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CHAPTER THREE

3.0 LITEREATURE REVIEW

3.1 Theoretical Literature

3.1.1 The Production Function

Literature identifies two contrasting theoretical arguments regarding the relationship between energy use and economic growth discussed below.

The Standard theory of growth by Solow (1956) places minor importance on the role of energy in production process and therefore in economic growth. It considers only capital and labor as the primary factors of production and energy is treated as an intermediate input which can be replaced by capital or labor, assuming a unity elasticity of substitution between factors of production. Hence energy has a negligible influence on production and economic growth. It further states that long run economic growth results from technological process and accumulation of labor and capital inputs. Model is specified as follows;

……………………………………….…………….. (1)

Where Y represents total output of the economy, K represents capital units, L is labor units and A is technology.

Solow’s theory, however, did not explain the origins of this technology progress and empirically it is measured as a residual of economic growth not accounted for by labor and capital. Therefore, in this way, this growth model does not take into account the role of energy use in its explanation of economic growth.

This limitation led to the Endogenous growth model which explains technological progress as an intended result of deliberate actions of economic agents driven by financial incentives (Romer, 1994). The model specification includes technology as a decision variable, i.e.

………………..………………………….………. (2)

On the other hand, Resource and Ecological economists have criticized the theory that energy plays a minor role in economic growth on a number of grounds, especially the implications of thermodynamics for economic production and the long-term prospects of the economy, Stern and Cleveland (2004); Kummel et al (2010); Hall et al (2001); and Stern (2010). They argue that energy is a critical primary factor of production basing on the definition of a primary factor of production offered by the Neo-classical economic growth theory, that is, that factor of production that is neither created nor used up within the production process, only degraded.

The Ecological growth model presents 3 channels through which energy influences economic growth;

For any production to take place, energy is required to activate capital, and in this way directly increasing economic growth. It is energy, capital and labor that are active in value addition.
Energy increases productivity of labor and capital. It speeds up production processes thus increasing the volume of output per unit of capital or labor which in turn reduces cost of production and permits savings and further investments.
A dependable supply and consumption of quality energy increases the rate of innovation which also increases economic growth.

Although theoretical debate between the Ecological economic theory and Neo-classical economic theory of growth seems to be inconclusive regarding the role of energy, the work of Stern (2010), seems to reconcile the two. He extended the Neo-classical growth model by adding the energy variable in a nested CES production function as follows;

……………………………….. (3)

Where and is the elasticity of substitution between energy and non-energy inputs, is a measure of the relative influence of energy and non-energy inputs on economic growth, and are labor and energy augmenting parameters respectively. However, Stern did not explain why there is no capital augmenting parameter in his model.

From equation 3 above, the relationship between energy and an aggregate of output such as GDP can then be affected by substitution between energy and other inputs, technological change (that is, a change in A), shifts in the composition of the energy input, and shifts in the composition of output. Also, shifts in the mix of the other inputs for example, shift to a more capital-intensive economy from a more labor-intensive economy can affect the relationship between energy and output (Stern et al, 2017).

The Ecological growth theory assumes that (which places a restriction in the model that at least some positive quantity of energy is required for production to take place), while elasticity of capital and labor is one as in the neoclassical growth model. This means that if energy supply is in deficit, it seriously constrains production and therefore economic growth and when it is in abundance, it ceases to be a constraint on production and economic growth, hence economic growth will be constrained by augments of capital and labor as in the neoclassical growth theory. In other words, the neoclassical growth theory assumes that energy is in abundance across all nations hence not considered as a limiting factor to economic growth, which isn’t the case for Uganda, an energy scarce economy.

Therefore, theoretical literature succeeded in reconciling the ecological economists and neoclassical growth theory in their perspectives regarding the role energy plays in growth of the economy. Energy use is recognized to be very vital for economic growth, such that a reduction in energy use will heavily constrain economic growth. Hence following the theoretical model in equation 3 above, the theoretical framework that will inform the analysis of the relationship between economic growth and electricity use is specified as follows;

…………………………………………… (4)

The labor and capital augmenting parameters that capture the indirect impact in this relationship have been dropped because the study is restricted to analyzing only the direct relationship between economic growth and electricity consumption.

3.1.2 Theories of Demand

A static model of representative firm

This is a short run model of energy demand for both a firm and household however, the discussion will be confined to a firm’s problem. A firm problem is generally considered as profit maximization for a given level of output; since energy is treated as an input therefore the problem of the firm is cost minimization to maintain same level of output. The firm demand for energy is given as a function of its output, prices of all inputs with energy inclusive. A firm seeks to minimize cost for a given level of output, such that output (Q) is a function of capital
(K), labor (L), energy (E) and materials (M):

………………………………………………………………………… (5)

Whereas costs are sum of payments to the factors of production;

…………………………………………………………… (6)

Where r is rent payment to capital, w is wage to labor, PE is a price of energy and PM is the price of materials inputs. So a firm problem is:

Subject to;

……………………………………………………………………..…… (7)

However, the total cost of capital incorporates energy utilization cost then, the equation for energy use above enters the constraint hence the firm problem can be restated as:

……………….. (8)

Where is a cost of efficiency improvements, therefore the first order condition for the solution of minimization problem is that firm will choose input K, L, E, M and (efficiency of capital) and capital utilization rate u. In general form it is given as:

…………………………………………………………………….. (9)

However, in the short run firms can only adjust capital utilization rate of deployed capital when capital and technology are fixed. Thus an expression for a firms short run demand for energy is given as;

……………………………………………………….. (10)

The static model however ignores the intertemporal choices aspects of the choices that an energy
consumer faces when choosing type of capital, utilization rate of capital and efficiency of capital. The model treats long and short run responses as equivalent such that it does not incorporate size and characteristics of energy-using capital stock.

Dynamic models of the household

These models considers the intertemporal choices that a consumer, or firm must make when choosing their optimal objective function. The model captures the three simultaneous decisions to consume energy, which is decision to purchase and maintain energy-using capital equipment; of which the latter is an investment problem. A household problem is a utility maximization of the representative consumer, and energy is consumed in proportional to the services it renders hence utility of a consumer is affected by energy demand. Therefore, consumers seek to maximize discounted present value of lifetime utility.

………………………………………………………… (11)

Subjected to the constraint that purchases of energy E, other consumption goods Ct, investment good It, capital stock Kt and savings St in each period cannot exceed this period’s income Y plus the returns on the last period savings. Depreciation rate of capital is savings earn a rate of return r, and the discount rate is such that. Therefore, the consumer’s problem is therefore formulated as:

Subject to

…………………………………………… (12)

Note that the above equation is enters the consumer’s problem through a second constraint that show how the relationship between energy and capital is accounted for. Substituting the above constraint into the utility function, and the first-order condition for the maximum for the consumer’s problem is;

…………………………………………….. (13)

Asterisk denotes optimal values; the consumer will allocate income among purchases of energy,
capital, savings and all other goods such that the marginal value of the energy services accrued from capital stock is equal to the marginal value of consumption of all other goods. However, the consumer is interested in energy services then the decision is on the condition that there is energy cost of capital utilization. Therefore, the term in the brackets is the user cost capital defined as;

…………………………………………………………. (14)

So is the user cost of capital stock and the first term indicates consumer choice of the user cost such that capital utilization is a choice variable. Thus the whole set of first-order condition for this consumer’s problem has a system of simultaneous equations that can be solved for each choice variable. Then, after we obtain the solution for and for a given , then solution for energy consumption can be obtained using the energy use expression and the optimal level of energy demand is derived from optimal capital utilization rate, optimal size of the capital stock and efficiency. Energy demand is a function of user cost of capital, capital stocks and capacity utilization. Generally, user cost of capital is a function of energy price, energy efficiency, and the rental price of capital. Whereas, capital stocks are a function of the rental price of capital and income and capacity utilization is a function of energy price and income. Then, the general function of energy demand can be expressed as;

…………………………………………………………… (15)

Energy consumption is modeled as a function of dynamic response to price and income changes, and since long run price elasticity is different for its short run value because price adjustments takes longer to be felt then past prices also affect current consumption of energy.

Since in most developing countries, the public sector plays an important role in allocating available supplies to end uses of energy, therefore instead of relying on trans-log cost function a simple model of energy consumption behavior is used (Rahman, 1982).

……..…………………………………………………….. (16)

Where the current consumption of energy is, is the lagged prices, is past consumption of energy and is output and e is the error term.

The consumption equation uses a simpler model that considers dynamic responses to prices and income changes. The use of a simple model is attributed by the fact that in most developing economies, the public sector plays a dominant role in allocating supplies to end uses of energy, instead of using trans-log cost functions or multinomial logit models for fuel choices, (Rahman, 1982).

3.2 Empirical Literature

Numerous ideas and views exist about the potential linkages between energy and economic growth. Following earlier studies of (Kraft & Kraft, 1978), literature identifies four hypotheses that describe the types of causal relationships between electricity consumption and economic growth which are summarized below (Ozturk, 2010; Payne, 2010; Rögnvaldur, 2009; Shahateet, 2014). These are discussed below;

The neutrality hypothesis

The neutrality hypothesis assumes no causal link between energy consumption and economic growth. An increase or decrease in energy use will not affect economic growth and vice-versa. The empirical confirmation of the neutrality hypothesis is usually interpreted to imply that neither conservation nor expansive policies in relation to electricity consumption have any effect on economic growth. A number of studies have confirmed the neutrality hypothesis such as (Payne, 2010) who used Yoda–Yamamoto causality test on USA, (Ozturk & Acaravci, 2011) who used ARDL bounds testing procedure on 11 Middle East and North Africa (MENA) countries among others.

The growth hypothesis

The growth hypothesis assumes a unidirectional causal link from energy consumption to economic growth. It states that the economy depends on energy consumption for economic growth so that the more energy the economy consumes, the more the economy will grow. Hence energy consumption drives economic growth. This relationship suggests that shocks to electricity consumption may adversely affect growth, while expanding energy consumption may lead to the expansion of the economy. A number of studies have confirmed the growth hypothesis in developing countries. (Akinlo, 2008) investigated the causality relationship between energy consumption and economic growth for Nigeria and showed that there is a unidirectional Granger causality running from electricity consumption to real GDP. Similar findings in developing countries have been documented by (Odhiambo, 2009a) who used ARDL methods on Tanzania; (Odhiambo, 2010) who used ARDL methods in a tri-variate framework for South Africa, Kenya and DRC and found the growth hypothesis to hold for South Africa and Kenya.

The conservation hypothesis

The conservation hypothesis assumes a unidirectional causal link from economic growth to energy consumption. However, this hypothesis differs from the growth hypothesis as it postulates that energy consumption depends on the growth of the economy such that as the economy grows, the more energy will be demanded and consumed to support that kind of growth. This implies that the economy does not strongly depend on energy consumption for growth and that any policies concerning electricity may be implemented with minimal effects on economic growth. Some of the empirical studies that support this hypothesis include; (Odhiambo, 2010) used ARDL methods to show that it is economic growth driving energy consumption in the Democratic Republic of Congo (DRC). Other studies include (Ghosh, 2002) for India, (Adom, 2011).

The feedback hypothesis

The feedback hypothesis assumes bidirectional causal links between energy consumption and economic growth. Changes in energy consumption will have an effect on economic growth whilst changes in economic growth will impact the demand for energy. In other words, efficient energy use and energy development policies geared toward increasing electricity generation can impact positively on economic growth. In the same way, electricity shocks hurt GDP growth and GDP shocks simultaneously hurt energy consumption. (Odhiambo, 2009b) uncovered a bidirectional Granger causality relationship between GDP and electricity consumption in South Africa using employment as an intermittent variable in a simple tri-variate framework. Similar findings discussing a bidirectional relationship have been documented for Malawi (Jumbe, 2004); India (Paul & Bhattacharya, 2004); and Uganda (Sekantsiand & Motlokoa, 2015); among other developing countries.

The inconclusive results of the earlier tests of Granger causality are probably due to the omission of necessary variables, either the quantities of other inputs (and quality adjustment of the energy input) or energy prices especially due to availability of data (Stern, 2010).