Actuarial Notes

Agricultural Insurance

Study guide: Exam 6C

Agricultural Insurance in Canada is a suite of cost-shared federal-provincial programs protecting farm income against production and market risk: AgriInsurance (production/crop insurance), AgriStability (margin decline), AgriInvest (matched savings) and AgriRecovery (disaster response). Premiums are heavily subsidised, and the programs are delivered by provincial crown agencies rather than by private insurers.

  • AgriInsurance is the closest to conventional insurance: it indemnifies yield or production loss from insured perils (drought, flood, hail, frost, disease) against a coverage level set as a percentage of the producer's probable yield. Governments pay a large share of the premium and the full administrative cost, and the federal government reinsures.
  • AgriStability is a whole-farm margin program, not a peril-based one: it pays when a producer's program margin falls below a reference margin derived from their own history, so it responds to price collapse as well as production loss. This makes it a business-risk program rather than an insurance contract.
  • AgriInvest is a savings-matching account for small income declines — self-insurance with a government match — and AgriRecovery is an ad hoc framework for disasters the other programs do not address.
  • Why the private market does not serve this risk. Crop losses are highly correlated across a region (one drought hits every farm at once), so the law of large numbers fails; Moral Hazard and Adverse Selection are severe because the producer controls inputs and knows their own land; and the data required for pricing is expensive relative to farm-level premiums. Private hail insurance exists — hail is localised and therefore diversifiable — which is the exception that proves the rule.
  • Actuarial features: yield distributions are skewed and spatially correlated; area-yield and weather-index designs reduce moral hazard at the cost of basis risk (the index moves but the individual farm does not); and the programs' liability is catastrophe-like, requiring reinsurance or government backstop rather than ordinary reserving.
  • Evaluation. The programs achieve broad participation and stabilise farm income, but subsidised premiums distort planting decisions toward risky crops and marginal land, and cost-sharing formulas are a standing federal-provincial dispute.

Individual Yield Versus Area Yield A producer's probable yield is 50 bushels per acre and coverage is 80\%. The area's probable yield is also 50. In a drought year the producer harvests 30 and the area averages 35. Price is \$8 per bushel.

Compare an individual-yield policy with an area-yield policy.

Answer Individual yield. The guarantee is 0.80 \times 50 = 40 bushels; the producer harvested 30:

\begin{align*}
\text{Indemnity} &= (40 - 30) \times \$8 \\
&= \$80 \text{ per acre}
\end{align*}

Area yield. The trigger is 0.80 \times 50 = 40 area bushels; the area averaged 35:

\begin{align*}
\text{Indemnity} &= (40 - 35) \times \$8 \\
&= \$40 \text{ per acre}
\end{align*}

The producer suffered a 20-bushel loss and is paid for 10 under the individual policy and 5 under the area policy — the \$40 gap is basis risk, the cost of a design that does not look at the individual farm.

The trade-off. The area policy cannot be manipulated: the producer cannot increase their indemnity by farming poorly, under-reporting, or abandoning a crop, because the payout depends on the neighbours. It is also far cheaper to administer — no farm-level inspection or yield audit. The individual policy compensates accurately but requires verification of every claim and carries real Moral Hazard.

This is the same trade-off found in every index-based product, including parametric catastrophe covers: accuracy of indemnity against immunity from manipulation, and one cannot have both.