Responses of energy demand in UK manufacturing to the energy price increases of 1973 and 197980

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Alan Ingham

ABSTRACT

This chapter presents estimates of energy elasticities based on a vintage model of UK manufacturing (excluding the iron and steel industries). Energy price changes affect energy demand in the model in two ways. The first is through the design of newly installed equipment. This depends on expectations of future factor prices. The second is though changing the use of existing equipment. This depends upon actual factor prices. The model thus allows for differing ex ante and ex post responses. The magnitude of the first response will determine the long-run elasticity.

The chapter takes an estimated model for the period 1971-90 and considers how the observed changes in the energy-output ratio over that time can be decomposed into that part explained by technical progress, that part explained by changes in the level of production, that part explained by changes in wage rates and that part explained by changes in energy prices in terms of (i) the expectation of future energy prices and (ii) their realized value. In particular the effect of energy price changes in 1973 and 1981 will be decomposed into that part which worked through changing expectations and that part which worked through changing current factor prices.

INTRODUCTION

The discussion of the proposed European Union carbon/energy tax has led to considerable interest in energy demand elasticities, as they are vital to an understanding of the economic and environmental impact of such policies. The purpose of this chapter is to consider what insights might be obtained from a dynamic model based on economic structure rather than of a statistical time-series nature. Ideally, such a model would be used to separate out short-run from long-run consequences and to estimate the length of adjustment to taxes, especially if environmental problems arising out of energy use need to be addressed within a particular time period. Furthermore, an analysis of the effect of the announcement of future taxes on present energy consumption would be desirable. Ideally, the model should be structural as the use of a purely statistical model might run into regime shift problems.

In order to answer these questions, the use of a vintage model, such as that which has been constructed for the Department of Trade and Industry (formerly the Department of Energy) to assist in the evaluation of long-run forecasts, is appropriate. The original motivation for the study was to explain the changes in energy demand that resulted from the large energy price changes of 1973 and 1980. Box-Jenkins type studies had not been able to explain the fall in energy demand after the 1980 price rise. By considering a more detailed structural model of the decisions made by industry it was hoped that the delays in reacting to price changes could be explained. The model has been moderately successful in this respect and the purpose of this chapter is to consider what the price elasticities of energy demand were during periods of large price changes. This will allow for the estimation of the extent to which energy demand falls both in the short run immediately following price rises and in the long run if these price rises continue into the future.

One disadvantage of the model used is that the specification of the model does not allow for a simple answer to this question. The first reason for this is that there are no simple closed-form solutions dependent upon a few parameter estimates, so it is generally necessary to undertake simulations. The second problem is that the magnitude of the response depends potentially on all the exogenous variables. Thus it is necessary to undertake a series of ceteris paribus simulations. This is handled by considering several scenarios, varying the magnitude of the price rise and the growth of output.

An early version of the model was described by Ingham et al. (1988). More recently, work has concentrated on the simulation of possible carbon/energy taxation policies. These simulations are reported in Ingham and Ulph (1991a, b) and Ingham et al. (1991a). In this chapter the concern is strictly with energy demand changes by United Kingdom manufacturing during the period 1971-90, in particular in the years of the two oil shocks.

The effect of an increase in the rate of growth of price increases on the economy works through several channels. There will be the immediate substitution out of energy, depending on the degree of substitutability. Next the increase in energy prices will cause certain plants to become uneconomic. They will be closed down and possibly replaced. Any new plants will embody more energy-saving technology, with the extent of energy saving dependent upon the expected price increase. Faster growth in price increases will change expectations more rapidly and so more rapid transformation of the capital stock and a greater degree of adjustment would be expected.

The degree of adjustment will also affect the extent to which new investment is taking place, irrespective of new investment caused by premature scrapping. While some of this investment occurs because of routine replacement of depreciated equipment, the rest is determined by the need for extra capacity. The faster this new capacity is installed the faster the effects of increasing prices should be felt. This will be considered by simulating the effects of increasing energy prices for different growth rates of output for the manufacturing sector. This is an important question for energy and environ- mental policy since policies which increase energy prices may slow down the rate of growth of output and lead to less, rather than more, substitution.

These effects depend upon the expectational mechanism. The mechanism employed in the model is an adaptive process where expected prices are extrapolations of trends calculated from linear regressions using past observations. The length of the data set for these regressions determines the extent to which the past is incorporated as an estimated parameter in the model. Expectations enter into the model through a present value expression, which means that the changed expectations are very slow to take effect. Two alternative possibilities are also considered. One is that of perfect foresight, which is similar to a rational expectations formulation. Given the data sets available, this formulation can only be applied in so far as there are sufficient observations. The existence of missing observations is overcome by extending the data using existing trends. The calculation of the effect of such a formulation is important since a likely policy would be to announce, in a credible way, increased energy taxes in the future, thereby obtaining immediate energy reductions through changes in the design of newly installed equipment.

A second alternative is to consider a purely myopic form of expectations, wherein the current real energy price is expected to rule for ever. As will be seen this has, at first sight, some surprising effects. A final set of simulations looks at the effect of a sudden increase in energy prices. This is carried out under two scenarios, one wherein the increase is expected by industry and the other where it is unexpected. The first case corresponds to the perfect foresight scenario, with the second case corresponding to perfect foresight until the price increase, adaptive expectations in the period following the increase, and perfect foresight thereafter. It is hoped that this gives an impression of the extent to which perfect foresight anticipates future price changes, and the delay before which the effect of an unanticipated price change wears off.

The chapter proceeds in the following manner. Section 5.1 considers the specification of the vintage model. This is done in a descriptive and intuitive way. A more formal mathematical specification of the model is provided in Appendix 5A, and details of the estimated parameters are provided in Appendix 5B. Section 5.2 considers data availability on the nature of vintage changes over time, and the consequent implications of such changes for the short-run and long-run behaviour of the model. Section 5.3 considers the results from applying the model to simulations. This is divided into two parts. The first set of simulations is designed to calculate energy price elasticities and to consider the various factors that will influence them. The second set of simulations looks at the role that price expectations may have played in determining changes in energy demand. Finally Section 5.4 provides conclusions.

A DESCRIPTION OF THE VINTAGE MODEL

An important aspect of a vintage model of factor demands is that it allows for the analysis of the dynamics by which producers will respond to price changes. In the short run, producers can respond either by adjusting the mix of variable factors employed on machines already installed (e.g. there may be some scope for fuel switching) or by varying the output produced on machines of different ages (vintages). But in the long run there is the more important response of changes in the capital stock by scrapping old machines and investing in new ones employing different factor proportions.

In early developments of the vintage model (e.g. Salter 1966; Malcomson and Prior 1979), it was assumed that technology had a structure characterized as 'putty-clay'. Thus it was assumed that the scope for varying the mix of factors (e.g. labour, raw materials, energy) employed on a machine installed at a particular time (vintage) occurred only at the design stage (an ex ante decision), and once the machine was installed factors such as labour or energy would be employed on that machine in fixed proportion to the output produced; the only way in which firms could vary the mix of factors they employed on machines which were already available would be to vary how much output was produced on different machines (an ex post decision).

In the model employed, based on Fuss (1977a), there is some scope for varying the input-output ratios even at the ex post stage, though the scope for doing so will in general be less than at the ex ante stage; moreover producers decide at the ex ante stage how much ex post substitution (flexibility) they wish to have (within technology limits) depending on how much they expect relative prices to vary over the design life of the machine. This structure is called putty-semi-putty. The full details of this model are provided in Appendix 5A.

The model can be characterized in simple terms as follows. Begin with the producer's choice of design of machine ex ante and choice of actual factor mix ex post, assuming that there are only two factors, labour and energy, and that the producer knows what output level will be produced on a machine once it is operational. At the time of designing the machine the prices of labour and energy are expected to be W and P respectively, while actual factor prices turn out to be W and P. Figure 5.1 depicts the situation with putty-clay technology. AA is the ex ante isoquant, representing the mixes of labour and energy that the machine could be designed to operate with. Given expected factor prices, the producer chooses to operate with the mix represented by point X. Ex post there is no scope for varying the mix of factors, so the ex post isoquant is BB, and if actual factor prices turn out to be W and P the producers will be operating with a mix of factors which is considerably more expensive than would have been the case if they had predicted relative factor prices correctly (point Y). The putty-semi-putty model is illustrated in Figure 5.2. The situation is more complicated, so the description will be rather more intuitive.

Figure 5.1 Ex ante technology putty-clay

Again given the ratio of expected future prices the producer must choose from the ex ante isoquant AA the ratio of labour to energy that would be employed ex post if actual factor prices equalled expected prices; this is shown by the point X, or more precisely the entire set of such prices is shown by the ray through X. Corresponding to this point is a family of ex post isoquants (BB and CC are two examples) with differing degrees of ex post factor substitution. Depending on the extent to which relative factor prices are expected to change over the life of the machine (i.e. the expected variability in factor prices), the producer will select the appropriate ex post isoquant. If it is expected that factor prices will not differ much from the ratio represented by P and II ', an isoquant such as CC is chosen, with little potential for ex post substitution, since that will minimize production costs; however, if quite wide variations are expected, e.g. P and W, then it will be cheaper to have an isoquant like BB which allows for some degree of ex post substitution. In that case when actual prices are P and W the firm could move from factor mix X to factor mix Y.

In order to see how producers decide how much output to produce from each vintage at each point in time, note first that given the ex post choice of input-output coefficients for variable factors firms can first calculate the unit variable cost of production on each available vintage and then rank them in increasing order of unit cost, as shown in Figure 5.3, where the maximum amount of output that can be produced on each vintage depends on the original installed capacity and any subsequent depreciation, which is assumed to be reflected solely in terms of reduced available capacity, as if some fraction of machines become obsolete each period while the rest continue operating at their design efficiency. This gives the supply curve of producers and Figure 5.3 shows two ways in which overall output is determined. In the first case, total output Yt is simply specified exogenously, in which case vintages will be employed in order of increasing unit variable cost until aggregate available capacity exceeds output required. In the figure, vintages 1 and 2 will be fully employed, vintages 4 onwards will not be employed and vintage 3 will be the marginal vintage, with the machine operating at less than full capacity.

Figure 5.2 Ex ante technology putty-semi-putty

In the second case, the output produced depends on the price of output (e.g. as shown by the demand curve DD), and in this case price and output are determined simultaneously by supply and demand. Specifically, price is set equal to the variable cost of the marginal vintage employed plus a mark-up reflecting the fact that the output market may not be fully competitive. In fact, output and price are not determined simultaneously; rather, a model of price adjustment, which is described shortly, is employed.

And finally, the determination of rates of investment and scrapping must be addressed. Producers use their expectations of future factor prices to compare the present value of operating costs on existing vintages over the planning horizon with the present value of total production costs (operating and capital costs) on a new machine. Old machines have the advantage that their capital costs have been sunk, but new machines have the advantage of being designed specifically to meet the relative factor prices expected to prevail in the future and of embodying any improvement in technology. Old machines which are more expensive than a new machine are scrapped. Firms compare the capacity that they plan to have available on old machines at the date a new machine could be installed with the output they expect to have to produce at that date in order to meet demand; if capacity falls short of expected demand, new machines are commissioned to provide the additional capacity; if capacity exceeds expected demand, there is no new investment, and the more expensive of the old machines will be scrapped until some specific margin of excess capacity remains. It should therefore be clear that a sharp change in expected factor prices relative to those which were expected to prevail when old machines were built is likely to lead to a lot of old machines being scrapped and new ones ordered. The capital stock parameters have been estimated on quarterly data for the UK manufacturing sector for the period 1971Q1-1989Q4. Details are provided in Appendix 5B.

Figure 5.3 Ex post decision

THE ESTIMATED MODEL AND ITS USE IN SIMULATION

The goodness of fit

The tables and figures which follow are the results obtained from the best fit over the sample period. Turning first to the labour, energy and investment series, displays of the actual and fitted series are produced in Figures 5.4-5.6. Figure 5.4 shows that employment is fitted quite well. Turning points and sharp declines are predicted well. The model tends to react more quickly than the economy actually does, and the upturn in 1973 and the decline in 1975 are predicted to have happened one quarter too early. The fitted series is more variable than the actual path, even though the employment series is taken to be hours worked multiplied by the PUL index of labour utilization (see Smith-Gavine and Bennett 1993). Neither of these effects is too surprising. There is nothing in the model which prevents manufacturing from responding immediately to changes in factor prices and demand, apart from the nature of the capital stock. Hence the fitted employment series will be that level of labour services which manufacturing would like to employ, rather than that level which it has to employ because of hiring and firing costs, redundancy legislation and other labour market characteristics.

The other main comment to be made on the performance of the model in explaining labour demand is that the model tends to underpredict labour demand for the period up to 1983 and overpredict demand for the period after 1983. This is consistent with the notion that there was a structural break in the labour market and industrial relations in the 1980s, following the legislative programme of the first Thatcher Conservative government and the increase in credibility that followed from the resolution of the miners' strike.

71 74 77 80 83 86 89

Year

71 74 77 80 83 86 89

Year

Figure 5.4 Fit of model: labour

The performance of the model in fitting energy demand is shown in Figure 5.5. This is not as good as the estimation of the model over previous, shorter, sample periods. However, the model does capture the decline in energy demand in 1974-5 and 1981, while other models have been unable to capture these phenomena. The main problem is that the data display a remarkably constant level of energy demand through the 1980s whilst output was increasing. The model explains some of this decreasing energy-output ratio but fails to capture the decline after 1986. It appears that, in minimizing the error over this period, the model distorts the fit for the other part of the sample period.

Investment is displayed in Figure 5.6. The fit here is quite good. The fitted values tend to smooth out the cycle in the early 1970s and then to anticipate the increase in investment in the 1976-80 period. Post-1979 the model fits the series well and captures period-by-period fluctuations. Table 5.1 gives the number of vintages used and available, and this gives an indication of the extent of capacity utilization. The latter numbers are somewhat low, certainly compared with the length of service lives used in the capital stock series produced by the CSO, but they are consistent with the length of life found in other countries. A possible reason for the shortness of life, and the rather high rate of depreciation that goes with it (see the parameter estimates in Appendix 5B), is the aggregation across firms. For an individual firm, investment may be rather lumpy in that plants may only be installed in a limited number of years. However, different firms will exhibit 'lumpiness' in different years, so that the pattern of investment will be much smoother for the economy as a whole than for individual firms.

By treating the manufacturing sector as a representative firm it appears that capital is being replaced much faster than is actually the case. For the purposes of forecasting energy demand due to price rises or tax changes this would not be particularly serious if firms were alike in their energy-using characteristics or the aggregation problem was not serious. However, it is known that this is almost certainly not the case and therefore there will be an aggregation error in our results, which could be in either direction. The reaction to an energy tax will be rapid if it occurs just as a high-energy-using firm is replacing its equipment and slow

Figure 5.5 Fit of model: energy if it occurs just after high-energy-using firms have replaced their equipment. The analysis employed here is only concerned with temporal disaggregation. Whilst it would be most desirable to disaggregate across sectors of industry, if not firms, the data are not available to allow this to be done.

Table 5.1 Number of vintages available and used

Date Used Available Date Used Available

1971.1

22

59

1980.3

26

79

1971.2

22

60

1980.4

24

80

1971.3

22

61

1981.1

24

81

1971.4

22

62

1981.2

25

81

1972.1

21

63

1981.3

26

81

1972.2

23

64

1981.4

28

82

1972.3

24

65

1982.1

28

83

1972.4

26

65

1982.2

29

84

1973.1

28

66

1982.3

30

85

1973.2

28

67

1982.4

31

84

1973.3

29

68

1983.1

33

84

1973.4

29

69

1983.2

34

83

1974.1

26

70

1983.3

36

84

1974.2

29

71

1983.4

38

83

1974.3

28

72

1984.1

40

83

1974.4

26

73

1984.2

41

80

Figure 5.6 Fit of model: investment

Date

Used

Available

Date

Used

Available

1975.1

25

74

1984.3

42

81

1975.2

23

75

1984.4

43

82

1975.3

22

76

1985.1

44

80

1975.4

23

77

1985.2

45

80

1976.1

24

78

1985.3

44

81

1976.2

25

79

1985.4

42

82

1976.3

25

80

1986.1

42

81

1976.4

27

81

1986.2

42

82

1977.1

28

82

1986.3

42

83

1977.2

27

83

1986.4

44

81

1977.3

27

84

1987.1

43

81

1977.4

28

85

1987.2

46

82

1978.1

29

86

1987.3

47

79

1978.2

30

87

1987.4

47

76

1978.3

31

86

1988.1

48

74

1978.4

31

83

1988.2

47

74

1979.1

30

83

1988.3

49

74

1979.2

32

80

1988.4

48

73

1979.3

30

81

1989.1

48

73

1979.4

31

80

1989.2

46

74

Date

Used

Available

Date

Used

Available

1980.1

30

81

1989.3

42

73

1980.2

27

78

1989.4

39

Differences in vintages

In considering an estimated econometric model it is usual to consider the magnitude of the parameter estimates and to interpret their value. The putty-semi-putty vintage nature of the model with generalized Leontief technology does not allow this to be done as easily as the basic estimated parameters from the matrix A, which drives the ex ante and ex post substitution.

As is shown in Appendix 5A, each vintage is characterized by the (derived) parameters b", b^, b^ (equations (5.3a) and (5.3b)) which depend on the parameters in the matrix A. These are more easily interpreted as the ex post input-output coefficients. These coefficients are important in answering the question of the extent to which it is possible to aggregate different vintages of capital, which in turn depends on how similar the different vintages are. If these parameters were constant, then all vintages would be the same in terms of the factor input-output ratios, and so quality change in the sense of Denison would not occur. As noted earlier, this is an important question from the point of view of trying to investigate the long-run response of energy demand to changes in energy prices.

If there is substantial quality change in capital then simple aggregation will be inappropriate. The extent to which b ,u, b", b", bA vary measures the size of the aggregation problem. The values of these parameters for vintages from 1955 to 1989 are shown in Figures 5.7-5.10. For all of the bs there is an initial 'settling-down' period since they depend upon expected prices, which within the model are extrapolations of past fitted trends. At the beginning of the sample period, as there are only a few observations over which to calculate these trends, expected future prices show considerable fluctuation. This should not affect the model over the period for which factor demands are fitted as these early vintages are not used.

For the period after 1960 the figures show that the bs vary over time, b , —the constant in the labouroutput ratio ex post (see equation (5.1a) of Appendix 5A)—declines slowly up to 1975, reflecting the effect of exogenous technological progress. However, it shows a more marked decline in the next ten years, generating increases in labour productivity. It could be claimed on the basis of this that improvements in labour productivity, purported to be a consequence of decisions taken in the 1980s, started much earlier. It appears to be relatively constant again after 1985. b2 . the constant in the energy-output ratio, follows the expected pattern in that it increases up to 1975, decreases thereafter to a minimum in 1985 after which it increases again. ¿>3 , the capital-output ratio for investment of different vintages, is perhaps the parameter of most interest. It appears to be less variable than the other two. Nevertheless, within the period 1960-89 it varies between 0.3 and 0.2, a quite substantial variation. This means that output per unit of investment is going to be quite different for different periods. As a final (derived) characteristic of vintages the retirement pattern for vintages is considered. Vintages retire in two ways. The first is that depreciation reduces the amount of each vintage in operation in successive quarters. The second is that vintages are deleted from the list of those available. This means that all the equipment of that vintage is obsolete, and as such this phenomenon will be referred to as the 'scrapping' of that vintage. However, in terms of the conventional use of the concept of scrapping, it will probably be the case that some of the retirement allocated to depreciation will in fact be machinery which is scrapped. In particular, the effect of exponential depreciation, even when the rate estimated is relatively modest, is to reduce the quantity of a particular vintage to zero relatively

Figure 5. coefficient rapidly. In the next section there will be a discussion of the estimates of depreciation rates, but for the moment the question of the dates at which different vintages are retired will be considered.

Table 5.2 lists the dates at which each vintage is retired. This shows that whilst scrapping is not consecutive at the start of the sample period, it becomes so later. The scrapping out of order of the first twenty vintages may be due to the model 'settling down' in the initial periods. In particular, the results of the expectation-formation submodel will be relatively unstable for the first vintages. Once the initial period of instability is passed, vintages are scrapped consecutively, although not in a particularly even pattern. There are quarters when no vintages are scrapped and others, such as quarter 131, when four vintages are scrapped. It can also be seen that there has been a slight decline in the life of vintages, from approximately eighty quarters down to approximately seventy quarters.

Table 5.2 Scrapping dates for vintages (period 1=1955Q1)

Vintage

Scrapping date

Vintage

Scrapping date

Vintage

Scrapping date

1

65

24

107

47

131

2

65

25

112

48

131

3

65

26

112

49

131

4

65

27

113

50

131

5

72

28

114

51

132

6

95

29

114

52

132

7

102

30

116

53

132

8

96

31

116

54

132

9

95

32

117

55

133

Figure 5.8bv2 coefficient

Vintage

Scrapping date

Vintage

Scrapping date

Vintage

Scrapping date

10

102

33

118

56

133

11

102

34

118

57

133

12

98

35

118

58

134

13

98

36

118

59

135

14

96

37

121

60

136

15

96

38

121

61

136

16

96

39

122

62

137

17

98

40

121

63

139

18

100

41

125

64

139

19

98

42

125

65

140

20

97

43

128

66

140

21

100

44

128

67

141

22

102

45

128

68

142

23

106

46

129

69

142

70

142

Note: Vintages installed after quarter 71 (1972Q3) are still available at the end of the sample period.

Note: Vintages installed after quarter 71 (1972Q3) are still available at the end of the sample period.

Figure 5.9^U3Coefficient

Relative merits of the vintage model approach

The main advantage of the vintage approach is that it captures the effects of both history and the future on current decisions. This means that price changes may not have immediate effects. The speed at which price effects feed through the economy is based on optimization, rather than being due to an unexplained cost of adjustment. This adjustment reflects two effects, which can be separated out one from the other. The first is delay in adjusting due to the quantity of capital stock, its depreciation and normal life. The second is the role of price expectations which determine the factor use coefficients of newly installed equipment.

It is important to distinguish between these two factors as they have quite different policy implications. For the first, adjustment to price changes will occur faster the faster the economy is growing. Thus energy taxes that slow growth of the economy will slow down the response to them. A further consequence of this is that there will be a cost of energy taxes in the extra investment due to replacement of capital earlier than would otherwise be the case. An estimate of this cost can be obtained, and will depend on how fast taxes are imposed. The cost can therefore be minimized by imposing the taxes in such a way that capital is replaced no faster than would otherwise be the case. This implies that a policy designed to reduce energy should be implemented substantially in advance of the date at which the reduction in energy use is required. For some calculations of this see Ingham et al. (1991a). The second effect, the response which is dependent upon expectations, implies that adjustment would be faster the closer the new path of prices is to the old. Taxes may need to be high in order to induce correct design. Alternatively if price expectations can be changed by announcements then taxes may only be needed to obtain the correct usage of factors ex post, and not to influence the ex ante design.

Figure 5. coefficient

The first disadvantage of the model arises from the complexity of the likelihood function. There are a large number of parameters, and because of the vintage structure the likelihood function for the model is of a non-standard form. Maximizing the likelihood is not possible by the usual 'hill climbing' techniques and is undertaken using the Nelder-Mead algorithm. This ensures convergence to a maximum, and the use of a variety of starting points is used to investigate the possibility that a local rather than a global maximum is obtained. The Nelder-Mead algorithm requires a large number of iterations, each of which requires the calculation of the costs in order to sort the vintages by cost. To minimize the computations required, a specification with linear calculations is used as far as possible. This can be done by using the generalized Leontief functional form. Although this is a flexible form, studies such as that of Lau (1986) suggest that it may not be as good as other functional forms in approximating the data.

A second disadvantage arises from the type of simulations that one might want to undertake. Typically in considering long-run responses one would want to consider how an economy moves from one steady state to another. So one might consider a simulation in which exogenous variables are either held constant or grow at some specified rate. Energy prices are then increased and the reaction of the model to this is observed. Eventually the economy adjusts to the new long-run state. This adjustment depends on the parameters of the model, especially those determining the shape of the ex post isoquant. As outlined in the previous section ex post substitution is determined by b4 in connection with the relative price of the variable factors.

It is expected that ex post substitutability will come at a cost and, indeed, this is the case. Situations in which is high and b4 is low, such as in the period around 1983, correspond to a higher energy-output ratio than situations in which the reverse is the case, such as in the period around 1971. Whilst the specification of the ex ante technology does not allow for recording variability in prices or changes in their trends, it is the

Figure 5.11 Divisia index of real energy prices, 1965=100

case that, if factor prices follow a trend similar to that which occurred over the sample period, then is driven down to zero and, if permitted, even becomes negative. Driving to zero is consistent with intuition. If relative factor prices behave in a predictable way then there should be no desire for ex post flexibility. However, if there is a linear trade-off between flexibility and overall input level then b4 will become negative. However, this is not consistent with intuition as it suggests perverse input demand. Falls in the actual price of a factor will lead to increases in its use. The problem is that there is no guarantee that the generalized Leontief cost function will be concave. Functional forms which guarantee a concave cost function have been developed, such as the modified Barnett (see Diewert and Wales 1987). As this is too complex, computationally, to be incorporated, a simple device of prohibiting b4 from falling below zero is adopted. The model is estimated with this constraint. However, it also restricts the use of the model for simulation. Simulations for which ¿4V=0 correspond to simulations with a putty-clay technology, and this loses the point of having estimated a putty-semi-putty technology. Consequently, the simulations undertaken use data on exogenous variables for the period 1971-90, and as such contain some price variability.

Year

Figure 5.11 Divisia index of real energy prices, 1965=100

case that, if factor prices follow a trend similar to that which occurred over the sample period, then is driven down to zero and, if permitted, even becomes negative. Driving to zero is consistent with intuition. If relative factor prices behave in a predictable way then there should be no desire for ex post flexibility. However, if there is a linear trade-off between flexibility and overall input level then b4 will become negative. However, this is not consistent with intuition as it suggests perverse input demand. Falls in the actual price of a factor will lead to increases in its use. The problem is that there is no guarantee that the generalized Leontief cost function will be concave. Functional forms which guarantee a concave cost function have been developed, such as the modified Barnett (see Diewert and Wales 1987). As this is too complex, computationally, to be incorporated, a simple device of prohibiting b4 from falling below zero is adopted. The model is estimated with this constraint. However, it also restricts the use of the model for simulation. Simulations for which ¿4V=0 correspond to simulations with a putty-clay technology, and this loses the point of having estimated a putty-semi-putty technology. Consequently, the simulations undertaken use data on exogenous variables for the period 1971-90, and as such contain some price variability.

THE RESULTS OF THE SIMULATIONS

Figure 5.11 shows the path of a Divisia index of real energy prices over the period 1965-85. This shows three periods of basically constant prices with two periods of sudden increases. The relative factor cost of energy prices to wage costs in United Kingdom manufacturing, displayed in Figure 5.12, also shows considerable variability. The fact that the United Kingdom has experienced such large price changes in 1973 and 1979-80 suggests that it might be possible to calculate the sort of taxation levels that might be needed

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Figure 5.12 Energy price/wage costs, 1965=100

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Figure 5.12 Energy price/wage costs, 1965=100

if reductions in energy use by manufacturing are required. However, whether or not the experience of the oil shocks is a useful indicator depends on both the perceived durability of a cartel (OPEC) and the perceived credibility of government policy (a carbon tax). Even if the price increases are equal in magnitude, firms may adjust their capital and fuel expenditures in a very different manner depending on the perceived permanence of the increase.

From Section 5.2 it can be seen that the important aspect of the model is that long-run adjustments to price changes are modelled endogenously, rather than long-run adaptation being due either to a cost of adjustment, which is not modelled or explained, or to some dynamic statistical specification. The first set of simulations calculates energy elasticities from the model by considering different scenarios for energy prices after 1973. Energy prices showed a dramatic increase at that time after having fallen, in real terms, for much of the previous two decades. After this, real energy prices were almost constant until 1979 when they rose again, quite sharply, during the next nine quarters, again reaching a plateau. Meanwhile the energy-output ratio declines over time, although closer inspection reveals that this is not a constant decline. The period from 1975 to 1980 shows an almost constant ratio.

An interesting way of depicting this is that of Semple (1989), who graphed energy usage against output and obtained a Z-like pattern as shown in Figures 5.13 and 5.14. Figure 5.13 plots the actual relationship, and Figure 5.14 plots the relationship corresponding to actual energy demand and as fitted by the model. The decline in the energy-output ratio before 1975 and after 1980 corresponds to the horizontal parts of the Z, whereas the diagonal corresponds to the period between 1975 and 1980 when the energy-output ratio was relatively constant.

The base scenario is one in which all exogenous variables, apart from fuel prices (i.e. factor prices and interest rates), follow their actual values up to 1990 after which they are extended by using the trend growth rate throughout the period 1955-90. Fuel prices after 1973 are taken as growing at the trend growth rate for

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Figure 5.13 Energy-output ratio the period up to 1973, which corresponds to a quarterly decline of -0.4 per cent. This provides the base case in which the energy-output ratio rises slowly at first but more rapidly as factor substitution takes place. Different scenarios are considered for output growth. The first is that output remains constant, the others are that output grows at either 0.5 per cent per quarter or 1 per cent per quarter. This should enable an assessment as to whether more growth in output would allow the capital stock to respond more rapidly to energy price changes.

A growth factor of 1, 1.5, 2 and 2.5 per cent is then added to fuel prices. All the resulting energy-output ratios, shown in Figures 5.15 and 5.16, exhibit marked declines. The most remarkable feature is that the difference between the base case and 1 per cent is much greater than the difference between the other cases. In consequence the elasticities are much greater for small price increases than for larger ones. The elasticities for the various scenarios are shown in Figures 5.17, 5.18 and 5.19. These elasticities are calculated by taking the base energy demand to be for the path of prices and by taking the simulation of the oath for energy demand of {E'} for the path of prices {!'",. The elasticity is then given by t], = {E\ — $)$/<?>} - '

The pattern of the elasticities, as shown in Figure 5.17, tells the expected story. To start with there is not much reduction in energy use with an estimated elasticity of around -0.1. This does not vary much with the rate of increase in prices. The elasticity starts to increase in magnitude after five quarters as this change starts to affect expected factor prices and ex ante substitution takes place. As is to be expected this now depends on the rate at which prices are rising. Energy demand is determined by the exogenous technological progress as well as factor prices so that the effect of the price change is attenuated by technological change eventually and the elasticity starts to fall. This represents the transition to long-run phenomena from the short run. The greater the rate of price increase the earlier this transition takes place, as

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Figure 5.14 Fit of model: energy-output ratio expected. The faster prices rise the faster expectations will adjust. If this interpretation is correct, adjustment to the long run takes around twenty quarters. This seems to depend very little on output growth. Thus, for the fastest growth in prices and 1 per cent growth in output per quarter full adjustment takes place two quarters earlier.

The second task is to assess the role of expectations. As noted before, the importance of this arises from the possibility that taxes on energy may not be imposed immediately but may be announced for implementation at some future date. If this policy is credible it might be thought that this will lead to a lower tax being required than if a tax were implemented without announcement, or if there were doubts about the credibility of the policy.

To consider this, some simulations are run in which the technical parameters of the model remain unchanged but the manner in which prices enter into expectations changes. The first is to consider what energy demand would have been if prices had been perfectly anticipated. Given that the present value of future prices is calculated over a horizon of forty-five quarters, this can only be done for the period 197188, for the extended data set. This is contrasted with the formation of expectations within the estimated model and a situation in which expectations are myopic in the sense that the current real price is expected to rule indefinitely. The results of doing this are presented in Figures 5.20-5.24.

Figures 5.20 and 5.21 depict the base case where all variables are at their actual values up to 1990 and trend values thereafter. There is little difference between the three for much of the sample period. At first this might seem rather surprising, but two explanations can be put forward. The first is that at the start of the period in 1971 real energy prices were falling, so that the extrapolated expectations of the model would have also predicted a decline in real prices. As real prices were in fact rising, myopic expectations would be closer to the prices actually realized, i.e. perfect foresight. Thus myopic expectations lead to lower energy use in the period of increased prices because myopia turns out to be closer to what actually occurred than expectations under the model assumptions. Substantial change in energy demand between the simulations appears during the 1986-90 period. In fact, this is a period in which the model, as estimated, overpredicts energy usage. So whereas extrapolative expectations seem to explain behaviour well in the 1970s and early 1980s, it seems that perfect foresight may be more appropriate for the late 1980s. The

Figure 5.15 Energy-output ratio: output constant

second explanation is related to the ex post flexibility built into the capital stock. This may well be fairly large, making incorrect expectations relatively unimportant in terms of factor usage.

As before, the effect of price increases on expectations is considered. Figure 5.22 considers the case wherein fuel prices increase at their 1955-73 trend plus 1 per cent per quarter. This causes trend expectations, perfect foresight and myopic expectations to move together, and so there is really very little difference between them. However, suppose some lack of smoothness is incorporated into this scenario. The scenario assumed is that of a large price increase in 1980, such as an energy tax of the magnitude some have proposed. In the scenario real energy prices are doubled and the effects of different expectations formation are considered. These are shown in Figure 5.23. The first series is the base case corresponding to Figure 5.22. The second is the base case with a doubling of prices in 1980. This leads to a reduction in energy usage which gradually increases to around 20 per cent. The myopic expectations path is close to the others up to 1980 where the price increase is built into newly installed machinery immediately. Perfect foresight leads to quite an interesting path in that it does not reduce energy use below that of myopic expectations, as might have been expected. There is an increase in energy usage in the period before, however, with a large adjustment when the increase takes place. The reason for this increase is the plateau in prices that occurs after the 1973 increase. This means that with perfect foresight investment will have been determined by a constant real energy price, whereas under trend expectations the energy price will

Figure 5.16 Energy-output ratio: 0.5 per cent growth

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Figure 5.16 Energy-output ratio: 0.5 per cent growth have been expected to increase. So under trend expectations less-energy-using equipment would be installed.

Figure 5.24 considers the case where expectations are adaptive before the increase but perfect foresight is assumed thereafter. In this case, the doubling in price is unanticipated, but the effect of future price changes is fully accommodated. Comparing this with the case of perfect foresight throughout shows that perfect foresight makes a noticeable difference to the reduction that takes place when prices increase, and to the level. Although the two paths converge after the increase, it takes four years for the two to become indistinguishable.

CONCLUSIONS

Although many other simulations could be carried out, it is hoped that those conducted give an indication of the estimation of the model interpreted in both a short-run and long-run elasticity format. The magnitude of the elasticity depends upon the magnitude of the price increase, and there is a non-linear relationship of a concave nature. This is not surprising, given the generalized Leontief cost function employed. Elasticities increase just after price increases take place; starting from a value of -0.1 they increase to -0.8 depending on the price increase envisaged. This elasticity falls over time as the magnitude of the price increase rises

Figure 5.17 Price elasticities: output constant

and technological progress takes place. These numbers are not inconsistent with those found from other studies. It should be emphasized that a wide range of own-price elasticities for energy have been calculated. For example, Waverman (1992) reports elasticities ranging from -0.08 to -1.56 for industrial use of different fuels in the United States.

The effect of changing output growth is to speed up adjustment, but not significantly. This is again not surprising as the basic model incorporates constant returns to scale. A conclusion which could be drawn is that the energy-output ratio is much more dependent on the energy price than on the output level. The effect of changing expectations is surprising. The lack of much noticeable effect seems to depend on the pattern that energy prices have followed in the past. For much of the sample period myopic expectations have, perhaps, been a better predictor than an adaptive model. Although it should be added that it is possible for the estimated model to select this, and a crude test (because of its non-nested nature) for this favoured the adaptive model. A clearer indication of the effect of different expectations is obtained from the comparison of an expected and an unexpected doubling of energy prices. In this simulation it takes some sixteen quarters for the effect of incorrectly anticipated prices to dissipate.

Figure 5.18 Price elasticities: 0.5 per cent growth

APPENDIX 5A: MATHEMATICAL SPECIFICATION OF THE MODEL

Factor utilization decisions

At any point in time t, producers have available to them a set of machines of different vintages, indexed by v<t. (Not all possible past vintages will necessarily be available.) A machine of vintage u is characterized by five parameters—four design parameters, . 7=1 .4. and its available capacity )')'. Given current variable factor prices, pt, wt for energy and labour respectively, the input-output ratios can be calculated for labour, energy and capital that will be chosen for this machine, namely:

It will be recognized that these are the input-output ratios for a generalized Leontief production function, a flexible functional form. Two further points need to be made, following from what was said in the introduction. First, this model allows for ex post substitution between variable factor inputs. Second, the

Figure 5.19 Price elasticities: 1 per cent growth degree of ex post substitution, as reflected in the parameter - 0. is chosen endogenously by producers, as described shortly, and can be varied vintage by vintage. The unit variable cost of vintage u at time 1 can then be defined as

where the assumption of constant returns to scale has implicitly been introduced. Vintages are then ranked in order of increasing unit variable cost and, given that a level of output y has to be produced at time t, will be employed in that order until total available capacity exceeds required output. All previous infra-marginal vintages will be employed at full capacity; all subsequent extra-marginal vintages will not be employed at all; the marginal vintage will produce sufficient output to meet required output exactly. Given the level of output for each vintage, and their input-output coefficients, the total demand can be calculated for variable factor inputs at each period.

Figure 5.19 Price elasticities: 1 per cent growth degree of ex post substitution, as reflected in the parameter - 0. is chosen endogenously by producers, as described shortly, and can be varied vintage by vintage. The unit variable cost of vintage u at time 1 can then be defined as

where the assumption of constant returns to scale has implicitly been introduced. Vintages are then ranked in order of increasing unit variable cost and, given that a level of output y has to be produced at time t, will be employed in that order until total available capacity exceeds required output. All previous infra-marginal vintages will be employed at full capacity; all subsequent extra-marginal vintages will not be employed at all; the marginal vintage will produce sufficient output to meet required output exactly. Given the level of output for each vintage, and their input-output coefficients, the total demand can be calculated for variable factor inputs at each period.

Design parameters for new vintage

At time period t, a new machine of vintage 1 is to be designed. It will be installed at time period i+LD, and the firm lias a planning horizon of [i+ LD,i+LD+LT] (LD and LT are to be estimated). Let WJ • K be the expected values of the energy price, wage rate and real interest rate at time period t, t+LD < t < t+LD

Figure 5.20 Energy demand: different expectations

+LT expectations being formed at t (in a manner to be discussed shortly); let Z) be the expected value at r of finally, let AT, be the price of a macliine at time t, known with certainty.

Then the following pseudo-factor prices can be defined; let w i be the present value of the stream of over the planning period, using the as discount rates; let be the corresponding present value of expected energy prices over the planning period; let be Kt: let <0i be the present value of the stream of over the planning horizon; finally, let^s be (<y 1^3) " and a)i be (.0*2^3) • These pseudo-factor prices are essentially the present values of the expectations of all the basic factor prices and the square roots of the products of these factor prices; the latter capture the extent of correlation between (variable) factor prices over the planning horizon.

Then the four design parameters of a new machine of vintage t are calculated as follows. Let A be a 4*6 matrix of parameters [a^] which describe the structure of production; these are parameters to be estimated. It is now possible to calculate, for i=1, ...,4,

Figure 5.21 Energy-output ratio: different expectations

where the ui are the exogenous rates of technological progress. Equation (5.3a) shows that the design parameters are themselves outputs from a form of generalized Leontief production function using the pseudo-factor prices and so depend on both the expected level and correlation between basic factor prices. The level of factor prices will determine the extent to which producers design their machines to economize on factors which are expected to become relatively more expensive over the planning horizon, and thus represent a form of endogenous technological progress. The correlation between variable factor prices is important for assessing the extent to which producers will need to design more ex post flexibility into their machines to protect against future fluctuations in relative prices of variable factors. Equation (5.3b) introduces exogenous, factor-augmenting, technological progress; technological progress also applies to the parameter representing ex post flexibility.

Scrapping and investment

It is important to recognize that in this model existing machines are assumed not to deteriorate in efficiency over time (i.e. their running costs do not change unless variable factor prices change, so there is no increase in maintenance costs) and in principle can last indefinitely; depreciation takes the form of a certain proportion of machines 'evaporating' each period—see below. So existing machines need to be evaluated over the same future time horizon as new machines. There are therefore two reasons why producers might

Figure 5.22 Energy demand: 1 per cent price increas

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