Factors Affecting Cow-Calf Herd Performance and Greenhouse Gas

Factors Affecting Cow-Calf Herd Performance and Greenhouse Gas

Journal of Agricultural and Resource Economics 38(3):435–456 Copyright 2013 Western Agricultural Economics Association ISSN 1068-5502 Factors Affect...

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Journal of Agricultural and Resource Economics 38(3):435–456 Copyright 2013 Western Agricultural Economics Association

ISSN 1068-5502

Factors Affecting Cow-Calf Herd Performance and Greenhouse Gas Emissions Tong Wang, Seong C. Park, Stan Bevers, Richard Teague, and Jaesung Cho A Cobb-Douglas stochastic frontier function is estimated for the cow-calf enterprises in the Texas Rolling Plains using Standardized Performance Analysis (SPA) data. We find that factors promoting higher herd productivity include machinery investment, pasture-quality improvement, and protein supplement. In contrast, herd productivity is compromised by a longer breeding season, percentage of hired labor, and deviation from mean annual rainfall. Interestingly, more technically efficient farms tend to emit fewer greenhouse gas units per unit of output. For example, net greenhouse gas emissions are 6.12 and -8.70 pounds of carbon equivalent, respectively, for farms with technical efficiency below 0.8 and above 0.96. Key words: greenhouse gas emission, standardized performance analysis, stochastic frontier analysis, technical efficiency

Introduction The beef cattle industry in the Rolling Plains region of Texas is inherently risky due to frequent drought conditions, volatile cattle prices, and rising input costs. Moreover, national beef consumption has declined steadily in the past three decades, dropping from 94.4 pounds per capita in 1976 to 59.7 pounds in 2010. In the face of these challenges, the Beef Cow-Calf Standardized Performance Analysis (SPA) provides an analytical tool to help farmers and ranchers identify their strengths and weaknesses in production and financial performance. In 1992, the National Cattlemen’s Beef Association adopted the SPA program that had been developed through efforts of their member producers, the National Integrated Resource Management Coordinating Committee, and Cooperative Extension Specialists from multiple universities. The goal of the Beef Cow-Calf SPA analysis is to integrate production and financial records into a single analytical tool for cow-calf operations. Typically, an SPA is completed by a rancher and an extension specialist working together. The results of each complete analysis are sent to a regional coordinator, who checks the results for accuracy and enters them into a regional database. Texas leads the country in the number of analyses completed since the SPA program began. Two decades after its inception, the SPA data provides a key tool for analyzing herd performance over multiple production regions and years. Most previous literature analyzing SPA data has attempted to identify factors that affect the cost, production, and profit of cow-calf enterprises (Falconer, Parker, and McGrann, 1999; Dunn, 2000; Miller et al., 2001; Ramsey et al., 2005). Scant attention had been paid to determining efficiency measurements among beef cow-calf enterprises until Cho, Park, and Bevers (2011) evaluated technical efficiency and its determinants among cow herd operations. Tong Wang is a postdoc research associate at Texas A&M AgriLife Research; Seong C. Park is an assistant professor at Texas A&M AgriLife Research; Stan Bevers is a professor at Texas A&M AgriLife Extension Services; Richard Teague is a professor at Texas A&M AgriLife Research; Jaesung Cho is a research fellow at the Korea Rural Economic Institute. We are grateful for administrative support from Texas A&M AgriLife Research-Vernon. Funding support from USDANIFA/HATCH Project, TEX093967 is gratefully acknowledged. Review coordinated by Hayley Chouinard.

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The study of efficiency measurements began with seminal work by Farrell (1957), who suggested constructing the production function either as a parametric function or as a nonparametric piecewiselinear convex isoquant. There are two approaches to estimate a parametric model. One is the deterministic estimation, which uses a linear programming method introduced by Aigner and Chu (1968). This method ensures nonviolation of the monotonicity conditions and parametric restrictions (Färe et al., 2005). The other approach is Stochastic Frontier Analysis (SFA), which was simultaneously introduced by Aigner, Lovell, and Schmidt (1977) and Meeusen and van den Broeck (1977). Their model specification added stochastic elements to the deterministic frontiers, thus overcoming a major shortcoming of the deterministic estimation method, in which all variation from the production frontier is interpreted as inefficiency. The most popular method for constructing a nonparametric model is the Data Envelopment Analysis (DEA) method, which became widely used after Charnes, Cooper, and Rhodes (1978) reformulated Farrel’s (1957) approach. DEA employs a linear programming technique to construct a nonparametric piecewise-linear frontier. Unlike the parametric model, DEA can be implemented without knowing the relationship between input and output. The analysis of efficiency measurement is now widely used, with a few applications to the beef cattle sector. For example, Trestini (2006) used the SFA approach to study the technical efficiency of Italian beef cattle production and concluded that the inefficiency term is negatively correlated with herd size and the proportion of concentrated feed in the whole diet. Otieno, Hubbard, and Ruto (2012) applied the same method and found that promoting controlled cattle-breeding methods improved efficiency. Nonparametric production analysis has also been applied to study the efficiency of Kansas beef-cow farms (Featherstone, Langemeier, and Ismet, 1997). Factors that have been identified as influencing inefficiency include herd size and the percentage of income from beef cows. Rakipova, Gillespie, and Franke (2003) studied technical efficiency determinants in Louisiana beef production with a DEA model and discovered that, besides a higher level of improved pasture and better breeding practices, technical efficiency also increases with farmers’ experience and formal education. This paper analyzes cow-calf enterprises in the Rolling Plains region of Texas, comprising approximately 24,000,000 acres of primarily grassland characterized by low rolling hills to rough canyon lands (Gould, 1975). The location of the Rolling Plains is depicted in figure 1. Using SPA data from 1996 to 2011, we attempt to determine the factors that affect the production output of cow-calf enterprises and to measure the technical efficiency of cow-calf herds in the region. We also investigate whether firms that are more technically efficient are also more efficient in greenhouse gas emissions per unit of product. The climate impact of the beef industry has received increasing consideration in recent years, and an emerging literature investigates greenhouse gas (GHG) emissions among different beef production systems in various regions of the world. In line with current environmental impact concerns, this paper also attempts to establish the relationship between technical efficiency and GHG emission per pound weaned. Data The analysis uses SPA data for cow-calf producers from 1996 to 2011. Considering the geographic differences and disparities in farm practices among the vast regions covered by SPA data, we focus on the subset of cow-calf farms from the Texas Rolling Plains. A total of forty-two ranches participated in the study during this sixteen-year period. Among them, thirty ranches (71.4%) participated for only one year, eight (19.0%) participated for two to three years, and nine (9.5%) participated for more than five years. There are a total of seventy-six observations.

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Cow-Calf Herd Performance and GHG Emissions 437

Figure 1. Location of Texas Rolling Plains Variables in the Cobb-Douglas Stochastic Frontier Production Following Ramsey et al. (2005) and Cho, Park, and Bevers (2011), we choose the variable pounds weaned per exposed female as the production output (i.e., the dependent variable). This variable is defined as the total pounds of calves weaned divided by the total number of females either exposed to bulls or in an artificial insemination program. Eight input factors are chosen as independent variables in the stochastic frontier production function. The average age of weaning is included as a time input variable, as we expect that calves weaned at an older age will weigh more than calves weaned at a younger age. We also include three investment variables—real estate assets, machinery assets, and livestock assets on the cost basis—used in Ramsey et al. (2005) and Cho, Park, and Bevers (2011). These values are the total average assets value divided by the total number of breeding cows at the beginning of the fiscal year. As Ramsey et al. (2005) note, real estate assets may affect production negatively or positively depending on their management. The input of machinery assets is expected to play a positive role in production due to the increased capital intensity of the farm (Cho, Park, and Bevers, 2011). The sign of the coefficient of livestock assets is also equivocal, as we are not sure whether the investment in livestock is for better quality breeding stock with increased reproduction rates (Ramsey et al., 2005). The variable purchased feed fed contains four components: roughage, complete feed, mineral and salt, and protein supplement. As each component has a different unit price and is likely to play a different role in production, we choose not to add them up as one aggregate variable. Instead, two major categories, pounds of roughage fed and pounds of protein supplement fed, are chosen as two independent variables in the study. The variables of complete feed and mineral and salt are not included, as they are not widely used. Our choice of feed variables is different from those used by Ramsey et al. (2005) and Cho, Park, and Bevers (2011), who use total pounds of feed as a single explanatory variable, but did not find it to be significant in the production function. Koger et al. (1975) point out that improved pasture is more likely to increase cow production compared to native pasture because improved pasture typically provides forage of both higher quality and greater quantity. No direct data is available on the percentage of improved pasture, but we do have observations on costs of chemicals, fertilizer and lime, and seed and plants per breeding cow. Since these three inputs are essential for improved pasture, we add expenditures on these three variables as a proxy for percentage of improved pasture.

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Similar to Battese and Coelli (1992), we include an adjusted input cost variable that includes gasoline, fuel and oil, hired labor and management, family living withdrawal (operator labor), and veterinary care and breeding. Expenses on these four categories are most likely to contribute to a higher productivity.1 Costs on machine work, repairs and maintenance, supplies, utilities, professional fees, depreciation data, insurance, and property taxes are not included here, as they are unlikely to have any impact on pounds weaned per exposed female. Variables in the Technical Inefficiency Effect Model To investigate sources of productivity inefficiencies, we include five variables that capture farm and environmental characteristics. Calving season length is defined as the number of days from the beginning to the end of the breeding season. Shorter breeding seasons are typically an indicator of advanced management, as they result in better use of labor and productivity improvements (Ramsey et al., 2005). However, Deutscher, Stotts, and Nielsen (1991) found that a 70-day breeding season was better than 30- and 45-day seasons in terms of calf weaning weight per breeding female. They pointed out that optimal breeding season length should be determined with considerable care, as a shorter breeding season is not always better for productivity. In contrast, using SPA data from 1991 to 2001 for Texas, Oklahoma, and New Mexico, Ramsey et al. (2005) found that a shorter breeding season significantly improves pounds weaned per exposed females. Cho, Park, and Bevers (2011) showed that herd inefficiency level increases as the breeding season becomes longer, but this relationship was not significant using SPA Southern Plains data from 2004 to 2008. The variable percentage of owned land is calculated as the acres of cattle land that are owned divided by the acres of cattle land that are owned and rented on the farm. A farmer who leases land is less likely to use sustainable practices and maintain long-term economic viability (Rakipova, Gillespie, and Franke, 2003); therefore, they are more likely to maximize their short-term profit. We also include the percentage of operator labor, which is the operator labor cost divided by the costs of operator and hired labor, to check whether farmers’ who spend less time on their farms will have lower technical efficiency. A favorable production condition for a cow-calf operation can be defined as favorable weather conditions. Therefore we include a rainfall variable to capture efficiency variances across years. Cho, Park, and Bevers (2011) directly used the variable of fiscal rainfall, which is the absolute value of rainfall during the fiscal year, and found it negatively affected herd productivity. Although above-average rainfall produces more grass growth if cattle numbers stay the same, forage quality decreases. Conversely, drier than average conditions can cause such low grass-growth rate that there is not enough to sustain animal numbers. In extreme cases plant mortality is increased. As both too little and too much rainfall can compromise herd productivity, we use a new variable, deviation from mean annual rainfall (MAR), as the absolute difference between percentage of MAR and 100. For example, if the percentage of MAR is 70, then deviation from MAR is |70 − 100| = 30. It is hypothesized that herd inefficiency levels will increase in proportion to deviation from MAR. Finally, we include the variable total acres as an indicator of herd size. This variable captures the effects of two interconnected variables: the number of breeding females and acres per female, both of which may affect herd productivity. Featherstone, Langemeier, and Ismet (1997) found a positive relationship between herd size and technical efficiency, but Cho, Park, and Bevers (2011) demonstrated exactly the opposite result. We can infer that the relationship between herd size and efficiency may vary depending on whether the average herd size in the sample exceeds the optimal herd size. 1

Personal communication with Professor S. Bevers, Extension Economist of Texas A&M AgriLife Center.

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Cow-Calf Herd Performance and GHG Emissions 439

Table 1. SPA Variable Summary Statistics for Texas Rolling Plains (1996–2011) Variable



Std Dev




Pounds Weaned Per Exposed Female Average Age at Weaning Livestock Assets (Cost Basis) Machinery Assets (Cost Basis) Real Estate Assets (Cost Basis) Roughage Protein Supplement Improved Pasture Proxy Adjusted Input Cost Breeding Season Length Percentage of Owned Land Percentage of Operator Labor Total Acre Deviation from Mean Annual Rainfall (MAR)

76 76 76 76 76 76 76 76 76 76 76 76 76 76

455 8 782 258 2,295 1,131 379 40 119 125 53 29 8.10 26

88 1 320 490 3,673 1,254 308 40 49 86 41 36 14.92 17

225 3 46 0 0 0 0 0 24 45 0 0 0.381 0

638 12 1,838 3,842 25,551 5,217 2,066 177 251 365 100 100 102.63 81

Pounds Months Dollars Dollars Dollars Pounds Pounds Dollars Dollars Days Percent Percent Thousand Percent

Summary Statistics Table 1 provides a summary of statistics for the variables defined above. Other than the five variables included in the inefficiency model (that is, percentage of owned land, percentage of operator labor, breeding season length, deviation from MAR and total acre) all of the variables included in the stochastic frontier function are measured on the basis of number of exposed females on the farm. Statistics in table 1 reflect diversity in farm characteristics and practices as well as environmental conditions across years. For example, the improved pasture proxy varies from $0 to $177 in the cost of chemical, fertilizer, and plant and seed categories of inputs. This means that the grazing land includes native rangeland, where the land is managed as a seminatural ecosystem, and improved pasture, where seed, establishment, and fertilizer are required to produce forage for grazing and hay production. Both machinery and real estate assets on a cost basis have a minimum of $0 and a maximum of $3,842 and $25,551 for range and cultivated pasture, respectively.2 This demonstrates the dramatic differences in capital intensity. Similarly, both roughage and protein supplement range from a common minimum value of 0 pounds to a maximum of 5,217 and 2,066 pounds for range and cultivated pasture, respectively. This reflects a large difference in extensive and intensive grazing systems but also indicates the range of environmental conditions that inevitably affect farm grazing conditions and potential. Deviation from MAR provides a more specific measurement of abnormal environment conditions. A mean deviation of 26% with 17% standard error suggests considerable rainfall differences across years. Breeding season length varies from a minimum of 45 days to a maximum of an entire year, indicating a big difference in management intensity among farms. Finally, the huge range that exists in the total acre category reveals the coexistence of extremely small and large farms in the Texas Rolling Plains. Methodology To accommodate the analysis of unbalanced panel data, we use the SFA method, which is the most suitable approach for our purpose (Battese, Coelli, and Colby, 1989; Seale, 1990; Battese and Coelli, 1992, 1995). The SFA method has been used in a wide range of research dealing with unbalanced panels, as evidenced by recent works (see Jin et al., 2010; Mukherjee, Bravo-Ureta, and De Vries, 2013; Wang and Wong, 2012). 2

Machinery assets value will be $0 if the machinery asset has been used past its depreciated life, while real estate assets value is assigned $0 if the ranch operates exclusively on leased land.

440 December 2013

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General Stochastic Frontier Production Function We propose a stochastic frontier production function for unbalanced panel data (Battese and Coelli, 1992). On the observed dataset with N farms over T periods, the model can be defined as Yit = f (Xit ; β ) exp(Vit − Uit )

(1) and (2)

Uit = ηit Ui = {exp[−η(t − Ti )]}Ui ,t ∈ T (i); i = 1, 2, . . . , N;

where Yit represents production output for the ith firm at the tth period of observation; f (Xit ; β ) is a function of a vector of input variables Xit and a vector of unknown parameters β ; Vit denotes random errors that are independent and identically distributed as normal distribution N(0, σv2 ), accounting for the factors that are not under the control of the farm. A nonnegative term, Uit , is included to account for the technical inefficiency in production. It is assumed to be independent and identically distributed as nonnegative truncations of the normal distribution N(µ, σ 2 ), where µ = zit δ . Additionally, zit is a vector of explanatory variables associated with technical inefficiency in the cow-calf industry and δ is a vector of unknown parameters. The technical inefficiency effect Uit can be specified as Uit = zit δ + Wit .


The random variable Wit follows truncated normal distribution of N(0, σ 2 ), where the truncated point is −zit δ , so that Wit ≥ −zit δ and Uit ≥ 0. We can test whether the stochastic frontier production function is necessary by testing the significance of the parameter γ = σu2 /(σv2 + σu2 ). For example, if γ is close to 1, then σv2 is zero, and a deterministic frontier function suffices. But if the null hypothesis, γ = 0, is accepted, then σu2 is zero and term Ui can be removed from the model; the parameters can be consistently estimated using an ordinary least square method. Parameter η is an unknown scalar to be estimated; a positive η means that farms tend to improve their technical efficiency over time, while a negative η stands for a decreasing level of technical efficiency and η = 0 indicates a constant technical efficiency over time. Here T (i) is a subset of the integers, 1, 2, . . . , T , representing the periods of observations involved. The mean technical efficiency of farm i over the observed periods can be defined as (4)

T Ei =

E(Yit |Ui , Xit ,t ∈ T (i)) = E[exp(−Uit )]. E(Yit |Ui = 0, Xit ,t ∈ T (i))

This measure has values between 0 and 1. For example, if a farm has a technical efficiency of 0.90, then the farm realizes 90% of the output that is possible for a fully efficient farm employing comparable inputs. Stochastic Frontier Production Function in Cobb-Douglas Form The stochastic frontier function for the panel data on cow-calf enterprises in the Texas Rolling Plains can be tentatively specified in the following Cobb-Douglas form,3 where subscripts i and t refer to the ith enterprise and the tth year, respectively: 3 We also estimated the model using Translog form. Using the likelihood test, however, we find the Cobb-Douglas specification is preferred in our case.

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Cow-Calf Herd Performance and GHG Emissions 441

ln(PoundWeanedit ) = β0 + β1 ln(AgeWeaningit ) + β2 ln(Livestockit ) + β3 ln(Machineryit ) + β4 ln(RealEstateit ) + β5 ln(Roughageit ) + β6 ln(Proteinit ) +


β7 ln(ImprovedPastureit ) + β8 ln(InputCostit ) + Vit − Uit ; where the technical inefficiency effect Uit is defined as Uit (6)

= δ0 + δ1 BreedingLengthit + δ2 PercentOwnedLandit + δ3 PercentOperatorLaborit + δ4 TotalAcreit + δ5 RainDevit + Wit .

As two-stage estimation may cause serious econometric problems (Kumbhakar, 2000, pp. 264), we estimate the parameters of equations (5) and (6) simultaneously using the Frontier 4.1 program written by Coelli (1996), which permits the unbalanced panel data to be estimated. Technical Efficiency and GHG Emissions To establish the relationship between technical efficiency and net GHG emissions per pound weaned,4 we divide farms into several groups according to their technical efficiency levels. For each efficiency group, we choose an “average” farm, which takes the average variable values of all the farms in that group. We calculate GHG emissions from six sources: 1) enteric CH4 emissions; 2) manure CH4 emissions; 3) manure N2 O emissions and soil GHG emissions; 4) protein supplement; 5) energy use; and 6) fertilizer use. Using the most recent methods specified by the Intergovernmental Panel on Climate Change (2006), we obtain net GHG emissions for each technical efficiency group. From SPA data, we can obtain the average conventional inputs related to GHG emissions for each group. For example, to calculate enteric CH4 emission of a selected group, we first compute the average number of females and the percentage females that weaned a calf. Other input variables associated with GHG calculation include gasoline, fuel and oil expenses, and fertilizer and lime expenses. Besides the data available in SPA, other values or parameters required to calculate GHG emissions are assumed using the literature and local expert opinion.5 The calculation for enteric and manure CH4 requires the average number of bulls and heifers on the farm. As only number of cows is available in SPA data, we rely on expert opinion and assume the number of bulls and the number of stocker heifers make up 3.75% and 15% of the total number of cows. Detailed methods using the example of a representative farm in the Texas Rolling Plains are described in the Appendix. We use the most recent method specified by the Intergovernmental Panel on Climate Change to calculate GHG emissions and sequestration for each technical efficiency category. Sources of parameter or input values that are needed for GHG emissions or sequestration are also provided. Methods for calculating the carbon emissions are provided on a production cycle basis, which were converted to a yearly basis after we obtained the results. Results Table 2 provides estimates of the stochastic frontier production function as specified in equation (5). Four explanatory variables (livestock assets, real estate assets, roughage, and adjusted input cost) in 4 Net GHG emissions per pound weaned is defined as total net GHG emissions divided by the farm’s total output in pounds, which is calculated as pounds weaned per exposed female multiplied by the number of cows. 5 Professor S. Bevers, Extension Economist, Texas A&M AgriLife Center, Vernon Texas.

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Table 2. Maximum-Likelihood Estimates for Parameters of Cobb-Douglas Stochastic Frontier Production Functions for Cow-Calf Enterprises on Texas Rolling Plains (1996–2011) MLE Estimates Variable




Model 1 2.2663∗∗∗ (0.1796)

ln(Average Age at Weaning)


ln(Livestock Assets)


0.0980 ∗ ∗ (0.0495) 0.0358

Model 2 2.3898∗∗∗ (0.1152) 0.0928∗ (0.0508) –

(0.0486) ln(Machinery Assets)


ln(Real Estate Assets)


0.0213∗∗ (0.0103) 0.0026

0.0207∗∗ (0.0091) –

(0.0045) ln(Roughage)



(0.0040) ln(Protein Supplement)


ln(Improved Pasture Proxy)


ln(Adjusted Input Cost)


0.0295∗∗∗ (0.0116) 0.0110∗∗ (0.0054) 0.0020

0.0301∗∗∗ (0.0094) 0.0111∗∗∗ (0.0041) –

(0.0458) σ 2 = σv2 + σu2

0.0063∗∗∗ (0.0020)

σ2 γ = σu2 /σ

0.5529∗∗∗ (0.1421)



0.0088∗∗∗ (0.0034) 0.7232∗∗∗ (0.1161) 104.00

Notes: Estimated standard errors are given in parentheses. Single, doube, and triple asterisks (*, **, ***) indicate significance at the 10%, 5%, and 1% level.

Model 1 are not significant, thus we eliminate them and estimate the alternative model, referred to as Model 2, that includes the rest of the variables in equation (5). The coefficients for Model 2 are shown in table 2. Not surprisingly, average weaning age significantly increases the pounds weaned per exposed female, providing the greatest elasticity among all the explanatory variables. Without taking this factor into account, farmers who wean calves at an earlier age are likely to be assigned to the low-efficiency category. The only reason to wean at a younger age would be to ensure that rebreeding of the cows was not compromised, as the cows need to recover body condition after weaning to ensure a high conception rate. The variable that generates the second greatest elasticity is protein supplement. Using pounds of feed fed as an explanatory variable directly, Ramsey et al. (2005) concluded that it did not lead to higher productivity. To understand the impact of this input, we divided pounds of feed fed into protein supplement and roughage. Protein supplement plays an important role in improving productivity, while the coefficient for roughage had a negative sign and is not significant. A plausible explanation is that roughage is most often fed as a substitute for forage grown on the farm when it is in short supply due to abnormal weather conditions. Therefore, roughage might be viewed as a proxy for unfavorable weather conditions. Plus, feeding of roughage to make up for a shortage of forage biomass is a practice that reduces profitability and causes damage to the rangeland or pasture (Díaz-Solís et al., 2009). Similar to Cho, Park, and Bevers (2011), we also found that an increase in machinery and equipment assets significantly improves productivity, while livestock assets and real estate assets play no significant role. As an indicator of farm management and capital intensity, it is not surprising

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Cow-Calf Herd Performance and GHG Emissions 443

Table 3. Tests of Hypothesis for Parameters of the Inefficiency Stochastic Frontier Production Function for Cow-Calf Farmers Null Hypothesis H0 : β2 = β4 = β5 = β8 = 0 H0 : γ = δi = 0 for i = 0, . . . , 5 H0 : δ1 = δ2 = δ3 = δ4 = δ5 = 0 H0 : η = 0

Log (Likelihood)

Test Statistic λ

Critical Value


104.00 83.25 88.75 91.83

2.46 41.50 30.50 1.20

9.49 14.07 11.07 3.84

Accept H0 Reject H0 Reject H0 Accept H0

to find that the variable of machinery and equipment assets has a positive effect on productivity. As Ramsey et al. (2005) point out, the ambiguous relationship found between livestock assets and productivity indicates that investment in livestock is not directly related to enhanced productivity. Also, investment in real estate assets may only reflect producers’ personal goals, such as wealth accumulation, and will therefore have little to do with productivity. The improved pasture proxy variable also had a positive impact on productivity, as improved pasture typically provides higher quality forage with greater quantity per acre. Koger et al. (1975) and Rakipova, Gillespie, and Franke (2003) observe the same positive relationship between improved pasture and cow productivity. Adjusted input cost, however, plays no significant role in productivity. Thus we can infer that labor and veterinary services actually contribute little to overall herd productivity in the Texas Rolling Plains area. Hypothesis Testing We carried out a series of tests on the joint significance of the four insignificant terms of Model 1 and some null hypotheses on technical efficiency. The results of those likelihood-ratio tests are provided in table 3. The likelihood-ratio test statistic is calculated as λ = −2[ln(L(H0 )) − ln(L(H1 ))], where ln(L(H0 )) denotes the log(likelihood) of the restricted model and ln(L(H1 )) represents the log(likelihood) of the unrestricted model. Table 3 also lists the log(likelihood) value of each restricted model. The test statistic, λ , has approximately chi-square distribution with degrees of freedom equal to the number of parameters restricted to be zero. For example, for the first hypothesis, H0 : β2 = β4 = β5 = β8 = 0, λ follows chi-square distribution with degrees of freedom equal to 4. Since this hypothesis is accepted, Model 2 is preferred to Model 1. The second hypothesis states that the inefficiency effect is completely absent from Model 2. Here γ ≡ σu2 /(σv2 + σu2 ) = 0 involves parameters associated with the variance of the technical inefficiency variable Uit and random variable Vit . If the null hypothesis γ = 0 is accepted, then σu2 is zero and the inefficiency term Ui can be removed from the model. In other words, all farms are efficient and the model can be consistently estimated using the ordinary least square method. As this hypothesis is also rejected, it means technical inefficiencies exist in Model 2. The third hypothesis states that the inefficiency effect for Model 2 exists, but it is not a linear function of the five explanatory variables specified in equation (6). This null hypothesis is rejected. Consequently, the joint effects of these five variables on the production inefficiencies are significant, although the individual effects of some variables may not be. The last hypothesis states that the technical inefficiency effect for Model 2 does not vary over time. This hypothesis is accepted, which means there was no improvement in technical efficiency from 1996 to 2011 for cow-calf farmers in the Texas Rolling Plains. Determinants of Technical Inefficiency Technical efficiency provides a measure of the output of farm i over time t relative to the output that can be produced by the most efficient farm in the sample using the same inputs. The average technical efficiency level for the seventy-six cow-calf farms is 95.1%, which is comparable to the

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Table 4. Estimation of Inefficiency Effect Model Variable




Breeding Season Length


Percentage of Owned Land


Percentage of Operator Labor


Total acre


Deviation from Mean Annual Rainfall (MAR)

δ5 σ2 γ

MLE Estimates −0.0955 (0.0868) 0.0008∗∗∗ (0.0003) −0.0009 (0.0007) −0.0032∗∗∗ (0.0009) −0.0065 (0.0052) 0.0029∗ (0.0016) 0.0088∗∗∗ (0.0034) 0.7232∗∗∗ (0.1250)

beef-cow production efficiency level obtained by Cho, Park, and Bevers (2011) using SPA data from three southern states from 2004 to 2008 and Rakipova, Gillespie, and Franke (2003), who studied the efficiency of Louisiana beef-cow producers. Meanwhile, our estimated efficiency level is far greater than the 78% found for beef-cow herds in Kansas (Featherstone, Langemeier, and Ismet, 1997) and the 69% found for beef-cow herds in Kenya (Otieno, Hubbard, and Ruto, 2012). This confirms that technical inefficiency, though it exists, is not a serious problem for most cow-calf farms in the Texas Rolling Plains. Estimates for the technical inefficiency effect of Model 2 are provided in table 4. Breeding season length is positively related to the technical inefficiency. Thus farms with a longer breeding season have a significant lower productivity. This result is in accordance with that of Ramsey et al. (2005), suggesting that in the Texas Rolling Plains, an average farm can still improve its productivity by reducing breeding season length. Another variable that significantly affects technical efficiency is percentage of operator labor, which indicates that farm owners who devote more time on the beefcow operation to decrease spending on hired labor will achieve higher efficiency. A positive relationship exists between deviation from mean annual rainfall and technical inefficiency. A rainfall level close to mean annual rainfall will promote productivity, while too little or too much rain are both counterproductive. Severe drought is a serious threat to the beef industry in Texas (Independent Cattlemen’s Association, 2011). We find that an 80% deviation from MAR increased technical inefficiency by 23.2%. Using absolute rainfall level as an explanatory variable (Cho, Park, and Bevers, 2011) was less instructive than the deviation from MAR used in this study. Similar to Rakipova, Gillespie, and Franke (2003), we also found both percentage of owned land and total acres had negative values and were not significant in the inefficiency model. Technical Efficiencies of Different Categories Table 5 gives the technical efficiencies of cow-calf operations in the Texas Rolling Plains in three categories. The first is by farm, giving the average technical efficiency of each farm from 1996 to 2011. The second is by observation, where we treat the same farm sample in a different year as a different observation. The last is by year, where we average all farms’ efficiency levels observed in the same year. The average technical efficiency level for each farm (first column) outperformed that for individual observations (second column). This suggests that although herd productivity may occasionally be negatively affected by some uncontrollable factors such as abnormal rainfall in

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Cow-Calf Herd Performance and GHG Emissions 445

Table 5. Frequencies and Percentages of Technical Efficiencies for Cow-Calf Farms Frequencies and Percentages Technical Efficiency

By Farm

By Observation

By Year


0 (0%)

3 (3.95%)

0 (0%)


1 (2.5%)

3 (3.95%)

0 (0%)


3 (7.50%)

3 (3.95%)

2 (14.29%)


5 (12.50%)

13 (17.11%)

3 (21.43%)


31 (77.50%)

54 (71.05%)

9 (64.29%)


40 (100%)

76 (100%)

14 (100%)

Table 6. Technical Efficiency by Size of Cow-Calf Farms Size (Acres)


Technical Efficiency

Size (No. of Breeding Females)


Technical Efficiency

Below 1,000



Below 100















Above 10,000



Above 300









specific years, such unfavorable effects seem to level off over the years. From the perspective of the year (third column), we found a lower proportion of farms with efficiency values lying in the 0.96 to 1.00 range because all of the farms tend to be affected by the unfavorable environment in the same year, thus the average inefficiency level for those years can be relatively low. To further understand how technical efficiency relates to herd scale, table 6 presents average technical efficiency for different categories of herd size, measured in total acreage and number of breeding females. No clear relationship exists between technical efficiency and number of breeding females. This can be seen from the ranking of technical efficiency, where herd size of 200–300 comes first, then herds with size over 300, then herds with size below 100, while the lowest technical efficiency occurs for herds of size 100–200. Although economy of scale is generally found when attempting to reducing costs, no study has shown that a larger herd is associated with increased productivity (Langemeier, McGrann, and Parker, 2004; Featherstone, Langemeier, and Ismet, 1997; Ramsey et al., 2005). However, when it comes to the total farm area, table 6 clearly shows that farms occupying a larger area generally have greater technical efficiency. Technical Efficiency and GHG Emission Based on the technical efficiency level, we divided observations into five groups according to their technical efficiency levels (70%–79%, 80%–85%, 86%–90%, 91%–95%, and 96%–100%) and refer them as efficiency groups 1 to 5. Then we applied the methods specified in the Appendix to obtain net GHG emissions for each group. The final results are provided in table 7. We found that, in agreement with DeRamus et al. (2003), GHG emissions per pound weaned decline as technical efficiency increases. This is caused partly by the positive relationship between technical efficiency and pounds weaned. The average pounds weaned per exposed female for efficiency groups 1 to 5 are 300, 345, 354, 431, and 481, suggesting that the inputs generating GHG emissions are used more efficiently to produce each unit of output by groups with higher technical efficiency. Group 1 has the highest GHG emissions per pound weaned due to high fertilizer and protein supplement use and low pounds weaned. While GHG emissions tend to decline for groups with increased technical efficiency, GHG sequestration generally displays

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Table 7. GHG Net Emissions among Five Technical Efficiency Categories for Cow-Calf Farms Technical Efficiency




Enteric CH4






Manure CH4








1.09 0.04

Manure N2 O





Protein Supplement





Energy Use






Fertilizer Use






GHG Emission






GHG Sequestration






Net GHG Emission






Notes: Units are pounds of carbon equivalent per pound weaned.

the opposite pattern. This is because GHG sequestration is solely determined by total farm acres in our calculation, while a positive relationship exists between total acre and technical efficiency (table 6). The average total acres for efficiency groups 1 to 5 are 427, 458, 1,795, 4,982, and 10,054. In addition, the higher efficiency groups tend to have a higher number of acres per female, averaging 3.5, 7.3, 7.5, 17.1, and 23.5 for efficiency groups 1 to 5. This suggests that beef-cow operations with lower cow density (lower stocking rate) are more likely to be both technically more efficient and to have lower net carbon emission rates per pound weaned. For net GHG emissions, a negative sign indicates net sequestration rather than net emission. Cow-calf farmers in efficiency groups 4 and 5 produce net carbon sequestration rather than carbon emission (table 7). More technically efficient farms also have more net carbon sequestration, suggesting that environment quality will not be compromised by pursuing higher technical efficiency. This will benefit more technically efficient cow-calf farmers who would likely be rewarded by any future carbon credit program. However, farms in lower efficiency categories, mostly those farms with dense (heavily stocked) beef-cow populations are not likely to benefit from a GHG reduction program. Discussion This paper investigates the relationship between various farm management practices and technical efficiencies. The stochastic frontier function used to investigate the factors that promote higher productivity for a typical cow-calf farmer indicated that there were significant but small increases in elasticity from different management factors. A 10% increase in each management action increased pounds weaned per breeding cow by 0.98% for average age at weaning, 0.30% for protein supplementation, 0.21% for investment in machinery, and 0.11% for pasture-quality improvement. In contrast, investment in real estate and livestock assets had no significant effect. The roles played by roughage feed and adjusted input cost—including labor and veterinary services—were also not significant. The level of technical efficiency is assessed for cow-calf enterprises sampled by SPA data in the Texas Rolling Plains. At 95%, the average technical efficiency for cow-calf farms on Texas Rolling Plains is comparable to that of beef-cow herds in the U.S. Southern Plains (Cho, Park, and Bevers, 2011; Rakipova, Gillespie, and Franke, 2003), but greater than that of beef-cow herds in Kansas at 78% (Featherstone, Langemeier, and Ismet, 1997) and in Kenya at 69% (Otieno, Hubbard, and Ruto, 2012). Average technical efficiency is also found to increase as farm area increases. For example, average technical efficiency is 91.3% for farms below 1,000 acres and 97% for farms above 10,000 acres, suggesting increasing returns to scale as farm size increases. However, no significant improvement in technical efficiency was found over time during the 1996 to 2011 survey period. Significant variables resulting in lower technical efficiency include a longer breeding season, lower operator labor percentage, and increasing deviation from MAR. We found that technical

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Cow-Calf Herd Performance and GHG Emissions 447

efficiency increased 8% if breeding season length decreased by 100 days. In addition, in the case of extreme drought (50% of MAR), estimated technical efficiency was reduced by 14.5%., which underscores the importance of favorable weather conditions for cow-calf operations. To help cowcalf operations mitigate losses due to severe drought, measures such as using management-intensive grazing with multiple paddocks and drought insurance should be promoted. In addition, we also find farm efficiency increases on average by 3.2% with a 10% increase in the percentage of operator labor. This paper also aimed to determine the relationship between technical efficiency and environmental impact. Life-cycle analyses indicated that enteric CH4 , energy use, and manure N2 O generate about 95% of all GHG emissions for all efficiency groups, with 45%, 20%, and 20% attributable to enteric CH4 , energy use, and manure N2 O, respectively. In comparison, manure CH4 , protein supplement, and fertilizer use have little effect on GHG emissions per unit of output. Direct linkages can be found between farm efficiency and carbon emission and sequestration. We found that carbon emissions per unit of output decrease as farm efficiency increases. This is partly due to the positive correlation between farm efficiency and output level. However, higher carbon sequestration occurs on farms that are more technically efficient as a result of more acres allocated to each breeding cow. The greatest net carbon sequestration was found for the two most technically efficient groups, indicating that pursuing technical efficiency will not compromise environmental quality. Conclusion This paper addresses two equally important issues. First, we use an SFA method and find that direct expenditures on protein supplement, machinery investment, and pasture-quality improvement enhance farm productivity. Factors that affect technical efficiency include breeding season length, percentage of operator labor, and deviation from MAR. Second, this paper provides the first study on the relationship between cow-calf farm technical efficiency and environmental consequences as indicated by greenhouse gas emission. Results suggest that for the cow-calf industry, pursuing farm efficiency aligns with environmental protection goals. The focus of the SFA model in this paper is on output, or pounds weaned per breeding female, rather than profitability. In addition to our finding, future research could investigate whether the incentive to pursue financial profitability conflicts with environmental protection objectives. Future efforts could also extend the method to model the link between pursuing efficiency and environmental protection in different industries, such as cropping, or in different regions. [Received April 2013; final revision received October 2013.] References Aigner, D. J., and S. F. Chu. “On Estimating the Industry Production Function.” American Economic Review 58(1968):826–839. Aigner, D. J., C. A. K. Lovell, and P. Schmidt. “Formulation and Estimation of Stochastic Frontier Production Function Models.” Journal of Econometrics 6(1977):21–37. American Soybean Association. “Soybeans...The Miracle Crop.” 2012. Available online at http://www.soystats.com/2012/page_04.htm. Battese, G. E., and T. J. Coelli. “Frontier Production Functions, Technical Efficiency and Panel Data: With Application to Paddy Farmers in India.” Journal of Productivity Analysis 3(1992):153–169. ———. “A Model for Technical Inefficiency Effects in a Stochastic Frontier Production Function for Panel Data.” Empirical Economics 20(1995):325–332.

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Battese, G. E., T. J. Coelli, and T. C. Colby. “Estimation of Frontier Production Functions and the Efficiencies of Indian Farms Using Panel Data from ICRISAT’s Village Level Studies.” Journal of Quantitative Economics 5(1989):327–348. Charnes, A., W. W. Cooper, and E. Rhodes. “Measuring the Efficiency of Decision Making Units.” European Journal of Operational Research 2(1978):429–444. Cho, J., S. C. Park, and S. J. Bevers. “An Economic Performance Analysis of the Beef Cow-Herd Enterprise Using a Stochastic Frontier Function.” Corpus Christi, TX: Southern Agricultural Economics Association, 2011. Coelli, T. “A Guide to FRONTIER Version 4.1: A Computer Program for Stochastic Frontier Production and Cost Function Estimation.” CEPA Working Paper 96/07, University of New England, Department of Econometrics, Armidale, Australia, 1996. DeRamus, H. A., T. C. Clement, D. D. Giampola, and P. C. Dickison. “Methane Emissions of Beef Cattle on Forages.” Journal of Environment Quality 32(2003):269–277. Deutscher, G. H., J. A. Stotts, and M. K. Nielsen. “Effects of Breeding Season Length and Calving Season on Range Beef Cow Productivity.” Journal of Animal Science 69(1991):3453–3460. Díaz-Solís, H., W. E. Grant, M. M. Kothmann, W. R. Teague, and J. A. Díaz-García. “Adaptive Management of Stocking Rates to Reduce Effects of Drought on Cow-Calf Production Systems in Semi-Arid Rangelands.” Agricultural Systems 100(2009):43–50. Dunn, B. H. Characterization and Analysis of the Beef Cow-Calf Enterprises of the Northern Great Plains Using Standardized Performance Analysis. Ph.D., South Dakota State University, Brookings, SD, 2000. Falconer, L. L., J. L. Parker, and J. M. McGrann. “Cost of Production Analysis for the Texas CowCalf Industry.” Texas Journal of Agriculture and Natural Resources 12(1999):7–13. Färe, R., S. Grosskopf, D. W. Noh, and W. Weber. “Characteristics of a Polluting Technology: Theory and Practice.” Journal of Econometrics 126(2005):469–492. Farrell, M. J. “The Measurement of Productive Efficiency.” Journal of the Royal Statistical Society: Series A (General) 120(1957):253–290. Featherstone, A. M., M. R. Langemeier, and M. Ismet. “A Nonparametric Analysis of Efficiency for a Sample of Kansas Beef Cow Farms.” Journal of Agricultural & Applied Economics 29(1997):175–184. Field to Market. “Environmental and Socioeconomic Indicators for Measuring Outcomes of On-Farm Agricultural Production in the United States.” Summary Report Second Report, Field to Market, 2012. Available online at http://www.fieldtomarket.org/report/national2/PNT_SummaryReport_A11.pdf. Global Change Program Office, Office of the Chief Economist. “U.S. Agriculture and Forestry Greenhouse Gas Inventory: 1990–2005.” USDA Technical Bulletin No. 1921, U.S. Department of Agriculture, Washington, DC, 2008. Available online at http://www.usda.gov/oce/climate_change/AFGG_Inventory/USDA_GHG_Inventory.pdf. Gould, F. W. “Texas Plants: A Checklist and Ecological Summary.” Texas A&M University Bulletin MP-585, Texas A&M Agricultural Experiment Station, College Station, TX, 1975. ICF Consulting. Methods for Estimating Greenhouse Gas Emissions from Agricultural Soils. Prepared for Greenhouse Gas Committee Emission Inventory Improvement Program, U.S. EPA, 1999a. Available online at http://www.azclimatechange.gov/download/O40F6841.pdf. ———. Methods for Estimating Greenhouse Gas Emissions from Manure Management. Prepared for Greenhouse Gas Committee Emission Inventory Improvement Program, U.S. EPA, 1999b. Available online at http://webexch.azdeq.gov/download/O40F6840.pdf. Independent Cattlemen’s Association. “Severe Drought Testing Texas Cattle Industry’s Survival Instincts.” CattleNetwork.com (2011). Intergovernmental Panel on Climate Change. 2006 IPCC Guidelines for National Greenhouse Gas Inventories. Prepared for the National Greenhouse Gas Inventories Programme. Japan: IGES, 2006. Available online at http://www.ipcc-nggip.iges.or.jp/public/2006gl/.

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Jin, S., H. Ma, J. Huang, R. Hu, and S. Rozelle. “Productivity, Efficiency and Technical Change: Measuring the Performance of China’s Transforming Agriculture.” Journal of Productivity Analysis 33(2010):191–207. Koger, M., F. M. Peacock, W. G. Kirk, and J. R. Crockett. “Heterosis Effects on Weaning Performance of Brahman-Shorthorn Calves.” Journal of Animal Science 40(1975):826–833. Kumbhakar, S. Stochastic Frontier Analysis. Cambridge, UK: Cambridge University Press, 2000. Lal, R. “Carbon Emission from Farm Operations.” Environment International 30(2004):981–990. Langemeier, M. R., J. M. McGrann, and J. Parker. “Economies of Size in Cow-Calf Production.” Beef Cattle Handbook BCH-8100, Iowa State University Iowa Beef Center, Ames, IA, 2004. Available online at http://www.iowabeefcenter.org/Beef%20Cattle%20Handbook/ Economies_Size_Cow-calf.pdf. Meeusen, W., and J. van den Broeck. “Efficiency Estimation from Cobb-Douglas Production Functions with Composed Error.” International Economic Review 18(1977):435–444. Miller, A. J., D. B. Faulkner, R. K. Knipe, D. R. Strohbehn, D. F. Parrett, and L. L. Berger. “Critical Control Points for Profitability in the Cow-Calf Enterprise.” Professional Animal Scientist 17(2001):295–302. Mukherjee, D., B. E. Bravo-Ureta, and A. De Vries. “Dairy Productivity and Climate Conditions: Econometric Evidence from South-Eastern United States.” Australian Journal of Agricultural and Resource Economics 57(2013):123–140. Otieno, D. J., L. J. Hubbard, and E. Ruto. “Determinants of Technical Efficiency in Beef Cattle Production in Kenya.” Foz do Iguacu, Brazil: International Association of Agricultural Economists, 2012. Potter, K. N., H. A. Torbert, H. B. Johnson, and C. R. Tischler. “Carbon Storage after Long-term Grass Establishment on Degraded Soils.” Soil Science 164(1999):718–725. Rakipova, A. N., J. M. Gillespie, and D. E. Franke. “Determinants of Technical Efficiency in Louisiana Beef Cattle.” Journal of the ASFMRA 66(2003):99–107. Ramsey, R., D. Doye, C. E. Ward, J. M. McGrann, L. L. Falconer, and S. J. Bevers. “Factors Affecting Beef Cow-Herd Costs, Production, and Profits.” Journal of Agricultural and Applied Economics 37(2005):91–99. Ryan, B., and D. G. Tiffany. Minnesota Agricultural Energy Use and the Incidence of a Carbon Tax. Institute for Local Self Reliance, Minneapolis, MN, 1998. Available online at http://www.apec.umn.edu/staff/dtiffany/ILSRcarbontax.pdf. Seale, J. L. “Estimating Stochastic Frontier Systems with Unbalanced Panel Data: The Case of Floor Tile Manufactories in Egypt.” Journal of Applied Econometrics 5(1990):59–74. Trestini, S. “Technical Efficiency of Italian Beef Cattle Production under a Heteroscedastic NonNeutral Production Frontier Approach.” Duluth, MN: University of Minnesota, Center for International Food and Agricultural Policy, 2006. U.S. Environmental Protection Agency. “Inventory of U.S. Greenhouse Gas Emissions and Sinks: 1990-2010. Annex 3 Methodological Descriptions for Additional Source or Sink Categories.” EPA 430-R-12-001, Washington, DC, 2012. Available online at http://www.epa.gov/ climatechange/Downloads/ghgemissions/US-GHG-Inventory-2013-Main-Text.pdf. Wang, M., and M. C. S. Wong. “International R&D Transfer and Technical Efficiency: Evidence from Panel Study Using Stochastic Frontier Analysis.” World Development 40(2012):1982–1998.

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Appendix A: Methods for Calculating Total GHG Emissions of a Representative Cow-Calf Farm Data are provided by Stan J. Bevers, Professor and Extension Economist-Management for Texas A&M AgriLife Extension Service, who specializes in ranch management and analysis. Farm Description Calculatations are based on a herd size of 800 cattle, including 400 cows, 60 heifers, 325 calves, and 15 bulls. All of the calves except sixty heifers are sold immediately after weaning. We assume a breeding season from April to August and a birth season from January to May. For simplicity, we assume a 90% pregnancy and lactating rate (actual pregnancy rates range from 90–92% and lactating rates are about 88%). Weaning occurs from September to November. The life cycle we consider here is defined as the entire production period, which lasts from April to November of the following year. During the breeding season from April to August, the breeding cows also feed the previous batch of calves. For calculation purposes, the lactation period lasts 120 days. During the gestation period from August to the following May (based on a 283-day pregnancy) we assume 133 days of overlap between pregnancy and lactation and 150 days of pregnancy only. From May till the weaning season, we assume there are 90 days of lactation only and 120 days of overlap during which the lactating cows are pregnant with the next generation of calves. In a production cycle, we assume that a typical cow spend 210 days lactating, 150 days pregnant while not lactating, and 253 days both lactating and pregnant, for a total of 613 days. We assume a 100% pasture manure management system, given that managing a dry-lot manure system is too costly. We also assume leaching and runoff does not occur on the pasture. Supplemental feed is either Coastal Bermuda hay or Sudan hay. However, supplemental hay is rarely used in the Southern Plains except in years of severe drought, so we ignore GHG emissions from this source. Typically, supplemental protein is used from December to March, when the grass protein is low. The 400 cows were fed two pounds of supplemental protein per head per day for 120 days, for a total of 96,000 pounds per production season. Supplemental proteins include grain-based protein made of corn and oil-based protein made of cottonseed and soybean meals. Here we calculate the GHG emissions from soybean meal as an example of protein supplement source. Methodologies We describe the methodologies used to calculate GHG emissions for five components of emissions on a typical cow-calf farm, including enteric methane emission, manure methane emission, manure N2 O emission, supplemental protein CO2 emission, and GHG emission from farm energy use and fertilizer use. Carbon sequestration was also calculated. Enteric CH4 According to the Intergovernmental Panel on Climate Change (2006), we have CH4enteric = EF × N/106 Gg CH4 per production cycle, where N is the number of head of livestock species and EF is the emission factor for the defined livestock population in kilograms of CH4 per head per year. According to the Tier 2 approach,6 EF should be developed by (A1)

EF =

Ym )365 GE( 100 , 55.65

6 IPCC suggests the Tier 2 approach for beef cattle when estimating emissions from enteric fermentation. According to IPCC, “The Tier 2 method should be used if enteric fermentation is a key source category for the animal category that represents a large portion of the country’s total emissions.”

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Table A1. Energy Use and Carbon Dioxide Emissions by Fuel Source on U.S. Farms, 2005 Energy Consumed (BTUs)

Fuels Diesel Gasoline LP Gas Natural Gas Electricity

CO2 Emissions (g CO2 eq)

408.5 128.5 76 53 135

29.58 9.01 4.74 2.80 23.28

Source: Global Change Program Office, Office of the Chief Economist (2008, table 5-2)

where Ym is the methane conversion factor, which is the percent to gross energy in feed converted to methane. According to the Intergovernmental Panel on Climate Change (2006, table 10.12), Ym = 6.5% ± 1.0%. The lower bound is more appropriate for feed with high digestibility and high energy value, and vice versa. For calves fed entirely on milk, Ym = 0. As a result, we use Ym = 0 for the preweaning calves. Factor 55.65 (MJ/kg CH4 ) stands for the energy content of methane. If an animal subcategory is staying on the farm for less than 365 days, we replaced 365 with the number days that the animals actually stayed on the farm; GE is the gross energy intake in MJ per head per day, which is further defined as (A2)

GE =

NEm +NEa +NEl +NE p REM DE% 100




where NEm is the net energy for maintenance, which is required by the animal so that the body energy is neither gained or lost. It can be calculated as: NEm = C fi × (Weight)0.75 . For nonlactating cows, C fi = 0.322; for lactating cows, C fi = 0.386; for bulls, C fi = 0.370; Weight is the live-weight of animal in kilograms. According to the U.S. Environmental Protection Agency (2012, table A-173), Typical Animal Mass (TAM) in the year 2010 is 613 kilograms/head for cows and 919 for bulls. TAM for steers and heifers are 234 and 220, respectively, according to the expert’s description. Therefore, for nonlactating and lactating cows, we have NEm = 0.322 × (613)0.75 = 39.67 and NEm = 0.386 × (613)0.75 = 47.55. For bulls, NEm = 0.370 × (919)0.75 = 61.76. The net energies for maintenance for steers and heifers are NEm = 0.322 × (234)0.75 = 19.26 and NEm = 0.322 × (220)0.75 = 18.39. Next, NEa = Ca × NEm stands for the net energy for activity, which is energy needed by the animal to obtain food, water, and shelter. It is based on the feeding situation rather than the feed itself; for cattle confined in a small area such as a barn, Ca = 0; for cattle confined in areas with sufficient forage such as a pasture, Ca = 0.17; for cattle grazing in open range land, Ca = 0.36 In the Rolling Plains, most cattle feed on pasture, so we choose Ca = 0.17. Additionally, the NEa for nonlactating cows, lactating cows, bulls, steers, and heifers are 6.74, 8.08, 10.50, 3.27, and 3.13. Third, NEl = Milk × (1.47 + 0.40 × f at) is the net energy necessary for lactation, where Milk is the amount of milk produced (kg/day) and f at is the fat content of milk (%). According to the U.S. Environmental Protection Agency (2012), the lactation estimates for beef cow from January to December are 3.3, 5.1, 8.7, 12.0, 13.6, 13.3, 11.7, 9.3, 6.9, 4.4, 3.0, and 2.8 lbs milk/beef cow/day. As we choose April to August as the breeding season, calves are born between January and May and weaned between September and November. If cows give birth in January, February, and March and wean the calves eight months later, the average daily milk production would be 9.32, 9.44, and 9.21 pounds. Thus we choose the average milk production as 9.32 lbs/day (4.24 kg/day). Also according to the U.S. Environmental Protection Agency (2012), the percentage of fat in milk is 4%. Therefore for lactating cows we have NEl = 4.24 × (1.47 + 0.40 × 4) = 13.02. Also, for pregnant cows, NE p is the net energy required for pregnancy (MJ per day), where NE p = 0.1 × NEm = 0.1 × 39.67 = 3.97. For heifers and steers, NEg is the net energy for growth (MJ per day), defined as NEg = 22.02 × [BW /(C × MW )]0.75 × W G1.097 , where BW is the average live body weight (BW) of the animals in the population (kg); C is a coefficient with a value of 0.8 for

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females, 1.0 for castrates, and 1.2 for bulls; MW is the mature live body weight of an adult female in moderate body condition (kg); and W G is the average daily weight gain of the animals in the population. BW and W G data for heifers and MW data are directly obtained from Professor Bevers. For heifers, we have NEg = 22.02 × [220/(0.8 × 613)]0.75 × 2.51.097 = 32.98. Cattle feed digestibility, denoted by DE%, ranges from 45% to 55% for crop byproducts and range lands; 55% to 75% for good pastures, good preserved forages, and grain-supplemented foragebased diets. Following the expert’s opinion, for the Rolling Plains we chose the second category, thus the average DE% is 65%. Finally, based on DE%, we can calculate REM, the ratio of net energy available in diet for maintenance to digestible energy consumed: (A3) REM = 1.123 − 4.092 × 10−3 × DE% + 1.126 × 10−5 × (DE%)2 − 25.4/DE% = 0.51. We can also calculate REG, is the ratio of net energy available in diet for growth to digestible energy consumed: (A4)

REG = 1.164 − 5.160 × 10−3 × DE% + 1.308 × 10−5 × (DE%) − 37.4/DE% = 0.31.

Now we are ready to calculate enteric methane emissions. For lactating only cows: (A5)

GE =

(NEm + NEa + NEl )/REM (47.55 + 8.08 + 13.02)/0.51 = = 207.09; DE%/100 65/100



GE × (Ym /100) × days on lactating only 55.65


207.09 × (6.5/100) × 210 = 50.80; 55.65


CH4enteric = EF × N/106 = 50.80 ×


400 × 90% = 0.018. 106

For pregnant and not lactating cows: (A8)

GE =

(NEm + NEa + NE p )/REM (39.67 + 6.74 + 3.97)/0.51 = = 151.98; DE%/100 65/100



GE × (Ym /100) × days on gestation only 55.65


151.98 × (6.5/100) × 150 = 26.63; 55.65



CH4enteric = EF × N/106 = 26.63 × 400 × 90%/106 = 0.010.

For pregnant and lactating cows: GE


(NEm + NEa + NEl + NE p )/REM DE%/100


(47.55 + 8.08 + 13.02 + 3.97)/0.51 = 219.06; 65/100


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Cow-Calf Herd Performance and GHG Emissions 453



GE × (Ym /100) × days both lactating and pregnant 55.65


219.06 × (6.5/100) × 253 = 64.73; 55.65



CH4enteric = EF × N/106 = 64.73 × 400 × 90%/106 = 0.023.

For cows that are neither lactating nor pregnant (for simplicity we assume 10% of cows remain nonproductive in the 613-day period): (A14)



GE =

EF =

(NEm + NEa )/REM (39.67 + 6.74)/0.51 = = 140; DE%/100 65/100

GE × (Ym /100) × 613 140 × (6.5/100) × 613 = = 100.24; 55.65 55.65

CH4enteric = EF × N/106 = 100.24 × 400 × 10%/106 = 0.004.

For bulls: (A17)


GE =

EF =

(NEm + NEa )/REM (61.76 + 10.50)/0.51 = = 217.98; DE%/100 65/100

GE × (Ym /100) × 613 217.98 × (6.5/100) × 613 = = 156.07; 55.65 55.65 CH4enteric = EF × N/106 = 156.07 × 15/106 = 0.002.


For stocking heifers: GE


(NEm + NEa )/REM + NEg /REG DE%/100


(18.39 + 3.13)/0.51 + 32.98/0.31 = 228.59; 65/100




EF =

GE × (Ym /100) × 613 228.59 × (6.5/100) × 613 = = 163.67; 55.65 55.65 CH4enteric = EF × N/106 = 163.67 × 60/106 = 0.010.

Together, on the representative farm we defined in the previous section, overall enteric emissions can be added up as CH4enteric

= 0.018 + 0.010 + 0.023 + 0.004 + 0.002 + 0.010

(A23) = 0.067 Gg CH4 (67, 000 kg CH4 ) per production cycle. Thus, the enteric methane emission is equivalent to 1,407,000 kg CO2 per production cycle, or 1,551 tons CO2 per production cycle (1 unit of CH4 has a global warming potential of 21 units of CO2 ).

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Manure CH4 The method we describe in this section is provided by ICF Consulting (1999b),which is similar to the Tier 2 method in IPCC, but is more informative in that it treats each U.S. state differently, rather than treating the North American region as a whole. Overall, the manure methane emissions can be calculated as: CH4manure = Total V Si × B0 × MCFj × W S%i j ; where Total V Si stands for the volatile solid produced by all the animals in each subcategory per year; it can be computed from (A24)

Total VSi =Population of subcategory i (head) × TAMi (lbs/head) × VS coefficient

Typical Animal Mass (TAM) is 397 lbs/head for calves, 794 for steers and heifers, 1,102 for cows and 1,587 for bulls. From ICF Consulting (1999b, table 7.4–11), we know that the VS coefficient is 2.6 lbs VS/lb animal mass/year. Thus TAMi × VS coefficient values for calves, heifers, cows, and bulls can be calculated as 469, 938, 1,302, and 1,875 kg/animal/year for all states. Estimates by ICF Consulting (1999b) will be used, as they include all four of the categories we need. Meanwhile, we adjust those values by a factor of (1, 600/1, 302 = 1.23) to match the EPA’s updated information.7 The adjusted TAMi × VS coefficient values for calves, heifers, cows, and bulls are 577, 1,154, 1,602, and 2,307 kg/animal/year (1,270, 2,539, 3,524, and 5,075 lbs/animal/year). B0 is the estimate of the maximum methane-producing capacity of U.S. livestock. For beef not in feedlots, B0 = 2.72 ft3 per lb VS;8 MCF stands for the methane conversion factor for manure system j (%). In Texas, MCF is 1.4% for pasture/range/paddock manure system and 2.1% for dry lot manure system. In Oklahoma, those values are 1.4% and 1.9%. As we only consider a pasture/range/paddock manure system (since the dry lot system is too costly to maintain), we choose MCF = 1.4%. W S%i j stands for the percentage of animal i’s manure managed in manure system j. Here we assume a 100% pasture manure system based on the expert’s opinion. We calculate manure methane emission as CH4manure

= Total VSi × B0 × MCFj × W S%i j = (325 × 1, 270 + 60 × 2, 539 + 400 × 3, 524 + 15 × 5, 075)

(A25) × 2.72 × 1.4% × 100% = 78, 094 ft3 CH4 per year. This is equivalent to 3,225 lbs of CH4 per year given that 1 ft3 = 0.0413 lbs; or 1466 kg CH4 per year which equals 2,462 kg of CH4 per production cycle. Thus the manure methane emission on this farm is 51,702 kg CO2 per production cycle, or 57 tons CO2 per production cycle. Manure N2 O N2 O emissions generated by manure in a “pasture, range, and paddock” system occur directly and indirectly from the soil (Intergovernmental Panel on Climate Change, 2006). Thus, we refer to the methods provided in (Intergovernmental Panel on Climate Change, 2006, Section 11.2), ‘N2 O emissions from managed soils.’ 7 In EPA (2012), the calculation TAM (lbs/head)×VS coefficient (lbs VS/lb animal mass/year) is provided as a single i value V S (kg/animal/year) for the year 2010. Three categories are provided in EPS Annex 3, Table A-193: Cow, Heifer, and Steer. Those values are 1,589, 1,013, and 923 for Oklahoma and 1664, 1,053, and 971 for Texas. Since the average value for a cow for those two states is roughly 1,600 in 2010 and 1,302 in 1999 (U.S. Environmental Protection Agency, 2012), we adjust the ICF Consulting (1999b) estimates by a factor of 1600/1302 = 1.23 to obtain the updated estimates. 8 Note that coefficients such as B provided in ICF Consulting (1999b) require us to use inputs in English units, while 0 inputs in metric units are required for calculations such as equation (1), where factor 55.65 has units of MJ/kg CH4 , according to Intergovernmental Panel on Climate Change (2006). To maintain the traceability of the original formulas and factors/coefficients, we choose different units correspondingly. In the main paper we convert all the final GHG net emissions uniformly into English units.

Wang et al.

Cow-Calf Herd Performance and GHG Emissions 455

Direct N2 O emissions from urine and dung inputs to grazed soils can be calculated as N2 Odirect = F × EF3 × 44/28 kg N2 O/year, where F is the annual amount of urine and dung in kg N/year deposited by grazing animals on pasture, range, and paddock. The value of F can be estimated using the method from ICF Consulting (1999a): = unvolatilized N excreted by subcategory i


= 0.8 × Population of subcategory i (head) × [TAMi (kg/head)/1,000] × (A26) Kjeldahl N per day per 1,000 kg mass (kg/day) × percentage of manure i on pasture/range/paddock × 365 days per year. We take the Typical Animal Mass (TAM) in the year 2010 according to the U.S. Environmental Protection Agency (2012, table A-173) and convert it to kg/head. The TAM for calves is 40 kg at birth and 234 kg at weaning, averaging 137 kg; the TAM for steers stockers, heifers stockers, cows, and bulls are 330, 324, 613, and 919 respectively. Kjeldahl N per day per 1,000 kg mass (kg/day) takes the value of 0.34 for all subcategories listed above. Thus, F can be calculated as: F

= 0.8 × (325 × 137 + 60 × 324 + 400 × 613 + 15 × 919)/1, 000 × 0.34 × 100% × 365


= 32, 062. EF3 is the emission factor for N2 O emissions from urine and dung deposited by grazing animals on pasture, range and paddock in kg N2 O/kg N. EF3 takes a default value of 0.02 with uncertainty range between 0.007 and 0.06 (Intergovernmental Panel on Climate Change, 2006, table 1 1.1). Therefore: N2 Odirect

= F × EF3 × 44/28 = 32, 062 × 0.02 × 44/28

(A28) = 1, 008 kg N2 O/year; or 1, 692 kg N2 O/production period. In addition to direct N2 O emissions, emissions of N2 O also occur through the volatilization and deposition of N as NH3 and nitrogen oxides and their products back into soils,9 which can be calculated as N2 Ovolatilization = F × Frac1 × EF4 × 44/28, where F is the annual amount of urine and dung deposited by grazing animals on pasture, range, and paddock in kg N/year, which can be calculated as: F

= Population of subcategory i (head) × [TAMi (kg/head)/1,000] × Kjeldahl N per day per 1,000 kg mass (kg/day) ×


percentage of manure i on pasture/range/paddock × 365 days per year = (325 × 137 + 60 × 324 + 400 × 613 + 15 × 919)/1, 000 × 0.34 × 365 = 40078.

The fraction of F that volatilizes as NH3 and NOx is denoted as Frac1 , which takes a default value of 0.2 with uncertainty range between 0.05 and 0.5 (Intergovernmental Panel on Climate Change, 2006, table 11.3). EF4 is the emission factor for the atmospheric deposition of N on soils. EF4 takes a default value of 0.01 with uncertainty range between 0.002 and 0.05 (Intergovernmental Panel on 9 The other possible way is through nitrogen leaching and runoff in some regions. In the Rolling Plains we regard it as zero based on expert opinion.

456 December 2013

Journal of Agricultural and Resource Economics

Climate Change, 2006, table 11.3), thus: N2 Ovolatilization

= F × Frac1 × EF4 × 44/28 = 40078 × 0.2 × 0.01 × 44/28


= 126 kg N2 O/year; or 212 kg N2 O/production period. Together these equations yield: (A31)

N2 Odirect + N2 Ovolatilization = 1, 692 + 212 = 1, 904 kg N2 O/production period.

Give that one unit of N2 O has the same global warming potential as 310 units of CO2 , manure N2 O emissions are equivalent to 590,240 kg CO2 per production cycle, or 651 tons CO2 per production cycle. Protein Supplement We calculate GHG emissions in one pound of supplemental protein using soybean meal. According to the American Soybean Association (2012), one bushel (sixty pounds) of soybean yields about forty-eight pounds of soybean meal. Five-year average GHG emissions for soybeans between 1996 and 2000 are estimated as 15.1 pounds of CO2 per bushel (Field to Market, 2012). To produce the 96,000 pounds of soybean meal required by the typical farm in the 120-day period, GHG emissions are estimated to be 96, 000/48 × 15.1 = 30, 200 pounds CO2 , or 15.1 tons CO2 equivalent. CO2 from Energy Use Ryan and Tiffany (1998) report fuel-related energy expenses of $10.24 per head for cow-calf operators in 1995. We use the energy-use data breakdown from Ryan and Tiffany (1998): 6.07 gallons for diesel, 0.74 for gasoline, and 1.62 for LP gas, and 59.24 kWh for electric. After converting all the units to BTU based on 124,884 BTU/gallon and 3,413 BTU/kWh, we have 758,048 BTU for diesel, 92,414 for gasoline, 202,312 for LP gas, and 202,186 for electric. According to the conversion unit provided in table S1, GHG emissions from diesel, gasoline, LP gas, and electric are 54.89, 64.80, 126.18, and 348.66 kg CO2 equivalent. Overall, CO2 emissions per head for cow-calf operators are 1,088.55 kg CO2 equivalent. Given 400 head of cattle on our example farm, farm energy use generates 435,420 kg, or 480 tons CO2 equivalent. Use of Fertilizers (Nitrogen, Phosphorus, Potassium, Lime) The price of N and P is 0.6 dollars per pound, obtained from district 2 (Southern Plains) data accessible from http://agecoext.tamu.edu/resources/crop-livestock-budgets/by-district.html. The ratio of N and P applied to the grass per acre in one production season on a representative farm is 2.5:1. Equivalent carbon emission for the production, packaging, storage, and distribution of N and P takes the mean value of 1.3 kg CE/kg and 0.2 kg CE/kg (Lal, 2004, table 5). Carbon Sequestration Total GHG sequestration per year for Texas rangeland is 447 kg C per hectare (Potter et al., 1999), or 180.90 kg C per acre.