2. The Integrated Agricultural Model

The framework used in this analysis is a dynamic partial equilibrium model that determines changes in prices and quantities relative to baseline values for U.S. livestock products, livestock, and crops in response to production shocks from drought conditions. The model baseline includes quarterly values calculated from the annual U.S. Department of Agriculture (USDA) baseline using seasonal adjustment factors. U.S. agricultural sectors are modeled by crops and forage and pasture sectors that are used as inputs by animal agriculture sectors that are vertically linked to animal processing sectors and, ultimately, demand for final goods. The seven input sectors for animal agriculture include wheat, coarse grains, rice, soybeans, soybean meal, soybean oil, and forage and pasture. The six animal agriculture sectors include cattle, hogs, birds, lamb and sheep, eggs, and dairy. Animal processing comprises four sectors including beef and cattle, pork and hogs, lamb and sheep meat, and poultry meat and birds. The final goods available for consumption include beef, pork, poultry meat, lamb and sheep meat, dairy products, eggs, rice, coarse grains, wheat, and soybean oil (Paarlberg et al., Reference Paarlberg, Seitzinger, Lee and Mathews2008).

Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008) used this framework in tandem with an epidemiological model to assess the impacts of foreign animal disease on U.S. livestock sectors. Accordingly, the authors investigated the effects of a hypothetical outbreak of foot-and-mouth disease (FMD) by integrating results for livestock production impacts from an epidemiological model into the economic model that we use for this research. Although Paarlberg et al. invoke disease-related production shocks to livestock sectors and account for FMD-related trade embargoes in the economic model, our work employs historically observed drought-induced production and yield shocks to both crop and livestock sectors in the economic model alone. As our work does not consider disease impacts, we refrain from using an epidemiological model. This integrated agricultural model is ideal for the study of drought impacts because it allows for the dynamic analysis of the effects of drought-induced supply shocks to crops and livestock sectors over an 8-year time horizon.

Although work on the economy-wide effects of drought in Australia has employed computable general equilibrium (CGE) modeling frameworks (Banerjee et al., Reference Banerjee, Bark, Connor and Crossman2013; Horridge, Madden, and Wittwer, Reference Horridge, Madden and Wittwer2005), we find that this detailed partial equilibrium model for the U.S. agricultural economy is best suited for our analysis. This framework allows for the detailed accounting of the intricacies of the agricultural supply chain that is not permissible given the simplifying assumptions that are necessary in CGE frameworks with more highly aggregated agricultural sectors. Furthermore, CGE frameworks that are annual in nature do not account for the seasonality that occurs for crop production by sector, which we are able to include given our quarterly modeling framework. The economic model we employ has the structure of a specific-factors model with perfect competition. This framework is based on key assumptions for economic agents and economic activity. Producers and consumers are assumed to be price takers that maximize well-defined objective functions. Consumers maximize a well-defined, homothetic utility function, given income and prices, which results in a set of per capita demand functions for final goods. According to Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008), per capita consumption of final goods in quarter t is defined as DP _t . Final goods are beef, pork, poultry meat, lamb meat, eggs, milk, wheat, coarse grains, rice, and soybean oil. Per capita demand functions defined by the vector DP _t depend on a vector of prices for final goods, PR _t , and per capita income, y_t :

(1) \begin{equation} {\bf DP}_t = {\bf DP}_t ({\bf PR}_t ,y_ t).\end{equation}

Total U.S. consumption in quarter t depends on per capita consumption multiplied by population at time t, pop _t . DF _t is the vector of total consumption of final goods:

(2) \begin{equation} {\bf DF}_t = {\rm pop}_t * {\bf DP}_t .\end{equation}

Producers maximize profit given a well-defined, constant-returns-to-scale production function. The model includes four factors of production for each sector including mobile factors, sector-specific intermediate goods, sector-specific primary factors, and land that is used for crop production and pasture for livestock use. The model vertically links farm prices for crops and livestock; wholesale prices for meats, milk, and eggs; and retail prices for all final goods by calculated marketing margins. The model is solved in Microsoft Excel by satisfying market-clearing conditions for prices and quantities.

Meats, milk, and eggs represent separate production sectors, with zero-profit conditions holding for each, with production occurring at time t. Factors are in perfectly elastic supply with exogenous prices described by a column vector, W _t . The vector PA _t describes the prices for animal intermediate inputs, and R _t denotes prices for sector-specific primary factors. Unit cost given constant returns to scale is only a function of factor prices, CM(W _t , PA _t , R _t ). Wholesale prices of meats, milk, and eggs at time t are described by PM _t . Constant returns to scale and perfect competition lead to the following zero-profit conditions:

(3) \begin{equation} {\bf CM}({\bf W}_t ,\,{\bf PA}_t ,{\bf R}_t ) = {\bf PM}_t .\end{equation}

The production of meats, milk, and eggs is determined by factor-market-clearing conditions. AM is the matrix of per unit demands for factors of production for meats, milk, and eggs, and QM _t is the column vector of meats, milk, and eggs outputs at time t. The column vector Z consists of a partition [K _t , DA _t ] ^T , where K _t indicates primary, sector-specific factors in fixed supply and DA _t indicates the derived demands for animals at time t. Therefore, AM only depends on factor prices, given the following factor-market-clearing conditions:

(4) \begin{equation} {\bf AM}({\bf W}_t ,{\bf PA}_t ,{\bf R}_t ) \times {\bf QM}_t = {\bf Z}.\end{equation}

The sector-specific factors and derived demands for animals create the vertical linkages to animal agriculture, final products, as well as linkages for derived demand for feedstuff, crops, and the factors of production used in the crop sector. Because each type of animal has unique features, the model explicitly accounts for each type as described in detail in the appendix of Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008).

Livestock are intermediate inputs into meat production. The model explicitly tracks livestock going through the production system over time. Cattle, sheep, and hogs have production cycles that span longer than one quarter. Changes in breeding and replacement inventories are determined by changes in salvage values and the expected relative profitability of producing animals or products for future sale. For example, cow inventories adjust endogenously to changes in input prices and expected returns. Cow/calf producers are assumed to form expectations for future returns based on the returns in the previous quarter. Declines in live cattle prices combined with rising feed costs causes cow/calf operators to reduce breeding cow inventories, which in turn results in fewer calves and market cattle for slaughter several quarters later as cattle move through the production cycle. Wheat, coarse grains, soybean meal, and forage and pasture are available for feedstocks for each livestock type and corresponding growth stage. This feature creates unique derived input demands for feedstocks (Paarlberg et al., Reference Paarlberg, Seitzinger, Lee and Mathews2008).

Livestock and crop production adjust across time based on biological limitations. Crop production by type occurs at set times of the year and then becomes carry-in stock in subsequent quarters until a new crop is harvested. Acreage allocations for future crops are set in the January–March quarter of each year based on expected returns for each crop at harvest, which are equal to the previous harvest prices plus any government payments. For winter crops, such as winter wheat, this means that the area for planting in the next fall is determined by the cropping decisions in the first quarter of the year. Rice is harvested in the third quarter, and soybeans are assumed to be harvested in the fourth quarter. Coarse grains are harvested in quarters 3 and 4. Forage and pasture production occurs in quarters 2 and 3.

The vector of expected crop returns calculated in the first quarter, P ^e ₁, given the assumption of zero-profits, determines crop production for quarter t (Paarlberg et al., Reference Paarlberg, Seitzinger, Lee and Mathews2008):

(5) \begin{equation} {\bf C}_t ({\bf W},{\bf R}^{\bf e} ,{\bm \tau }) = {\bf P}_1^{\bf e} ,\end{equation}

where R^e is the vector of expected returns to capital that is calculated by the zero-profit condition, τ is the return to land, and W is exogenous, given the perfectly elastic supply of the mobile input.

Crop output for quarter t is determined by sector-specific, factor-market-clearing conditions, given expected rent and factor prices in quarter 1:

(6) \begin{equation} {\bf a}_{\rm K} ({\bf W},{\bf R}^{\bf e} ,{\bm \tau }) \times {\bf Q}_t = {\bf K}_1 .\end{equation}

The return to land, which is mobile among crops, is determined in the first quarter by the demand and supply for land for the upcoming crops in period t:

(7) \begin{equation} {\bf a}_t ({\bf W},{\bf R}^{\bf e} ,{\bm \tau} ) \times {\bf Q}_t = {\bf T},\end{equation}

where T is total land available for crops in t.

Expected returns to sector-specific factors determine crop output, yet actual returns to the sector-specific factors, R _t , can differ from expected returns. The market-clearing identities determine actual market prices, Pm _t . When the market prices of crops are determined, government payments (including loan deficiency payments and countercyclical payments) are calculated for the crop produced at time t, which holds for 85% of crops enrolled in traditional government programs. The actual return to the program crop, P _t , is determined by including government payments:

(8) \begin{equation} {\bf P}_t = {\bf Pm}_t + 0.85 \times {\bf DP} \times ({\bf y} \times {\bf A})/{\bf Q} + {\bf Z}_1 + {\bf Z}_2 ,\end{equation}

\begin{equation*} {\bf where}\,{\bf Z}_1 = \left\{ {\begin{array}{*{20}l} {0.85 * \displaystyle\frac{{({\bf TP}_t - {\bf Pm}_t )({\bf y}\, * {\bf A})}}{{\bf Q}},\ {\rm if}\ {\bf Pm}_{_t } < {\bf TP}_t ,} \hfill \\ {0,{\rm if}\,{\bf Pm}_t > {\bf TP}_t } \hfill \end{array}} \right. \end{equation*}

\begin{equation*} {\bf Z}_2 = \left\{ {\begin{array}{*{20}l} {({\bf LR}_t - {\bf Pm}_t )\ {\rm if}\ {\bf Pm}_t < {\bf LR}_t } \hfill \\ {0,{\rm if}\,{\bf Pm}_t > {\bf TP}_t } \hfill \end{array}} \right., \end{equation*}

where y is a vector of program yields defined by the U.S. government, A is a vector of base acreages, and Q is a vector of quarterly production. In addition, approximately 15% of crops were covered under the Average Crop Revenue Election program with payments calculated using a moving average of crop prices and yields. Finally, there is no government program for forage and pasture. Therefore, the market price is the return to forage and pasture. Accordingly, the actual return to physical and human capital in period t, R _t , is determined by the zero-profit condition:

(9) \begin{equation} {\bf C}({\bf W},{\bf R}_t ,{\bm \tau }) = {\bf P}_t .\end{equation}

3. Parameters

We use the logarithmic differential version of the integrated agricultural sector model, which is driven by a suite of parameters. The three sets of parameters that drive the model include livestock feed-balance calculators, the revenue shares for all industries, and elasticities, which are based on estimates in the literature. The livestock-feed balance calculators link the stocks and flow of animals to available feed supplies throughout the supply chain. Each animal species has specific feed demands (rations) at each production stage and corresponding typical weight gain during each production phase. Unique rations composed of feed grains, wheat, soybean meal, and forage and pasture are determined by species and production phase. The average weight gain for each phase of production determines total feed consumption for a given phase, and average daily weight gain determines the length of time each species remains in a given production phase. The time from birth to market age is then calculated according to the total amount of time spent in each production phase to reach the finished, market stage for each animal species.

Revenue and factor shares are determined by sector. Cost-of-production data for corn, wheat, soybeans, rice, hogs, cattle, and milk are divided by production revenue to calculate the respective revenue shares. Government payments are included as revenue for relevant crop sectors. Overall, crops have relatively even allocations among exogenous inputs, land, and the residual cost of capital and management. The major revenue share for live animals is feed costs, followed by the residual return to capital and management. Meat industries show relatively low returns to capital and management because the majority of revenue is allocated to animal costs. Exceptions exist for meat, eggs, and poultry, as detailed by Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008). Revenue shares for individual feed ingredients result from the livestock-feed balances, which calculate feed use on a per animal basis by species and production phase.

Elasticities employed in the model and are grouped into several sets, all of which can be found in the appendix of Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008), with the exception of own-price elasticity estimates for meats. The own- and cross-price elasticities of retail demand are based on estimates from econometric models in the literature or estimated by Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008) and are listed in Table 1. The cross-price effects are nonnegative, which implies that commodities in the model are substitutes. The own-price elasticities for meats used in this analysis are inelastic, which is consistent with the literature on meat demand elasticity estimates (Eales and Unnevehr, Reference Eales and Unnevehr1988; Seale et al., 2003; Tonsor, Mintert, and Schroeder, Reference Tonsor, Mintert and Schroeder2009; USDA-ERS, 2012), yet differs from the elastic meat demand that is assumed in Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008). Elasticities range from −0.4 for lamb meat to −0.9 for pork. Pork is the most price sensitive meat, whereas poultry (−0.7) is less sensitive to price changes than pork or beef (−0.8), as is consistent in studies of U.S. meat demand (Brester and Schroeder, Reference Brester and Schroeder1995; Tonsor and Marsh, Reference Tonsor and Marsh2007). Derived demand behaviors that determine commodity outputs are affected by substitution elasticities. The substitution elasticities for meat and feed use, along with their estimations, are detailed in Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008) and are consistent with the literature. The substitution elasticities govern the ability to substitute feeds in response to price changes. In most instances, these substitution elasticities are approximately 1 so that the cost shares of feed ingredients are very stable and change little in response to relative price changes. The exception is the substitution elasticity for forages in beef cattle, which is elastic. Thus, as drought increases, the price of concentrates allows for the replacement of forages enough to reduce the cost share for forages in beef cattle rations.

Table 1.

Price Elasticities for Final Goods

Source: Paarlberg et al. (Reference Paarlberg, Seitzinger, Lee and Mathews2008).

4. Shocks for Crops and Livestock in 2011 and 2012

Livestock and crop drought effects are calculated by comparing forecasts from the spring of 2011 before the drought began with actual outcomes. Exogenous shocks to national crop production are introduced in the harvest quarter and function as shifts in supply curves within the model. Table 2 lists the exogenous quarterly percentage change shocks administered for each crop and livestock sector. Each integrated sector adjusts after the shocks are administered according to the market-clearing conditions that dictate how producers and consumers adjust to changes in prices and quantities, which is described further in the “Results” section. Shocks are based on the differences between yields in the World Agricultural Supply and Demand Estimates (WASDE) report issued prior to crop years 2011 and 2012 (May) and yields given in the January reports after crops were harvested (USDA-WAOB, 2013). The intention is to capture the difference between the anticipated yield and the realized yield. Average per acre yield is used as the metric for drought effects instead of production because yield is more strongly affected by drought (Peel, Reference Peel2013a). The WASDE report released before the crop year uses historical trend yields, whereas the values in the WASDE report for area planted are the planting intentions for the coming crop year as reported by farmers. By using crop yields as the measure for drought effects, any forecast error for yields is embedded in the calculated reductions.

Table 2.

Quarterly Percentage Change Shocks by Commodity

Note: Exogenous percentage change shocks to national crop production for each sector are introduced in the harvest quarter. Shocks are based on the differences between yields in the World Agricultural Supply and Demand Estimates report (USDA-WAOB, 2013) issued prior to crop years 2011 and 2012 (May) and yields given in the January reports after crops have been harvested to capture the differences between the anticipated and realized yields.

Considerable differences between trend and realized yields are found. The WASDE report indicates that the 2011 yield for winter wheat was 5.2% greater than the trend for 2010. Winter wheat harvested in the summer of 2011 was planted in the fall of 2010 and had matured considerably prior to the damaging impact of the 2011 drought. Winter wheat yield in 2012 was 1.1% lower than trend. Spring wheat yield in the third quarter of 2011 was 20% lower than initial expectations based on trend but was more than 21% higher in 2012. Although some areas experienced a decrease in yield as a result of drought conditions, there was rain in the spring wheat areas during 2012. Winter and spring coarse grains experienced yield decreases in both drought years. Winter coarse grain yield decreased by 1% in both 2011 and 2012, and spring grain yield—corn and sorghum—decreased by 7% in 2011 and by 26% in 2012. Soybean yield decreased by 4% and 10% in 2011 and 2012, respectively.

Changes in pasture and forage yields are derived from data provided by the Livestock Marketing Information Center (LMIC). Compared with trend yields, yield data reported by the LMIC for all hay types decreased by 6% in 2011 and by 15% in 2012. Drought effects on livestock slaughter in 2011 and 2012 are also based on LMIC data.Footnote ¹

The baseline database of the model relies on LMIC cattle slaughter and cattle inventory data from before the drought. The database in this analysis was constructed in early 2011 and is treated as the anticipated levels of cattle slaughter. Comparison of cattle slaughter for 2011 and 2012 in the database constructed prior to the drought and observed cattle slaughter in current data for 2011 and 2012 suggests unanticipated slaughter in all quarters (except the first quarter of 2012). Drought-induced slaughter of lighter cattle occurred in the second through fourth quarters of 2011. The increased slaughter in 2011 was largest in the second quarter and fell in the third and fourth quarters. The data from the first quarter of 2012 suggest that beef cattle producers held cattle in the hope of better crop and pasture conditions the following summer. As the drought did not improve in 2012, drought-induced slaughter increased again. Because the increase in cattle slaughter must come from lighter backgrounder cattle being slaughtered early, there are corresponding decreases in the supply of background beef cattle flowing into the next quarter. The percentage changes vary, but the total head decrease experienced by background cattle is the same as the increase in number of head for finished beef cattle.