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Storage capacity and water use in the 21 water-resource regions of the United States geological survey
Int. J. Production Economics 81–82 (2003) 1–12
Storage capacity and water use in the 21 water-resource regions of the United States geological survey Andrew Stern Department of Economics, CSULB, Long Beach, CA 90840, USA
Abstract The development of reservoir storage capacity has been most closely connected to water demand for irrigation purposes. But water demand for this purpose is relatively elastic, while that for other uses is much less so. A model estimated here suggests also a positive relation between the price of irrigation water and an aggregate comprising mainly urban water use. As the pressure of rising demand against a relatively constant supply drives water prices upward, irrigation is thus likely to suffer in comparison to urban demand, and this should free up existing storage capacity for alternative uses. By implication, water managers should take this eventuality into account when formulating water resource strategies to meet future water needs. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Water; Storage; Government policy
1. Introduction The factors propelling the demand for water in the United States have been growing at a steady rate, but the supply of water has increased very little during the past 20 years. One effect of the resulting imbalance has been the recognition that water is an economic rather than a free good, and that its allocation, in order to be efficient, must favor its highest valued uses1. Prior to the 1980s the preponderant manner of ‘producing’ water (increasing its supply) outside of the hydrologic cycle and apart (or in conjunction with) the greater use of ground water was by way of the develop1 We shall, in what follows, ignore qualitative differences between the various ‘waters’ in use (but see Spulber and Sabbaghi (1998) for a theoretical discussion of these differences). We might assume in this instance that the desired quality can be achieved by appropriate treatment, and that the cost of such treatment does not vary between qualities.
ment of storage capacity, and during the three decades spanning 1950–1980 most of this development took place in the western part of the US, specifically in connection with the effort to promote agricultural irrigation in semi-arid regions.2 Because the demand for irrigation water is relatively elastic while that for residential (end use) purposes is highly inelastic, it follows that the continuing growth of urban population and industrial activity will steadily shift water use 2
It should be noted that the use of stored water is technically most closely associated with irrigation. If precipitation occurs during the winter months while irrigation needs arise during the summer, the availability of reservoir storage becomes essential. By the same token, substantial year to year variation in stream flow can also be regulated by the development of reservoirs. In other off-stream uses of water, the seasonal pattern is much less pronounced. Historically, cities have not depended upon rain to provide drinking water. Instead, they have grown around springs, lakes, and rivers. The term ‘drought’ is almost exclusively associated with agriculture.
0925-5273/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 0 2 ) 0 0 2 9 5 - 5
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A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
away from irrigation3 and thus make redundant some of the storage capacity developed over the years. But reservoirs are inherently adaptable, and what our findings suggest is that in planning infrastructure to meet future water needs expansion of the means of effectuating water transfers should take precedence over increases in storage capacity in the composition of water resources portfolios. Our findings are presented in the following order: In Section 2, we document the nature of trends in the factors underlying the demand, supply, and use of water in the US. This is followed by a discussion of the limits to reservoir development, sources and uses of water, possibilities for substitution, and the resulting elasticities. In Section 3, we present a statistical analysis which reveals the singular importance of storage capacity as a determinant of water for irrigation purposes. Section 4 looks at alternative pricing schemes and their effects upon the allocation of water use for residential and irrigation purposes. This also includes a statistical analysis of the effects of actual prices from a cross-sectional model. A review of the findings and their implication for aggregate water management concludes the paper.
2. Trends in the relevant variables, the characteristics of stream flows, and the limits to reservoir development Off-stream withdrawals of water in the US satisfy three broad purposes: the cooling of thermoelectric power plants, the irrigation of agricultural crops, and other uses, chief among which are public supply, which essentially satisfies 3 The price of irrigation water is likely to increase for yet another reason. The developmental history of water storage in the US is a history of both direct and indirect Federal involvement and both overt and implicit subsidies (USDA, 1997, Agricultural Resources etc., p. 77). For instance, in California it costs the government $42 to produce water sold to irrigators for much less. (Spulber and Sabbaghi, 1998, p. 289). Federal irrigation subsidies via the Bureau of Reclamation have been estimated to exceed 86% of construction costs on average (National Research Council, 1996, p. 69). But ever since 1992 the Omnibus Water Act has tried to make water supply more responsive to cost (Spulber and Sabbaghi, 1998, p. 289).
residential and commercial uses4. In-stream uses— those that do not require diversion and therefore compete with off-stream withdrawals—include the generation of hydroelectric power, the use of waterways for navigation, recreation and wildlife preservation. On the surface, a general model of water use should include all the above sectors. Unfortunately, however, some of the in-stream uses are almost impossible to quantify by traditional methods. In fact, the only in-stream use that is thus quantifiable is hydroelectric power production, and this therefore is the sector that will represent all in-stream uses in what follows. This approach is all the more reasonable since stream flow availability for the other in-stream uses is governed by law and regulation rather than by the interaction of supply and demand. Over the years, the dynamics of the water economy has evolved in a somewhat paradoxical pattern. As Table 1 shows, the factors propelling demand, such as population growth and various measures of output, have continued to grow. Yet water utilization for most purposes has leveled off since 1980. The only category that shows an increase during this period is public supply, a great part of which consists of residential and commercial water use. The leveling off of other water uses since 1980 has, over time, become the theme of a standard set of justifications (Solley et al., 1998, p. 64); these include: the decline in the expansion of irrigation systems and increases in energy development after 1980, the development of more efficient irrigation techniques, the increased cost of energy, the increased competition for water and a downturn in the farm economy, the transition from water supply to water demand management, new technologies in the industrial sector, increased water recycling, and the increased awareness of the public of the need for water conservation. It is of course the increased competition for water, its origins and prospective impacts that form the core of the present paper. While the relevance of the trends reported in Table 1 is for the most part self-evident, there is yet a need to dwell on the role of storage capacity as a 4 In addition to these, ‘other’ uses also include livestock, industrial, and mining withdrawals. These are relatively small.
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
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Table 1 Trends in water withdrawals and related variables: 1950–90 Year variable
1950
1955
1960
1965
1970
1975
1980
1985
1990
Factors affecting demand for water Population (millions) Agric. prod. (1982=100) Industr. prod. (1987=100)
150.7 46 25.8
164 54 33.7
179.3 60 38.1
193.8 67 51.7
205.9 72 61.4
216.4 82 66.3
229.6 90 84.1
242.4 105 94.4
252.3 112 106
Hydro power (quad.BTU) Thermo power (b/kWh) Hydro power (b/kWh)
1.42 233 96
1.36 434 113
1.61 610 146
2.06 861 194
2.63 1284 248
3.15 1618 300
2.9 2010 276
2.94 2189 281
2.93 2528 280
3050
3290
Instream use of water Hydro water (bg/d) Offstream uses of water Industr. water (bg/d) Irrigation water (bg/d) Thermo water (bg/d) Public supply water (bg/d) Factors affecting supply of water Storage capacity(macre-feet)
1100
1500
2000
2300
2800
3300
3300
37 89 40 14
39 110 72 17
38 110 100 21
46 120 130 24
47 130 170 27
45 140 200 29
45 150 210 34
30.5 137 187 36.5
29.9 137 195 38.5
165
235
250
300
375
425
432
440
450
Sources: Water withdrawals from Solley et al., 1998 in billions of gallons per day hydro and thermo power from Annual Energy Review, 1991 in quadr. Brit. Thermal Units or billions of kilowatt hour. Population in millions from Solley et al, 1998. Agricultural production and Industrial Production indexes from Economic Report of the President, 1995. Water storage capacity estimated from Solley, 1997. In millions of acre-feet (1 acre-foot=325,851 gallons. 1 mg/d=1120 acre-feet per year).
measure of ‘water supply’. Storage of a commodity for the purpose of subsequent use is the theme of inventory theory. In manufacturing and trade, inventories are held for ‘production smoothing’ and ‘buffer stock’ motives (Blinder and Maccini, 1991). In the case of storable commodities (which may be held for their own sake or as inventories of raw materials in the production process) the decision to store is typically governed by ‘arbitrage equations’ in which the spread between the spot price and the discounted expected future price is compared to storage costs (Williams and Wright, 1991). The storage of water is unique in that ‘price’ has not been, at least up to the present, a determinant of the decision to store. More relevant is the concept of ‘safe yield’ of a reservoir, in which the role of storage is to provide a reliable supply of water. This need may arise because of the variability of precipitation and/or stream flow, because of the variability of demand, or because of
both. By making up for these vagaries in stream flow and demand, reservoir capacity is seen to effectively ‘produce’ water (the term used in Hirshleifer et al., 1960). The variability of stream flow in the 21 water regions of the USGS is considerable. The coefficient of variation of annual stream flow ranges from a low of 19% in the Great Lakes and Pacific Northwest Regions to a high of almost 80% in the Lower Colorado Region. These flows have been estimated by government hydrologists over a period of many years, and several measures of stream flow and variability have been compiled.. Annual data on year to year variability have been collected by Graczyk et al. (1986) while measures of within year variability are reported in the WRC report (1978). The simultaneity between stream flow variability and storage capacity makes it difficult to model the relationship between these two variables: variable stream flow requires storage for
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A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
regulation, while regulation reduces the variability of stream flow. Ignoring this inherent simultaneity, OLS estimates of the regression of variation upon storage capacity, providing a dummy variable to distinguish between the Eastern (the first eight) and the Western Regions, reveal a significant relationship which is insensitive to the choice of additional independent variables in the regression equation. There remain two issues to be dealt with in this section. First, water reservoirs may be either multipurpose or else they may be dedicated to a specific use. This heterogeneity may bias calculations, and we therefore try to assess its importance. Second, after decades of development, water storage capacity may be approaching its physical limits. If this is so, then we can better assess the future of water supply in the US. A partial measure of the first item is obtained from reservoir statistics for the State of California, which is representative of an area where water is plentiful but unevenly distributed both in timing and location. Of the 102 largest dams/reservoirs in the State, 75 are ‘multipurpose’ by initial design, the remaining being dedicated to specific purposes (California Statistical Abstract, 1999). Irrigation represents a preponderant use of the multipurpose reservoirs in the California sample. This characteristic is generally true of the larger reservoirs in the Western Water Resource Regions of the US. But modern techniques of storage utilization permit the formation of systems of reservoirs (Lund and Guzman, 1999) in which the original purpose becomes irrelevant. An example of such multiple use would be a reservoir/dam dedicated to hydropower which produces a flow sufficient to provide for irrigation downstream from the power plant (Viessman and Welty, 1985). The second issue, namely the physical limitations on reservoir development, has been a subject of inquiry since the 1970s. ‘Mass curve’ analysis (Viessman and Welty, 1985) suggests that the level of storage capacity needed to maintain water withdrawals at their average level was achieved by 1980 (both in the range of 400 bg/d). By that time, the ratio of storage to renewable water supply had reached near-optimal levels in some of the irrigation-intensive regions of the South
Western US. (USGS National Water Summary, 1983)5 Another measure of the extent of development is reservoir surface area per acre of land. This measure also suggests that reservoir capacity in the most arid and thus relevant regions of the US may be near maximal expansion. Thus when the USGS Water Summary concludes that developed storage is only somewhat less than half the 1250 million acre-feet maximum, it fails to indicate that much of the yet-to-be-developed storage capacity is located in areas of relatively little need. Before turning to the statistical analysis of the relationship between storage and water use, it is useful to pause for a brief examination of some economic characteristics of the ‘market’ for water.6 Among its various uses, only a small part—residential use—is ‘end use’. The rest, almost 95%, is for intermediate use, such as irrigation, thermo, and industrial. But the allocation among these uses is important, because while the ‘end use’ demand (as in residential) is highly inelastic, the demand for water—especially surface water—in its intermediate uses is more elastic, the most elastic being the demand for irrigation water (see Viessman and Welty, 1985, p. 136 and WRC, 1976). In the case of irrigation, elasticity is relatively large because substitutes are available: in the extreme, ground water can be used, the crop mix can be changed, dry land farming can be instituted or crops can be grown elsewhere. In the case of thermo, recycling and other modern cooling techniques can substantially reduce water use. On the side of supply, most thermo water is ‘self supplied’ meaning that it is directly withdrawn from a stream (or reservoir). Irrigation water is, as 5 As the reservoir capacity-to-renewable water supply (a euphemism for stream flow) ratio increases, so does surface evaporation. The result is that ‘safe yield’ may actually decrease as reservoir capacity increases. This phenomenon is reported to kick in when the ratio is in the range 160–420 (USGS National Water Summary, 1983). By 1980, this ratio had been reached in some of the South-western Regions. 6 The term market is only loosely adaptable to the water economy: because of the nature of property rights in water, and because third party impacts are typically important and complicated, all of which makes for extraordinarily high transactions costs, the evolution of an efficient market in water may not occur under any circumstance (see Colby, B., in Hall, 1996, pp. 211–223).
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
will be shown presently, most importantly connected to reservoir storage. Water for hydroelectric power is generally an in stream use; such power can be generated from run-of-the-river (natural) facilities or else artificially by means of dams and reservoirs. 3. Storage capacity and the uses of water: A statistical analysis With these basic facts and figures in hand, we are now in position to examine the statistical relationship between storage capacity and the various uses of water. Because some of the data are available across water resource regions while other data are in the form of country-wide time series, both sources are used in our analysis, albeit with different specification of the two models by reason of data availability. First, we look at quinquennial data spanning the period 1950– 1990. Table 2 shows estimates calculated by means of three-stage least-squares of a system of equations relating water withdrawals to storage, water utilization, and a time trend to measure the secular change in the technology of water use.7 Because stream flow depends upon factors related to the hydrologic cycle and its year-to-year variations do not contain any trend or predictable pattern, the water supply variable consists of reservoir capacity only, which has grown along an approximate S curve during the time span under review (Solley, 1997). Storage coefficients are C(2), (6), (10), and (14), and the results suggest that only water withdrawn for irrigation purposes has a significant relationship with this variable. Of interest are the trend coefficients, which reflect the greater economies in the use of water in some of its purposes. In particular, the trend coefficients for thermo water and public supply water are negative and significant. 7
For the purpose of estimation, total withdrawals are divided into three parts: irrigation, thermo, and ‘other’. Estimating all three components as a system would not be valid, as the residuals would sum to one for each case. The introduction of the ‘hydro’ equation should alleviate the problem. Elsewhere, only n1 of the component parts are estimated in the same system.
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Because of the implicit simultaneity between water withdrawals and storage capacity, the threestage least-squares estimator was selected. The system was then re-estimated, this time with an additional equation granting explicit recognition to this simultaneity. The results preserve the findings of Table 2 and reinforce the conclusion that irrigation is most significantly associated with storage capacity. An alternative model, based upon the cross section of the 18 water resource regions located in the conterminous US, confirms the unique relationship between irrigation withdrawals and storage. Table 3 reports estimates from a system which relates withdrawals for a given purpose to storage capacity and to withdrawals for competing purposes. While the OLS method is not designed to address the simultaneity inherent in the relationship (and even less to include it explicitly), the results nevertheless bear a strong resemblance to the time series model, particularly insofar as the irrigation-storage nexus is concerned. 3SLS estimates shown in Table 4 confirm the results, but the R2 coefficient of the last equation, which makes the simultaneity explicit, tends to blow up and this renders the system difficult to interpret. The model reported in Table 4 is closer in structure to the time-series model of Table 2. But the model of Table 3, when re-estimated using 3SLS (not shown here), produces qualitatively similar results: the estimates’ significance and signs are preserved, but the last equation’s R2 blows up.
4. The sensitivity of water allocation to changes in water prices and costs Section 3 has established the unique importance of storage capacity in the provision of water for irrigation. In this section, we examine the effect of price and cost changes upon the allocation of water to its various uses. This is important because the vast investment in water storage capacity is affected by the choice of water usage, and a shift into or out of irrigation use is seen to have an impact upon storage capacity.
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A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
Table 2 Time series estimates of the relationship between water withdrawals and storage capacity Estimation method: iterative three-stage least-squares Included observations: 9 Total system (balanced) observations: 36 Instruments: C LSTOR LPOPUL LINDUSTR LAGR Convergence achieved after: 6 weight matricies, 7 total coefficient iterations
C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12) C(13) C(14) C(15) C(16) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
4.175939 0.602307 0.730595 0.059258 2.333425 0.689201 1.793792 0.251124 3.165310 0.284794 1.185960 0.005874 13.27240 0.080943 3.271302 0.074528
2.638713 0.089520 0.706086 0.077301 0.708652 0.384476 0.250481 0.028835 1.420814 0.529732 0.368348 0.030152 1.718318 0.068084 0.397428 0.019746 1.25E-13
1.582567 6.728151 1.034711 0.766584 3.292763 1.792572 7.161378 8.709150 2.227814 0.537619 3.219670 0.194798 7.724066 1.188857 8.231178 3.774418
0.1292 0.0000 0.3132 0.4523 0.0036 0.0882 0.0000 0.0000 0.0375 0.5968 0.0043 0.8475 0.0000 0.2484 0.0000 0.0012
Equation: LIRRIG=C(1)+C(2) LSTOR+C(3) LAGR+C(4) TIME Observations: 9 R-squared 0.962931 Adjusted R-squared 0.940690 S.E. of regression 0.039702 Durbin–Watson stat 2.045651 Equation: LTHERMWA=C(5)+C(6) LSTOR+C(7) LTHERMO+C(8) TIME Observations: 9 R-squared 0.997475 Adjusted R-squared 0.995960 S.E. of regression 0.036169 Durbin–Watson stat 2.975528 Equation: LHYDRO=C(9)+C(10) LSTOR+C(11) LHYDPOW+C(12) TIME Observations: 9 R-squared 0.958295 Adjusted R-squared 0.933272 S.E. of regression 0.101957 Durbin–Watson stat 1.901902 Equation: LPUBSUP=C(13)+C(14) LSTOR+C(15) LPOPUL+C(16) TIME Observations: 9 R-squared 0.998163 Adjusted R-squared 0.997060 S.E. of regression 0.018843 Durbin–Watson stat 2.393350 Abbreviations explained in the appendix.
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
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Table 3 Cross-section estimates of the relationship between withdrawals and storage Estimation method: least-squares Included observations: 18 Total system (balanced) observations: 90
C(1) C(2) C(3) C(12) C(13) C(14) C(30) C(31) C(32) C(40) C(41) C(42) C(50) C(51) C(52) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
6.392488 1.375310 0.463848 8.656637 0.061501 0.762606 4.201321 0.296335 0.230683 0.262335 0.005589 0.782232 0.146830 0.318125 0.152247
2.254135 0.451720 0.245936 0.794523 0.265288 0.149721 5.120155 0.828391 0.676403 1.611727 0.251475 0.186986 0.991940 0.093878 0.072727 2.368055
2.835894 3.044607 1.886050 10.89539 0.231825 5.093529 0.820546 0.357723 0.341044 0.162766 0.022224 4.183374 0.148024 3.388688 2.093390
0.0059 0.0032 0.0632 0.0000 0.8173 0.0000 0.4145 0.7216 0.7340 0.8711 0.9823 0.0001 0.8827 0.0011 0.0397
Equation: LIRR=C(1)+C(2) LSTOR+C(3) LTOTIRR Observations: 18 R-squared 0.421053 Adjusted R-squared 0.343860 S.E. of regression 1.849597 Equation: LHYDRO=C(12)+C(13) LSTOR+C(14) LRENOFF Observations: 18 R-squared 0.672306 Adjusted R-squared 0.628613 S.E. of regression 1.000408 Equation: LTHERMO=C(30)+C(31) LSTOR+C(32) LTOTHERM Observations: 18 R-squared 0.028885 Adjusted R-squared 0.100597 S.E. of regression 3.092154 Equation: LOTHER=C(40)+C(41) LSTOR+C(42) LTOTOTHE Observations: 18 R-squared 0.567486 Adjusted R-squared 0.509817 S.E. of regression 0.994453 Equation: LSTOR=C(50)+C(51) LIRR+C(52) LTHERMO Observations: 18 R-squared 0.445699 Adjusted R-squared 0.371792 S.E. of regression 0.804731
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A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
Table 4 Cross-section estimates of the relationship between withdrawals and storage Estimation method: iterative three-stage least-squares Included observations: 18 Total system (balanced) observations: 90 Instruments: C LRENEW LSTOR LPOPUL Convergence achieved after: 62 weight matricies, 63 total coefficient iterations
C(1) C(2) C(4) C(12) C(13) C(15) C(30) C(31) C(33) C(40) C(41) C(43) C(50) C(51) C(52) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
3.611449 1.041545 0.000934 1.746138 0.246503 1.183504 8.868614 0.127982 1.459733 2.210619 0.187133 0.982790 3.467217 0.960791 0.000224
2.808478 0.011806 0.383202 1.609486 0.278206 0.217528 3.312419 0.454959 0.299051 1.058944 0.139342 0.112385 2.643254 0.295565 0.083294 1.99E-07
1.285910 88.22531 0.002438 1.084904 0.886045 5.440691 2.677383 0.281305 4.881221 2.087570 1.342974 8.744816 1.311723 3.250689 0.002692
0.2024 0.0000 0.9981 0.2814 0.3784 0.0000 0.0091 0.7793 0.0000 0.0402 0.1833 0.0000 0.1936 0.0017 0.9979
Equation: LIRR=C(1)+C(2) LSTOR+C(4) LACRESIRR Observations: 18 R-squared 0.278164 Adjusted R-squared 0.181919 S.E. of regression 2.065271 Equation: LHYDRO=C(12)+C(13) LSTOR+C(15) LPOWER Observations: 18 R-squared 0.576391 Adjusted R-squared 0.519910 S.E. of regression 1.137431 Equation: LTHERMO=C(30)+C(31) LSTOR+C(33) LTHERPOWER Observations: 18 R-squared 0.554641 Adjusted R-squared 0.495259 S.E. of regression 2.094022 Equation: LOTHER=C(40)+C(41) LSTOR+C(43) LPOPUL Observations: 18 R-squared 0.823649 Adjusted R-squared 0.800135 S.E. of regression 0.634999 Equation: LSTOR=C(50)+C(51) LIRR+C(52) LTHERMO Observations: 18 R-squared 2.365540 Adjusted R-squared 2.814278 S.E. of regression 1.982920
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The price of water in its various uses shows considerable variation. In its 1966 report Farm and Ranch Irrigation Survey (FRIS, 1996) the Census of Agriculture reports an average price of $16.23 per acre-foot of water in the 18 conterminous Water Resource Regions. An earlier survey of residential water prices (Van der Leeden et al., 1991) suggests a price of $477 per acre-foot for that use. One published demand equation for water lists price as a determinant of residential water demand but not for other uses (Chesnutt and McSpadden, 1994). Another attempt includes price variables for both residential and irrigation uses (WRC, Water Use Price/Cost analysis, 1976). Price elasticities for residential water are reported in Hall (1996) and irrigation water demand elasticites are available in WRC (1996).8 Using these prices and elasticities and a method suggested by Pyndick and Rubinfeld (1992, pp. 45–48), we construct demand curves for residential and irrigation water (Table 5).9 What is obvious from these calculations is that as the allocation of water becomes more rational, the quantity demanded of residential water is likely to change but little or increase, while that for irrigation water is likely to fall drastically. The finding that the choice of water uses is responsive to price changes is confirmed by regression results across the Water Resources Regions. Table 6 shows convincingly that a rise (fall) in the price of irrigation water causes a fall (rise) in withdrawals for irrigation and a rise (fall) in the withdrawal of 8
Agricultural (irrigation) water demand elasticity is also reported in CALFED Bay-Delta Program (October 1999). That elasticity is much lower than the 0.9 used here, but it refers to the special case of Central California, where high-valued crops, such as fruits and vegetables, are less impacted by changes in water price. Low-valued yet extensive crops, such as hay, register water demand elasticities as high as 1.89! (see Draft PEIS Central Valley Project Improvement Act, September 1997, A-11). WRC had national coverage and the elasticity implied by its analysis was adopted here. 9 The demand curves constructed in Table 5 are linear. Conceivably, a constant elasticity formulation may be more realistic for drinking water, while a linear one is more appropriate for irrigation water. For constant elasticity estimates for both types of demand see CALFED Bay-Delta Program (October 1999). Over the relevant range of values, the distinction may be trivial.
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Table 5 Demand for irrigation and residential water Irrigation Elasticity: 0.9* Price*: $16.23 Quantity: 134,000 bg/d (1995)
Residential Elasticity: 0.25 Price*: $500 Quantity: 22,700 bg/d (1995)
Demand curve for residential water: or: Demand curve for irrigation water:
Q=28,374–11.348P P=$2500.35–$0.088Q
Q=255,725–7,500P or: P=$34.10–$0.000133Q Assuming a marginal cost of $30 per unit, a price discriminating monopolist would seek the following price-output combinations: Residential: Price: $1265.17 per Quantity: 14,036 units unit, Irrigation: Price: $32.05 per unit, Quantity: 15,413.5 units With marginal cost pricing:a when MC=$30, Residential: Price: $30 per unit Quantity: 28,072 units Irrigation: Price: $30 per unit Quantity: 30,827 units When MC=$100, Residential: Price: $100 per unit Irrigation: Price: $100 per unit
Quantity: 27,277 units Quantity: 0 units
a
The calculations assume equal production costs for the various uses of water. This may be an oversimplification. Where reservoirs are concerned specifically, the cost may be determined by the frequency of cycling. In this connection, Public supply water is cycled more frequently than irrigation water. The unit cost attributable to reservoir storage is thus higher for irrigation water (Hirshleifer et al., 1960).
water for other uses (the one included in the model is ‘other’ uses which includes importantly residential use; expanding the model to include thermo preserves the findings). These findings are confirmed by joint estimation using iterative 3SLS. Both single equation and system estimation methods confirm our expectations: the price of water is an important determinant of its use.
5. Concluding remarks This paper has documented the likely effect of prospective changes in the water economy of the US upon the uses of water and, in particular,
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A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
Table 6 Impact of water price upon water uses: OLS Estimation method: least-squares Included observations: 18 Total system (balanced) observations: 36
C(1) C(2) C(3) C(4) C(5) C(6) C(10) C(11) C(12) C(13) C(14) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
4.618493 2.003065 1.234509 2.727642 0.512372 0.982159 0.546992 0.258107 1.470809 0.477940 0.314206
2.012737 0.897713 0.356001 0.772917 0.182571 0.297624 1.491230 0.112949 0.506942 0.075122 0.243331 0.260069
2.294633 2.231297 3.467709 3.529024 2.806430 3.299995 0.366806 2.285160 2.901335 6.362143 1.291269
0.0304 0.0349 0.0019 0.0016 0.0096 0.0029 0.7169 0.0311 0.0076 0.0000 0.2084
Equation: LIRR=C(1)+C(2) LCOST94+C(3) LOTHER+C(4) DUMMY+C(5) LTHERMO+C(6) LSTOR Observations: 18 R-squared 0.837687 Adjusted R-squared 0.770056 S.E. of regression 1.094939 Equation: LOTHER=C(10)+C(11) LIRR+C(12) LCOST94+C(13) LTHERMO+C(14) LSTOR Observations: 18 R-squared 0.801284 Adjusted R-squared 0.740141 S.E. of regression 0.724059
the utilization of storage capacity. These expected changes have provided the basis for innumerable studies, and water management has evolved into a sophisticated science. But the emphasis in water management has remained constrained by two limitations: The emphasis upon regional solutions, and the relative lack of attention to the effects of new water management proposals upon the already existing water provision infrastructure. Water management, as any profession, is molded by trends and prevailing attitudes.10 10
In this connection, see Alaskan Water for California? (OTA, 1992, p. 11.) ‘‘although the current trend is away from interregional water transfers, at some point, then, such schemes could again receive serious attention. A subsea pipeline to transport water from Alaska, diverting some water from the Columbia River, or various proposals for diverting water from Western Canada’s riversy..might then be considered.’’
What is implied by our findings here is that in making the cost–benefit calculations underlying the choice of water policy options, particularly when choosing between storage and transfer, managers should pay greater attention to the write-offs on already installed capacity—particularly storage capacity—resulting from their decisions. It has been estimated that a mere 10% reduction in water devoted to irrigation could double the amount available for municipal and industrial uses.11 With the negative effect of higher water prices upon irrigational use (shown in Section 4), it would then remain a matter of merely transferring that water to its new use. Past investment in reservoir capacity would not then 11 A New Era For Irrigation (National Research Council, 1996, p. 68).
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
have to be written off, and the construction of new reservoirs would become less important as a water management option.12
Appendix. Explanation of abbreviations
Abbreviation
Data set
Variable
LCOST94 LIRR LOTHER
CS CS CS
LTHERMO DUMMY
CS CS
LSTOR LTOTIRR LHYDRO LRENOFF
CS CS CS CS
LTOTHERM
CS
LTOTOTHE
CS
LACRESSIR LPOWER LTHERPOWER LPOPUL LRENEW
CS CS CS CS CS
Price of irrigation water (per a-f) Log of water for irrig. In mg/d Log of withdrawals other than irr and thermo Log of water for thermo plants 1 for eight Eastern Regions 0 otherwise Log of storage capacity in bg Log of total withdrawal less irrig. Log of water for hydropower Log of renewable water supply less off stream withdrawals Log of total withdrawals less water for thermo Log of total withdrawals less water for ‘other’ uses Log of acres irrigated Log of hydropower generated Log of thermopower generated Log of Population Log of renewable water supply
LIRRIG LTHERMWA LTHERMO LHYDRO LHYDPOW LPOPUL LPUBSUP
TS TS TS TS TS TS TS
LSTOR
TS
Log of Log of Log of Log of Log of Log of Log of supply Log of
water for irrigation water for thermo thermopower generated water for hydropower hydropower generated population water withdrawn for public storage capacity
12 But see the January 2001 Press Release of the Metropolitan Water District of Southern California: ‘‘y..In the ten years since the state’s last drought, Southern California has invested billions of dollars in conservation, recycling, storage and infrastructure programs. Foremost among the new safeguards is Diamond Valley Lake, the 4500 acre reservoir in southwest Riverside County. Capable of holding 800,000 acre-feet, the reservoir was dedicated last Marchy.’’.(mwh2o.com). To meet its anticipated future needs, by contrast, New York City is building Water Tunnel No. 3, a 60 mile project described as ‘‘by far the largest construction project in New York City’s history’’ (ita-aites.org/tribune8).
LAGR LINDUSTR
TS TS
TIME
TS
11 Log of index of agricultural output Log of index of industrial production Time trend (T ¼ 1; 5; 10; 15; y)
CS—cross-section of Water Resource Regions (usually 18 observations). TS—time series of quinquennial observations 1950–1990 (9 observations).
References Annual Energy Review, 1991. Energy Administration, US Department of Energy, Washington, DC, June 1992. Blinder, A., Maccini, L.J., 1991. The resurgence of inventory research: What have we learned? Journal of Economic Surveys 5 (4), 292–327. California Statistical Abstract, 1999. Senate of the State of California. Central Valley Project Improvement Act PEIS, 1997. US Department of the Interior, Bureau of Reclamation, Sacramento, CA. Chesnutt, T.W., McSpadden, C.S., 1994. Putting the Pieces Together: Decision Support for Integrated Resource Planning Using IRPSIM. A&N Technical Services Inc., April. Economic Evaluation of Water Management Alternatives: Screening Analysis and Scenario Development, 1999. CALFED Bay-Delta Program, October, 1999. Economic Report of the President, 1995. USGPO, Washington, DC. FRIS, 1996. 1994 Farm and Ranch Irrigation Survey, 1992. Census of Agriculture, US Department of Commerce, Washington, DC, August 1996. Graczyk, D.J., Krug, W.R., Gebert, W.A., 1986. A History of Annual Streamflows from the 21 Water-Resource Regions in the US and Puerto Rico, 151-1983. Open-File Report 86128 Department of the Interior, US Geological Survey, Madison. Hall, D.C. (Ed.), 1996. Advances in the Economics of Environmental Resources, Vol 1: Marginal Cost Rate Design and Wholesale Water Markets. JAI Press, Greenwich, CT. Hirshleifer, J., DeHaven, J.C., Milliman, J.W., 1960. Water Supply, Economics, Technology, and Policy. The University of Chicago Press, Chicago, IL. Lund, J.R., Guzman, J., 1999. Derived operating rules for reservoirs in series and in parallel. Journal of Water Resources Planning and Management 125 (3), 134–154. National Research Council, 1996. A New Era for Irrigation. National Academy Press, Washington, DC. National Water Summary, 1983. Hydrologic Events and Issues, US Geological Survey, Water Supply Paper 2250, USGPO, Washington, DC.
12
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OTA, 1992. Alaskan Water for California? The Subsea Pipeline Option. Office of Technology Assessment, Congress of the United States, Washington, DC, January. Pyndick, R.S., Rubinfeld, D., 1992. Microeconomics, 4th Edition. Prentice-Hall, Upper Saddle River, NJ. Solley, W.B., 1997. Estimates of Water Use in the Western United States. Report to the Western Water Policy Review Advisory Committee. Solley, W.B., Pierce, R.R., Perlman, H.A., 1998. Estimated Use of Water in the US in 1995. US Geological Survey, Circular 1200. Spulber, N., Sabbaghi, A., 1998. Economics of Water Resources: from Regulation to Privatization, 2nd Edition. Kluwer Academic Publishers, Boston.
USDA, 1997. Agricultural Resources and Environmental Indicators 1996–97, Agricultural Handbook #712, US Department of Agriculture, Washington, DC. Van der Leeden, F., Troise, F.L., Todd, D.K., 1991. The Water Encyclopedia. Lewis Publishers, Chelsea, MI. Viessman Jr., W., Welty, C., 1985. Water Management: Technology and Institutions. Harper & Row, New York. Water Use Price/Cost Sensitivity Analysis, 1976. Appendix J., US Water Resources Council: Nationwide Analysis Report, Washington, DC. Williams, J.C., Wright, B.D., 1991. Storage and Commodity Markets. Cambridge University Press, Cambridge. WRC, 1978. The Nation’s Water Resources, 1975–2000, Vol. 2: Water Quantity, Quality, and Related Water Considerations, US Water Resources Council, (WRC) Washington, DC, December.
Storage capacity and water use in the 21 water-resource regions of the United States geological survey Andrew Stern Department of Economics, CSULB, Long Beach, CA 90840, USA
Abstract The development of reservoir storage capacity has been most closely connected to water demand for irrigation purposes. But water demand for this purpose is relatively elastic, while that for other uses is much less so. A model estimated here suggests also a positive relation between the price of irrigation water and an aggregate comprising mainly urban water use. As the pressure of rising demand against a relatively constant supply drives water prices upward, irrigation is thus likely to suffer in comparison to urban demand, and this should free up existing storage capacity for alternative uses. By implication, water managers should take this eventuality into account when formulating water resource strategies to meet future water needs. r 2002 Elsevier Science B.V. All rights reserved. Keywords: Water; Storage; Government policy
1. Introduction The factors propelling the demand for water in the United States have been growing at a steady rate, but the supply of water has increased very little during the past 20 years. One effect of the resulting imbalance has been the recognition that water is an economic rather than a free good, and that its allocation, in order to be efficient, must favor its highest valued uses1. Prior to the 1980s the preponderant manner of ‘producing’ water (increasing its supply) outside of the hydrologic cycle and apart (or in conjunction with) the greater use of ground water was by way of the develop1 We shall, in what follows, ignore qualitative differences between the various ‘waters’ in use (but see Spulber and Sabbaghi (1998) for a theoretical discussion of these differences). We might assume in this instance that the desired quality can be achieved by appropriate treatment, and that the cost of such treatment does not vary between qualities.
ment of storage capacity, and during the three decades spanning 1950–1980 most of this development took place in the western part of the US, specifically in connection with the effort to promote agricultural irrigation in semi-arid regions.2 Because the demand for irrigation water is relatively elastic while that for residential (end use) purposes is highly inelastic, it follows that the continuing growth of urban population and industrial activity will steadily shift water use 2
It should be noted that the use of stored water is technically most closely associated with irrigation. If precipitation occurs during the winter months while irrigation needs arise during the summer, the availability of reservoir storage becomes essential. By the same token, substantial year to year variation in stream flow can also be regulated by the development of reservoirs. In other off-stream uses of water, the seasonal pattern is much less pronounced. Historically, cities have not depended upon rain to provide drinking water. Instead, they have grown around springs, lakes, and rivers. The term ‘drought’ is almost exclusively associated with agriculture.
0925-5273/02/$ - see front matter r 2002 Elsevier Science B.V. All rights reserved. PII: S 0 9 2 5 - 5 2 7 3 ( 0 2 ) 0 0 2 9 5 - 5
2
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
away from irrigation3 and thus make redundant some of the storage capacity developed over the years. But reservoirs are inherently adaptable, and what our findings suggest is that in planning infrastructure to meet future water needs expansion of the means of effectuating water transfers should take precedence over increases in storage capacity in the composition of water resources portfolios. Our findings are presented in the following order: In Section 2, we document the nature of trends in the factors underlying the demand, supply, and use of water in the US. This is followed by a discussion of the limits to reservoir development, sources and uses of water, possibilities for substitution, and the resulting elasticities. In Section 3, we present a statistical analysis which reveals the singular importance of storage capacity as a determinant of water for irrigation purposes. Section 4 looks at alternative pricing schemes and their effects upon the allocation of water use for residential and irrigation purposes. This also includes a statistical analysis of the effects of actual prices from a cross-sectional model. A review of the findings and their implication for aggregate water management concludes the paper.
2. Trends in the relevant variables, the characteristics of stream flows, and the limits to reservoir development Off-stream withdrawals of water in the US satisfy three broad purposes: the cooling of thermoelectric power plants, the irrigation of agricultural crops, and other uses, chief among which are public supply, which essentially satisfies 3 The price of irrigation water is likely to increase for yet another reason. The developmental history of water storage in the US is a history of both direct and indirect Federal involvement and both overt and implicit subsidies (USDA, 1997, Agricultural Resources etc., p. 77). For instance, in California it costs the government $42 to produce water sold to irrigators for much less. (Spulber and Sabbaghi, 1998, p. 289). Federal irrigation subsidies via the Bureau of Reclamation have been estimated to exceed 86% of construction costs on average (National Research Council, 1996, p. 69). But ever since 1992 the Omnibus Water Act has tried to make water supply more responsive to cost (Spulber and Sabbaghi, 1998, p. 289).
residential and commercial uses4. In-stream uses— those that do not require diversion and therefore compete with off-stream withdrawals—include the generation of hydroelectric power, the use of waterways for navigation, recreation and wildlife preservation. On the surface, a general model of water use should include all the above sectors. Unfortunately, however, some of the in-stream uses are almost impossible to quantify by traditional methods. In fact, the only in-stream use that is thus quantifiable is hydroelectric power production, and this therefore is the sector that will represent all in-stream uses in what follows. This approach is all the more reasonable since stream flow availability for the other in-stream uses is governed by law and regulation rather than by the interaction of supply and demand. Over the years, the dynamics of the water economy has evolved in a somewhat paradoxical pattern. As Table 1 shows, the factors propelling demand, such as population growth and various measures of output, have continued to grow. Yet water utilization for most purposes has leveled off since 1980. The only category that shows an increase during this period is public supply, a great part of which consists of residential and commercial water use. The leveling off of other water uses since 1980 has, over time, become the theme of a standard set of justifications (Solley et al., 1998, p. 64); these include: the decline in the expansion of irrigation systems and increases in energy development after 1980, the development of more efficient irrigation techniques, the increased cost of energy, the increased competition for water and a downturn in the farm economy, the transition from water supply to water demand management, new technologies in the industrial sector, increased water recycling, and the increased awareness of the public of the need for water conservation. It is of course the increased competition for water, its origins and prospective impacts that form the core of the present paper. While the relevance of the trends reported in Table 1 is for the most part self-evident, there is yet a need to dwell on the role of storage capacity as a 4 In addition to these, ‘other’ uses also include livestock, industrial, and mining withdrawals. These are relatively small.
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3
Table 1 Trends in water withdrawals and related variables: 1950–90 Year variable
1950
1955
1960
1965
1970
1975
1980
1985
1990
Factors affecting demand for water Population (millions) Agric. prod. (1982=100) Industr. prod. (1987=100)
150.7 46 25.8
164 54 33.7
179.3 60 38.1
193.8 67 51.7
205.9 72 61.4
216.4 82 66.3
229.6 90 84.1
242.4 105 94.4
252.3 112 106
Hydro power (quad.BTU) Thermo power (b/kWh) Hydro power (b/kWh)
1.42 233 96
1.36 434 113
1.61 610 146
2.06 861 194
2.63 1284 248
3.15 1618 300
2.9 2010 276
2.94 2189 281
2.93 2528 280
3050
3290
Instream use of water Hydro water (bg/d) Offstream uses of water Industr. water (bg/d) Irrigation water (bg/d) Thermo water (bg/d) Public supply water (bg/d) Factors affecting supply of water Storage capacity(macre-feet)
1100
1500
2000
2300
2800
3300
3300
37 89 40 14
39 110 72 17
38 110 100 21
46 120 130 24
47 130 170 27
45 140 200 29
45 150 210 34
30.5 137 187 36.5
29.9 137 195 38.5
165
235
250
300
375
425
432
440
450
Sources: Water withdrawals from Solley et al., 1998 in billions of gallons per day hydro and thermo power from Annual Energy Review, 1991 in quadr. Brit. Thermal Units or billions of kilowatt hour. Population in millions from Solley et al, 1998. Agricultural production and Industrial Production indexes from Economic Report of the President, 1995. Water storage capacity estimated from Solley, 1997. In millions of acre-feet (1 acre-foot=325,851 gallons. 1 mg/d=1120 acre-feet per year).
measure of ‘water supply’. Storage of a commodity for the purpose of subsequent use is the theme of inventory theory. In manufacturing and trade, inventories are held for ‘production smoothing’ and ‘buffer stock’ motives (Blinder and Maccini, 1991). In the case of storable commodities (which may be held for their own sake or as inventories of raw materials in the production process) the decision to store is typically governed by ‘arbitrage equations’ in which the spread between the spot price and the discounted expected future price is compared to storage costs (Williams and Wright, 1991). The storage of water is unique in that ‘price’ has not been, at least up to the present, a determinant of the decision to store. More relevant is the concept of ‘safe yield’ of a reservoir, in which the role of storage is to provide a reliable supply of water. This need may arise because of the variability of precipitation and/or stream flow, because of the variability of demand, or because of
both. By making up for these vagaries in stream flow and demand, reservoir capacity is seen to effectively ‘produce’ water (the term used in Hirshleifer et al., 1960). The variability of stream flow in the 21 water regions of the USGS is considerable. The coefficient of variation of annual stream flow ranges from a low of 19% in the Great Lakes and Pacific Northwest Regions to a high of almost 80% in the Lower Colorado Region. These flows have been estimated by government hydrologists over a period of many years, and several measures of stream flow and variability have been compiled.. Annual data on year to year variability have been collected by Graczyk et al. (1986) while measures of within year variability are reported in the WRC report (1978). The simultaneity between stream flow variability and storage capacity makes it difficult to model the relationship between these two variables: variable stream flow requires storage for
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regulation, while regulation reduces the variability of stream flow. Ignoring this inherent simultaneity, OLS estimates of the regression of variation upon storage capacity, providing a dummy variable to distinguish between the Eastern (the first eight) and the Western Regions, reveal a significant relationship which is insensitive to the choice of additional independent variables in the regression equation. There remain two issues to be dealt with in this section. First, water reservoirs may be either multipurpose or else they may be dedicated to a specific use. This heterogeneity may bias calculations, and we therefore try to assess its importance. Second, after decades of development, water storage capacity may be approaching its physical limits. If this is so, then we can better assess the future of water supply in the US. A partial measure of the first item is obtained from reservoir statistics for the State of California, which is representative of an area where water is plentiful but unevenly distributed both in timing and location. Of the 102 largest dams/reservoirs in the State, 75 are ‘multipurpose’ by initial design, the remaining being dedicated to specific purposes (California Statistical Abstract, 1999). Irrigation represents a preponderant use of the multipurpose reservoirs in the California sample. This characteristic is generally true of the larger reservoirs in the Western Water Resource Regions of the US. But modern techniques of storage utilization permit the formation of systems of reservoirs (Lund and Guzman, 1999) in which the original purpose becomes irrelevant. An example of such multiple use would be a reservoir/dam dedicated to hydropower which produces a flow sufficient to provide for irrigation downstream from the power plant (Viessman and Welty, 1985). The second issue, namely the physical limitations on reservoir development, has been a subject of inquiry since the 1970s. ‘Mass curve’ analysis (Viessman and Welty, 1985) suggests that the level of storage capacity needed to maintain water withdrawals at their average level was achieved by 1980 (both in the range of 400 bg/d). By that time, the ratio of storage to renewable water supply had reached near-optimal levels in some of the irrigation-intensive regions of the South
Western US. (USGS National Water Summary, 1983)5 Another measure of the extent of development is reservoir surface area per acre of land. This measure also suggests that reservoir capacity in the most arid and thus relevant regions of the US may be near maximal expansion. Thus when the USGS Water Summary concludes that developed storage is only somewhat less than half the 1250 million acre-feet maximum, it fails to indicate that much of the yet-to-be-developed storage capacity is located in areas of relatively little need. Before turning to the statistical analysis of the relationship between storage and water use, it is useful to pause for a brief examination of some economic characteristics of the ‘market’ for water.6 Among its various uses, only a small part—residential use—is ‘end use’. The rest, almost 95%, is for intermediate use, such as irrigation, thermo, and industrial. But the allocation among these uses is important, because while the ‘end use’ demand (as in residential) is highly inelastic, the demand for water—especially surface water—in its intermediate uses is more elastic, the most elastic being the demand for irrigation water (see Viessman and Welty, 1985, p. 136 and WRC, 1976). In the case of irrigation, elasticity is relatively large because substitutes are available: in the extreme, ground water can be used, the crop mix can be changed, dry land farming can be instituted or crops can be grown elsewhere. In the case of thermo, recycling and other modern cooling techniques can substantially reduce water use. On the side of supply, most thermo water is ‘self supplied’ meaning that it is directly withdrawn from a stream (or reservoir). Irrigation water is, as 5 As the reservoir capacity-to-renewable water supply (a euphemism for stream flow) ratio increases, so does surface evaporation. The result is that ‘safe yield’ may actually decrease as reservoir capacity increases. This phenomenon is reported to kick in when the ratio is in the range 160–420 (USGS National Water Summary, 1983). By 1980, this ratio had been reached in some of the South-western Regions. 6 The term market is only loosely adaptable to the water economy: because of the nature of property rights in water, and because third party impacts are typically important and complicated, all of which makes for extraordinarily high transactions costs, the evolution of an efficient market in water may not occur under any circumstance (see Colby, B., in Hall, 1996, pp. 211–223).
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will be shown presently, most importantly connected to reservoir storage. Water for hydroelectric power is generally an in stream use; such power can be generated from run-of-the-river (natural) facilities or else artificially by means of dams and reservoirs. 3. Storage capacity and the uses of water: A statistical analysis With these basic facts and figures in hand, we are now in position to examine the statistical relationship between storage capacity and the various uses of water. Because some of the data are available across water resource regions while other data are in the form of country-wide time series, both sources are used in our analysis, albeit with different specification of the two models by reason of data availability. First, we look at quinquennial data spanning the period 1950– 1990. Table 2 shows estimates calculated by means of three-stage least-squares of a system of equations relating water withdrawals to storage, water utilization, and a time trend to measure the secular change in the technology of water use.7 Because stream flow depends upon factors related to the hydrologic cycle and its year-to-year variations do not contain any trend or predictable pattern, the water supply variable consists of reservoir capacity only, which has grown along an approximate S curve during the time span under review (Solley, 1997). Storage coefficients are C(2), (6), (10), and (14), and the results suggest that only water withdrawn for irrigation purposes has a significant relationship with this variable. Of interest are the trend coefficients, which reflect the greater economies in the use of water in some of its purposes. In particular, the trend coefficients for thermo water and public supply water are negative and significant. 7
For the purpose of estimation, total withdrawals are divided into three parts: irrigation, thermo, and ‘other’. Estimating all three components as a system would not be valid, as the residuals would sum to one for each case. The introduction of the ‘hydro’ equation should alleviate the problem. Elsewhere, only n1 of the component parts are estimated in the same system.
5
Because of the implicit simultaneity between water withdrawals and storage capacity, the threestage least-squares estimator was selected. The system was then re-estimated, this time with an additional equation granting explicit recognition to this simultaneity. The results preserve the findings of Table 2 and reinforce the conclusion that irrigation is most significantly associated with storage capacity. An alternative model, based upon the cross section of the 18 water resource regions located in the conterminous US, confirms the unique relationship between irrigation withdrawals and storage. Table 3 reports estimates from a system which relates withdrawals for a given purpose to storage capacity and to withdrawals for competing purposes. While the OLS method is not designed to address the simultaneity inherent in the relationship (and even less to include it explicitly), the results nevertheless bear a strong resemblance to the time series model, particularly insofar as the irrigation-storage nexus is concerned. 3SLS estimates shown in Table 4 confirm the results, but the R2 coefficient of the last equation, which makes the simultaneity explicit, tends to blow up and this renders the system difficult to interpret. The model reported in Table 4 is closer in structure to the time-series model of Table 2. But the model of Table 3, when re-estimated using 3SLS (not shown here), produces qualitatively similar results: the estimates’ significance and signs are preserved, but the last equation’s R2 blows up.
4. The sensitivity of water allocation to changes in water prices and costs Section 3 has established the unique importance of storage capacity in the provision of water for irrigation. In this section, we examine the effect of price and cost changes upon the allocation of water to its various uses. This is important because the vast investment in water storage capacity is affected by the choice of water usage, and a shift into or out of irrigation use is seen to have an impact upon storage capacity.
6
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Table 2 Time series estimates of the relationship between water withdrawals and storage capacity Estimation method: iterative three-stage least-squares Included observations: 9 Total system (balanced) observations: 36 Instruments: C LSTOR LPOPUL LINDUSTR LAGR Convergence achieved after: 6 weight matricies, 7 total coefficient iterations
C(1) C(2) C(3) C(4) C(5) C(6) C(7) C(8) C(9) C(10) C(11) C(12) C(13) C(14) C(15) C(16) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
4.175939 0.602307 0.730595 0.059258 2.333425 0.689201 1.793792 0.251124 3.165310 0.284794 1.185960 0.005874 13.27240 0.080943 3.271302 0.074528
2.638713 0.089520 0.706086 0.077301 0.708652 0.384476 0.250481 0.028835 1.420814 0.529732 0.368348 0.030152 1.718318 0.068084 0.397428 0.019746 1.25E-13
1.582567 6.728151 1.034711 0.766584 3.292763 1.792572 7.161378 8.709150 2.227814 0.537619 3.219670 0.194798 7.724066 1.188857 8.231178 3.774418
0.1292 0.0000 0.3132 0.4523 0.0036 0.0882 0.0000 0.0000 0.0375 0.5968 0.0043 0.8475 0.0000 0.2484 0.0000 0.0012
Equation: LIRRIG=C(1)+C(2) LSTOR+C(3) LAGR+C(4) TIME Observations: 9 R-squared 0.962931 Adjusted R-squared 0.940690 S.E. of regression 0.039702 Durbin–Watson stat 2.045651 Equation: LTHERMWA=C(5)+C(6) LSTOR+C(7) LTHERMO+C(8) TIME Observations: 9 R-squared 0.997475 Adjusted R-squared 0.995960 S.E. of regression 0.036169 Durbin–Watson stat 2.975528 Equation: LHYDRO=C(9)+C(10) LSTOR+C(11) LHYDPOW+C(12) TIME Observations: 9 R-squared 0.958295 Adjusted R-squared 0.933272 S.E. of regression 0.101957 Durbin–Watson stat 1.901902 Equation: LPUBSUP=C(13)+C(14) LSTOR+C(15) LPOPUL+C(16) TIME Observations: 9 R-squared 0.998163 Adjusted R-squared 0.997060 S.E. of regression 0.018843 Durbin–Watson stat 2.393350 Abbreviations explained in the appendix.
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
7
Table 3 Cross-section estimates of the relationship between withdrawals and storage Estimation method: least-squares Included observations: 18 Total system (balanced) observations: 90
C(1) C(2) C(3) C(12) C(13) C(14) C(30) C(31) C(32) C(40) C(41) C(42) C(50) C(51) C(52) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
6.392488 1.375310 0.463848 8.656637 0.061501 0.762606 4.201321 0.296335 0.230683 0.262335 0.005589 0.782232 0.146830 0.318125 0.152247
2.254135 0.451720 0.245936 0.794523 0.265288 0.149721 5.120155 0.828391 0.676403 1.611727 0.251475 0.186986 0.991940 0.093878 0.072727 2.368055
2.835894 3.044607 1.886050 10.89539 0.231825 5.093529 0.820546 0.357723 0.341044 0.162766 0.022224 4.183374 0.148024 3.388688 2.093390
0.0059 0.0032 0.0632 0.0000 0.8173 0.0000 0.4145 0.7216 0.7340 0.8711 0.9823 0.0001 0.8827 0.0011 0.0397
Equation: LIRR=C(1)+C(2) LSTOR+C(3) LTOTIRR Observations: 18 R-squared 0.421053 Adjusted R-squared 0.343860 S.E. of regression 1.849597 Equation: LHYDRO=C(12)+C(13) LSTOR+C(14) LRENOFF Observations: 18 R-squared 0.672306 Adjusted R-squared 0.628613 S.E. of regression 1.000408 Equation: LTHERMO=C(30)+C(31) LSTOR+C(32) LTOTHERM Observations: 18 R-squared 0.028885 Adjusted R-squared 0.100597 S.E. of regression 3.092154 Equation: LOTHER=C(40)+C(41) LSTOR+C(42) LTOTOTHE Observations: 18 R-squared 0.567486 Adjusted R-squared 0.509817 S.E. of regression 0.994453 Equation: LSTOR=C(50)+C(51) LIRR+C(52) LTHERMO Observations: 18 R-squared 0.445699 Adjusted R-squared 0.371792 S.E. of regression 0.804731
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Table 4 Cross-section estimates of the relationship between withdrawals and storage Estimation method: iterative three-stage least-squares Included observations: 18 Total system (balanced) observations: 90 Instruments: C LRENEW LSTOR LPOPUL Convergence achieved after: 62 weight matricies, 63 total coefficient iterations
C(1) C(2) C(4) C(12) C(13) C(15) C(30) C(31) C(33) C(40) C(41) C(43) C(50) C(51) C(52) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
3.611449 1.041545 0.000934 1.746138 0.246503 1.183504 8.868614 0.127982 1.459733 2.210619 0.187133 0.982790 3.467217 0.960791 0.000224
2.808478 0.011806 0.383202 1.609486 0.278206 0.217528 3.312419 0.454959 0.299051 1.058944 0.139342 0.112385 2.643254 0.295565 0.083294 1.99E-07
1.285910 88.22531 0.002438 1.084904 0.886045 5.440691 2.677383 0.281305 4.881221 2.087570 1.342974 8.744816 1.311723 3.250689 0.002692
0.2024 0.0000 0.9981 0.2814 0.3784 0.0000 0.0091 0.7793 0.0000 0.0402 0.1833 0.0000 0.1936 0.0017 0.9979
Equation: LIRR=C(1)+C(2) LSTOR+C(4) LACRESIRR Observations: 18 R-squared 0.278164 Adjusted R-squared 0.181919 S.E. of regression 2.065271 Equation: LHYDRO=C(12)+C(13) LSTOR+C(15) LPOWER Observations: 18 R-squared 0.576391 Adjusted R-squared 0.519910 S.E. of regression 1.137431 Equation: LTHERMO=C(30)+C(31) LSTOR+C(33) LTHERPOWER Observations: 18 R-squared 0.554641 Adjusted R-squared 0.495259 S.E. of regression 2.094022 Equation: LOTHER=C(40)+C(41) LSTOR+C(43) LPOPUL Observations: 18 R-squared 0.823649 Adjusted R-squared 0.800135 S.E. of regression 0.634999 Equation: LSTOR=C(50)+C(51) LIRR+C(52) LTHERMO Observations: 18 R-squared 2.365540 Adjusted R-squared 2.814278 S.E. of regression 1.982920
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
The price of water in its various uses shows considerable variation. In its 1966 report Farm and Ranch Irrigation Survey (FRIS, 1996) the Census of Agriculture reports an average price of $16.23 per acre-foot of water in the 18 conterminous Water Resource Regions. An earlier survey of residential water prices (Van der Leeden et al., 1991) suggests a price of $477 per acre-foot for that use. One published demand equation for water lists price as a determinant of residential water demand but not for other uses (Chesnutt and McSpadden, 1994). Another attempt includes price variables for both residential and irrigation uses (WRC, Water Use Price/Cost analysis, 1976). Price elasticities for residential water are reported in Hall (1996) and irrigation water demand elasticites are available in WRC (1996).8 Using these prices and elasticities and a method suggested by Pyndick and Rubinfeld (1992, pp. 45–48), we construct demand curves for residential and irrigation water (Table 5).9 What is obvious from these calculations is that as the allocation of water becomes more rational, the quantity demanded of residential water is likely to change but little or increase, while that for irrigation water is likely to fall drastically. The finding that the choice of water uses is responsive to price changes is confirmed by regression results across the Water Resources Regions. Table 6 shows convincingly that a rise (fall) in the price of irrigation water causes a fall (rise) in withdrawals for irrigation and a rise (fall) in the withdrawal of 8
Agricultural (irrigation) water demand elasticity is also reported in CALFED Bay-Delta Program (October 1999). That elasticity is much lower than the 0.9 used here, but it refers to the special case of Central California, where high-valued crops, such as fruits and vegetables, are less impacted by changes in water price. Low-valued yet extensive crops, such as hay, register water demand elasticities as high as 1.89! (see Draft PEIS Central Valley Project Improvement Act, September 1997, A-11). WRC had national coverage and the elasticity implied by its analysis was adopted here. 9 The demand curves constructed in Table 5 are linear. Conceivably, a constant elasticity formulation may be more realistic for drinking water, while a linear one is more appropriate for irrigation water. For constant elasticity estimates for both types of demand see CALFED Bay-Delta Program (October 1999). Over the relevant range of values, the distinction may be trivial.
9
Table 5 Demand for irrigation and residential water Irrigation Elasticity: 0.9* Price*: $16.23 Quantity: 134,000 bg/d (1995)
Residential Elasticity: 0.25 Price*: $500 Quantity: 22,700 bg/d (1995)
Demand curve for residential water: or: Demand curve for irrigation water:
Q=28,374–11.348P P=$2500.35–$0.088Q
Q=255,725–7,500P or: P=$34.10–$0.000133Q Assuming a marginal cost of $30 per unit, a price discriminating monopolist would seek the following price-output combinations: Residential: Price: $1265.17 per Quantity: 14,036 units unit, Irrigation: Price: $32.05 per unit, Quantity: 15,413.5 units With marginal cost pricing:a when MC=$30, Residential: Price: $30 per unit Quantity: 28,072 units Irrigation: Price: $30 per unit Quantity: 30,827 units When MC=$100, Residential: Price: $100 per unit Irrigation: Price: $100 per unit
Quantity: 27,277 units Quantity: 0 units
a
The calculations assume equal production costs for the various uses of water. This may be an oversimplification. Where reservoirs are concerned specifically, the cost may be determined by the frequency of cycling. In this connection, Public supply water is cycled more frequently than irrigation water. The unit cost attributable to reservoir storage is thus higher for irrigation water (Hirshleifer et al., 1960).
water for other uses (the one included in the model is ‘other’ uses which includes importantly residential use; expanding the model to include thermo preserves the findings). These findings are confirmed by joint estimation using iterative 3SLS. Both single equation and system estimation methods confirm our expectations: the price of water is an important determinant of its use.
5. Concluding remarks This paper has documented the likely effect of prospective changes in the water economy of the US upon the uses of water and, in particular,
10
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
Table 6 Impact of water price upon water uses: OLS Estimation method: least-squares Included observations: 18 Total system (balanced) observations: 36
C(1) C(2) C(3) C(4) C(5) C(6) C(10) C(11) C(12) C(13) C(14) Determinant residual covariance
Coefficient
S.E.
t-Statistic
Prob
4.618493 2.003065 1.234509 2.727642 0.512372 0.982159 0.546992 0.258107 1.470809 0.477940 0.314206
2.012737 0.897713 0.356001 0.772917 0.182571 0.297624 1.491230 0.112949 0.506942 0.075122 0.243331 0.260069
2.294633 2.231297 3.467709 3.529024 2.806430 3.299995 0.366806 2.285160 2.901335 6.362143 1.291269
0.0304 0.0349 0.0019 0.0016 0.0096 0.0029 0.7169 0.0311 0.0076 0.0000 0.2084
Equation: LIRR=C(1)+C(2) LCOST94+C(3) LOTHER+C(4) DUMMY+C(5) LTHERMO+C(6) LSTOR Observations: 18 R-squared 0.837687 Adjusted R-squared 0.770056 S.E. of regression 1.094939 Equation: LOTHER=C(10)+C(11) LIRR+C(12) LCOST94+C(13) LTHERMO+C(14) LSTOR Observations: 18 R-squared 0.801284 Adjusted R-squared 0.740141 S.E. of regression 0.724059
the utilization of storage capacity. These expected changes have provided the basis for innumerable studies, and water management has evolved into a sophisticated science. But the emphasis in water management has remained constrained by two limitations: The emphasis upon regional solutions, and the relative lack of attention to the effects of new water management proposals upon the already existing water provision infrastructure. Water management, as any profession, is molded by trends and prevailing attitudes.10 10
In this connection, see Alaskan Water for California? (OTA, 1992, p. 11.) ‘‘although the current trend is away from interregional water transfers, at some point, then, such schemes could again receive serious attention. A subsea pipeline to transport water from Alaska, diverting some water from the Columbia River, or various proposals for diverting water from Western Canada’s riversy..might then be considered.’’
What is implied by our findings here is that in making the cost–benefit calculations underlying the choice of water policy options, particularly when choosing between storage and transfer, managers should pay greater attention to the write-offs on already installed capacity—particularly storage capacity—resulting from their decisions. It has been estimated that a mere 10% reduction in water devoted to irrigation could double the amount available for municipal and industrial uses.11 With the negative effect of higher water prices upon irrigational use (shown in Section 4), it would then remain a matter of merely transferring that water to its new use. Past investment in reservoir capacity would not then 11 A New Era For Irrigation (National Research Council, 1996, p. 68).
A. Stern / Int. J. Production Economics 81–82 (2003) 1–12
have to be written off, and the construction of new reservoirs would become less important as a water management option.12
Appendix. Explanation of abbreviations
Abbreviation
Data set
Variable
LCOST94 LIRR LOTHER
CS CS CS
LTHERMO DUMMY
CS CS
LSTOR LTOTIRR LHYDRO LRENOFF
CS CS CS CS
LTOTHERM
CS
LTOTOTHE
CS
LACRESSIR LPOWER LTHERPOWER LPOPUL LRENEW
CS CS CS CS CS
Price of irrigation water (per a-f) Log of water for irrig. In mg/d Log of withdrawals other than irr and thermo Log of water for thermo plants 1 for eight Eastern Regions 0 otherwise Log of storage capacity in bg Log of total withdrawal less irrig. Log of water for hydropower Log of renewable water supply less off stream withdrawals Log of total withdrawals less water for thermo Log of total withdrawals less water for ‘other’ uses Log of acres irrigated Log of hydropower generated Log of thermopower generated Log of Population Log of renewable water supply
LIRRIG LTHERMWA LTHERMO LHYDRO LHYDPOW LPOPUL LPUBSUP
TS TS TS TS TS TS TS
LSTOR
TS
Log of Log of Log of Log of Log of Log of Log of supply Log of
water for irrigation water for thermo thermopower generated water for hydropower hydropower generated population water withdrawn for public storage capacity
12 But see the January 2001 Press Release of the Metropolitan Water District of Southern California: ‘‘y..In the ten years since the state’s last drought, Southern California has invested billions of dollars in conservation, recycling, storage and infrastructure programs. Foremost among the new safeguards is Diamond Valley Lake, the 4500 acre reservoir in southwest Riverside County. Capable of holding 800,000 acre-feet, the reservoir was dedicated last Marchy.’’.(mwh2o.com). To meet its anticipated future needs, by contrast, New York City is building Water Tunnel No. 3, a 60 mile project described as ‘‘by far the largest construction project in New York City’s history’’ (ita-aites.org/tribune8).
LAGR LINDUSTR
TS TS
TIME
TS
11 Log of index of agricultural output Log of index of industrial production Time trend (T ¼ 1; 5; 10; 15; y)
CS—cross-section of Water Resource Regions (usually 18 observations). TS—time series of quinquennial observations 1950–1990 (9 observations).
References Annual Energy Review, 1991. Energy Administration, US Department of Energy, Washington, DC, June 1992. Blinder, A., Maccini, L.J., 1991. The resurgence of inventory research: What have we learned? Journal of Economic Surveys 5 (4), 292–327. California Statistical Abstract, 1999. Senate of the State of California. Central Valley Project Improvement Act PEIS, 1997. US Department of the Interior, Bureau of Reclamation, Sacramento, CA. Chesnutt, T.W., McSpadden, C.S., 1994. Putting the Pieces Together: Decision Support for Integrated Resource Planning Using IRPSIM. A&N Technical Services Inc., April. Economic Evaluation of Water Management Alternatives: Screening Analysis and Scenario Development, 1999. CALFED Bay-Delta Program, October, 1999. Economic Report of the President, 1995. USGPO, Washington, DC. FRIS, 1996. 1994 Farm and Ranch Irrigation Survey, 1992. Census of Agriculture, US Department of Commerce, Washington, DC, August 1996. Graczyk, D.J., Krug, W.R., Gebert, W.A., 1986. A History of Annual Streamflows from the 21 Water-Resource Regions in the US and Puerto Rico, 151-1983. Open-File Report 86128 Department of the Interior, US Geological Survey, Madison. Hall, D.C. (Ed.), 1996. Advances in the Economics of Environmental Resources, Vol 1: Marginal Cost Rate Design and Wholesale Water Markets. JAI Press, Greenwich, CT. Hirshleifer, J., DeHaven, J.C., Milliman, J.W., 1960. Water Supply, Economics, Technology, and Policy. The University of Chicago Press, Chicago, IL. Lund, J.R., Guzman, J., 1999. Derived operating rules for reservoirs in series and in parallel. Journal of Water Resources Planning and Management 125 (3), 134–154. National Research Council, 1996. A New Era for Irrigation. National Academy Press, Washington, DC. National Water Summary, 1983. Hydrologic Events and Issues, US Geological Survey, Water Supply Paper 2250, USGPO, Washington, DC.
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OTA, 1992. Alaskan Water for California? The Subsea Pipeline Option. Office of Technology Assessment, Congress of the United States, Washington, DC, January. Pyndick, R.S., Rubinfeld, D., 1992. Microeconomics, 4th Edition. Prentice-Hall, Upper Saddle River, NJ. Solley, W.B., 1997. Estimates of Water Use in the Western United States. Report to the Western Water Policy Review Advisory Committee. Solley, W.B., Pierce, R.R., Perlman, H.A., 1998. Estimated Use of Water in the US in 1995. US Geological Survey, Circular 1200. Spulber, N., Sabbaghi, A., 1998. Economics of Water Resources: from Regulation to Privatization, 2nd Edition. Kluwer Academic Publishers, Boston.
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