- Email: [email protected]
Can the small dairy farm remain competitive in US agriculture?
Food Policy 31 (2006) 458–468 www.elsevier.com/locate/foodpol
Can the small dairy farm remain competitive in US agriculture? Loren W. Tauer a
a,*
, Ashok K. Mishra
b
Department of Applied Economics and Management, 451 Warren Hall, Cornell University, Ithaca, NY 14853-7801, United States b Economic Research Service, USDA, Washington D.C. 20036-5831, United States Accepted 6 December 2005
Abstract Smaller dairy farms in the US are observed to have higher costs than larger farms, and whether those higher costs are due to technology or inefficiency has implications for policy to address the small farm. If high cost of production on smaller farms is due to a higher cost frontier, then to make small farms competitive would require research to devise and design technology that is suitable for small farms. If instead high cost is due to inefficiency, then educational approaches are needed to ensure small dairy farms use technology efficiently. To determine the cause of higher costs on small farms, the cost of milk production by farm size was decomposed into frontier and efficiency components with a stochastic cost curve using data on USA dairy farms. Although the frontier cost of production decreases with farm size, that cost reduction is not as pronounced as a cost curve that includes inefficiency. The higher cost of production on many smaller farms is caused by inefficiency rather than technology. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Cost curve; Dairy farms; Farm efficiency; Farm size; Stochastic frontier function
Introduction A common topic of conversation heard in rural coffee shops, agricultural colleges, and on Capitol Hill in Washington, DC, involves the future of the small dairy farm in the *
Corresponding author. Tel.: +1 607 255 4402; fax: +1 607 255 9984. E-mail address: [email protected] (L.W. Tauer).
0306-9192/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodpol.2005.12.005
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
459
United States (US Department of Agriculture, 1998). A large number of small dairy farms have ceased operation in traditional dairy areas, and many wonder how many more small dairy farms will be lost. These discussions center on whether and how the small dairy farm can survive. Some believe there is no future for the small dairy farm in US agriculture since its cost of production per unit of milk produced is thought to be higher than the cost of production per unit of milk on larger farms. Indeed, engineering cost studies of dairy production have shown lower unit costs with larger production units (Matulich, 1980). In a competitive market like milk, the survival of the small dairy farm hinges upon whether those farms are competitive with larger dairy farms, and their long-run survival depends upon having low cost of production. A discussion of the continued existence of the small farm is not limited to dairy or to the US, but is a world-wide issue in both developed and developing countries. That there has been a reduction in the number of small dairy farms and remaining dairy farms have become larger is undeniable. During the decade of the 1990s, the number of dairy farms in the United States decreased by 42%, from 180,640 farms in 1991 to 105,250 farms in 2000. This reduction came almost exclusively from a decline in the number of small dairy farms. Farms with fewer than 100 cows decreased from 159,866 operations in 1991 to 84,410 operations in 2000, while the number of farms with over 100 cows increased slightly over that period, from 20,774 to 20,840 operations (Blayney, 2002). Since low cost of production is critical for dairy farm survival in a competitive market, our research estimates the cost of milk production by farm size using individual farm production data from the year 2000 National USDA Dairy Production Practices and Costs and Returns Survey. However, there are two components to the cost of production for an individual farm. The first is the lowest cost for the specific technology and practices that a farmer can use at a given farm size. This can be referred to as the best practice or frontier cost curve. The second component of cost is how efficient an individual farm is in using the techniques available for a given farm size. Costs greater than the best practice cost can occur if a farmer is inefficient in using best practice techniques. In this research both of these cost components were modeled and estimated as a function of the number of cows. The modeling procedure allows both frontier and efficiency cost components to vary by farm size. There may be a number of social and political reasons to support the small farm. Whether high cost of production is due to inefficiency or a higher cost frontier has significant implications for policy. If high cost of production on smaller farms is due to a higher cost frontier, then to make small farms competitive would require research to devise and design technology that is suitable for small farms. If instead high cost is due to inefficiency, and not a high cost frontier, then current technology exists that would allow small farms to be competitive with larger farms. Educational programs would be necessary to ensure that small farms use more efficiently the technology currently available to them at their respective size. Review of literature Cost of production studies have a long tradition in the agricultural economics literature. Through the years the cost of production by farm size has been estimated for various commodities and regions of the US (Madden, 1967; Stefanou and Madden, 1988). Recent cost studies of dairy production have found lower unit costs with larger production units
460
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
(Bailey et al., 1997). These procedures estimate average cost of production by farm output or size without estimating the distribution of costs around these averages by farm size. Our research model estimates the distribution of costs around the means by farm size. The deviations are assumed to be due to inefficiency and data error. Inefficiency is estimated as a function of farm size, and a frontier cost function of efficient farms is simultaneously estimated as a function of farm size. Tauer (2001) used this approach to estimate the cost of production for New York dairy farms for the production year 1999 and estimated that farms with an average of 50 cows had average costs of $16.95 per hundredweight ($0.36 per kilogram), but $3.34 ($0.07 per kilogram) of that was due to inefficiency. If those farms had all been operated as efficiently as the most efficient 50-cow farm, average costs would have been much lower at $13.61 ($0.30 per kilogram). However, this was still $0.58 ($0.01 per kilogram) higher than the average costs for the efficient 500-cow farm. Although efficient small farms had lower costs than did the average large farm, the efficient large farm still had slightly lower costs. These results clearly show that most of the observed high cost on New York small dairy farms is due to inefficiency. Alvarez and Arias (2003) estimated economies of size of Spanish dairy farms assuming fixed managerial ability of each farm operator. These Spanish dairy farms were smaller than many dairy farms in the US. They modeled and estimated managerial ability as the technical efficiency of individual farms, with managerial ability and farm size separately impacting the average cost curve. Since they had panel data, they were able to determine unique farm results. Size elasticity averaged 0.28 with a minimum value of 0.60 and a maximum value of 0.15. The elasticity of managerial ability on average cost averaged 0.26 with a range from 1.12 to 0.82. Method The procedure used is typically referred to as a stochastic cost function. Aigner et al. (1977); Battese and Corra (1977) and Meeusen and van den Broeck (1977) introduced stochastic frontier production functions. They decomposed the typical error term of a regression model into an efficiency component plus a measurement error, and used maximum likelihood estimation to estimate simultaneously the parameters of the production function as well as efficiency and measurement error. The approach is now routinely used to estimate not only production but also profit and cost functions. More recently, beginning with Kumbhaker et al. (1991) and Battese and Coelli (1995), the efficiency component has also been simultaneously estimated as a function of causation factors. In our research, both the frontier and the efficiency components were modeled and estimated as a function of dairy farm size in order to decompose cost of production by size into both frontier cost and inefficiency components. This contrasts to the typical approach of estimating cost as a function of output and input prices. Input price data were not collected by the data survey but would be available from secondary sources. Although the farm data are for one year only, some price variability would exit across the US. However, state dummy variables are used to model technology and climate variation across states, and these dummy variables would include the impact of other variations across states, including prices, so input prices were not incorporated into the cost equation. This cost equation is estimated to be a function of the number of cows rather than output since cow numbers are commonly used in the USA as a measure of dairy farm size and serves as an excellent
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
461
proxy for output in these data since the correlation between milk output and the number of cows on a farm is 0.97. An advantage of using the number of cows as a proxy for quantity of output is that the number of cows on the farm is predetermined in the short run (exogenous) and thus not stochastic as milk output would be. Stochastic output could be correlated with the error term. Another important advantage of using cows as the single variable in both the frontier and efficiency components of the model is that it allows comparing frontier cost and cost inefficiency with a single common consistent measure. An average cost curve across dairy farms is estimated as a function of cow numbers on the farm and an error term, Cost=cwti ¼ f ðCowsi Þ þ ei ;
ð1Þ
where Cost/cwti is the cost of production per hundredweight of milk on farm i, Cowsi are the number of cows on farm i, and the ei error term for a single farm observation i, can be broken into a stochastic term, v, due to data error, and an efficiency term, u, such that ei = vi + ui. The efficiency term, u, is further specified as a function of cow numbers, ui ¼ gðCowsi Þ.
ð2Þ
The stochastic term, v, is modeled as a normal distribution, iid N(0, r2), while the efficiency term, u, is modeled as a truncated positive half-normal distribution with mean specified by Eq. (2), N+ (g(Cowsi), r2). This allows the stochastic term for an individual farm observation to be either negative or positive, but the expected efficiency term will be equal to or greater than zero. Estimation of this model is by maximum likelihood simultaneously estimating the f and g functions specified in Eqs. (1) and (2) with the specified error and efficiency structures stated above. The data had been collected using a stratified random sample with an enhanced sample of larger farms since few large farms would have been surveyed with a random sample. Since a stratified random sample was used, a weighted maximum likelihood model was employed with the weights applied outside the likelihood function to correct for this bias. The number of cows on the farm is serving as a latent variable to represent cost and efficiency components which change as the number of cows increase on the farm. Some of these components could be incorporated into either the cost frontier or efficiency segment of the specification, but any variable list from the survey data is not exhaustive, and most of these variables in themselves may not be primary factors. A case in point is milk production per cow. Low milk production per cow may lead to higher costs per unit or output, but it would not be known whether it was low quality feed, poor genetics, disease, or poor cow comfort among many other causes which lead to low milk production per cow. Individual farm cost inefficiency was computed as E[ujv + u] derived in Jondrow et al. (1982). This provides an estimate of the cost inefficiency of individual farms expressed in dollars per hundredweight of milk produced. Rather than plotting these computed farm inefficiencies by farm size, a smooth function was fitted by regressing individual farm inefficiency on cow numbers using weighted OLS. Frontier cost of milk production per hundredweight of milk by farm size was obtained by inserting cow numbers into function f. Total cost of production by farm size was constructed as the sum of frontier cost and cost inefficiency. Total cost of production per hundredweight of milk was further decomposed into variable and fixed costs of production, and separate functions were estimated for each cost
462
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
component, permitting determination whether efficiency differs by farm size when inputs are variable versus fixed in nature. Variable costs include those inputs which can easily be adjusted over the calendar year, and include such inputs as feed, worker labor, and energy. Fixed costs, in contrast, include those inputs that are not easily changed as more or less milk is produced over the calendar year. Fixed costs include capital and operator’s labor. Frontier cost curves estimated for the various cost components also provide information concerning the degree of economies or diseconomies in fixed versus variable inputs. Although economies and diseconomies of size are believed to result mostly from fixed factors of production, it is possible that variable costs display a corresponding or contrary pattern to the fixed cost frontier. Dairy technology does vary across the US, even for farms of the same size. Open lot housing can be used in warm climates but not in cold climates. Feeds and other production inputs vary by region. To reflect the impact of regional variations on cost of production, 21 state dummy variables with the 22nd state in the intercept, were included in the frontier component of the regression. Data Data are from the Dairy Production Practices and Costs and Returns Report (Agricultural Resource Management Survey Phase II, commonly referred to as ARMS). These data were collected by a survey jointly administered by the National Agricultural Statistics Service and Economic Research Service of the USDA for dairy production during the calendar year 2000. ARMS surveys are done each year, but in years where dairy is not specifically targeted to be sampled, only about 120 dairy farms are estimated to be in the sample, precluding a rich multiyear dairy data set.1 The target population was farms milking 10 or more cows in the 22 major dairy states. The sample is a multi-frame, probabilitybased survey in which farms are randomly selected from groups of dairy farms stratified by farm characteristics such as farm size, with greater coverage in the primary dairy production states. The survey design allows each sampled farm to represent a number of farms that are similar, the number of which being the survey expansion factor. The expansion factor, in turn, is defined as the inverse of the probability of the surveyed farm being selected. The survey collects data to measure the financial condition and operating characteristics of farm businesses, the cost of producing agricultural commodities, information on technology use and management practices, and the well being of farm operator households. On-farm enumerators collected the data using a 36-page survey instrument. Dairy costs and returns for each farm have been calculated by the USDA and are used to compute the cost of production per hundredweight of milk sold (Short, 2004). The costs include all costs, including family labor and capital costs. Three cost measures were computed for each farm. These are variable or operating cost, fixed cost, and then total cost. These are farm costs and reflect the cost of producing not just milk, but other commodities and cull cows. To calculate the total cost of producing milk per hundredweight of milk, 1 Dairy farms as such are not identified in the ARMS data, but using the criterion of cash sales from milk reported in the income section of the survey, fewer than 120 farms would be classified as dairy farms. Creating a panel from a stratified sample like ARMS is difficult. The same farm is not surveyed in a following year and the sample selection and weighting scheme used by the USDA makes matching similar farms challenging, if one wants to create a pseudo-panel.
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
463
sales of livestock and other non-milk income were subtracted from total farm costs, which were then divided by the hundredweight of milk sold. This approach presumes that the primary operation on these farms is milk production and the cost of producing other income is equal to that income. On average, 88% of the total revenue on the farms surveyed was from milk sales. Total cost per hundredweight of milk was separated into variable and fixed components. Total costs per hundredweight of milk ranged from 2 negative values to 17 observations with costs over $100 per hundredweight of milk ($2.20 per kilogram). Scrutiny of these farms revealed a variety of possible reasons for these extreme cost values. Some had large cattle sales, probably reflecting a profitable cattle-breeding program. Others had extremely low production levels. Since many other reasons may also have been responsible for extreme values, it was decided to use only farms with total cost greater than $4.00 ($0.09 per kilogram) and less than $35.00 per hundredweight of milk ($0.77 per kilogram) sold. This resulted in 755 observations.2 New weights were computed for the maximum likelihood estimation. The average number of cows on the 755 farms was 216, with 29 farms having more than 1000 cows. The average total cost of production per hundredweight of milk was $18.46 ($0.41 per kilogram), composed of $9.81 ($0.22 per kilogram) fixed cost and $8.65 ($0.19 per kilogram) variable cost. The relationship between total cost per hundredweight of milk sold and farm size as measured by the number of dairy cows is decreasing in number of cows but with greater variability in costs at smaller farm sizes.3 Surprisingly, however, there are a large number of small farms that have total costs that are as low as or lower than the costs of many large farms. Results Two functional forms were tried for both the frontier function f, and the efficiency function, g. These were the quadratic specified as: b1 þ b2 ðCowsi Þ þ b2 ðCowsi Þ2 ; and the natural log specified as: a1 þ a2 lnðCowsi Þ; with dummy state variables included in the frontier component. This resulted in four separate maximum likelihood estimates, and the best fit as determined by lowest total variance, ðr2v þ r2u Þ, was the natural log for both the frontier function, f, and the efficiency function, g, although all four combinations generated similar quantitative results for numerical frontier and efficient costs by farm size. The inclusion of the 21 dummy variables for the 22 states into the frontier cost component was done to allow for climate, feed, and other differences across states that should be independent of farm size. Yet, some size effects undoubtedly may be reflected in these state dummy estimates. Much of Arizona has a much different climate than does Wisconsin, but Arizona also has a larger proportion of large farms than does Wisconsin.
2 3
There were 872 original observations. A plot showing individual farm observations cannot be shown given the confidential nature of the data.
464
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
Table 1 Estimated cost curves for US dairy farms with no inefficiency modeled, year 2000 Variable
Variable cost
Fixed cost
Intercept Ln(Cows) State1 State2 State3 State4 State5 State6 State7 State8 State9 State10 State11 State12 State13 State14 State15 State16 State17 State18 State19 State20 State21 Adjusted R2
7.27 (10.10)* 0.0014 (0.01) 0.16 (0.06) 0.67 (1.08) 1.63 (0.94) 2.48 (1.72) 1.78 (2.04)* 1.85 (2.42)* 0.98 (1.46) 1.47 (2.58)* 1.09 (1.37) 2.08 (3.65)* 0.34 (0.91) 1.51 (2.56)* 0.18 (0.08) 1.37 (3.33)* 1.25 (2.69)* 1.59 (4.13)* 2.18 (2.07)* 2.45 (2.98)* 2.68 (3.50)* 2.76 (3.19)* 2.17 (2.18)* 0.04
25.76 3.47 2.06 0.47 2.05 1.38 1.24 1.00 0.71 0.03 1.06 1.05 2.66 2.33 2.45 0.68 2.69 0.13 0.87 0.24 0.02 0.74 0.97 0.31
(22.33)* (13.40)* (0.49) (0.47) (0.74) (0.60) (0.88) (0.82) (0.66) (0.03) (0.83) (1.16) (4.48)* (2.47)* (0.65) (1.04) (3.62)* (0.21) (0.52) (0.18) (0.02) (0.54) (0.61)
Total cost 33.03 3.48 2.22 1.14 3.68 3.86 3.03 2.85 1.69 1.44 2.15 3.14 2.99 3.83 2.63 2.05 1.44 1.72 3.05 2.69 2.70 2.01 1.19 0.19
(21.81)* (10.21)* (0.40) (0.87) (1.01) (1.27) (1.64) (1.77) (1.19) (1.20) (1.28) (2.61)* (3.84)* (3.09)* (0.53) (2.37)* (1.48) (2.12)* (1.37) (1.55) (1.67) (1.11) (0.57)
(Coefficient estimate and in parenthesis the ratio of coefficient estimate to standard error). Dependent variables are cost of producing 100 pounds of milk. * Represents estimated coefficient statistically different from zero at probability = 0.05.
The estimated cost curves for variable cost, fixed cost, and total cost without inefficiency modeled in the cost curves and estimated by weighted OLS are reported in Table 1.4 Total cost decreases with greater cow numbers, but that decrease is strictly due to a decrease in fixed costs. The ln(cow) variable is not statistically significantly different from zero in the variable cost curve, implying that the variable cost of milk production is flat at $7.27 per hundredweight of milk ($0.16 per kilogram) regardless of how many cows are present in the herd. The ln(cow) variable is statistically significant in both the fixed cost and total cost curves. These results carry over when these three cost curves are estimated with the inclusion of inefficiency within the model, as reported in Table 2. The variable cost frontier curve is statistically flat, with no inefficiency estimated. In contrast, both the frontier fixed cost curve and the inefficiency of fixed costs decrease as cow numbers increase. Although the frontier total cost curve decreases with increasing cow numbers, that decrease is minor and not statistically significant. In contrast, the total cost curve, like the fixed cost curve, displays a decrease in inefficiency as cow numbers increase. Frontier costs by farm size are calculated using the estimated coefficients of the frontier cost component shown in the top half of Table 2. The estimated coefficients of the 4
These coefficients are used for the starting values for the maximum likelihood efficiency estimates.
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
465
Table 2 Estimated cost curves for US dairy farms with inefficiency modeled, year 2000 Variable Frontier cost component Intercept Ln(Cows) State1 State2 State3 State4 State5 State6 State7 State8 State9 State10 State11 State12 State13 State14 State15 State16 State17 State18 State19 State20 State21 Inefficiency Component Intercept Ln(Cows) Standard deviations rv ru
Variable cost 4.94 (6.39)* 0.104 (0.59) 0.18 (0.04) 0.50 (0.90) 1.73 (1.03) 2.44 (2.24)* 1.49 (1.74) 1.48 (2.21)* 0.77 (1.34) 0.86 (1.94) 0.35 (0.58) 2.19 (3.44)* 0.18 (0.56) 1.30 (2.92)* 0.17 (0.09) 0.57 (1.68) 0.37 (0.97) 1.23 (3.54)* 2.25 (2.18)* 2.02 (3.01)* 2.30 (3.37)* 2.34 (3.20)* 0.55 (0.63) 455.74 (0.12) 32.22 (0.06) 1.76 36.27
Fixed cost
Total cost
5.89 (6.83)* 0.358 (1.99)* 1.03 (0.27) 1.40 (2.40)* 0.18 (0.19) 0.02 (0.02) 0.84 (1.02) 0.03 (0.04) 0.77 (0.78) 0.05 (0.09) 0.37 (0.48) 1.27 (1.68) 1.12 (2.99)* 0.14 (0.30) 1.87 (0.78) 0.20 (0.50) 1.89 (2.12)* 0.09 (0.23) 0.69 (0.80) 1.43 (1.90) 0.42 (0.56) 1.14 (1.35) 1.07 (0.97)
11.41 (5.04)* 0.376 (0.90) 0.29 (0.04) 0.34 (0.32) 2.45 (0.84) 3.00 (1.56) 1.03 (0.69) 2.10 (1.30) 1.34 (0.98) 1.29 (1.27) 1.02 (0.85) 3.71 (2.62)* 1.68 (2.39)* 1.75 (2.01)* 1.51 (0.50) 1.12 (1.55) 2.27 (2.64)* 1.77 (2.45)* 3.08 (1.59) 1.44 (1.11) 2.98 (2.10)* 1.54 (1.17) 0.21 (0.13)
34.89 (3.73)* 7.43 (7.96)*
33.85 (5.50)* 6.68 (4.91)*
0.80 6.39
2.26 7.62
(Coefficient estimate and in parenthesis the ratio of coefficient estimate to standard error.) Dependent variables are total cost of producing 100 pounds of milk. Inefficiency is modeled as a positive half-normal distribution with Mean = a1 + a2*ln(cows). The stochastic error is modeled as a normal distribution with mean = 0. Estimation by weighted maximum likelihood using 755 observations. * Represents estimated coefficient statistically different from zero at probability = 0.05.
inefficiency component in Table 2 could not be directly used to compute inefficiency costs by farm size since inefficiency was fitted to a positive half-normal distribution with nonconstant mean. Individual farm efficiency was estimated as E[ujv + u] as derived in Jondrow et al. (1982). Given the confidentiality of the data these could not be individually plotted as a function of cows. However, regressing these individual farm efficiency estimates on log of cows on each farm using weighted linear regression produced an equation to calculate efficiency by farm size. These equations are listed at the bottom of Tables 3 and 4. They have high F values but relatively low R2 values, suggesting good statistical fit, but large differences in efficiency even for farms of identical size. The composite cost is the frontier and efficiency values combined at each farm size. The estimated frontier curve is much flatter than the composite cost curve, and although the frontier cost of
466
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
Table 3 Separation of total cost of milk production into efficiency, inefficiency, and size components, US dairy farms, estimated by stochastic cost curve, year 2000 Number of cows
Frontier cost
Inefficiency costa
Composite cost
Cost due to sizeb
50 100 150 200 500 1000
$9.94 9.68 9.53 9.42 9.07 8.81
$12.05 10.18 9.08 8.30 5.83 3.96
$21.99 19.86 18.61 17.72 14.90 12.77
$1.13 0.87 0.72 0.61 0.26 –
(0.22) (0.21) (0.21) (0.21) (0.20) (0.19)
(0.27) (0.22) (0.20) (0.18) (0.13) (0.09)
(0.48) (0.44) (0.41) (0.39) (0.33) (0.28)
(0.02) (0.02) (0.02) (0.01) (0.10)
(Costs are $US per hundredweight of milk and in parenthesis $US per kilogram of milk). a Calculated from the estimate effi = 22.61–2.70*ln(cowsi), F[1, 753] = 131, R2 = 0.15, where effi for each farm estimated by the Jondrow et al. procedure and cowsi are the number of cows on each farm. b Cost difference for efficient farms compared to efficient 1000-cow size.
Table 4 Separation of fixed cost of milk production into efficiency, inefficiency, and size components, US dairy farms, estimated by stochastic cost curve, year 2000 Number of cows
Frontier cost
Inefficiency costa
Composite cost
Cost due to sizeb
50 100 150 200 500 1000
$4.49 4.24 4.10 3.99 3.66 3.42
$8.57 6.62 5.48 4.67 2.08 0.13
$13.06 10.86 9.58 8.66 5.74 3.55
$1.07 0.82 0.68 0.57 0.24 –
(0.10) (0.09) (0.09) (0.09) (0.08) (0.08)
(0.19) (0.15) (0.12) (0.10) (0.05) (0.00)
(0.29) (0.24) (0.21) (0.19) (0.13) (0.08)
(0.02) (0.02) (0.01) (0.01) (0.01)
(Costs are $US per hundredweight of milk and in parenthesis $US per kilogram of milk). a Calculated from the estimate effi = 19.61–2.82*ln(cowsi), F[1, 753] = 204, R2 = 0.21, where effi for each farm estimated by the Jondrow et al. procedure and cowsi are the number of cows on each farm. b Cost difference for efficient farms compared to efficient 1000-cow size.
production decreases with farm size, that cost reduction is not as pronounced as the cost curve that includes inefficiency. Indeed, the higher cost of production of many smaller farms is estimated to be caused by inefficiency, and that inefficiency decreases as the farm becomes larger. As Table 3 illustrates, the 50-cow farm has a frontier total cost of production of only $9.94 per cwt of milk ($0.22 per kilogram), but a large inefficiency cost of $12.05 per cwt ($0.27 per kilogram).5 In contrast, the 1000-cow herd has a frontier total cost of production of $8.81 ($0.19 per kilogram) and an inefficiency cost of $3.96 ($0.09 per kilogram), for a composite cost of $12.77 ($0.28 per kilogram). Thus, the efficient 50-cow farm has a $2.83 ($0.06 per kilogram) lower total cost than the inefficient 1000-cow farm, but the efficient 1000-cow farm has a lower total cost of $1.13 ($0.02 per kilogram) than the efficient 50-cow farm. The implication is that the efficient 50-cow farm is competitive with the average 1000-cow farm, but not the efficient 1000-cow farm. There is a future for the small US dairy farm in a competitive market, but probably only if that small dairy farm is close to being cost efficient.
5
The alternative functional forms also produced large cost inefficiency for the 50-cow farm.
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
467
Table 4 reports these cost relationships for the fixed cost component of the farm. Cost economies exist in the frontier cost component, and inefficiency decreases with increasing cow numbers. As compared to the total cost relationships shown in Table 3, fixed cost demonstrates greater economies of size and less cost reduction with greater efficiency. It appears that both cost economies and inefficiencies occur in the fixed cost component of the dairy farm. Technologies embedded in fixed costs lower the cost of production per hundredweight of milk produced for larger farms, and those larger farms are more efficient in using that technology. There is no inefficiency estimated in the variable cost curve by farm size, but there is inefficiency in the fixed cost curve by farm size. Consequently, efforts aimed at decreasing the inefficiency of the small dairy farm should be aimed at decreasing this fixed cost inefficiency. Research efforts are needed to determine why small farms often do not efficiently use their fixed assets. Mishra and Morehart (2001) found that participation in extension activities and use of extension agents were positively associated with US dairy farm financial performance. It might be that better record keeping and monitoring could allow farms to determine the source of cost inefficiency. However, Jackson-Smith et al. (2004) found only a weak link between understanding of financial concepts and greater dairy financial returns. It may be that the remedy for each farm is unique. The estimated frontier cost curve can be used to conjecture the size of surviving farms in the long run if survival requires that unit costs be lower than the milk price. Essentially, any efficient size farm can survive with a milk price above $10.00 per cwt ($0.22 per kilogram), with the efficient large 1000-cow farm only having a $1.13 ($0.02 per kilogram) frontier cost advantage over the 50-cow farm. The US Federal milk support price is set at $9.90 ($0.22 per kilogram) through 2007, which should allow any efficient US Dairy farm to survive. Also, efficiency may not be static, and if the price of milk falls below the US Year 2000 average of $12.40 per cwt there will be an incentive for inefficient farms to become more cost efficient. Since our data are cross-sectional for one year only, we are not able to analyse any change in efficiency in reaction to lower milk prices. Yet, it would appear that many small farms would be lost since on average they are less efficient than the large farms. On the other hand, there are individual small farms that are very efficient and these farms would survive. Conclusions It appears that both economies of size and inefficiency exist in the fixed cost but not the variable cost component of the typical US dairy farm. The variable cost of producing a unit of milk shows no significant decrease with farm size, nor does variable cost show a reduction in efficiency with farm size. In contrast, the fixed cost of producing milk decreases with farm size and the farm becomes more cost efficient. These relationships were obtained by estimating a stochastic cost curve where cost of production per hundredweight of milk was regressed on the natural logarithm of cow numbers, with cost efficiency simultaneously estimated as the natural logarithm of cow numbers. Data were from a USDA stratified random sample of US dairy farms for the production year 2000. These results imply that for the small US dairy farm to become competitive with the large US dairy farm requires some new technology appropriate for smaller farms. However, a much larger cost reduction on smaller farms would be possible if those farms would
468
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
learn how to use the technology represented by those fixed costs more efficiently. Although new technology for the small dairy farm would be useful, it appears that current technologies are in place which would make the small dairy farm more competitive if those farms used that technology efficiently. Acknowledgements This project was supported by the National Research Initiative of the Cooperative State Research, Education and Extension Service, USDA, Grant # 2002-01488. The views in this manuscript are those of the authors and do not necessarily represent those of Cornell University or the USDA. The authors thank Spiro Stefanou for his comments. References Aigner, D.J., Lovell, C.A.K., Schmidt, P., 1977. Formulation and estimation of stochastic frontier production function models. J. Econometrics 6, 21–37. Alvarez, A., Arias, C., 2003. Diseconomies of size with fixed managerial ability. Amer. J. Agr. Econ. 85, 134–142. Bailey, K., Hardin, D., Spain, J., Garrett, J., Hoehne, J., Randle, R., Ricketts, R., Stevens, B., Zulovich, J., 1997. An economic simulation study of large-scale dairy units in the midwest. J. Dairy Sci. 80, 205–214. Battese, G.E., Coelli, T.J., 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Econ. 20, 325–332. Battese, G.E., Corra, G.S., 1977. Estimation of a production frontier model: with application to the pastoral zone of eastern Australia. J. Agr. Econ. 21, 169–179. Blayney, D.P., 2002. The Changing Landscape of US Milk Production. US Department of Agriculture, Economic Research Services, Statistical Bulletin SB-978, Washington, DC. Jackson-Smith, D., Trechter, D., Splett, N., 2004. The contribution of financial management training and knowledge to dairy farm financial performance. R. Agr. Econ. 26, 132–146. Jondrow, J., Lovell, C.A.K., Materov, I.S., Schmidt, P., 1982. On the estimation of technical inefficiency in the stochastic frontier production function model. J. Econometrics 19, 233–235. Kumbhaker, S.C., Ghosh, S., McGuckin, J.T., 1991. A generalized production frontier approach for estimating determinants of inefficiency in US dairy farms. J. Bus. Econ. Stat. 9, 279–286. Madden, J.P., 1967. Economics of Size in Farming. US Department of Agriculture, Economic Research Service, Bulletin AER-107, Washington, DC. Matulich, S.C., 1980. Efficiencies in large-scale dairying: incentives for future structural change. Amer. J. Agr. Econ. 60, 642–647. Meeusen, W., van den Broeck, J., 1977. Efficiency estimation from cobb-douglas production functions with composed error. Int. Econ. Rev. 18, 435–444. Mishra, A.K., Morehart, M.J., 2001. Factors affecting returns to labor and management on US dairy farms. Agr. Fin. Rev. 61, 123–140. Short, S., 2004. Characteristics and Production Costs of US Dairy Operations. USDA, ERS. Statistical Bulletin No. (SB974-6), February. Stefanou, S., Madden, J.P., 1988. Economies of size revisited. J. Agr. Econ. 60, 727–737. Tauer, L., 2001. Efficiency and competitiveness of the small New York dairy farm. J. Dairy Sci. 84, 2573–2576. US Department of Agriculture., 1998. A Time to Act: A Report of the National Small Farm Commission on Small Farms. USDA National Commission on Small Farms, Washington DC, January 1998.
Can the small dairy farm remain competitive in US agriculture? Loren W. Tauer a
a,*
, Ashok K. Mishra
b
Department of Applied Economics and Management, 451 Warren Hall, Cornell University, Ithaca, NY 14853-7801, United States b Economic Research Service, USDA, Washington D.C. 20036-5831, United States Accepted 6 December 2005
Abstract Smaller dairy farms in the US are observed to have higher costs than larger farms, and whether those higher costs are due to technology or inefficiency has implications for policy to address the small farm. If high cost of production on smaller farms is due to a higher cost frontier, then to make small farms competitive would require research to devise and design technology that is suitable for small farms. If instead high cost is due to inefficiency, then educational approaches are needed to ensure small dairy farms use technology efficiently. To determine the cause of higher costs on small farms, the cost of milk production by farm size was decomposed into frontier and efficiency components with a stochastic cost curve using data on USA dairy farms. Although the frontier cost of production decreases with farm size, that cost reduction is not as pronounced as a cost curve that includes inefficiency. The higher cost of production on many smaller farms is caused by inefficiency rather than technology. Ó 2005 Elsevier Ltd. All rights reserved. Keywords: Cost curve; Dairy farms; Farm efficiency; Farm size; Stochastic frontier function
Introduction A common topic of conversation heard in rural coffee shops, agricultural colleges, and on Capitol Hill in Washington, DC, involves the future of the small dairy farm in the *
Corresponding author. Tel.: +1 607 255 4402; fax: +1 607 255 9984. E-mail address: [email protected] (L.W. Tauer).
0306-9192/$ - see front matter Ó 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.foodpol.2005.12.005
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
459
United States (US Department of Agriculture, 1998). A large number of small dairy farms have ceased operation in traditional dairy areas, and many wonder how many more small dairy farms will be lost. These discussions center on whether and how the small dairy farm can survive. Some believe there is no future for the small dairy farm in US agriculture since its cost of production per unit of milk produced is thought to be higher than the cost of production per unit of milk on larger farms. Indeed, engineering cost studies of dairy production have shown lower unit costs with larger production units (Matulich, 1980). In a competitive market like milk, the survival of the small dairy farm hinges upon whether those farms are competitive with larger dairy farms, and their long-run survival depends upon having low cost of production. A discussion of the continued existence of the small farm is not limited to dairy or to the US, but is a world-wide issue in both developed and developing countries. That there has been a reduction in the number of small dairy farms and remaining dairy farms have become larger is undeniable. During the decade of the 1990s, the number of dairy farms in the United States decreased by 42%, from 180,640 farms in 1991 to 105,250 farms in 2000. This reduction came almost exclusively from a decline in the number of small dairy farms. Farms with fewer than 100 cows decreased from 159,866 operations in 1991 to 84,410 operations in 2000, while the number of farms with over 100 cows increased slightly over that period, from 20,774 to 20,840 operations (Blayney, 2002). Since low cost of production is critical for dairy farm survival in a competitive market, our research estimates the cost of milk production by farm size using individual farm production data from the year 2000 National USDA Dairy Production Practices and Costs and Returns Survey. However, there are two components to the cost of production for an individual farm. The first is the lowest cost for the specific technology and practices that a farmer can use at a given farm size. This can be referred to as the best practice or frontier cost curve. The second component of cost is how efficient an individual farm is in using the techniques available for a given farm size. Costs greater than the best practice cost can occur if a farmer is inefficient in using best practice techniques. In this research both of these cost components were modeled and estimated as a function of the number of cows. The modeling procedure allows both frontier and efficiency cost components to vary by farm size. There may be a number of social and political reasons to support the small farm. Whether high cost of production is due to inefficiency or a higher cost frontier has significant implications for policy. If high cost of production on smaller farms is due to a higher cost frontier, then to make small farms competitive would require research to devise and design technology that is suitable for small farms. If instead high cost is due to inefficiency, and not a high cost frontier, then current technology exists that would allow small farms to be competitive with larger farms. Educational programs would be necessary to ensure that small farms use more efficiently the technology currently available to them at their respective size. Review of literature Cost of production studies have a long tradition in the agricultural economics literature. Through the years the cost of production by farm size has been estimated for various commodities and regions of the US (Madden, 1967; Stefanou and Madden, 1988). Recent cost studies of dairy production have found lower unit costs with larger production units
460
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
(Bailey et al., 1997). These procedures estimate average cost of production by farm output or size without estimating the distribution of costs around these averages by farm size. Our research model estimates the distribution of costs around the means by farm size. The deviations are assumed to be due to inefficiency and data error. Inefficiency is estimated as a function of farm size, and a frontier cost function of efficient farms is simultaneously estimated as a function of farm size. Tauer (2001) used this approach to estimate the cost of production for New York dairy farms for the production year 1999 and estimated that farms with an average of 50 cows had average costs of $16.95 per hundredweight ($0.36 per kilogram), but $3.34 ($0.07 per kilogram) of that was due to inefficiency. If those farms had all been operated as efficiently as the most efficient 50-cow farm, average costs would have been much lower at $13.61 ($0.30 per kilogram). However, this was still $0.58 ($0.01 per kilogram) higher than the average costs for the efficient 500-cow farm. Although efficient small farms had lower costs than did the average large farm, the efficient large farm still had slightly lower costs. These results clearly show that most of the observed high cost on New York small dairy farms is due to inefficiency. Alvarez and Arias (2003) estimated economies of size of Spanish dairy farms assuming fixed managerial ability of each farm operator. These Spanish dairy farms were smaller than many dairy farms in the US. They modeled and estimated managerial ability as the technical efficiency of individual farms, with managerial ability and farm size separately impacting the average cost curve. Since they had panel data, they were able to determine unique farm results. Size elasticity averaged 0.28 with a minimum value of 0.60 and a maximum value of 0.15. The elasticity of managerial ability on average cost averaged 0.26 with a range from 1.12 to 0.82. Method The procedure used is typically referred to as a stochastic cost function. Aigner et al. (1977); Battese and Corra (1977) and Meeusen and van den Broeck (1977) introduced stochastic frontier production functions. They decomposed the typical error term of a regression model into an efficiency component plus a measurement error, and used maximum likelihood estimation to estimate simultaneously the parameters of the production function as well as efficiency and measurement error. The approach is now routinely used to estimate not only production but also profit and cost functions. More recently, beginning with Kumbhaker et al. (1991) and Battese and Coelli (1995), the efficiency component has also been simultaneously estimated as a function of causation factors. In our research, both the frontier and the efficiency components were modeled and estimated as a function of dairy farm size in order to decompose cost of production by size into both frontier cost and inefficiency components. This contrasts to the typical approach of estimating cost as a function of output and input prices. Input price data were not collected by the data survey but would be available from secondary sources. Although the farm data are for one year only, some price variability would exit across the US. However, state dummy variables are used to model technology and climate variation across states, and these dummy variables would include the impact of other variations across states, including prices, so input prices were not incorporated into the cost equation. This cost equation is estimated to be a function of the number of cows rather than output since cow numbers are commonly used in the USA as a measure of dairy farm size and serves as an excellent
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
461
proxy for output in these data since the correlation between milk output and the number of cows on a farm is 0.97. An advantage of using the number of cows as a proxy for quantity of output is that the number of cows on the farm is predetermined in the short run (exogenous) and thus not stochastic as milk output would be. Stochastic output could be correlated with the error term. Another important advantage of using cows as the single variable in both the frontier and efficiency components of the model is that it allows comparing frontier cost and cost inefficiency with a single common consistent measure. An average cost curve across dairy farms is estimated as a function of cow numbers on the farm and an error term, Cost=cwti ¼ f ðCowsi Þ þ ei ;
ð1Þ
where Cost/cwti is the cost of production per hundredweight of milk on farm i, Cowsi are the number of cows on farm i, and the ei error term for a single farm observation i, can be broken into a stochastic term, v, due to data error, and an efficiency term, u, such that ei = vi + ui. The efficiency term, u, is further specified as a function of cow numbers, ui ¼ gðCowsi Þ.
ð2Þ
The stochastic term, v, is modeled as a normal distribution, iid N(0, r2), while the efficiency term, u, is modeled as a truncated positive half-normal distribution with mean specified by Eq. (2), N+ (g(Cowsi), r2). This allows the stochastic term for an individual farm observation to be either negative or positive, but the expected efficiency term will be equal to or greater than zero. Estimation of this model is by maximum likelihood simultaneously estimating the f and g functions specified in Eqs. (1) and (2) with the specified error and efficiency structures stated above. The data had been collected using a stratified random sample with an enhanced sample of larger farms since few large farms would have been surveyed with a random sample. Since a stratified random sample was used, a weighted maximum likelihood model was employed with the weights applied outside the likelihood function to correct for this bias. The number of cows on the farm is serving as a latent variable to represent cost and efficiency components which change as the number of cows increase on the farm. Some of these components could be incorporated into either the cost frontier or efficiency segment of the specification, but any variable list from the survey data is not exhaustive, and most of these variables in themselves may not be primary factors. A case in point is milk production per cow. Low milk production per cow may lead to higher costs per unit or output, but it would not be known whether it was low quality feed, poor genetics, disease, or poor cow comfort among many other causes which lead to low milk production per cow. Individual farm cost inefficiency was computed as E[ujv + u] derived in Jondrow et al. (1982). This provides an estimate of the cost inefficiency of individual farms expressed in dollars per hundredweight of milk produced. Rather than plotting these computed farm inefficiencies by farm size, a smooth function was fitted by regressing individual farm inefficiency on cow numbers using weighted OLS. Frontier cost of milk production per hundredweight of milk by farm size was obtained by inserting cow numbers into function f. Total cost of production by farm size was constructed as the sum of frontier cost and cost inefficiency. Total cost of production per hundredweight of milk was further decomposed into variable and fixed costs of production, and separate functions were estimated for each cost
462
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
component, permitting determination whether efficiency differs by farm size when inputs are variable versus fixed in nature. Variable costs include those inputs which can easily be adjusted over the calendar year, and include such inputs as feed, worker labor, and energy. Fixed costs, in contrast, include those inputs that are not easily changed as more or less milk is produced over the calendar year. Fixed costs include capital and operator’s labor. Frontier cost curves estimated for the various cost components also provide information concerning the degree of economies or diseconomies in fixed versus variable inputs. Although economies and diseconomies of size are believed to result mostly from fixed factors of production, it is possible that variable costs display a corresponding or contrary pattern to the fixed cost frontier. Dairy technology does vary across the US, even for farms of the same size. Open lot housing can be used in warm climates but not in cold climates. Feeds and other production inputs vary by region. To reflect the impact of regional variations on cost of production, 21 state dummy variables with the 22nd state in the intercept, were included in the frontier component of the regression. Data Data are from the Dairy Production Practices and Costs and Returns Report (Agricultural Resource Management Survey Phase II, commonly referred to as ARMS). These data were collected by a survey jointly administered by the National Agricultural Statistics Service and Economic Research Service of the USDA for dairy production during the calendar year 2000. ARMS surveys are done each year, but in years where dairy is not specifically targeted to be sampled, only about 120 dairy farms are estimated to be in the sample, precluding a rich multiyear dairy data set.1 The target population was farms milking 10 or more cows in the 22 major dairy states. The sample is a multi-frame, probabilitybased survey in which farms are randomly selected from groups of dairy farms stratified by farm characteristics such as farm size, with greater coverage in the primary dairy production states. The survey design allows each sampled farm to represent a number of farms that are similar, the number of which being the survey expansion factor. The expansion factor, in turn, is defined as the inverse of the probability of the surveyed farm being selected. The survey collects data to measure the financial condition and operating characteristics of farm businesses, the cost of producing agricultural commodities, information on technology use and management practices, and the well being of farm operator households. On-farm enumerators collected the data using a 36-page survey instrument. Dairy costs and returns for each farm have been calculated by the USDA and are used to compute the cost of production per hundredweight of milk sold (Short, 2004). The costs include all costs, including family labor and capital costs. Three cost measures were computed for each farm. These are variable or operating cost, fixed cost, and then total cost. These are farm costs and reflect the cost of producing not just milk, but other commodities and cull cows. To calculate the total cost of producing milk per hundredweight of milk, 1 Dairy farms as such are not identified in the ARMS data, but using the criterion of cash sales from milk reported in the income section of the survey, fewer than 120 farms would be classified as dairy farms. Creating a panel from a stratified sample like ARMS is difficult. The same farm is not surveyed in a following year and the sample selection and weighting scheme used by the USDA makes matching similar farms challenging, if one wants to create a pseudo-panel.
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
463
sales of livestock and other non-milk income were subtracted from total farm costs, which were then divided by the hundredweight of milk sold. This approach presumes that the primary operation on these farms is milk production and the cost of producing other income is equal to that income. On average, 88% of the total revenue on the farms surveyed was from milk sales. Total cost per hundredweight of milk was separated into variable and fixed components. Total costs per hundredweight of milk ranged from 2 negative values to 17 observations with costs over $100 per hundredweight of milk ($2.20 per kilogram). Scrutiny of these farms revealed a variety of possible reasons for these extreme cost values. Some had large cattle sales, probably reflecting a profitable cattle-breeding program. Others had extremely low production levels. Since many other reasons may also have been responsible for extreme values, it was decided to use only farms with total cost greater than $4.00 ($0.09 per kilogram) and less than $35.00 per hundredweight of milk ($0.77 per kilogram) sold. This resulted in 755 observations.2 New weights were computed for the maximum likelihood estimation. The average number of cows on the 755 farms was 216, with 29 farms having more than 1000 cows. The average total cost of production per hundredweight of milk was $18.46 ($0.41 per kilogram), composed of $9.81 ($0.22 per kilogram) fixed cost and $8.65 ($0.19 per kilogram) variable cost. The relationship between total cost per hundredweight of milk sold and farm size as measured by the number of dairy cows is decreasing in number of cows but with greater variability in costs at smaller farm sizes.3 Surprisingly, however, there are a large number of small farms that have total costs that are as low as or lower than the costs of many large farms. Results Two functional forms were tried for both the frontier function f, and the efficiency function, g. These were the quadratic specified as: b1 þ b2 ðCowsi Þ þ b2 ðCowsi Þ2 ; and the natural log specified as: a1 þ a2 lnðCowsi Þ; with dummy state variables included in the frontier component. This resulted in four separate maximum likelihood estimates, and the best fit as determined by lowest total variance, ðr2v þ r2u Þ, was the natural log for both the frontier function, f, and the efficiency function, g, although all four combinations generated similar quantitative results for numerical frontier and efficient costs by farm size. The inclusion of the 21 dummy variables for the 22 states into the frontier cost component was done to allow for climate, feed, and other differences across states that should be independent of farm size. Yet, some size effects undoubtedly may be reflected in these state dummy estimates. Much of Arizona has a much different climate than does Wisconsin, but Arizona also has a larger proportion of large farms than does Wisconsin.
2 3
There were 872 original observations. A plot showing individual farm observations cannot be shown given the confidential nature of the data.
464
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
Table 1 Estimated cost curves for US dairy farms with no inefficiency modeled, year 2000 Variable
Variable cost
Fixed cost
Intercept Ln(Cows) State1 State2 State3 State4 State5 State6 State7 State8 State9 State10 State11 State12 State13 State14 State15 State16 State17 State18 State19 State20 State21 Adjusted R2
7.27 (10.10)* 0.0014 (0.01) 0.16 (0.06) 0.67 (1.08) 1.63 (0.94) 2.48 (1.72) 1.78 (2.04)* 1.85 (2.42)* 0.98 (1.46) 1.47 (2.58)* 1.09 (1.37) 2.08 (3.65)* 0.34 (0.91) 1.51 (2.56)* 0.18 (0.08) 1.37 (3.33)* 1.25 (2.69)* 1.59 (4.13)* 2.18 (2.07)* 2.45 (2.98)* 2.68 (3.50)* 2.76 (3.19)* 2.17 (2.18)* 0.04
25.76 3.47 2.06 0.47 2.05 1.38 1.24 1.00 0.71 0.03 1.06 1.05 2.66 2.33 2.45 0.68 2.69 0.13 0.87 0.24 0.02 0.74 0.97 0.31
(22.33)* (13.40)* (0.49) (0.47) (0.74) (0.60) (0.88) (0.82) (0.66) (0.03) (0.83) (1.16) (4.48)* (2.47)* (0.65) (1.04) (3.62)* (0.21) (0.52) (0.18) (0.02) (0.54) (0.61)
Total cost 33.03 3.48 2.22 1.14 3.68 3.86 3.03 2.85 1.69 1.44 2.15 3.14 2.99 3.83 2.63 2.05 1.44 1.72 3.05 2.69 2.70 2.01 1.19 0.19
(21.81)* (10.21)* (0.40) (0.87) (1.01) (1.27) (1.64) (1.77) (1.19) (1.20) (1.28) (2.61)* (3.84)* (3.09)* (0.53) (2.37)* (1.48) (2.12)* (1.37) (1.55) (1.67) (1.11) (0.57)
(Coefficient estimate and in parenthesis the ratio of coefficient estimate to standard error). Dependent variables are cost of producing 100 pounds of milk. * Represents estimated coefficient statistically different from zero at probability = 0.05.
The estimated cost curves for variable cost, fixed cost, and total cost without inefficiency modeled in the cost curves and estimated by weighted OLS are reported in Table 1.4 Total cost decreases with greater cow numbers, but that decrease is strictly due to a decrease in fixed costs. The ln(cow) variable is not statistically significantly different from zero in the variable cost curve, implying that the variable cost of milk production is flat at $7.27 per hundredweight of milk ($0.16 per kilogram) regardless of how many cows are present in the herd. The ln(cow) variable is statistically significant in both the fixed cost and total cost curves. These results carry over when these three cost curves are estimated with the inclusion of inefficiency within the model, as reported in Table 2. The variable cost frontier curve is statistically flat, with no inefficiency estimated. In contrast, both the frontier fixed cost curve and the inefficiency of fixed costs decrease as cow numbers increase. Although the frontier total cost curve decreases with increasing cow numbers, that decrease is minor and not statistically significant. In contrast, the total cost curve, like the fixed cost curve, displays a decrease in inefficiency as cow numbers increase. Frontier costs by farm size are calculated using the estimated coefficients of the frontier cost component shown in the top half of Table 2. The estimated coefficients of the 4
These coefficients are used for the starting values for the maximum likelihood efficiency estimates.
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
465
Table 2 Estimated cost curves for US dairy farms with inefficiency modeled, year 2000 Variable Frontier cost component Intercept Ln(Cows) State1 State2 State3 State4 State5 State6 State7 State8 State9 State10 State11 State12 State13 State14 State15 State16 State17 State18 State19 State20 State21 Inefficiency Component Intercept Ln(Cows) Standard deviations rv ru
Variable cost 4.94 (6.39)* 0.104 (0.59) 0.18 (0.04) 0.50 (0.90) 1.73 (1.03) 2.44 (2.24)* 1.49 (1.74) 1.48 (2.21)* 0.77 (1.34) 0.86 (1.94) 0.35 (0.58) 2.19 (3.44)* 0.18 (0.56) 1.30 (2.92)* 0.17 (0.09) 0.57 (1.68) 0.37 (0.97) 1.23 (3.54)* 2.25 (2.18)* 2.02 (3.01)* 2.30 (3.37)* 2.34 (3.20)* 0.55 (0.63) 455.74 (0.12) 32.22 (0.06) 1.76 36.27
Fixed cost
Total cost
5.89 (6.83)* 0.358 (1.99)* 1.03 (0.27) 1.40 (2.40)* 0.18 (0.19) 0.02 (0.02) 0.84 (1.02) 0.03 (0.04) 0.77 (0.78) 0.05 (0.09) 0.37 (0.48) 1.27 (1.68) 1.12 (2.99)* 0.14 (0.30) 1.87 (0.78) 0.20 (0.50) 1.89 (2.12)* 0.09 (0.23) 0.69 (0.80) 1.43 (1.90) 0.42 (0.56) 1.14 (1.35) 1.07 (0.97)
11.41 (5.04)* 0.376 (0.90) 0.29 (0.04) 0.34 (0.32) 2.45 (0.84) 3.00 (1.56) 1.03 (0.69) 2.10 (1.30) 1.34 (0.98) 1.29 (1.27) 1.02 (0.85) 3.71 (2.62)* 1.68 (2.39)* 1.75 (2.01)* 1.51 (0.50) 1.12 (1.55) 2.27 (2.64)* 1.77 (2.45)* 3.08 (1.59) 1.44 (1.11) 2.98 (2.10)* 1.54 (1.17) 0.21 (0.13)
34.89 (3.73)* 7.43 (7.96)*
33.85 (5.50)* 6.68 (4.91)*
0.80 6.39
2.26 7.62
(Coefficient estimate and in parenthesis the ratio of coefficient estimate to standard error.) Dependent variables are total cost of producing 100 pounds of milk. Inefficiency is modeled as a positive half-normal distribution with Mean = a1 + a2*ln(cows). The stochastic error is modeled as a normal distribution with mean = 0. Estimation by weighted maximum likelihood using 755 observations. * Represents estimated coefficient statistically different from zero at probability = 0.05.
inefficiency component in Table 2 could not be directly used to compute inefficiency costs by farm size since inefficiency was fitted to a positive half-normal distribution with nonconstant mean. Individual farm efficiency was estimated as E[ujv + u] as derived in Jondrow et al. (1982). Given the confidentiality of the data these could not be individually plotted as a function of cows. However, regressing these individual farm efficiency estimates on log of cows on each farm using weighted linear regression produced an equation to calculate efficiency by farm size. These equations are listed at the bottom of Tables 3 and 4. They have high F values but relatively low R2 values, suggesting good statistical fit, but large differences in efficiency even for farms of identical size. The composite cost is the frontier and efficiency values combined at each farm size. The estimated frontier curve is much flatter than the composite cost curve, and although the frontier cost of
466
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
Table 3 Separation of total cost of milk production into efficiency, inefficiency, and size components, US dairy farms, estimated by stochastic cost curve, year 2000 Number of cows
Frontier cost
Inefficiency costa
Composite cost
Cost due to sizeb
50 100 150 200 500 1000
$9.94 9.68 9.53 9.42 9.07 8.81
$12.05 10.18 9.08 8.30 5.83 3.96
$21.99 19.86 18.61 17.72 14.90 12.77
$1.13 0.87 0.72 0.61 0.26 –
(0.22) (0.21) (0.21) (0.21) (0.20) (0.19)
(0.27) (0.22) (0.20) (0.18) (0.13) (0.09)
(0.48) (0.44) (0.41) (0.39) (0.33) (0.28)
(0.02) (0.02) (0.02) (0.01) (0.10)
(Costs are $US per hundredweight of milk and in parenthesis $US per kilogram of milk). a Calculated from the estimate effi = 22.61–2.70*ln(cowsi), F[1, 753] = 131, R2 = 0.15, where effi for each farm estimated by the Jondrow et al. procedure and cowsi are the number of cows on each farm. b Cost difference for efficient farms compared to efficient 1000-cow size.
Table 4 Separation of fixed cost of milk production into efficiency, inefficiency, and size components, US dairy farms, estimated by stochastic cost curve, year 2000 Number of cows
Frontier cost
Inefficiency costa
Composite cost
Cost due to sizeb
50 100 150 200 500 1000
$4.49 4.24 4.10 3.99 3.66 3.42
$8.57 6.62 5.48 4.67 2.08 0.13
$13.06 10.86 9.58 8.66 5.74 3.55
$1.07 0.82 0.68 0.57 0.24 –
(0.10) (0.09) (0.09) (0.09) (0.08) (0.08)
(0.19) (0.15) (0.12) (0.10) (0.05) (0.00)
(0.29) (0.24) (0.21) (0.19) (0.13) (0.08)
(0.02) (0.02) (0.01) (0.01) (0.01)
(Costs are $US per hundredweight of milk and in parenthesis $US per kilogram of milk). a Calculated from the estimate effi = 19.61–2.82*ln(cowsi), F[1, 753] = 204, R2 = 0.21, where effi for each farm estimated by the Jondrow et al. procedure and cowsi are the number of cows on each farm. b Cost difference for efficient farms compared to efficient 1000-cow size.
production decreases with farm size, that cost reduction is not as pronounced as the cost curve that includes inefficiency. Indeed, the higher cost of production of many smaller farms is estimated to be caused by inefficiency, and that inefficiency decreases as the farm becomes larger. As Table 3 illustrates, the 50-cow farm has a frontier total cost of production of only $9.94 per cwt of milk ($0.22 per kilogram), but a large inefficiency cost of $12.05 per cwt ($0.27 per kilogram).5 In contrast, the 1000-cow herd has a frontier total cost of production of $8.81 ($0.19 per kilogram) and an inefficiency cost of $3.96 ($0.09 per kilogram), for a composite cost of $12.77 ($0.28 per kilogram). Thus, the efficient 50-cow farm has a $2.83 ($0.06 per kilogram) lower total cost than the inefficient 1000-cow farm, but the efficient 1000-cow farm has a lower total cost of $1.13 ($0.02 per kilogram) than the efficient 50-cow farm. The implication is that the efficient 50-cow farm is competitive with the average 1000-cow farm, but not the efficient 1000-cow farm. There is a future for the small US dairy farm in a competitive market, but probably only if that small dairy farm is close to being cost efficient.
5
The alternative functional forms also produced large cost inefficiency for the 50-cow farm.
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
467
Table 4 reports these cost relationships for the fixed cost component of the farm. Cost economies exist in the frontier cost component, and inefficiency decreases with increasing cow numbers. As compared to the total cost relationships shown in Table 3, fixed cost demonstrates greater economies of size and less cost reduction with greater efficiency. It appears that both cost economies and inefficiencies occur in the fixed cost component of the dairy farm. Technologies embedded in fixed costs lower the cost of production per hundredweight of milk produced for larger farms, and those larger farms are more efficient in using that technology. There is no inefficiency estimated in the variable cost curve by farm size, but there is inefficiency in the fixed cost curve by farm size. Consequently, efforts aimed at decreasing the inefficiency of the small dairy farm should be aimed at decreasing this fixed cost inefficiency. Research efforts are needed to determine why small farms often do not efficiently use their fixed assets. Mishra and Morehart (2001) found that participation in extension activities and use of extension agents were positively associated with US dairy farm financial performance. It might be that better record keeping and monitoring could allow farms to determine the source of cost inefficiency. However, Jackson-Smith et al. (2004) found only a weak link between understanding of financial concepts and greater dairy financial returns. It may be that the remedy for each farm is unique. The estimated frontier cost curve can be used to conjecture the size of surviving farms in the long run if survival requires that unit costs be lower than the milk price. Essentially, any efficient size farm can survive with a milk price above $10.00 per cwt ($0.22 per kilogram), with the efficient large 1000-cow farm only having a $1.13 ($0.02 per kilogram) frontier cost advantage over the 50-cow farm. The US Federal milk support price is set at $9.90 ($0.22 per kilogram) through 2007, which should allow any efficient US Dairy farm to survive. Also, efficiency may not be static, and if the price of milk falls below the US Year 2000 average of $12.40 per cwt there will be an incentive for inefficient farms to become more cost efficient. Since our data are cross-sectional for one year only, we are not able to analyse any change in efficiency in reaction to lower milk prices. Yet, it would appear that many small farms would be lost since on average they are less efficient than the large farms. On the other hand, there are individual small farms that are very efficient and these farms would survive. Conclusions It appears that both economies of size and inefficiency exist in the fixed cost but not the variable cost component of the typical US dairy farm. The variable cost of producing a unit of milk shows no significant decrease with farm size, nor does variable cost show a reduction in efficiency with farm size. In contrast, the fixed cost of producing milk decreases with farm size and the farm becomes more cost efficient. These relationships were obtained by estimating a stochastic cost curve where cost of production per hundredweight of milk was regressed on the natural logarithm of cow numbers, with cost efficiency simultaneously estimated as the natural logarithm of cow numbers. Data were from a USDA stratified random sample of US dairy farms for the production year 2000. These results imply that for the small US dairy farm to become competitive with the large US dairy farm requires some new technology appropriate for smaller farms. However, a much larger cost reduction on smaller farms would be possible if those farms would
468
L.W. Tauer, A.K. Mishra / Food Policy 31 (2006) 458–468
learn how to use the technology represented by those fixed costs more efficiently. Although new technology for the small dairy farm would be useful, it appears that current technologies are in place which would make the small dairy farm more competitive if those farms used that technology efficiently. Acknowledgements This project was supported by the National Research Initiative of the Cooperative State Research, Education and Extension Service, USDA, Grant # 2002-01488. The views in this manuscript are those of the authors and do not necessarily represent those of Cornell University or the USDA. The authors thank Spiro Stefanou for his comments. References Aigner, D.J., Lovell, C.A.K., Schmidt, P., 1977. Formulation and estimation of stochastic frontier production function models. J. Econometrics 6, 21–37. Alvarez, A., Arias, C., 2003. Diseconomies of size with fixed managerial ability. Amer. J. Agr. Econ. 85, 134–142. Bailey, K., Hardin, D., Spain, J., Garrett, J., Hoehne, J., Randle, R., Ricketts, R., Stevens, B., Zulovich, J., 1997. An economic simulation study of large-scale dairy units in the midwest. J. Dairy Sci. 80, 205–214. Battese, G.E., Coelli, T.J., 1995. A model for technical inefficiency effects in a stochastic frontier production function for panel data. Empirical Econ. 20, 325–332. Battese, G.E., Corra, G.S., 1977. Estimation of a production frontier model: with application to the pastoral zone of eastern Australia. J. Agr. Econ. 21, 169–179. Blayney, D.P., 2002. The Changing Landscape of US Milk Production. US Department of Agriculture, Economic Research Services, Statistical Bulletin SB-978, Washington, DC. Jackson-Smith, D., Trechter, D., Splett, N., 2004. The contribution of financial management training and knowledge to dairy farm financial performance. R. Agr. Econ. 26, 132–146. Jondrow, J., Lovell, C.A.K., Materov, I.S., Schmidt, P., 1982. On the estimation of technical inefficiency in the stochastic frontier production function model. J. Econometrics 19, 233–235. Kumbhaker, S.C., Ghosh, S., McGuckin, J.T., 1991. A generalized production frontier approach for estimating determinants of inefficiency in US dairy farms. J. Bus. Econ. Stat. 9, 279–286. Madden, J.P., 1967. Economics of Size in Farming. US Department of Agriculture, Economic Research Service, Bulletin AER-107, Washington, DC. Matulich, S.C., 1980. Efficiencies in large-scale dairying: incentives for future structural change. Amer. J. Agr. Econ. 60, 642–647. Meeusen, W., van den Broeck, J., 1977. Efficiency estimation from cobb-douglas production functions with composed error. Int. Econ. Rev. 18, 435–444. Mishra, A.K., Morehart, M.J., 2001. Factors affecting returns to labor and management on US dairy farms. Agr. Fin. Rev. 61, 123–140. Short, S., 2004. Characteristics and Production Costs of US Dairy Operations. USDA, ERS. Statistical Bulletin No. (SB974-6), February. Stefanou, S., Madden, J.P., 1988. Economies of size revisited. J. Agr. Econ. 60, 727–737. Tauer, L., 2001. Efficiency and competitiveness of the small New York dairy farm. J. Dairy Sci. 84, 2573–2576. US Department of Agriculture., 1998. A Time to Act: A Report of the National Small Farm Commission on Small Farms. USDA National Commission on Small Farms, Washington DC, January 1998.