“Protectionism, Trade, and Measures of Damage from Exotic Species Introductions”

1. “Protectionism, Trade, and Measures of Damage from Exotic Species Introductions” Costello & McAuslandAJAE 2003

2. Jenkins (1996) • “broad tools such as bans or restrictions on imports may be necessary to protect biodiversity”

3. Invasive Species - Rules of Thumb* • In estimates of damages from invasives, most are attributed to agriculture • OTA (1993): 90-93% of estimated $4.7-$6.5 million annual cost from invasives • Pimental et al (2000): >50% of estimated >$100 billion annual cost from invasives *Some of these are ignored in this paper; Costello, Springborn, McAusland and Solow (2007) incorporates these mathematically and empirically.

4. Invasive Species - Rules of Thumb continued. • Disturbed land is more susceptible to invasion (e.g. agricultural use versus primeval forest) • Trade in goods and services provides platform for unintentional introductions of non-native species (esp. agricultural imports, shipping and packing materials, ballast water, tourism) • *Successful introductions are facilitated by bio-geographic similarities between host and source region

5. Invasive Species - Rules of Thumb continued. • Likelihood that an “arrival” will become established is increasing in the number of times the species is “exposed” to host region • “tens rule”: 10% of introduced species become casual , 10% of these become established (10% of these become a pest) • *A Source’s potential pool of exotics is finite---sampling without replacement • *Newly arrived exotics aren’t usually discovered for quite some time (chance, damages high, systematic species survey)

6. Notation • λ: average time between arrivals • q: probability an arrival successfully invades Home • k: type of damage • dik: r.v. measuring type-k instantaneous damage imposed by ith successful invader • A: agricultural output • Y: manufacturing output • C: Home demand for agricultural goods • M: net import volume • Mj: net imports of product j • r: discount rate • D: discounted damages • P: price of agricultural goods • τ: ad valorem tariff rate

7. Statistical model

8. Successful Arrivals • “arrivals” distributed exponentially (with pdf = λe-λx where • rate variable λ(M) is increasing in M • 1/λ equals expected time between arrivals • q = (exogenous) fraction of arrivals that succeed (i.e. become invasive) • Assume arrivals are independent of one another. Then over one unit of time we’d expect qλ successful arrivals to occur. • More formally, define J(T) = Number of successful introductions by time T • Because arrivals are independently, identically exponentially distributed then J(T) is a poison process with rate μ(M)≡ qλ(M).

9. Damages • There are k=1,...,K different types of damages • E.g. damages to crops (weeds), ecosystems (extinctions), human health (disease) • dik= instantaneous damages of type k from successful introduction i • dik is a random variable with CDF Φk(x;A)

10. Aggregate damage • Dik(T)=present value of type k damage occurring through time T by ith successful introduction = = dik x (discount factor dependent on when invader i arrived) • Dik(T) will have conditional density function Ftik(δ;A) (= probability that a successful arrival at time ti has type-k damage of less than δ) • Dk(T)=present value of type k damage from all successful introductions to time T

11. Dk(T) Dk(T) is a Compound Poisson random variable with Poisson Parameter Tμ • A Compound Poisson random variable is the sum of a "Poisson-distributed number" of independent identically-distributed random variables. • In our model the number of invading species is a Poisson-distributed number, however the damages are not i.i.d. because the discount terms depend on arrival times, and thus so does the distribution. However Ross (1996) offers the following: • Calculate the distribution of Dkconditioning on J. • Ross (1996) theorem 2.3.1 tells you that, even though the arrival times of the species are unknown, they’ll have the same distribution as the “order statistics” corresponding to J independent random variables uniformly distributed over the interval (0,T) with CDFs . • Allowing for J to instead be a Poisson random variable, then we know our distribution Dk(T) has the same distribution as does a Poisson compound distribution with Poisson parameter Tμ(M)---just like J---and compound distributions just like those order statistics.

12. Why is the distribution of Dk(T) important? • Calculate E[Dk(T)] and examine how it changes with M and A • The expected value of a compound random variable Y=ΣiNXi is E(Y)=E(N)E(X). • Since J has expected value Tμ and the expected value of the order statistics (i.e. X) is /T Then E[Dk(T)]=

13. The model so far: we’ve got expected damages as a product of functions of the volume of imports M and the scale of agricultural output A.

14. The obvious trade stuff

15. two sectors: • agriculture A • domestic price = P • ROW price = P* • manufactures Y (numeraire) • misc assumptions: • balanced trade • CRS production technologies • perfect competition • Home is Small

16. M≡ max{MA,MY} • . = elasticity of import demand with respect to domestic agriculture price • .

17. Proposition 1 • Starting from an initial tariff of zero, increasing the tariff rate decreases the rate of successful exotic species introductions to Home; that is

18. Proof • dμ(M)/dτ = qλ’(M)dM/dτ • What’s the sign of dM/dτ?

19. If are an Ag Importer • If MA>0 then • P=P*(1+τ) • dP/dτ=P*>0 • . • Hence dMA/dτ<0 both are positive

20. If are an Ag Exporter • If MY>0 then • P=P*/[1+τ] • dP/dτ<0 • . • Hence dMY/dτ<0

21. Implication of Proposition 1: • Tariffs shrink platform for arrivals

22. 1 P What’s impact of a tariff on Expected type-k damage? sign depends on importer status (+) >0 (+) positive provided expected damages are positive This term missing in the paper

23. What’s the sign of εFk? • Recall Fk gives the CDF of type k damage from invasive i • If i is likely to cause more damage when agricultural activity is high then expect εFk>0 • “augmented damage” • e.g. crop weeds • If i is likely to cause same damage ... then εFk=0 • “neutral damage” • e.g. aquatic invasions (zebra mussel) • If i is likely to cause less damage ... then εFk<0 • “diminished damage” • e.g. ???

24. Proposition 2 • For a small open economy that initially imports agricultural goods, an increase in the tariff rate τ • unambiguously reduces expected Neutral and Diminished type damages and • raises expected Augmented type damages k if and only if

25. if instead the country exports agricultural goods, then an increase in its tariff rate • unambiguously reduces expected Augmented and Neutral type damages and • raises expected Diminished type damages k if and only if

26. Implication of Proposition 2 • If are an Ag. importer, raising the tariff • shrinks the platform for arrivals • expands agricultural activity • increasing volume of crops susceptible to crop damage • increasing amount of land disturbed • expanding platform for species incursions into habitat for indigenous species • diminished and neutral type damages unambiguously decline, augmented type damages may rise • If are an Ag. exporter, raising the tariff • shrinks platform for arrivals • drives mobile factors out of agricultural production, causing agriculture to shrink • only diminished type damages have potential to increase.

27. Example - Sugar • US support for sugar generate US price = 2 x ROW price • is similar to a 100% tariff except no beneficial tariff rent • Since 1934 harvested acreage for all crops in US fell by .1%/annum • over same period, land under sugarcane production grew at average annual rate of 1.6%

28. currently infests 20% of texas sugarcane believed to have come in on imported goods detected on sugarcane, lemon grass, sorghum and broomcorn imports Texas damages estimated at $10 -$20 million (/yr?) while harvest valued only at $64 million Mexican rice borer Source: Texas A&M U http://insects.tamu.edu/images/insects/color/sorghum/sor069.jpg

29. So if we see estimates of crop damage fall, are overall damages falling? • model suggests tariff liberalization (regarding agricultural imports) may reduce estimates of crop damages from invasives • however “neutral” type damages (species extinctions) may simultaneously rise • Ecological damages are non-trivial! • Invasives implicated in decline of 400 of US’s listed endangered species (as of 2000) • Point: estimates of crop damage are a poor proxy for ecological damage from invasives • Jenkins may be right!