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Efficiency in Welsh coal mining: A comment
Efficiency in Welsh coal mining a comment :
S.P. Chakravarty and D.E. Hojman
Comparison of labourproductivities and wage-to-price ratios suggests that the Coal Board’s behaviour was not profit-maximizing. This does not make the use of production functions to determine optimal scale very relevant. In particular, the current debates about efficiency and closures cannot be approached solely or mainly from production function analysis. Keywords: Welsh coal mining; Production functions; Optimal policies
After some soul searching, and since our original article’ and data provided the starting point for Fare and Yoon’s article,* we have decided to comment on the latter. We estimated a production function for the Welsh coal industry, and this production function approach on the same data has recently been extended by Fare and Yoon to investigate returns to scale. They argue that the optimal level of production during the sample period was greater than the actual level. More coal should have been produced. Their conclusions may well be right - we do not know - although many other elements which Fare and Yoon do not include explicitly or implicitly in their analysis should be taken into account. Reliance on estimates of production functions to arrive at their view is perhaps not advisable for the reasons discussed below. The sample period is 1961-1976. During this period output and employment declined in the coal industry in Wales, and indeed throughout the UK. Some Welsh collieries, if not Welsh coal mining as a whole, were subsidized by more productive coalfields elsewhere in the UK, or by the taxpayer. Extramarginal mines were being shut down (even if the criteria for identifying a mine as ‘extramarginal’ were never made explicit), thereby inflating observed productivity. Part of this effect is perhaps captured in the time trend variable. The mines closure programme was accompanied by a conscious attempt at achieving manpower reduction through voluntary means. However, the considerations were not limited to profit maximization for the coal industry taken in isolation from the rest of the economy. There were ill specified social cost-benefit criteria. Thus, it would be inappropriate to assume that ‘the observed data were generated under the
conditions of expected profit maximisation’.3 Moreover, the measurement of capital stock in nationalized industries poses special difficulties which, for reasons of space, we cannot discuss here.
Review In the original article, where Chakravarty and Hojman’s production function was presented, data limitations were pointed out, but perhaps not adequately emphasized. One of the purposes of that article was to argue that if the data were assumed to have derived from a profit maximizing scheme, often implied as a desirable goal by politicians in charge of the coal industry, increases in wages could not be held responsible for the entire increase in prices. During the period in question, wages policies were alleged to be essential to controlling inflation. Our objective was to highlight that the political rhetoric did not add up. We did not suggest that any part of the rhetoric was necessarily sensible, providing a basis for policy. We should certainly dissent from the view that profit maximization in the coal industry should be pursued without reference to the wider economy. With hindsight, it is clear that reservations about the data and also about the production function approach should have been given more prominence. If this omission has led Fare and Yoon to place undue trust in their assumption that the data came from some profit maximizing exercise undertaken by the National Coal Board, we share the blame. The record needs to be corrected.
Profit maximization The authors are with the Economics Department, University College of North Wales, Bangor, Gwynedd, LL57 2DG, UK and Economics Department, University of Liverpool, PO Box 147, Liverpool, L69 38X, UK, respectively.
RESOURCES
POLICY March 1985
If profit maximization point, it would follow labour would equal the coal. We constructed
were to be assumed at each data that the marginal productivity of ratio of wage rates to the price of a wage/price index (1970=100)
63
Efficiency in Welsh coal mining Table 1. Marginal productivity wages to prices.’ Year
Marginal productivity of labour
1961 1962 1963
1.0787
1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
1.0066 1.0643
1.0643 1.0200
1.1661 1.3361 1.4785 1.5023 1.5322 1.5531 1.6851 2.2371 2.6831 2.9272 3.0694
of labour compared
to the ratio of
Wage/price index
Marginal productivity index 70.4039 69.4636 66.5739 65.6997 69.4624 76.1057 87.2012 96.3237 98.0525
84.1358 82.2193 88.6153 90.3300 95.5624 91.2259 96.7007 101.3430
101.8420 100.0000 128.4220 96.1712 90.8795 72.5948 81.4634 72.4279
100.0000 101.3673 109.9828 146.0068
175.1169 191.0450 200.3283
Contribution
“According to Equation (2) and Fire and Yoon’s estimated coefficients.
adult male workers’ earnings per manshift by proceeds per tonne of output. These data were available in index is preCoal Board accounts,4 and the respective sented in the last column of Table 1. We have also calculated the marginal productivity of labour following from Fare and Yoon, and expressed it in index form (1970=100). It is shown in Table 1. The production function estimated by F3re and Yoon is as follows dividing
Y = c + at* inT + ak* [KI(K + L)i* inK + al* (LI(K + L)/* inL + u where Y, T, K and L stand for output, labour, respectively; c is a constant term, the production function parameters, and The partial derivative with respect to
to GDP
In the example cited above, if the contribution to GDP from alternative activities upon release of the resources due to colliery closure exceeds f100, the colliery would be uneconomic for the country as a whole as well. If, however, the manpower reduction by the Coal Board is simply reflected in an increase in unemployment, there will be a net loss to GDP. Depending on the assumptions about the expected redeployment of manpower - or lack of it - and capital released by pit closures, pits which are uneconomical for the Coal Board could become desirable from the wider viewpoint of the national economy.
Realistic case (1)
time, capital and at, ak and al are u is the residual. L is ’
I’L = al* [inLl(K + L) - iLI(K + L)** 2/* inL + l/(K + L)] - ak* [K/(K + L)** 21 * in K (2) Parameters al and ak were estimated by Fire and Yoon to be 52707.47 and 24176.64, respectively.6 We have used them here in calculating the series in columns 1 and 2 of the table. It is clear from this table that the labour productivity index and the wage/price index are not related at all. The correlation coefficient between them is (minus) -0.440.
Conclusions The production function approach is an inadequate tool for drawing firm conclusions about ‘optimal’ policies in this particular case. At best, production functions can be used for attracting attention to seeming anomalies as was done in the original article by Chakravarty and Hojman. Assumption of profit maximization at each instant of time for the industry does not hold. Nor should it, given the interaction between coal and other sectors. This is a specially important consideration when there are unutilized resources in the rest of the economy. For example, consider a colliery producing 2100 worth
64
of coal, paying f90 in wages and making f20 in interest payment for investment already sunk in the ground. It makes a loss of El0 to the Coal Board. However, both for the Coal Board and for the UK economy as a whole, there could be a larger loss if this colliery were shut. As regards the Coal Board, closing the colliery would increase losses from f10 to f20, since the interest payments should still be met, even after closure. By contrast, regardless of whether the closure makes good economic sense for the Coal Board or not, what happens in relation to the overall British economy depends on what is reasonable to assume about the redeployment of resources released in the attempt by the Coal Board to reduce its own losses.
Obviously, in the more realistic case the most likely outcome lies between these two extremes. Released resources can be employed somewhere else but only after some possibly substantial time lag. Then, other relevant aspects are how long redeployment takes, how large or small the implicit time preference is, and the magnitude of the social rate of discount. Incidentally, intertemporal preferences are also to be taken into account in the valuation of output (&loo) if coal is stocked for very long periods in power station yards, rather than consumed shortly after extraction. These are important considerations which are not appreciated in the production function approach.
References ‘S.P. Chakravarty and D.E. Hojman, ‘An empirical analysis of productivity: Welsh coal industry’, Resources Policy, Vol8, No 2, June 1982, pp 125-132. ‘R. Fare and B.J. Yoon, ‘An empirical investigation of returns to scale: the Welsh coal industry’, Resources Policy, Vol 10, No 2, June 1984, pp 134-l 37. 3Ftire and Yoon, op tit, Ref 2, p 135. 4Data taken from various issues of National Coal Board, Reports and Accounts, and Welsh Office, Digest of Welsh Statistics, Cardiff. ‘The expression for the marginal productivity of labour appearing in Fire and Yoon, op tit, Ref 2, contains a typing error. ‘There is a printing error in Fare and Yoon’s Table 1, on p 136, Ref 2. The estimated coefficient for the parameter ak should be only one-tenth of the value printed in their table: the correct value is 24176.64 and not 247176.64.
RESOURCES
POLICY March 1985
S.P. Chakravarty and D.E. Hojman
Comparison of labourproductivities and wage-to-price ratios suggests that the Coal Board’s behaviour was not profit-maximizing. This does not make the use of production functions to determine optimal scale very relevant. In particular, the current debates about efficiency and closures cannot be approached solely or mainly from production function analysis. Keywords: Welsh coal mining; Production functions; Optimal policies
After some soul searching, and since our original article’ and data provided the starting point for Fare and Yoon’s article,* we have decided to comment on the latter. We estimated a production function for the Welsh coal industry, and this production function approach on the same data has recently been extended by Fare and Yoon to investigate returns to scale. They argue that the optimal level of production during the sample period was greater than the actual level. More coal should have been produced. Their conclusions may well be right - we do not know - although many other elements which Fare and Yoon do not include explicitly or implicitly in their analysis should be taken into account. Reliance on estimates of production functions to arrive at their view is perhaps not advisable for the reasons discussed below. The sample period is 1961-1976. During this period output and employment declined in the coal industry in Wales, and indeed throughout the UK. Some Welsh collieries, if not Welsh coal mining as a whole, were subsidized by more productive coalfields elsewhere in the UK, or by the taxpayer. Extramarginal mines were being shut down (even if the criteria for identifying a mine as ‘extramarginal’ were never made explicit), thereby inflating observed productivity. Part of this effect is perhaps captured in the time trend variable. The mines closure programme was accompanied by a conscious attempt at achieving manpower reduction through voluntary means. However, the considerations were not limited to profit maximization for the coal industry taken in isolation from the rest of the economy. There were ill specified social cost-benefit criteria. Thus, it would be inappropriate to assume that ‘the observed data were generated under the
conditions of expected profit maximisation’.3 Moreover, the measurement of capital stock in nationalized industries poses special difficulties which, for reasons of space, we cannot discuss here.
Review In the original article, where Chakravarty and Hojman’s production function was presented, data limitations were pointed out, but perhaps not adequately emphasized. One of the purposes of that article was to argue that if the data were assumed to have derived from a profit maximizing scheme, often implied as a desirable goal by politicians in charge of the coal industry, increases in wages could not be held responsible for the entire increase in prices. During the period in question, wages policies were alleged to be essential to controlling inflation. Our objective was to highlight that the political rhetoric did not add up. We did not suggest that any part of the rhetoric was necessarily sensible, providing a basis for policy. We should certainly dissent from the view that profit maximization in the coal industry should be pursued without reference to the wider economy. With hindsight, it is clear that reservations about the data and also about the production function approach should have been given more prominence. If this omission has led Fare and Yoon to place undue trust in their assumption that the data came from some profit maximizing exercise undertaken by the National Coal Board, we share the blame. The record needs to be corrected.
Profit maximization The authors are with the Economics Department, University College of North Wales, Bangor, Gwynedd, LL57 2DG, UK and Economics Department, University of Liverpool, PO Box 147, Liverpool, L69 38X, UK, respectively.
RESOURCES
POLICY March 1985
If profit maximization point, it would follow labour would equal the coal. We constructed
were to be assumed at each data that the marginal productivity of ratio of wage rates to the price of a wage/price index (1970=100)
63
Efficiency in Welsh coal mining Table 1. Marginal productivity wages to prices.’ Year
Marginal productivity of labour
1961 1962 1963
1.0787
1964 1965 1966 1967 1968 1969 1970 1971 1972 1973 1974 1975 1976
1.0066 1.0643
1.0643 1.0200
1.1661 1.3361 1.4785 1.5023 1.5322 1.5531 1.6851 2.2371 2.6831 2.9272 3.0694
of labour compared
to the ratio of
Wage/price index
Marginal productivity index 70.4039 69.4636 66.5739 65.6997 69.4624 76.1057 87.2012 96.3237 98.0525
84.1358 82.2193 88.6153 90.3300 95.5624 91.2259 96.7007 101.3430
101.8420 100.0000 128.4220 96.1712 90.8795 72.5948 81.4634 72.4279
100.0000 101.3673 109.9828 146.0068
175.1169 191.0450 200.3283
Contribution
“According to Equation (2) and Fire and Yoon’s estimated coefficients.
adult male workers’ earnings per manshift by proceeds per tonne of output. These data were available in index is preCoal Board accounts,4 and the respective sented in the last column of Table 1. We have also calculated the marginal productivity of labour following from Fare and Yoon, and expressed it in index form (1970=100). It is shown in Table 1. The production function estimated by F3re and Yoon is as follows dividing
Y = c + at* inT + ak* [KI(K + L)i* inK + al* (LI(K + L)/* inL + u where Y, T, K and L stand for output, labour, respectively; c is a constant term, the production function parameters, and The partial derivative with respect to
to GDP
In the example cited above, if the contribution to GDP from alternative activities upon release of the resources due to colliery closure exceeds f100, the colliery would be uneconomic for the country as a whole as well. If, however, the manpower reduction by the Coal Board is simply reflected in an increase in unemployment, there will be a net loss to GDP. Depending on the assumptions about the expected redeployment of manpower - or lack of it - and capital released by pit closures, pits which are uneconomical for the Coal Board could become desirable from the wider viewpoint of the national economy.
Realistic case (1)
time, capital and at, ak and al are u is the residual. L is ’
I’L = al* [inLl(K + L) - iLI(K + L)** 2/* inL + l/(K + L)] - ak* [K/(K + L)** 21 * in K (2) Parameters al and ak were estimated by Fire and Yoon to be 52707.47 and 24176.64, respectively.6 We have used them here in calculating the series in columns 1 and 2 of the table. It is clear from this table that the labour productivity index and the wage/price index are not related at all. The correlation coefficient between them is (minus) -0.440.
Conclusions The production function approach is an inadequate tool for drawing firm conclusions about ‘optimal’ policies in this particular case. At best, production functions can be used for attracting attention to seeming anomalies as was done in the original article by Chakravarty and Hojman. Assumption of profit maximization at each instant of time for the industry does not hold. Nor should it, given the interaction between coal and other sectors. This is a specially important consideration when there are unutilized resources in the rest of the economy. For example, consider a colliery producing 2100 worth
64
of coal, paying f90 in wages and making f20 in interest payment for investment already sunk in the ground. It makes a loss of El0 to the Coal Board. However, both for the Coal Board and for the UK economy as a whole, there could be a larger loss if this colliery were shut. As regards the Coal Board, closing the colliery would increase losses from f10 to f20, since the interest payments should still be met, even after closure. By contrast, regardless of whether the closure makes good economic sense for the Coal Board or not, what happens in relation to the overall British economy depends on what is reasonable to assume about the redeployment of resources released in the attempt by the Coal Board to reduce its own losses.
Obviously, in the more realistic case the most likely outcome lies between these two extremes. Released resources can be employed somewhere else but only after some possibly substantial time lag. Then, other relevant aspects are how long redeployment takes, how large or small the implicit time preference is, and the magnitude of the social rate of discount. Incidentally, intertemporal preferences are also to be taken into account in the valuation of output (&loo) if coal is stocked for very long periods in power station yards, rather than consumed shortly after extraction. These are important considerations which are not appreciated in the production function approach.
References ‘S.P. Chakravarty and D.E. Hojman, ‘An empirical analysis of productivity: Welsh coal industry’, Resources Policy, Vol8, No 2, June 1982, pp 125-132. ‘R. Fare and B.J. Yoon, ‘An empirical investigation of returns to scale: the Welsh coal industry’, Resources Policy, Vol 10, No 2, June 1984, pp 134-l 37. 3Ftire and Yoon, op tit, Ref 2, p 135. 4Data taken from various issues of National Coal Board, Reports and Accounts, and Welsh Office, Digest of Welsh Statistics, Cardiff. ‘The expression for the marginal productivity of labour appearing in Fire and Yoon, op tit, Ref 2, contains a typing error. ‘There is a printing error in Fare and Yoon’s Table 1, on p 136, Ref 2. The estimated coefficient for the parameter ak should be only one-tenth of the value printed in their table: the correct value is 24176.64 and not 247176.64.
RESOURCES
POLICY March 1985