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Commercial electricity demand in a Central AmericaneconomyGlenn D. Westley aa Inter–American Development Bank , 1300 New York Avenue, Washington, DC, 20577, USAPublished online: 29 Oct 2009.

To cite this article: Glenn D. Westley (1989) Commercial electricity demand in a Central American economy, AppliedEconomics, 21:1, 1-17, DOI: 10.1080/772284227

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Applied Economics, 1989, 21, 1-17

Commercial electricity demand in a Central American economy

G L E N N D. WESTLEY

Inter-American Development Bank, 1300 New York Avenue, Washington, DC, 20577, USA

Panel data for 51 regions over the years 1970-79 are used to explain the commercial demand for electricity in a middle-income level Latin American country, Costa Rica. Price, income, and other elasticities are estimated. Methodologically, we combine the two stage least squares and error components estimators in order to remedy both the simultaneity and specification issues that are present in this and, we argue, in many other electricity demand studies.

I . I N T R O D U C T I O N

Little is known about the determinants of the demand for electricity in the developing world. After a thorough survey of both published and unpublished studies (Westley, 1988), there appear to be no commercial electricity demand studies in Latin America that approach even the level of the works reviewed by Taylor (1975). Mostly what is available in the region are simple projection models in which commercial electricity consumption is regressed against an income measure (such as value added in the commercial-services sector), against the number of commercial clients, or against residential electricity consumption. Clearly, such over-simplified models give little insight into the effect on electricity consumption of changes in electricity rates, income levels, the prices of substitute fuels and complementary appliances, the process of urbanization, and so forth. The present paper, on Costa Rica, is a contribution towards filling this vacuum in our knowledge.

In the electricity demand literature, which is dominated by studies of developed countries, several investigators have used the two stage least squares (2SLS) estimator to redress the simultaneous equation bias that adversely affects the demand equation estimates when there is block rate pricing (e.g. Berndt and Samaniego, 1984; Halvorsen, 1976; Lyman, 1976). Other investigators have employed the error components (EC) estimator to help compensate for missing or mis-specified variables in studies that use time-series, cross-section data (e.g. Cohn, Hirst and Jackson, 1977; Gill and Maddala, 1976; Houthakker, Verleger and Sheehan, 1974). In many of these cases, and in others as well, both problems are present, and it would be desirable to combine the benefits of using both 2SLS and EC estimation. Sections 111 and IV explain why such a combination appeared to be necessary in the present study and how these two techniques were fused in a way that yields a consistent estimator. An alternative method for combining the two techniques, proposed by Maddala (1977, p. 332) and included by Baltagi (1984) in his Monte Carlo study, is shown to be inconsistent.

0003-6846189 %03.00+.12 0 1989 ,Chapman and Hall Ltd. 1

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2 G. D. Westley

The organization of the rest of the paper is as follows. Section I1 discusses the data and variables, Section I11 presents the modelling approach, Section IV gives results, and Section V provides a britf conclusion. For further discussion of the topics covered in this paper, and the complete data set, see Westley (1984b).

11. DATA A N D VARIABLES

Costa Rica is a small, Central American country. In 1979, the last year of the sample period, its population was 2.2 million people and its G D P per capita was US$ 1430. It is, therefore, a middle-income-level Latin American country. It is also one with moderate inflation; over the 1970-79 sample period the consumer price index increased at a compounded annual rate of 11%.

As in most countries, the commercial electricity class in Costa Rica is very heterogeneous. It consists of commercial and service sector establishments and non-profit and government institutions. Electricity is not widely used id farming applications in Costa Rica; for example, the 1973 Agricultural Census reveals that only 4% of the farms use any electrical energy in production-oriented activities.

Because of the diversity of the commercial class it is always difficult to be very precise about what should be the nature and form of the explanatory variables. It is reasonable, however, to assert that they should include the real prices of electricity, possible substitute fuels (such as LPG and kerosene), and complementary goods (electric appliances), together with an activity level variable, such as the number of workers, real sales, or the real wage bill. These can be taken as the core economic explanatory variables. Other variables are also considered, as is discussed below.

Our analysis of electricity demand is based on an extensive set of good quality annual data, covering 51 Costa Rican cantons (entities similar to US counties), over the period 1970-79. Since many cantons received electricity for the first time during the sample period and since one-year lagged variables are employed in the regressions (so that the 1970 data are used only to provide lagged values), our regression analysis is based on a total of 262 observations, still a sizable number.

The data employed in this study have several important advantages. First, they appear to be reasonably accurate. An extensive analysis of the data reveals that not only has each series been compiled with care but that all variables display reasonable patterns of variation across cantons and over time (see Westley, 1984b, for further details). Second, the range of values taken on by the dependent and almost all of the explanatory variables is quite wide, an important factor in obtaining more precise parameter estimates that are valid over a sizable observation space. This wide range is primarily the result of substantial cross-sectional variation in the data, which in turn is the result of using a large number of regions with diverse characteristics. Third, the regressors employed in this study are not strongly correlated with each other; for example, almost all of the simple correlations are less than 0.25 in absolute value. This stands in strong contrast to what one frequently finds when using aggregate time series data, where simple correlations are often much higher and multi- collinearity problems are of central concern (which they are not here). A regionally disaggregated data set was pursued for the present study with this consideration in mind. In fact, regional disaggregation has been an important boon in (a) dramatically increasing the number of observations, (b) widening the range of variation, and (c) probably reducing substantially the collinearity in the data.

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Commercial electricity demand 3

Variables

The following specific variables are used in the analysis that follows. The dependent variable is annual electricity consumption per client in the commercial class and is denoted q. The independent variables are as follows (with symbols in parentheses): real marginal price of electricity (P), real price of stoves lagged one year (PSTOVEI), real price of refrigerators lagged one year (PREFI), real personal income per household (Y), a measure of urbaniz- ation (URB), the share of clients served by each of the eight electricity distribution companies (Sl-S8), and the lagged dependent variable (ql). There are three additional real activity measures, which may be considered alternatives to Y. Each refers to firms in the commercial-services sector: the number of workers per establishment, real sales per establishment, and the real wage bill per establishment. Finally, there is a set of 11 standard block price (SBP) variables. These measure the marginal price of electricity (in real terms) in 11 predetermined, mutually exclusive, collectively exhaustive consumption blocks. These variables describe all the rate schedules (supply curves) in effect in Costa Rica during the sample period, and hence are basic to two stage least squares estimation of the electricity demand function (see Section 1II.A). In all the above cases, 'real' indicates that the corresponding nominal variable is deflated by the consumer price index.

Price of electricity

Block rate pricing is used by all eight distribution companies during the entire sample period. In all cases, prices increase with electricity consumption throughout all or most of the consumption range. Since we are attempting to explain mean consumption, it is logical to employ a measure of mean marginal price as part of the overall group means demand relationship. To obtain such a measure we have combined two data sources: (1) a compendium of all 58 rate schedules used by the eight distribution companies during the sample period (inclusive of fuel adjustment charges and taxes), and (2) bill frequency data, for each canton in each year, showing the share of clients in each rate schedule consumption block. If, for example, there are three blocks, with marginal prices P, , P,, and P,, and the share of clients in each block is s,, s,, and s, (where s, + s, + s, = l), then the correct mean marginal price, calculated and used in this study, is s, PI + s,P, + s,P,.' Although it required a substantial effort to obtain and process all this information, in return, an accurate measure of mean marginal price at the canton level has been obtained. To the best of my knowledge, this has not been attempted in other electricity demand studies, even in the US.

Appliance prices

Data for the price of stoves and refrigerators were obtained from the individual commodity records of the consumer prick index. According to the 1975 Census of Commerce and Services, nearly half the major electrical appliances in use in the commercial-services sector consist of stoves and refrigerators. Hence, our coverage appears fairly good. Further, it seems resonable to suppose that these two prices have moved to some degree in tandem with the prices of other electrical appliances since most electric appliances are considered luxury imports and have been given similar high rates of duty which have tended to fluctuate

'Mean marginal price (P) is, therefore, a weighted average of the 11 SBPs. Since the weights vary by observation, however, P and the 11 SBPs are not linearly dependent.

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G. D. Westley

together over time. Therefore, in the electricity demand regressions, stove and refrigerator prices may, in effect, represent the prices for most of the commercial sector appliances.

Most explanatory vaiiables (such as income and electricity price) potentially affect both the electric appliance stock the consumer chooses to own and its utilization rate. Appliance prices, however, should affect only the initial purchase decision and should have no effect on subsequent utilization rates. As a result, electricity consumption levels may not react immediately to a change in these prices. Because of this, one year lags for the appliance prices are tested. Current (unlagged) forms are also tried since there still may be a substantial stock effect in the first year.

Income (or activity level)

While it is clear that a larger enterprise (of a given type) will generally have greater electricity demands, it is not clear how 'larger' should best be measured. As noted above, four alternative activity level indicators have been tried in the present study. Three are based on average, firm-level data in the commercial-services sector (mean sales, wage bill and number of workers). Although these directly measure somewhat different aspects of economic activity, they have the disadvantage of not representing approximately 30% of the clients in the commercial electricity class, namely, government and non-profit institutions.

In light of this, it is desirable to consider a fourth activity variable, personal income per household. This is actually an indirect indicator of commercial activity level. It seems reasonable to assert that together with urbanization (and perhaps other variables), mean household income determines average commercial client activity levels. Higher income (and more urbanized) areas may, for example, support larger general stores, bars, restaurants, movie theatres, churches, etc. Since urbanization is already included in the electricity demand equation, we need add only the mean income variable.

Urbanization

We measure how urbanized a canton is by the share of all canton households located in urban areas. In determining what constitutes an urban area, many Latin American countries use arbitrary criteria, such as including only towns that are county seats or state capitals. The Costa Ricans go to great lengths to ensure that a more reasonable set of criteria are applied in making their determination of what is urban. Detailed geographical divisions are made and physical criteria are employed, such as the presence of urban services, sidewalks, roads, blocks, etc.

We expected increasing urbanization levels to have a positive impact on electricity consumption. This is because the larger and more electric-intensive commercial electricity clients seemed to be located in Costa Rica's urban areas.

Company share variables

Variables measuring the share of users served by each of the eight distribution companies are useful because these companies vary widely in the type of clients they serve: three serve metropolitan San JosC (the capital), four are rural cooperatives, and the last covers a variety of users outside the capital. Distributors thus differ greatly in the degree to which they serve the more rural and lower income areas of any given canton (partly for reasons of company

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Commercial electricity demand 5

mandate). The company share variables may be viewed as complements to the canton-level urbanization and mean income (or activity level) series; they are included to help correct for the discrepancy between the mean levels of commercial economic activity and urbanization for an entire canton and for the subset of electricity consumers in that canton.' Specifically, we expect the coefficients of the co-op share variables to be negative since cooperatives serve the lower income, more rural areas of cantons, which are likely to support smaller commercial establishments. Conversely, the companies serving the San Jost area should have positive share variables since they serve higher income, urban areas, where the commercial establishments are liable to be larger.

Other variables

The inclusion of a lagged dependent variable in the regression equation reflects the use of the well-known partial adjustment model. In the electricity demand literature this is probably the most commonly employed method for capturing dynamic adjustment considerations. Finally, real LPG and kerosene prices were included in the demand equation to test the importance of inter-fuel substitution effects.

111. M O D E L L I N G A P P R O A C H

Two topics are discussed in this section: (a) the two-equation system and the 2SLS estimator, and (b) omitted effects, error components, and the 2SLS-GLS estimator. While much of the short exposition given in (a) is required for the extensions suggested in (b), we believe that (a) is useful in and of itself in order to clear up misconceptions which still appear even in reputable sources. For example, Beierlein, Dunn and McConnon (1981, p. 403) state: 'Since the supply price of each fuel [electricity and natural gas] is administered, the price is generally not felt to be simultaneously determined, meaning demand can be modelled separately.' As we show below, even though electricity prices are administered, simultaneity persists.

A. The two equation system

The starting point is a demand equation for a single consumer in which electricity consumption (q) is a function of marginal electricity price (P), a vector of other variables (X), and an additive disturbance term (U).

When there is block rate pricing of electricity (with either increasing or decreasing blocks or some mixture of the two) then the marginal price of electricity (P) is a function of the quantity consumed (9). But since q is a function of P in demand Equation 1, there is two-way causation and the simultaneous equation system and an estimator appropriate to it must be considered. A straightforward way to proceed is to write out the electricity price equation.

2The potential for some discrepancy exists since the Costa Rican grid was not complete during the 1970s sample period. While it is difficult to know exactly the relation between the actual and potential size of the commercial electricity class, about 60% of Costa Rica's households enjoyed electric service during the study period.

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G. D. Westley

s

91 Q QZ Quantity (kwh)

Fig. 1. The demand and supply for electricity

To fix ideas, consider the case shown by Fig. 1 of a 3-step increasing block tariff. In this case, the electricity supply curve (s) can be completely described by knowing the marginal prices pursuant to each of the consumption blocks, that is, P I , P, and P3 for the blocks (O,q,), (q,,q,) and (q,, a), respectively. The marginal price at the actual point of consumption (here, price P, at quantity qj, can be obtained by knowing q in addition to the block prices, P I , P, and P,. The following deterministic equation for marginal price, P, can therefore be written:

Equations 1 and 2 together constitute the supply-demand system. Most commonly, the functions f and g are assumed to be linear in the parameters. 2SLS can then be used to estimate demand Equation 1, which is over-identified in the'present example since there are three exogenous variables excluded from that equation (PI, P, and P,) and only one right- hand-side endogenous variable (P). In the present study we have averaged across com- mercial clients in a canton, thus passing directly from the single-client relations discussed up until now to the canton mean relations used for estimation. This does not alter the essentials of the above discussion in any way.

The fact that Equation 2 is deterministic does not eliminate the correlation between P and U in Equation 1. Consequently, simultaneous equation bias still adversely affects ordinary least squares (OLS) estimates of Equation 1. To see why this correlation persists, hold all explanatory variables in Equation 1 constant for the moment and assume U increases (for example, due to a taste change in favour of products that use electricity). Because of this, consumption (q) will rise. Figure 1 shows that if consumption rises above q,, then the marginal electricity price will rise to P3. On the other hand, if U had decreased initially, q would have fallen. If q had fallen below q,, then the marginal electricity price would have fallen to PI. In both cases, we can see that there is positive correlation between U and P. The fact that P rises and falls in discrete jumps rather than continuously does not alter this. The fact that 'the supply price is administered', so that Equation 2 is deterministic and known (rather than stochastic and uncertain) also does not negate the positive correlation between U and P, as we have just demonstrated.

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Commercial electricity demand '7

B. Omitted eflects and the 2SLS-GLS estimator

While the set of explanatory variables that have been used in the demand analysis is a fairly good one even by deyeloped country standards, there are important omissions. The absenq of a comprehensive activity level variable, focusing directly on all commercial electricity clients, is perhaps the most prominent of these. Activity mix variables, showing the share of economic activity originating in electric-intensive subsectors, would also be desirable additions. Like most of the variables included in the demand relation (for which data are available) these activity level and mix variables would almost certainly vary much more strongly in the cross-section than over time, due to the great diversity of the 51 Costa Rican cantons and to the comparatively short time span covered by the study.

How shall these shortcomings be compensated? When time series, cross-section data are used, a complete set of cross-section dummy variables (DV) may reasonably substitute for missing or misspecified variables whose variation is sirongly cross-sectional. Because of its efficiency, error components (EC) is often a more desirable alternative to the use of dummy variables since it accomplishes much the same objective but requires that only one additional parameter beestimated (versus 50 additional dummy variable coefficients in the present study).

A set of temporal dummy variables (one for each year) were also included in a number of regressions and generally found to be insignificant individually and as a group. This is consistent with the observation made above that the omitted effects are likely to be predominantly cross-sectional, rather than temporal. As Fuller and Battese (1974) make clear, with a highly unbalanced set such as the present one, there would be a 'large computational cost associated with including a time-series (in addition to a cross-sectional) error component in the EC analysk3 Since a time-series error component was not supported by a priori reasoning or by the temporal DV analysis, it was not included in the present study.4 \

The problems found with the activity level and activity mix variables in Costa Rica are the rule rather than the exception in the US commercial electricity demand literature as well. A number of major studies (Mount, Chapman and ~yrrell,,i973; McFadden and Puig, 1975; Halvorsen, 1976; Lyman, 1978) all use a household income measure to explain commercial electricity consumption. They employ neither a direct, comprehensive indicator of aggregate

3When the data are unbalanced, that is, when data on some cross-sectional units are missing in some years, we must include, strictly for computational purposes, one dummy variable for each of the missing observations. In the present study, this would imply the addition of nearly 200 dummy variables in each of the EC regressions! Fortunately, this is not necessary when there is only a cross- sectional error component. 4Some readers may ask why the more general random coefficients (RC) model has not been used instead of the more specialized EC model. (While the latter allows random variation in the intercept term, the former permits random variation in the intercept term and in all of the slope coefficients.) There are several parts to the answer. First, the basic hypothesis is not that the demand relationship varies structurally across observations (as postulated by the RC models), but, rather, that there are certain data weaknesses that lead naturally to the use of an EC model in place of a classical fixed- coefficients model. These ,data weaknesses do not naturally generate an RC model. Second, as Maddala (1977, p. 403) points out, RC models are complicated, and the present data may not be rich enough for thew to give us any more than 'woolly' (i.e., very imprecise) answers. Third, Swamy's (1970) RC model, perhaps the simplest RC model designed for use with panel data,. requires that there be more observations on each cross-sectional unit than independent variables. This condition is not met with the present data set for any ofthe 51 Costa Rican cantons, making even this model impossible to use.

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8 G. D. West ley

commercial activity nor any measures of activity mix. Murray et al. (1978) use a more direct aggregate activity indicator, taxable income in the commercial sector, but do not account for activity mix either. Clearly, the specification issue being addressed here is a common one. The fact that such difficulties normally occur in the US in conjunction with block rate pricing (true in all five studies above) makes an estimator that can handle both problems at once potentially very useful. Such an estimator is now discussed at the somewhat more general level of combining 2SLS with generalized least squares (GLS), in order to obtain the two-stage generalized least squares (2SLS-GLS) estimator.

2SLS-GLS estimation

Consider the following equation, which is one of a simultaneous system of N linear equations,

The observation subscript is t and may vary over both regions and time. There are a total of T observations. The dependent variable, yo,, is explained by n ( 6 N) endogenous variables, the y,,, m predetermined variables, the x j , , and a disturbance, u,. The m predetermined variables included in Equation 3 are a subset of the M predetermined variables found in the entire simultaneous equation system.

It is easiest to explain 2SLS-GLS by means of an example. Suppose that u,, instead of being white noise, is heteroskedastic, with variance proportional to the square of population, i.e., v a r ( u , ) = k , h ? , where ko is a constant and h, is population, an exogenous variable. Equation 3, then, suffers from two problems, correlation between u, and the y,, and heteroskedastic u,. The former problem is usually remedied by 'purging' the y,,, that is, regressing each y,, on all predetermined variables in the system, and then replacing y,, by its estimated value, Ji, . The latter problem is redressed by transforming Equation 3 in a way that renders the disturbance white noise. Is it sensible to combine these two operations, and if so, which should be done first, purging or transforming? The answer is that it is sensible but only if transforming is done before purging. We look at this procedure and then consider the problem with the reverse method.

To render Equation 3 an equation with white noise error, we divide both sides by h,, yielding

Since u,/h, is white noise, the usual 2SLS consistency proof goes through and it is completely appropriate to apply 2SLS to Equation 4.' The bi and aj will be consistently estimated.

The reverse procedure

Now the inconsistency of the reverse estimator, suggested by Maddala (1977, p. 332), is demonstrated. Here, the y,, is first purged and then heteroskedasticity is corrected for. That

'To do this we need estimated values for the y,,/h, ratio variables, i.e., we need to purge the yi,/ht, not they,. To obtain the estimated yi,/h,, we apply the same transformation to the reduced form equations for the yir (i.e. divide through by h,) and estimate them by OLS.

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Commercial electricity demand 9

is, ji, is obtained by applying OLS to the reduced form equations for the y,,. yi, in Equation 3 is then replaced by j,, and the resulting equation is divided through by h, to correct for heteroskedasticity. This yields:

where wit = y,, - j,,, the OLS residuals from the reduced form equations. In Equation 5 the second of the two bracketed error terms comes from the initial substitution of ji, for y,,. It is this second bracketed term that creates the problems. This is because, in general, it is no longer orthogonal to the regressors, the j,,/h, and the xj,/h,. Consequently, while the rest of the usual 2SLS consistency proof is unaltered, this last term fails to drop out of the formulas for the second stage OLS (i.e., 2SLS) parameter estimates, leaving a generally inconsistent estimator.

To see the non-orthogonality problem, note that since the fitted residuals and the regressors are always orthogonal in an OLS-estimated equation, then for any 1 ,< i',<n, wi., is orthogonal to each xj,(j = 1, . . . , m) and thus also to every ji,(i= 1, . . . , n).6 That is,

T T

However, the required orthogonality is

Since h, is arbitrary, this latter condition will not hold in general. Naturally, it does hold if h, is constant across observations, i.e., if there is no heteroskedasticity.

The general case

Having illustrated the proposed estimator with the case of heteroskedasticity, it is a simple matter to generalize to any non-white-noise disturbance. Returning to Equation 3, suppose that the disturbance has T x T covariance matrix R. Since R is positive definite, a non- singular matrix Po can be found such that !2 = POP;. The general 2SLS-GLS procedure, then, is to apply the PC1 transformation to the structural equation of interest (here Equation 3) and then 2SLS to the resulting equation. As a part of this we obtain the reduced form estimates of P; ' y,, where y; = (y,,, . . . , y,,), as a function of the transformed predetermined variables.

Feasible 2SLS-GLS application in Costa Rica

Returning to the equation for commercial electricity demand in Costa Rica, we find ourselves in the common situation of knowing the structure (or at least postulating an apparently reasonable structure) for the disturbance term but not knowing the values of the parameters that underlie this structure. In the present case, an error components structure with a cross-section and a random component was postulated but the variance of both components is unknown. How should we proceed? Stripped to the essentials and put in

6This is because j i , is a linear combination of the x,,.

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10 G. D. Westley

terms of the 2SLS-GLS framework, Baltagi (1981) suggests the following 2-step estimator, which is the simultaneous equation analogue of feasible GLS. (i) Estimate the demand equation (and perhaps variants of it7) by ordinary 2SLS and use

these 2SLS estimates to obtain an estimate of the error component variances. (ii) Utilizing the estimated error component variances, formulate a transformation8 that

will render the demand equation disturbance white noise (assuming the estimated variances are correct). Apply this transformation to all predetermined and both endogenous variables in the supply-demand system. Then estimate the transformed demand equation with 2SLS.

The simplicity of this procedure helps to make it an attractive option for applied work. All that is required is the two (or three in our case) 2SLS regressions in steps (i) and (ii) plus some relatively simple, intermediate calculations to obtain the error component variance esti- mates. Hence, it can be implemented easily with most regression packages in use today.

We have used two methods to estimate the error component variances, namely Nerlove's (1971) 2RC method and the 'fitting of constants' technique first expounded by Henderson (1953) and later popularized by Fuller and Battese (1973, 1974). While Nerlove's method is computationally simpler, that of Henderson is designed to deal with unbalanced data. Since our data are highly unbalanced (i.e. there is a great deal of variation in the number of years of data available on each cross-sectional unit), Henderson's method is more appropriate and is the principal estimator relied upon in this study.

Baltagi (1981) notes that his combination of 2SLS and the Swamy and Arora (1972) EC estimator is consistent; it is straightforward to show that this extends immediately to the two feasible 2SLS-GLS estimators used here.

I V . R E S U L T S

Following Learner's (1983, 1985) prudent call for sensitivity analysis, a range of demand equation specifications was estimated, using the favoured Henderson error components estimator. Almost all the long-run elasticity values obtained fall in the fairly narrow ranges shown in Table 1.

Electricity price and income elasticities

Of particular interest are the long-run electricity price and income elasticities, which cluster around -0.5 and 0.5, respectively. These values contradict the notion held by some Laiin American planners in the energy and electricity fields, that electricity consumption grows in a fixed-coefficients way, that is, in proportion to income and with a zero own price elasticity. We consistently find that: (a) the electricity price elasticity is negative and significantly different from zero, and (b) the income elasticity is positive and significantly different from the unitary elasticity suggested by proportionality (and from a zero ela~ticity).~

'For example, given the error component variance. estimators we have used, two 2SLS regressions must be estimated in step (i), namely, the demand equation with and without a complete set of cross- sectional dummy variables. 'We use the transformation suggested by Fuller and Battese (1973). gThe,se statements are true at the 5% significance level or better.

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Commercial electricity demand

Table 1. Summary ojlong-run elasticity ranges"

Variable Long-run elasticity range

1. Real marginal electricity price -0.3 to -0.7 2. Real income or activity measure 0.3 to 0.7 3. Appliance prices, lagged 1 year Sum of elasticities is between

(stove and refrigerator) -0.15 and -0.55 4. Urbanization 0.1 to 0.2

(with the effect of a one point change = 0.4 to 0.85%)

"The values shown here are based on the Henderson error components estimator.

While Paraguay's combined residential-commercial electricity class, investigated by Westley (1984a), probably consists of about 30% commercial and 70% residential electricity consumption, it is still of some interest to compare the long-run electricity price and income elasticities obtained there with those derived in the present study. In the Paraguay case these elasticities are estimated to be -0.56 and 0.42, respectively, very similar to the values obtained here. Two surveys (Taylor, 1975; Bohi, 1981) of the major US commercial electricity demand studies indicate that in the United States both of these elasticities are around one or slightly higher in magnitude, well above the values obtained in the two Latin American investigations.

The difference between the US and Latin American price elasticities may be at least partially explained by the virtual absence of inter-fuel substitution possibilities in the Costa Rican and Paraguayan cases. Fuel switching effects are thought by many to make an important contribution to the relatively high US electricity price elasticity (e.g. see NERA, 1977). The higher US income elasticity may be the result of the addition of air conditioning and other major loads during the time periods analysed by the US studies, especially the 1960s and 1970s. Air conditioning is seldom used in the commercial sectors in Paraguay and

, Costa Rica.

Other elasticities

Overall, electric appliance prices are found to have a consistent negative impact on electricity use. The sum of the long-run elasticities for stove and refrigerator prices clusters around -0.35. Electricity consumption is positively related to urbanization, as expected. The effect on electricity consumption of a one point change in the percentage of total households that are urban (e.g. a change from 10% to 11%) is estimated to be 0.4 to 0.85%.

The regression results indicate that substitute fuel prices (namely, those for LPG and kerosene) have little to do with electricity consumption levels, almost certainly reflecting the dearth of inter-fuel substitution possibilities. For example, kerosene refrigerators are rarely found in Costa Rica at all, and kerosene and LPG stoves are seldom used in commercial applications. Since the two fuel price variables were consistently wrong signed in the regressions estimated here, they were dropped from the analysis.

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12 G . D. Westley

Reference point for sensitivity analysis

The sensitivity analysis, which yields the elasticity values just discussed, can be best understood by use of a reference point. Table 2 provides this, showing parameter estimates and t-statistics for a static and a dynamic demand equation (i.e. without and with the lagged dependent variable, respectively). All the variables discussed in Section I1 (except LPG and kerosene prices) appear in Table 2, referenced by the symbols established there. The following points should be noted.

Table 2. Means, standard deviations, and regression results'

Standard Regression 1 - Regression 2 - Variable Meanb deviationb Static Dynamic

PSTOVEl 2636

PREFl 5202

URB 0.257

In(ql) 3.76

Constant 1

&,(cross-section component)

&,(purely random component)

"t-statistics are in parentheses. Both regressions utilize 262 observations.. Regression estimates are based on the use of two stage least squares with error components, employing Henderson's variance estimators. "Where logrithms have been taken, means and standard deviations are still presented for the untransformed variable (e.g. mean of q, not In(¶)).

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Commercial electricity .demand 13

1. One of the eight company share variables, S1, does not appear in the regression in order to avoid the 'dummy variable trap' (the sum of S1 to S8 being always equal to the constant term). S2 and S3 refer to companies serving the San Jost metropolitan area and hence should have positive coefficients (as they do) whereas S5-S8 refer to rural co-ops, which should have negative coefficients (as they do). S4 refers to a company serving a wide variety of users throughout Costa Rica.

2. Some variables enter in logarithmic form (those prefixed by 'In'); others are un- transformed. See below.

3. It sometimes occurs, as it does in regression 2, that the price of refrigerators is wrong signed in the dynamic equations. This variable is dropped in those cases. The occurrence of a wrong sign may reflect the tendency, noted earlier, of the two appliance prices to move together, with collinearity perhaps exacerbated by the inclusion of the lagged dependent variable. Dropping one of the two appliance price variables still leaves us with the other to represent the set of appliance prices.

Sensitivity analysis. As frequently occurs in empirical work, individual regressions, such as 1 and 2, have many arbitrary elements. In order to alleviate this problem variants of these two demand equations were estimated. The following lines of inquiry (titled following Learner's (1983) jocose example) are addressed. Income probers - Household income (Y) is replaced by each of the three direct measures of commercial-services activity discussed in Section 11. ~ a g g e d effecters -The rationale for current period and one-year lags for appliance prices was discussed earlier. Curve testers - While double-log functional forms are often used for reasons of convenience, this choice of curvature is essentially arbitrary. All combinations of linear and logarithmic transformations for the dependent variable, income, and electricity price (the major variables) were tried. Some inverse transformations were also tried, but the fits were so poor (substantial drops in the inverse variable's t-statistic and noticeable rises in the equation's sum of squared errors) that we did not systematically apply this alternative. In view of Sonnenschein's (1973) .result that market demand functions are characterized only by homogeneity and budget exhaustion, no effort was made to estimate equations conforming to a complete system. Variable droppers- Two sets of variables that were insignificant at the 5% level (t c 1.96), namely, the two appliance prices and five of the company share variables (S2, S3, S4, S5, and S8) were dropped.

The fact that all these variations are tried on both a static and a dynamic equation reflects a fifth line of inquiry. Dynamic doubters-Included in this class would be Bohi (1981, Chapter 3) who argues that inclusion of a lagged dependent variable in the electricity demand equation may lead to erratic and unreliable elasticity estimates.

As can be appreciated by the relatively narrow ranges shown in Table 1, the effect of these changes on the long-run elasticity estimates is not great. Hence, the estimates do not appear to be particularly sensitive, at least to the variations explored here. For variable dropping this may be due to the relative absence of multicollinearity, noted earlier.

Table 3 presents a selection of these sensitivity analysis results and shows that the static equations yield elasticities which are not that different in absolute terms from the long-run elasticities in the equivalent dynamic equations. This is particularly so when the sum of the

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Table 3. Selected sensitivity analysis results"

Regression Regression Regression Regression Regression Regression 1 -static 2 -dynamic 3 -static 4-dynamic 5 -static 6 -dynamic

Long run elasticitiesb (From Table 2)

(Same as regressions 1 and 2 (Same as regressions 1 and 2 -but omit insignificant -but omit appliance prices) company share variables)

1. Real marginal electricity price

2. Real household personal income

3. Real stove price, lagged 1 year

4. Real refrigerator price, lagged 1 year

5. Urbanization

Other results 6. Coefficient of lagged

dependent variable 7. &,(cross-section

component) 8. B,(purely random

component)

'The t-statistics, shown in parentheses, refer to the original regression coefficients. All results are based on the use of 2SLS with error components, using Henderson's variance estimators. 262 observations are utilized throughout. bWhere variables are not in logarithmic form, the mean values, shown in Table 2, are used in the elasticity computations.

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Commercial electricity demand 15

two appliance price elasticities is considered instead of their individual values, as is reasonable given the representational nature of these variables. The tendency for static equations to yield long-run elasticities when the data are cross-sectional (or predominantly cross-sectional) may explain this phenomenon.

Table 3 also illustrates the general finding that eliminating the appliance price variables or the insignificant company share variables does not greatly affect the remaining elasticity estimates.

In all the sensitivity analysis regressions, the electricity price and income (or activity level) elasticities are always right-signed and highly significant (well beyond the 5% level), with t-statistics similar to those shown in Table 3. This, together with the fact that these elasticities are reasonably insensitive to specification changes, means that rather firm estimates for these critical parameters have been obtained.

Comparison of estimators. The parameter values obtained with five different estimators: OLS, 2SLS, 2SLS-DV, 2SLS-ECN, and 2SLS-ECH, are now compared. The last three of these estimators respectively employ 2SLS in conjunction with a complete set of cross- section dummy variables (DV), and with the Nerlove (ECN) and Henderson (ECH) error components estimators discussed in Section 111.

All the empirical results presented up until now are based on the Henderson procedure (2SLS-ECH). All of the same equations were estimated by ZSLS and by 2SLS-DV since doing so is a prerequisite to 2SLS-ECH. Nerlove's estimator (2SLS-ECN) and OLS were also applied to many of these equations. The general conclusions from all this work are that the dummy variable and the error component estimators (i.e. 2SLS-DV, 2SLS-ECN and 2SLS-ECH) give mostly similar results, which differ in important ways from the OLS and 2SLS estimates.

With OLS, the electricity price coefficients are consistently wrong signed (positive) in both the static and dynamic regressions and statistically very significant in the former. In all equations estimated by 2SLS the electricity price elasticities move in the negative direction from the levels of their OLS counterparts. Given that the Costa Rican rate schedules are basically increasing block, this is exactly what theoretical considerations lead us to expect (e.g. see Rao and Miller, 1971, Chapter 8). While ZSLS represents an improvement over OLS, the 2SLS estimates are still not very satisfactory. The estimates of the electricity price elasticity are often wrong signed, erratic in size, and generally insignificant. Further, in examining the 2SLS residual plots, one encounters strong evidence for omitted cross- sectional effects. The values of the residuals for a given canton are often nearly equal to each other and different in value from the residuals in other cantons (e.g. the residuals in canton 1 might all be approximately -0.4, whereas those in canton 2 might cluster around 0.8, etc.). Failure to control for omitted cross-sectional effects appears responsible for this residual pattern and for the weak 2SLS estimates.

The residual pattern noted above disappears when any of the 2SLS-DV, 2SLS-ECN or 2SLS-ECH estimators are used; it now appears essentially random. In addition, the elasticity estimates become much less volatile. Hence, these estimators appear to serve their corrective purpose, offering substantial improvements over 2SLS.

All three of these estimators yield rather similar long-run elasticities, and this is reassuring. They differ, however, in their estimates of short-run elasticities. The Henderson estimates of the coefficient of the lagged dependent variable cluster around 0.5, while the Nerlove and DV estimates are about 0.25. I-Ience, for the Henderson estimator, one-year elasticities are about one-half of the long-run elasticities, while for the Nerlove and DV estimators this ratio is around three-quarters. For the reasons given earlier we prefer the Henderson estimates.

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16 G. D. Westley

V. C O N C L U S I O N S

This paper has presehted elasticity and rate of adjustment estimates for commercial electricity demand in the Central American country of Costa Rica. These estimates should be of particular interest since so little is known about electricity consumption relations in developing countries. Yet such knowledge is important, not only for policy analyses and forecasts in these countries, but also for contributing to our understanding of the part played by the developing world in the evolving global balance between energy demand and supply.

Methodologically, this paper discusses and employs a combination estimator which addresses both the simultaneity and misspecification problems common to many electricity demand studies. Such an estimator, to my knowledge, has not been used in any previous electricity demand study despite the need for it in many cases.

A C K N O W L E D G E M E N T S

The author would like to acknowledge the help and advice of Luis Soto, Stephane Conte, Jeanne Holzgrefe, and an anonymous referee.

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Commercial electricity demand 17

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