Nitrous Oxide EmissionReductions from Cutting
Excessive Nitrogen Fertilizer Applications
Francisco Rosas*
Bvar. España 2633
Department of Economics
Universidad ORT Uruguay
Montevideo, Uruguay
Phone: (598) 2707 1833 extension 2233
Bruce A. Babcock
578F Heady Hall
Department of Economics
Iowa State University
Ames, IA 50010
Dermot J. Hayes
568C Heady Hall
Department of Economics
Iowa State University
Ames, IA 50010
* corresponding author
Electronic Supplementary Material
- Equivalency between a tax and an offset: A sketch of the proof
Equation (2) in the manuscript, states farmer’s optimization problem when they are paid for their emissions (or application) reductions with offsets:
(2)
where . If farmers were to be levied on their N purchases, their optimization problem objective function is as shown in equation (2’).
eqn (2’)
Assuming independence between and , the first order conditions of both problems end up to be the same, i.e:
The equality of both instruments (tax and offsets) holds provided the following conditions are met:
i) There is a progressive tax structure, which
ii) The tax revenue curve as a function of N be equal to
iii) The tax structure has to adjust to changes in carbon prices,
However, the distributional and welfare effects of each instrument is different.
- Discussion on practical implementation of an offset program
The implementation of this program requires the farmer to report verified nitrogen application records and knowledge by the regulator of certain field characteristics (those included in parameter ) to determine the baseline () and actual () application rates, and the payment function. Because farmers may have the incentive to misreport these values in order to claim more offsets, verification and monitoring are an implementation challenge that is not new to the treatment of NPS pollution in agriculture.
While implementation of the program we describe is beyond the scope of this study, methodologies for quantification of N2O emissions reduction in the U.S. North-Central region were recently designed and adopted by the Verified Carbon Standard (VCS) and the American Carbon Registry (ACR).[1] These “rate-based” protocols require the farmer to report only a verified crop history and fertilizer records. These are complemented by the so-called Best Management Practices (BMP) in the use of fertilizers, such as the “Right Source-Rate-Time-Place (4R) Nutrient Stewardship” proposed by the International Plant Nutrition Institute (IPNI 2011) and the Nutrient BMP Endorsement for Crop Revenue Coverage Insurance (USDA-RMA 2003), which would reduce uncertainty about on-farm practices while simultaneously contributing to reduce N application rates. These consist of using ammonium-based fertilizers, slow/controlled release fertilizers or inhibitors (right source); injected or band applications (right place); split applications in spring, and fall applications only if slow/controlled released fertilizers or inhibitors are used (right time); and applications based on field variability requirements and nitrogen balance (right rate) all overviewed by a professional advisor.
Moreover, and regarding the payoff function, these N2O reduction protocols simplify the implementation of the scheme by relying on an N2O-N response curve that is extrapolated for the U.S. North-Central region and used to calculate emission reductions for any farmer voluntary enrolled from that region (Millar et al. 2013; Millar et al. 2012; CAR 2013).
The European Union has in place limits on the amount of nitrogen that can be applied to the soil, specifically a “limitation of the land application of fertilizers based on a balance between the foreseeable nitrogen requirements of the crops, and the nitrogen supply to the crops from the soil and from fertilization.”[2] Implementation of this directive has been left up to the member states and typically involves the record keeping, soil analysis and/or a restriction on the maximum mineral N in the soil after harvest (Van Grinsven et al. 2012). These regulations have proven effective (Van Grinsven et al. 2012). We would anticipate a similar combination of record keeping and soil testing to implement the concept proposed here. The farm level costs of proving compliance would be the additional costs associated with maintaining records. Soil testing is normally conducted after corn is grown and may not represent an incremental cost.
Another initiative, which is more information intensive, has also been introduced in Alberta, Canada, and allows farmers to earn carbon credits for their quantifiable and verifiable N application reductions (Government of Alberta 2010; CFI 2011).
- Estimation of a Conditional Yield Distribution
We show a detailed explanation of the procedure used the estimate the crop yield distribution function conditional on the nitrogen application rate. The yield response to nitrogen was estimated using 600 observations collected from field-plot experiments on continuous corn conducted between 1987 and 1991 on four different farms located in widely dispersed locations across Iowa.[3] Yields were updated to 2014 levels using a proportional yield adjustment based on Iowa corn yield growth.
One of the objectives of the experiment was to isolate the effect on yields of increasing nitrogen application rates, leaving everything else constant. This dataset was also used in past studies by Babcock and Hennessy (1996) and Roosen and Hennessy (2003). The experiment consisted of 10 nitrogen application rates (0, 25.06, 56.10, 84.14, 112.18, 140.23, 168.28, 224.37, 280.46, 336.55 kg N/ha)[i]with three replications on each of the four farms (sites) and in each of the five years. So there are 600 observations or 60 observations for each N application rate. TableA.II shows mean and standard deviation of corn yields by site and by year.
Table A.II. Yields (tons per hectare) from Continuous Corn Field Experiments in Iowa
Yields by site / Yields by year1 / 2 / 3 / 4 / 1987 / 1988 / 1989 / 1990 / 1991
Mean / 11.57
(3.28) / 11.71
(4.21) / 12.46
(4.28) / 11.11
(3.12) / 13.28
(3.00) / 7.41
(2.60) / 12.69
(3.66) / 12.89
(3.31) / 12.30
(2.84)
Note: Standard deviation in parentheses.
Following Babcock and Hennessy (1996),we assume that, conditional on a given N application rate, yields behave according to a beta distribution with shape parameters and . We further assume that yield randomness comes from the interaction of factors that are unobserved by the researchers (such as weather or pests). The beta distribution is usually specified because it describes the nonsymmetric historical behavior of yields with respect to these unobservables.
The moments of the yield distribution depend on the N application rate, and given that moments of the beta distribution are completely defined by the shape parameters, we specify them as a function of N rate, that is, and . Then the conditional beta distribution can be written as follows:
/ (A.1)where is the Gamma function. Parameters are estimated by maximum likelihood.[4] Results are shown in tableA.III.
Table A.III. Maximum Likelihood Estimation of Beta Parameters
Functional forms: ;4.160 / -0.114 / 0.005 / 12.832 / -1.377 / 0.043
(0.515) / (0.094) / (0.005) / (1.416) / (0.205) / (0.008)
By feeding equation A.2 with one value of N rate, we obtain the probability distribution of yields conditional on that N and on the estimated parameters. Figure A.2 shows the estimated yields density function conditional on N application rates between zero and 325 kg/ha. We observe that the first two moments (mean and variance) of the density function change with the N rate. We use Equation A.1 to draw beta distributed random deviates for any given nitrogen application rate using the inversion method.
Figure A.2. Parametric estimation of a conditional beta probability density function of Iowa corn yields for different N rates
- Simulation of Correlated Yields and Price Draws
We show a detailed explanation of the procedure used to generate random crop prices that are correlated with crop yields. The optimization problem is to maximize expected utility of profits, where uncertainty comes from both random yields and random output prices. Random corn prices were generated assuming a lognormal distribution. This is a standard assumption given that the percentage change of daily commodity prices can be approximated by a normal distribution with certain mean and variance, and therefore the variable in levels (the commodity price) is lognormally distributed (Hull 2009, p. 271). So the price vector is generated from the equation , where, and . is the rth commodity price deviate generated; indicates the rthdeviate from the random variables distributed standard normal; is the mean of corn prices; and is the volatility of corn prices interpreted as the percentage change of prices with respect to their mean. The mean of corn prices was set equal to $196.57 per ton, which is the average of the Chicago Mercantile Exchange (CME) quotation on April 1and April 15of the December futures price for 2014. Price volatility was calibrated at 0.29 and calculated using the implied volatility from Blackswith an “at the money” call option on corn futures on the same days.
We remove the independence assumption between corn prices and yields of the previous section by following Johnson and Tenenbein (1981) to generate correlated draws from these two distributions. Given a target level of correlation , the method consists of generating draws from two standard normal random variables and and creating another random variable as a linear combination of the previous two. The linear combination is what creates correlation between and the other variables. The linear combination weightis optimally selected so that the target correlation is achieved. By plugging into the random price generator formula and by substituting by a vector of randomly generated corn yields, we obtain correlated corn and yield draws.
- N2O Emissions and the N Application Rate for Sensitivity Analysis
Measures of N2O emissions as a function of N application rates were collected from corn field experiments conducted in the northern U.S. and Canada. They consist of more than 20 studies summarized by Rochette et al. (2008); Grant et al. (2006); Li, Narayanan, and Harriss (1996);Bouwman (1996); and Thornton and Valente (1996). A list is available from the authors upon request. We fit the following emissions curve to the data that controls for soil type (), a time trend (), and tillage practices ():
/ (A.2)where are estimated parameters (shown in table A.I) and is the nitrogen rate at which the estimated curve has slope equal to zero.
Table A.I. Estimation Results of Emissions Curve,: equation (A.2)
Variable / Coefficient / Standard error / t-stat / p-valueIntercept / 1.23667 / 0.93817 / 1.3182 / 0.1913
/ 0.03191 / 0.01769 / 1.8042 / 0.0751
/ -0.00035 / 0.00019 / -1.8110 / 0.0740
/ 1.12E-06 / 5.36E-07 / 2.0923 / 0.0397
SoilType / 0.06135 / 0.18078 / 0.3394 / 0.7352
Trend / -0.03854 / 0.02378 / -1.6207 / 0.1091
Tillage / 0.12780 / 0.13161 / 0.9710 / 0.3345
- Distribution of Probability of Rainfall and Temperature
We describe in detail the procedure to obtain a distribution of probability of rainfall and temperature. We used data for the State of Iowa in the period 1895-2008 from the National Climate Center at the National Oceanic and Atmospheric Administration. Rainfall is the total annual precipitation for the state and is measured in centimeters per year (1 inch of rain = 2.5 cm). Temperature is the annual average temperature for the state and is measured in degrees Celsius. For each of the annual time series, we fitted a nonparametric density function using an Epanechnicov kernel (DiNardo and Tobias, 2001).[ii] As shown in lower panels of figure A.3, both rainfall and temperature densities are bell-shaped. They respectively average 89 cm/yr (with a range between 56 and 122) and 8.8 degrees Celsius (ranging between 7 and 11).
Random draws were then generated from these nonparametric probability density functions. It must be noted that rainfall and temperature are two correlated events. In fact, a correlation of 0.64 is found for the same Iowa monthly time series; however, when we aggregate to annual data the observed correlation is virtually zero. Therefore we do not generate correlated deviates of rainfall and temperature but instead draw them independently.
References
Alberta, Canada, Government of. 2010. Quantification Protocol for Agricultural Nitrous Oxide Emissions Reductions. Version 1.0.
Babcock, B. A., and D. A. Hennessy. 1996. Input Demand Under Yield and Revenue Insurance. American Journal of Agricultural Economics 78(2): 416-427.
Bouwman, A. F., L. J. M. Boumans, and N. H. Batjes. 2002. Emissions of N2O and NO from Fertilized Fields: Summary of Available Measurement Data. Global Biogeochemical Cycles 16(4): 1058.
Canadian Fertilizer Institute (CFI). 2011. The Nitrous Oxide Emission Reduction Protocol (NERP). Available at: (Accessed on March 2012)
Climate Action Reserve - CAR. 2013. Nitrogen Management Project Protocol. Climate Action Reserve, Los Angeles, CA.
DiNardo, J. and J. Tobias. 2001. Nonparametric Density and Regression Estimation. Journal of Economic Perspectives 15(4): 11-28.
Hull, J. C. 2009. Options, Futures, and Other Derivatives. Upper Saddle River, NJ: Prentice-Hall.
Johnson, M. E., and A. Tenenbein. 1981. A Bivariate Distribution Family with Specified Marginals. Journal of the American Statistical Association 73(373): 198-201.
Millar, N., G.P. Robertson, A. Diamant, R.J. Gehl,P.R. Grace, and J.P. Hoben. 2013. Quantifying N2O Emissions Reductions in Agricultural Crops trough Nitrogen FertilizerRate Reduction. Verified Cabron Standard, Washington, DC.
Millar, N., G.P. Robertson, A. Diamant, R.J. Gehl,P.R. Grace, and J.P. Hoben. 2012. Methodology forQuantifying Nitrous Oxide (N2O) Emissions Reductions by Reducing Nitrogen Fertilizer Use on Agricultural Crops. American Carbon Registry, Winrock International, Little Rock, Arkansas.
Roosen, J., and D. A. Hennessy. 2003. Tests for the Role of Risk Aversion on Input Use. American Journal of Agricultural Economics 85(1): 30-43.
U.S. Department of Agriculture, Risk Management Agency (USDA-RMA). 2003. Nutrient BMP Endorsement for CRC Policy. Washington, DC. Available at (accessed on March 2014).
Van Grinsven, H. J. M., H. F. M. ten Berge, T. Dalgaard, B. Fraters, P. Durand, A. Hart, G. Hofman, G. H. Jacobsen, S. T. J. Lalor, J. P. Lesschen, B. Osterburg, K. G. Richards, A.-K.Techen, F. Vertès, J. Webb, and W. J. Willems. 2012. Management, regulation and environmental impacts of nitrogen fertilization in northwestern Europe under the Nitrates Directive; a benchmark study, Biogeosciences, 9: 5143-5160.
1
[1]The Climate Action Reserve (CAR) is currently evaluating its adoption.
[2]See
[3] Conclusions are conditional on the representativeness of the dataset to Iowa agronomic and weather conditions.
[4] The value of in , omitted to ease notation, is set at the average over the sample points from the State of Iowa.
[i] These are, respectively, 0, 25, 50, 75, 100, 125, 150, 200, 250, and 300 pounds per acre.
[ii]Bandwidth ; is the sample standard deviation; IQR is the interquartile range (difference between the 75th and 25th percentile), and n is the number of observations.