Journal of Economics, Management & Agricultural Development Vol. 4, No. 2 45

Valuing Groundwater in a Productive Aquifer Using the Production Function Approach: The Case of Rice Production in , ,

1 2 3 Antonio Jesus A. Quilloy , Jose M. Yorobe, Jr. , Victor B. Ella , Felino P. Lansigan4, and Rex Victor O. Cruz5

Abstract Establishment of the price of groundwater is a necessary step in designing means for its sustainable management in rice production. There are several techniques that can be used in groundwater valuation. It is important to identify a valuation method that is appropriate to existing natural conditions within which the groundwater is situated. This paper aims to estimate the value of groundwater in a productive aquifer that is located in Lumban, Laguna, Philippines. Based on an estimated rice production function, the paper revealed that the value of groundwater extracted for rice production is approximately PhP 1.13 per m3. Out of this estimated economic value, resource rent is roughly 66% while the remainder covers the financial cost associated with groundwater extraction.

Keywords: production function, revealed preference, resource rent

Introduction Externalities in groundwater use persist because of the incompleteness or lack of property rights over the groundwater resource. The incompleteness or lack of property rights incentivizes groundwater users to act strategically, which means that each user has the tendency to over-extract the resource before other farmers do. From the economic perspective, the lack of property rights results in a situation where the price of the resource cannot be established, hence the users would not have a form of signal that can efficiently regulate individual extraction. Therefore, valuation of groundwater resources is an important step in determining ways to efficiently manage and use the resource. Groundwater valuation studies started in the late 1960s. Strand (2010) noted that the relatively sizeable literature started with Burt (1967), and became notable in Brown and Deacon (1972), Brown (1974), Gisser and Mercado (1973), Gisser and Sanchez (1980), Gisser (1983), and Burness and Martin (1988). These early studies focused on the determination of efficient groundwater values, which served as bases for recommending optimal groundwater extraction policies.

1Associate Professor, Department of Agricultural and Applied Economics, College of Economics and Management, University of the Philippines Los Baños, [email protected] (corresponding author) 2Retired Professor, Department of Agricultural and Applied Economics, College of Economics and Management, University of the Philippines Los Baños, [email protected] 3Professor, Land and Water Resources Division, Institute of Agricultural Engineering, College of Engineering and Agro-Industrial Technology, University of the Philippines Los Baños, [email protected] 4Professor, Institute of Statistics, College of Arts and Sciences, University of the Philippines Los Baños, [email protected] 5Institute of Renewable Natural Resources, College of Forestry and Natural Resources, University of the Philippines Los Baños, [email protected] 46 Quilloy, Yorobe, Ella, Lansigan, and Cruz

Strand (2010) reported that the value of groundwater comprises of its pumping cost (the direct cost) and the value of its marginal unit (or the shadow price). Pumping cost may be directly measured based on the user’s actual expense on groundwater extraction. However, the estimation of the marginal value of groundwater, comprising of the extractive value and the “in situ” value, is more complex. Strand (2010) defined the extractive value of groundwater as its value as standing groundwater for future use. Meanwhile, the author referred to the “in situ” value as the value of the groundwater that reflects ecosystem services provided by the groundwater stock. These ecosystem services may include (Birol et al. 2006 and Bann and Wood 2011) the following: a) provision of services as water use for domestic, agricultural, and industrial purposes; b) regulatory services such as infiltration of surface water and carbon storage; and c) cultural services such as tourism relating to wildlife and groundwater-fed watering holes. According to Birol et al. (2006), groundwater values may be measured using stated preference or revealed preference approaches. Techniques based on the principles of the stated preference approach directly elicit responses from the users of the resource as regards their own valuation. Generally, this category of valuation techniques can estimate use, non-use, option, and bequest values; hence can measure the resource’s total economic value. Contemporary techniques under this category are the contingent valuation method and choice experiment method. In contrast with the stated preference approach, the revealed preference approach values groundwater based on the production behavior of the farmers. The revealed preference approach measures direct and indirect use values of groundwater and generally comprises the following techniques: a) hedonic pricing, b) net factor income approach, and c) production function approach6. Between the two general approaches, the revealed preference approach is more appropriate for valuing groundwater in a productive aquifer. The stated preference approach would not yield reliable value estimates because respondents would need to have experiential references on poor groundwater conditions in order for them to place value on the resource (Birol et al. 2006). As for the revealed preference approach, the production function approach would be the best as it treats groundwater as a production input and value estimation is deeply anchored on producers’ economic behavior. In the production function approach, groundwater is treated as a production input. Ellis and Fisher (1987), Barbier (1994, 2000, and 2007), Freeman (2003), and Heal et al. (2005) referred to this approach as the “valuing the environment as an input” approach. It is assumed in this technique that any change in the quantity and/or quality of the groundwater resource affects the production of a marketed good. Therefore, changes in the groundwater stock would affect the farm cost structure, which resonate as optimal adjustments in production decisions. The value of groundwater using this approach is reflected by the value of the marginal contribution of groundwater, or the portion of farm profit that is accounted for the use of groundwater. According to Barbier (1994), the production function approach is a two-step process. The first step concerns the determination of the physical effects of changes in the groundwater stock on production, while the second step pertains to the valuation of the said physical effects.

6 Birol et al. (2006) also mentioned travel cost approach, replacement cost approach, use of market prices, and cost-of- illness approach, as among the revealed preference approaches. However, these techniques do not apply to the valuation of extracted groundwater as they generally concern the valuation of ecosystem sites and water quality improvements relating to pollution and health. Journal of Economics, Management & Agricultural Development Vol. 4, No. 2 47

In Acharya and Barbier (2002), the production function was used in valuing groundwater recharge in Hadeja-Jama’Are wetlands in northern Nigeria. The study specified a dry season groundwater recharge function, modeled as a function of groundwater abstraction for irrigation. Changes in farm profit (or producer’s welfare) associated with the change in groundwater recharge account for the value of the groundwater resource. The literature on the use of the production function approach continues to grow and the approach is increasingly being applied to various types of natural resources and assessment of environmental impacts. This paper aims to contribute to the body of literature on groundwater economics by demonstrating the use of the production function approach in valuing groundwater in a productive aquifer. In the absence of farmers’ experience on water shortage, an appropriate technique to groundwater valuation besides the stated preference approach must be used. The paper is organized as follows: Section 2 presents a brief review of groundwater valuation literature, Section 3 discusses the approach and methodology, Section 4 presents the results of the estimation, and Section 5 concludes the paper.

Methodology Study Area and Data Collection The municipality of Lumban, province of Laguna, Philippines was selected as the study area because it has rice land areas that use groundwater exclusively for irrigation. The National Irrigation Administration (NIA) reported that majority of the rice farmers in the municipality use shallow tubewells (STWs) for groundwater extraction, particularly during the dry season. The study area has hydrologic significance to the Watershed. The Laguna Lake Development Authority (LLDA) reported that the -Lumban River, which passes through the municipality, contributes roughly 20% to the total fresh water inflow in Laguna Lake. The study used primary data, which consisted of farm-level input-output data pertaining to the dry planting season. Specifically, the input data included the quantities and costs of land, labor, fertilizer, seeds, and groundwater used in rice production. Meanwhile, the output data comprised of estimated volume (in metric ton) and price of rice harvested (in Philippine peso). The respondents comprised a complete enumeration of the 112 rice farmers in the municipality of Lumban who used STW during the dry season production cycle from November 2014 to June 2015. The names and addresses of these farmers were based on a list obtained from the Office of the Municipal Agriculturist of Lumban, Laguna. The farmers were individually interviewed face-to-face using a pre-tested interview schedule.

48 Quilloy, Yorobe, Ella, Lansigan, and Cruz

Analytical Procedure The following Cobb-Douglas production function model was used to estimate the economic value of groundwater extracted for use in rice production:

(1)

th where: qj = rice output (metric ton) of the j farmer, j = 1, …, 112; x1j = area planted (hectare); x2j = labor (manday); x3j = seeds (kilogram); x4j = nitrogen fertilizer (kilogram); x5j = phosphorus fertilizer (kilogram); x6j = chemicals (liter); x7j = water s usage (cubic meter); b0, bi = model parameters to be estimated; and j = error term. Equation 1 was estimated using the ordinary least squares (OLS) method. Diagnostic tests on the regression model were conducted to detect errors in the model’s specification. These specification errors included omitted variable bias, multicollinearity, and heteroscedasticity. Ramsey regression specification error test (RESET) was used to determine the presence of omitted variable bias which could arise from the failure to include all relevant variables in the model. Multicollinearity was determined by calculating the variance inflation factors (VIF). As a rule of thumb, if the VIF of the overall model is greater than 10, then it can be concluded that multicollinearity is high (Kutner et al. 2004). Finally, the presence of heteroscedasticity was determined through the Breusch-Pagan/Cook-Weisberg test. Correcting for heteroscedasticity was done by using heteroscedasticity-consistent (HC3) robust standard errors in the final OLS estimation of the production function. One-tailed t-test was used to determine the significance of individual regression 2 coefficients. Assuming that the error term is normally distributed (j ~ N (0, )), the hypotheses for the t-test were:

Ho: bi = 0

Ha: bi > 0 The hypothesis test was evaluated based on 1%, 5%, and 10% levels of significance. Meanwhile, the overall significance or goodness-of-fit of the regression model was evaluated using the F-test. The corresponding hypotheses were:

Ho: b1 = … = b7 = 0 Ha: Not all slope coefficients are simultaneously zero

The adjusted R2 was also used to determine the model’s goodness-of-fit. The price of groundwater was computed as its marginal value product (MVP), since in theory the MVP reflects the shadow price of a specific resource. The MVP for groundwater was calculated as the first partial derivative (evaluated at the mean quantities of the output and inputs) of the production function with respect to groundwater then multiplied by the output price:

Journal of Economics, Management & Agricultural Development Vol. 4, No. 2 49

(2)

where: bi = production elasticity (regression coefficient) of input i, qj = observed th th output of the j farmer, xij = observed quantity of input i of the j farmer, and pqj = output price received by the jth farmer.

Results and Discussion Mean Yield and Input Usage Levels The mean annual yield of the respondents is 5.94 mt/ha (Table 1). On average, this volume of yield is obtained by employing 154.51 mandays of labor, 55.50 kg of seeds, 82.53 kg of nitrogren, 13.2 kg of phosphorus, 2.63 liters of chemicals, and 1,590 m3 of groundwater. The estimated levels of usage of nitrogen and seeds are lower as compared to the dry season estimates in Carambas et al. (2015) for STW-irrigated rice farms in the neighboring municipality of Sta. Cruz. In Carambas et al. (2015), nitrogen application is 152.45 kg/ha and the seeding rate is 70 kg. However, the estimated yields in Sta. Cruz, as reported by the same study was roughly 5.097 mt/ha, which is approximately 14% lower than that of the estimates for the respondents in this study. Table 1. Mean values of output and inputs, 112 rice farmers, Lumban, Laguna, Philippines, 2015

Mean Quantities Item Per hectare/year Per farm/year a Output (metric ton) 5.94 13.38 Area planted (ha) - 1.70 Labor usage (manday) 154.51 286.98 Seeding rate (kilogram) 55.50 87.72 Nitrogen usage (kilogram) 82.53 175.27 Phosphorus usage (kilogram) 13.12 30.30 Chemical application (liter) 2.63 4.84 Water consumption (m3) 1,590 3,994.47 a Weighted average based on farm size

50 Quilloy, Yorobe, Ella, Lansigan, and Cruz

Estimates of the Parameters of the Rice Production Function Model Table 2 shows the results of the first statistical estimation of the parameters of the rice production function model. Before any inferential analyses, the study performed a series of regression diagnostic tests on the production function model. These tests were: a) the Breusch-Pagan/Cook-Weisberg test for heteroscedasticity, b) Ramsey RESET test for omitted variable bias, and c) inspection of the variance inflation factors (VIF) to detect multicollinearity. Results of these tests are shown in Tables 3 and 4. Table 2. Initial estimates of the parameters of the Cobb-Douglas rice production function, 112 rice farmers, Lumban, Laguna, Philippines, 2015

Variable Coefficient Standard Error t-Ratio p-Value

Constant 3.01930 *** 0.42881 7.04 0.000 Land (ha) 0.30925 *** 0.07056 4.38 0.000 Labor (manday) 0.30535 *** 0.08125 3.76 0.000 Seeds (kg) 0.04995 0.03650 1.37 0.174 Nitrogen (kg) 0.00244 0.01096 0.22 0.824 Phosphorus (kg) 0.00104 0.00301 0.35 0.730 Chemicals (li) 0.05840 * 0.03477 1.68 0.096 Groundwater (m3) 0.02077 *** 0.00305 6.82 0.000 F-ratio 47.74 P-value 0.000 R2 0.76 Adjusted R2 0.74

***, **, * Significant at 1%, 5% and 10% probability levels, respectively

Table 3 indicates that the first run of the model produced heteroscedastic error terms at 10% level of significance since the probability value of the 2 is equal to 0.37. The presence of heteroscedasticity violates the Gauss-Markov assumption that states that OLS estimators produce the best, linear and unbiased estimates and that the standard errors of the estimators are the lowest of all other unbiased estimators. In short, although heteroscedasticity does not cause biased regression coefficients, it can result to under-estimation of the respective standard errors of the individual regression parameter estimates. Therefore, ignoring heteroscedasticity would lead to incorrect statistical inference.

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Table 3. Results of the test for heteroscedasticity and omitted variable bias of the Cobb-Douglas rice production function, 112 rice farmers, Lumban, Laguna, Philippines, 2015

Specification Test Item Breusch-Pagan/Cook-Weisberg Ramsey RESET Null hypothesis Constant variance No omitted variables 2 0.37 F-ratio (3, 107) 36.12*** Probability value 0.5425 0.000 *** Significant at 1% probability level The model, on the other hand, did not have omitted variable bias given that the probability of the test statistic (F) is equal to 0.000. This result suggests that the model did not leave out important factors and did not violate the assumption that the error term is uncorrelated with the model’s regressors. The absence of the omitted variable bias implies that the parameter estimates of the rice production function model are consistent and unbiased. Finally, the model did not show any sign of severe multicollinearity given that the estimated VIFs for all parameters are less than 10 (Table 4). The parameter with highest VIF is land with an estimated value of 2.21, which suggests that the variable’s standard error is 1.49 times as large as it would be if land is correlated with any of the remaining variables. Meanwhile, the variable with lowest VIF is seeds at 1.08. For this parameter, the standard error is 1.04 times larger if seeds were correlated with the model’s other variables. Table 4. Results of the test for multicollinearity of the Cobb-Douglas rice production function, 112 rice farmers, Lumban, Laguna, Philippines, 2015 Variable Variance Inflation Factor (VIF) 1/VIF Land 2.21 0.453006 Labor 2.12 0.471249 Groundwater 1.40 0.715950 Chemicals 1.40 0.716136 Phosphorus 1.18 0.844863 Nitrogen 1.11 0.898051 Seeds 1.08 0.929394 Mean 1.50 Given these diagnostic tests, a second statistical estimation of the model was conducted to specifically correct only for heteroscedasticity since no other types of misspecification were committed. The final regression estimates are shown in Table 5.

52 Quilloy, Yorobe, Ella, Lansigan, and Cruz

Table 5. Final estimates of the parameters of the Cobb-Douglas rice production function, 112 rice farmers, Lumban, Laguna, Philippines, 2015

Variable Coefficient Standard Error t-Ratio p-Value Constant 3.01930 *** 0.56630 5.33 0.000 Land (ha) 0.30925 ** 0.13456 2.30 0.024 Labor (manday) 0.30535 *** 0.10304 2.96 0.004 Seeds (kg) 0.04995 0.04005 1.25 0.215 Nitrogen (kg) 0.00244 0.04158 0.06 0.953 Phosphorus (kg) 0.00104 0.00312 0.33 0.739 Chemicals (li) 0.05840 * 0.03280 1.78 0.078 Groundwater (m3) 0.02077 *** 0.00305 6.80 0.000 F-ratio 31.27 P-value 0.000 R2 0.76

***, **, * Significant at 1%, 5% and 10% probability levels, respectively

There were no differences in the parameter estimates and in the overall goodness -of-fit between the first and final OLS estimations of the rice production function model since heteroscedasticity does not cause any bias and loss of overall statistical reliability of the model. However, correcting for heteroscedasticity by using HC3 robust standard errors adjusted the variances of the respective parameters; hence, increasing the accuracy of inferential tests based on the model. Specifically, correcting for heteroscedasticity reduced the standard errors of the coefficients for land, labor, seeds, nitrogen, and phosphorus.

Table 5 further shows that the rice production function model has good statistical fit based on the estimated R2 and the probability value associated with the F-ratio. The model’s R2 is 0.7609, which implies that the regression model has around 76% improvement in predictive power compared to a null model where there are no informative predictor variables. Moreover, the R2 value suggests that approximately 76% of the variations in rice output can be explained by the variations in the explanatory variables, especially by land, labor, chemicals, and groundwater use.

The significance of the model was also verified using the F-test. The null hypothesis that all regression coefficients are equal to zero was rejected since the model’s F-ratio is 31.27 at degrees of freedom ~ (7, 105) with a probability value of 0.000. Therefore, the rice production function model has at least one parameter whose value is not equal to zero. This also implies that the observed R2 is reliable and that there is no spurious result of oddities in the dataset.

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Based on Table 5, the production inputs whose coefficients are statistically significant at 10% level are land, labor, chemicals, and groundwater use. Specifically, the coefficients for labor and groundwater, alongside the constant term, are statistically significant at 1% level. Meanwhile, the coefficients for seeds, nitrogen, and phosphorus were found to be statistically insignificant at 10% level. This could have resulted because, even though the standard errors of these coefficients are relatively low, the contributions of these production inputs to rice output are likewise smaller as compared with those of land and labor, whose output contributions are 0.309 and 0.305, respectively. Furthermore, since the soil in the study area has been officially classified by the municipality as being fairly suitable or productive for rice production, then an increase in seeding rate, nitrogen application, and phosphorus application would result only in marginal increases in output.

The statistically significant coefficients for land, labor, chemicals, and groundwater use, based on the final OLS estimation, had theoretically consistent signs. These parameter estimates, which can directly be interpreted as production elasticities, are all positive, thereby suggesting that rice output is an increasing function of land, labor, chemicals, and groundwater. For instance, a 1% increase in groundwater extraction rate would increase rice output by about 0.021%, ceteris paribus. Furthermore, simultaneously increasing the usage of all production inputs by 1% would increase output by roughly 0.694%, which implies that the estimated rice production function exhibits diminishing returns to scale. These properties indicate that the estimated rice production function is well-behaved in terms of having a production function that is positively monotonic and strictly concave with respect to all production inputs.

Estimating the Economic Value of Groundwater The economic price of groundwater is equal to its marginal value product provided that the underlying production function is well-behaved, a theoretical proposition that has been verified in the preceding section. The economic price of groundwater comprises of the direct marginal cost, which includes all financial expenses incurred by the farmer, and the groundwater’s resource rent or scarcity rent, which refers to the market value of the marginal or last unit of the resource. The scarcity rent may be equivalent to the user cost if it is positive and takes into account the present value of future sacrifices arising from the current consumption of the groundwater resource.

Financial Price of Groundwater

The financial price of groundwater was calculated as the sum of the cash and non-cash expenses associated with groundwater extraction. On average, the cash expenses account for about 51% of the financial price and the remainder (roughly 49%) takes the form of non-cash expenses (Table 6). Specifically, the cash cost items were: a) labor cost in groundwater pumping and b) cost of fuel used to operate the STW. On the other hand, the non-cash expense only included the fixed cost relating to the depreciation of the STW unit.

54 Quilloy, Yorobe, Ella, Lansigan, and Cruz

Table 6. Estimation of the financial price of groundwater, 112 rice farmers, Lumban, Laguna, Philippines, 2015

Item Value (PhP/m3) Percent (%) Cash Expenses 0.2003 Labor cost 0.0779 20.03 Fuel cost 0.1224 31.47 Non-Cash Expense 0.1887 STW depreciation cost 0.1887 48.50 Total Financial Cost 0.3890 100.00

On average, the financial price of groundwater is roughly PhP 0.389/m3. Labor and fuel costs constitute about 20% (PhP 0.08/m3) and 9% (PhP 0.12/m3), of the financial price of groundwater, respectively. The largest component of the financial price, accounting for around 49% (PhP 0.19/m3), is the fixed costs due to the depreciation of the STW unit.

Economic Price of Groundwater Since statistical tests show that the estimated production function is well- behaved, then the use of the MVP to represent the economic price of groundwater is justified. The calculation of the economic price of groundwater is shown in Table 7. On average, the economic price of groundwater based on the estimated MVP is PhP 1.13/m3, which is roughly three times larger than the resource’s financial price of PhP 0.39/m3. In theory, the economic price covers all costs associated with groundwater extraction and usage. About 34% of the economic price is due to labor cost (PhP 0.078/m3), fuel cost (PhP 0.122/m3), and STW depreciation cost (PhP 0.189/m3). The resource rent, which covers the cost of all negative externalities associated with groundwater extraction shares approximately 66% of the economic price.

Table 7. Estimation of the economic price of groundwater, 112 rice farmers, Lumban, Laguna, Philippines, 2015

Item Value

Mean output price (PhP/mt) 16,154.00

Mean marginal physical product of groundwater (mt/m3) a 0.00007 Mean marginal value product of water (PhP/m3) 1.13

a Estimated using the “per farm” values as reported in Table 1

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Conclusions and Implications This paper demonstrated the valuation of groundwater in Lumban, a municipality in the Philippines that hosts a productive aquifer. Using a production function that was estimated based on input-output data obtained from a complete enumeration of 112 rice farmers in Lumban, the paper revealed that the value of groundwater is approximately PhP 1.13 per m3. Out of this estimated economic value, resource rent accounts for roughly 66% with the remainder covering the financial cost associated with groundwater extraction. The large difference between the financial and economic price of groundwater, which is accounted for by the resource rent, could indicate that competitive behavior in groundwater extraction may result in large future social costs. A large resource rent relative to the financial price means that the users of groundwater pay less than what is economically efficient because they account only for the direct cost in groundwater extraction and fail to take the foregone net benefits from future usage of groundwater into consideration. Everything else being the same, this scenario suggests that the groundwater resource is prone to rapid exhaustion and underscores the need for the institution of effective and efficient price mechanisms for the use of groundwater in rice production.

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