979 (BSO, 1982) 1985 RCP 1985 (BSO, 1987) Deflators for Producer price indexes (formerly wholesale price in dexes for home sales, from BrBu and its predecessors, various issu es; some unpublished indexes were specially supplied by the BSO. The def lator for MLH 485/486 (newspapers and periodicals) was the corres ponding retail price index. Producer price indexes with reference years 1954, 1963, 1970, 1975 and 1980 were spliced together using overlappi ng years. For 1985, indexes are for Activity Headings and for other yea rs they are for Minimum List Headings. Investment in plant 1948-68 HRCP (by MLH) and machinery (Available years differ between industries). (acquisitions less 1970-79 RCP, various issues (by ML H) disposals, current prices) 1980-83 unpublished data supplied by BSO (by AH) 1984, 1985 RCP 1984 and 1985 (by AH) Deflators for Before 1956 One deflator for all manuf acturing (CSO, unpublished) investment 1956-79 Separate deflators for ten industry groups within manufacturing (CSO, unpublished) 1980-85 Separate deflators for 27 industry groups within manufacturing from `Price index numbers for current cost accounting' (BSO, various issues)

(b) Reclassification from 1980 SIC to 1968 SIC From 1948 up to 1979 Census of Production data is available under the 1968 SIC. From 1980 on, Census data has been published according to the 1980 SIC. The 1980 SIC is more detailed than the 1968 one; there are some 206 Activity Headings (AH) in manufacturing in the former, compared with some 137 Minimum List Headings (MLH) or sub-sections of MLH for which data is available more or less consistently back to 1948 under the 1968 SIC (though the definitions of the manufacturing sector differ somewhat). Hence it was decided to reclassify data on the 1980 SIC basis back to the 1968 one rather than the other way round.

The CSO has published a `reconciliation' between the two classification (CSO, 1980) which shows for each AH the one or more MLH or sub-sections of MLH to which it corresponds. The problem of reclassification is to decide in what proportions an AH must be divided on the numerous occasions when it has to be split between two or more MLH. It is important note that these unknown proportions will in general be different for different variables, for example net output, employment or investment. A solution is possible since the 1979 Census was published on the basis of both SIC. With the aid of the two Census reports and the `reconciliation', computer programs were written which can calculate the unknown proportions for any Census variable and then using these proportions reclassify data on an AH basis back to an MLH basis. The reclassification problem and the solution proposed are more fully discussed in Oulton (1988, Appendix C). By these means the post-1979 data on net output, employment and investment were made comparable with data for earlier years. For producer prices, the AH level indexes were aggregated using gross output weights (derived from the reclassification procedure) to arrive at MLH level indexes. (c) Adjustment for stock appreciation The Census of Production concept of net output is gross of stock appreciation. An adjustment conceptually identical to the one in the national accounts which turns the increase in the value of stocks into what is called `Value of the physical increase in stocks at current prices' is required also at the industry level. The Census distinguishes three kinds of stocks--materials and fuel, work in progress and goods on hand for sale (the last two usually being aggregated) and records both the value of the stocks at a reference date and the increase in value over the preceding year. For most, though not all, respondents the reference date is the end of the Census year. Ideally, separate price indexes should be used for each stock. Also, while net output is deflated by an index which is an annual average, calculating stock appreciation requires an end-of-year index. In practice, partly owing to the absence of adequate price indexes for materials and fuel in the earlier years, a much rougher method of adjustment was employed. The same price index was used for all three stocks and for all industries, namely the price index for aggregate manufacturing output. Using this method, stock appreciation as a percentage of unadjusted net output was on average about 6 per cent in 1973 and 1979 and considerably less in other years. (d) Interpolation and extrapolation of Census investment data Since 1948, questions about capital expenditure have been included in the Census. However, prior to 1970 the Census was not annual so there are missing values (the number varies between industries--nearly all industries have data for 1948, 1954, 1958, 1963 and 1968; some have more). The missing values between 1948 and 1970 were filled in by interpolation, using annual investment series on 25 industry groups in manufacturing (1968 SIC) as a control. For years prior to 1948 annual investment series on 11 industry groups were available and these were disaggregated to the MLH level using the average share of each industry in total investment by the group over the period 1948-54. Obviously, this extrapolation procedure can produce at best a reasonable guess for an industry's investment prior to 1948. However the main use for investment in the distant past is in estimating the constants a and [b.sub.0], to which the results of the vintage capital model are unlikely to be sensitive. Two of the 25 post-1948 annual series were for single MLH, 370 (Shipbuilding) and 383 (Aerospace), and these were taken from various issues of the Blue Book. The remaining 23 post-1948 annual series and the 11 pre-1948 series are unpublished CSO material which was used in their perpetual inventory model of the capital stock before they switched their estimates to a 1980 SIC basis. I am very grateful to R.J. Allard for making these data available to me. The procedures for interpolating and extrapolating the Census data on investment are more fully explained in O'Mahony and Oulton (1989). (e) Adjustment for financial leasing The basis for the adjustment for financial leasing is an unpublished CSO series giving gross investment in plant and machinery by financial institutions for the purpose of leasing, 1980 prices, 1967-85. Prior to 1967 financial leasing is generally agreed to have been negligible. I am grateful to my colleague Tony Smith for making this series available to me. It was assumed that one half of this investment was for leasing to manufacturing, a `guesstimate' derived from table 1 of Penneck and Woods (1982). The total amount was then apportioned among the industries using the share of each industry in `Hire of plant, machinery and vehicles' recorded in the 1979 RCP (SIC 1980 version). This is the only year in which payments for hiring plant and machinery are shown separately from rents of building and land. NOTES (1)In the short run there are other, cyclical influences on the observed growth rate of labour productivity. Typically, the labour force is adjusted more slowly than output, so that productivity growth falls during a recession and rises during a recovery. (2)There have been a number of attempts, such as Mizon and Nickell (1983) and Ingham et al. (1987), to estimate vintage models econometrically. These often require elaborate estimation methods which it would be impractical to use at the industry level. Also, they assume the underlying productivity growth rate to be constant, while it is one of the purposes of the present paper to test whether in fact it is. (3)The equations were: [Mathematical Expression Omitted] (4)The use of cyclical peaks means that measuring productivity in terms of employment rather than hours worked, which are anyway only available for operatives, is likely to have very little effect on the results, except perhaps for the 1960s. To illustrate, the index of hours worked per operative for selected years is as follows (1980=100):

1964 108.6 1968 105.5 1973 103.9 1979 103.3 1986 102.6

(5)Table 3 might be criticised as logically inconsistent, since for each sub-period it is assumed the vintage model, with given, constant value of b, is correct up to the start of that sub-period. However the table itself refutes this assumption. An alternative is, when calculating c and n for a given sub-period, to employ the values of c and n calculated for the preceding sub-periods. This has been done, but produces results which are even more implausible than those of table 3. (6)A more complex vintage model for total manufacturing is described in Wren-Lewis (1988). (7)Some of these extreme values can probably be explained by labour hoarding, contrary to the model's assumptions. The clearest example of this probably MLH 311 (Iron and steel), where there was a huge fall in output between 1973 and 1979 but a much smaller fall in the labour force. Between 1979 and 1985, output rose but the labour force more than halved. Most likely, labour was being hoarded in 1979 but was subsequently dishoarded. The role of labour hoarding is examined in Oulton (1989). (8)This is, of course, not a new conclusion. Candidates for this common factor include the first oil price shock, inflation and over-optimistic expectations of future output, leading to labour hoarding in 1979 (Wren-Lewis, 1986). If the oil price shock were the culprit, this would work by inducing substitution of labour for energy and capital (if energy and capital are complements), thus reducing the growth rate of labour productivity, a possibility ruled out in the present model by the `clay-clay' assumption (Ingham et al., 1987). The oil price hypothesis has recently come under attack from Hulten et al. (1987) who find that the relative prices of second-hand, energy-intensive capital goods in the US did not fall after 1973, as one might have expected if there had been accelerated scrapping of such equipment. (9)The 94 industries can be identified from the list of 96 industries given in Oulton (1988, Appendix B), except that MLH 262 and 263 have been excluded in the present paper since they are no longer part of the 1980 definition of manufacturing. (10)Some other explanations of the experience of the 1980s, in particular the roles of labour shakeout and of the shock of the 1980--1 recession, are explored in Oulton (1989); see also Layard and Nickell (1988) and Metcalf (1988). REFERENCES Central Statistical Office (1980), Standard Industrial Classification Revised 1980: reconciliation with Standard Industrial Classification 1968, London, HMSO. Central Statistical Office (1985), United Kingdom national account: sources and methods, 3rd edition, London, HMSO. Griffin, T. (1979), `The stock of fixed assets in the United Kingdom: how to make best use of the statistics', in Patterson, K.D. and Schott, K. (eds.) The measurement of capital: theory and practice, Macmillan, London. Hulten, C.R., Robertson, J.W. and Wykoff, F.C. (1987), `Energy, obsolescence and the productivity slowdown', NBER Working Paper No. 2404. Ingham, A., Ulph, A., and Toker, M. (1987), `A vintage model of scrapping and investment', University of Southampton, mimeo. Johansen, L. (1972), Production functions: an integration of micro and macro, short-and long-run aspects, North-Holland, Amsterdam. Layard, R. and Nickell, S. (1988), `The Thatcher miracle?', Centre for Labour Economics, mimeo. Metcalf, D. (1988), `Water notes dry up', London School of Economics, Centre for Labour Economics, Discussion Paper No. 320. Mizon, G. and Nickell, S.J. (1983), `Vintage production models of UK manufacturing industry', Scandinavian Journal of Economics, vol. 85, no. 2, pp. 295-310. Muellbauer, J. (1986), `Productivity and competitiveness in British manufacturing', Oxford Review of Economic Policy, vol. 2, no. 3, Autumn, pp. i-xxv. O'Mahony, M. and Oulton, N. (1989), `Industry-level estimates of the capital stock in UK manufacturing, 1948-85', mimeo. Oulton, N. (1987), `Plant closures and the productivity `miracle' in manufacturing', National Institute Economic Review, no. 121, August, pp. 53-o. Oulton, N. (1988), `Productivity, investment and scrapping in UK manufacturing: a vintage capital approach', National Institute of Economic and Social Research Discussion Paper 148, November, London. Oulton, N. (1989), `The productivity improvement of the 1980s: tests of some alternative hypotheses', National Institute of Economic and Social Research, mimeo. Penneck, S. and Woods, R. (1982), `Effects of leasing on statistics of manufacturing capital expenditure', Economic Trends, February, pp. 97-104. Prais, S.J. (1986), `Some international comparisons of the age of the machine stock', Journal of Industrial Economics, vol. 34, no. 3, pp. 261-77. Salter, W.E.G. (1960), `Productivity and technical change', Cambridge University Press, Cambridge. Solow, R.M. (1969), Growth theory: an exposition, Clarendon Press, Oxford. Solow, R.M., Tobin, J., von Weizsacker, C.C. and Yaari, M. (1966), `Neoclassical growth with fixed factor proportions', Review of Economic Studies', vol. 33, pp. 79-115. Steedman, H. and Wagner, K. (1987), `A second look at productivity, machinery and skills in Britain and Germany', National Institute Economic Review, no. 122, November, pp. 84-95. Wadhwani, S. and Wall, M. (1986), `The UK capital stock--new estimates of premature scrapping', Oxford Review of Economic Policy, vol. 2, no. 3, pp. 44-55. Wren-Lewis, S. (1986), `An econometric model of UK manufacturing employment using survey data on expected output', Journal of Applied Econometrics, vol. 1, pp. 297-316. Wren-Lewis, S. (1988), `Supply, liquidity and credit: a new version of the Institute's domestic econometric macromodel', National Institute Economic Review, no. 126, November, pp. 32-43. ACKNOWLEDGEMENTS I should like to thank Bart van Ark, Mary O'Mahony, Sig Prais, Hilary Steedman, Simon Wren-Lewis and a referee for helpful comments on an earlier draft. Some of the results reported here draw on joint work with Mary O'Mahony. Darinka Martin provided research assistance. I am very grateful to Dick Allard and Tony Smith for generously making data on investment available to me. This research was made possible by a grant from the Leverhulme Trust.

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Author: | Oulton, Nicholas |
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Publication: | National Institute Economic Review |

Date: | Feb 1, 1989 |

Words: | 8237 |

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