Somatic cell counts in dairy marketing: quantile regression for count data

We study the determinants of somatic cell count (SCC) for farm milk among US dairies. We synthesise much of the work that has been done to model SCC determinants in order to identify the potential impacts of buyer-imposed penalties and incentives within the supply chain. Additionally, we estimate quantile regression for count data to measure impacts specifically for those operations with the highest SCC and to account for the statistical properties of the data. Premiums in particular have the potential to reduce SCC considerably where it is currently the highest. We draw implications for profitability in relation to SCC reduction.


Introduction
The quality of agricultural commodities in the United States, broadly defined, has wide-ranging economic implications. Quality drives prices received by producers as well as those ultimately paid by consumers in the retail sector. Consumers and all agents of the post-farm gate food supply chain increasingly demand food that is safe and traceable, factors tied directly to quality. The quality of US agricultural output, relative to that of other nations, shapes international supply, demand and trade. We draw upon a wealth of research across disciplines to develop an economic model to understand the quality determinants of farm milk, or bulk-tank fluid milk, as measured by somatic cell count (SCC). A great deal of work in the dairy industry, much of it summarised by Blowey and Edmondson (2010), has focused on SCC, because it shares a wellestablished, inverse relationship with quality. A growing body of international evidence (e.g. Bennett, 2003) suggests that reductions in SCC in the US dairy industry can mitigate the economic costs of diminished yields or infectious diseases that have been linked to elevated SCC and related bovine health issues.
Farm milk is one of the United States' most important agricultural commodities. The factors most important in shaping farm milk quality are relevant to welfare considerations throughout the dairy industry and for consumers, as a factor shaping retail food prices, and to the competitiveness of US agriculture in the global market. Dairy products rank third among all agricultural commodities in terms of total receipts (Economic Research Service, 2013) and 12th according to the total value of exports (Economic Research Service, 2011). With respect to global agriculture, it has been argued that comparatively lax federal regulations regarding allowable SCC in farm milk leaves the US dairy industry at a competitive disadvantage relative to other major exporters (Dong, Hennessy and Jensen, 2012). Several states have begun imposing stricter SCC limits, which are more comparable to those of other major dairy-producing nations. One consideration that factored into undertaking this study concerns the extent to which economic incentives themselves are associated with lower levels of SCC.
Our results provide implications for both dairy producers and buyers with respect to increasing farm milk quality via reductions in SCC. In particular, we investigate how incentives or penalties, which can be imposed without high fixed costs (as compared with adjustments in capital or technology) within the dairy industry, may be exploited to significantly reduce SCC. We also investigate important potential linkages between SCC and producer profitability. According to the Agricultural Resource Management Survey (ARMS), the majority of dairy producers in the United States are not profitable, in that they do not have positive net returns. There appears to be a connection between average SCC levels and the probability of being profitable, particularly among smaller operations. Meeting certain SCC thresholds, set lower than the federally regulated maximum, may be reasonably attainable for a range of operations according to our results and can increase the likelihood of dairy producers establishing profitability.

The economics of SCC and the dairy industry
Farm milk in the United States is marketed according to a grading system. The federal government has set standards to determine quality as being of Grade A or Grade B, the standards for the former being more stringent. Only Grade A milk can be marketed for fluid consumption, while Grade B milk is used for the production of cheese, butter and other products. Approximately 99 per cent of all milk produced in the United States is Grade A (USDA National Agriculture Statistics Service, 2015). The remainder is often referred to as 'manufacturing grade' milk within the dairy industry. SCC is one of the two measures, the other being standard plate count, used nationally to assess quality and to distinguish Grade A from Grade B milk. The premium commanded by Grade A milk and its suitability for a wider range of commercial uses have generated interest among economists regarding how dairy producers may be incentivised to reduce SCC and obtain Grade A-status for their output (Balagtas, Smith and Sumner, 2007).
The majority of economic research related to SCC, however, has focused on the direct and indirect costs associated with bovine diseases and other issues attributable to high SCC. These costs, broadly defined, stem from multiple sources. Increased SCC in raw milk is associated with adverse effects on product quality for a variety of products including reduced cheese yield, development of off-flavours and reduced shelf life for milk (Barbano, Ma and Santos, 2006) as well as reduced yields from dairy cows (Howard et al., 1991;Green, Schukken and Green, 2006). The price commanded by farm milk likely bears an inverse relationship with SCC, ceteris paribus. Atsbeha, Kristofersson and Rickertsen (2012) estimated a hedonic pricing function for bulk-tank farm milk and found it to decrease nearly linearly with SCC. Dekkers, Van Erp and Schukken (1996) estimated that the pecuniary benefits dairy producers may achieve, per cow, by reducing SCC below various threshold levels. The benefits were drawn mostly from the increased yields and higher milk prices that would result from lower SCC.
High SCC is strongly associated with the incidence of bovine mastitis disease, which is one of the most significant and quantifiable sources of the costs arising from high SCC levels. Importantly, dairy cows afflicted with mastitis are unable to produce milk, at least temporarily. The mammary gland may cease production entirely, and the udder sac becomes inflamed and firm (Rodenburg, 2012). It is the single most costly disease to dairy producers (Bennett and IJpelaar, 2005;Rodenburg, 2012). Recently economists have come to recognise that the capacity to control outcomes such as mastitis may be enhanced from insights gleaned through modelling techniques and empirical approaches commonly used in the field (McInerney, 2008). Huijps, Lam and Hogoveen (2008) found that dairy producers are likely to underestimate considerably the costs associated with bovine mastitis, suggesting that further research and education on the economic impacts of the disease as well as an improved incentive structure towards reducing SCC are likely motivated. To that end, Huijps et al. (2010) demonstrated penalties to be more effective than bonuses in reducing SCC and mitigating mastitis. Bocqueno, Jacquet and Reynaud (2013) provide meaningful background for this finding, demonstrating that farmers throughout agriculture are far more sensitive to losses than they are to gains. As demand for organic foods continues to expand in the United States and organic production grows concomitantly, it remains unclear as to whether there is a systematic difference in SCC or the incidence of mastitis between organic and conventional operations and, if so, the direction of the difference (Richards et al., 2002;Dong, Hennessy and Jensen, 2012).
Several studies have attempted to estimate the total economic costs associated with increases in or high levels of SCC. The identification of costs associated with SCC is difficult due to the large number mechanisms by which SCC can generate economic loss as well as the multitude of agents, including consumers, tied to farm milk output and quality. Bulk-tank SCC spiked in the United States in 1996 and a large number of studies attempted to estimate the related economic impacts. In a survey of this literature, Losinger (2005) estimated that this short-term increase in average SCC levels resulted in a net loss of approximately USD 810 million to the US economy. Bennett (2003) found that mastitis alone is responsible for a net loss of GBP 57-185 million to the UK economy annually. It is not an objective of this article to refine the estimation of the economic costs of SCC, but rather to improve our understanding of the determinants of SCC, including economic incentives, given the potential for improvement in the US dairy industry and the myriad-related costs of excessive SCC.

Econometric model
Our study is not the first to examine empirically the determinants of SCC or closely related bovine diseases, such as mastitis. SCC has been modelled in many different ways, oftentimes as the basis of a case study, and almost uniformly for European countries. Our empirical approach can be thought of as a synthesis of different approaches to the problem, applied to the United States and with a data set that stands out in the extant literature for its depth and richness, namely the ARMS.
Broadly speaking, models of SCC to date have focused primarily on production practices and managerial factors. Production practices that have been studied, which are often tied to SCC via biological mechanisms, include the adoption of organic status (Richards et al., 2002;Haskell et al., 2009) or the method of milking (Green, Schukken and Green, 2006;Sauer and Zilberman, 2012). Relevant managerial factors include attributes of managers such as location or capital intensity as well as linkages to the buyers and the supply chain (Howard et al., 1991;Huijps et al., 2010;Dong, Hennessy and Jensen, 2012). In this latter category, some studies have focused specifically on the roles of premiums or penalties imposed by buyers (Nightingale et al., 2008;Hand, Godkin and Kelton, 2012).
To be sure, there is often some degree of overlap among these studies, particularly since production practices and managerial factors are typically interrelated. However, owing largely to data limitations and small sample sizes, few studies have incorporated key elements from both categories. Dong, Hennessy and Jensen (2012), who use the same data utilised in our study, are an exception to this although they do not examine the importance of incentives within the dairy supply chain, generated through the buyer-producer relationship that can be so important to shaping milk quality. We argue that it is these factors, endemic to the terms established between buyers and dairy producers, that provide fertile ground for the identification of cost-effective and logistically practical means by which to reduce SCC in the US dairy industry. This is a contention strongly supported by the work of Huijps et al. (2010). Drawing on the implications of previous research on SCC and mastitis, we model milk quality among dairy producers as Milk Quality = f (Buyer Terms, Production Practices, where Buyer Terms serves as an umbrella term for the quality-based requirements imposed upon producers by milk buyers and any related penalties or bonuses. Model (1) is designed to control for key determinants of SCC as evidenced by the existing literature on the topic in order to flesh out the potential role of buyer requirements or standards. The econometric specification is therefore

Data and variable construction
The data used in the empirical analysis are drawn from the USDA's 2005 ARMS Phase III, administered jointly by the USDA's Economic Research Service and National Agricultural Statistics Service (NASS). The ARMS Dairy Costs and Returns Report provides detailed data on a large and varied sample of dairy farms. The underlying survey is part of a larger data collection endeavour by the USDA and responses are obtained through a sequence of in-depth structured interviews with producers. The survey is conducted approximately every 5 years, but the most recent 2010 Dairy survey does not include information on SCC. All variables are drawn directly from ARMS. The survey targeted dairy operations in 24 states that account for more than 90 per cent of national milk production and covered all major production areas (McBride and . The survey had a total of 1,814 observations. Omitting plausible outliers in the distribution of reported SCC as well as those operations lacking responses to key questions yielded 1,552 usable observations. The complete list of variables used in the analysis, including brief definitions and sample summary statistics, is available in Table 1. We include key quantiles, those same used in our empirical framework, for each variable to illustrate the extent to which SCC and many other producer characteristics vary within the sample. The dependent variable, SCC, gives the annual average bulk-tank SCC for dairy producer i. For the purpose of ARMS data collection, SCC is reported in thousands, suggesting the importance of accounting for the statistical properties of count data. We revisit this point in detail below. We examine two variables representing bonuses or rewards. SCCPremium reports the value of the premium, in dollars per hundred weight (cwt), offered  by the buyer in return for yielding SCC levels below an agreed-upon threshold. This variable can take the value of zero. It represents the combination of responses to two questions in ARMS. One question asks if a SCC premium is offered at all, and the follow-up question asks the value of the premium if one is offered. Over 59 per cent of dairies were offered an SCC premium with the premium averaging about 24¢ per cwt. A preliminary investigation revealed that operations which dealt with buyers offering a premium had lower average SCC levels (244 thousand cells per ml) compared with the dairies that had no premium structure in place (294 thousand cells per ml). We sorted the dairies in the observed sample retained for the model into quartiles by the reported SCC. The average premium paid for dairies in the lowest quartile of SCC was USD 0.36 per cwt, dropping to USD 0.12 per cwt for dairies in the highest quartile of SCC. The empirical regularity is that higher premium payments are associated with lower SCC values or higher quality milk from the dairy producer.
VolPremium is a dummy variable equal to one if the producer was offered a premium for meeting an annual volume threshold, also agreed upon between the buyer and seller. Over 43 per cent of the surveyed operations were offered a volume premium for their milk production. The proportion of operations receiving a volume premium increases with size. For the smallest dairies (1 -49 milk cows), only 18 per cent receive a premium while premiums are reported by over 60 per cent of dairies in the largest size class (over 500 cows).The potential impact of the volume premium on SCC is unclear: higher overall milk yield is typically associated with lower SCC (Green, Schukken and Green, 2006); however, given herd size, high yielding cows are more prone to mastitis which is associated with higher SCC and reduction in yield.
We also focus on two variables representing penalties imposed by buyers for failing to meet imposed standards. Respondents to ARMS are presented with a series of eight requirements that are commonly set by buyers and asked to indicate how many requirements are imposed to them and, if imposed, the respective ramifications of failure. TestPenalty reports the number of these standards for which the penalty of failure is a re-testing of milk quality, specifically SCC levels, by the buyer. PricePenalty reports the number of questions for which the penalty is a potential reduction or renegotiation of the milk selling price. The full details behind the construction of these variables are available in Appendix A.
The next set of variables address managerial factors, which largely describe dairy operations in an effort to control for key SCC determinants as shown by the literature. Most of these are relatively time-invariant or very costly to adjust, though exhibit a large degree of cross-sectional variation. HerdSize and Herd-SizeSq are linear and quadatric, respectively, counts of dairy cows in the operation, in 1,000s. Allore, Oltenacu and Erb (1997) and Oleggini, Ely and Smith (2001) found larger herds to be associated with lower bulk-tank SCC. These studies showed that larger operations, with larger herds, may target markets with lower SCC thresholds (e.g. export markets) and are more likely to invest in and utilise technology to maximise milk yields per cow, which are factors that may reduce SCCs at the margin. The ARMS data confirm that larger herd sizes tend to have lower SCC levels while also reducing the variability of SCC. Operations with the largest herd size (500 or more cows) report the mean SCC levels that are about 6 per cent lower than the smallest dairies (less than 50 cows). The variability of SCC for the largest herds is almost 18 per cent lower compared with the smallest dairies.
Several studies on the dairy industry have uncovered systematic differences in performance, profitability, quality and yields by geographic region. MacDonald et al. (2007) surveyed the dairy industry using ARMS data and organised dairy-producing states into traditional, western, southern and 'other' categories. We use this classification to construct a vector of geographical dummies Location. 1 CowAge is the average age of the cows in the milking herd, as Harmon (1994) and Dong, Hennessy and Jensen (2012) showed the age of dairy cattle to be a small but significant factor driving up SCC. This is particularly true among cows affected by mastitis. HousingAge is the average age of the housing units used for dairy cows. Following Dong, Hennessy and Jensen (2012), we include this as a measurement of the extent to which housing facilities are modern and equipped to contain or reduce SCC.
The final set of variables focuses on production practices, which are related to managerial factors but more closely determined according to operators' choices and typically more elastic over time. SecurityGuidelines is an index that reports the extent to which operators abide by a series of common biosecurity measures, categorised within ARMS. MgmtPractices is also an index, showing the extent to which operators engage in a series of practices listed in ARMS that involve the use of modern milking or testing methods, digital technology and marketing techniques. The complete details behind the construction of this variable are available in Appendix B. 2 Finally, Organic is a dummy variable equal to one for certified organic operations. Recall that the expected relationship between SCC and organic status is not clear. Richards et al. (2002) note that organically produced milk may have higher SCC due to the increased incidence of infections among cattle on these operations, but that organic producers typically hold their milk with the highest SCC back from the market in order to achieve average SCC levels below certain thresholds. Richards et al. (2002) also note that there may be reason to expect SCC to increase with cow age more rapidly on organic operations, as compared with conventional. We initially interacted CowAge with Organic to investigate this possibility and found no evidence to support this.

Estimation issues
The ultimate objective of this study is to identify means by which dairy operations can feasibly reduce SCC in order to meet lower thresholds, or higher quality standards. Naturally, this exercise has the strongest implications for those producers exhibiting the highest SCC. Estimating Equation (2) with ordinary least squares (OLS) or any approach that imposes the requirement that the conditional probability distribution must be approximated by a few moments of a parametric distribution limits our interpretation of coefficients to estimated impacts on mean SCC. As Dong, Hennessy and Jensen (2012) argued, quantile regression is a potentially valuable tool for this research question as it allows for the estimation of effects on SCC specific to operators with different levels of SCC, most importantly those with the highest and greatest need for improvement.
Moreover, we argue that it is appropriate to model SCC as count data, given that it consists of discrete, non-negative integers. The variable includes no information past 1,000, therefore as an example, an actual SCC between 55,000 and 56,000 is recorded in ARMS as 55. OLS relies on the assumption of normality, which is typically violated by the highly skewed nature of count data, and this can lead to inefficient estimates (Cameron and Trivedi, 1998). Taking these factors into account, we subject Equation (2) to a generalised Poisson estimation, which is widely considered appropriate for use with count data, as well as quantile regression for count data. Via the latter approach, we examine how quantiles of the conditional distribution of a response variable recorded in discrete units (1,000s of SCC) depend on a set of explanatory variables.
In addition to modelling the entire distribution of SCC within the survey, the quantile regression approach relaxes important restrictions in the parametric specifications of count data models. When using more common count data approaches, such as the generalised Poisson or negative binomial, the relationships between explanatory variables and response variables are determined explicitly by a few moments of the parametric distribution (Winkelmann, 2006). In our context, these restrictions would ensure that SCC increases yield only a single switch between positive and negative marginal effects. The quantile model for count data relaxes these restrictions and allows for a richer determination of the relative magnitudes of marginal effects.
The quantile regression for count data approach was developed by Machado and Santos Silva (2005). The methodology is based on a smoothing algorithm that constructs a continuous variable with conditional quantiles that have a one-to-one relationship with the conditional quantiles of the counts. The discrete count response, y i , is replaced with a smooth, continuous transformation so that linear quantile regression methods can be applied. An auxiliary variable is created such that z i ¼ y i + U i [0, 1), where U i is a uniform random variable in the interval [0, 1). Any continuous distribution that has support on [0, 1) can be used in the transformation and standard quantile techniques can be applied to a monotonic transformation of the auxiliary variable z i . The estimated quantiles of z i are non-negative and the transformed quantile function is linear in the parameters when a monotonic transformation is used.
Let Q y (t|X) and Q z (t|X) denote the tth quantiles (0 ≤ t ≤ 1) of the conditional distribution of y i and z i and define The set of explanatory variables is denoted by X and b represents the estimated parameters. The predictive equation includes the additive term t because Q z (t|X) is bounded from below by t due to the additive random variable U [0, 1). The model can be estimated in a linear form using the following logarithmic transformation of z and regressing these values on X. The 6 term represents a suitably small positive number. The transformation back to the y i counts uses the ceiling function The estimated quantile functions for z i (denoted as the jittered y i ) provide a smooth linear interpolation among the step functions for y i . The y i are described as 'jittered' to signify that uniformly distributed random noise is added to the original data. The result is that Q y (t|X) can be recovered from information on Q z (t|X). The quantile function is not everywhere differentiable because the distribution function has corners. But when the explanatory variables in the model include at least one continuous variable, the corner points have measure zero. Machado and Santos Silver (2005) prove that the estimator is consistent and asymptotically normal so that inference about the coefficients can be based on Wald tests, which we perform.
To further motivate the approach, Figure 1 plots SCC as a function of number of milk cows per operation. The sample of dairy farmers was split into quartiles by herd size and then the SCC was computed for each dairy size quartile. The medians of the SCC for each dairy size are represented by the horizontal lines with the edges of the boxes revealing the 25th percentile and 75th percentile (the lower and upper quartiles), respectively. Particularly among the three largest quartiles, both median SCC and variability across farms decrease with herd size. The variability of SCC for the largest herds is almost 18 per cent lower compared with the smallest dairies. These observations conform with the findings of Allore, Oltenacu and Erb (1997) and Oleggini, Ely and Smith (2001) and also serve to suggest that SCC likely exhibits structural differences across dairy farms of varying characteristics. While boxplots and related Somatic cell counts in dairy marketing 341 Downloaded from https://academic.oup.com/erae/article/43/2/331/2367262 by Iowa State University user on 03 November 2020 statistical tools are limited to examining the distribution of SCC with respect to a single variable, the quantile regression method offers a powerful framework with which to estimate models for the conditional median function along with the full range of other conditional quantile functions, each as a function of a set of explanatory variables.
One final concern in estimating Equation (2) is the possibility of endogeneity. We discuss this possibility first with respect to SCCPremium. If dairy operators select buyers based on characteristics such as incentives offered, then it is conceivable that dairies with relatively low SCCs seek out buyers offering premiums in order to reap benefits. In that case, then the estimated coefficient on SCCPremium would only partially capture the effects of such offers on SCC and would also include the effects of dairy self-selection.
There is intuitive reason to expect that endogeneity may not be a concern in this setting. In an investigation of market power in the dairy industry, Sumner and Ahn (2008) make two important observations on the market for farm milk. One is that the bulk of the economic evidence on the dairy industry indicates that dairy operations are competitive and are therefore price takers. Additionally, raw milk is expensive to transport and the market for most farm milk is local. These notions, taken in tandem, suggest that it is unlikely that milk producers have the ability to shop among buyers based on a menu of characteristics or prices offered. This pertains to prices, inputs, schedules and a host of other factors. These contentions are supported broadly for US agriculture as well. Sexton (2013) notes that control in food industry contracts is nearly always exercised downstream. We also consider the possibility of endogeneity resulting from the CowAge and its relationship with milk prices. Practically, if milk prices are high, cows may be culled less quickly, which may consequently increase CowAge and then SCC. The converse is also true. But the culling/replacement decisionmaking stems from a complicated process. Other factors such as feed cost, cow's health condition and productivity, as well as replacement cow's productivity and transition cost also need to be considered in making these decisions. Therefore, a study using time-series or panel data is necessary to identify the effects of prices and other factors on cowage and consequently effects on SCC. Prices can certainly affect CowAge in such analysis, but the effect is also conditional on other factors. Our data are cross-sectional and a single year of annual data cannot reflect price effects on culling decisions or cow age, both of which develop in the longer term. The market-level milk price, moreover, will not be influenced by decisions of an individual dairy to change the culling practices, further mitigating endogeneity concerns.
We also conduct a series of exercises to test for endogeneity in Equation (2), and it is consistently rejected in the linear model. The details of our testing for the SCCPremium are available in Appendix C. To investigate this issue for CowAge, we estimated an alternative model with an added price variable. The main results are virtually unchanged and our interpretations are robust. We can find no evidence that omitting the price variable induces bias in the results of the SCC model.

Results and discussion
In our approach, we estimate Equation (2) for five quantiles, q ¼ 0.05, 0.25, 0.50, 0.75 and 0.95. When studying a variable that exhibits a significant degree of variation (SCC in our sample has a mean of 257 and a standard deviation of 115), it is a common practice to use quartiles as the quantiles selected for the regression analysis, as did Machado and Santos Silva (2005). Doing so lends the results to more straightforward interpretation and yields estimates of key relationships throughout the range of the data. In our own case, we are also interested in the extremes of the distribution, hence the inclusion of the 0.05 and 0.95 quantiles. The 0.95 quantile, in particular, is intended to provide insights into the factors most important in driving variation in the 95th percentile of the SCC distribution. The significant factors of the 0.95 quantile regression have the strongest implications for those dairies with the highest average SCC. We quickly recognised that regressions based on the 0.05 quantile yielded no significant findings, and given that those operations with the lowest SCC levels are of the least policy concern, we dropped these results from our tables. Table 2 shows the regression results for both the generalised Poisson (GPoisson) regression and the quantile regressions.
Given that we only have one year of ARMS data with which to work, we are limited to a cross-section analysis in estimating Equation (2). Therefore, care must be taken in interpreting the regression results. We include a rich set of controls as supported by the literature on fluid milk production, SCC and the Somatic cell counts in dairy marketing 343 Downloaded from https://academic.oup.com/erae/article/43/2/331/2367262 by Iowa State University user on 03 November 2020 incidence of mastitis. Equation (2) is intended to describe empirically the relationships between SCC and largely unexplored factors such as the buyer/producer relationship given the conditions in place as of 2005. Dynamic factors, which we are unable to observe, have the potential to enrich the story and establish the case for causality for many of our estimated relationships.
A striking feature of the results is the extent to which the GPoisson results can differ from the quantile regression results. For example, according to the GPoisson results, management practices have a positive and significant impact on SCC, meaning that they reduce average milk quality. However, this index is  (1). Coefficient is significant *at the 0.10 level, **at the 0.05 level and ***at the 0.01 level.
negatively and significantly associated with the 0.95 quantile for SCC among dairy farms and is insignificant for the rest. This suggests important differences in efficacy between the two approaches.
To investigate this further, we examine predicted SCC versus actual. We predict SCC for a conventional (non-organic) dairy located in a traditional dairy-producing state that receives a volume premium. The continuous explanatory variables from the model are set at their mean values. Figure 2 plots the hit rate for both the quantile regression and GPoisson results, by SCC quantile. We experimented with a number of different possibilities for conditioning the predicted SCC based on the variables in Equation (2). The percentage of accurate predictions using count regression can change somewhat, but for high levels of SCC the GPoisson estimation robustly gets 0 per cent of predictions correct. Our hit rate methodology is drawn from Benoit and Van den Poel (2009), whereby a prediction is considered accurate if the observed SCC meets or exceeds the prediction. At the 70th percentile, the quantile regression for the count model successfully predicts 32 per cent of the dairies with SCC levels at least that level, well above the 2 per cent hit rate of the GPoisson. In fact, the GPoisson has no predictive power for the highest levels of SCC, which translate for our estimation purposes to the 0.75 and 0.95 quantiles. We focus the remainder of our discussion on the richer and more flexible quantile regression results.
The factors shown to be important in shaping SCC at the 0.75 and 0.95 quantile are of the highest salience in understanding the means by which bulk-tank SCC in the United States may be reduced via cost-effective means. And in general, the number of statistically significant explanatory variables grows with quantile size. While not reported, no component of Equation (2) is significant for the 0.05 quantile, suggesting that certain operations are structurally oriented towards low SCC and high milk quality, likely owing to long-term investments in capital and established relationships with buyers. Geographic location is surely one of the important structural differences in determining SCC among producers. We found that 77 per cent of dairy operations below the 0.25 quantile are located in western or traditional dairy states, while only 57 per cent of operations at the 0.75 quantile or above are located in these states. Nine of the regressors are significant for the 0.95 quantile of SCC, the highest we examine. Dong, Hennessy and Jensen (2012) found similar lack of statistically significant explanatory factors for the 0.05 quantile, except for buyer requirements for testing. They found that requirements for testing for pasteurisation incubation and for standard plate count were associated with lower SCC levels for the 0.05 quantile.
Several factors, some of which are comparatively easy to adjust on a per-farm basis, are shown to significantly impact SCC at the highest quantiles. The aforementioned management practices are negatively and significantly associated with SCC at the 0.95 quantile. Several of the included practices are used by relatively few operations, meaning that the wide-scale adoption of forward purchasing or individual cow production records could lead to economically significant SCC reductions. Organic certification is associated with reduced SCC for the 0.50, 0.75 and 0.95 quantiles. Taking this finding into account, the overall impact of organic production on SCC and milk quality remains unclear, particularly in a dynamic setting, given that the results do not inform as to the long-or short-run effects of obtaining certification on SCC. But it is evident that it is associated with improvement among the operations with the highest SCC levels.
There is ample evidence that penalty and reward schemes, as constructed within buyer-producer relationships, have the potential to reduce SCC where it is the highest. Premiums based on achieving SCC below agreed-upon thresholds effectively reduce SCC for the 0.50 and 0.75 quantiles. Volume premiums are significant in lowering SCC for the three largest quantiles. This finding may be capturing, in part, increased efforts on the part of producers to increase yields, which have been inversely linked to SCC. In this respect, we observe another case where the quantile-based results differ importantly from those of the GPoisson, which measures a small but positive and significant impact on SCC. Increased milk testing is shown to reduce modestly SCC for the 0.75 and 0.95 quantiles.
Rounding out the significant findings, larger herd sizes are associated with decreased SCC at the 0.95 quantile. The quadratic herd size term is positive and significant, conforming to expectations and indicating that herd size shares a 'u-shaped' relationship with SCC among those farms with lowest milk quality. Among the highest quantiles, SCC is lower in both the western states and the traditional dairy states, as compared with the remaining states in the survey. Dong, Hennessy and Jensen (2012) found a relatively consistent and positive effect on SCC levels across the quantiles for states in the southeastern region (Tennessee, Kentucky, Florida and Georgia). The average age of the dairy herd significantly contributes to SCC for the 0.50 and 0.95 quantiles, a finding similar to that of Dong, Hennessy and Jensen (2012), who measured herd age in the same fashion. We find little to no effects on SCC for housing age, biosecurity guidelines or buyer-imposed penalties related to the potential price decreases.

Conditional SCC predictions and marginal effects
The interpretation of coefficients in quantile regression for count data is not entirely intuitive. Following Miranda (2008), we calculate the predicted SCC and marginal effects for all explanatory variables, by quantile. The marginal effect of a change in x j from x 0 j to x 1 j is given by where Q SCC is the value of the conditional quantile of SCC, a is the quantile itself (0.25, 0.50, 0.75, 0.95) and X is still the vector of remaining explanatory variables, with continuous variables held at their means and dummy variables at their modes. The marginal effects can be interpreted as the predicted impact of an incremental change in the variable of interest on SCC. As Miranda (2008) notes, this procedure is important in the quantile regression setting because a significant regression coefficient does not necessarily mean that the marginal impact is also statistically significant. The results are reported in Table 3.
Once again it is evident that many factors have the strong potential to impact SCC at the highest quantiles, particularly 0.95. For those farms in the highest quantile in terms of SCC, each additional management practice leads to a reduction in SCC of 10,600. The implementation of additional practices such as those listed in Appendix B certainly requires case-by-case consideration, but as noted, several of the individual practices were only in place at fewer than half of all operations as of 2005. Organic certification is associated with a marginal reduction of 41,000 for the 0.75 quantile and 87,000 for the 0.95 quantile. The SCC-based premium can lead to a marginal decrease of 75,000-90,000 for farms in the upper half of average SCC, although the effect is not significant for the 0.95 quantile. The volume-based premium has significant marginal effects for the three largest quantiles which grow in magnitude with average SCC. It has a marginal impact of 64,000 for farms in the 0.95 quantile.
The marginal effects for many of the remaining variables are in line with the signs and statistical significance of the estimated coefficients in Table 2. Large marginal impacts persist across quantiles for operating in western or traditional dairy states. Each additional year in average age of the dairy herd has a marginal increase of 11,000 for the operations with the highest SCC.
The marginal effects with respect to herd size are somewhat surprising, at first glance. Given that larger operations tend to have lower SCC, we might expect herd size to have a negative impact on SCC. In most cases, the marginal effect of increasing herd size by 1,000 cows is insignificant, though for the 0.95 this effect (accounting for the linear and quadratic regression coefficients) Somatic cell counts in dairy marketing 347 is positive and significant. Since the operations with the highest average SCC are likely to be the smallest, this may reflect the notion that these small operations are best suited to very small herds and produce lower quality milk given increases in herd size.
It is interesting to note that, among those dairies in the 0.75 and 0.95 quantiles, several of the controls that are capital-intensive or involving high fixed costs have small or insignificant marginal effects on SCC. While more work, ideally with a longitudinal data set, is called for to estimate dynamic impacts of the imposition of premiums or penalties, the results demonstrate that such factors alone have the potential to significantly reduce SCC in the dairy industry. Given that each marginal effect is calculated holding all others constant, we have evidence that the role of incentives is distinct from that of investment, as premiums are associated with large decreases in SCC without important changes in factors such as housing age, herd size or biosecurity measures. Organic certification is costly for US dairy producers ), but given our findings and the potential  Miranda (2008). a The marginal effect for herd size takes into account both the linear and quadratic terms estimated and reported in Table 2. Coefficient is significant *at the 0.10 level, **at the 0.05 level and ***at the 0.01 level.
benefits in terms of SCC reduction, there is reason to evaluate the costs associated with certification in comparison to those associated with capital investments aimed at SCC reduction. The observed benefits of organic production on SCC also have policy implications, for example potential certification cost sharing.

Predicted SCC and dairy operation profitability
Many of the economic studies on SCC, mastitis and related issues have conducted measurements of economic loss, much of which is due to lost revenues or profits on the part of dairy producers. Recall that SCC is inversely related to both yields and prices for farm milk. Following MacDonald et al. (2007), we define net returns as the difference between the gross value of production and total costs, where the gross value of production for the dairy enterprise includes payments from milk production, from sales of dairy animals, and from other sources. Positive net returns indicate that the dairy is able to cover all costs, including costs of capital recovery. Henceforth, we describe operations having positive net returns as being profitable. By this definition, only 29 per cent of the surveyed dairy operations were profitable as of 2005, as shown in Table 4. 3 The average net return across the entire survey is 2USD 6.96 per cwt. However, the incidence of dairy farm profitability can differ importantly by SCC levels. The 75th percentile (P75) of SCC in our sample, or 275,000, is one convenient threshold to use as an example. Thirtytwo per cent of operations with SCC below P75 are profitable, while 22 per cent of those above this threshold are profitable. Hence those below this threshold are 10 percentage points, or nearly 50 per cent, more likely to be profitable. Additionally, P75 is in between the predicted SCC levels for the 0.50 and 0.75 quantiles in Table 3. Since so many marginal effects are significant for dairies in the 0.75 quantile, it is straightforward to observe the means by which predicted SCC levels below the P75 threshold can be attained.
Via the marginal effects reported in Table 3, we are able to visualise a number of means by which dairy operations with SCC levels above P75 can slip below that threshold and improve the likelihood of profitability. Naturally, effective and cost-effective SCC reduction is a process that, in practice, needs to be evaluated and carried out on a per-operation basis. However, let us assume for this exercise that each operation in the 0.75 quantile has the predicted SCC of 320,000. For those operations whose buyers do not offer an SCC premium, implementing one is predicted to lower SCC by 75,000, thereby reducing SCC to beneath P75. There are paths to P75 even for those operations in the 0.95 quantile. For example, switching to organic production, the addition of a volume premium and a reduction in the average age of the dairy herd by two years can achieve predicted SCC of below P75.
The P75 threshold is of course illustrative and arbitrary. More importantly, the dairy operations in ARMS illustrate an important economic relationship between SCC levels and profitability. Table 4 reports average net returns and percentage of profitable operations by SCC decile. The relationship is not perfectly inverse, as SCC is not the only element that affects profitability. However, the highest SCC decile has the lowest share of profitable operations, at 18 per cent. The eighth, ninth and tenth SCC deciles have three of the four lowest average net returns. Our results indicate that there are numerous strategies that dairy operations as well as buyers can undertake to reduce SCC such that expected net returns and the likelihood of dairy profitability can increase in economically significant numbers. Therefore, the incentives are in place, at the firm level, to reduce SCC domestically. Numerous caveats apply here, most importantly that our investigation between SCC and net returns is exploratory and that the moving from one SCC decile to another does not necessarily yield higher net returns. Additionally, this discussion highlights the importance of fully understanding the costs associated with any of these potential changes, and weighing these costs against the benefits of increased profitability owing to higher milk quality. Our results alone do not provide a recipe for producers to achieve positive net returns.
While it is not a goal of this article to analyse or predict dairy farm returns or profitability, there are certainly factors at play, beyond SCC, in determining profitability in the US dairy industry alone. Several of these are likely to be confounding factors, shaping net returns and SCC jointly. MacDonald et al. (2007) suggests that dairy size is likely to be an important example of such considerations. To that end, we also break down profitability by SCC decile for only those operations with herds larger than 500 cows, as shown in the two columns on the right in Table 4. It is immediately apparent that larger dairies are far more likely to be profitable, as 68 per cent of these 284 large operations have positive net returns and the average for the group is $1.43 per cwt. But also importantly, the link between SCC and profitability is not at all obvious among these larger operations. Recall that Figure 1 demonstrated that the variability in SCC was the smallest among this group of the largest dairies. All factors considered, reductions in SCC may be particularly relevant to smaller dairy operations, and more work is called for in this regard.

Conclusions
We synthesise much of the work that has been done on measuring the biological, managerial and economic determinants of SCC in farm milk. We develop and estimate a model of SCC that draws upon several key factors, with the intent of highlighting incentive-based means by which SCC may be reduced among US dairy operations. Importantly, we apply quantile regression to count data to account for the statistical properties of the ARMS dairy data and to measure directly the impacts of management and production practices and various incentives on dairy producers with the highest SCC levels, as these are the operations standing to benefit most from novel approaches to SCC reduction.
Our results indicate that many managerial factors and production practices have the potential to reduce significantly SCC for those operations with the highest average levels. Possibilities include volume-based premiums and increased testing requirements on the part of buyers, organic certification and the utilisation and maintenance of younger dairy herds. Given that we corroborate many findings drawn from research on milk quality among international producers, particularly those in the EU, our results with respect to SCC have international relevance as well.
We also uncover a potentially important link between high SCC and low dairy profitability and discuss several means by which dairy farms can reduce their SCC in order to increase their potential net returns substantially. There appear to be economically important differences across SCC levels in terms of the likelihood of positive net returns. However, it is important to note that these implications do not necessarily pertain to the largest dairy operations in the United States, which are the most profitable and do not exhibit a clear relationship between returns and SCC.
In terms of policy implications, our work suggests that for many dairy operations, SCC can be reduced substantially through cost-effective means. One efficient approach may be through efforts to forge closer relationships between dairy producers and their buyers, as relationships involving more detailed reward and punishment schemes seem to have potential to reduce SCC among those producers with the highest levels. We demonstrate that organic production is associated with significantly lower SCC among dairies with high levels, suggesting that policies to subsidise or streamline the often costly organic certification process may have benefits in this respect. Efforts to achieve SCC reductions may be less effective among the largest dairies, those with greater than 500 cows, but this is not to say they should be ignored. On the other hand, the results may help Somatic cell counts in dairy marketing 351 Downloaded from https://academic.oup.com/erae/article/43/2/331/2367262 by Iowa State University user on 03 November 2020 to provide a roadmap towards greater profitability and competitiveness among smaller dairies. Therefore, our results have implications for rural economies and producer welfare.
There are several limitations and cautions to the findings reported in this article. The SCC level is reported as an annual average level. This value smooths considerable variation that may occur during the year. We find that the level of SCC premium received is associated with state level indicators. This suggests aspects of the buyer-dairy market may be important and therefore warrant further investigation. Although this market environment may be captured in part by the regional binary variables, there may be other buyer practices that are not fully controlled for by our regional variables.
Our results leave much room for future work. One strongly motivated avenue is an improved understanding of the determinants of net returns, or profitability, in the dairy industry. Such research must account for SCC, given the large number of potential confounding factors involved. But increases in our understanding of profitability would greatly enrich this story and likely provide insights into how SCC may be effectively reduced even among the largest dairies in the United States. Many of the insights gleaned from our work could be reinforced and incorporated into a framework of entry and exit from the industry through the use of longitudinal data. Investigating SCC in this regard is not possible with the ARMS data due to changes in the questionnaire, so future research on this topic must seek out alternative avenues.