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3 J. Steinbuks, V. Foster / Energy Economics 32 (2010) Table 1 Probit and Tobit regression results. Variable we employed two modelling approaches. The first approach follows the binary choice model of Reinikka and Svensson (2002) is based on the following stochastic specification: PrðY i =1Þ = Φ α 1x i ; α 2Z i σ! ; ð1þ where Y i is the probability that firm i invests in a, Φ is the standard normal distribution function, x i is the frequency of power outages, Z i is a vector of controls, including country and firm characteristics, and σ is a standard deviation of normally distributed error term. The second approach employs censored regression approach: PrðY i N 0Þ =1 Φ Probit regression ( ownership) Estimated coefficient α 1x i ; α 2Z i σ! Tobit regression ( capacity) Elasticity P-value Estimated coefficient (Elasticity) P-value Days of power outages (log) Age (log) Employment (log) PKM (log) Size1 lost days (log) Size2 lost days (log) Size4 lost days (log) Size5 lost days (log) Exporter statistically significant at 1 percent level; statistically significant at 5 percent level; statistically significant at 10 percent level. ; ð2þ where Y i is the logarithm of the capacity of firm's i (leftcensored at zero), and the explanatory variables are the same as in Eq. (1). Eq. (1) is estimated using the probit method. Eq. (2) is estimated using the tobit method. Selected estimated parameters are presented in Table 1, with the complete set appearing in Appendix A, Tables 2 and 3. Reliability of power supply and various firm characteristics age, size (as measured by number of employees), and export orientation all have a significant positive impact on the estimated probability of investing in generating capacity and the size of the. 7 The probability that a firm will own a can be expressed as a function of the reliability of power supply and the firm's size. The probability of finding a on the premises increases by nearly 50% as one moves from small firms (less than 10 employees) to very large ones (more than 500 employees) (Fig. 1). The probability of having a remains high (about 20%) even where power supply is completely reliable. 8 For large firms the probability of having a in the absence of power outages is even higher (about 50%). The evidence thus suggests that both ownership and its capacity are greatly affected by firm characteristics, such as size, sector, corporate structure, and export orientation. Large firms that operate 24 h Fig. 1. Probability that a firm will own a, by number of employees. per day are more likely than smaller firms to install backup generation capacity compared to smaller firms, which operate only during daylight hours and therefore are less affected by evening blackouts. Mining firms tend to require own power to keep elevators, air pumps, and other safety devices fully operational regardless of the power supply from public grid. Petroleum firms have very sensitive and delicate equipment that must be protected from damage stemming from power outages. Exporters may need to generate their own power to meet ISO standards (e.g., relating to cold chains). Informal firms may be unable to accumulate significant generating capacity because of security concerns, which may include police raids, unstable land or lease tenure, and other factors. The composite effect of size and reliability of power supply is generally not significant across firms, except for small firms and microenterprises (Table 1). The significant negative coefficient on the product of small firms and large power outages indicates that small firms suffer the most from unreliable power supply, because they lack the resources to invest in own-generation The and benefits of own-generation 5.1. Costs We use the revealed preference approach to analyze the economic of own-generation. 10 This approach is based on the presumption that rational, profit-maximizing firms will insure themselves against the risk of frequent power outages. Because insurance contracts for unreliable power supply are not available in developing countries, the only way to minimize losses is to acquire backup generating power. The firm's problem is to choose the optimal amount of backup power that minimizes the sunk incurred by acquiring generation capacity as well as the damage that unsupplied power would cause. A competitive, risk-neutral firm will maximize expected profits by equating at the margin the expected cost of generating a kwh of its own power to the expected gain due to that kwh. That gain consists of the continued production (even if partial) that the self-generated electricity makes possible, and the avoided damage to equipment that would have been caused by a power failure. Under profit-maximizing conditions, the expected marginal gain from a self-generated kwh is also the expected marginal loss from the kwh that is not supplied by the utility. Therefore the marginal cost of self-generated power may serve as an estimate for the marginal cost of an outage. 7 The price-cost margin (PKM) variable was not statistically significant, possibly because of simultaneity bias between firm's profitability and decision to own a. 8 This finding is consistent with firms' insurance behavior. Large and risk-averse firms incurring high marginal from power outages will invest in back-up even if current power supply is completely reliable to keep the option value of insurance from future outages. 9 Further discussion of this subject becomes complicated because access to electricity and access to finance are frequently simultaneous. For example, in Nigeria small firms may lack internal funds to obtain a, and owning a may be a prerequisite to secure loan from the bank. 10 See earlier citations to the revealed preference approach in the literature review section of this paper.

4 508 J. Steinbuks, V. Foster / Energy Economics 32 (2010) Table 2 The comparative of self generated and publicly supplied electricity, and the effect of own generation on the marginal cost of electricity, in Africa. Country Average variable cost of own electricity (A) Average capital cost of own electricity (B) Average total cost of own electricity (C=A+B) Price of kwh purchased from public grid (D) Algeria c 0.05 Benin c 0.27 Burkina Faso a c 0.23 Cameroon a c 0.16 Cape Verde a c 0.26 Egypt, Arab Rep c 0.12 Eritrea Kenya Madagascar Malawi c 0.09 Mali Mauritius c 0.25 Morocco c 0.15 Niger a c 0.26 Senegal Senegal b South Africa Tanzania Uganda Zambia Share of total electricity consumption coming from own generation. = data not available. a Tourism industry (hotels and restaurants sector) only. b Survey of informal sector. c Data not reported in the enterprise surveys (obtained from the public utilities). Weighted average cost of electricity (E= C+(1 ) D) The cost to the firm of generating its own power consists of two elements. The first is the yearly capacity cost of the and other capital outlays. Following earlier literature, that cost will be denoted by b (Kg), where Kg is the 's capacity measured in kw. The second is the variable cost per kwh-chiefly fuel cost, which is practically constant. 11 If the is used to capacity during power cuts, the variable cost per year will then be v H Kg, where v is the fuel cost per kwh, and H is the expected total duration of outages, measured in hours per year. The total expected yearly cost per kw of backup generating power is then CðKgÞ = bðkgþ + v H Kg: The expected respective marginal cost is C ðkgþ = b ðkgþ + v H and the expected marginal cost of a kwh generated is simply given by C ðkgþ kwh = b ðkgþ H ð3þ ð4þ + v: ð5þ Applying Eq. (5) to the enterprise survey data allows us (using reasonable assumptions) to estimate the (marginal) cost of owngeneration from observed information about the acquisition and running of in-house generating capacity, and from data on the frequency of power outages. 12 For these purposes, values for b, H, andv must be obtained. The operating cost, v, is calculated as a product of the unit cost of fuel and the 's fuel efficiency (fuel consumption per kwh). Assuming that most firms in the enterprise survey dataset rely on thermal generation, the unit cost of fuel is approximated by an average price per liter of diesel fuel. 13 Fuel efficiency data was obtained from the Web sites of leading manufacturers of s. 14 The unit capital cost of self-generated electricity, b, depends on price schedules for s, tax and depreciation rules, and the interest rates. Original price schedules (in national currencies) and data on year of acquisition are reported in the enterprise surveys. We converted the original price schedules into current U.S. dollars. First, we deflated the price schedules, applying the corresponding value of the country's GDP deflator and then converting into dollars at the prevailing exchange rate. 15 We then obtained the capital cost per kw of installed capacity (in 2004 dollars, assuming thermal generation, no tax rules, and an internal rate of return of 10%) 16 using the data from the World Bank's Energy and Water Department (2005). Our data on the duration of power outages, H, came from the enterprise surveys. Data on the average duration of power outages were generally not available. We assumed a value of 8 h per day. 17 In most of the countries of Africa, the average cost of generating electricity in-house is significantly higher than the cost of electricity from the public grid (Table 2). This finding reflects the differences in efficiency between the small backup s used by commercial firms and the large plants that produce electricity for the public grid. The major exceptions are the countries in which fuel is heavily subsidized (Algeria, Arab Republic of Egypt, and Eritrea), where the average cost of self-generated electricity is close to the cost of the electricity from the public grid. 11 This measure does not account for other variable, such as rental of house, maintenance, wages, and salaries. Omission of these does not significantly bias our estimates, because they are likely to be substantial for firms with huge back-up capacity. In our dataset among 1352 firms that owned electric s, only 2 firms had large (1 MW or larger) back-up capacity. 12 This measure of marginal cost does not account for incomplete backup that may result in additional losses such as destruction of raw materials and damage to equipment. These losses are inversely related to the percentage of backup and the reliability of the firm's backup equipment. 13 The fuel prices came from GTZ International Fuel Prices These manufacturers included Wärtsilä and Cummins. 15 Nominal exchange rates were adjusted for price volatility using the World Bank Atlas method. 16 The results from the enterprise surveys show that most firms in Africa rely on internal rather than external financing. Therefore, given limited access to finance, the internal rate of return is preferred to interest rates. 17 Other assumptions about the duration of power outages were considered, including 4 and 12 h. It follows from Eq. (4) that under these assumptions the estimates of the unit capital cost of self-generated electricity will vary within the 50% confidence interval.

6 510 J. Steinbuks, V. Foster / Energy Economics 32 (2010) Table 5a Cost benefit analysis of own-generation, by country. Percent Country Investment Own-generation Total Reduced sales losses Benefit cost margin Algeria Benin Egypt Eritrea Kenya Madagascar Malawi Mali Mauritius Morocco Senegal Senegal a South Africa Tanzania Uganda Zambia = data not available. a Survey of informal sector. Statistically significant at 1 percent level. Statistically significant at 5 percent level. Lost sales without operating of generation. The fixed of own-generation were annualized assuming linear depreciation. The net annual operating were calculated as the product of the firm's consumption of selfgenerated electricity and the difference between the per kwh of self-generated electricity and of electricity from the public grid. 21 We use two approaches to calculate the benefits of own-generation. In the first, more conservative approach we assume that firms that own a may incur lost sales from power outages, for example, because of disruptions in 's fuel supply. The marginal benefit of own generation is calculated as the reduced sales loss from the regression analysis in the previous section, adjusted for a corresponding fixed-effect. 22 In the second approach we assume that firms that own a do not lose sales from power outages. The marginal benefit of own generation is computed as an opportunity cost of not having a, e.g. the lost sales from power outages by firms without. 23 Both and benefits of owning a are expressed as percentages of sales. The resulting difference between the benefits from the first approach and the of own-generation (the benefit-cost margin) was tested for statistical significance from zero using the Student's t test. 24 The results are summarized in Tables 5a 5c below. The results from the first approach indicate that in most countries, the of own-generation outweigh the benefits (Table 5a). However, only in Egypt and Zambia this difference is statistically significant. In four countries (Mauritius, Senegal, South Africa, and Uganda) the benefits outweigh the, and the difference between the benefits and the is not statistically significant from zero. These results imply that investment in in-house generation at least allows firms to break even. The results from the second approach indicate that benefits of own generation outweigh the for all 21 The exact computational procedure is outlined in a technical appendix, which is available upon request. 22 This measure represents a lower bound estimate of own-generation benefits, because firms that own s have little lost load, and given various considerations not related to reliability of power supply as discussed earlier in this paper. 23 This measure represents an upper bound estimate of own-generation benefits given that some owners reported lost sales from power outages, or because firms without can be less productive and incur higher losses from power outages. The degree of this bias cannot be determined without proper counterfactual. 24 One cannot statistically compare the benefits from the second approach and the of own generation, because these estimates are based on different set of firms. countries. The results from two approaches can be reconciled under less restrictive assumptions. First, the fixed of own-generation can be sunk or depreciated nonlinearly. In Egypt and Zambia the negative and statistically significant difference between benefits and of own generation is driven by fixed. Second, the analysis presented above does not account for other potential gains from owngeneration, such as reductions in damaged equipment. This is especially important in Benin, where the average losses from damaged equipment account for 1.5% of sales (see Appendix A, Table 2). Third, the results of the analysis do not incorporate the option value of lost load due to future shocks to power supply (e.g. unexpected droughts or power infrastructure damages). The and benefits of own-generation differ according to firm size (Table 5b). The total of own-generation vary nonlinearly by firm size, being most efficient for medium-sized firms. For small firms own-generation imposes relatively low fixed but higher variable. Larger firms have relatively high fixed, and increasing variable. The total benefits of own-generation calculated as reduced sales losses increase non-linearly with firm size, being the highest for medium-size firms. Larger firms without are found to incur smaller losses from the power outages. The difference between the and benefits of own-generation calculated as reduced sales losses is negative across all size categories, except for the medium size. However, it is statistically significant only for large firms. The difference is insignificant or marginally significant for microenterprises, small medium, and very large firms. For all size categories the average sales losses of firms without are higher than total of own generation. The and benefits of own-generation vary significantly across industries (Table 5c). The are highest in energy-intensive industries chemicals, nonmetal and plastic materials, and mining, and lowest in light industries, such as textiles and wood. Chemicals and construction have the highest fixed of own-generation, whereas nonmetal and plastic materials and mining have the highest operational. The highest gains from own-generation calculated as reduced sales losses are observed in mining, chemicals, and construction. In most industries, the difference between the and the benefits of own generation is not statistically significant. The of own-generation significantly outweigh the benefits in food and beverages and metals and machinery. However, these two industries, as well as nonmetallic and plastic products also have the highest average sales losses for firms without. Therefore, the difference between two approaches is

7 J. Steinbuks, V. Foster / Energy Economics 32 (2010) Table 5b Cost benefit analysis of own generation, by size of firm. Percent Size Investment Own-generation Total Reduced sales losses Benefit-cost margin Micro Small Medium Large Very large Statistically significant at 5 percent level. Statistically significant at 10 percent level. Lost sales without Table 5c Cost benefit analysis of own-generation, by sector. World Bank, Enterprise Survey Database. Percent Industry Investment Own-generation Total Reduced sales losses Benefit cost margin Textiles Food and beverages Metals and machinery Chemicals Construction Wood and furniture Nonmetallic and plastic materials Mining and quarrying Statistically significant at 1 percent level. Statistically significant at 5 percent level. Lost sales without likely to be caused by industry's idiosyncratic factors (for example, sales losses because of reductions in damaged equipment are important in the food processing industry) With improvements in quality of public power supply The results of the probit model discussed earlier can be used to evaluate the extent to which an improvement in the reliability of power supply will affect ownership. The marginal effects of the probit model (Eq. (1)) suggest that the probability of a firm's owning a is not very sensitive to power supply reliability. Reducing power outages by half the mean outage reduces ownership by less than 2% (Table 6). It appears that thoroughly reliable power would reduce ownership by no more than 12%. The predictions of the probit regression are extended to individual countries in Appendix A, Table 4. Raising the reliability of power supply to the level of South Africa results in a mere 3 5% reduction in ownership. Although the regression results suggest that improving the reliability of power supply would have a relatively small effect on ownership, there are several reasons to expect that the Table 6 Simulated change in ownership. Change in probability that firm will own a Variable Mean MinNMax ½ mean change ½ std change Days of power outages Age Employment Exporter n.a. n.a. Source: World Bank, Enterprise Survey Database. Note. Exporter is a binary variable, therefore ½ mean change and ½ std change statistics are not reported. n.a. = not applicable. effect would be greater. First, the regression analysis does not account for unobserved explanatory variables, such as firms' access to finance and productivity, which may bias the regression results downward. Second, because investment in in-house generation is irreversible, reductions in ownership will occur with a lag as public power supply is improved. The cross-sectional data analysis conducted in this study does not capture these dynamics. Third, the gains to be had by improving the reliability of power supply may be greater if the effects of unreliable power supply on observed industrial structure and external competitiveness are taken into account. Because energy-intensive industries require more stable power supplies, improving reliability will diversify country's production base and result in additional economic gains. 6. Conclusions and policy recommendations This paper aims to deepen our understanding of the widespread phenomenon of own generation of electric power by firms, as well as its relationship to unreliable public power supplies in the African context. It does so by analyzing the World Bank's Enterprise Survey Database, which provides a detailed set of attitudinal and behavioral information about decisions relating to own power generation at the firm level; at least for the case of larger formal sector manufacturing enterprises. Thedecision ofa firm to maintain its own-generation capability is driven by a variety of factors. Our empirical analysis shows that unreliable public power supplies, though an important constraint to business operations, is far from being the only or the largest factor driving ownership. Firm characteristics such as size, age, industrial sector and export orientation all have a major influence. In particular, the probability owning a doubles in large firms relative to small ones. Moreover, the behavioral model predicts that the percentage of firms owning their own s would remain high (at around 20%) even if power supplies were perfectly reliable, suggesting that other factors such as emergency driven back-up

9 J. Steinbuks, V. Foster / Energy Economics 32 (2010) Table 2 Probit regression results ( ownership). Variable Estimated coefficient Elasticity P-value Days of power outages (log) Age (log) Employment (log) PKM (log) Micro Lost Days (log) Small Lost Days (log) Large Lost Days (log) Very large Lost Days (log) Exporter Algeria Benin Botswana Burkina Faso Burundi Cameroon Cape Verde Egypt Eritrea Ethiopia Kenya Madagascar Malawi Mali Mauritania Mauritius Namibia Niger Senegal Swaziland Tanzania Uganda Zambia Food and beverages Metals and machinery Chemicals and pharmaceutics Construction Wood and furniture Nonmetallic and plastic materials Other manufacturing Other services Hotels and restaurants Mining and quarrying Constant Χ 2 Statistic Pseudo R N 4246 Note: Base country: South Africa; base industry: textiles; base size category: medium size ( employees), Source: World Bank, Enterprise Survey Database. Table 3 Tobit regression results ( capacity). Variable Estimated coefficient/elasticity P-value Days of power outages (log) Age (log) Employment (log) PKM (log) Micro Lost Days (log) Small Lost Days (log) Large Lost Days (log) Very large Lost Days (log) Exporter Algeria Benin Burkina Faso Cameroon Cape Verde Egypt (continued on next page) Table 3 (continued) Variable Estimated coefficient/elasticity P-value Eritrea Kenya Madagascar Malawi Mali Mauritius Niger Senegal Tanzania Uganda Zambia Food and beverages Metals and machinery Chemicals and pharmaceutics Construction Wood and furniture Nonmetallic and plastic materials Other manufacturing Other services Hotels and restaurants Mining and quarrying Constant χ 2 -Statistic Pseudo R N 3756 Note: Base country: South Africa; base industry: textiles; base size category: medium size ( employees), Source: World Bank, Enterprise Survey Database. Table 4 Marginal benefit of ownership (lost sales). Variable Estimated Coeff. P-value Days of power outages (log) Generator ownership Algeria Benin Botswana Burkina Faso Burundi Cameroon Cape Verde Egypt Eritrea Ethiopia Kenya Kenya (informal) Madagascar Malawi Mali Mauritania Mauritius Morocco Namibia Niger Senegal Senegal (informal) South Africa Swaziland Uganda Uganda (informal) Agroindustry Metals and machinery Chemicals and pharmaceutics Construction Wood and furniture Non-metallic and plastic materials Other manufacturing Other services Hotels and restaurants Mining and quarrying Micro Small (continued on next page)

10 514 J. Steinbuks, V. Foster / Energy Economics 32 (2010) Table 4 (continued) Variable Estimated Coeff. P-value Large Very Large Constant F-Statistics R N 4254 Source: World Bank, Enterprise Survey Database. Note: Base country: Zambia; base industry: textiles; base size category: medium size ( employees). Table 5 Simulated change in ownership from improved reliability of power supply. Country Power outages Predicted ownership Simulated ownership (no power outages) Algeria Benin Botswana Burkina Faso Burundi Cameroon Cape Verde Egypt Eritrea Ethiopia Kenya Madagascar Malawi Mali Mauritania Mauritius Namibia Niger Senegal South Africa Swaziland Tanzania Uganda Zambia Simulated ownership (outages at South African average) Beenstock, M., Goldin, E., Haitovsky, Y., The cost of power outages in the business and public sectors in Israel: revealed preference vs. subjective valuations. The Energy Journal 18 (2), Bental, B., Ravid, S., A simple method for evaluating the marginal cost of unsupplied electricity. Bell Journal of Economics 13, Caves, D.W., Herriges, J.A., Windle, R.J., The cost of electric power interruptions in the industrial sector: estimates derived from interruptible service programs. Land Economics 68 (1), Foster, V., Steinbuks, J., Paying the price for unreliable power Supplies: In-House generation of electricity by firms in Africa. World Bank Policy Research Paper April. Karekezi, S., Kimani, J., Status of power sector reform in Africa: impact on the poor. Energy Policy 30, Karekezi, S., Mutiso, D., Information and Statistics on the Power Sector and the Reform Process in Sub-Saharan Africa. In: Bhagavan, M. (Ed.), Reforming the Power Sector in Africa. Zed Books Ltd., in association with African Energy Policy Research Network, London, pp Kariuki, K.K., Allan, R.N., Reliability Worth in Distribution Plant Replacement Programmes. Proceedings of the Second International Conference on the Reliability of Transmission and Distribution Equipment, Coventry, U.K, pp March. Kessides, C., The Contributions of Infrastructure to Economic Development: A Review of Experience and Policy Implications. World Bank Discussion Paper 213. Washington, DC. Lee, K.S., Anas, A., Impacts of Infrastructure Deficiencies on Nigerian Manufacturing: Private Alternatives and Policy Options. Infrastructure and Urban Development Department Report 98. World Bank, Washington, DC. Reinikka, R., Svensson, J., Coping with poor public capital. Journal of Development Economics 69, World Bank. Technical and Economic Assessment: Off Grid, Mini-Grid, and Grid Electrification Technologies. Discussion paper, Energy and Water Department, World Bank, Washington, DC; November, References Adenikinju, A, Analysis of the cost of infrastructure failures in a developing economy: the case of the electricity sector in Nigeria. AERC Research Paper 148, African Economic Research Consortium, Nairobi. February.

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