J. Dairy Sci. 89:49374943 American Dairy Science Association, 2006.

Dairy Farm Cost Efficiency

L. W. Tauer*1 and A. K. Mishra*Department of Applied Economics and Management, Cornell University, Ithaca, NY 14853Economic Research Service, USDA, Washington, DC 20036

ABSTRACT

A stochastic cost equation was estimated for US dairyfarms using national data from the production year2000 to determine how farmers might reduce their costof production. Cost of producing a unit of milk wasestimated into separate frontier (efficient) and ineffi-ciency components, with both components estimatedas a function of management and causation variables.Variables were entered as impacting the frontier com-ponent as well as the efficiency component of the sto-chastic curve because a priori both components couldbe impacted. A factor that has an impact on the costfrontier was the number of hours per day the milkingfacility is used. Using the milking facility for more hoursper day decreased frontier costs; however, inefficiencyincreased with increased hours of milking facility use.Thus, farmers can decrease costs with increased utiliza-tion of the milking facility, but only if they are efficientin this strategy. Parlors compared with stanchions usedfor milking did not decrease frontier costs, but de-creased costs because of increased efficiency, as did theuse of a nutritionist. Use of rotational grazing decreasedfrontier costs but also increased inefficiency. Olderfarmers were less efficient.Key words: cost, efficiency, stochastic cost function

INTRODUCTION

Profits vary across dairy farms, and various studieshave investigated factors determining dairy farm suc-cess or profitability (Kauffman and Tauer, 1986; Wil-liams et al., 1987; McGilliard et al., 1990). Recently,Gloy et al. (2002) found production management factorssuch as larger farm size, greater rate of milk production,and use of parlors rather than stanchion milking sys-tems, had a positive impact on dairy farm profitability.They found that measures of human capital such aseducation and age did not affect profits. Type of account-ing systems used and debt use did affect profits. It mightbe that better record keeping and monitoring could

Received December 20, 2005.Accepted July 6, 2006.1Corresponding author: loren_tauer@cornell.edu

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allow farms to determine the source of cost inefficiency.Jackson-Smith et al. (2004) found only a weak linkbetween understanding of financial concepts andgreater dairy financial returns. Mishra and Morehart(2001) found that participation in extension activitiesand the use of extension agents were positively associ-ated with dairy farm financial performance.

Using a latent variable approach, Ford and Shonk-wiler (1994) found that management of the dairy herdand herd size were more important determinants offarm financial success than financial or crop manage-ment. They concluded that increases in dairy manage-rial ability would have a greater relative payoff thanincreasing herd size, supporting the findings of Tauerand Mishra (2006) that efficiency was more importantthan farm size in reducing net production costs. Alvarezand Arias (2003) found in Spanish dairy farms thatobserved diseconomies of size might be offset by suffi-cient increases in managerial ability, in which manage-rial ability is measured by technical efficiency.

Adoption of various production practices or techno-logies also may impact profitability (Foltz and Chang,2002). El-Osta and Johnson (1998) investigated use ofadvanced milking parlors but concluded that this tech-nology did not have a significant effect on net farmincome in traditional dairy states. Instead, these stud-ies found that production per cow was a strong factorassociated with dairy farm profitability. A number ofreasons explain why production per cow is limited, in-cluding inferior genetics, low quality feeds, and dis-ease incidence.

The number of dairy farms in the United States de-creased significantly during the last decade, from180,640 operations in 1991 to 105,250 operations in2000 (Blayney, 2002). Most of this decline came fromsmall dairy farms. Much research shows that cost de-creases with farm size (Stefanou and Madden, 1987).Recent cost studies of dairy production found smallerunit costs associated with larger production units, ex-plaining why smaller farms may have exited the dairyindustry (Bailey et al., 1997). Tauer and Mishra (2006)found the efficient small US dairy farm produced milkat a cost only slighter greater than the efficient largefarm, but the typical inefficient small dairy farm had

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much greater cost than the efficient, or even the ineffi-cient large dairy farm.

The purpose of this paper is to explore determinantsof cost and inefficiency to identify the managerialchanges that dairy farms can make to reduce the costof production. That is accomplished by estimating astochastic unit cost curve in which both the frontier andefficiency components of that cost curve are functions ofcausation variables. Frontier costs are minimum costsproducing milk using some given technology or tech-nique when the farmer is completely efficient. Ineffi-ciency causes the costs of using the technology or tech-nique to be greater than these minimum costs. Somefarmers using the technique are able to produce at mini-mum cost, whereas other farmers using the techniquehave greater costs and are thus measured as cost ineffi-cient. Separation of costs into frontier and inefficiencycomponents would be valuable in devising educationprograms to ensure the US dairy farm remains competi-tive in the world market. Frontier costs are feasiblefor the very best farmers and should be achieved byall farmers.

MATERIALS AND METHODS

Frontier Curve and Efficiency

A technology or management practice may reduceunit cost of production but only if a farmer is efficientimplementing the technology or practice. Some farmersmay find that the technology or practice does not reducecost of production as expected because they are ineffi-cient in implementation. In an empirical estimation ofthe impact of technology and practice on cost of produc-tion, it is important to separate out the 2 types of costcomponents. Frontier costs are the costs with the verybest management; inefficiency costs are greater ob-served costs because of poor management. This ap-proach is in contrast to estimating a cost curve fittingaverage costs, explaining what the average farmer iscapable of accomplishing.

We decompose observed total unit cost into frontierand efficiency components and estimate determinantsthat may impact the frontier cost and cost efficiency.Most producers would like to minimize total per unitcost of production in a competitive market. That canbe accomplished by reducing frontier cost production,becoming more cost efficient, or both. An average orunit total cost curve for a farm is estimated as a functionof a covariate set Xi, an error term vi, and an efficiencyterm u,

ci = f(Xi, ) + vi + u(Zi,), u(Zi,) 0 [1]

Journal of Dairy Science Vol. 89 No. 12, 2006

where ci is the cost of production per hundredweight(cwt) of milk on farm i, Xi are the covariates that affectcosts, and the vi error term is independent of Xi, Zi, andu. The efficiency term, u, is specified as a function of aset of covariates Zi, containing set elements that mayoverlap with the covariate set Xi. The vector is thecoefficient for the frontier cost curve, whereas the vector is the coefficient for the efficiency cost curve.

The measurement error term, v, is modeled as anindependent, identically distributed normal distribu-tion N(0,2), and the efficiency term, u, is modeled asa truncated positive half-normal distribution, N+(g(Zi),2). This allows the measurement error term for anindividual farm observation to be either negative orpositive, but the efficiency term u, which will be greaterthan 0, will shift with covariates Zi. An alternative spec-ification for the efficiency term is N+ (0, h(Zi)2), wherethe variance of the truncated half-normal changes withthe covariates. In addition, both mean and varianceof the truncated half-normal can shift with covariates.We elect to shift the mean only because shifting thevariance as well as the frontier cost with the samecovariates did not provide estimated results because ofnonconvergence. Even then, because g(Zi) is the meanof the underlying distribution before truncation, boththe mean and variance of the efficiency u are functionsof g(Zi) and 2. Estimation is by maximum likelihoodsimultaneously estimating the f and g functions withthe specified error and efficiency structures.

The procedure used is typically referred to as a sto-chastic cost function. Others (Aigner et al., 1977; Bat-tese and Corra, 1977; Meeusen and van den Broeck,1977) introduced stochastic frontier production func-tions. They decomposed the typical error term of a re-gression model into an efficiency component plus a mea-surement error and used maximum likelihood estima-tion to estimate simultaneously the parameters of theproduction function as well as inefficiency and measure-ment error. The approach is now routinely used to esti-mate not only production but also profit and cost func-tions. More recently, beginning with Kumbhakar et al.(1991) and Battese and Coelli (1995), the inefficiencycomponent also has been simultaneously estimated as afunction of causation factors. Wang and Schmidt (2002)provided a discussion and assessment of the technique.Lawson et al. (2004) recently applied a stochastic pro-duction function to the dairy industry and emphasizedthe impact of disease control on production efficiencybut also looked at the impact of other managementfactors, such as housing type.

Because variables in set X and set Z may overlap, achange in those variables impacts cost in 2 ways. Oneimpact will be a shift in the frontier curve; the otherimpact will be a change in efficiency. The impact from

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the frontier cost curve is simply the first derivativeof the frontier cost curve with respect to the variablexk as follows:

f(Xi,)/xk [2]

where the marginal impact is the same for each farmwith identical covariate values.

Impact of a variable k on efficiency will be farm spe-cific; however, Wang (2002) showed how the marginaleffect on farm efficiency is calculated when either orboth the mean and variance of the truncated normalare functions of the covariates. We estimated only themean as a function of the covariates. Specifying g as alinear function, g = Z such that i = Zi , anddefining = i/i, and = ()/(), where is thenormal probability function and is the normal cumu-lative function allows computation of the expected mar-ginal efficiency impact of a variable xk on farm i asfollows:

E(i)/xk = k (1 2) [3]

where the term (1 2) varies by farm, but kis constant across farms.

Frontier and efficiency components of Equation [1]were estimated jointly using maximum likelihood esti-mation. The data were collected using a stratified ran-dom sample with an enhanced sample of larger farmsbecause few large farms would have been surveyed witha random sample. Estimation was by weighted maxi-mum likelihood with weights applied outside the likeli-hood value of each observation to account for the stra-tified random sample with unequal probability weights.

Survey Data

Data were extracted from the Dairy Production Prac-tices and Costs and Returns Report (Agricultural Re-source Management Survey Phase II, commonly re-ferred to as ARMS). Observations were collected usinga survey jointly administered by the National Agricul-tural Statistics Service and Economic Research Serviceof the USDA for dairy production during calendar year2000. The survey collects data to measure the financialcondition and operating characteristics of farm busi-nesses, the cost of producing agricultural commodities,and information on technology use and managementpractices. Unfortunately, prices of inputs were not col-lected, and thus it was not possible to estimate a stan-dard cost function in which cost is a function of inputprices. Rather, cost per cwt of milk produced was esti-mated as a function of farm characteristics and prac-tices, which we will refer to as a cost equation.

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The target population for the survey was farms milk-ing 10 or more cows in the 22 major dairy states. Thesample is a multiframe, probability-based survey inwhich farms were selected randomly from groups ofdairy farms stratified by farm characteristics such asfarm size, with greater coverage in the primary dairyproduction states. The survey design allowed each sam-pled farm to represent a number of farms that are simi-lar. That number is referred to as the expansion factor,which is defined as the inverse of the probability of thesurveyed farm being selected. The expansion factor isalso referred to as the observations weight. Each ver-sion of the survey has a unique expansion factor thatexpands the sample to the target population. On-farmenumerators collected the data using a 36-page sur-vey instrument.

Dairy costs and returns for each farm have been cal-culated by USDA and are used to compute the cost ofproduction per cwt of milk sold (Short, 2004). Costsinclude all costs, including family labor and capitalcosts. To calculate the total cost of producing milk percwt of milk, sales of livestock and other nonmilk incomewere subtracted from total farm costs, which were thendivided by the cwt of milk sold. This approach presumesthe primary operation on these farms is milk productionand the cost of producing other income is equal to thatincome. Fixed costs include family labor and capitalcosts. The dependent variable was the total unit costof producing milk where units are the cwt of milk soldfrom each farm. Milk is priced and sold in the UnitedStates by cwt.

Total costs per cwt of milk ranged from 2 negativevalues to 17 observations with costs over $100 per cwtof milk. Scrutiny of these farms revealed a variety ofpossible reasons for these extreme cost values. Somehad large cattle sales, probably reflecting a profitablecattle-breeding program or partial herd liquidation.Others had extremely small production levels. Becausemany other reasons may have been responsible for ex-treme values, it was decided to use only farms withtotal cost greater than $4.00 and less than $35.00 percwt of milk sold. Other farms were deleted because ofmissing age. This resulted in 749 observations. Newweights were computed for the maximum likelihoodestimation and estimated average efficiencies.

Variables that might influence cost of production andcost efficiency of an individual dairy farm are uncom-mon in farm data sets, but a number of these werecollected in the survey instrument. These are reportedand defined in Table 1. Each variable was entered asimpacting the frontier component as well as the effi-ciency component of the stochastic curve because a pri-ori both components could be impacted. An example isthe years of formal education of the farmer. Greater

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Table 1. Variables used to estimate frontier and efficiency unit costs for US dairy farms during 20001

WeightedVariable meanname Definition value

COWS Average number of milking cows during the year 125FARMORGD Type of ownership: 1 = partnership, family corporation, nonfamily corporation, or other; 0.22

or 0 = individualOP_AGE Age of first or principal operator 48PARLORD Use of parlor to milk cows: 1 = parlor or 0 = no parlor (stanchion milking) 0.39EDUC Years of formal education: 1 = beyond high school or 0 = high school or less 0.30COM_MILK Computerized milking system: 1 = yes or 0 = no 0.07COM_FEED Computerized feeding system: 1 = yes or 0 = no 0.09FEED_NUT Use of a nutritionist: 1 = yes or 0 = no 0.72FOR_TEST Uses forage testing: 1 = yes or 0 = no 0.60INTENSE Hours per day milking system used 5.5GRAZE Use of rotational grazing: 1 = yes or 0 = no 0.22

1Data are from the Dairy Production Practices and Costs and Returns Report (Agricultural Resource Management Survey Phase II,commonly referred to as ARMS).

formal education may allow farmers to select the small-est cost technology to define the frontier cost function,and education also may allow farmers to be efficient intheir use of leading-edge technology. The continuousvariables COWS, AGE, and INTENSE were entered innatural logarithmic form to produce a nonlinear re-sponse to these variables. All remaining variables have0 or 1 values. Because the included explanatory vari-ables are not exhaustive, farm size as determined bythe number of cows was included in the regressions topick up residual frontier and efficiency costs correlatedwith farm size, serving as a proxy for these latent man-agement variables.

Often variables that have been regressed on farmprofitability or efficiency and found to be statisticallysignificant are not true causation or management vari-ables, but rather indicators of poor or good manage-ment. One such variable is production per cow. Produc-tion per cow may be small because of inferior genetics,low quality feeds, lack of disease control, or other poormanagement factors. A number of techniques collectedin the data survey instrument, such as whether themilking units had automatic takeoffs, were highly col-linear with included regression variables and thus werenot included in the analysis. McBride et al. (2004), usingthe same data, did not find recombinant bovine somato-tropin profitable, so that variable was not included.Finally, estimation with included state dummy vari-ables was not successful even after trying various opti-mization algorithms and convergence tolerances.

RESULTS AND DISCUSSION

Table 2 reports estimated total unit cost stochasticcost curve, decomposed into frontier and inefficiencycomponents. The frontier component shows the costcurve for an efficient farm. Results, however, also in-

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clude inefficient farms, so the inefficiency componentmeasures the inefficiency of those farms by variable.Estimated frontier unit cost curve has an intercept of19.01 and a coefficient of 1.22 on ln(COWS). This im-plies that frontier unit cost increases slightly with sizeof the farm. This is in contrast to the results of Tauerand Mishra (2006) who found no relationship betweenfrontier unit cost and size when farm size was the soleexplanatory variable. Hoch (1976) and Dawson (1985)have found diseconomies of size in dairy farming, sowhen management factors are added to the cost equa-tion that decrease costs, many of which are associatedwith farm size, the residual frontier cost curve appar-ently displays diseconomies of size. Increased size perse does not decrease costsit is the factors associatedwith size that decrease costs. Two factors found to bestatistically significant are efficiency and utilization ofthe milking facility.

Because the unit cost frontier displays diseconomiesof size, going from the sample average of 125 to 225cows, for instance, would increase the frontier unit costcurve by $0.85/cwt. Movement from 225 to 1,000 cowsfurther increases frontier unit cost by an additional$1.69/cwt. These larger farms, however, are more costefficient as discussed later, leading to a net unit costreduction. Larger farms are most cost efficient as ob-served by Tauer and Mishra (2006).

Utilizing the milking system more intensively eachday reduces the frontier total unit cost. Wagner et al.(2001) also discovered reduced costs in parlors usedmore hours per day. The average time that milkingsystems were used each day on the surveyed farms was5.5 h. If those systems were used up to 10.5 h per day,the frontier total unit cost would fall by $2.67/cwt. Aswill be discussed later, however, efficiency decreaseswith greater intensity of use, offsetting much, if not all,

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Table 2. Estimated frontier and efficiency unit cost components for US dairy farms during 2000

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