As outlined in Sumner and Leiby and Sumner , the human capital element remains prevalent through economic explanations of farm exit. Of course, age of the farm operators plays key role. Macdonald et al. discuss the role of the advanced age of many dairy farmers and the fact that many dairy farms are family-run, suggesting that there will be an increase in exits as more farmers choose to retire. Furthermore, the study relates the probability of exit to farm size, finding that not only does the age of the operator increase the likelihood of exit, but the smaller the farm size also increases the probability of exit.This section discusses the sample used in this analysis and details changes in the COA questions that are relevant to this analysis. The research utilizes COA data from 2002, 2007,2012, and 2017 for six select states: California, Idaho, New Mexico, New York, Texas, and Wisconsin. The results presented have gone through a disclosure review process and no data on individual/farm-specific is specific to individual farms and instead characterizes them more generally. Although the COA is federally mandated, it does not collect data on every U.S. farm and as such weights responses to create the most accurate sample that reflects the true U.S. farm sample. As discussed in Chapter 2, I use a specific definition of a commercial dairy in order to capture dairies with significant engagement with the dairy industry. A commercial dairy for the purposes of this analysis is defined as a farm with at least 20 milk cows on the farm as of December 31 of the Census year and the farm must have dairy or milk sales revenue above the dollars of milk sale revenue that would have been generated by 30 milk cows.

The survey questions asked of farmers and ranchers by the COA change slightly every Census round, hydroponic flood tray although most remain the same across time. Below are descriptions of question changes for relevant variables to the analysis. First, in 2002 and 2007, farms were asked for the total amount of dairy sales in that year, but in 2012 and 2017, this question was dropped and replaced with the total amount of milk sales. Furthermore, whether the dairy farm had any level of organic production was only asked in 2007, 2012, and 2017. Second, operator characteristic questions have become more detailed over the years and allowed more information about operators to be collected. In 2002, 2007, and 2012, the COA asked detailed operator characteristic questions about up to three operators, but only one operator was identified as the principal operator. In 2017, the COA expanded its detailed operator questions to include up to four operators and allowed for up to four operators to be identified as principal operators. In this Chapter, the operators for which the number per farm is limited and detailed information is provided will be referred to as the “core operators.”There is other no limit to the number other operators listed per farm and only the gender of each such operator and the total number per farm are provided in the Census. The COA has three potentially relevant farm size variables for dairy farms, the number of milk cows, the value of farm production, and the value of milk or dairy sales. I utilize all three in this chapter. However, I focus particular attention on the number of milk cows for the kernel density graphs. I characterize the distributions of number of milk cows per commercial dairy farm using two approaches. One approach is to fit a nonparametric distribution by year, and by state for each year to the data on milk cow herd size per farm. The other approach is to fit two commonly used parametric distributions to characterize dairy farm size distributions for the national and individual states over census years.

One aim of my thesis is to characterize the farm size distribution of dairy farms and fitting parametric density functions serves as a starting point for characterizing and analyzing dairy size distribution. As explained above, there is previous literature that utilizes parametric distributions to characterize farm size and this research provides evidence that commonly used distributions do not fit well with the U.S. commercial dairy industry. It is common in farm size analysis to fit parametric density functions to characterize farm size distribution . I create kernel density plots for the herd size distribution by state across the years and then find and fit two common parametric density functions to the distribution. This section will be structures as follows: a brief overview of the mathematics used in fitting parametric density functions. First, I hypothesize based on the kernel density plots what distributions seem reasonable. For this analysis I use the log normal and the exponential function, as those are two common distributions used in farm size literature and are likely shapes for most farm size distributions. Lognormal is the typical selection, as it is referenced in Gibrat’s Law. The exponential distribution was selected because it can account for the same skewed shape but has more flexibility. Second, I estimate the parameters of interest needed to form that distribution in order to create an estimated distribution of random numbers that follow the specific distribution. For this analysis, the measures of farm size, the number of milk cows for each farm, are random variables x1, x2, x3, …, xn, where n is the sample size of farms, for which the joint distribution depends on distribution parameters. For example, using the log normal the parameters are the mean and variance, and there are two related parameters for the exponential distribution.

The estimates of the parameters are functions of the milk cow herd size variable in question. From there, we can calculate the estimates of these parameters to create a different distribution with those same parameters and compare them to the actual distribution of the number of milk cows. Some estimated parametric distributions appear to have slight irregularities, this is due to the number of observations and the impose parameters.This section will summarize the resulting farm size graphs and detail the trends across time and states. Overall, when looking at the six select states together commercial dairy farm distributions have shifted towards larger dairies. In 2002, there was a clear peak in the number of farms with less than 200 milk cows, but the peak falls significantly from 2002 to 2017 . Whereas farm size distribution shows a clear increase in the farms with larger herd sizes in 2017. Although this graph gives interesting detail about the trends in herd size for the U.S. overall it is mostly characterized by Wisconsin and New York which have a significantly larger share of the number of commercial dairies and tend to have smaller herd sizes relative to other states. This graph clearly shows that there remains a large share of dairies that have a herd size of less than 200 milk cows, despite the relative shift in herd size.Moving to state-specific trends, overall California dairies have had larger herd sizes than other states, such as New York or Wisconsin across all years . California had a peak in the share of dairies with less than 1,000 milk cows from 2002 to 2017, but the peak fell significantly between 2007 and 2012. There was a clear shift in 2012 with an increase in the 1,000 to 2,000 milk cow herd size in 2012 and then another shift in 2017 in the 2,000 to 3,000 milk cow herd size. This documents a clear movement of California dairies towards larger herd sizes and a decrease in smaller herd sizes. Idaho had a large peak in commercial dairies with less than 500 milk cows in 2002 and then a significant drop in that peak in 2007 with smaller subsequent decreases in 2012 and 2017 . Interestingly, in 2007 there was an increase in the number of dairies with a milk cow herd size between 500 to 1,000, hydro flood table but then a subsequent decrease the following year. In 2017 there was a clear increase in the number of commercial dairies with a milk cow herd size between 1,500 and 2,000. New Mexico had one of the more unique herd size distributions with no clear peak in the smaller herd size ranges . From 2002 to 2007, there was a clear drop in the density of commercial dairies with less than 1,000 milk cows and a relative increase in the density of commercial dairies with 1,000 milk cows. Then in 2012, there was a shift towards commercial dairies with more than 2,000 milk cows and a downward shift in commercial dairies in the 500 to 1,000 milk cow herd size range. This trend continued in 2017 with even further shifts in each direction. From 2002 to 2017, New York has seen a slight decrease in the smaller herd sizes and a little increase in the larger herd sizes .In Texas, the most distinct trend was a significant drop in the density of commercial dairies with herd sizes of less than 500 milk cows between 2012 and 2017 .

There has previously been a trend of decreases in this herd size range, but these follow a similar pattern as compared to most other states. However, in other states, there was not such a significant drop. In 2017, there was an increase in commercial dairies with more than 1,000 milk cows. There was a significant decrease the commercial dairies in Wisconsin with less than 100 milk cows from 2007 to 2012 and then again from 2012 to 2017 . In 2017, there was an increase in commercial dairies with a herd size of between 150 and 200 milk cows. Wisconsin’s dairy industry is characterized by a significant number of smaller dairies and few dairies with large milk cow herd sizes. Across the states, there is a trend of consolidation with few commercial dairies and an increase in the number of dairies with larger herd sizes. Despite the decrease in the number of farms in each state, the number of milk cows increased in some states and broadly remained relatively stable . California had a 6.7% increase in the number of milk cows from 2002 to 2017, but Idaho had a 55% increase. The number of milk cows in New Mexico and Wisconsin both remained roughly the same. There was a 6% decrease in the number of milk cows in New York and number of Texas grew by more than 70%. Neither of the two parametric distributions fit the national data well. In particular, both the log normal and exponential distributions failed to capture the very high mode at the low herd size in 2002. The herd sizes in California did not fit any distribution well in 2002 or 2017 . Idaho has a large peak in the smaller ranges that is well above either the log normal or the exponential distribution in 2002 . The herd size does fall significantly when looking at the Idaho herd size distribution in 2017, this does some what follow a log normal pattern, but not very well . New York follows a similar pattern with the smaller herd size peak being significantly higher than either the log normal or the exponential peaks in 2002 or 2017 . As we saw across years in Texas, the herd size shifted dramatically. In 2002, the herd size distribution slightly resembled a log normal trend but had definite deviations and in 2017 did not follow any distribution well . Wisconsin follows a similar pattern to New York with no clear distribution trend in 2002 or 2017, but with significantly high peaks in the lower herd size range that deviate from the distributions.As explained above there are several possible influences, but given the Census data, I have chosen the following variables: characteristics of the operators , farm sales diversification across commodities, and share of farm operators who have off-farm employment. I also account for state fixed effects and Census year fixed effects. Clearly sales diversification and off farm work are jointly determined with dairy farm size, so I do not claim to be measuring a causal impact in the regressions presented discussed in this section. The aim here is to discuss statistical relationships between these characteristics and the farm size measures because although they cannot be thought of as directly influencing farm size the relationship between such measures is of interest and allows for discussion about the characteristics of the U.S commercial dairy.