# Labour productivity in UK manufacturing in the 1970s and in the 1980s.

What accounts for the productivity improvement experienced in
manufacturing since 1979? Answers to this question are sought from a
regression analysis of 93 manufacturing industries over the period
1971-86. The main findings are that when other influences, such as raw
material prices and the shock of the 1980-1 recession, are eliminated,
there has been an improvement in the 1980s in the growth rate of
productivity whose impact effect averaged 4 per cent per annum. Between
a quarter and a half of this is attributable to a decline in the
disadvantages of unionisation.

1. Introduction

The growth rate of labour productivity has increased in most industries since 1979 and particularly since 1982; by contrast, it was negative in many industries in the period 1973-9 (Oulton, 1988). What accounts for this improvement? In an earlier article in this Review (Oulton, 1989), I have shown by means of a vintage capital model that the differences between industries' productivity growth rates in the 1980s cannot be explained by differences in new investment or scrapping, though such an explanation has some power for earlier periods. In the present paper I explore some alternative hypotheses to account for the improvement, employing a sample of 94 manufacturing industries. In particular, the roles of the labour shakeout which accompanied the 1980-1 recession and of the shock caused by the recession will be investigated. Attention will also be paid to the role of trade unions and to that of plant size-for example, is the productivity improvement greater or smaller in the most heavily unionised industries and/or in industries characterised by large plant size?

If neither new investment nor scrapping can adequately explain the pattern of productivity growth across industries in the 1980s, what can? A number of explanations, not mutually exclusive, have been suggested. (1) First, the pattern may be explicable as the effect of a shakeout of labour. Some industries may have hoarded labour more than others in the 1970s. When they subsequently dishoarded labour in the 1980s, they would have experienced higher than average productivity growth. Second, there is the `shock' (or `fear') hypothesis, first analysed by Metcalf (1989) and subsequently considered by Layard and Nickell (1988) and by Bean and Symons (1989). According to this hypothesis, the shock of the 1980-1 recession, with its massive employment losses, forced firms and workers to adapt or die. If so, then we would expect that the bigger the shock sustained by an industry, the bigger the improvement in its performance compared with the 1970s. Third, the 1980s may look good for productivity only by comparison with the 1970s, when there were exceptional reasons for poor performance, such as the huge rise in raw materials prices after 1973.

The plan of this article is as follows. in section 21 discuss the shock hypothesis and the role of unionisation. Section 3 describes the data employed-94 manufacturing industries, for which the main source was the Census of Production. in section 4 are presented the results of some preliminary tests of the linkages between the productivity improvement, unionisation and the 1980-1 recession. These replicate, on different data, the tests employed by Metcalf and the other authors just cited. However, an important part of the argument of this section is that these tests, though suggestive, are potentially misleading since they do not take proper account of the lagged response of employment to changes in output. The task of section 5 is accordingly to develop a more general model which does take account of these lags; in addition, this model incorporates the influence of (a) unionisation; (b) shock effects; (c) new investment and scrapping; (d) changing capital intensity due to changing relative factor prices; and (e) changes in raw material prices. The results of this more general model, which was estimated on a panel of industries over the period 1971-86, are discussed from an econometric point of view in section 6. Then section 7 attempts an economic appraisal. Finally, section 8 presents the conclusions.

2. The shock hypothesis and the role of unionisation

There are a number of modes through which a shock could be propagated. Insofar as the shock is to workers, it might affect their behaviour in one or more of the following ways: (1) The bigger the loss of employment, the more likely that the groups of workers most resistant to change are eliminated from the work-force; that is, the survivors' behaviour is unchanged, but `cooperative' workers now represent a larger proportion of the total. (2) The survivors' beliefs about the environment may have changed-the experience of the recession may have made them feel less secure in their jobs, more willing to credit management worries about competitiveness and profitability and thus more willing to cooperate in changing work practices. insofar as the shock is to managers, the bigger the reduction in employment that they have been able to `get away' with, the more willing they may have become to `take on' the trade unions. Also, since the recession put managers' jobs at risk as well as workers', the beliefs of managers too about the environment they face may have changed, so that they have become more concerned with remaining competitive and consequently less willing to countenance restrictive practices. Of course, none of these alternatives are mutually exclusive. It is likely that the recession changed the attitudes of both workers and managers. If it led them to believe that they had a common interest in survival, then it might have engendered a greater concern with efficiency and a more cooperative approach to implementing change, attitudes favourable to productivity growth.

While the shock hypothesis does not require for its validity the presence of strong trade unions, such a presence certainly enhances its plausibility, at least if the common characterisation of British trade unions is correct. According to this view, trade unions were able to prevent the adjustment of the labour force required by the first oil shock and the 1974-5 recession and to maintain customary restrictive practices up till the end of the 1970s, but the 1980-1 recession, coupled with the Thatcher government's various Employment Acts, broke their power. Hence, if this view is correct, we should expect that the recession would have had its biggest effect in the most heavily unionised industries.

Much evidence indicates that industrial relations have been particularly poor in large plants (Prais, 1981, chapter 7). it is also true that the number of unions represented in a plant rises with plant size. The 1980 Workplace Industrial Relations Survey found that 55 per cent of establishments employing 1000-1 999 people had 3-5 unions represented and 14 per cent of such establishments had 6 or more; for establishments employing 2000 or more people the corresponding figures were 41 per cent and 38 per cent. By contrast, only 23 per cent of all establishments had 3-5 unions and only 14 per cent overall had 6 unions or more (Daniel and Millward, 1983, table II.21). The importance of this finding stems from the fact that large establishments, though comparatively few in number, employ a disproportionately large share of the manufacturing labour force. Thus in 1973 establishments with 1000 or more employees employed 42 per cent of the manufacturing labour force and even in 1984, after a wave of closures of large plants, still employed 32 per cent (Oulton, 1987, table 2). It would seem likely that the larger the number of unions present, the greater the difficulty of reaching agreement on changes in the organisation of work. For example, if there are 3 unions represented in a plant, then there are 3 different 2-union coalitions possible; if 6 unions are represented, there are 15 possible 2-union coalitions, 20 3-union coalitions, 15 4-union coalitions and 6 5-union coalitions. As the number of unions rises, the chances of any single union or coalition of unions finding it in its interests to block an agreement clearly increases. (2) if the productivity improvement is due in part to an improvement in industrial relations (because unions are unable or unwilling to block change as they were accustomed to do), we would expect that it would be greater in industries characterised by large plants.

It turns out to be possible (see below) to obtain data at the industry level on the proportion of workers covered by collective agreements and on the proportion employed in large plants. These variables will therefore play an important role in the analysis. It is important to realise however that both are proxy measures of the underlying state of labour relations, which cannot be measured directly. In part the difficulty is a theoretical one-we do not know precisely which features of trade unionism are favourable to productivity and which are not.(3)

3. The data

The data for this study come from a sample of 94 industries which make up most of manufacturing and (for the preliminary tests) cover the period 1973-85; for the more general model the sample period is extended to 1971-86. The choice of industries was governed by the availability of the price deflators needed to deflate current price output to a constant price basis. Productivity is measured by net output in constant prices per person employed. Net output and employment come from the Census of Production and the price indexes used are producer price indexes (home sales). The Census net output figures were adjusted to exclude stock appreciation by a method conceptually analogous to the one used by the CSO (see CSO (1985), chapter 13). Up to 1979, the Census of Production was classified on the basis of the 1968 Standard Industrial Classification SIC), but after 1979 on the basis of the 1980 SIC. It was therefore necessary to reclassify all the data to a common basis, for which the 1968 SIC was chosen. The method by which this was done is explained in Oulton (1988, Appendix C).

Three variables designed to proxy for union power have been included; these are the proportions of the full time, male, manual workforce of each industry in 1973 which were covered by both national and supplementary collective agreements (CAl), by a national agreement only (CA2), and by a company agreement only (CA3) (4). The sum of these three proportions is termed CA. The source was the 1973 New Earnings Survey. The reason for using male manual workers rather than all workers in these union coverage variables is that it is with this group that restrictive practices and adherence to demarcation lines are usually most strongly associated.

To analyse the effects of large plants, the 1973 proportion of total employment in plants employing 400 or more people has been used. These figures were taken from the 1973 Census of Production (table 4 of the individual reports). The 400 cut-off point was chosen to maximise the number of observations; even so, data for only 84 industries were available.

Account must of course also be taken of the fact that productivity growth is influenced by investment in new equipment and scrapping of old. The method adopted here was to calculate the productivity growth which would have been expected for the 1970s and the 1980s on the basis of past experience of the course of investment 'predicted productivity growth') and subtract this from actual growth to obtain `residual' productivity growth. Predicted productivity was calculated by means of the vintage capital model described in my earlier article.(5) The model parameters are estimated on data which predate 1973, the starting year for the tests. Since however no model of productivity growth is likely to command unanimous assent, results will be presented for actual as well as residual productivity growth. The investment concept employed in the vintage capital model was gross investment in plant and machinery; current price series, taken again from the Census of Production, were adjusted to constant prices by CSO deflators.(6)

The measure used for testing the shock, hypothesis will be the reduction in employment between 1979 and 1981. It is important to measure productivity growth over a period which does not overlap with that of the shock; the period chosen is 1982-5. More particularly, we shall be concerned with the acceleration in productivity growth in this period over productivity growth in the comparable period of recovery from the previous recession, 1976-9.

Further details of the sources and methods of construction of all these variables will be found in the Appendix to my earlier article (Oulton, 1989). A list of the industries in the study is in Oulton (1988, Appendix B). Summary statistics of all the variables are in table 1 (7).

4. Some preliminary tests

Some preliminary tests of the relationship between the productivity improvement and its putative causes (unionisation and the shock of the recession) will now be presented; these will serve to motivate the more elaborate analysis of the panel model, to be developed in the next section. It is also of interest to check whether the results of others who have tested similar relationships (Metcalf, 1989; Layard and Nickell (1988); and Bean and Symons (1989)) can be replicated on the present dataset.

The results of these preliminary tests are in table 2. The dependent variable in columns 1 and 2 is the acceleration in residual productivity growth between 1982-5 on the one hand and 1976-9 on the other, where residual productivity growth is the difference between actual productivity growth and growth predicted by the vintage capital model. in columns 3 and 4, the dependent variable is the acceleration in actual productivity growth between these two time periods. (8) This specification of the dependent variable ensures that any industry fixed effects which influence the level of productivity growth will cancel out. The two time periods, 1976-9 and 1982-5, are comparable in that, obviously, they are of the same length and, more importantly, represent similar periods of recovery from recession (from that of 1974-5 in the first case and from that of 1980-1 in the second).

Taking first the larger sample of 94 industries (the upper panel of table 2), whether we look at actual or residual productivity and whether or not the union coverage' variables are included, the 'shock' variable is always highly significant. A reduction in the labour force of 10 per cent (total, not per annum) between 1979 and 1981 results in a rise in the productivity growth rate of about 2.5 percentage points in the subsequent period.

The main difference between the results for actual and residual productivity is that in the former the `union coverage' variables are highly significant while in the latter they are not. A possible explanation is that new investment and scrapping (the factors emphasised by the vintage model) were more important in the more unionised industries, so that once these effects are removed there is nothing left for unionisation to explain.

When plant size is added to the regressions (the lower panel of table 2) it is positive and significant for both actual and residual productivity. Thus the productivity improvement has been greater, the greater the proportion of employment accounted for by large plants. It is true that the F test suggests that when PL is present the union coverage variables no longer add significant explanatory power (though for actual productivity CAl is significant when considered alone). However as noted above, the plant size and unionisation variables may well be measuring aspects of the same phenomenon, namely the state of labour relations, so this loss of significance is not necessarily a worry. Note finally that the shock variable remains highly significant in the smaller sample.

How do these results compare with others? Exact comparison is impossible since specifications, levels of aggregation and variable definitions differ. Insofar as they overlap, the results in Metcalf (1989), who was the first to discuss the `shock' (or `fear') hypothesis, are similar to the ones reported here. Layard and Nickell (1 988) tested the shock hypothesis on 54 3-digit industries; the shock variable was found to be highly significant, but union coverage insignificant (either for actual or total factor productivity). They did not test the plant size effect. Bean and Symons (1989) tested the shock hypothesis on 15 2-digit manufacturing industries. They found both shock and plant size to be highly significant, but the results for union coverage were less clear-cut (9).

There is however a difficulty with these (and others') tests of the shock hypothesis, since it might be argued that the high productivity growth rates of the period 1982-5 represent a cyclical response to the 1980-1 recession, given that employment typically lags behind output. (10) Consider a simple employment equation:

n[sub.t] = an[sub.t-1], + by[sub.t], 0 < a < 1. where n is the log of employment, y is the log of output and where for simplicity trend productivity growth is ignored. If t = 0 in 1979, then the shock that we have considered is n[sub.2] - n[sub.0] and productivity growth in 1982-5 is (y[sub.6] - n[sub.6]) - (y[sub.3] - n[sub.3]). Assume that, just after t = 0, y (set by exogenous demand) falls to a new constant level of y*. Then solving the difference equation and choosing units so that n[sub.0] = 0, we find that:

Shock = n[sub.0] - n[sub.2] = -by*(1 + a) and productivity growth

(y[sub.6] - y[sub.3]) + (n[sub.3] - n[sub.6])

= n[sub.3] - n[sub.6]

= -by*a[sup.3] (1 + a + a[sup.2])

The ratio of growth to shock is

a[sup.3] (1 + a + a[sup.2])/(1 + a).

If a=0.8 for example, a value which implies that only 36 per cent of employment adjustment to a shock is completed after 2 years but which is consistent with values typically found in macro analysis, then this ratio is 0.69. in reality, the employment fall of 1979-81 averaged about 23 per cent and the productivity rise of 1985 over 1982 was about 17 per cent, so the ratio of growth to shock was about 0.74 (see table 1). On the face of it therefore cyclical effects could explain the rapid rise in productivity post 1981. To see whether in fact this was the case, a panel regression analysis will be employed.

5. A panel regression model of employment and productivity

5.1 The model

In outline, the model consists of three elements: (1) an industry-level production function, assumed for tractability to be Cobb-Douglas; (2) a partial adjustment mechanism relating actual to desired employment; and (3) a forecasting scheme relating expected long run 'permanent') output to current and past output. Assuming constant returns to scale, the production function, in logs, can be written:

y[sub.t]= a[sub.t] + f[sub.t] + [alpha(n)[sub.t]+ (1-[alpha]])k[sub.t] + v[sub.1t]

0 < [alpha] < 1 (1) where y[sub.t] is the log of `permanent' output, n[sub.t] is the log of desired employment and k[sub.t] is the log of the desired capital stock. As will be made clear in a moment, output is assumed to be demand-determined. v[sub.1t], is a white noise error. a[sub.t] is the basic, `normal' level of total factor productivity; it will be influenced by investment in new equipment and scrapping of old equipment, if newer equipment embodies more up-to-date technology. f[sub.t] by contrast represents all other influences on the level and growth rate of productivity-for example, institutional and legal changes, as well as subtler changes in the `climate' of industrial relations. In contrast to a[sub.t], f[sub.t] is thought of as not directly observable; its presence can only be detected by its effects, if any.

Note that f[sub.t] constitutes a very general specification, incorporating any or all of the following special cases:

(1) a temporary effect on the productivity level at time s:

f[sub.t] = [delta], t = s(delta constant)

= 0, t [is not equal to] s

(2) a permanent change in the productivity level from time s onwards:

f[sub.t] = [delta], t [is greater than or equal to] s

= 0, t [is less than] s

(3) a permanent change in the productivity growth rate from time s onwards:

f[sub.t] = [gamma]t [is greater than or equal to] s([gamma] constant)

= 0, t [is less than] s.

Rearranging (1) we obtain,

n[sub.t] = y[sub.t] - g[sub.t] - f[sub.t] - v[sub.1t] (2) where we have put

g[sub.t] = a[sub.t] + (1 - [alpha])(k[sub.t] - n[sub.t]) (3)

Now, k[sub.t] - n[sub.t], the log of the capital-labour ratio, depends on relative factor prices. In fact, in the Cobb-Douglas case the dual cost function is proportional to w[sub.t][sup.alpha]r[sub.t][sup.1 - alpha], where w[sub.t] is the wage and r[sub.t] is the rental on capital (Varian, 1984, p.29). Hence applying Shephard's Lemma (11) we find

k[sub.t]- n[sub.t] = In[(1 - alpha)/alpha] + In(w[sub.t]/r[sub.t]) and substituting this into (3):

g[sub.t] = a[sub.t] + (1 - [alpha])In[(1 - alpha)/alpha]

+ (1 - [alpha])In(w[sub.t]/r[sub.t]) (4)

Actual employment n[sub.t] is assumed to be adjusted to desired employment with a lag. However, it seems plausible that the lag length may differ according to the reason for the divergence between actual and desired employment. In particular, the response to a normal cyclical fall in output, which is expected to be reversed shortly, may be quite different from the response to a shock which is considered permanent. Again, consider the case where legislative changes reduce the power of trade unions to prevent some change which the management has long desired to introduce; once the law has been changed, the response may be quite quick. For these reasons, the response to changes in f[sub.t] is allowed to be different from the response to other determinants of n[sub.t]. The adjustment mechanism is therefore assumed to take the following form:

[delta]n[sub.t] = [lamdal][(n[sub.t] + f[sub.t] - f[sub.t-1]) - n[sub.t-1] - [micro](f[sub.t] - f[sub.t-1]) + v[sub.2t]

0 [is less than] [lamdal] [is less than or equal to] 1, 0 [is less than] v [is less than or equal to] 1 (5) where v[sub. 2t] is a white noise error. In this equation, n[sub.t] + f[sub.t], - f[sub.t-1], is what desired employment would have been had there been no change in the unobserved component f[sub.t]. Note that if [micro] = [lamdal] or if [delta]f[sub.t] = 0, all t, then (5) reduces to the simplest type of partial adjustment equation.

The theoretical specification is completed by assuming a simple forecasting scheme for y[sub.t]:

y[sub.t] = [zeta][sub.0] + [zeta][sub.1]y[sub.1] + (1 - [zeta][sub.1])y[sub.t-1] + v[sub.3t] (6) where v[sub.3t] is a white noise error. (12) Combining (2), (5) and (6), we obtain

[delta]n[sub.t] = [lamdal][zeta][sub.0] + [lamdal][zeta][sub.1][delta]y[sub.t] + [lamdal]y[sub.t-1]

- [lamdal]n[sub.t-1] - [lamdal]g[sub.t] - h[sub.t] - [lamdal]v[sub.1t] + v[sub.2t] + [lamdal]v[sub.3t] (7) where we have put

h[sub.t] = [micro](f[sub.t] - f[sub.t-1]) + [lamdal]f[sub.t-1]. (8)

As mentioned above, g[sub.t] is assumed to be measurable; f[sub.t] on the other hand is considered to be not directly observable.(13) Given sufficient data however we could clearly estimate [lamdal] and, using dummy variables, h[sub.t] in equation (7). is it then possible to recover the f[sub.t] ? The answer is no, since [micro] is not identified. However, a plausible range for [micro] is spanned by [micro = 1] (all adjustment is completed within the period) and [micro] = [lamdal] (adjustment takes place at the same speed whatever the source of the disturbance). A practical procedure is to estimate the ht by means of the coefficients on a set of time dummies; with the normalisation f[sub.1]=0, the other f[sub.t] (t=2,...,T) can then be recovered from (8), conditional on the value chosen for [micro].

In fact equation (7) will be estimated as a panel model in which there are T observations on each of N industries. Introducing a subscript i to represent the ith industry, the panel equation to be estimated can be rewritten from (7) as:

[delta]n[sub.it] = B[sub.0i] + B[sub.1i]n[sub.it-1] + B[sub.2i][delta]y[sub.it]

+ B[sub.3i]y[sub.it-1] + B[sub.4i]g[sub.it]

+ [summation][sup.t][sub.s=2] B[sub.3 + s,i]D[sub.st] + E[it],

i=1,...,N; t=1,...,T (9) where E[sub.t] is a random error and the D[sub.st] = 0 are a set of time dummies with D[sub.st]=1 if s=t and D[sub.st] =0 otherwise. Note that each of the coefficients B[sub.ji] may in principle vary across industries. There are some restrictions on the coefficients of (9), in particular, from (7),

B[sub.1i] = -B[sub.3i] = - [lamdal]

The regression model which we desire to test can now be written compactly as follows:

[delta]n[sub.t] = x[sub.t]B + E[sub.t] (10) where [delta]n[sub.t] is an NTx1 vector of observations on the dependent variable, x, is an NTxp matrix of NT observations on p explanatory variables, B is a px1 vector of coefficients and E[sub.t] is a NTx1 vector of random errors. In more detail, [delta]n[sub.t] consists of T observations on the first industry, [delta]n[sub.1t], followed by T observations on the second industry, [delta]n[sub.2t], and so on to the Nth industry; x[sub.t] and E[sub.t] are similarly defined.

5.2 Empirical implementation

(a) The data: Continuous annual observations on (nominal) net output (14) and employment are available from the Census of Production only from 1970 onwards. With one lag in both variables, the estimation period is 1971-86, so that T= 16. Apart from the extra years, the data for these two variables is the same as in the analysis of the earlier sections. As before, each industry's nominal net output is deflated by the appropriate producer price index, leading again to a sample of 94 industries (N=94).

Equation (4) for g[sub.t] may be re-written as follows, adding subscripts i and t where necessary to distinguish industries and time periods:

g[sub.it] = a[sub.it] + LSH[sub.it] + WR{sub.it],

i = 1,...,N; t = 1,...,T (4) where LSH[sub.it] = (1 - [alpha][sub.it])In([(1 - [alpha][sub.it]/[alpha][sub.it]] and

WR[sub.it] = (1 - [alpha][sub.it])In(w[sub.it]/r[sub.it]).

The components of g[sub.it] were measured as follows. First of all, a[sub.it] was constructed from the growth rates predicted by the vintage model described in Oulton (1989). For each industry, the model was run for 1970-3, 1973-6, 1976-9, 1979-82, 1982-6 (5 periods). Essentially, the vintage model predicts productivity growth by cumulating investment, assuming no change in the capital-labour ratio. Next, in constructing LSH[sub.it], the production function parameter [alpha][sub.it] was approximated by the observed share of labour in net output, to which it is theoretically equal under perfect competition; labour shares, computed as the total wage bill divided by net output, come from the Census of Production. Finally, to construct WR, we need the nominal wage rate w and the nominal return on capital r. The nominal wage rate, also from the Census, is the total wage bill divided by the total employed.(15) The nominal return on capital is computed from the standard Hall and Jorgenson (1968) formula, drawing also on the work of Melliss and Richardson (1976) and Kelly and Owen (1985); the price index employed is that for investment in plant and machinery and the interest rate is that on long period gilts.(16) Because of the approximations necessary to construct g[sub.it], each of its three components, namely a[sub.it], LSH[sub.it] and WR[sub.it] were entered separately in the regressions.(17)

b) Specification of the coefficients: The cross-industry variation of the coefficients in (9) was modelled as follows. First of all, the constant term B[sub.0i] was specified so as to incorporate a fixed effect for each industry: B[sub.0i] = 1 for observations on industry i, 0 otherwise (i = 2,...,N). In other words, each regression included a constant plus N-1 industry dummies, one for every industry except the first.

In their most general form the coefficients on the time dummies D were specified as follows:

B[sub.3+s,i] = [lamdal][sub.0s] + [lamdal][sub.1s]CA[sub.i] + [lamdal]{sub.2s]PL[sub.i] + [omega][sub.3+s,i]

s = 2,...,16 (12) where CA = proportion of male manual workforce which was covered by a collective agreement in 1973 (18) (from the 1973 New Earnings Survey) PL = proportion of labour force employed in plants with 400 or more employees in 1973 (from the Census of Production) and the [omega][sub.3+si] are white noise errors. Data on CA is available for all 94 industries; PL is available for 84 industries only. The presence of CA[sub.i] and PL[sub.i], in (12) allows us to test whether the underlying shocks (the f[sub.t]) have varied across industries in accordance with unionisation or plant size. (More restricted versions of (12) in which either CA[sub.i], or PL[sub.i] or both were dropped were also tested). If CA[sub.i] and/or PL[sub.i] are included they give rise to a set of interaction variables - D[sub.st] x CA[sub.i]: DCA72,...,DCA86 (15 variables)

D[sub.st] x PL[sub.i]: DPL72,...,DPL86 (15 variables).

The other coefficients in (9), B[sub.1i], B[sub.2i], B[sub.3i], and B[sub.4i], involve the adjustment parameter [lamdal] (see also (7)). In principle, there is no reason to expect the latter to be the same in all industries and assuming it to be so might seriously bias the results (though, anticipating, this turned out not to be a problem). To cope with this potential difficulty, it was assumed that the speed of adjustment might vary with the capital-labour ratio and with the proportion of the labour force characterised as white-collar. In general, we might expect high capital intensity and a high white-collar proportion to reduce the speed of adjustment. Accordingly, we assume

[lamdal][sub.i] = [lamdal][sub.3] + [lamdal][sub.4]KL[sub.i] + [lamdal][sub.5]WHC[sub.i] + [omega][sub.1i]

i = 1,...,N where KL[sub.i], is the log of the capital-labour ratio, WHC[sub.i] is the white-collar proportion and [omega][sub.1i] is a white noise error.(19) This auxiliary hypothesis for [lamdal] means that B[sub.1i], B[sub.2i], B[sub.3i] and B[sub.4i] will also vary across industries; this is handled by including a number of interaction variables (up to 16) in each regression, namely

KLN1 = KL x n[sub.-1] ; WHCN1 = WHC x n[sub.-1]

KLDY = KL x [delta] y; WHCDY = WHC x [delta] y

KLY1 = KL x y[sub.-1] ; WHCY1 = WHC x y[sub.-1]

KLA = KL x a; WHCA = WHC x a

KLLSH = KL x LSH; WHCLSH = WHC x LSH

KLLSH1 = KL x LSH[sub-1]; WHCLSH1 = WHC x LSH[sub.-1]

KLWR = KL x WR; WHCWR = WHC x WR

KLWR1 = KL x WR[sub.-1] ; WHCWR1 = WHC x WR[sub.-1].

This completes the description of the empirical implementation of the basic panel model (9). Additional hypotheses, in particular the shock hypothesis and the role of intermediate input prices, were also tested by adding variables to this equation on a more ad hoc basis. The shock hypothesis was tested by adding a sat of 5 interaction variables SHD82,...,SHD86, defined as follows:

SHD82[sub.it] = D[sub.82] x SH[sub.i],...,SHD86[sub.it], = D[sub.86] x SH[sub.i]

i=1,...,N;

t= 1,...,T where SH[sub.i] is the shock experienced by industry i over 1979-81, measured as before by the fall in employment over this period (a decline is measured as a positive number). In other words, each of these variables is the product of a time dummy and the shock each industry received. in this way, we allow for the possibility, for example, that the effects of the shock (if any) may have faded away as the recession became more distant in time.

The special treatment of the 1980-1 recession may be criticised. Why not apply the same approach to the 1974-5 recession as well or indeed to the whole period? But treating the 1980-1 recession as a special case may be justified firstly because of its exceptional severity and secondly because the reaction of workers and firms to the 1980-1 shock may very well have been different from their reactions to earlier ones-in 1974-5 firms in difficulties had a reasonable expectation of being bailed out by the government, an assurance which was lacking in 1980-1.

Since many have argued that the energy and materials price rises of the 1970s were behind the worldwide productivity slowdown experienced then, it was thought important to test this by adding a variable embodying the cost of intermediate inputs:

INTP[sub.it] = INT[sub.it]/GO[sub.it]) x In(P[sub.it]/r[sub.it]) where INT is intermediate purchases, GO is gross output and P is the price of intermediate inputs. INT was defined as gross output less net output. P was measured by the CSO's producer price index for raw materials and fuel for each industry. (20) In words, INTP is the log of each industry's intermediate input price (relative to the cost of capital) weighted by the share of intermediate purchases in each industry's total costs.

5.3 Estimation methods and diagnostic tests

The method of estimation employed was Ordinary Least Squares (OLS).(21) There are three potential difficulties which require discussion: (a) heteroskedasticity; (b) outliers and (c) autocorrelation. Each of these, if present, could lead to incorrect estimates of the standard errors and hence erroneous conclusions on significance.

(a) Heteroskedasticity.- The presence of random errors in equations (11) and (12) specifying the B[sub.ji] by itself means that the random error in the regression equation, E[sub.it], can be expected to be heteroskedastic. All standard errors and t statistics were therefore corrected for heteroskedasticity by the method originated by White (1980).

(b) Outliers: Outlying observations, to which OLS is known to be sensitive, may give exceptionally valuable information; on the other hand, if they are due to data errors or arise from untypical or anomalous behaviour, they may seriously distort the conclusions. Either way, it is important to check to what extent the results are dependent on outliers. A number of checks were run. First, the diagonal of the 'hat' matrix (see Belsey et al., 1980) was examined, to see if large values corresponded to a particular industry or industries or alternatively to a particular year. Second, the root mean square error (RMSE) was computed for each industry separately over the sample period 1971-86 and compared with the standard error of the whole regression. Third, the RMSE was computed across industries for each year separately and compared with the standard error of the regression. Though the latter two methods do not rest on a rigorous statistical foundation, in practice no great difficulty of principle arose in applying them.

(c) Autocorrelation: In the model as specified, the error term in equation (9) should be serially uncorrelated. This is because, first, the underlying error processes are assumed to be white noise. Second, because of the presence of time dummies in this equation, it is reasonable to assume that Ee[sub.it]e[sub.jt] = 0,i [is not equal to]j, all t. Hence, if detected, serial correlation would indicate some form of misspecification (e.g. an omitted variable). One diagnostic test employed was a variant of the Ljung-Box statistic Ljung and Box, 1978), itself a refinement of the Box-Pierce statistic (Box and Pierce, 1970); the formula employed is discussed in Annex A. Less formally, the correlogram was also examined.

The Ljung-Box statistic is not entirely appropriate for two reasons: first, the regressions include a lagged dependent variable, and second, the test assumes that we are looking at a single realisation of an error process, of length NT, whereas it would be nearer the truth to say that we have N realisations of the same process, each of length T. These two objections can be partially addressed by calculating Durbin's h statistic for each of the N industries separately (for the formula, see again Annex A). This statistic, which remains valid in the presence of a lagged dependent variable, is distributed as N (0,1) under the null of no first order serial correlation. If we were to regard the values of Durbin's h for the N industries as independent drawings from the standard normal distribution, then we would expect the cross-industry mean to be zero and no more than 4 or 5 industries (out of 93 -see below) to have h greater in absolute value than 1.96.

6. Results from the panel model: econometric considerations

Results will be presented for two samples of industries, the smaller sample being the one for which PL is available. Preliminary tests showed that on the `hat' matrix diagonal test one industry (MLH 102/103) was highly influential; in addition, the RMSE for this industry was typically four to five times the standard error of the whole regression and its presence substantially reduced R[sup.2]. Accordingly this industry was dropped, leaving 93 industries in the larger sample (83 in the sample for which PL is available). in the regression results to be reported, it was calculated for how many observations the hat matrix diagonal element exceeded twice the ratio of the number of right hand side variables to the number of observations (see Belsley et al, 1980, for the rationale of this test). in every regression reported, the number of such observations was very small; in no case did such observations form a substantial proportion of the observations on a whole industry, still less of those on a whole year.

All the regressions to be reported included (a) the basic time series variables n[sub.it-1], [delta]y[sub.it], y[sub.it-1]; (b) a constant plus 92 industry dummies (82 in the smaller sample) to account for industry fixed effects; (c) up to 16 variables to capture variation in [lamdal] across industries; (d) 15 time-period dummies (for 1972-86). The other variables included vary between equations. A selection of results is reported in tables 3 and 4. In these tables, the estimates for the constant and the industry dummies are omitted in the interests of brevity; however, the total number of right hand side variables, including the constant, is recorded as NVARS.(22) LB is the Ljung-Box statistic for serial correlation up to order 6 (see Annex A). Since the sample period is 1971-86, the number of observations is either (93 x 16 =) 1488 or (83 x 16 =) 1328. In interpreting the coefficients, recall that (except in the case of output y[sub.t]) a negative number implies that an increase in the variable is predicted to increase productivity. The results for the larger sample of 93 industries (table 3) will be discussed first from an econometric viewpoint, before going on to the economic interpretation. Table 3 reports 4 variants of the most general model tested, each of which incorporate shock and intermediate price effects. The regressions differ in whether or not they include the relative wage variables (LSH and WR), for reasons to be discussed in a moment, and in whether or not they include the unionisation dummies (DCA72-86). The form of the regressions was selected as a result of experimentation with longer and shorter lags. The data suggested overwhelmingly that at least one lag should be included-regressions otherwise identical to those of table 3 except containing only current values of employment and output produced massive serial correlation (LB over 1300!). Entering two lags in employment and output was found to increase serial correlation at lags 1-4, while reducing it slightly at lags 5 and 6. On grounds of parsimony, the equations with one lag seemed preferable. Even so, it must be admitted that the reported equations fail the LjungBox test at conventional levels of significance (at the 5 per cent level, the critical value is 12.6). However, this is a tough test to beat; because of the large sample size, to do so requires sample serial correlation coefficients which average less than 0.04 in absolute value. In fact, the first six sample coefficients for regression 1 of table 3 were 0.03, -0.09, 0.02, -0.03, -0.08, and -0.05; similarly low values could be quoted for the other regressions.

The results of calculating Durbin's h by industry for each of the regressions in table 3 may be summarised as follows: (23) Statistics of Durbin's h (93 industries)

Regression Mean SD min max No.[greater than or equal to]~1.96~

1 0.23 0.83 -2.02 2.05 2

2 0.25 0.85 1.99 2.22 2

3 0.06 0.87 -2.15 1.93 1

4 0.07 0.88 -2.24 1.94 2 In view of the low absolute level of the sample serial correlations and these latter results for Durbin's h, the regressions were judged acceptable from the serial correlation point of view.

Fixed effects Inclusion of fixed effects substantially improved the goodness of fit and was easily justified by an F test. Apart from the fit, their main effect was on the estimated value of the speed of adjustment parameter [lamdal]-without them, the estimate of [lamdal] was implausibly low.

Dynamic adjustment The first block of variables in table 3 all involve the estimation of [lamdal]. When, in contrast to the results reported in that table, [lamdal] was constrained to take the same value in all industries, its value was found to be about 0.20 in regressions excluding relative wages and about 0.16 in regressions including them, values which are consistent with those typically found in macro studies; furthermore, the coefficient on n[sub.-1], was found to be very nearly equal, except for sign, to that on y[sub.-1], as the theory requires (see equation (7)) and both n[sub.-1], and y[sub.-1], were highly significant (t values of 8 or 9). However, inclusion of the extra variables which allow [lamdal] to vary across industries considerably improved the fit and was supported by an F test, hence this more general form is the one preferred. The average value of [lamdal] across industries, based on the variables involving n[sub.-1], was 0.18 in the case of regression 4 (excluding relative wages), but only 0.013 in the case of regression 2; based on variables involving y[sub.-1], the average value was 0.42 and 0.43 respectively. (24) In principle the two estimates for [lamdal] should be equal and therefore on these grounds regression 4, excluding relative wage variables, is preferable.(25)

While aspects of the estimated coefficients involving [lamdal] are difficult to reconcile with the theory, it must be remembered that the main purpose is not to study the dynamic adjustment process but rather the growth of productivity. If a constant , is imposed, then, as mentioned above, economically reasonable and statistically highly significant results are obtained. The extra variables which seek to account for the variation of k across industries are only included in case it should be claimed that the opposite strategy of imposing a constant [lamdal] has biased the conclusions about productivity.

Relative wage variables The addition of LSH and WR in current and lagged form, together with their interactions with KL and WHC, a group which will be referred to collectively as the relative wage variables, causes a striking improvement in goodness of fit (compare R[sup.2] for regressions 1 and 2 with R[sup.2] for regressions 3 and 4). However, the long run coefficient on LSH implied by these estimates is positive, while the long run coefficient on WR is negative, whereas according to the theory (see equations (7) and (4')) both should be negative.(26)

There is an identification problem with the relative wage variables. It has been assumed that firms are price takers in factor markets; firms who experience for example high wage growth will substitute capital for labour, thus raising labour productivity and lowering employment at given output levels. However an alternative possibility is that firms who for whatever reason experience high productivity growth choose, or are forced, to grant large wage increases; in other words, the causation might run from productivity to wages and not from wages, via capital intensity, to productivity.

The only satisfactory way of resolving this issue is to specify a model of the wage setting process and estimate it simultaneously with the employment equation, a task which would be far beyond the scope of the present article. (Instrumental variable methods may give the appearance of solving the problem but the results are crucially dependent on the choice of instruments.) Therefore, in order to indicate to what extent the results are likely to be affected by this issue, all equations have also been estimated without the relative wage variables (WR, WR[sub.-1] LSH and LSH[sub.-1]) and the associated interactions with KL and WHC. When these variables are omitted, we are assuming that the effects of capital investment have been captured entirely by the vintage model. When they are included, we are assuming that rising wages can proxy for rising capital intensity, the lafter being over and above what is already measured by the vintage model. The truth presumably lies somewhere between these two extremes.

Vintage capital effects The variable a[sub.it] measures the effect of investment from a vintage capital point of view. The importance of this effect is measured by the size and significance of the coefficients on a[sub.it], KLA and WHCA in table 3. The mean value across industries of the coefficient on a[sub.it] is negative, as predicted by theory -O.0051 in regression 2 and -0.0088 in regression 4). However this group of variables fails an F test: for example, the F value for the exclusion of these three variables from regression 4 is 1.4, against a critical value at the 5 per cent level of 2.6. Hence vintage capital effects would appear not to contribute significantly to the explanation of productivity growth over this period, a finding consistent with earlier results (Oulton, 1989).(27) This does not mean that investment and scrapping, the factors emphasised by the vintage capital model, are unimportant, only that they have not varied sufficiently over time or between industries to explain the variation in productivity growth. There would appear therefore to be a statistical case for excluding a[sub.it] from the regressions. However, it was thought preferable to retain it in order to show that the conclusions on productivity and unionisation are not being biased by ignoring vintage capital effects (though in practice these would have been little affected had vintage effects been excluded).

The dummy variables The period dummies (D72-86) are frequently significant in individual years, particularly in regressions excluding relative wages, and contribute substantially to the goodness of fit. The unionisation dummies (DCA72-86), which are almost invariably positive, are less significant on an individual basis and make a fairly small contribution to improving the fit. Testing for the exclusion of these variables, we find an F value of 2.3, comparing regressions 3 and 4, and one of 1.6 comparing regressions 1 and 2. Since, in this case, the critical value of F is 1.7 at the 5 per cent level and 2.0 at the 1 per cent -level, the inclusion of these variables is supported at the 1 per cent level for the regression without relative wages, but just fails to be significant at the 5 per cent level in the regression with relative wages. This difference could be explained if, as is plausible, unionisation does in fact affect wage behaviour, so that the relative wage variables are picking up the effects of unionisation (which are anyway measured only imperfectly by CA). Pursuing this line of enquiry would however take us too far afield.

Intermediate input prices This variable is included in current and lagged form; in both cases it is highly significant. The difference between the current and lagged coefficients is about 0.04 in all regressions, indicating that a doubling of intermediate input prices, relative to other factor prices, in an industry where such inputs were, say, half of total costs would lead after one year to a proportionate fall in productivity of [0.5 x 0.04 x In2l or 1.4 per cent. Economically, a rise in intermediate input prices could lower labour productivity in two principal ways. First, if capital and intermediate input are complements, firms may substitute labour for these other two factors. Second, and more trivially, a rise in intermediate input prices, if not fully passed forward into output prices, could lower measured productivity; the reason is that in the present article the output measure (`net output', which is close to value added) has been deflated by an output price deflator, rather than a value added price deflator.

The fact that intermediate price rises only have a small effect may underestimate their influence, since the first oil shock certainly led to other changes which may have been inimical to productivity. Candidates here include the resulting general inflation and the policies to which the lafter gave rise-a restrictive macro stance, incomes policies which distorted pay relativities and legislative changes giving more power to unions in the workplace.(28) In so far as any of these are important, they should be picked up by the time-period dummies, which do indeed indicate the presence of adverse shocks in this period.

Shock effects None of the shock variables SHDU82-86 are individually significant, except in 1983 in regression 4. Once again, it makes a big difference whether one includes the relative wage variables. With them (regression 2), the shock variables fail an F test (F = 2.1, against a 5 per cent critical value of 2.2); without relative wages (regression 4), the shock variables pass (F = 5.8). The improvement in goodness of fit is slight (R [sup.2] = 0.6258 with the shock variables and 0.6178 without them), so clearly one can get almost as good an explanation without recourse to this hypothesis. On the other hand, some at least of the shock variable coefficients are large in absolute value. For example, the largest of all, that for 1983 in regression 4, implies that in the latter year the 1979-81 shock caused a proportional rise in productivity of, on average, [0.2502 x 0.2222] or 5.7 per cent, where 0.2222 is the sample mean of the shock (SH)-certainly not a negligible effect. But some doubt still lingers around the shock hypothesis, since using the fall in output rather than in employment to measure the 1979-81 shock produced far less significant results; adding an extra shock variable for 1981, which using output rather than employment permits one to do, also failed to improve things. This suggests that the shock variables may still be picking up some part of the dynamic adjustment process, even though the specification of the latter is a fairly general one. The pattern of the coefficients is also rather odd, if they are indeed picking up the effect of the 1980-1 recession: although, reasonably enough, they rise (in absolute value) in 1983 and decline in 1984 and 1985, they then show a puzzling second rise in 1986, which is surely an implausibly delayed reaction to the events of 6 years earlier.

Plant size effects The plant size dummies, DPL72-86, are available for a somewhat smaller sample of 83 industries. Similar regressions to those of table 3 are reported for this smaller sample in table 4. There is no need to repeat the econometric discussion, since the points which arise here have already been covered, so we concentrate on the plant size dummies. The inclusion of these variables on their own without the unionisation dummies is supported by the F test: F = 2.0 in regression 1 and 2.2 in regression 3, against critical values at 5 per cent of 1.7 and at 1 per cent of 2.0. The further inclusion of the unionisation dummies, in equations which already contain the plant size

dummies, is supported for regression 4, which excludes relative wages (F = 2.2), but not for regression 2 (F = 1.4). The plant size dummies are almost invariably negative. (29)

7. The growth of productivity: an economic appraisal

Summarising the discussion of the previous section, the panel model has been found to fit the data reasonably well and to perform satisfactorily from an econometric point of view. Most of the influences on productivity which it has been possible to measure-unionisation, plant size, the 1980-1 shock, intermediate input prices, but not vintage capital effects-have found some statistical support, though unionisation and the shock were not significant when relative wages were also included. It is now time to attempt an economic appraisal.

Chart 1 graphs the coefficients on the time-period dummies from regression 2 of table 3; chart 2 does the same for regression 4. These numbers (recall that a negative number means an improvement in productivity) are our estimates of the period-specific shocks to productivity which were common to all industries.(30) Both pictures tell a similar story. There was an adverse shock to productivity in 1974 (despite the presence in both equations of variables measuring intermediate input prices). For the rest of the 1970s and throughout the 1980s the shocks were favourable. In the case of regression 2, the shocks appear if anything to have become less favourable as the 1980s wore on; in the case of regression 4, no clear trend is discernible.

Next, charts 3 and 4 graph the effects of unionisation for the same two regressions. (31) Note first of all that in both regressions the numbers are almost invariably positive, that is, if these results are to be believed, unionisation has reduced productivity growth throughout the whole period. In chart 3, there is a clear upward trend in the coefficient till 1979 and thereafter it generally falls. Chart 4 shows a similar pattern, though the post-1979 decline is less clear.

The time-period and the unionisation dummies are combined together in charts 5 and 6, with unionisation evaluated at its sample mean.(32) With relative wages included (chart 5), there is a clear improvement in performance, comparing the 1970s and the 1980s. Although there has been some falling away since 1981, there is no sign by 1986 of a return to the `bad old days'. With relative wages excluded (chart 6), the picture is less clear-cut. The improvement, though real enough, has not been so great, because on this reckoning the mid 1970s were not so bad. Both charts agree that 1981 was an exceptional year; the most natural interpretation is that a large oncefor-all shakeout of labour occurred at that time.

Another way to assess the differences between the 1970s and the 1980s is to consider average values of the coefficients, which were as follows:

Regression 2 Regression 4

1972-9 1980-6 1972-9 1980-6

Time-period dummies -0.0385 -0.0626 -0.0769 -0.1109

Unionisation dummies 0.0490 0.0282 0.0863 0.0752

Both combined -0.0011 -0.0411 -0.0109 -0.0534

Both regressions therefore agree that there has been an improvement in productivity growth in the following sense:during the 1980s there was a favourable shock to productivity whose impact effect averaged 4 percentage points higher than the comparable figure for the 1970s. Regression 2 would attribute about half of this (2 percentage points) to a decline in the disadvantages of unionisation, whereas regression 4 would attribute only a quarter (1 percentage point) to this cause. Note that these estimates do not include the effects of the 1980-1 recession nor those of intermediate input prices, both of which are accounted for separately in the regressions. It is appropriate to exclude these last two effects, since in the case of the first its influence is likely to wane over time, while the second is beyond the reach of policy.

Another way to assess the size of the productivity improvement is to ask, how much higher is productivity by the end of our period in 1986 than it would have been if the coefficients on the dummy variables had had the same value from 1980-6 as they had on average from 1972-9? The answer, assuming that all other variables apart from employment itself had unchanged paths, can be calculated from equation (7); it turns out that productivity is about 17 per cent higher in 1986 than it otherwise would have been. (33)

It is also important to note that the inclusion or exclusion of the relative wage variables has no influence on the size of the overall improvement, whether measured in impact terms or as a cumulative effect. In other words, even if increased capital intensity is correctly proxied by rising relative wages, it cannot on average explain the improvement, even though it may play a role in particular industries.

In the earlier tests of section 4 we found that the more heavily unionised industries had improved their performance the most after 1979. The present finding from the panel model, that unionisation has depressed productivity growth throughout the period, but less so in the 1980s, is not in conflict with the earlier one. For consider two hypothetical industries, A which is highly unionised and B which is not. Suppose that they differ only in the degree of unionisation. Let their productivity growth rates be as follows:

1971-9 1979-86

A 1 4

B 3 5

Clearly A, the highly unionised industry, has enjoyed the biggest improvement, but its performance is still depressed relative to that of B.(34)

Our findings on unionisation do however conflict to some extent with those of Nickell, Wadhwani and Wall (1989). Using company data for the period 1975-86 they found, at least in their preferred results, that unionisation was positively and significantly associated with productivity growth in 1980-4, that is, unionised firms grew more rapidly, but that for 1975-8 unionisation was not significant. However, these conclusions were derived from an unbalanced panel, with many fewer firms after 1982, and some of their other results are closer to the present ones. For example, when they restrict their sample to be a balanced panel, which is what our sample is too, they find almost the opposite, namely that unionisation significantly reduces productivity growth in 1975-8; in 198G-4 unionisation was found to increase productivity growth, though not significantly so (see column 2 of their table 2).

Finally, in chart 7 is shown the time pattern of the coefficients on the plant size dummy variables (the coefficients on DPL72-86, from table 4). Both regressions show a clear peak in the coefficient in 1977 or 1978 followed by a substantial decline. This is evidence in favour of the view that the UK disadvantage in operating large plants has been substantially reduced in the 1980s. (35)

8. Conclusions

The main results of the preliminary tests of section 4 were: (a) The shock of the 1980-1 recession was highly significant; the bigger the shock, the bigger the improvement in productivity growth from 1982 onwards; (b) the most heavily unionised industries were the ones which enjoyed the largest improvement in productivity growth after 1982; (c) other things equal, the greater the proportion of an industry's employment in large plants, the bigger the improvement in productivity growth. Unionisation and plant size were, it was argued, both proxy measures for the underlying state of labour relations.

On the whole, the panel model confirms these findings. There are however some qualifications. For example, the evidence for the importance of the 1980-1 recession now seems weaker. The main results of the panel model were:

(1) Neither investment in new technology nor scrapping were found to contribute significantly to the explanation of productivity growth. This confirms the conclusion already reached on the basis of a more limited analysis

in my earlier article (Oulton, 1989).(36)

(2) Rises in intermediate input prices were found to reduce productivity but these are far f rom being the whole explanation of the 1970s slowdown, as a glance at charts 1 and 2 will indicate.

(3) The shock of the 1980-1 recession was found to play a significant, but far from dominant, role after 1981, although only if the relative wage variables are excluded; when these variables are included, the shock variables become insignificant.

(4) Exclusive of any of the above influences, there has been an improvement in the growth rate of productivity in the 1980s whose impact effect was about 4 percentage points per annum higher than in the 1970s. Between a quarter and a half of this (1-2 percentage points) is attributable to a decline in the disadvantages of unionisation: that is, when all other effects are taken into account, unionisation still seems to reduce productivity growth, but to a lesser extent than it used to. if so, the Thatcher government's programme of trade union reform should receive a share of the credit.(37)

As a final comment, two notes of caution are in order. First, the improvement we have noted is relative to the 1970s. Basing themselves on data for aggregate manufacturing, Darby and Wren-Lewis (1 989) have argued for a common trend rate of productivity growth running through the 1960s, the 1970s and the 1980s. Nothing in the present article is necessarily inconsistent with this view. it was in the 1960s that it came to be recognised that Britain was failing behind its major European competitors. Second, most of the improvement is due to factors which it has not proved possible to measure and which therefore had to be captured by time-period dummies. Consequently, uncertainty must remain about the cause of the improvement and still more so about whether it is likely to continue. However, our findings on unionisation and plant size, together with the elimination of other candidate explanations, suggest that the difficulty or ease that firms experience in adapting or changing work practices has been the strongest influence on productivity growth in the period studied.

NOTES

(1) For a general overview of the issues involved in explaining the productivity improvement, see Muellbauer (1986).

(2) For a more elaborate theoretical argument on multi-unionism, see Bean and Symons (1989). By contrast, Machin and Wadhwani (1989), in a study based on data from the second WIRS of the determinants of organisational change (which they argue is correlated with productivity improvement), find that multi-unionism is not significant when entered in regressions in which plant size also appears.

(3) That trade unionism can under some circumstances assist productivity growth seems apparent, for example, from the record of Japan after the second world war, as well as from theoretical considerations (Freeman and Medoff, 1984).

(4) These variables are mutually exclusive; the omitted variable is the percentage of the workforce not covered by any collective agreement. Union density (the proportion of an industry's labour force who are union members) is an alternative measure, but reliable figures at the industry level are not available.

(5) Residual productivity growth as defined here is analogous to total factor productivity growth as derived from a neo-classical model, since it is that part of productivity growth which is not (apparently) explained by the growth of factor inputs.

(6) In calculating residual productivity growth, two runs of the vintage capital model were needed for the periods 1976-9 and 1982-5. These were done in the same manner as the ones described in Oulton (1 989). Since neither 1976 nor 1982 were cyclical peaks, these calculations must be regarded as less firmly based than the ones reported in that article.

(7) Perusal of this table shows that the predicted productivity growth rates are greatly in excess of the actual ones. Apart from the presence of special factors in the period after 1973, which it is one of the purposes of the present article to uncover, the over-prediction could be due to some bias in the estimation of the vintage capital model. But this lafter possibility need not invalidate the results to be reported here, provided that this bias (if it exists) is common to all industries.

(8) In symbols, if q and q[sup.R] are the natural logs of the levels of actual and residual productivity, then the dependent variable in columns 1 and 2 is [(q[sup.R][sub.85] - q[sup.R][sub.82])] - (q[sup.R][sub.79] - q[sup.R][sub.76] and in columns 3 and 4 is [(q[sub.85] - q[sub.82]) - (q[sub.79] - q[sub.76])]

(9) Other related studies include Wadhwani (1988) and Denny and Muellbauer(1988). For a survey of work on the effects of trade unions, see Metcalf (1 988) and Wadhwani (1 989).

(10) I owe this point to my colleague Simon Wren-Lewis.

(11) Shephard's Lemma states that the partial derivative of the cost function with respect to any factor price is the demand for that factor (Varian, 1984, p. 54).

(12) The backward nature of the forecasting scheme for output, together with the partial adjustment assumption for employment, may seem unrealistic, particularly when the model is to be fitted to a period which includes the 1980-1 recession. However, recall that the model also includes the unobserved variable f[sub.t] response to which can be immediate (if [micro]= 1), and which can be thought of as overriding the 'normal' mechanisms of adjustment.

(13) The distinction between f[sub.t] and g[sub.t], is really a pragmatic one. if more data were available or if theoretical understanding were greater, some of the factors which lie behind f[sub.t] would be transferred to g[sub.t].

(14) The production function (1) is specified in `value added' form. Gross value added', which is close to but not identical to an economic definition of value added, is available from the Census, but only from 1973. Hence the Census concept of `net output' was used instead. The main difference between gross value added and net output is that the former excludes the purchase of non-industrial services.

(15) The share of labour is likely in practice to be affected also by the process of collective bargaining. Hence LSH and WR may pick up some of the effect due to unionisation. However, unionisation effects are probably dominated, at least as far as cross-industry variation is concerned, by other factors, such as technology and the composition of the labour force, in particular the male/female split. Partly for this reason, the empirical results to follow are presented with LSH and WR both included and excluded (see below).

(16) The Hall-Jorgenson formula is:

r = [[rho] + [delta] - (dp[sub.1]/dt)/p[sub.1]][(1 - uA)/(1 - u)]p[sub.1] where [rho] is the nominal post-tax discount rate, [delta] is the depreciation rate, p, is the price of investment goods, u is the corporation tax rate and A is the real, post-tax present value of subsidies to investment, measured per [British pound] spent on investment. I am grateful to my colleague Mary O'Mahony for providing me with the basis for these estimates.

(17) The vintage model assumes that none of the investment carried out was of a capital deepening nature. On the other hand, the rationale for employing the relative wage variables, LSH and WR, is that capital deepening may have occurred. There is a danger therefore of double-counting: the same piece of investment may be being counted once as replacement of scrapped equipment by the vintage model but also as capital deepening via the relative wage variables. in the present context this is a relatively minor matter, since we are principally concerned that the role of investment not be underrated.

(18) This variable is the sum of the variables defined earlier, CA1, CA2 and CA3.

(19) Both KL and WHC are 1973 values and hence do not have a time subscript. The capital stock is from O'Mahony and Oulton (1990), using short lives and assuming exponential depreciation. The total and white-collar labour force, the latter being those workers characterised as `administrative, technical and clerical', are from the 1973 Census of Production.

(20) From 1979, these price indexes have been published on an Activity Heading basis in British Business. Unpublished indexes on the same basis were obtained from the BSO for the period 1974-9. These series were reclassified to a MLH basis using 1979 intermediate purchases as the weights. For 1970-3, the indexes were estimated by weighting together the producer price indexes for output (home sales), the weights being obtained from table D of the 1974 input-Output tables.

(21) The model contains a lagged dependent variable and while in this case OLS remains the maximum likelihood estimator, it ceases to be consistent for fixed T. Consistent instrumental variable estimators are available (Hsiao, 1 986, chapter 4), but as these require lagged values, their use entails the loss of valuable time series information. Hence in the present context it is not clear that there is any gain from using them.

(22) It was not in fact necessary to carry out regressions with the complete list of explanatory variables. The actual estimation procedure used was to subtract from the observations on each industry the sample period average for that industry and then to carry out the regression of the transformed dependent variable on the transformed independent ones, excluding from the latter the constant and the industry dummies. Under OLS this procedure generates the same estimates of the coefficients as would a regression of the untransformed dependent variable on the full list (including constant and industry dummies) of untransformed independent variables (Hsiao, 1986, chapter 3). The t ratios, R[sup.2] and other statistics produced by the regression on transformed values will not however be identical to those which would have been produced by the regression on untransformed values, but it is straightforward to convert from one to the other. In the results below it is the statistics appropriate to the original, untransformed regressions which are reported.

(23) Regressions 1-4 allow the coefficient on the lagged dependent variable, B,,, to vary across industries, through the variables KLN1, WHCN1, etc. Hence it is not quite clear how the variance of the estimate of this coefficient, which is required for Durbin's h (see Annex A), should be calculated. The solution adopted was to re-estimate regressions 1-4 without these variables and use the estimated variance of [Beta][sub.1i] from these latter regressions together with the residuals from the original regressions in calculating h. I also calculated Durbin's h wholly from the regressions which imposed a constant speed of adjustment across industries. Judging from the correlogram, these latter regressions have very similar autocorrelation properties to the ones in table 3. The results for Durbin's h were very similar to the ones reported in the text.

(24) The average for variables involving n[sub.-1], was computed as follows: coefficient on n-, + (coefficient on KLN1 x sample mean of KL) + (coefficient on WHCN1 x sample mean of WHC). A similar calculation was used for variables involving y[sub-1]. The sample mean of KL was 9.4584 and of WHC was 0.2545.

(25) It was suggested above that both high capital intensity and a high white collar proportion would reduce the speed of adjustment, which implies that the coefficients on both KLN1 and WHCN1 should be positive (and those on KLY1 and WHCY1 negative). The coefficient on KLN1 did turn out to be positive, that on WHCN1 to be negative; however, as they were individually insignificant, no strong conclusions can be drawn.

(26) In regression 2, the mean value across industries of the coefficient on LSH is -0. 1 553, of that on LSH[sub.-1] is 0.1 624; the mean values for WR and WR[sub.-1] are respectively -0.2170 and 0.1533. These calculations make use of the fact that the sample mean of KL is 9.4584 and of WHC is 0.2545.

(27) When [lamdal] is constrained to be constant across industries, the coefficient on a, is correctly signed but again not significant at the 5 per cent level.

(28) Sometimes attention is focused on energy prices, rather than intermediate input prices in general. It is not clear why this should be so, especially since energy is a very small part of total costs for most industries. However that may be, Kilpatrick and Naisbitt (1988) found a negative effect of energy intensity on total factor productivity in the 1970s, though the significance level was not high.

(29) As was stressed earlier, plant size and unionisation may be different proxy measures for the same phenomenon; however, in the sample the simple correlation between the two is only 0.37.

(30) They are in fact estimates of the parameters [gamma][sub.0s] (s = 2,...,16) of equation (12).

(31) These numbers are estimates of the parameters [gamma][sub.1s], of equation (12).

(32) That is, the number graphed is: coefficient on time-period dummy + (coefficient on unionisation dummy x sample mean of CA). The sample mean of CA was 0.7643.

(33) From equation (7), the effect on employment and productivity in period T of a sequence of shocks h[sub.t][sup.1], from period 0 to T, in place of an alternative sequence of shocks h[sub.t][sup.1], is: [summation][sup.j = t],[sub.j = 0] (1 - [lamdal])[sup.j](h[sub.T-j - h[sup.1][sub.T-j]) The actual calculation is a little more complicated than this because of the need to take account of the shock effect, which however turns out to be small.

(34) Machin and Wadhwani (1989) found, using data from WIRS, that heavily unionised plants were more likely to undergo reorganisation in the early 1980s. Arguably, this finding too is consistent with unionised plants achieving bigger improvements in productivity, but not necessarily enjoying an absolutely higher level of productivity growth.

(35) The fact that the coefficient is almost invariably negative presumably indicates that industries in which large plants predominate were for some reason more technically progressive in this period.

(36) See also Oulton (1987), which casts doubt on the scrapping hypothesis from a different point of view.

(37) The previous issue of the Review contained a detailed discussion of this programme by members of the Clare group (Brown and Wadhwani, 1990). As far as its effects on productivity are concerned, they reached a very sceptical conclusion, as did Nickell, Wadhwani and Wall (1989). Clearly my evaluation is a much more favourable one, closer to that of Metcalf (1990) who has recently carried out a detailed review of the evidence.

ACKNOWLEDGEMENTS

I am grateful to a number of colleagues at the National institute and elsewhere for helpful advice, comments and encouragement; in particular, I would like to thank Ray Barrell, Andrew Britton, John Ermisch, Jonathen Haskel, David Metcalf, Mary O'Mahony, Sig Prais and Simon Wren-Lewis. This article also benefited greatly from detailed comments by Sushil Wadhwani and an anonymous referee. An earlier version was given at an Institute seminar and the comments received from participants were very useful. This research was financed by a grant from the Leverhulme Trust.

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1. Introduction

The growth rate of labour productivity has increased in most industries since 1979 and particularly since 1982; by contrast, it was negative in many industries in the period 1973-9 (Oulton, 1988). What accounts for this improvement? In an earlier article in this Review (Oulton, 1989), I have shown by means of a vintage capital model that the differences between industries' productivity growth rates in the 1980s cannot be explained by differences in new investment or scrapping, though such an explanation has some power for earlier periods. In the present paper I explore some alternative hypotheses to account for the improvement, employing a sample of 94 manufacturing industries. In particular, the roles of the labour shakeout which accompanied the 1980-1 recession and of the shock caused by the recession will be investigated. Attention will also be paid to the role of trade unions and to that of plant size-for example, is the productivity improvement greater or smaller in the most heavily unionised industries and/or in industries characterised by large plant size?

If neither new investment nor scrapping can adequately explain the pattern of productivity growth across industries in the 1980s, what can? A number of explanations, not mutually exclusive, have been suggested. (1) First, the pattern may be explicable as the effect of a shakeout of labour. Some industries may have hoarded labour more than others in the 1970s. When they subsequently dishoarded labour in the 1980s, they would have experienced higher than average productivity growth. Second, there is the `shock' (or `fear') hypothesis, first analysed by Metcalf (1989) and subsequently considered by Layard and Nickell (1988) and by Bean and Symons (1989). According to this hypothesis, the shock of the 1980-1 recession, with its massive employment losses, forced firms and workers to adapt or die. If so, then we would expect that the bigger the shock sustained by an industry, the bigger the improvement in its performance compared with the 1970s. Third, the 1980s may look good for productivity only by comparison with the 1970s, when there were exceptional reasons for poor performance, such as the huge rise in raw materials prices after 1973.

The plan of this article is as follows. in section 21 discuss the shock hypothesis and the role of unionisation. Section 3 describes the data employed-94 manufacturing industries, for which the main source was the Census of Production. in section 4 are presented the results of some preliminary tests of the linkages between the productivity improvement, unionisation and the 1980-1 recession. These replicate, on different data, the tests employed by Metcalf and the other authors just cited. However, an important part of the argument of this section is that these tests, though suggestive, are potentially misleading since they do not take proper account of the lagged response of employment to changes in output. The task of section 5 is accordingly to develop a more general model which does take account of these lags; in addition, this model incorporates the influence of (a) unionisation; (b) shock effects; (c) new investment and scrapping; (d) changing capital intensity due to changing relative factor prices; and (e) changes in raw material prices. The results of this more general model, which was estimated on a panel of industries over the period 1971-86, are discussed from an econometric point of view in section 6. Then section 7 attempts an economic appraisal. Finally, section 8 presents the conclusions.

2. The shock hypothesis and the role of unionisation

There are a number of modes through which a shock could be propagated. Insofar as the shock is to workers, it might affect their behaviour in one or more of the following ways: (1) The bigger the loss of employment, the more likely that the groups of workers most resistant to change are eliminated from the work-force; that is, the survivors' behaviour is unchanged, but `cooperative' workers now represent a larger proportion of the total. (2) The survivors' beliefs about the environment may have changed-the experience of the recession may have made them feel less secure in their jobs, more willing to credit management worries about competitiveness and profitability and thus more willing to cooperate in changing work practices. insofar as the shock is to managers, the bigger the reduction in employment that they have been able to `get away' with, the more willing they may have become to `take on' the trade unions. Also, since the recession put managers' jobs at risk as well as workers', the beliefs of managers too about the environment they face may have changed, so that they have become more concerned with remaining competitive and consequently less willing to countenance restrictive practices. Of course, none of these alternatives are mutually exclusive. It is likely that the recession changed the attitudes of both workers and managers. If it led them to believe that they had a common interest in survival, then it might have engendered a greater concern with efficiency and a more cooperative approach to implementing change, attitudes favourable to productivity growth.

While the shock hypothesis does not require for its validity the presence of strong trade unions, such a presence certainly enhances its plausibility, at least if the common characterisation of British trade unions is correct. According to this view, trade unions were able to prevent the adjustment of the labour force required by the first oil shock and the 1974-5 recession and to maintain customary restrictive practices up till the end of the 1970s, but the 1980-1 recession, coupled with the Thatcher government's various Employment Acts, broke their power. Hence, if this view is correct, we should expect that the recession would have had its biggest effect in the most heavily unionised industries.

Much evidence indicates that industrial relations have been particularly poor in large plants (Prais, 1981, chapter 7). it is also true that the number of unions represented in a plant rises with plant size. The 1980 Workplace Industrial Relations Survey found that 55 per cent of establishments employing 1000-1 999 people had 3-5 unions represented and 14 per cent of such establishments had 6 or more; for establishments employing 2000 or more people the corresponding figures were 41 per cent and 38 per cent. By contrast, only 23 per cent of all establishments had 3-5 unions and only 14 per cent overall had 6 unions or more (Daniel and Millward, 1983, table II.21). The importance of this finding stems from the fact that large establishments, though comparatively few in number, employ a disproportionately large share of the manufacturing labour force. Thus in 1973 establishments with 1000 or more employees employed 42 per cent of the manufacturing labour force and even in 1984, after a wave of closures of large plants, still employed 32 per cent (Oulton, 1987, table 2). It would seem likely that the larger the number of unions present, the greater the difficulty of reaching agreement on changes in the organisation of work. For example, if there are 3 unions represented in a plant, then there are 3 different 2-union coalitions possible; if 6 unions are represented, there are 15 possible 2-union coalitions, 20 3-union coalitions, 15 4-union coalitions and 6 5-union coalitions. As the number of unions rises, the chances of any single union or coalition of unions finding it in its interests to block an agreement clearly increases. (2) if the productivity improvement is due in part to an improvement in industrial relations (because unions are unable or unwilling to block change as they were accustomed to do), we would expect that it would be greater in industries characterised by large plants.

It turns out to be possible (see below) to obtain data at the industry level on the proportion of workers covered by collective agreements and on the proportion employed in large plants. These variables will therefore play an important role in the analysis. It is important to realise however that both are proxy measures of the underlying state of labour relations, which cannot be measured directly. In part the difficulty is a theoretical one-we do not know precisely which features of trade unionism are favourable to productivity and which are not.(3)

3. The data

The data for this study come from a sample of 94 industries which make up most of manufacturing and (for the preliminary tests) cover the period 1973-85; for the more general model the sample period is extended to 1971-86. The choice of industries was governed by the availability of the price deflators needed to deflate current price output to a constant price basis. Productivity is measured by net output in constant prices per person employed. Net output and employment come from the Census of Production and the price indexes used are producer price indexes (home sales). The Census net output figures were adjusted to exclude stock appreciation by a method conceptually analogous to the one used by the CSO (see CSO (1985), chapter 13). Up to 1979, the Census of Production was classified on the basis of the 1968 Standard Industrial Classification SIC), but after 1979 on the basis of the 1980 SIC. It was therefore necessary to reclassify all the data to a common basis, for which the 1968 SIC was chosen. The method by which this was done is explained in Oulton (1988, Appendix C).

Three variables designed to proxy for union power have been included; these are the proportions of the full time, male, manual workforce of each industry in 1973 which were covered by both national and supplementary collective agreements (CAl), by a national agreement only (CA2), and by a company agreement only (CA3) (4). The sum of these three proportions is termed CA. The source was the 1973 New Earnings Survey. The reason for using male manual workers rather than all workers in these union coverage variables is that it is with this group that restrictive practices and adherence to demarcation lines are usually most strongly associated.

To analyse the effects of large plants, the 1973 proportion of total employment in plants employing 400 or more people has been used. These figures were taken from the 1973 Census of Production (table 4 of the individual reports). The 400 cut-off point was chosen to maximise the number of observations; even so, data for only 84 industries were available.

Account must of course also be taken of the fact that productivity growth is influenced by investment in new equipment and scrapping of old. The method adopted here was to calculate the productivity growth which would have been expected for the 1970s and the 1980s on the basis of past experience of the course of investment 'predicted productivity growth') and subtract this from actual growth to obtain `residual' productivity growth. Predicted productivity was calculated by means of the vintage capital model described in my earlier article.(5) The model parameters are estimated on data which predate 1973, the starting year for the tests. Since however no model of productivity growth is likely to command unanimous assent, results will be presented for actual as well as residual productivity growth. The investment concept employed in the vintage capital model was gross investment in plant and machinery; current price series, taken again from the Census of Production, were adjusted to constant prices by CSO deflators.(6)

The measure used for testing the shock, hypothesis will be the reduction in employment between 1979 and 1981. It is important to measure productivity growth over a period which does not overlap with that of the shock; the period chosen is 1982-5. More particularly, we shall be concerned with the acceleration in productivity growth in this period over productivity growth in the comparable period of recovery from the previous recession, 1976-9.

Further details of the sources and methods of construction of all these variables will be found in the Appendix to my earlier article (Oulton, 1989). A list of the industries in the study is in Oulton (1988, Appendix B). Summary statistics of all the variables are in table 1 (7).

4. Some preliminary tests

Some preliminary tests of the relationship between the productivity improvement and its putative causes (unionisation and the shock of the recession) will now be presented; these will serve to motivate the more elaborate analysis of the panel model, to be developed in the next section. It is also of interest to check whether the results of others who have tested similar relationships (Metcalf, 1989; Layard and Nickell (1988); and Bean and Symons (1989)) can be replicated on the present dataset.

The results of these preliminary tests are in table 2. The dependent variable in columns 1 and 2 is the acceleration in residual productivity growth between 1982-5 on the one hand and 1976-9 on the other, where residual productivity growth is the difference between actual productivity growth and growth predicted by the vintage capital model. in columns 3 and 4, the dependent variable is the acceleration in actual productivity growth between these two time periods. (8) This specification of the dependent variable ensures that any industry fixed effects which influence the level of productivity growth will cancel out. The two time periods, 1976-9 and 1982-5, are comparable in that, obviously, they are of the same length and, more importantly, represent similar periods of recovery from recession (from that of 1974-5 in the first case and from that of 1980-1 in the second).

Taking first the larger sample of 94 industries (the upper panel of table 2), whether we look at actual or residual productivity and whether or not the union coverage' variables are included, the 'shock' variable is always highly significant. A reduction in the labour force of 10 per cent (total, not per annum) between 1979 and 1981 results in a rise in the productivity growth rate of about 2.5 percentage points in the subsequent period.

The main difference between the results for actual and residual productivity is that in the former the `union coverage' variables are highly significant while in the latter they are not. A possible explanation is that new investment and scrapping (the factors emphasised by the vintage model) were more important in the more unionised industries, so that once these effects are removed there is nothing left for unionisation to explain.

When plant size is added to the regressions (the lower panel of table 2) it is positive and significant for both actual and residual productivity. Thus the productivity improvement has been greater, the greater the proportion of employment accounted for by large plants. It is true that the F test suggests that when PL is present the union coverage variables no longer add significant explanatory power (though for actual productivity CAl is significant when considered alone). However as noted above, the plant size and unionisation variables may well be measuring aspects of the same phenomenon, namely the state of labour relations, so this loss of significance is not necessarily a worry. Note finally that the shock variable remains highly significant in the smaller sample.

How do these results compare with others? Exact comparison is impossible since specifications, levels of aggregation and variable definitions differ. Insofar as they overlap, the results in Metcalf (1989), who was the first to discuss the `shock' (or `fear') hypothesis, are similar to the ones reported here. Layard and Nickell (1 988) tested the shock hypothesis on 54 3-digit industries; the shock variable was found to be highly significant, but union coverage insignificant (either for actual or total factor productivity). They did not test the plant size effect. Bean and Symons (1989) tested the shock hypothesis on 15 2-digit manufacturing industries. They found both shock and plant size to be highly significant, but the results for union coverage were less clear-cut (9).

There is however a difficulty with these (and others') tests of the shock hypothesis, since it might be argued that the high productivity growth rates of the period 1982-5 represent a cyclical response to the 1980-1 recession, given that employment typically lags behind output. (10) Consider a simple employment equation:

n[sub.t] = an[sub.t-1], + by[sub.t], 0 < a < 1. where n is the log of employment, y is the log of output and where for simplicity trend productivity growth is ignored. If t = 0 in 1979, then the shock that we have considered is n[sub.2] - n[sub.0] and productivity growth in 1982-5 is (y[sub.6] - n[sub.6]) - (y[sub.3] - n[sub.3]). Assume that, just after t = 0, y (set by exogenous demand) falls to a new constant level of y*. Then solving the difference equation and choosing units so that n[sub.0] = 0, we find that:

Shock = n[sub.0] - n[sub.2] = -by*(1 + a) and productivity growth

(y[sub.6] - y[sub.3]) + (n[sub.3] - n[sub.6])

= n[sub.3] - n[sub.6]

= -by*a[sup.3] (1 + a + a[sup.2])

The ratio of growth to shock is

a[sup.3] (1 + a + a[sup.2])/(1 + a).

If a=0.8 for example, a value which implies that only 36 per cent of employment adjustment to a shock is completed after 2 years but which is consistent with values typically found in macro analysis, then this ratio is 0.69. in reality, the employment fall of 1979-81 averaged about 23 per cent and the productivity rise of 1985 over 1982 was about 17 per cent, so the ratio of growth to shock was about 0.74 (see table 1). On the face of it therefore cyclical effects could explain the rapid rise in productivity post 1981. To see whether in fact this was the case, a panel regression analysis will be employed.

5. A panel regression model of employment and productivity

5.1 The model

In outline, the model consists of three elements: (1) an industry-level production function, assumed for tractability to be Cobb-Douglas; (2) a partial adjustment mechanism relating actual to desired employment; and (3) a forecasting scheme relating expected long run 'permanent') output to current and past output. Assuming constant returns to scale, the production function, in logs, can be written:

y[sub.t]= a[sub.t] + f[sub.t] + [alpha(n)[sub.t]+ (1-[alpha]])k[sub.t] + v[sub.1t]

0 < [alpha] < 1 (1) where y[sub.t] is the log of `permanent' output, n[sub.t] is the log of desired employment and k[sub.t] is the log of the desired capital stock. As will be made clear in a moment, output is assumed to be demand-determined. v[sub.1t], is a white noise error. a[sub.t] is the basic, `normal' level of total factor productivity; it will be influenced by investment in new equipment and scrapping of old equipment, if newer equipment embodies more up-to-date technology. f[sub.t] by contrast represents all other influences on the level and growth rate of productivity-for example, institutional and legal changes, as well as subtler changes in the `climate' of industrial relations. In contrast to a[sub.t], f[sub.t] is thought of as not directly observable; its presence can only be detected by its effects, if any.

Note that f[sub.t] constitutes a very general specification, incorporating any or all of the following special cases:

(1) a temporary effect on the productivity level at time s:

f[sub.t] = [delta], t = s(delta constant)

= 0, t [is not equal to] s

(2) a permanent change in the productivity level from time s onwards:

f[sub.t] = [delta], t [is greater than or equal to] s

= 0, t [is less than] s

(3) a permanent change in the productivity growth rate from time s onwards:

f[sub.t] = [gamma]t [is greater than or equal to] s([gamma] constant)

= 0, t [is less than] s.

Rearranging (1) we obtain,

n[sub.t] = y[sub.t] - g[sub.t] - f[sub.t] - v[sub.1t] (2) where we have put

g[sub.t] = a[sub.t] + (1 - [alpha])(k[sub.t] - n[sub.t]) (3)

Now, k[sub.t] - n[sub.t], the log of the capital-labour ratio, depends on relative factor prices. In fact, in the Cobb-Douglas case the dual cost function is proportional to w[sub.t][sup.alpha]r[sub.t][sup.1 - alpha], where w[sub.t] is the wage and r[sub.t] is the rental on capital (Varian, 1984, p.29). Hence applying Shephard's Lemma (11) we find

k[sub.t]- n[sub.t] = In[(1 - alpha)/alpha] + In(w[sub.t]/r[sub.t]) and substituting this into (3):

g[sub.t] = a[sub.t] + (1 - [alpha])In[(1 - alpha)/alpha]

+ (1 - [alpha])In(w[sub.t]/r[sub.t]) (4)

Actual employment n[sub.t] is assumed to be adjusted to desired employment with a lag. However, it seems plausible that the lag length may differ according to the reason for the divergence between actual and desired employment. In particular, the response to a normal cyclical fall in output, which is expected to be reversed shortly, may be quite different from the response to a shock which is considered permanent. Again, consider the case where legislative changes reduce the power of trade unions to prevent some change which the management has long desired to introduce; once the law has been changed, the response may be quite quick. For these reasons, the response to changes in f[sub.t] is allowed to be different from the response to other determinants of n[sub.t]. The adjustment mechanism is therefore assumed to take the following form:

[delta]n[sub.t] = [lamdal][(n[sub.t] + f[sub.t] - f[sub.t-1]) - n[sub.t-1] - [micro](f[sub.t] - f[sub.t-1]) + v[sub.2t]

0 [is less than] [lamdal] [is less than or equal to] 1, 0 [is less than] v [is less than or equal to] 1 (5) where v[sub. 2t] is a white noise error. In this equation, n[sub.t] + f[sub.t], - f[sub.t-1], is what desired employment would have been had there been no change in the unobserved component f[sub.t]. Note that if [micro] = [lamdal] or if [delta]f[sub.t] = 0, all t, then (5) reduces to the simplest type of partial adjustment equation.

The theoretical specification is completed by assuming a simple forecasting scheme for y[sub.t]:

y[sub.t] = [zeta][sub.0] + [zeta][sub.1]y[sub.1] + (1 - [zeta][sub.1])y[sub.t-1] + v[sub.3t] (6) where v[sub.3t] is a white noise error. (12) Combining (2), (5) and (6), we obtain

[delta]n[sub.t] = [lamdal][zeta][sub.0] + [lamdal][zeta][sub.1][delta]y[sub.t] + [lamdal]y[sub.t-1]

- [lamdal]n[sub.t-1] - [lamdal]g[sub.t] - h[sub.t] - [lamdal]v[sub.1t] + v[sub.2t] + [lamdal]v[sub.3t] (7) where we have put

h[sub.t] = [micro](f[sub.t] - f[sub.t-1]) + [lamdal]f[sub.t-1]. (8)

As mentioned above, g[sub.t] is assumed to be measurable; f[sub.t] on the other hand is considered to be not directly observable.(13) Given sufficient data however we could clearly estimate [lamdal] and, using dummy variables, h[sub.t] in equation (7). is it then possible to recover the f[sub.t] ? The answer is no, since [micro] is not identified. However, a plausible range for [micro] is spanned by [micro = 1] (all adjustment is completed within the period) and [micro] = [lamdal] (adjustment takes place at the same speed whatever the source of the disturbance). A practical procedure is to estimate the ht by means of the coefficients on a set of time dummies; with the normalisation f[sub.1]=0, the other f[sub.t] (t=2,...,T) can then be recovered from (8), conditional on the value chosen for [micro].

In fact equation (7) will be estimated as a panel model in which there are T observations on each of N industries. Introducing a subscript i to represent the ith industry, the panel equation to be estimated can be rewritten from (7) as:

[delta]n[sub.it] = B[sub.0i] + B[sub.1i]n[sub.it-1] + B[sub.2i][delta]y[sub.it]

+ B[sub.3i]y[sub.it-1] + B[sub.4i]g[sub.it]

+ [summation][sup.t][sub.s=2] B[sub.3 + s,i]D[sub.st] + E[it],

i=1,...,N; t=1,...,T (9) where E[sub.t] is a random error and the D[sub.st] = 0 are a set of time dummies with D[sub.st]=1 if s=t and D[sub.st] =0 otherwise. Note that each of the coefficients B[sub.ji] may in principle vary across industries. There are some restrictions on the coefficients of (9), in particular, from (7),

B[sub.1i] = -B[sub.3i] = - [lamdal]

The regression model which we desire to test can now be written compactly as follows:

[delta]n[sub.t] = x[sub.t]B + E[sub.t] (10) where [delta]n[sub.t] is an NTx1 vector of observations on the dependent variable, x, is an NTxp matrix of NT observations on p explanatory variables, B is a px1 vector of coefficients and E[sub.t] is a NTx1 vector of random errors. In more detail, [delta]n[sub.t] consists of T observations on the first industry, [delta]n[sub.1t], followed by T observations on the second industry, [delta]n[sub.2t], and so on to the Nth industry; x[sub.t] and E[sub.t] are similarly defined.

5.2 Empirical implementation

(a) The data: Continuous annual observations on (nominal) net output (14) and employment are available from the Census of Production only from 1970 onwards. With one lag in both variables, the estimation period is 1971-86, so that T= 16. Apart from the extra years, the data for these two variables is the same as in the analysis of the earlier sections. As before, each industry's nominal net output is deflated by the appropriate producer price index, leading again to a sample of 94 industries (N=94).

Equation (4) for g[sub.t] may be re-written as follows, adding subscripts i and t where necessary to distinguish industries and time periods:

g[sub.it] = a[sub.it] + LSH[sub.it] + WR{sub.it],

i = 1,...,N; t = 1,...,T (4) where LSH[sub.it] = (1 - [alpha][sub.it])In([(1 - [alpha][sub.it]/[alpha][sub.it]] and

WR[sub.it] = (1 - [alpha][sub.it])In(w[sub.it]/r[sub.it]).

The components of g[sub.it] were measured as follows. First of all, a[sub.it] was constructed from the growth rates predicted by the vintage model described in Oulton (1989). For each industry, the model was run for 1970-3, 1973-6, 1976-9, 1979-82, 1982-6 (5 periods). Essentially, the vintage model predicts productivity growth by cumulating investment, assuming no change in the capital-labour ratio. Next, in constructing LSH[sub.it], the production function parameter [alpha][sub.it] was approximated by the observed share of labour in net output, to which it is theoretically equal under perfect competition; labour shares, computed as the total wage bill divided by net output, come from the Census of Production. Finally, to construct WR, we need the nominal wage rate w and the nominal return on capital r. The nominal wage rate, also from the Census, is the total wage bill divided by the total employed.(15) The nominal return on capital is computed from the standard Hall and Jorgenson (1968) formula, drawing also on the work of Melliss and Richardson (1976) and Kelly and Owen (1985); the price index employed is that for investment in plant and machinery and the interest rate is that on long period gilts.(16) Because of the approximations necessary to construct g[sub.it], each of its three components, namely a[sub.it], LSH[sub.it] and WR[sub.it] were entered separately in the regressions.(17)

b) Specification of the coefficients: The cross-industry variation of the coefficients in (9) was modelled as follows. First of all, the constant term B[sub.0i] was specified so as to incorporate a fixed effect for each industry: B[sub.0i] = 1 for observations on industry i, 0 otherwise (i = 2,...,N). In other words, each regression included a constant plus N-1 industry dummies, one for every industry except the first.

In their most general form the coefficients on the time dummies D were specified as follows:

B[sub.3+s,i] = [lamdal][sub.0s] + [lamdal][sub.1s]CA[sub.i] + [lamdal]{sub.2s]PL[sub.i] + [omega][sub.3+s,i]

s = 2,...,16 (12) where CA = proportion of male manual workforce which was covered by a collective agreement in 1973 (18) (from the 1973 New Earnings Survey) PL = proportion of labour force employed in plants with 400 or more employees in 1973 (from the Census of Production) and the [omega][sub.3+si] are white noise errors. Data on CA is available for all 94 industries; PL is available for 84 industries only. The presence of CA[sub.i] and PL[sub.i], in (12) allows us to test whether the underlying shocks (the f[sub.t]) have varied across industries in accordance with unionisation or plant size. (More restricted versions of (12) in which either CA[sub.i], or PL[sub.i] or both were dropped were also tested). If CA[sub.i] and/or PL[sub.i] are included they give rise to a set of interaction variables - D[sub.st] x CA[sub.i]: DCA72,...,DCA86 (15 variables)

D[sub.st] x PL[sub.i]: DPL72,...,DPL86 (15 variables).

The other coefficients in (9), B[sub.1i], B[sub.2i], B[sub.3i], and B[sub.4i], involve the adjustment parameter [lamdal] (see also (7)). In principle, there is no reason to expect the latter to be the same in all industries and assuming it to be so might seriously bias the results (though, anticipating, this turned out not to be a problem). To cope with this potential difficulty, it was assumed that the speed of adjustment might vary with the capital-labour ratio and with the proportion of the labour force characterised as white-collar. In general, we might expect high capital intensity and a high white-collar proportion to reduce the speed of adjustment. Accordingly, we assume

[lamdal][sub.i] = [lamdal][sub.3] + [lamdal][sub.4]KL[sub.i] + [lamdal][sub.5]WHC[sub.i] + [omega][sub.1i]

i = 1,...,N where KL[sub.i], is the log of the capital-labour ratio, WHC[sub.i] is the white-collar proportion and [omega][sub.1i] is a white noise error.(19) This auxiliary hypothesis for [lamdal] means that B[sub.1i], B[sub.2i], B[sub.3i] and B[sub.4i] will also vary across industries; this is handled by including a number of interaction variables (up to 16) in each regression, namely

KLN1 = KL x n[sub.-1] ; WHCN1 = WHC x n[sub.-1]

KLDY = KL x [delta] y; WHCDY = WHC x [delta] y

KLY1 = KL x y[sub.-1] ; WHCY1 = WHC x y[sub.-1]

KLA = KL x a; WHCA = WHC x a

KLLSH = KL x LSH; WHCLSH = WHC x LSH

KLLSH1 = KL x LSH[sub-1]; WHCLSH1 = WHC x LSH[sub.-1]

KLWR = KL x WR; WHCWR = WHC x WR

KLWR1 = KL x WR[sub.-1] ; WHCWR1 = WHC x WR[sub.-1].

This completes the description of the empirical implementation of the basic panel model (9). Additional hypotheses, in particular the shock hypothesis and the role of intermediate input prices, were also tested by adding variables to this equation on a more ad hoc basis. The shock hypothesis was tested by adding a sat of 5 interaction variables SHD82,...,SHD86, defined as follows:

SHD82[sub.it] = D[sub.82] x SH[sub.i],...,SHD86[sub.it], = D[sub.86] x SH[sub.i]

i=1,...,N;

t= 1,...,T where SH[sub.i] is the shock experienced by industry i over 1979-81, measured as before by the fall in employment over this period (a decline is measured as a positive number). In other words, each of these variables is the product of a time dummy and the shock each industry received. in this way, we allow for the possibility, for example, that the effects of the shock (if any) may have faded away as the recession became more distant in time.

The special treatment of the 1980-1 recession may be criticised. Why not apply the same approach to the 1974-5 recession as well or indeed to the whole period? But treating the 1980-1 recession as a special case may be justified firstly because of its exceptional severity and secondly because the reaction of workers and firms to the 1980-1 shock may very well have been different from their reactions to earlier ones-in 1974-5 firms in difficulties had a reasonable expectation of being bailed out by the government, an assurance which was lacking in 1980-1.

Since many have argued that the energy and materials price rises of the 1970s were behind the worldwide productivity slowdown experienced then, it was thought important to test this by adding a variable embodying the cost of intermediate inputs:

INTP[sub.it] = INT[sub.it]/GO[sub.it]) x In(P[sub.it]/r[sub.it]) where INT is intermediate purchases, GO is gross output and P is the price of intermediate inputs. INT was defined as gross output less net output. P was measured by the CSO's producer price index for raw materials and fuel for each industry. (20) In words, INTP is the log of each industry's intermediate input price (relative to the cost of capital) weighted by the share of intermediate purchases in each industry's total costs.

5.3 Estimation methods and diagnostic tests

The method of estimation employed was Ordinary Least Squares (OLS).(21) There are three potential difficulties which require discussion: (a) heteroskedasticity; (b) outliers and (c) autocorrelation. Each of these, if present, could lead to incorrect estimates of the standard errors and hence erroneous conclusions on significance.

(a) Heteroskedasticity.- The presence of random errors in equations (11) and (12) specifying the B[sub.ji] by itself means that the random error in the regression equation, E[sub.it], can be expected to be heteroskedastic. All standard errors and t statistics were therefore corrected for heteroskedasticity by the method originated by White (1980).

(b) Outliers: Outlying observations, to which OLS is known to be sensitive, may give exceptionally valuable information; on the other hand, if they are due to data errors or arise from untypical or anomalous behaviour, they may seriously distort the conclusions. Either way, it is important to check to what extent the results are dependent on outliers. A number of checks were run. First, the diagonal of the 'hat' matrix (see Belsey et al., 1980) was examined, to see if large values corresponded to a particular industry or industries or alternatively to a particular year. Second, the root mean square error (RMSE) was computed for each industry separately over the sample period 1971-86 and compared with the standard error of the whole regression. Third, the RMSE was computed across industries for each year separately and compared with the standard error of the regression. Though the latter two methods do not rest on a rigorous statistical foundation, in practice no great difficulty of principle arose in applying them.

(c) Autocorrelation: In the model as specified, the error term in equation (9) should be serially uncorrelated. This is because, first, the underlying error processes are assumed to be white noise. Second, because of the presence of time dummies in this equation, it is reasonable to assume that Ee[sub.it]e[sub.jt] = 0,i [is not equal to]j, all t. Hence, if detected, serial correlation would indicate some form of misspecification (e.g. an omitted variable). One diagnostic test employed was a variant of the Ljung-Box statistic Ljung and Box, 1978), itself a refinement of the Box-Pierce statistic (Box and Pierce, 1970); the formula employed is discussed in Annex A. Less formally, the correlogram was also examined.

The Ljung-Box statistic is not entirely appropriate for two reasons: first, the regressions include a lagged dependent variable, and second, the test assumes that we are looking at a single realisation of an error process, of length NT, whereas it would be nearer the truth to say that we have N realisations of the same process, each of length T. These two objections can be partially addressed by calculating Durbin's h statistic for each of the N industries separately (for the formula, see again Annex A). This statistic, which remains valid in the presence of a lagged dependent variable, is distributed as N (0,1) under the null of no first order serial correlation. If we were to regard the values of Durbin's h for the N industries as independent drawings from the standard normal distribution, then we would expect the cross-industry mean to be zero and no more than 4 or 5 industries (out of 93 -see below) to have h greater in absolute value than 1.96.

6. Results from the panel model: econometric considerations

Results will be presented for two samples of industries, the smaller sample being the one for which PL is available. Preliminary tests showed that on the `hat' matrix diagonal test one industry (MLH 102/103) was highly influential; in addition, the RMSE for this industry was typically four to five times the standard error of the whole regression and its presence substantially reduced R[sup.2]. Accordingly this industry was dropped, leaving 93 industries in the larger sample (83 in the sample for which PL is available). in the regression results to be reported, it was calculated for how many observations the hat matrix diagonal element exceeded twice the ratio of the number of right hand side variables to the number of observations (see Belsley et al, 1980, for the rationale of this test). in every regression reported, the number of such observations was very small; in no case did such observations form a substantial proportion of the observations on a whole industry, still less of those on a whole year.

All the regressions to be reported included (a) the basic time series variables n[sub.it-1], [delta]y[sub.it], y[sub.it-1]; (b) a constant plus 92 industry dummies (82 in the smaller sample) to account for industry fixed effects; (c) up to 16 variables to capture variation in [lamdal] across industries; (d) 15 time-period dummies (for 1972-86). The other variables included vary between equations. A selection of results is reported in tables 3 and 4. In these tables, the estimates for the constant and the industry dummies are omitted in the interests of brevity; however, the total number of right hand side variables, including the constant, is recorded as NVARS.(22) LB is the Ljung-Box statistic for serial correlation up to order 6 (see Annex A). Since the sample period is 1971-86, the number of observations is either (93 x 16 =) 1488 or (83 x 16 =) 1328. In interpreting the coefficients, recall that (except in the case of output y[sub.t]) a negative number implies that an increase in the variable is predicted to increase productivity. The results for the larger sample of 93 industries (table 3) will be discussed first from an econometric viewpoint, before going on to the economic interpretation. Table 3 reports 4 variants of the most general model tested, each of which incorporate shock and intermediate price effects. The regressions differ in whether or not they include the relative wage variables (LSH and WR), for reasons to be discussed in a moment, and in whether or not they include the unionisation dummies (DCA72-86). The form of the regressions was selected as a result of experimentation with longer and shorter lags. The data suggested overwhelmingly that at least one lag should be included-regressions otherwise identical to those of table 3 except containing only current values of employment and output produced massive serial correlation (LB over 1300!). Entering two lags in employment and output was found to increase serial correlation at lags 1-4, while reducing it slightly at lags 5 and 6. On grounds of parsimony, the equations with one lag seemed preferable. Even so, it must be admitted that the reported equations fail the LjungBox test at conventional levels of significance (at the 5 per cent level, the critical value is 12.6). However, this is a tough test to beat; because of the large sample size, to do so requires sample serial correlation coefficients which average less than 0.04 in absolute value. In fact, the first six sample coefficients for regression 1 of table 3 were 0.03, -0.09, 0.02, -0.03, -0.08, and -0.05; similarly low values could be quoted for the other regressions.

The results of calculating Durbin's h by industry for each of the regressions in table 3 may be summarised as follows: (23) Statistics of Durbin's h (93 industries)

Regression Mean SD min max No.[greater than or equal to]~1.96~

1 0.23 0.83 -2.02 2.05 2

2 0.25 0.85 1.99 2.22 2

3 0.06 0.87 -2.15 1.93 1

4 0.07 0.88 -2.24 1.94 2 In view of the low absolute level of the sample serial correlations and these latter results for Durbin's h, the regressions were judged acceptable from the serial correlation point of view.

Fixed effects Inclusion of fixed effects substantially improved the goodness of fit and was easily justified by an F test. Apart from the fit, their main effect was on the estimated value of the speed of adjustment parameter [lamdal]-without them, the estimate of [lamdal] was implausibly low.

Dynamic adjustment The first block of variables in table 3 all involve the estimation of [lamdal]. When, in contrast to the results reported in that table, [lamdal] was constrained to take the same value in all industries, its value was found to be about 0.20 in regressions excluding relative wages and about 0.16 in regressions including them, values which are consistent with those typically found in macro studies; furthermore, the coefficient on n[sub.-1], was found to be very nearly equal, except for sign, to that on y[sub.-1], as the theory requires (see equation (7)) and both n[sub.-1], and y[sub.-1], were highly significant (t values of 8 or 9). However, inclusion of the extra variables which allow [lamdal] to vary across industries considerably improved the fit and was supported by an F test, hence this more general form is the one preferred. The average value of [lamdal] across industries, based on the variables involving n[sub.-1], was 0.18 in the case of regression 4 (excluding relative wages), but only 0.013 in the case of regression 2; based on variables involving y[sub.-1], the average value was 0.42 and 0.43 respectively. (24) In principle the two estimates for [lamdal] should be equal and therefore on these grounds regression 4, excluding relative wage variables, is preferable.(25)

While aspects of the estimated coefficients involving [lamdal] are difficult to reconcile with the theory, it must be remembered that the main purpose is not to study the dynamic adjustment process but rather the growth of productivity. If a constant , is imposed, then, as mentioned above, economically reasonable and statistically highly significant results are obtained. The extra variables which seek to account for the variation of k across industries are only included in case it should be claimed that the opposite strategy of imposing a constant [lamdal] has biased the conclusions about productivity.

Relative wage variables The addition of LSH and WR in current and lagged form, together with their interactions with KL and WHC, a group which will be referred to collectively as the relative wage variables, causes a striking improvement in goodness of fit (compare R[sup.2] for regressions 1 and 2 with R[sup.2] for regressions 3 and 4). However, the long run coefficient on LSH implied by these estimates is positive, while the long run coefficient on WR is negative, whereas according to the theory (see equations (7) and (4')) both should be negative.(26)

There is an identification problem with the relative wage variables. It has been assumed that firms are price takers in factor markets; firms who experience for example high wage growth will substitute capital for labour, thus raising labour productivity and lowering employment at given output levels. However an alternative possibility is that firms who for whatever reason experience high productivity growth choose, or are forced, to grant large wage increases; in other words, the causation might run from productivity to wages and not from wages, via capital intensity, to productivity.

The only satisfactory way of resolving this issue is to specify a model of the wage setting process and estimate it simultaneously with the employment equation, a task which would be far beyond the scope of the present article. (Instrumental variable methods may give the appearance of solving the problem but the results are crucially dependent on the choice of instruments.) Therefore, in order to indicate to what extent the results are likely to be affected by this issue, all equations have also been estimated without the relative wage variables (WR, WR[sub.-1] LSH and LSH[sub.-1]) and the associated interactions with KL and WHC. When these variables are omitted, we are assuming that the effects of capital investment have been captured entirely by the vintage model. When they are included, we are assuming that rising wages can proxy for rising capital intensity, the lafter being over and above what is already measured by the vintage model. The truth presumably lies somewhere between these two extremes.

Vintage capital effects The variable a[sub.it] measures the effect of investment from a vintage capital point of view. The importance of this effect is measured by the size and significance of the coefficients on a[sub.it], KLA and WHCA in table 3. The mean value across industries of the coefficient on a[sub.it] is negative, as predicted by theory -O.0051 in regression 2 and -0.0088 in regression 4). However this group of variables fails an F test: for example, the F value for the exclusion of these three variables from regression 4 is 1.4, against a critical value at the 5 per cent level of 2.6. Hence vintage capital effects would appear not to contribute significantly to the explanation of productivity growth over this period, a finding consistent with earlier results (Oulton, 1989).(27) This does not mean that investment and scrapping, the factors emphasised by the vintage capital model, are unimportant, only that they have not varied sufficiently over time or between industries to explain the variation in productivity growth. There would appear therefore to be a statistical case for excluding a[sub.it] from the regressions. However, it was thought preferable to retain it in order to show that the conclusions on productivity and unionisation are not being biased by ignoring vintage capital effects (though in practice these would have been little affected had vintage effects been excluded).

The dummy variables The period dummies (D72-86) are frequently significant in individual years, particularly in regressions excluding relative wages, and contribute substantially to the goodness of fit. The unionisation dummies (DCA72-86), which are almost invariably positive, are less significant on an individual basis and make a fairly small contribution to improving the fit. Testing for the exclusion of these variables, we find an F value of 2.3, comparing regressions 3 and 4, and one of 1.6 comparing regressions 1 and 2. Since, in this case, the critical value of F is 1.7 at the 5 per cent level and 2.0 at the 1 per cent -level, the inclusion of these variables is supported at the 1 per cent level for the regression without relative wages, but just fails to be significant at the 5 per cent level in the regression with relative wages. This difference could be explained if, as is plausible, unionisation does in fact affect wage behaviour, so that the relative wage variables are picking up the effects of unionisation (which are anyway measured only imperfectly by CA). Pursuing this line of enquiry would however take us too far afield.

Intermediate input prices This variable is included in current and lagged form; in both cases it is highly significant. The difference between the current and lagged coefficients is about 0.04 in all regressions, indicating that a doubling of intermediate input prices, relative to other factor prices, in an industry where such inputs were, say, half of total costs would lead after one year to a proportionate fall in productivity of [0.5 x 0.04 x In2l or 1.4 per cent. Economically, a rise in intermediate input prices could lower labour productivity in two principal ways. First, if capital and intermediate input are complements, firms may substitute labour for these other two factors. Second, and more trivially, a rise in intermediate input prices, if not fully passed forward into output prices, could lower measured productivity; the reason is that in the present article the output measure (`net output', which is close to value added) has been deflated by an output price deflator, rather than a value added price deflator.

The fact that intermediate price rises only have a small effect may underestimate their influence, since the first oil shock certainly led to other changes which may have been inimical to productivity. Candidates here include the resulting general inflation and the policies to which the lafter gave rise-a restrictive macro stance, incomes policies which distorted pay relativities and legislative changes giving more power to unions in the workplace.(28) In so far as any of these are important, they should be picked up by the time-period dummies, which do indeed indicate the presence of adverse shocks in this period.

Shock effects None of the shock variables SHDU82-86 are individually significant, except in 1983 in regression 4. Once again, it makes a big difference whether one includes the relative wage variables. With them (regression 2), the shock variables fail an F test (F = 2.1, against a 5 per cent critical value of 2.2); without relative wages (regression 4), the shock variables pass (F = 5.8). The improvement in goodness of fit is slight (R [sup.2] = 0.6258 with the shock variables and 0.6178 without them), so clearly one can get almost as good an explanation without recourse to this hypothesis. On the other hand, some at least of the shock variable coefficients are large in absolute value. For example, the largest of all, that for 1983 in regression 4, implies that in the latter year the 1979-81 shock caused a proportional rise in productivity of, on average, [0.2502 x 0.2222] or 5.7 per cent, where 0.2222 is the sample mean of the shock (SH)-certainly not a negligible effect. But some doubt still lingers around the shock hypothesis, since using the fall in output rather than in employment to measure the 1979-81 shock produced far less significant results; adding an extra shock variable for 1981, which using output rather than employment permits one to do, also failed to improve things. This suggests that the shock variables may still be picking up some part of the dynamic adjustment process, even though the specification of the latter is a fairly general one. The pattern of the coefficients is also rather odd, if they are indeed picking up the effect of the 1980-1 recession: although, reasonably enough, they rise (in absolute value) in 1983 and decline in 1984 and 1985, they then show a puzzling second rise in 1986, which is surely an implausibly delayed reaction to the events of 6 years earlier.

Plant size effects The plant size dummies, DPL72-86, are available for a somewhat smaller sample of 83 industries. Similar regressions to those of table 3 are reported for this smaller sample in table 4. There is no need to repeat the econometric discussion, since the points which arise here have already been covered, so we concentrate on the plant size dummies. The inclusion of these variables on their own without the unionisation dummies is supported by the F test: F = 2.0 in regression 1 and 2.2 in regression 3, against critical values at 5 per cent of 1.7 and at 1 per cent of 2.0. The further inclusion of the unionisation dummies, in equations which already contain the plant size

dummies, is supported for regression 4, which excludes relative wages (F = 2.2), but not for regression 2 (F = 1.4). The plant size dummies are almost invariably negative. (29)

7. The growth of productivity: an economic appraisal

Summarising the discussion of the previous section, the panel model has been found to fit the data reasonably well and to perform satisfactorily from an econometric point of view. Most of the influences on productivity which it has been possible to measure-unionisation, plant size, the 1980-1 shock, intermediate input prices, but not vintage capital effects-have found some statistical support, though unionisation and the shock were not significant when relative wages were also included. It is now time to attempt an economic appraisal.

Chart 1 graphs the coefficients on the time-period dummies from regression 2 of table 3; chart 2 does the same for regression 4. These numbers (recall that a negative number means an improvement in productivity) are our estimates of the period-specific shocks to productivity which were common to all industries.(30) Both pictures tell a similar story. There was an adverse shock to productivity in 1974 (despite the presence in both equations of variables measuring intermediate input prices). For the rest of the 1970s and throughout the 1980s the shocks were favourable. In the case of regression 2, the shocks appear if anything to have become less favourable as the 1980s wore on; in the case of regression 4, no clear trend is discernible.

Next, charts 3 and 4 graph the effects of unionisation for the same two regressions. (31) Note first of all that in both regressions the numbers are almost invariably positive, that is, if these results are to be believed, unionisation has reduced productivity growth throughout the whole period. In chart 3, there is a clear upward trend in the coefficient till 1979 and thereafter it generally falls. Chart 4 shows a similar pattern, though the post-1979 decline is less clear.

The time-period and the unionisation dummies are combined together in charts 5 and 6, with unionisation evaluated at its sample mean.(32) With relative wages included (chart 5), there is a clear improvement in performance, comparing the 1970s and the 1980s. Although there has been some falling away since 1981, there is no sign by 1986 of a return to the `bad old days'. With relative wages excluded (chart 6), the picture is less clear-cut. The improvement, though real enough, has not been so great, because on this reckoning the mid 1970s were not so bad. Both charts agree that 1981 was an exceptional year; the most natural interpretation is that a large oncefor-all shakeout of labour occurred at that time.

Another way to assess the differences between the 1970s and the 1980s is to consider average values of the coefficients, which were as follows:

Regression 2 Regression 4

1972-9 1980-6 1972-9 1980-6

Time-period dummies -0.0385 -0.0626 -0.0769 -0.1109

Unionisation dummies 0.0490 0.0282 0.0863 0.0752

Both combined -0.0011 -0.0411 -0.0109 -0.0534

Both regressions therefore agree that there has been an improvement in productivity growth in the following sense:during the 1980s there was a favourable shock to productivity whose impact effect averaged 4 percentage points higher than the comparable figure for the 1970s. Regression 2 would attribute about half of this (2 percentage points) to a decline in the disadvantages of unionisation, whereas regression 4 would attribute only a quarter (1 percentage point) to this cause. Note that these estimates do not include the effects of the 1980-1 recession nor those of intermediate input prices, both of which are accounted for separately in the regressions. It is appropriate to exclude these last two effects, since in the case of the first its influence is likely to wane over time, while the second is beyond the reach of policy.

Another way to assess the size of the productivity improvement is to ask, how much higher is productivity by the end of our period in 1986 than it would have been if the coefficients on the dummy variables had had the same value from 1980-6 as they had on average from 1972-9? The answer, assuming that all other variables apart from employment itself had unchanged paths, can be calculated from equation (7); it turns out that productivity is about 17 per cent higher in 1986 than it otherwise would have been. (33)

It is also important to note that the inclusion or exclusion of the relative wage variables has no influence on the size of the overall improvement, whether measured in impact terms or as a cumulative effect. In other words, even if increased capital intensity is correctly proxied by rising relative wages, it cannot on average explain the improvement, even though it may play a role in particular industries.

In the earlier tests of section 4 we found that the more heavily unionised industries had improved their performance the most after 1979. The present finding from the panel model, that unionisation has depressed productivity growth throughout the period, but less so in the 1980s, is not in conflict with the earlier one. For consider two hypothetical industries, A which is highly unionised and B which is not. Suppose that they differ only in the degree of unionisation. Let their productivity growth rates be as follows:

1971-9 1979-86

A 1 4

B 3 5

Clearly A, the highly unionised industry, has enjoyed the biggest improvement, but its performance is still depressed relative to that of B.(34)

Our findings on unionisation do however conflict to some extent with those of Nickell, Wadhwani and Wall (1989). Using company data for the period 1975-86 they found, at least in their preferred results, that unionisation was positively and significantly associated with productivity growth in 1980-4, that is, unionised firms grew more rapidly, but that for 1975-8 unionisation was not significant. However, these conclusions were derived from an unbalanced panel, with many fewer firms after 1982, and some of their other results are closer to the present ones. For example, when they restrict their sample to be a balanced panel, which is what our sample is too, they find almost the opposite, namely that unionisation significantly reduces productivity growth in 1975-8; in 198G-4 unionisation was found to increase productivity growth, though not significantly so (see column 2 of their table 2).

Finally, in chart 7 is shown the time pattern of the coefficients on the plant size dummy variables (the coefficients on DPL72-86, from table 4). Both regressions show a clear peak in the coefficient in 1977 or 1978 followed by a substantial decline. This is evidence in favour of the view that the UK disadvantage in operating large plants has been substantially reduced in the 1980s. (35)

8. Conclusions

The main results of the preliminary tests of section 4 were: (a) The shock of the 1980-1 recession was highly significant; the bigger the shock, the bigger the improvement in productivity growth from 1982 onwards; (b) the most heavily unionised industries were the ones which enjoyed the largest improvement in productivity growth after 1982; (c) other things equal, the greater the proportion of an industry's employment in large plants, the bigger the improvement in productivity growth. Unionisation and plant size were, it was argued, both proxy measures for the underlying state of labour relations.

On the whole, the panel model confirms these findings. There are however some qualifications. For example, the evidence for the importance of the 1980-1 recession now seems weaker. The main results of the panel model were:

(1) Neither investment in new technology nor scrapping were found to contribute significantly to the explanation of productivity growth. This confirms the conclusion already reached on the basis of a more limited analysis

in my earlier article (Oulton, 1989).(36)

(2) Rises in intermediate input prices were found to reduce productivity but these are far f rom being the whole explanation of the 1970s slowdown, as a glance at charts 1 and 2 will indicate.

(3) The shock of the 1980-1 recession was found to play a significant, but far from dominant, role after 1981, although only if the relative wage variables are excluded; when these variables are included, the shock variables become insignificant.

(4) Exclusive of any of the above influences, there has been an improvement in the growth rate of productivity in the 1980s whose impact effect was about 4 percentage points per annum higher than in the 1970s. Between a quarter and a half of this (1-2 percentage points) is attributable to a decline in the disadvantages of unionisation: that is, when all other effects are taken into account, unionisation still seems to reduce productivity growth, but to a lesser extent than it used to. if so, the Thatcher government's programme of trade union reform should receive a share of the credit.(37)

As a final comment, two notes of caution are in order. First, the improvement we have noted is relative to the 1970s. Basing themselves on data for aggregate manufacturing, Darby and Wren-Lewis (1 989) have argued for a common trend rate of productivity growth running through the 1960s, the 1970s and the 1980s. Nothing in the present article is necessarily inconsistent with this view. it was in the 1960s that it came to be recognised that Britain was failing behind its major European competitors. Second, most of the improvement is due to factors which it has not proved possible to measure and which therefore had to be captured by time-period dummies. Consequently, uncertainty must remain about the cause of the improvement and still more so about whether it is likely to continue. However, our findings on unionisation and plant size, together with the elimination of other candidate explanations, suggest that the difficulty or ease that firms experience in adapting or changing work practices has been the strongest influence on productivity growth in the period studied.

NOTES

(1) For a general overview of the issues involved in explaining the productivity improvement, see Muellbauer (1986).

(2) For a more elaborate theoretical argument on multi-unionism, see Bean and Symons (1989). By contrast, Machin and Wadhwani (1989), in a study based on data from the second WIRS of the determinants of organisational change (which they argue is correlated with productivity improvement), find that multi-unionism is not significant when entered in regressions in which plant size also appears.

(3) That trade unionism can under some circumstances assist productivity growth seems apparent, for example, from the record of Japan after the second world war, as well as from theoretical considerations (Freeman and Medoff, 1984).

(4) These variables are mutually exclusive; the omitted variable is the percentage of the workforce not covered by any collective agreement. Union density (the proportion of an industry's labour force who are union members) is an alternative measure, but reliable figures at the industry level are not available.

(5) Residual productivity growth as defined here is analogous to total factor productivity growth as derived from a neo-classical model, since it is that part of productivity growth which is not (apparently) explained by the growth of factor inputs.

(6) In calculating residual productivity growth, two runs of the vintage capital model were needed for the periods 1976-9 and 1982-5. These were done in the same manner as the ones described in Oulton (1 989). Since neither 1976 nor 1982 were cyclical peaks, these calculations must be regarded as less firmly based than the ones reported in that article.

(7) Perusal of this table shows that the predicted productivity growth rates are greatly in excess of the actual ones. Apart from the presence of special factors in the period after 1973, which it is one of the purposes of the present article to uncover, the over-prediction could be due to some bias in the estimation of the vintage capital model. But this lafter possibility need not invalidate the results to be reported here, provided that this bias (if it exists) is common to all industries.

(8) In symbols, if q and q[sup.R] are the natural logs of the levels of actual and residual productivity, then the dependent variable in columns 1 and 2 is [(q[sup.R][sub.85] - q[sup.R][sub.82])] - (q[sup.R][sub.79] - q[sup.R][sub.76] and in columns 3 and 4 is [(q[sub.85] - q[sub.82]) - (q[sub.79] - q[sub.76])]

(9) Other related studies include Wadhwani (1988) and Denny and Muellbauer(1988). For a survey of work on the effects of trade unions, see Metcalf (1 988) and Wadhwani (1 989).

(10) I owe this point to my colleague Simon Wren-Lewis.

(11) Shephard's Lemma states that the partial derivative of the cost function with respect to any factor price is the demand for that factor (Varian, 1984, p. 54).

(12) The backward nature of the forecasting scheme for output, together with the partial adjustment assumption for employment, may seem unrealistic, particularly when the model is to be fitted to a period which includes the 1980-1 recession. However, recall that the model also includes the unobserved variable f[sub.t] response to which can be immediate (if [micro]= 1), and which can be thought of as overriding the 'normal' mechanisms of adjustment.

(13) The distinction between f[sub.t] and g[sub.t], is really a pragmatic one. if more data were available or if theoretical understanding were greater, some of the factors which lie behind f[sub.t] would be transferred to g[sub.t].

(14) The production function (1) is specified in `value added' form. Gross value added', which is close to but not identical to an economic definition of value added, is available from the Census, but only from 1973. Hence the Census concept of `net output' was used instead. The main difference between gross value added and net output is that the former excludes the purchase of non-industrial services.

(15) The share of labour is likely in practice to be affected also by the process of collective bargaining. Hence LSH and WR may pick up some of the effect due to unionisation. However, unionisation effects are probably dominated, at least as far as cross-industry variation is concerned, by other factors, such as technology and the composition of the labour force, in particular the male/female split. Partly for this reason, the empirical results to follow are presented with LSH and WR both included and excluded (see below).

(16) The Hall-Jorgenson formula is:

r = [[rho] + [delta] - (dp[sub.1]/dt)/p[sub.1]][(1 - uA)/(1 - u)]p[sub.1] where [rho] is the nominal post-tax discount rate, [delta] is the depreciation rate, p, is the price of investment goods, u is the corporation tax rate and A is the real, post-tax present value of subsidies to investment, measured per [British pound] spent on investment. I am grateful to my colleague Mary O'Mahony for providing me with the basis for these estimates.

(17) The vintage model assumes that none of the investment carried out was of a capital deepening nature. On the other hand, the rationale for employing the relative wage variables, LSH and WR, is that capital deepening may have occurred. There is a danger therefore of double-counting: the same piece of investment may be being counted once as replacement of scrapped equipment by the vintage model but also as capital deepening via the relative wage variables. in the present context this is a relatively minor matter, since we are principally concerned that the role of investment not be underrated.

(18) This variable is the sum of the variables defined earlier, CA1, CA2 and CA3.

(19) Both KL and WHC are 1973 values and hence do not have a time subscript. The capital stock is from O'Mahony and Oulton (1990), using short lives and assuming exponential depreciation. The total and white-collar labour force, the latter being those workers characterised as `administrative, technical and clerical', are from the 1973 Census of Production.

(20) From 1979, these price indexes have been published on an Activity Heading basis in British Business. Unpublished indexes on the same basis were obtained from the BSO for the period 1974-9. These series were reclassified to a MLH basis using 1979 intermediate purchases as the weights. For 1970-3, the indexes were estimated by weighting together the producer price indexes for output (home sales), the weights being obtained from table D of the 1974 input-Output tables.

(21) The model contains a lagged dependent variable and while in this case OLS remains the maximum likelihood estimator, it ceases to be consistent for fixed T. Consistent instrumental variable estimators are available (Hsiao, 1 986, chapter 4), but as these require lagged values, their use entails the loss of valuable time series information. Hence in the present context it is not clear that there is any gain from using them.

(22) It was not in fact necessary to carry out regressions with the complete list of explanatory variables. The actual estimation procedure used was to subtract from the observations on each industry the sample period average for that industry and then to carry out the regression of the transformed dependent variable on the transformed independent ones, excluding from the latter the constant and the industry dummies. Under OLS this procedure generates the same estimates of the coefficients as would a regression of the untransformed dependent variable on the full list (including constant and industry dummies) of untransformed independent variables (Hsiao, 1986, chapter 3). The t ratios, R[sup.2] and other statistics produced by the regression on transformed values will not however be identical to those which would have been produced by the regression on untransformed values, but it is straightforward to convert from one to the other. In the results below it is the statistics appropriate to the original, untransformed regressions which are reported.

(23) Regressions 1-4 allow the coefficient on the lagged dependent variable, B,,, to vary across industries, through the variables KLN1, WHCN1, etc. Hence it is not quite clear how the variance of the estimate of this coefficient, which is required for Durbin's h (see Annex A), should be calculated. The solution adopted was to re-estimate regressions 1-4 without these variables and use the estimated variance of [Beta][sub.1i] from these latter regressions together with the residuals from the original regressions in calculating h. I also calculated Durbin's h wholly from the regressions which imposed a constant speed of adjustment across industries. Judging from the correlogram, these latter regressions have very similar autocorrelation properties to the ones in table 3. The results for Durbin's h were very similar to the ones reported in the text.

(24) The average for variables involving n[sub.-1], was computed as follows: coefficient on n-, + (coefficient on KLN1 x sample mean of KL) + (coefficient on WHCN1 x sample mean of WHC). A similar calculation was used for variables involving y[sub-1]. The sample mean of KL was 9.4584 and of WHC was 0.2545.

(25) It was suggested above that both high capital intensity and a high white collar proportion would reduce the speed of adjustment, which implies that the coefficients on both KLN1 and WHCN1 should be positive (and those on KLY1 and WHCY1 negative). The coefficient on KLN1 did turn out to be positive, that on WHCN1 to be negative; however, as they were individually insignificant, no strong conclusions can be drawn.

(26) In regression 2, the mean value across industries of the coefficient on LSH is -0. 1 553, of that on LSH[sub.-1] is 0.1 624; the mean values for WR and WR[sub.-1] are respectively -0.2170 and 0.1533. These calculations make use of the fact that the sample mean of KL is 9.4584 and of WHC is 0.2545.

(27) When [lamdal] is constrained to be constant across industries, the coefficient on a, is correctly signed but again not significant at the 5 per cent level.

(28) Sometimes attention is focused on energy prices, rather than intermediate input prices in general. It is not clear why this should be so, especially since energy is a very small part of total costs for most industries. However that may be, Kilpatrick and Naisbitt (1988) found a negative effect of energy intensity on total factor productivity in the 1970s, though the significance level was not high.

(29) As was stressed earlier, plant size and unionisation may be different proxy measures for the same phenomenon; however, in the sample the simple correlation between the two is only 0.37.

(30) They are in fact estimates of the parameters [gamma][sub.0s] (s = 2,...,16) of equation (12).

(31) These numbers are estimates of the parameters [gamma][sub.1s], of equation (12).

(32) That is, the number graphed is: coefficient on time-period dummy + (coefficient on unionisation dummy x sample mean of CA). The sample mean of CA was 0.7643.

(33) From equation (7), the effect on employment and productivity in period T of a sequence of shocks h[sub.t][sup.1], from period 0 to T, in place of an alternative sequence of shocks h[sub.t][sup.1], is: [summation][sup.j = t],[sub.j = 0] (1 - [lamdal])[sup.j](h[sub.T-j - h[sup.1][sub.T-j]) The actual calculation is a little more complicated than this because of the need to take account of the shock effect, which however turns out to be small.

(34) Machin and Wadhwani (1989) found, using data from WIRS, that heavily unionised plants were more likely to undergo reorganisation in the early 1980s. Arguably, this finding too is consistent with unionised plants achieving bigger improvements in productivity, but not necessarily enjoying an absolutely higher level of productivity growth.

(35) The fact that the coefficient is almost invariably negative presumably indicates that industries in which large plants predominate were for some reason more technically progressive in this period.

(36) See also Oulton (1987), which casts doubt on the scrapping hypothesis from a different point of view.

(37) The previous issue of the Review contained a detailed discussion of this programme by members of the Clare group (Brown and Wadhwani, 1990). As far as its effects on productivity are concerned, they reached a very sceptical conclusion, as did Nickell, Wadhwani and Wall (1989). Clearly my evaluation is a much more favourable one, closer to that of Metcalf (1990) who has recently carried out a detailed review of the evidence.

ACKNOWLEDGEMENTS

I am grateful to a number of colleagues at the National institute and elsewhere for helpful advice, comments and encouragement; in particular, I would like to thank Ray Barrell, Andrew Britton, John Ermisch, Jonathen Haskel, David Metcalf, Mary O'Mahony, Sig Prais and Simon Wren-Lewis. This article also benefited greatly from detailed comments by Sushil Wadhwani and an anonymous referee. An earlier version was given at an Institute seminar and the comments received from participants were very useful. This research was financed by a grant from the Leverhulme Trust.

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Title Annotation: | United Kingdom |
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Author: | Oulton, Nicholas |

Publication: | National Institute Economic Review |

Date: | May 1, 1990 |

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