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

2. Jenkins (1996) “broad tools such as bans or restrictions on imports may be necessary to protect biodiversity” “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 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 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 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) 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) 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 *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 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) “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 *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) *Newly arrived exotics aren’t usually discovered for quite some time (chance, damages high, systematic species survey)

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

7. Statistical model

8. Successful Arrivals “arrivals” distributed exponentially (with pdf = λe -λx where “arrivals” distributed exponentially (with pdf = λe -λx where rate variable λ(M) is increasing in M rate variable λ(M) is increasing in M 1/λ equals expected time between arrivals 1/λ equals expected time between arrivals q = (exogenous) fraction of arrivals that succeed (i.e. become invasive) 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. 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 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). 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 There are k=1,...,K different types of damages E.g. damages to crops (weeds), ecosystems (extinctions), human health (disease) E.g. damages to crops (weeds), ecosystems (extinctions), human health (disease) d i k = instantaneous damages of type k from successful introduction i d i k = instantaneous damages of type k from successful introduction i d i k is a random variable with CDF Φ k (x;A) d i k is a random variable with CDF Φ k (x;A)

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

11. D k (T) D k (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. 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. 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 D k conditioning on J. Calculate the distribution of D k conditioning 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 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 D k (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. Allowing for J to instead be a Poisson random variable, then we know our distribution D k (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 D k (T) important? Calculate E[D k (T)] and examine how it changes with M and A Calculate E[D k (T)] and examine how it changes with M and A The expected value of a compound random variable Y=Σ i N X i is E(Y)=E(N)E(X). The expected value of a compound random variable Y=Σ i N X i 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 Since J has expected value Tμ and the expected value of the order statistics (i.e. X) is /T /T Then E[D k (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. 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: two sectors: agriculture A agriculture A domestic price = P domestic price = P ROW price = P* ROW price = P* manufactures Y (numeraire) manufactures Y (numeraire) misc assumptions: misc assumptions: balanced trade balanced trade CRS production technologies CRS production technologies perfect competition perfect competition Home is Small Home is Small

16. M≡ max{M A,M Y } M≡ max{M A,M Y }.. = 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 dμ(M)/dτ = qλ’(M)dM/dτ What’s the sign of dM/dτ? What’s the sign of dM/dτ?

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

20. If are an Ag Exporter If M Y >0 then If M Y >0 then P=P*/[1+τ] P=P*/[1+τ] dP/dτ<0 dP/dτ<0.. Hence dM Y /dτ<0 Hence dM Y /dτ<0

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

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

23. What’s the sign of ε Fk ? Recall F k gives the CDF of type k damage from invasive i Recall F k 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 ε Fk >0 If i is likely to cause more damage when agricultural activity is high then expect ε Fk >0 “augmented damage” “augmented damage” e.g. crop weeds e.g. crop weeds If i is likely to cause same damage... then ε Fk =0 If i is likely to cause same damage... then ε Fk =0 “neutral damage” “neutral damage” e.g. aquatic invasions (zebra mussel) e.g. aquatic invasions (zebra mussel) If i is likely to cause less damage... then ε Fk <0 If i is likely to cause less damage... then ε Fk <0 “diminished damage” “diminished damage” e.g. ??? 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 If are an Ag. importer, raising the tariff shrinks the platform for arrivals shrinks the platform for arrivals expands agricultural activity expands agricultural activity increasing volume of crops susceptible to crop damage increasing volume of crops susceptible to crop damage increasing amount of land disturbed increasing amount of land disturbed expanding platform for species incursions into habitat for indigenous species expanding platform for species incursions into habitat for indigenous species diminished and neutral type damages unambiguously decline, augmented type damages may rise diminished and neutral type damages unambiguously decline, augmented type damages may rise If are an Ag. exporter, raising the tariff If are an Ag. exporter, raising the tariff shrinks platform for arrivals shrinks platform for arrivals drives mobile factors out of agricultural production, causing agriculture to shrink drives mobile factors out of agricultural production, causing agriculture to shrink only diminished type damages have potential to increase. only diminished type damages have potential to increase.

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

28. Mexican rice borer 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 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 model suggests tariff liberalization (regarding agricultural imports) may reduce estimates of crop damages from invasives however “neutral” type damages (species extinctions) may simultaneously rise however “neutral” type damages (species extinctions) may simultaneously rise Ecological damages are non-trivial! Ecological damages are non-trivial! Invasives implicated in decline of 400 of US’s listed endangered species (as of 2000) 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 Point: estimates of crop damage are a poor proxy for ecological damage from invasives Jenkins may be right! Jenkins may be right!