2. Background: Dairy Industry Expansion Effects on Hay Markets

Since 2000, substantial growth in dairy production has occurred in some U.S. states while it has been either stable or declining in others. Figure 1 shows a plot of milk cow inventories for 2000–2019 for the top five milk-producing states, based on 2019 dairy industry cash receipts as recorded by USDA-ERS. These states, in order from highest to lowest, are California, Wisconsin, Idaho, New York, and Texas. The data indicate that dairy cow inventories were higher in 2019 than in 2000 for California, Idaho, and Texas, but lower for Wisconsin and New York. Moreover, rapid expansion periods are observed for California in the early 2000s, Idaho for the early to mid-2000s, and Texas for the mid-2010s to 2019. Table A1 in the online supplementary appendix shows the rates of growth in cow inventories for the top 10 states considering dairy industry cash receipts from USDA-ERS for 2002–2019. In addition to California, Idaho, and Texas, another state with substantial dairy industry growth during this observation period is New Mexico. The remaining large dairy-producing states have not had as notable trends of substantial growth. However, Michigan and Washington have had a few years of relatively high growth.

Figure 1. Dairy cow inventories for top five (as of 2019) dairy-producing U.S. states, 2000–2019.

Source: USDA-NASS and USDA-ERS.

The substantial growth in the dairy industries observed in California, Idaho, and New Mexico can have substantial effects on linked markets, especially those for feed. The United States Department of Agriculture (USDA) does not demarcate among hay consumption segments, the main of which are feed, stocks, and exports, in its reports, as it does for corn. Estimation of hay consumption for feed is difficult given the tendency of dairy producers to substitute across feed types based on nutritionists’ preferences, market conditions, and/or other factors. However, to illustrate these effects, feed ration parameters established by the National Research Council (NRC) help to describe plausible changes in hay consumption for feed under a dairy industry expansion. The dairy feed-related parameters are about 20 kg of dry matter intake (DMI) per day per cow, with the ratio of forage (hay or corn silage) to concentrate at 3:2 (NRC, 2001). These parameters imply that the share of hay production used for dairy feed may experience growth rates like those of dairy cow inventories during a considerable dairy industry expansion.

Of the primary components of hay consumption, export demand is likely more price elastic than that for feed and stocks because foreign buyers can substitute among export competitors (Abbott, Reference Abbott2013). By comparison, commercial dairies tend to make adjustments in input purchase strategies, including those for feed, over longer periods of time (Wolf, Reference Wolf2010). This implies relatively price inelastic feed demand in comparison to that for exports.

The hay market is unique to those of other feed crops in several ways. First, trade on international markets is generally not a substantial share of total use or production, so market conditions are more driven by national and regional supply and demand factors (Wolf, Reference Wolf2010). California is an exceptional case regarding this, and export volumes vary across years for all analyzed states (see Table 1). Additionally, while there are several feed crop sources for the fiber component of dairy rations, there are few substitutes for alfalfa hay as a source of crude protein among forages (Hopper, Peterson, and Burton Jr., Reference Hopper, Peterson and Burton2004; Chahine, Reference Chahine2020).Footnote ² This means that a substitute dairy ration for hay requires the substitution of the fiber and protein sources (NRC, 2001). Such determinations are likely different and complex depending on the region, and so use of substitute feeds may occur out of necessity such as during a lack of hay availability, hay expected availability, or of funding (cash flow) availability during periods of unusual market conditions.

Table 1. Summary statistics for dairy industry expansion, exports, hay stocks-to-use ratios, and prices for 2002–2019

Figure 2 is a theoretical representation of a regional hay market in the U.S. before and after a dairy industry expansion. It builds on the theory of the U.S. corn market during the “ethanol boom” of 2006–2008 developed by Abbott (Reference Abbott2013). During the “ethanol boom,” the corn market was impacted by expanding ethanol production capacity and by intermittently binding capacity constraints in the ethanol industry (Abbott, Reference Abbott2013). The top left panel characterizes the conditions before dairy industry expansion. The two principal components related to demand are stocks and feed. Total demand is the sum of demand for stocks and feed. Consistent with the theory explained in Wright (Reference Wright2011), stocks demand is very price inelastic. Demand for feed is also price inelastic, but becomes more elastic at higher demand levels because alternative substitute feeds may become convenient at greater feed levels. Total demand at quantities greater than the short-run supply level ( ${S_{SR}}$ ) is perfectly price elastic because substitution becomes mandatory due to lack of availability. The last element of the top left panel assumes there is an increase in demand, perhaps due to exports. In such a case, demand shifts from ${D_{total}}$ to D'_total , and the price increases from ${p_0}$ to p'₀ (Δ ₀).

Figure 2. Representation of a regional hay market before and after dairy industry expansion.

Source: Authors.

Note: Δ for change.

The top right panel of Figure 2 shows the conditions in the hay market after a dairy industry expansion. The demand for stocks and feed is greater for both stocks and feed, which implies higher total demand. The shift in total demand to the higher level increases the base hay level price to ${p_1}$ , where ${p_1} \gt {p_0}$ .

The bottom panel of Figure 2 introduces the situation in which there is an increase in demand for hay in the period after the dairy expansion, once again considering an increase in exports. In such a case, demand shifts outward from ${D_{total}}$ to $D{'_{total}}$ , where the market equilibrium ( ${Q_s} = {Q_d}$ ) is now at the very price inelastic portion of the hay demand curve. This results in a price increase from ${p_1}$ to $p{'_1}$ ( ${\Delta _1}$ ), where ${\Delta _1} \gt {\Delta _0}$ . Any excess quantity demanded ( $Q{'_d}$ ) is met through substitution to other feed types.

There are several takeaways from Figure 2. First, the increased demand for stocks after the dairy industry expansion makes the overall hay market tighter. That is, for future feed purposes, there is less hay available for sale after the dairy industry expansion than was the case before. Second, with the increased demand and more inelastic demand associated with the dairy expansion, the price effects from changes in demand due to other factors are larger than they were prior to the dairy industry expansion. Third, excess demand beyond short-run supply is perfectly price elastic, where excess feed demand is fully met with substitutes.

The implications regarding the dairy industry expansion for the hay and milk price relationship are as follows. First, after the dairy industry expansion in which the hay market may be tighter, milk price changes would have a greater effect on hay prices than in the case prior to expansion. That is, in the post-expansion case, an increase (decrease) in the milk price would be more likely to translate to an increase (decrease) in the hay price than before the expansion because hay market equilibrium more plausibly occurs where demand is relatively price inelastic. Thus, hay and milk prices are expected to have a closer or higher dynamic relationship after the dairy expansion than before. Second, after the dairy expansion has occurred, other irregular “shocks” to demand, such as an unanticipated change from normal demand for exports, would have a greater influence on hay-to-milk price responsiveness than observed before the expansion.

Given this theoretical background, it is hypothesized that the extent to which hay and milk prices move together has varied over time. Specifically, there has likely been greater hay price responsiveness to milk prices after the high dairy industry growth period of the early 2000s for the analyzed states than before. Figure 3 includes plots of hay and milk prices for California, Idaho, and New Mexico for 2002–2019. The plots show that hay prices in each of these states had distinct trends and variations over time. Moreover, hay price levels were generally higher in the 2010s than in the 2000s for all states. These observations seem to support the conjecture that local market conditions are important for determining outcomes in hay markets but that some shared or similar exogenous factors also have effects. For the case of the milk price series, more similarity in trends and variability is apparent across states than in the case of hay. For Idaho and New Mexico, it appears that the trends in hay and milk prices were more similar in the latter part of the 2000s through 2019 than during the early 2000s.

Figure 3. California, Idaho, and New Mexico hay and milk prices, 2002–2019.

Source: USDA-NASS.

While the data appear to show that the hay-to-milk price responsiveness has changed over time, questions remain about whether our hypothesized factors regarding hay market demand characteristics help explain such changes. The objectives for the empirical analysis are to test whether the following theory-derived hypotheses are consistent with the data:

1. 1. Hay price variation is explained more by variation in the milk price after the dairy expansion than was the case before expansion.

2. 2. The hay and milk relationship is different in periods when stocks-to-use ratios are low and there is higher-than-normal export demand than under normal stocks and export conditions.

3. Data and Estimation Method

The price data are monthly observations covering the period of January 2002–December 2019 from the USDA-NASS. They are the hay prices received in $/ton and milk prices received in $/cwt, for California, Idaho, and New Mexico, respectively. January 2002 was chosen as the start date for the analysis based on the availability of state-level export data.

USDA-NASS data on annual dairy cow inventories were used to identify periods of rapid dairy industry expansion in the analyzed states. A dummy variable representing the period after rapid dairy industry expansion (post-expansion) was created. For this variable, the post-expansion period begins in the year in which the year-to-year growth rate was lower than the previous value, and the subsequent year growth values were also lower. Thus, these variables have a value of 1 for all months in years after the period of rapid dairy industry expansion, and a value of 0 otherwise. The post-expansion periods for each state were as follows: California, 2004–2019; Idaho, 2007–2019; and New Mexico, 2007–2019. The growth rates for cow inventories for the “expansion” and “post-expansion” as defined are included in the summary statistics (Table 1). A more technically accurate name for the variable is a “post-rapid expansion” since growth occurred in some years in the “post-expansion” period as defined. However, “post-expansion” is used for brevity since the variable for all analyzed states represents a similar change in hay market demand conditions from before and after a considerable dairy industry expansion.

Hay exports data for each state were obtained from the U.S. Census Bureau USA Trade Online data set. The data obtained were annual values in U.S. dollar (USD) termsFootnote ³ . These values were converted to quantities (tons) by dividing the annual USD value by the average marketing year price for each state. A “higher-than-normal exports” year was identified as one in which export values were one standard deviation greater than the mean value. These years are as follows for the respective states: 2015–2017 for California; 2009 and 2012–2013 for Idaho; and 2004 and 2018 for New Mexico. Dummy variables for each state were created to represent these periods. These variables had a value of 1 for all months in the years with higher-than-normal export volumes and a 0 otherwise.

USDA-NASS production and stocks data were used to calculate stocks-to-use ratios for each state, the Western regionFootnote ⁴ , and the U.S. Specifically, the “stocks” portion of the stocks-to-use ratio is the stocks level for May. To calculate the “use” piece of the ratio, the December stocks levels for the previous year and estimated production for the current year were added, and then the current year December stocks value was subtracted off of that summed value.

Based on the hay market being primarily influenced by local rather than external factors in most states (Wolf, Reference Wolf2010), it was expected that the stock levels at the local or regional (Western region) level would be more informative for market conditions. Stocks-to-use levels associated with each geographic area were included in the analysis for each state to investigate this conjecture. Regarding the annual stocks-to-use ratios, if the observed value was one standard deviation below the mean, then it was considered a “low stocks-to-use” year. In the econometric models that are described next, dummy variables for each state, the Western region, and the U.S., were included to represent low stocks-to-use years. These variables had a value of 1 for all months in years with low stocks-to-use conditions, and 0 otherwise. The low stocks-to-use thresholds were as follows: California, 2%; Idaho, 6%; New Mexico, 5%; West, 8%; and the U.S., 13%.

Summary statistics for dairy industry expansion, hay exports, hay, and milk prices, and stocks-to-use ratios data for California, Idaho, and New Mexico for 2002–2019 are shown in Table 1. It is apparent that the growth rates regarding dairy cow inventories differed substantially between the early 2000s and the mid-2000s to 2019. Additionally, average hay exports from California are far greater and less variable than those in Idaho and New Mexico. Mean stocks-to-use ratios are lower and more variable in California than in Idaho and New Mexico. Average hay prices were higher and less variable in New Mexico than in California and Idaho. Milk prices were relatively less variable than hay prices for all analyzed states, and mean milk prices were more similar across these states than was the case for hay prices. The main takeaway from Table 1 is that there was substantial variation regarding hay market conditions across California, Idaho, and New Mexico, while milk market conditions were relatively similar.

The above-described variables were included in econometric models analyzing the hay-to-milk price relationship. These models are price transmission versions of time series cointegration models, for which the literature is vast and is discussed in detail by Baffes (Reference Baffes1991). The cointegration framework was chosen based on the observed close linkages between the dairy and hay markets, and because the prices of other feed crops (e.g., barley, corn, and wheat) are determined outside of regional markets in most cases. Thus, it is expected that in the presence of a substantial dairy industry expansion hay and milk prices move together over the long run. This does not mean that the milk price is the only factor that influences hay prices. Recent studies such as Cann (Reference Cann2014) and Li (Reference Li2016) that seek to explain variation in hay prices include many potential factors, including milk prices, other dairy feed prices, and exports. The goal of this empirical analysis is not to explain all variation in hay prices. Rather, it is to test whether the relationship between hay and milk prices is stronger after a rapid dairy industry expansion than it is before the expansion. Given these goals, the cointegration framework is most appropriate for this study, after having tested positive for non-stationarity of the series. Since the cointegration framework is well known in the literature, a detailed discussion of technical details and series stationarity test results are included only in the online supplementary appendix.

The initial estimated models include the hay price for each month, ${p_{H,t}}$ , as the dependent variable, and the monthly milk price, ${p_{M,t}}$ , as the independent variable. The resulting price level regression model representing the hay and milk price relationship for a given month, t, for each state of California, Idaho, and New Mexico has the following form:

(1) $${p_{H,t}} = \alpha + {\rm{\;}}\beta {p_{M,t}} + {u_t,}$$

where $\alpha $ is the intercept, $\beta $ is the long-run price responsiveness parameter, and ${u_t}$ is a random error. Stationarity of the residuals obtained from the estimation of equation (1), ${ {\hat u}_t}$ , imply that the prices are cointegrated (Phillips and Ouliaris, Reference Phillips and Ouliaris1990). Evidence of cointegration means that the variables move together over the long run. Another indicator of cointegration is the statistical significance of the error correction mechanism (ECM) parameter in a regression that includes the estimated lagged residuals from the estimation of equation (1), ${ {\hat u}_{t-1}}$ , and the first difference of the milk price on the right-hand side with the first differenced hay price as the dependent variable (Banerjee et al., Reference Banerjee, Dolado, Galbraith and Hendry1993). In the results, the Dickey–Fuller (DF) and Phillips–Perron (PP) tests of stationarity of residuals and statistical significance level of the ECM parameters are reported as evidence regarding cointegration.

The main objective of the empirical analysis is to test whether the degree to which the hay and milk prices move together changes with a rapid expansion of the dairy industry in the state. Specifically, it is hypothesized that the price responsiveness parameter ( $\beta $ ) is greater in the post-dairy expansion period than before and may also be different during periods of higher-than-normal exports and low stocks-to-use ratios. To test whether there is evidence to support these hypotheses, the base-level models from equation (1) were adjusted to account for the factors that affect the characteristics of hay market demand. The adjusted models build upon the methods developed by Hatzenbuehler, Abbott, and Foster (Reference Hatzenbuehler, Abbott and Foster2016) based on the cointegration theory of Gregory and Hansen (Reference Gregory and Hansen1996). The resulting regression models for each state had the following form:

(2) $${p_{H,t}} = {\alpha _0} + {\alpha _j}{I_{j,t}} + {\rm{\;}}{\beta _0}{p_{M,t}} + {\beta _j}\left( {{p_{M,t}}{\rm{*}}{I_{j,t}}} \right) + {\varepsilon _t,}$$

where the prices and parameters ${\alpha _0}$ and ${\beta _0}$ are interpreted like the analogous parameters in equation (1) $;\;{I_{j,t}}$ is a generic dummy variable that represents periods of different hay market demand characteristics such that j represents either post-dairy expansion, higher-than-normal exports, or low stocks-to-use ratio periods. The parameters ${\alpha _j}$ and ${\beta _j}$ are the intercept and price responsiveness parameters associated with such periods, respectively, and ${\varepsilon _t}$ is a random error. The models were estimated considering (i) only one of the j hay market demand characteristic change factors, i.e. three models estimated and (ii) with all factors included in an expanded model.

The expectation of greater milk-to-hay price transmission in the period post-dairy industry expansion than the period preceding it implies an estimated price responsiveness parameter that is greater than 0 ( ${ {\widehat \beta}_j > 0}$ ). Regarding the periods of higher-than-normal exports and low stocks-to-use ratios, the expected sign of the estimated price responsiveness parameter associated with these periods is uncertain. This is because, depending on the amount of marketable hay and other substitute feed supply available, a milk price change may enhance or dampen hay price responsiveness.