Energy price responsiveness in Zimbabwean mining and manufacturing : a disaggregated demand analysis

This paper examines market signals that enhance efficiency in energy use and the allocation of energy resources, focusing on Zimbabwean manufacturing and mining. We estimate ownand cross -price elasticities of demand to determine how far industrial energy types consumed are substitutable for each other. Our main emphasis is on reducing imported liquid fuel and promoting the country’s coal resources. While liquid fuel claims a huge proportion of the country’s foreign exchange, there is plentiful supply of coal. Coal, however, is environmentally damaging. Elasticity estimates, obtained at a highly disaggregated industrial level, will provide information about the impact of energy taxes on the demand for the different energy types.


Introduction
Two important energy issues of public concern in Zimbabwe are: (a) reduced dependence on oil imports; and (b) correcting environmental damage from the use of coal.Except for ethanol, all liquid fuels in the country are important, claiming a major chunk of the foreign exchange resources, and all the coal is produced in the country.Often the pursuit of one goal limits the ability to satisfy the other.For example, an increased coal price due to environmental policy may increase relative oil use.Knowledge of the elasticity of demand for the energy types is a powerful instrument that can be used to determine the potential of fiscal measures to conserve energy: the more price-elastic the demand schedule, the smaller the tax rate necessary to achieve a given conservation target; if the demand for the energy type is highly price-inelastic, large taxes will be required to induce sizeable decreases in consumption.
The purpose of this paper is to determine price elasticity of demand and energy substitution responses in different industries.Focusing on mining and manufacturing industries, we begin by specifying, estimating and discussing a model of energy demand.Since it is unlikely that the technologies in different industries are the same, their response to changing energy prices will be different.Consequently, it is important to estimate elasticities at the disaggregated level to avoid misspecification, and to provide more detailed information about the effects of changing energy prices.
We use a translog function, originally introduced by Christensen, Jorgenson andLau (1971, 1973), to estimate the demand for the energy types and their relationships.The approach makes use of the duality theory positing, as analogue to the production function, a cost function of a general neo-classical specification.In conjunction with assumptions of perfect competition, factor input equations are derived which must be estimated simultaneously to allow the theoretically imposed restrictions on parameters.The distinct advantage of the method is that an explicit theoretical model serves as the basis for specification and reduces the problem of multicollinearity by decreasing the number of parameters to be estimated.
In what follows we discuss: model formulation; the desirable properties of a complete input demand system; the measures of energy price responsiveness; the estimation methods; and, ultimately, our empirical results.

Model formulation
As in literature, we assume that a given production function or industry is represented by a continuously twice-differentiable aggregate production function.Output produced (Q) from a bundle of inputs is defined by electricity (e), coal (c), and liquid fuels (l); and their corresponding prices given by Pe, Pc, and Pl respectively.This allows us to define the following relations and with q = (q1, . . ., qn) is a vector of all other inputs, and H as an energy-input aggregator function.
Omission of non-energy inputs will not bias our estimated price elasticities as long as the production function is homothetically weakly separable in the energy inputs.The duality theory implies that our production technology can be completely represented by a cost function satisfying regularity conditions if producers minimise input costs.The energy cost function dual to the energy-input function is given as C = H.C E (Pe,Pc,Pl), with C as total cost of energy, being a unit cost function satisfying regularity conditions.
Observed cost share equations can therefore be expressed as Si = αi +Σjγijlog Pj + ui i,j = e,c,l Because we are looking at three energy types, we have three share equations.We impose the following constraints/properties on cost share equations.First, the adding up constraint Σiαi = 1, which in turn implies that ΣiSi = 1 and that the disturbances are constrained by Σiui = 0 at each observation.The restriction of linear homogeneity implies that the energy cost share of each equation should not vary when all energy prices change by a common multiple.Third, we impose symmetry restrictions, γij = γji, for every i,j = e,c,l, meaning the Hessian matrix of second order derivations must be negative semi-definite at every data point.The condition of monotonicity requires the fitted cost function to be non-decreasing in input prices, since prices and the total cost of energy are always positive.The final restriction is that of concavity.Concavity implies that as prices rise, cost rises no more than linearly.This is essentially because the individual producer minimizes costs, rearranging purchases in order to take advantages of changes in the structure of prices.Concavity in input prices (see, for example, Burgess (1974) and Binswanger (1974) requires that the Hessian matrix of a secondorder derivative of the unit cost function with respect to prices is negative semi-definite at each point.Adding up and symmetry restrictions enable us to arbitrarily drop the n th equation and estimate n -1 equations.
With the parametric restrictions imposed, energy share equations can be re-written, adding a time subscript t, as: The ηij are measurements along a given isoquant with output (the total cost of energy) held constant in order to emphasize the inter-fuel substitution effects and give information of which input is more substitutable for the other.This is particularly useful where the desired policy objectives are in conflict.
The elasticity estimates vary as cost shares change.
Different elasticities are obtained for different periods although the parameter estimates γij remain constant.The estimation procedure to be followed is defined in the Appendix.

Restricted estimation
In estimating restricted equations, we follow the following procedure.
The 'feasible' estimator, , for β under the symmetry restriction, c′β = 0 is where , and , from the OLS-estimation, is consistent for Σ.
The estimated variance is It can be shown that is approximately distributed.
The estimation is done in two steps: Step 1: Calculate restricted OLS where is unrestricted OLS.We then calculate where .
Step 2: Our calculated results should be asymptotically efficient and equivalent to the maximum likelihood if the error terms are normally distributed.This procedure, however, does not depend on the normality of the error terms.

Results
Performance of the model First, we consider whether or not there is loss of fit by imposing symmetry restrictions.We do so by estimating energy share equations with and without the symmetry restrictions imposed, and comparing the results using a Wald Test statistic.All our fitted 2484 cost shares are positive, implying that the monotonicity condition is satisfied.
On concavity, of the 828 calculated Hessians, 572 (or 69 percent) are negative semi-definite.A necessary, but not sufficient, condition for the Hessians to be negative semi-definite is that the diagonal elements, indicating the response of an input to a change in its own price, are non-positive.From our results, 51 percent of the violations are in the own-price elasticity of coal, 38 percent with electricity and 11 percent for liquid fuel.A possible reason for the rejection of concavity in some industries may be the quality of data.It could also be that the maintained hypothesis of instantaneous price adjustment is too restrictive given the large price variations and other constraints (e.g.shortage of foreign exchange, restrictions on capital imports thereby affecting the flexibility for any fuel change, etc.,) faced by different industries in Zimbabwe.If the maintained hypothesis of producer equilibrium is false, concavity could be rejected even if technology is well behaved.Except for industries with minor violations (i.e.Copper and Nickel; Soft Drinks; Other Textiles; Soap; and Other Manufacturing Industries) our analysis excludes all industries where concanvity is violated.

Parameter estimates
Estimated parameters have a direct economic interpretation, and can be used to explain the price response of the distribution of the cost shares.The estimated are equal to the fitted cost shares at the means of data, and indicate the responsiveness of the unit cost of aggregate energy to the price of each type of energy at the means of data.The unit cost of aggregate energy is most responsive to the price of electricity, followed by the price of liquid fuel.
The γij coefficients tell us that if the share elasticity with respect to price is positive, the cost share increases with an increase in the corresponding price.If, on the other hand, the cost share is negative, the cost share decreases with the proportional increase in the price of the other input; and if zero, the cost share is independent of the price.We glean the following from  2 and 3.These elasticities are calculated under the assumption that total energy input of the production process is held constant: they are measurements along a given isoquant.The energy input is held constant in order to emphasise the interfuel substitution effects.Our price responsiveness of the energy types falls under the following categories: ηii > 1, energy input i is very price-elastic; ηii ≈ 1, energy input i is price-elastic; and ηii < 1, energy input i is price-inelastic.The implications of these elasticity estimates are that: • Electricity is price-inelastic in most industries.
Given the many non-substitutable uses for electricity, its inelasticity response is not surprising.Although the elasticity magnitudes are observed to differ from one industry to another, they are generally in agreement with the past studies on interfuel substitution.The only industries with price elastic results are: Structural Clay Products, Other Textile Products and Non-Metallics.If we assume that the electricity input is used primarily for heating and motive power in these industries, we can conclude that there is much flexibility for its use in these industries.
• Coal is price-elastic in fourteen industries, and price-inelastic in thirteen.A possible problem here was our inability to separate coking coal and steam coal.There are various grades of coal  (1974)) on American manufacturing suggest that coking coal is less responsive to price than steam coal, or not price responsive at all; it is possible that this problem is also reflected in our work.It is also possible that for some industries coal is used as a raw material and should be considered non-energy use.
• Liquid fuel is price-elastic in most industries.
Price-inelastic responses in some industries may be because liquid fuel is not used primarily for heating purposes as in motor vehicles.
Our calculated ηii's lead to some interesting observations.First, the estimated price elasticities vary over observations since estimated cost shares also vary.Second, own price elasticities tend to become more elastic as cost shares decline.This is because as the quantity of fuel input demanded approaches zero (and hence the cost shares approach zero) the price elasticity becomes infinite.Conversely, higher fuel cost shares tend to possess more inelastic fuel price responses.Finally, as also observed elsewhere (see Magnus and Woodland (1980)), the own price elasticity is negative if and only if γii < Si(1-Si).
We now turn to cross-price elasticities to examine the channels for interfuel substitution.Our cross-price elasticities measure the proportionate change of energy input i in response to the proportionate change of some other energy input j with output and other prices held constant.Information on these elasticities helps to determine if in the fuels substitution against i, j is particularly a strong substitute and so forth.Expenditures on fuel i are expected to increase with Pj as long as ηii > 0.
Ignoring complements (where ηij < 0) , a one percent increase in the price of liquid fuel relative to the price of other fuels implies the following effects with respect to coal input in the rest of the industry: Similarly, an increase in the price of liquid fuel relative to the price of other fuels implies the following effect with respect to the electricity input in the rest of the country: • a higher demand for electricity in the following industries: Chrome, Other Mining, Bakery Products, Beer and Wine, Soft Drinks, Tobacco Products, Wearing Apparel, Soap and Detergents, Non-ferrous Metal, Motor Vehicles and Equipment, and Other Manufacturing; and • a low demand for electricity in Cotton, Knitted Products, Fertilisers, Structural Clay Products, Metal Products and Other Vehicles.
Cross-elasticity estimates also show the impact of a percentage increase in prices or taxes of coal and electricity, relative to the price of liquid fuel.The potential impact of an increase in the price of electricity places a higher demand for liquid fuels in all industries except those that are complementarily.An increase in the price of coal, on the other hand, implies a significant demand for liquid fuel in Basic Industrial Chemicals; and a high demand for liquid fuel in most industries.

Policy implications
The effect of energy taxes can be explained this way.If energy type demand is price-inelastic, industries cannot do without this fuel and will continue consuming nearly the same quantities even if prices change significantly.If the demand for the energy type is elastic, an increase in its price results in a reduction of quantities consumed and therefore in its expenditure share in the total energy bill.In this situation, a small tax induces the conservation of energy.Conservation means using less expensive energy to reduce costs, thus making the potential for interfuel substitution critical.Our estimated results reveal that: • Liquid fuel is price elastic in most industries; coal is price elastic in four industries and electricity is price-inelastic in most industries.
• An increase in the price of liquid fuel leads to an increase in the demand for coal.
• Increasing the price of liquid fuel is also favourable to the demand of electricity.
Our results also show that the price increase of coal and electricity leads to demand for liquid fuels in most industries.While it can be argued that the energy price increased contributes in boosting inflation, there is justification for them to be seen as corrective in two respects.First, corrective pricing is preferred to subsidies which, by contrast, aggravate fiscal deficits and tend to have a more inflationary impact.Second, our data series covers a period when energy use was inefficient because of low prices over extended periods, use of old equipment and technology by industry, and constraints on for-eign exchange to allow industry to retool.It is therefore favourable to raise prices to their economic costs in order to sustain efficiency in energy use.
Pl)t +γcelog(Pe/Pl)t +uct Set = αe + γcelog(Pc/Pl)t +γeelog(Pe/Pl)t +uet t = 1, . . ., T Own price elasticity of demand is defined by i = e,c,l and the cross price elasticity of demand given by and i, j = e,c,l

Table 1 :
• Higher coal prices will lead to higher cost shares for liquid fuel in following industries: Tobacco Products; Other Textiles; Wearing Apparel; Pulp, Paper and Paperboard; Basic Industrial Chemicals; Glass, Cement; Non-ferrous Metals; and Other Motor Vehicles.An increase in the price of coal will lead to lower cost shares for liquid fuel for the following industries: Knitted Products; Structural Clay Products; and Metal Products.Finally, an increase in the price of coal will have no significant effect on the price of liquid fuel for the rest of the industries.• Higher coal prices will have the following effect on the cost share for electricity: higher cost shares in Other Textiles, Fertilisers and Other Manufacturing Industries; no significant effect in Chrome, Asbestos, Other Mining, Basic Industrial Chemicals, Plastic Products, Glass, Metal Products and Other Vehicles; lower cost shares in the rest of the industries.• Higher liquid fuel prices will affect the cost share for electricity as follows: higher cost shares in Bakery Products, Beer, Wine and Spirits, Soaps and Other Manufacturing Industries; lower cost shares in Copper and Nickel, Asbestos, Slaughtering and Processing of Meat, Other Textiles, Pulp, Paper and Paperboard, Basic Chemical Industries, Glass, Metal Products, Motor Vehicles, and Other Vehicles and Equipment; no significant effect in the rest of the industries.

Table 3 :
Price elasticities of substitution 54 Journal of Energy in Southern Africa • Vol 17 No 3 • August 2006