Skip to main content

Optimal Border Policies for Invasive Species Under Asymmetric Information


This paper analyzes the problem faced by a border protection agency if endogenous exporter abatement activities affect invasive species risk, allowing for unobservable differences in abatement cost. We show how the optimal inspection/penalty regime differs from the symmetric information case. Departing from previous literature, we allow for technical assistance, a policy instrument specifically permitted and commonly employed under Article 9 of the World Trade Organization Sanitary and Phytosanitary Agreement. We find the information asymmetry can make it optimal for the importing country to provide technical assistance grants for exporter risk abatement, even if it would otherwise be inefficient. Further, we show that fungibility of technical assistance with inputs in other sectors of the exporting economy affects the qualitative nature of optimal policy. If technical assistance has no outside value in the exporter’s country, optimal policy is characterized by a menu of contracts balancing higher tariffs with lower penalties for being caught with an invasive. If technical assistance can be used in other sectors of the exporter’s economy, it can introduce countervailing incentives making a uniform tariff/penalty combination optimal.

This is a preview of subscription content, access via your institution.


  1. McAusland and Costello (2004) briefly discuss an example in which differences in exporter characteristics may lead to a suboptimal outcome without formally solving the regulator’s problem.

  2. Regulators currently lack precise information about abatement costs. For example, even for a fairly standard technology as heat treatment of wood packaging, the high end of the range considered by the US Animal and Plant Health Inspection Service is twice as high as the low end (Chaloux 2010).

  3. An important difference between our model and the previous literature is our implicit assumption of barriers to entry. McAusland and Costello (2004), Mérel and Carter (2008), and Margolis and Shogren (2012) assume perfect competition with free entry and a corresponding zero profit condition. Such a framework does not allow for an equilibrium with heterogeneous exporters since those with low-costs would drive their competitors out of the market.

  4. As shown below, these assumptions allow us to get interesting results regarding technical assistance provision. If the cost to the regulator were smaller than the average exporter cost, then it would be optimal to provide it even if there were no information asymmetry. If it were much larger, provision would never be optimal.

  5. We later allow for the possibility that the regulator may design a policy such that some potential exporters may not wish to ship their cargo.

  6. The latter assumption ensures that environmental damage is always greater than consumer willingness to pay for the infected good. It conveniently allows us to focus on cases in which the regulator does not want a known infected cargo to enter the country.

  7. If the regulator’s cost of expediting inspections by a unit of time is \(\tau \), and is equal to the value of time to the exporter, then even the notation goes through unaltered.

  8. The model could be easily extended to cases in which \(I\) and \(\phi \) vary across exporters and \(t\) and \(\tau \) are set at a uniform level. Regarding the legality of a non-uniform policy, it is worth noting that countries currently differentiate in their application of tariffs and penalties, broadly defined, in the context of sanitary and phytosanitary measures (e.g., the US-Netherlands pre-clearance program). The specific approach described here would be less discriminatory inasmuch as all exporters would be able to choose from the same menu.

  9. This restriction is by no means the only way to model trade agreements, and rules out policies that effectively price exporters with high abatement costs out of the market. We leave analysis of alternative participation constraints to future research.

  10. Many components of the second-order conditions cannot be unambiguously signed.

  11. Specifically, we require \(\mathrm{d}[G(\theta )/g(\theta )]/\mathrm{d}\theta \) and \(\mathrm{d}\big [[G(\theta )-1]/g(\theta \big )]/\mathrm{d}\theta >G(\theta )/g(\theta )\theta \). See Bagnoli and Bergstrom (2005) for properties of likelihood ratios for many common distribution functions. For details regarding solution algorithms if potential separation does not hold, see Guesnerie and Laffont (1984).

  12. In particular, \(\int _0^1\int _\theta ^1e(z)\mathrm{d}z\mathrm{d}G(\theta )=\int _\theta ^1\left.e(z)\mathrm{d}zG(\theta )\right|_0^1+\int _0^1e(\theta )G(\theta )\mathrm{d}\theta =\int _0^1e(\theta )\frac{G(\theta )}{g(\theta )}\mathrm{d}G(\theta )\).

  13. In particular, \( \int _0^{\theta ^0(\phi )}\int _0^{\theta ^0(\phi )} [e(z)-\phi ]\mathrm{d}z\mathrm{d}G(\theta )=\int _0^{\theta ^0(\phi )}\left.[e(z)-\phi ]\mathrm{d}zG(\theta )\right|_0^{\theta ^0(\phi )}+\int _0^{\theta ^0(\phi )}[e(\theta )-\phi ]G(\theta )\mathrm{d}\theta =\int _0^{\theta ^0(\phi )}[e(\theta )-\phi ]\frac{G(\theta )}{g(\theta )}\mathrm{d}G(\theta )\), and \(\int _{\theta ^0(\phi )}^1\int _{\theta ^0(\phi )}^\theta [\phi -e(z)]\mathrm{d}z\mathrm{d}G(\theta )=\int _{\theta ^0(\phi )}^\theta [\phi -e(z)]\mathrm{d}z\left.G(\theta )\right|_{\theta ^0(\phi )}^1-\int _{\theta ^0(\phi )}^1[\phi -e(\theta )]G(\theta )\mathrm{d}\theta =\int _{\theta ^0(\phi )}^1[\phi -e(\theta )]\frac{1-G(\theta )}{g(\theta )}\mathrm{d}G(\theta )\).

  14. Recall that \(M=\int _0^1\left[1-q\Big (e(\theta )+\phi \Big )r(I)\right]\mathrm{d}G(\theta )\), so that by Leibniz’ rule, \(\mathrm{d}/\mathrm{d}t \left[\int _0^M P(z)\mathrm{d}z\right]=P(M)\int _0^1-q^{\prime }(e(\theta )+\phi )r(I)\partial e/\partial t\mathrm{d}G(\theta )\).


  • Bagnoli M, Bergstrom T (2005) Log-concave probability and its applications. Econ Theory 26:445–469

    Article  Google Scholar 

  • Batabyal AA, Beladi H (2009) Trade, the damage from alien species, and the effects of protectionism under alternate market structures. J Econ Behav Organ 70:389–401

    Article  Google Scholar 

  • Buhle ER, Margolis M, Ruesink JL (2005) Bang for buck: cost-effective control of invasive species with different life histories. Ecol Econ 52:355–366

    Article  Google Scholar 

  • Burnett KM, D’Evelyn S, Kaiser BA, Nantamanasikarn P, Roumasset JA (2008) Beyond the lamppost: optimal prevention and control of the brown tree snake in Hawaii. Ecol Econ 67:66–74

    Article  Google Scholar 

  • Chaloux P (2010) Personal communication. US Animal and Plant Health Inspection Service

  • Costello C, McAusland C (2003) Protectionism, trade and measures of damage from exotic species introductions. Am J Agric Econ 85(4):964–975

    Article  Google Scholar 

  • Costello C, Springborn M, McAusland C, Solow A (2007) Unintended biological invasions: Does risk vary by trading partner? J Environ Econ Manag 54:262–276

    Article  Google Scholar 

  • Eiswerth M, Johnson W (2002) Managing nonindigenous invasive species: insights from dynamic analysis. Environ Resour Econ 23(3):319–342

    Article  Google Scholar 

  • Gramig B, Horan R, Wolf C (2009) Livestock disease indemnity design when moral hazard is followed by adverse selection. Am J Agric Econ 91(3):627–641

    Article  Google Scholar 

  • Guesnerie R, Laffont J-J (1984) A complete solution to a class of principal-agent problems with an application to the control of a self-managed firm. J Pub Econ 25:329–369

    Google Scholar 

  • Horan RD, Lupi F (2005) Economic incentives for controlling trade-related biological invasions in the Great Lakes. Agric Resou Econ Rev 34(1):75–89

    Google Scholar 

  • Jullien B (2000) Participation constraints in adverse selection models. J Econ Theory 93:1–47

    Google Scholar 

  • Kim C, Lubowski R, Lewandrowski J, Eiswerth M (2006) Prevention or control: optimal government policies for invasive management. Agric Resour Econ Rev 35(1):29–40

    Google Scholar 

  • Lenis F (2006) Clean stock program Cost Rica farm visits report. Technical report, USDA-APHIS-PPQ, Miami, FL

  • Lewis T, Sappington D (1989) Countervailing incentives in agency problems. J Econ Theory 49(2):294–313

    Google Scholar 

  • Maggi G, Rodríguez-Clare A (1995) On countervailing incentives. J Econ Theory 66:238–263

    Google Scholar 

  • Margolis M, Shogren JF (2012) Disguised protectionism, global trade rules and alien invasive species. Environ Resour Econ 51:105–118

    Article  Google Scholar 

  • McAusland C, Costello C (2004) Avoiding invasives: Trade-related policies for controlling unintentional exotic species introductions. J Environ Econ Manag 48:954–977

    Article  Google Scholar 

  • Mérel PR, Carter CA (2008) A second look at managing import risk from invasive species. J Environ Econ Manag 56:286–290

    Article  Google Scholar 

  • Olson L, Roy S (2002) Economics of controlling a stochastic biological invasion. Am J Agric Econ 84(5): 1311–1316

    Google Scholar 

  • Olson L, Roy S (2005) On prevention and control of an uncertain biological invasion. Revi Agric Econ 27(3):491–497

    Article  Google Scholar 

  • Sheriff G, Osgood D (2010) Disease forecasts and livestock health disclosure: a shepherd’s dilemma. Am J Agric Econ 92(3):776–788

    Article  Google Scholar 

  • Shogren J (2000) Risk reduction strategies against the ‘explosive invader’. In: Perrings C, Williamson M, Dalmazzone S (eds) The economics of biological invasions. Elgar Ltd

  • Starbird SA (2005) Moral hazard, inspection policy, and food safety. Am J Agric Econ 87(1):15–27

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations


Corresponding author

Correspondence to Glenn Sheriff.

Additional information

The authors gratefully acknowledge helpful comments from Peyton Ferrier, Duncan Knowler, Frank Lupi, David Simpson, the editor and two anonymous referees. Funding was provided by a grant from the Program of Research on the Economics of Invasive Species Management administered by the Economic Research Service of the US Department of Agriculture. The views expressed here do not necessarily represent those of the US Environmental Protection Agency or the US Department of Agriculture.



Proof of Lemma 1

From Eq.(1), the effort maximization problem is

$$\begin{aligned} e(\theta )=\underset{e}{\arg \max }\;\left\{ P(M)-\tau (\theta )-\theta e- r(I)q(e+\phi )[P(M)+t(\theta )]\right\} . \end{aligned}$$

with first order conditions,

$$\begin{aligned} -r(I)q^{\prime }(e(\theta )+\phi )[P(M)+t(\theta )]-\theta&\le 0;\end{aligned}$$
$$\begin{aligned} e(\theta )[r(I)q^{\prime }(e(\theta )+\phi )[P(M)+t(\theta )]+\theta ]&= 0, \text{ for} \text{ all} \, \theta . \end{aligned}$$

For strictly positive levels of abatement effort, \(\partial e(\theta )/\partial \phi =-1\); increasing technical assistance offsets exporter effort without reducing risk. Only if there is a corner solution with zero effort will a marginal increase in technical assistance reduce overall risk. \(\square \)

Proof of Proposition 1

Solving Eq. (2) using pointwise optimization, the first order conditions for \(t(\theta )\) areFootnote 14

$$\begin{aligned} -q^{\prime }(e(\theta )+\phi )[r(I)P(M)+[1-r(I)]\delta ]-\theta&\le 0;\end{aligned}$$
$$\begin{aligned} e(\theta )\left[q^{\prime }(e(\theta )+\phi )[r(I)P(M)+[1-r(I)]\delta ]+\theta \right]&= 0\text{,} \text{ for} \text{ all} \, \theta . \end{aligned}$$

Combined with the Eqs. (27) and (28) these imply

$$\begin{aligned} e( \theta )\left[[1-r(I)]\delta -r(I)t(\theta )\right]=0,\quad \text{ for} \text{ all} \quad \theta . \end{aligned}$$

Since the optimal penalty does not vary by type, Eqs. (27) and (28) imply that induced effort is non-increasing in type. Let \(e^*_0(\theta )\) denote the optimally induced effort if there were no technical assistance. Since effort is non-increasing in \(\theta \) there is a threshold type \(\hat{\theta }^*(\phi )=\inf \{\theta :\phi = e^*_0(\theta )\}\) below which \(e^*_0(\theta )\) exceeds technical assistance, and above which technical assistance exceeds \(e^*_0(\theta )\). The assumptions on \(q(\cdot )\) ensure that \(\hat{\theta }^*(0)=1\). Using Eq. (29), the first order conditions for technical assistance are then

$$\begin{aligned} \int \limits _0^{\hat{\theta }^*(\phi )}\theta \mathrm{d}G(\theta )-\int \limits _{\hat{\theta }^*(\phi )}^1q^{\prime }(\phi )\left[r(I)P(M)+[1-r(I)]\delta \right]\mathrm{d}G(\theta )&\le \bar{\theta };\end{aligned}$$
$$\begin{aligned} \phi \left[\int \limits _0^{\hat{\theta }^*(\phi )}\theta \mathrm{d}G(\theta )-\int \limits _{\hat{\theta }^*(\phi )}^1q^{\prime }(\phi )\left[r(I)P(M)+[1-r(I)]\delta \right]\mathrm{d}G(\theta )-\bar{\theta }\right]&= 0. \end{aligned}$$

Since we assume \(\bar{\theta }>\int _0^1\theta \mathrm{d}G(\theta )\), this inequality in condition (32) is strict and it is optimal for the regulator to set \(\phi =0\). Equation (5) is simply the first order condition for the choice of \(I\). \(\square \)

Proof of Lemma 2

By (27), the first order condition for an interior solution to (6) is

$$\begin{aligned} -r(I)q(e(\theta )+\phi )t^{\prime }(\theta )-\tau ^{\prime }(\theta )=0 \text{ for} \text{ all} \,\theta . \end{aligned}$$

After differentiating this expression, the second order condition can be expressed as \(-\frac{\mathrm{d}t(\theta )}{\mathrm{d}\theta }\frac{ \mathrm{d}q(e(\theta )+\phi )}{\mathrm{d}\theta }/\frac{\mathrm{d}^2q(e(\theta )+\phi )}{\mathrm{d}\theta ^2}\le 0.\) Incentive compatibility thus requires \(\mathrm{d}t(\theta )/\mathrm{d}\theta \le 0\). Differentiating (1) and using (34) yields Eq. (8). \(\square \)

Proof of Proposition 2

The first-order conditions for \(t(\theta )\) are

$$\begin{aligned}&\displaystyle -q^{\prime }(e(\theta )+\phi )[r(I)P(M)+[1-r(I)]\delta ]-\theta \le \frac{G(\theta )}{g(\theta )};\end{aligned}$$
$$\begin{aligned}&\displaystyle e(\theta )\left[-q^{\prime }(e(\theta )+\phi )[r(I)P(M)+[1-r(I)]\delta ]-\theta -\frac{G(\theta )}{g(\theta )}\right]=0. \end{aligned}$$

Using Eqs. (27) and (28), Eq. (36) simplifies to

$$\begin{aligned} e(\theta )\left[-q^{\prime }(e(\theta )+\phi )[[1-r(I)]\delta -r(I)t(\theta )]-\frac{G(\theta )}{g(\theta )}\right]&= 0. \end{aligned}$$

Equations (27) and (28) imply \(\mathrm{d}e(\theta )/\mathrm{d}\theta \le 0\). Since effort is non-increasing in \(\theta \) there is a threshold type \(\hat{\theta }(\phi )\equiv \inf \{\theta :\phi = e_0(\theta )\}\). Similarly to the case without private information, the assumptions on \(q(\cdot )\) ensure that \(\hat{\theta }(0)=1\). Using Eq. (35), the first order conditions for technical assistance are

$$\begin{aligned}&\int \limits _{0}^{\hat{\theta }(\phi )}\left\{ \theta +\frac{G(\theta )}{g(\theta )}\right\} \mathrm{d}G(\theta )-\int \limits _{\hat{\theta }(\phi )}^1q^{\prime }(\phi )\left[r(I)P(M)+[1-r(I)]\delta \right]\mathrm{d}G(\theta )\le \bar{\theta };\end{aligned}$$
$$\begin{aligned}&\phi \left[\int \limits _{0}^{\hat{\theta }(\phi )}\left\{ \theta +\frac{G(\theta )}{g(\theta )}\right\} \mathrm{d}G(\theta )-\int \limits _{\hat{\theta }(\phi )}^1q^{\prime }(\phi )\left[r(I)P(M)+[1-r(I)]\delta \right]\mathrm{d}G(\theta )-\bar{\theta }\right]=0.\nonumber \\ \end{aligned}$$

In contrast to the benchmark, if there is no technical assistance then with \(\epsilon \) sufficiently small the left hand side of (38) is strictly greater than \(\bar{\theta }\equiv \int _0^1\theta \mathrm{d}G(\theta )+\epsilon \). This condition can then only be satisfied if the regulator provides a strictly positive amount of technical assistance. Using Eq. (35), the expression in Eq. (14) follows from first order condition for \(I\). \(\square \)

Proof of Lemma 3

The lemma follows from the first-order conditions for (16),

$$\begin{aligned} -q^{\prime }(e(\theta ))r(I)[P(M)+t(\theta )]&\le \theta ;\end{aligned}$$
$$\begin{aligned} e(\theta )\left[-q^{\prime }(e(\theta ))r(I)[P(M)+t(\theta )]-\theta \right]&= 0, \text{ for} \text{ all} \, \theta . \end{aligned}$$

since the optimal level of effort is independent of \(\phi \). \(\square \)

Proof of Lemma 4


$$\begin{aligned} \Lambda (\theta _a,\theta _b)=r(I)q(e(\theta _a,\theta _b))[P(M)+t(\theta _a)]+\theta _b e(\theta _a,\theta _b). \end{aligned}$$

From (6), incentive compatibility requires

$$\begin{aligned} -\Lambda (\theta _a,\theta _a)-\tau (\theta _a)&\ge -\Lambda (\theta _b,\theta _a)-\tau (\theta _b);\end{aligned}$$
$$\begin{aligned} -\Lambda (\theta _b,\theta _b)-\tau (\theta _b)&\ge -\Lambda (\theta _a,\theta _b)-\tau (\theta _a). \end{aligned}$$

Summing these two equations yields

$$\begin{aligned} \Lambda (\theta _a,\theta _b)-\Lambda (\theta _a,\theta _a)\ge \Lambda (\theta _b,\theta _b)-\Lambda (\theta _b,\theta _a). \end{aligned}$$

By the envelope theorem, expression \(\tfrac{\mathrm{d}\Lambda (\theta _a,\theta _b)}{\mathrm{d}t(\theta _a)}=\tfrac{\partial \Lambda (\theta _a,\theta _b)}{\partial t(\theta _a)}=r(I)q(e(\theta _a,\theta _b))>0\), and \(\tfrac{\mathrm{d}^2\Lambda (\theta _a,\theta _b)}{\mathrm{d}t(\theta _a)\mathrm{d}\theta _{b}}=r(I)q^{\prime }(e(\theta _a,\theta _b))\tfrac{\mathrm{d}e(\theta _a,\theta _b)}{\mathrm{d}\theta _b}\ge 0\). Therefore if \(\theta _a<\theta _b\) then inequality (45) requires \(t(\theta _a)\ge t(\theta _b)\). Differentiating (15) and using the envelope theorem yields Eq. (20). \(\square \)

Proof of Proposition 3

As Lemma 5 in Lewis and Sappington (1989) provides an in-depth formal analysis of a problem with similar structure (for a more general treatment, see Maggi and Rodríguez-Clare 1995; Jullien 2000), here we only provide a sketch of the proofs required to characterize the equilibrium contract. Condition (19) requires that \(t(\theta )\ge t^0\) for \(\theta <\theta ^0\) and \(t(\theta )\le t^0\) for \(\theta >\theta ^0\). Let \(\lambda (\theta )\) and \(\mu (\theta )\) be Lagrange multipliers for these two constraints. Using Eq. (40), if exporters undertake a positive amount of effort the first-order conditions for \(t(\theta )\) are

$$\begin{aligned}&\displaystyle \left[-q^{\prime }(e(\theta ))[[1-r(I)]\delta -r(I)t(\theta )]-\frac{G(\theta )}{g(\theta )}\right]\tfrac{\partial e(\theta )}{\partial t}+\lambda (\theta )=0\quad \text{ for}\quad \theta <\theta ^0(\phi );\quad \end{aligned}$$
$$\begin{aligned}&\displaystyle [1-r(I)]\delta -r(I)t^0=0 \text{ for}\quad \theta =\theta ^0(\phi );\end{aligned}$$
$$\begin{aligned}&\displaystyle \left[-q^{\prime }(e(\theta ))[[1-r(I)]\delta -r(I)t(\theta )]-\frac{G(\theta )-1}{g(\theta )}\right]\tfrac{\partial e(\theta )}{\partial t}-\mu (\theta )=0\quad \text{ for} \quad \theta >\theta ^0(\phi ).\nonumber \\ \end{aligned}$$

Let \(t^{G}(\theta )\) denote the penalty path defined by Eq. (46), setting \(\lambda (\theta )=0\):

$$\begin{aligned} t^G(\theta )=t^0+\frac{G(\theta )}{r(I)q^{\prime }(e(\theta ))g(\theta )}. \end{aligned}$$

Similarly, let \(t^{G-1}(\theta )\) denote the penalty path defined by Eq. (48), with \(\mu (\theta )=0\):

$$\begin{aligned} t^{G-1}(\theta )=t^0+\frac{G(\theta )-1}{r(I)q^{\prime }(e(\theta ))g(\theta )}. \end{aligned}$$

If \(\lambda (\theta )=\mu (\theta )=0\), the Potential Separation assumption (see footnote 11) ensures that the paths for \(t(\theta )\) as defined by Eqs. (49) and (50) are strictly decreasing as depicted in Fig. 1. Thus, any pooling interval contains \(\theta ^0(\phi )\). Since \(q^{\prime }(\cdot )<0\), it would be the case that \(t(\theta )<t^0\) for any \(\theta <\theta ^0(\phi )\) that were not in the pooling interval. Since such a result would violate monotonicity condition (45), \(t(\theta )=t^0\) for all \(\theta <\theta ^0(\phi )\). A similar result applies for \(\theta >\theta ^0(\phi )\).

Fig. 1
figure 1

If technical assistance is fungible, there is a uniform optimal penalty, \(t_0\), for being caught with an invasive

The first-order condition for \(\phi \) is

$$\begin{aligned} \int \limits _{0}^{\theta ^0(\phi )}G(\theta )\mathrm{d}\theta -\int \limits _{\theta ^0(\phi )}^{1}[1-G(\theta )]\mathrm{d}\theta =0. \end{aligned}$$

The first-order condition for \(I\) is

$$\begin{aligned}&\int \limits _{0}^{1}r^{\prime }(I)q(e(\theta ))[\delta -P(M)]\mathrm{d}G(\theta )-k\!=\!\int \limits _{0}^{\theta ^0(\phi )}G(\theta )\tfrac{\partial e}{\partial r}r^{\prime }(I)\mathrm{d}\theta -\int \limits _{\theta ^0(\phi )}^{1}[1-G(\theta )]\tfrac{\partial e}{\partial r}r^{\prime }(I)\mathrm{d}\theta \nonumber \\&\quad =\int \limits _{0}^{\theta ^0(\phi )}\tfrac{G(\theta )q^{\prime }(e(\theta ))r^{\prime }(I)}{r(I)q^{\prime \prime }(e(\theta ))}\mathrm{d}\theta -\int \limits _{\theta ^0(\phi )}^{1}\tfrac{[1-G(\theta )]q^{\prime }(e(\theta ))r^{\prime }(I)}{r(I)q^{\prime \prime }(e(\theta ))}\mathrm{d}\theta . \end{aligned}$$

\(\square \)

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Fernandez, L., Sheriff, G. Optimal Border Policies for Invasive Species Under Asymmetric Information. Environ Resource Econ 56, 27–45 (2013).

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: