Using Genetic Marker Selection to ReduceAsymmetric Information in the U.S. Beef

Supply Chain

Alex Kappes

27 April 2020

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Overview

Background and Objective

Theoretical Environment

Data

Empirical Methodology

Results and Discussion

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Background

Bovine Respiratory Disease (BRD)

- Multi-factorial disease

- Largest cause of morbidity and mortality

- $54.12 million estimated feedlot treatment costs

→ Underestimates total costs from BRD incidence

- Metaphylaxis treatment programs not significantly effective

- Calf stress and environment are important factors

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Background

Genetic Marker Selection

- Neibergs, H. et al. (2014) have shown that calf geneticsdetermine BRD susceptibility

- Select breeding stock with BRD resistant markers

- Effectively reduces BRD susceptibility compared to othertreatment/prevention programs

- Calf stress and environment still important factors

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Background

Production Environment

- Begins with cow-calf producers

→ calves raised alongside birthing cows→ weaned and pre-weaned separation occurs

- Feedlots ultimately source calves from cow-calf producers

- Livestock health risk shifts to feedlots after purchase

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Background

Agricultural Asymmetric Information

- Literature focused on crop production

→ input control and scheduled planting decisionsassumed by crop contractors

→ commodity cooperatives→ crop insurance

U.S. Beef Supply Setting

- Feedlots are uninformed about calf health during lotpurchase

- Cow-calf producers hold private information about calfhealth

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Objective

1. Show there exists a theoretical price premium mechanismthat provides incentive for cow-calf producers to reveal calfhealth type.

2. Show empirical support for theoretical results.

How are objectives accomplished?

- Develop feedlot’s problem in an adverse selectionenvironment

- Evaluate profit-maximizing model outcomes

- Specify functional forms and empirically analyze modeloutcomes

- Use a stochastic data generating process to test empiricalresults

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Contribution

New Markets

- Call attention to beef supply chains

Theoretical

- Show profit-maximizing conditions that support pricepremiums

Empirical

- Provide representative price premium values

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Theoretical EnvironmentFeedlot costs

Feedlot cost function C[q(θi), r, t]

Where

q(θi): calf q of health type θ for i = {MS,N}r: per unit production price

t: weekly time period following calf intake

Assumptions

θMS > θN

Ct[q(θN ), r, t] > 0 and Ctt[q(θN ), r, t] > 0

Ct[q(θMS), r, t] > 0 and Ctt[q(θMS), r, t] < 0

limt→t̄

Ct[q(θMS), r, t] = 0

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Theoretical EnvironmentFeedlot costs

Figure 1: Feedlot calf health type costs over time

t

C[q(θi), r, t]

C[q(θMS), r, t]

C[q(θN ), r, t]

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Theoretical EnvironmentFeedlot problem

Feedlot provides price schedule (TMS , TN ) to cow-calf producers

Expected profit maximization provides optimal (T ∗MS , T∗N )

Let

γ ∈ (0, 1) be the probability of calf type q(θN )

f [q(θi)] be the weight production function for i = {MS,N}p be dressed beef price received

β be the discount factor

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Theoretical EnvironmentFeedlot problem

maxq(θMS),q(θN )

T∑t=0

βt(1− γ) {pf [q(θMS)]− C[q(θMS), r, t]− TMS}

+ βtγ {pf [q(θN )]− C[q(θN ), r, t]− TN}

s.t. TMS − c[q(θMS), ZMS ] ≥ 0 (PCMS)

TN − c[q(θN ), ZN ] ≥ 0 (PCN )

TMS − c[q(θMS), ZMS ] ≥ TN − c[q(θMS), ZN ] (ICMS)

TN − c[q(θN ), ZN ] ≥ TMS − c[q(θN ), ZMS ] (ICN )

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Theoretical EnvironmentFeedlot problem

Recall θMS > θN

Participation Constraints

(PCMS) binds at the optimum

(PCN ) nonbinding at the optimum

Incentive Compatibility

(ICMS) nonbinding at the optimum

(ICN ) binds at the optimum

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Theoretical EnvironmentFeedlot problem

Constraints become

s.t. TMS − c[q(θMS), ZMS ] = 0 (PCMS)

TN − c[q(θN ), ZN ] = TMS − c[q(θN ), ZMS ] (ICN )

With substitution (PCMS)→ (ICN )

TMS = c[q(θMS), ZMS ] (PCMS)

TN = c[q(θMS), ZMS ] + {c[q(θN ), ZN ]− c[q(θN ), ZMS ]} (ICN )

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Theoretical EnvironmentFeedlot problem

maxq(θMS),q(θN )

T∑t=0

βt(1− γ) {pf [q(θMS)]− C[q(θMS), r, t]− c[q(θMS), ZMS ]}

+ βtγ {pf [q(θN )]− C[q(θN ), r, t]}

− βtγ {c[q(θMS), ZMS ] + (c[q(θN ), ZN ]− c[q(θN ), ZMS ])}

q∗MS and q∗N solve FOC optimality conditions

pf [q∗θMS] = C[q∗θMS

, r, t] +1

(1− γ)c[q∗θMS

, ZMS ] (1∗)

pf [q∗θN ] = C[q∗θN , r, t] + c[q∗θN , ZN ]− c[q∗θN , ZMS ] (2∗)

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Theoretical EnvironmentFeedlot problem

Constructing optimal price schedule (T ∗MS , T∗N ) from

TMS = c[q(θMS), ZMS ]

TN = c[q(θMS), ZMS ] + {c[q(θN ), ZN ]− c[q(θN ), ZMS ]}

From (1∗) for T ∗MS

T ∗MS = c[q∗θMS, ZMS ] = (1− γ)

(pf [q∗θMS

]− C[q∗θMS, r, t]

)(3∗)

From (2∗) and (3∗) for T ∗N

T ∗N =(1− γ){pf [q∗θMS

]− C[q∗θMS, r, t]

}(4∗)

−{C[q∗θN , r, t]− pf [q∗θN ]

}≥ 0

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Theoretical EnvironmentFeedlot problem

(3∗) and (4∗) admit price premium expression for q(θMS)

T ∗MS − T ∗

N = (1− γ){pf [q∗θMS

]− C[q∗θMS, r, t]

}−[(1− γ)

{pf [q∗θMS

]− C[q∗θMS, r, t]

}−{C[q∗θN , r, t]− pf [q∗θN ]

}]= C[q∗θN , r, t]− pf [q∗θN ] ≥ 0 (5∗)

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Data

Sourced from a large-scale U.S. commercial feedlot in Colorado

Sample includes 952 observations on

- Cattle health and treatment

- Arrival and processing dates

- Processing weight

Representative price and production cost data sourced fromUSDA AMS and LMIC

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DataBRD categorization

BRD categorization for feedlot data (Shaefer et al., 2012)

0-5 categorical scale for calf presentation

→ 0: normal respiratory function→ 3: ≥ 103◦F rectal temp, not tachypnic or dyspnic,

with nasal discharge→ 5: ≥ 103◦F rectal temp and tachypnic or dyspnic

Figure 2: Proportion Statistics for Calf Respiratory HealthCharacterization (n = 927)

Normal Respiratory Morbidity Morbidity BRDHealth Scale 3 Scale 5

Proportion 0.525 0.263 0.183 0.446

Note: Each value is a proportional representation of the calf respiratory healthcharacterization based on morbidity scale rankings within the data set

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Empirical MethodologyCalf level

Representative calf profit (loss) for i = {MS,N}- Data

E[π(q(θi))] = 1N

∑Nn=1

(pt,nfn[q(θi)]− Cn[q(θi), r, t]

)- Simulation

E[S(M){π(q(θi))}] = 1M

∑Mm=1

(E[s(l){π(q(θi))}]

)for

M sampling iterationsl number of random π(q(θi)) draws

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Empirical MethodologyAggregate level

Simulated aggregate profit (loss)

Π(S)(q(θMS), q(θN )) = E[S(M){π(q(θMS))}] + E[S(M){π(q(θN ))}]

Probability of non-genetic marker selection calf q(θN )

γ =1

M

M∑m=1

(∑Ll=1 I[s(l)(q(θN ))]

L

)

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ResultsData - calf level

Figure 3: Representative Per-Calf Revenue, Cost, andProfit Outcomes ($/head)

Healthy Calf BRD Calf

Mean Per-Calf Revenue 1786.820 1789.904Mean Per-Calf Cost 1755.227 1799.619Mean Per-Calf Profit 31.039 -11.359

Note: Representative revenue, cost, and profit for a normal res-piratory health and BRD calf are computed as the means ofper-calf costs, revenues, and profits. The means for mean cost,mean revenue, and mean profit of morbidity scale three and fivecalves are computed to represent a BRD calf.

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ResultsSimulated - calf level

Figure 4: Summary Statistics for MonteCarlo Representative Per-Calf Profit(-Loss) Outcomes ($/head)

Healthy Calf BRD

Mean 31.654 -15.719Std. Dev 19.553 20.127

Min -34.673 -75.951Max 95.816 57.106

Note: Per-calf profit (-loss) summary statis-tics are computed for Monte Carlo simula-tion profit outcomes of normal respiratoryhealth calves and calves considered to havecontracted BRD

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ResultsSimulated - aggregate level

Figure 5: Monte Carlo simulation profit ($) outcomes

Healthy Calf BRD Total Profits

Mean 1718.38 -714.461 1003.922Std. Dev 1066.25 905.943 1416.553Min -1698.99 -3949.47 -3353.120Max 5142.72 2284.23 5674.469

Pr(loss) 0.236γ 0.456

Note: Total profits (losses) are computed as the sum of per-calfprofit outcomes of normal respiratory health calves and calvesconsidered to have contracted BRD. The probability of feedlottotal loss, where total loss from BRD calves is greater than totalprofits from normal respiratory health calves, is the numberof simulated observations resulting in loss over the simulationsample space

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Discussion

How do we link BRD categorization to genetic markerselection?

Interpret data as

q(θMS) ≡ morbidity scale 0 ranking

q(θN ) ≡ morbidity scale 3 and 5 ranking

Genetic marker selection fee, price premium, and profits

T ∗MS = (1− γ)(pf [q∗θMS]− C[q∗θMS

, r, t]) = $17.22

T ∗MS − T ∗N = $15.72

π(q(θMS)) > 0

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Discussion

Asymmetric information

- Optimal price premium mechanism exists

- Empirical results support theoretical outcomes

- Simulation validates mechanism

Limitations

- Production data

- Cost assumptions

- BRD binary categorization in data

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Questions?

Thank you

alexander.kappes@wsu.edu

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