Model

Consider a border across which there is a difference in the price of an illicit good. There is a population of smugglers $S_i$, where $i \in { 1,\; ...,\; n} $, who can capture an arbitrage payoff of $w> 0$ from transporting this good across the border. Smugglers can transport their contraband via either the official crossing or the more costly unofficial crossing. The official crossing is established by the state at a location along the border that minimizes physical transportation costs, which is guarded by a border agent, $B$. Note that the state is not a player in this game, and the location of the official crossing is given. For simplicity, the border agent enjoys full control over the official crossing, so that she discovers all contraband that $S_i$ attempts to transport via that route. Although in reality border agents at official crossings may be unable to discover contraband with certainty, this assumption reflects their relatively higher capacity to discover contraband along official versus unofficial routes, while allowing us to focus on the smuggler's choice between the two types of routes and the agent's incentives to enforce the border or to engage in corruption.

In contrast, the state exercises weaker control over the unofficial route, so that agents posted along that route are able to interdict only $S_i$'s contraband with probability $p\in [ 0,\; 1) $. When $S_i$ is interdicted, she loses the value of the contraband, $w$. The probability $p$ that the state is able to discover smugglers’ contraband reflects the state's capacity to enforce its border along the unofficial route. A state that has invested greater long-run resources in enforcement will have a higher $p$.

While the chances of successfully evading detection are better along unofficial routes, $S_i$'s transportation costs are significantly greater, by $\tau _{it} w$, where $\tau _{it}> 0$. The parameter $\tau _{it}$ reflects the skill level of each individual smuggler $S_i$ in transporting contraband across the border during a given period, in addition to the costs from barriers and terrain that can affect transportation. High-skilled smugglers will have lower transportation costs ($\tau _{it}$), and low-skilled smugglers will have higher costs. $\tau _{it}$ is a random variable, drawn at the beginning of each period from a uniform distribution with support over $[ \tau -h,\; \tau + h] $, where $\tau$ is the mean transportation cost factor for all $i$ and $t$ via the unofficial route and $h$ is a parameter for the range of the transportation costs.Footnote ²⁵ In each period, the $\tau _{it}$ are reset, capturing random changes that affect smuggling decisions, such as weather and other environmental changes, or momentary advantages smugglers may acquire by developing new smuggling routes or using technology. This allows a realistic depiction of the dynamic nature of smuggling, which often resembles a cat-and-mouse game between border agents and smugglers.Footnote ²⁶

The cumulative distribution function for $\tau _{it}$ at a given threshold $x$ is

(1)$$\Phi_{\tau_{it}}( x) = \left\{\matrix{ 0 \hfill & \text{if } \,\,\, {\it x}< {\it \tau}-{\it h} \hfill \cr {x-( \tau-h) \over 2h} \hfill & \text{if } \,\,\,\tau-{\it h} < {\it x} < \tau + {\it h} \hfill \cr 1 \hfill & \text{if } \,\,\, {\it x} > \tau + {\it h} \hfill}\right.$$

A state that makes long-term investments in border fortifications can raise the mean transportation costs, $\tau$, that smugglers face along the unofficial route, shifting the cumulative distribution function of $\tau _{it}$ to the right. The parameters $p$ and $\tau$ are assumed to be determined by the terrain and the state's investments in interdiction efforts and border fortifications, respectively. From the perspective of border agent $B$, $p$ and $\tau$ are assumed to be exogenous, since $B$ has no influence over the state's high-level border control policy. That is, although the border agent is a player, the state is not a player in the game and enters into the game only by shaping its parameters. While the general population characteristics $p$ and $\tau$ are common knowledge to both $B$ and $S_i$, the individual parameter $\tau _{it}$ is known only to $S_i$ and not $B$, introducing asymmetric information on $S_i$'s transportation costs. Since $\tau _{it}$ is drawn anew at the beginning of each period, any information $B$ gains about $S_i$'s transportation costs in one period becomes irrelevant in the next period.

Although the state's official policy is to prevent illicit goods from crossing the border, we do not assume that the border agent will dutifully block all contraband. Instead we examine her incentives to enforce the border. Under what conditions does $B$ have an incentive to confiscate the contraband, versus accepting a bribe to allow $S_i$ to cross with her contraband?

If $S_i$ transports her contraband via the official border crossing, she is effectively declaring her goods to $B$, since they will be discovered with certainty. In this scenario, $B$ can either seize the goods or charge a fee for safe passage. $B$'s payoff for seizing the contraband is its value, $w$. If $B$ chooses to collude with $S_i$, $B$ receives a fixed fee, $fw$, where $f\in ( 0,\; 1) $, but risks incurring a penalty if she is caught.Footnote ²⁷ Note that if $B$ seizes the contraband, it is equivalent to charging a fee of 1. Thus, $B$'s decision effectively reduces to determining the level at which to set the fee $f\in ( 0,\; 1] $. $B$'s expected cost from colluding is $qsw$, where $q\in [ 0,\; 1] $ is the probability that the border agent will be caught for corruption and $s\geq 0$ is the penalty factor $B$ incurs if she is discovered to have engaged in corruption.Footnote ²⁸ If $B$ is caught, she incurs a penalty of $sw$. We scale $B$'s penalty by the value of the contraband, $w$, to capture the idea that the penalties for corruption should be proportional to the value of the contraband (higher-value contraband will incur greater penalties). Thus, $qs$ can be viewed as the expected penalty factor, which scales with the contraband value, $w$.

The probability, $q$, that $B$ will be caught for corruption reflects the state's capacity to police its own agents, such that states with stronger capacities are more likely to detect corruption among their agents. Notice that we distinguish between two aspects of state capacity: the capacity to detect smugglers, $p$, and the capacity to detect corruption among its agents, $q$.Footnote ²⁹ While the state's ability to detect corruption among its agents reflects both the state's capacity and preferences for investing in such capacities, the penalty $s$ that the state imposes on $B$ for corruption captures the state's preferences on corruption. From a revealed preferences perspective, a heavy penalty would indicate a strong preference against corruption by its agents, while a light penalty would indicate relative tolerance. In the latter case, bribes may be viewed by the state as a way to subsidize agents’ incomes or ensure the buy-in of its agents or even nonstate actors. Thus, our framework allows that states can be either strong or weak in their capacity to detect corruption, and that they can vary in their preferences over opposition to or tolerance of corruption.Footnote ³⁰

We assume that the probability that $B$'s corruption is detected and the penalties the state imposes are exogenous to the agent. Although there may be strategic interactions between individual agents and their immediate supervisors at the middle management level, $q$ and $s$ can be realistically viewed as exogenous since they reflect high-level policies that are designed and implemented by the central state in setting national border enforcement institutions and policies that shape border agents’ incentives. In this way, individual acts of corruption do not affect $q$ and $s$ on their own. Rather, it is the local bureaucratic environment that affects them. Moreover, bureaucracies are sticky and cannot change their policies in response to individual incidents of corruption. We believe this is a realistic way to treat the policies setting the monitoring and policing of agents. For example, between October 2004 and February 2018, the US Customs and Border Patrol reported 210 separate incidents of corruption among its agents, not including investigations for which there was insufficient evidence to warrant disciplining officers.Footnote ³¹ An assumption that $q$ and $s$ are endogenous to agent behavior would imply that the Customs and Border Patrol altered its policies in response to individual incidents, rather than the overall pattern of hundreds of reported incidents, as well as others that were investigated but not reported.

For simplicity, we evaluate $B$ and $S_i$ as risk-neutral actors. Thus, $B$'s expected payoff for charging a fee for safe passage is $fw-qsw$, while $S_i$'s payoff is $w-fw$. $S_i$'s participation constraint for bribing $B$ for safe passage is

(2)$$w-fw> 0$$

$S_i$'s other option is to attempt to evade the border authorities via the unofficial route.Footnote ³² If $S_i$ traverses the unofficial route safely, she will receive a payoff of $w-\tau _{it} w$. If she is caught (with probability $p$), she will not receive the arbitrage value but will still incur transportation costs $\tau _{it} w$.Footnote ³³ Thus, $S_i$'s expected profit from attempting to cross via the unofficial route is $w-E[ c_i] $. We can express $S_i$'s expected costs on the unofficial route as

(3)$$\begin{\split} E[ c_i] & = ( 1-p) \tau_{it}w + p( \tau_{it}w + w) \cr & = ( p + \tau_{it}) w $$

We can summarize a single interaction between the border agent and the smuggler in a given period as follows.

1. 1. Nature $N$ draws $\tau _{it}\in [ \tau -h,\; \tau + h] $.

2. 2. $S_i$ decides whether to attempt to smuggle contraband.

3. 3. $S_i$ chooses either to evade (via the unofficial route) or to declare the contraband and pay the fee for safe passage (via the official route).

4. 4. $B$ chooses either to seize the contraband or to charge a fee $fw$, where $f\in ( 0,\; 1) $, for safe passage (collude).

5. 5. If $S_i$ chooses the unofficial route, Nature $N$ determines whether the smuggler is caught, with probability $p$.

Figure 1 presents the stage game in extended form. For each outcome, the payoffs for $S_i$ followed by $B$ are presented in parentheses.Footnote ³⁴

Figure 1. Stage game of smuggling interaction

We begin with whether $S_i$ can profitably smuggle contraband across unofficial routes in contexts where crossing via official routes is not viable. The unofficial route is profitable when $p + \tau _{it}< 1$, which gives $S_i$ a positive expected payoff. Thus the threshold below which smugglers’ transportation costs $\tau _{it}$ are low enough for smuggling across the unofficial route to be profitable is $\tau _{it}< 1-p$. Based on $\Phi ( x) $ from equation (1), the proportion of smugglers for whom smuggling on the unofficial route is profitable is

(4)$$\Gamma = \left\{\matrix{ 0 \hfill & \text{if } \,\,\, {\it p} + \tau- {\it h}> 1\hfill \cr {1-\,{p}\,-\,\tau \,+ \,h\over 2h} \hfill & \text{if } \,\,\, {\it p} + {\it \tau}- {\it h} \leq 1 \text \,{ and } \,\, {\it p} + {\it \tau} + {\it h}\geq 1 \hfill \cr 1 \hfill & \text{if } \,\,\, {\it p} + \tau + h< 1 \hfill }\right.$$

If it is not possible for $S_i$ to collude with $B$ to cross via the official route, then $\Gamma$ will be equivalent to the total proportion of smugglers who can smuggle. Notice that for distributions of smugglers for whom even the highest-skilled smugglers (low $\tau _{it}$) cannot profitably cross the border (that is, $p + \tau -h> 1$), the volume of smugglers will be zero. However, if transportation costs are reduced such that at least the high-skilled smugglers can profitably cross ($p + \tau -h\leq 1$), there will be a nonzero proportion of smugglers who can profitably take the unofficial route. Here, since ${\partial \Gamma \over \partial p}< 0$ and ${\partial \Gamma \over \partial \tau }< 0$, decreases in $p$ and $\tau$ will result in a higher volume of smugglers across the unofficial route, until all smugglers can cross where $p + \tau + h< 1$. Where no smugglers or all smugglers can cross, marginal changes in $p$ or $\tau$ will not change the volume of smugglers who cross. Thus:

We now turn to the official route. Assuming that $B$ will collude if $S_i$ chooses the official route, $S_i$ will choose the official route if the net payoff $S_i$ would receive from corrupting the agent is at least the expected payoff of using the unofficial route. Thus, $S_i$ will choose the official route if the expected costs from the unofficial route are greater than the costs from the official route, $E[ c_i] > fw$. $S_i$'s expected costs on the unofficial route are $E[ c_i] = ( p + \tau _{it}) w$, while the costs on the the official route will be $fw$. Comparing these payoffs, $S_i$ will prefer the official route if $p + \tau _{it}\geq f$. The intuition here is that in order for the official route to be preferable to $S_i$, the expected losses due to interdiction and transportation costs must be greater than the fee. Thus, $S_i$ will prefer the official route when

(5)$$p + \tau_{it}\geq f$$

In a one-time interaction, if $S_i$ chooses the official route, it is sequentially rational for $B$ to confiscate the contraband, which would maximize her payoffs given that there would be no prospect of collusive payments in the future. In other words, $B$ cannot credibly commit to not seizing $S_i$'s contraband. Recognizing this time inconsistency problem, $S_i$ will choose the unofficial route. Thus:

Collusive Equilibria in the Repeated Game

When the game is repeated, equilibria that result in either collusion or evasion are both possible. Collusive equilibria exist in which $B$ can entice smugglers to take the official route by setting $f$ low enough to make it more profitable for smugglers than on the unofficial route, as in Inequality (5). $B$'s commitment to collude with smugglers is made credible by the future stream of profits that $B$ would forgo from defecting.

We employ subgame perfect equilibrium as the solution concept to determine the conditions that would support collusion over time. Let $a_B$ be a strategy from the set of all of $B$'s possible strategies, $A_B$; $a_{S_i}$, a strategy from the set of $S_i$'s possible strategies, $A_{S_i}$, for a given smuggler $S_i$; and $a = ( a_B,\; a_{S_1},\; ...,\; a_{S_n}) $, the strategy profile that results when these strategies are played by the agent and each of the smugglers. Since each smuggler is privy to only her own interactions with the agent, $S_i$'s interactions with $B$ can be treated independently from the other smugglers. That is, the game is a series of independent dyadic interactions between $B$ and each of the smugglers, $S_i$.

Thus we can focus on the nature of interactions between $B$ and a representative $S_i$. The discounted expected payoffs for $B$ and $S_i$ are $V_B( f,\; a,\; q,\; s) \equiv \sum _{t = 0}^\infty \pi _{B, t}\delta ^t$ and $V_{S_i}( f,\; a) \equiv \sum _{t = 0}^\infty \pi _{S_i, t}\delta ^t$, respectively, given the fee $f$, strategy profile $a$, and discount factor $\delta$, which applies to all actors. Here, $B$'s payoff in period $t$ is $\pi _{B, t}\in { 0,\;w( f-qs) ,\; w}$. $S_i$'s payoff in period $t$ is $\pi _{S_i, t}\in { 0,\; w( 1-f) ,$ $w( 1-p-\tau _{it}) } $. The specific payoffs in each period are determined by the strategy profile $a$ and the fee $f$. We define the average payoffs of the infinite sequence of payoffs for $B$ and $S_i$ as $\overline {V}_B( f,\; a,\; q,\; s) \equiv ( 1-\delta ) V_B( f,\; a,\; q,\; s) $ and $\overline {V}_{S_i}( f,\; a) \equiv ( 1-\delta ) V_{S_i}( f,\; a) $, respectively. For a given strategy profile $a$, $\overline {V}_B$ will be increasing in $f$ (that is, $\partial \overline {V}_B/\partial f> 0$) and decreasing in $q$ or $s$ (that is, $\partial \overline {V}_B/\partial q< 0$ and $\partial \overline {V}_B/\partial s< 0$), since the average payoff will be a linear combination of the possible cooperative payoffs, $w( f-qs) $. Moreover, $\overline {V}_{S_i}$ will be decreasing in $f$ ($\partial \overline {V}_{S_i}/\partial f< 0$), since the average payoff is a linear combination of the possible cooperative payoff, $w( 1-f) $, for $S_i$.

Following the Folk Theorem, as long as the discounted stream of payoffs from cooperation for a given $f$ and $a$ exceeds the stage-game Nash equilibrium payoffs for $B$ and $S_i$, such a cooperative arrangement can form a subgame perfect equilibrium. For $B$, this incentive compatibility constraint results from comparing the stream of cooperative payoffs with the one-time seizure of contraband, which can be written as

(6)$${\overline{V}_B( f,\; a,\; q,\; s) \over 1-\delta}\geq w$$

$S_i$'s stream of expected payoffs from exclusively using the unofficial route is ${( 1-p) ( w-\tau w) -p\tau w\over 1-\delta }$, which simplifies to ${w( 1-p-\tau ) \over 1-\delta }$.Footnote ³⁵ Her payoffs from cooperative arrangements with $B$ that use the official route would be ${\overline {V}_{S_i}( f,\; a) \over 1-\delta }$. Comparing the stream of payoffs from cooperation on the official route with those of the unofficial route yields $S_i$'s incentive compatibility constraint:

(7)$$\overline{V}_{S_i}( \,\, f,\; a) \geq w( 1-p-\tau) $$

We can now state the following lemma.

Lemma 2 Existence of collusive equilibrium: In a repeated game between border agent $B$ and smuggler $S_i$, a collusive strategy profile $a$ and fee $f\in \left[0,\; 1\right)$ can form a subgame perfect equilibrium under the following conditions:

(8)$$\delta\geq 1-{\overline{V}_B( f,\; a,\; q,\; s) \over w}$$

(9)$$p + \tau\geq 1-{\overline{V}_{S_i}( f,\; a) \over w}$$

The first condition implies that $B$ must value future interactions with $S_i$ highly enough to collude instead of seizing the contraband. A higher fee ($f$), lower probability ($q$) of being caught for collusion, lower penalty ($s$) for being caught for collusion, higher discount factor ($\delta$), or a strategy profile ($a$) that produces a higher average expected payoff ($\overline {V}_B( f,\; a,\; q,\; s) $) will be more likely to induce $B$ to accept bribes for safe passage. Although $B$'s discount factor may be a reflection of her individual weighting of future periods, it can also be affected by how much she expects to interact with $S_i$ in the future. Thus, if $B$ can expect to interact frequently with $S_i$, her discount factor will be higher. Importantly, if the state wants to drive down $B$'s discount factor, it could choose to disrupt $B$'s interactions with $S_i$ by frequently rotating $B$ out of staffing the official crossing.

The second condition implies that $S_i$'s probability of interdiction ($p$) and expected transportation costs ($\tau$) on the unofficial route must be high enough relative to costs from cooperation to incentivize $S_i$ to cooperate with $B$. For a given strategy profile $a$, an increase in $f$ will reduce $S_i$'s average payoff for cooperating, making it less likely that $S_i$'s incentive compatibility condition holds.

That is, collusive equilibria exist if the fee is high enough to compensate $B$ for the risk of being caught and incurring penalties, as well as to make it credible to $S_i$ that $B$ would not confiscate the contraband and forgo future bribes. At the same time, the fee must be low enough to make cooperation on the official route more attractive to the smuggler than exclusively using the unofficial route. The range of fees that support collusion along the official route narrows when (1) expected costs on the unofficial route decrease (for example, from lower transportation costs or lower interdiction rates), (2) border agents have shorter time horizons, (3) collusion between agents and smugglers is discovered at a higher probability, or (4) penalties for collusion increase. Notice that a state that has invested in the capacity to detect corruption among its agents and has strong preferences against corruption can decrease the range of fees that would allow collusive arrangements to occur. While a relatively permissive environment for corruption that results from weak state capacity or a lack of will, as exhibited by low penalties for corrupt agents, is a necessary condition for collusion to emerge, those conditions do not guarantee that corruption will occur if agents do not sufficiently value future interactions with smugglers.

The Fee for Crossing by the Official Route

The effect of border enforcement on smuggling flows is mediated by the fee that $B$ will charge smugglers in exchange for safe passage at the official border crossing. Thus, we now turn to determining the fee that maximizes $B$'s payoffs, given the population of smugglers.

To make the exposition more tractable, we limit our focus to a trigger strategy for $S_i$. As long as $B$ does not seize the contraband on the official route, $S_i$ will take the official route whenever the expected costs on the unofficial route exceed the fee on the official route: $\tau _{it} + p\geq f$ (Inequality (5)). $S_i$ will take the unofficial route in periods when the fee on the official route exceeds her expected costs on the unofficial route. If $B$ defects by seizing the contraband, $S_i$ will use the unofficial route indefinitely.Footnote ³⁶ In a context with abundant reasons for smugglers to distrust agents, such a harsh punishment for defection may be reasonable.

Turning to the border agent, recall that while $S_i$ knows her own individual transportation costs, $\tau _{it}$, $B$ knows only the mean transportation costs, $\tau$, for the population of smugglers, but not for any particular smuggler, since they reset in each period. That is, any information $B$ has gained from whether $S_i$ accepted the fee in the previous period does not confer any insights on $S_i$'s current transportation costs. Due to this information asymmetry, $B$ can usefully set a fee for only the population of smugglers, rather than price discriminating to extract greater rents according to the transportation costs of individual smugglers. We will show that there exist cooperative equilibria in which $B$ charges a fixed fee $f\in ( 0,\; 1) $ in exchange for safe passage for smugglers playing a trigger strategy.

We begin by determining the probability that it would be more profitable for smugglers to pay a fee for passage on the official route rather than to take the unofficial route. From Inequality (5), the threshold for the minimum transportation costs on the unofficial route that would compel $S_i$ to take the official route is

(10)$$\tau_{\text{min}}\equiv f-p$$

Given $\tau _{\text {min}}$ and the distribution of $\tau _{it}$ (Equation (1)), we can express the expected proportion ($\Psi$) of smugglers who would prefer the official route as a function of $f$:

(11)$$\Psi( f) = \left\{\matrix{ 1 \hfill & \text{if } \,\,\, {\it f} < {\it p} + \tau- {\it h} \hfill \cr {\,p + \tau + h-f\over 2h} \hfill & \text{if } \,\,\, {\it p} + \tau- {\it h}\leq {\it f} \leq {\it p} + \tau + {\it h} \hfill \cr 0 \hfill & \text{if } \,\,\, {\it f} > {\it p} + \tau + {\it h} \hfill }\right.$$

We plot the proportion of smugglers on the official route, $\Psi ( f) $, in panels A and B of Figure 2 for two values of $h$ and given $p$ and $\tau$.Footnote ³⁷ For a higher value of $h$ in panel A, the rate at which the proportion of smugglers on the official route declines for higher fees $f$ is slower than for lower values of $h$ in panel B.

Figure 2. Proportion of smugglers on official route and agent payoffs

We now turn to determining the agent's incentive compatibility constraint. Given that $S_i$ plays a trigger strategy, $B$'s discounted stream of payoffs for cooperation with $S_i$ must be at least as much as the one-time payoff from defection:

(12)$$\sum_{t = 0}^{\infty} \Psi( f) ( f-qs) w\delta^t \geq w$$

In the online supplement, we use Equations (11) and (12) to show that $B$'s incentive compatibility constraint is satisfied for the following values of $f$:

(13)$$f\in \left[{\,p + \tau + h + qs\over 2}-R,\; {\,p + \tau + h + qs\over 2} + R\right]$$

where

(14)$$R\equiv{\sqrt{( p + \tau + h + qs) ^2-4( qs( p + \tau + h) + 2h( 1-\delta) ) }\over 2}$$

Notice that, because $B$'s expected payoffs are concave, it is possible for cooperation to be incentive compatible for $B$ only for real values of $R$. This implies that it is possible for $B$ to credibly commit to cooperating (that is, not confiscating) when

(15)$$\delta\geq\delta_{\text{min}}$$

where $\delta _{\text {min}}\equiv ( -( p + \tau + h + qs) ^2 + 4qs \,\, ( p + \tau + h) + 8h) /8h$. That is, border agents who sufficiently value future interactions with smugglers are able to credibly commit to not confiscating their contraband. It is also possible to rearrange this incentive compatibility constraint in terms of $B$'s expected penalties:

(16)$$qs\leq \text{EP}_{\text{max}}$$

where $\text {EP}_{\text {max}}\equiv {\it p} + {\it \tau} + {\it h}-\sqrt {8 {\it h}( 1-\delta ) }$ is the maximum expected penalty that supports collusion. In other words, a sufficiently low expected penalty for corruption, $qs$, is necessary for $B$ to engage in corruption.

From Equation (7), we can determine $S_i$'s incentive compatibility constraint, in which the expected payoffs for cooperation under the trigger strategy are at least as high as the expected payoffs for the unofficial route:

(17)$$\Psi( f) ( 1-f) + ( 1-\Psi( f) ) ( 1-p-\tau_u) \geq 1-p-\tau$$

where $\tau _u$ is the average transportation cost when smugglers prefer to use the unofficial route (that is, $p + \tau _{it}\geq f$). In the online supplement, we show that $S_i$'s incentive compatibility constraint reduces to

(18)$$f\leq p + \tau + h$$

The upper bound of $\tau _{it}$ is $p + \tau + h$, so as long as the fee for passing via the official route is less than the highest expected cost on the unofficial route, the cooperative equilibrium is preferable to defecting (that is, taking the unofficial route indefinitely), since it gives $S_i$ a cheaper option when costs are too high on the unofficial route.

We can express the existence of a collusive equilibrium as

We now turn to $B$'s problem of determining the optimal fee, $f_{\text {opt}}$, that maximizes $B$'s payoffs in a cooperative equilibrium. This optimization problem will be the same in each period, since smugglers’ transportation costs will be drawn anew in each period from the uniform distribution, and smugglers who are in a collusive equilibrium with the agent will face the same incentives in each period. We can express $B$'s optimization problem in each period as

(19)$$\matrix{\max_f \quad \Psi( f) ( f-qs) w\hfill\cr {\rm subject\ to} \quad f\in\left[{\,p \, + \, \tau \, + \, h \, + \, qs\over 2}-R,\; {\,p \, + \, \tau \,+ \, h \, + \, qs\over 2} + R\right]\cr }$$

From Lemma 3, for a high enough discount factor $\delta \geq \delta _{\text {min}}$, the constraint constitutes a nonempty set, and therefore cooperation is possible. Since $\Psi ( f) $ is declining in $f$ and $( f-qs) w$ is increasing in $f$, the optimization problem of setting $f$ entails balancing the volume of smugglers using the official route, $\Psi ( f) $, against the fees collected per smuggler. In the online supplement, we show that $B$'s optimal fee is

(20)$$f_{\text{opt}} = \left\{\matrix{ p + \tau-h \hfill & \text{if } \,\,\, {\it h}< {\, {\it p} \, + \, {\it \tau}-{\it qs}\over 3}\hfill \cr {\,p \,+ \, \tau \, + \, h \, + \,qs\over 2} \hfill & \text{if } \,\,\, {\it h} \geq{\,{\it p} + {\it \tau}-{\it qs}\over 3}\hfill \cr \hfill }\right.$$

For sufficiently wide distributions of $\tau _{it}$, where $h\geq {p \, + \, \tau \, - \,qs\over 3}$, $B$'s payoffs are maximized by setting $f_{\text {opt}}$ at a point that induces less than 100 percent of smugglers to take the official route, that is, on the declining slope in panel A of Figure 2. This is because a marginal increase in fees collected per smuggler to the left of $f_{\text {opt}}$ will raise $B$'s payoffs more than the associated loss in smugglers opting for the official route (panel C). To the right of $f_{\text {opt}}$, marginal increases in fees collected per smuggler are outweighed by the loss in volume of smugglers.

For narrow distributions of $\tau _{it}$, where $h< {p \, + \, \tau \, - \,qs\over 3}$, the optimization problem results in all smugglers opting for the official route (panel B). That is, any marginal loss in the volume of smugglers outweighs the associated marginal gains from higher fees collected from each smuggler. Under those conditions, $B$'s optimal fee is the highest fee that ensures 100 percent use of the official route. Thus, from Equation (11), $B$ would set the fee at $f = p + \tau -h$. We illustrate $B$'s payoffs under this scenario in panel D.

In both cases, increases in the mean cost of transportation and probability of interdiction raise $B$'s optimal fee, since $\partial f_{\text {opt}}/\partial p> 0$ and $\partial f_{\text {opt}}/\partial \tau > 0$.Footnote ³⁸ Intuitively, this is because increased probability of interdiction or increased transportation costs from border enforcement activities on the unofficial route provide $B$ greater leverage to charge higher fees on the official route.

If the expected costs on the unofficial route are so high that the optimal fee would be greater than the arbitrage value of the goods ($f_{\text {opt}}> 1$), $B$ would simply set the proportional fee $f$ just below 1 to ensure that it is worthwhile for smugglers to continue to cross the border via the official route and so keep collecting fees. $B$ does not have an incentive to charge the full value of the contraband, $w$, as that would stop the flow of smugglers across the official route altogether. With agents able to charge higher fees, stricter border enforcement will make it more tempting for them to enter into collusive relationships with smugglers.

Lemma 4 Effect of border enforcement on bribes: If smugglers and the agent are colluding, which is possible only if $\delta \geq \delta _{\text {min}}$, or equivalently $qs\leq EP_{\text {max}}$, an increase in interdiction probability $p$ or mean transportation costs $\tau$ along the unofficial route will increase the optimal fee, $f_{\text {opt}}$, charged for safe passage on official routes, where

(21)$$f_{\text{opt}} = \left\{\matrix{ p + \tau-h \hfill & \text{if } \,\,\, {\it h} < {\it \,p \, + \tau-qs\over 3}\hfill \cr {\,p \, +\, \tau \, + \, h \,+ \,qs\over 2} \hfill & \text{if } \,\,\,{\it h}\geq{\it\,p \, + \, \tau \, - \, qs\over 3}\hfill }\right.$$

Note that any fee that deviates from $f_{\text {opt}}$ is less preferable for $B$, so $B$ will fix the fee at $f_{\text {opt}}$.

Smuggling Flows

What then is the effect of increased border enforcement on the flow of smuggling across a border? Here, we show that border enforcement has a sorting effect in which high-skilled smugglers will be undeterred, but low-skilled smugglers will be unable to cross unless the conditions supporting collusive relations with border agents hold.

Recall from Lemma 3 that collusive relations are possible when there are repeated interactions, high discount factors, and sufficiently low expected penalties. As long as these conditions prevail, the official route will remain an option for all smugglers to pass through profitably, since the net payoff for the official crossing is always positive, $w \, ( 1-f_{\text {opt}}) > 0$. Thus, if these conditions supporting collusion are met, fortifying borders to cut off unofficial crossings will not reduce the total volume of smuggling, since smugglers who cannot profitably traverse unofficial routes will simply cross by bribing their way through official routes. The underlying mechanism for this follows from the asymmetry of information between smugglers and agents. Since only smugglers know their own costs in a given period, border agents are unable to price discriminate to maximize the rents they capture from smugglers. Instead, agents can charge only a uniform fee for all smugglers who choose the official route, which must leave some net profit for smugglers, to entice them to use the official route.

When the conditions that support collusion prevail—that is, agents face low expected penalties for corruption ($qs\leq EP_{\text {max}}$) or sufficiently value future interactions with smugglers ($\delta \geq \delta _{\text {min}}$)—reinforcing borders affects only the routes that different types of smugglers choose, rather than the overall volume of smugglers. Following Inequality (5), high-skilled smugglers (those who have low expected costs along unofficial routes, such that $p + \tau _{it}< f_{\text {opt}}$) will choose the unofficial route. In contrast, low-skilled smugglers with high expected costs ($p + \tau _{it}> f_{\text {opt}}$) will opt for collusion along the official route because they are unable to profitably use the unofficial route but can still receive the payoff of $w \, ( 1-f_{\text {opt}}) $ along the official route. Thus, a fortified border acts as a sorting mechanism, diverting low-skilled smugglers to official crossings where they seek out collusive relations, while only high-skilled smugglers opt for unofficial crossings.

Since the effect of border enforcement on the routes smugglers choose is mediated by the fee, we can now obtain the flows in equilibrium over the official route:

(22)$$\Psi \, ( f_{\text{opt}}) = \left\{\matrix{ 1 \hfill & \text{if } \,\,\, {\it h}< {\, {\it p} \, +\, {\it \tau} \, - \, {\it qs} \over 3}\hfill \cr {\,p \, + \, \tau \, + \,{\it h} \, - \,qs\over 4h} \hfill & \text{if } \,\,\,{\it h}\geq{\, {\it p} \, + \, {\it \tau} \, - \, {\it qs}\over 3}\hfill }\right.$$

From this, we can see that an increase in the probability of interdiction $p$, increase in transportation costs $\tau$ on the unofficial route, or decrease in $B$'s expected penalties $qs$ will increase the proportion of smugglers on the official route, since $\partial \Psi /\partial p> 0$, $\partial \Psi /\partial \tau > 0$, $\partial \Psi /\partial q< 0$, and $\partial \Psi /\partial s< 0$ for $h\geq {p \, + \, \tau \, - \, qs\over 3}$. If $h< {p \, + \, \tau \, -\,qs\over 3}$, all smugglers will opt for the official route, so marginal changes in $p$, $\tau$, $q$, or $s$ will not affect the equilibrium proportion of smugglers on the official route until $h\geq {p \, + \, \tau \, - \, qs\over 3}$. Combined with Lemma 3, this yields

Since it is more theoretically interesting to examine cases in which smugglers may use official or unofficial routes, rather than only official routes, we will focus on cases in which the distribution of transportation costs is sufficiently wide—condition (c). Based on Propositions 1 and 2, we summarize the conditional effects of border enforcement on smuggling flows in four stylized pie charts (Figure 3), which depict the relative proportions of the smuggler population that will be deterred by enforcement (checkered fill) or will traverse the border through either official crossings (dark gray) or unofficial crossings (light gray). The vertical axis depicts variation in the strictness of enforcement of unofficial border crossings. The horizontal axis depicts variation in the degree to which agents are penalized for corruption and have high discount factors or lack either of these factors required to credibly commit to colluding with smugglers. The figures illustrate how enforcing borders generates a sorting mechanism among high-, medium-, and low-skilled smugglers.

Figure 3. Summary of effects of border enforcement on smuggling flows

When borders are strictly enforced, as in quadrants III and IV, only high-skilled smugglers (dark gray) will be able to use unofficial crossings, while low- and medium-skilled smugglers (light gray in quadrant III; checkered in quadrant IV) will not. If border agents have low expected penalties and high discount factors, then low- and medium-skilled smugglers will be able to bribe their way through official crossings (quadrant III). If agents’ expected penalties for corruption are high or discount factors are low, then low- and medium-skilled smugglers will be deterred by border enforcement (quadrant IV), reducing the volume of smugglers who can cross the border. Note that the proportion of smugglers deterred in quadrant IV may differ from the proportion who would use the official route in quadrant III if collusion is possible, since the former is determined only by the profitability of the unofficial route, while the latter is determined by both the profitability on the unofficial route and the incentives the agent faces.

When borders are lightly enforced, as in quadrants I and II, the costs of traversing the unofficial route are lower, enabling both medium- and high-skilled smugglers to use them. Low-skilled smugglers, however, will still be unable to do so. If agents have low expected penalties and a high discount factor (quadrant I), low-skilled smugglers will be able to bribe their way through official crossings. Otherwise, low-skilled smugglers will be deterred (quadrant II). As in the comparison between quadrants III and IV, the proportion deterred in quadrant II and the proportion using the official route in quadrant I may differ across the two scenarios.

Strict border enforcement, combined with high expected penalties or low discount factors, will let the fewest smugglers cross the border (quadrant IV), followed by light enforcement with high expected penalties or low discount factors (quadrant II). If agents have low expected penalties and high discount factors (quadrants I and III), all smugglers will be able to cross the border, regardless of the level of enforcement. From the perspective of the smugglers, the lightly enforced borders with low expected penalties and high discount factors (quadrant I) provide the greatest share of rents, since only low-skilled smugglers will have to bribe their way across the border and agents will be able to charge only a relatively low fee. For corrupt border agents, however, the most lucrative scenario is when there are low expected penalties and high discount factors, combined with a heavily enforced border (quadrant III), which increases both the fee and the volume of smugglers who pay it. In this way, stricter border enforcement can create greater incentives for border agents to engage in corruption.

To facilitate empirical tests of our theory, we express the movement between each of these quadrants as four propositions. Each presumes sufficient variation in transportation costs ($h\geq {p \, + \, \tau \, - \,qs\over 3}$) that not all smugglers will use the official route in equilibrium.

Strategic Environment

The Burma–Thailand border in the 1930s approximates the strategic environment of our model. The two sides of the border had different regulatory systems for opium, which incentivized smuggling. In the early twentieth century, Southeast Asia had legal opium markets. States claimed monopolies over the domestic supply of opium, and collected tax revenue from its popular consumption.Footnote ⁴⁴ In general, opium was imported from the British colony of India. However, poppy fields capable of producing opium also flourished in the northern Shan States of Burma, a territory under British indirect rule that abutted the far northern edge of Thailand, an independent country.Footnote ⁴⁵ The British permitted poppy cultivation and opium production for this specific area,Footnote ⁴⁶ while Thailand banned all non-Indian opium imports and tightly controlled nonstate opium production.Footnote ⁴⁷ Thus, opium was often abundant on the Shan side of the border, but scarce on the Thai side.

Public knowledge was widespread about the profitability of smuggling. According to Sao Hpom Lu, who was from Kengtung, the largest of the northern Shan States, everyone knew that selling opium in Thailand could be “fabulously profitable with something like 100 percent gain.”Footnote ⁴⁸ At the local bazaar of Kengtung's major town in 1935, Shan opium sold for around 2.5 ticals per unit. An enterprising smuggler could take this product, cross the border into Thailand, and sell it on the black market in the capital city of Bangkok. The Thai government's official retail price for imported Indian opium ranged from fifteen to twenty-three ticals per unit, which amounted to nearly one-third of the monthly wage of an average laborer. This extraordinarily expensive drug was in high demand: in Bangkok alone, the state counted 110,000 people who smoked opium; most were Chinese “coolie” laborers believed to “probably spend 50 percent of his total earnings on opium or dross [the residue from smoked opium] or both.”Footnote ⁴⁹ Unable to afford the government's legal product, many Thai opium consumers turned to illegal Shan opium, which had a black market price of six to eight ticals per unit. If successful, smugglers could see the value of their contraband nearly quadruple.Footnote ⁵⁰

However, crossing the border into Thailand was not a simple task, with transportation challenges due to geography and the presence of state authorities. The topography of the Shan States east of the Salween River was complex, featuring elevated plateaus, high mountain peaks, dense jungles, and gorges.Footnote ⁵¹ At the time of Sao Hpom Lu's journey, there was only one major paved road connecting Kengtung to Thailand. Crossing the border also required crossing the Mae Sai River, which served as a natural boundary. The major bridge over the river, on the only paved road between Kengtung and Thailand, was well guarded by agents of the Thai Excise and Customs Department.

Still, smuggling opium across the Mae Sai was hardly impossible, given the regulatory and political environment in which border officials operated. Those stationed at the bridge were low-level administrators of the Thai Excise and Customs Department, who had considerable discretionary power in enforcing the law against opium smugglers. While Thai law explicitly banned bringing Shan opium into Thailand, local administrators had many reasons to choose not to enforce this law. Their salaries were meager, barely more than what the average wage laborer in Bangkok would make; and the opium smuggling they were tasked with halting was famously lucrative.Footnote ⁵² Also, as the three border officials who colluded with Sao Hpom Lu would later reveal, they had little reason to fear penalties from their direct superior. Luang Narubesr Manit, the director-general of the Excise and Customs Department in 1935, had once been a lowly opium administrator himself. He was familiar with the political economy of smuggling that linked Thailand to Kengtung, and well connected to “certain highly placed officials and their wives who ... had for years cast covetous eyes on the cheap Shan opium.”Footnote ⁵³ Put differently, rent seeking at the northern Burma–Thailand border was tacitly sanctioned by central authorities, and thus wayward local officials could reasonably anticipate monetary rewards with little risk of punishment.

In sum, the border between the Shan State of Kengtung in Burma and northern Thailand generated opportunities for smuggling due to the higher price of illegal opium in Thailand ($w$). Transporting opium across the border was a challenging operation, given the complex geographical terrain, including jungles, unpaved roads, and rivers, which entailed high transportation costs ($\tau$). These difficulties were aggravated by the presence of Thai customs and excise officers stationed along official routes and the main bridge that facilitated border crossings. However, the surveillance capacity of the Thai state was unevenly distributed—there were also many unofficial routes across the border that eluded the gaze of the border officials, who could not be stationed everywhere, so there was less chance of being interdicted along the unofficial route ($p$). Moreover, although combating opium smuggling was an official policy of the Thai government, local officials stationed in this border area had weak expectations for effective law enforcement and faced low penalties for petty corruption ($qs$).

The Smuggler's Choices

The main smuggler, Sao Hpom Lu, was a thirty-one-year-old Shan man, described by his family members as “clever ... with greed and avarice.”Footnote ⁵⁴ He had often traveled from Kengtung Town to Bangkok, where he enjoyed gambling and was once implicated in coin counterfeiting.Footnote ⁵⁵ In late 1934, he decided to try his luck with opium.

There were two possible routes for the smuggler (Figure 4). The quicker route used the official border crossing at the Mae Sai bridge, with a fee to the border officials. It would take less than three days to travel over 1,000 kilometers. The paved road from Kengtung to Taichilek, the last town on the Burma side of the border, was around 150 kilometers long, and linked to another 300-kilometer road to the Thai town of Lampang, which had the nearest railroad station that connected directly to Bangkok, 600 kilometers away. Sao Hpom Lu calculated the transportation costs: in addition to paying for trucks, fuel, and labor, “we had to pay twenty [baht] a day demurrage” at the Lampang train station, where he reserved two train wagons to store the opium before loading it onto the train, which could travel overnight to arrive in Bangkok early the next morning.Footnote ⁵⁶

Figure 4. Official and unofficial routes from Kengtung (Burma) into Thailand

The other route avoided the Mae Sai bridge and fees to the border officers. It was a longer and less predictable journey that would deviate from the Kengtung–Taichilek road onto unpaved paths through jungle-covered hills. On reaching the banks of the Mae Sai River, smugglers would need to have brought their own boats—or, as was more typical for those bringing contraband into Thailand at the time, travel further east to the larger, busier Mekong River, where it was easy to hire and hide on boats to avoid border agents. Once in Thailand proper, smugglers could not enjoy the convenience of the Lampang–Bangkok railroad, but would need to either use roads or one of the “countless waterways on which there [was] very intensive traffic.”Footnote ⁵⁷

In sum, from Sao Hpom Lu's perspective, it was not necessary to use the Mae Sai bridge to smuggle opium into Thailand, but it was appealing for its lower transportation costs ($\tau _{it}$). However, using this official route, one was almost certain to meet border agents, who would have to be bribed, which would reduce the smuggler's profits, $( 1-f) w$. By contrast, the unofficial route carried higher transportation costs, which could change season by season, not least due to weather, shifting terrain, and other contingencies. But if the smuggler could evade the border agents (with probability $p$)—and for this it helped to avoid the Mae Sai bridge—such transport expenses and the expected losses from interdiction were the costs that cut into the profits by $( p + \tau _{it}) w$.

The Border Officials’ Choices

There were three officers of the Thai Customs and Excise Department stationed at the Mae Sai bridge on 9 January 1935.Footnote ⁵⁸ These men were poorly paid, with little fear of being penalized for taking petty bribes (low expected penalties, $qs$). They also had weak expectations that smuggling would cease even if they properly enforced the law. “It is estimated that 93 percent of the total smuggling into the Shan States escapes seizure,” attested third-party observers at the time, knowing that “existing conditions make its suppression well-nigh impossible.”Footnote ⁵⁹ Faced with pervasive smuggling that he doubted would ever totally cease, a pragmatic border agent had reason to strike deals with smugglers, rather than engage in futile law enforcement against them.

The corruptible agents of the Thai state had at least two ways of profiting from opium smuggling. One was to seize the contraband and sell it themselves on the black market. The other option was to allow the smugglers to cross the border with their opium, for a fee. Both were viable options. Standing on the Mae Sai bridge, the border agents could inspect every individual, cart, or truck that came over this official border crossing, which capitalized on the narrowest and shallowest part of the river, “about thirty yards broad and two feet deep, with a very strong current and pebbly bottom.”Footnote ⁶⁰ Confiscated opium from the Shan States could be sold surreptitiously in Bangkok, where varieties of non-Indian opium were sold in defiance of the Thai government's monopoly. Or the officials on the bridge could turn a blind eye to opium-laden vehicles and charge a fee for safe passage. In essence, it was a promise to collude and share the expected profits ($w$) from successfully smuggling opium across the border.

In sum, from the perspective of the Thai officials stationed at the border, colluding with smugglers like Sao Hpom Lu was an appealing choice, but not their only way of profiting from opium smuggling. By seizing the contraband, they stood to gain a large sum from the value of the contraband. By colluding with the smuggler, they would receive a fee and internalize the possible penalties from being caught by their superiors ($( f-qs) w$).

A Collusive Equilibrium

Under what conditions and through what interactions did the Shan smuggler and Thai border agents come to collude? “I now wish to tell the whole truth,” Sao Hpom Lu began.Footnote ⁶¹ He had struck an agreement with the Thai officials, agreeing to yield around 25 percent of the contraband opium's expected total value on the Bangkok black market. The plan was for Sao Hpom Lu's men, on 9 January 1935, to drive nine trucks filled with 9.3 tons of raw opium across the Mae Sai bridge in plain sight, which the border officers would let pass unchecked. After the contraband's safe arrival and sale in Bangkok, the smuggler and the border agents would divide the profits.Footnote ⁶² The fee was lower than the expected costs on the unofficial route, creating an incentive for the smuggler to enter into the agreement. According to Lemma 2, the penalties for colluding were low enough, and the fee high enough, to make the stream of payments more attractive to the border officials than seizing the contraband.

Nine months earlier, the two parties had settled on the terms of this agreement during a secret meeting in a private car. In Sao Hpom Lu's own words, a Thai officer “asked me about the output of opium in Kengtung, and I told him how we used to formerly supply opium to Siam.”Footnote ⁶³ It is likely that from his perspective, the illegality of the opium trade defined by the Thai state did not reflect Shan visions of law and morality, and indeed, interfered arbitrarily in the economic lives of Kengtung's inhabitants. So, “when he asked me whether we could supply as before,” Sao Hpom Lu replied affirmatively: “I told him that I thought we should be able to.”Footnote ⁶⁴

The Thai officials issued fake documents describing the 9.3 tons of opium as an authorized purchase by the director-general of the Excise and Customs Department aimed at “stopping contraband from coming into Siam” and sent them to Sao Hpom Lu.Footnote ⁶⁵ The smuggler was aware of the fraudulent nature of the documents, which were “typewritten on plain office paper without any seals” and merely meant to serve as an extra form of insurance, just in case he ran into other Thai officers unaware of the agreement.Footnote ⁶⁶ But “I did not mind what was written so long as we got the money soon,” Sao Hpom Lu stated explicitly, indicating that the document itself was not why he had confidence that the border agents would uphold their end of the agreement.Footnote ⁶⁷

Rather, the agreement was credible because of the regularity of the opium harvest, which enabled both parties to anticipate interacting with each other on a yearly basis, or perhaps even more frequently. Every winter, Kengtung and its environs flushed white and red with poppy flowers, launching a predictable cycle of extracting a milky sap from ripe pods (called “tapping”), which was dried in the hot sun, wrapped in banana leaves, and then congealed as raw opium. In the trans-Salween Shan States, harvesting opium was not a one-time event but took place multiple times between December and March because adept poppy farmers could tap a single pod several times and collect opium until early spring. Local production nearly always exceeded what Shan inhabitants consumed, so surplus opium was a fact of the Shan State political economy known to all. The seasonality of opium production thus guaranteed repeated interactions over opium smuggling.Footnote ⁶⁸

“I believed him,” Sao Hpom Lu said,Footnote ⁶⁹ referring to the Thai border officer; and the planned timing of the actual transport of opium helps explain why. It was scheduled to occur at the harvest season's beginning (in January), rather than its end (in March). If the border agents at the Mae Sai bridge broke their promise and confiscated the smuggler's opium, he could still plan a second or even third trip using an unofficial border crossing, evading the border agents, who would miss opportunities to profit from opium smuggling that were certain to continue over the next few months. According to Sao Hpom Lu, he thus believed his partners when they said “it will be beneficial to both sides,” and thought, “if there is no trouble ... perhaps they would continue taking large quantities of opium from us.”Footnote ⁷⁰

Compared with Sao Hpom Lu, the voices of the Thai border officers are quiet in the archival record. However, their mutual confidence in the smuggler and the rent-sharing agreement can be understood in light of the very large quantity of opium that was smuggled into Thailand and how, despite ample opportunities to renege on the agreement, they did not. “It is certain that the smugglers would not attempt to bring in a huge consignment in motor lorries unless they had some guarantee that the lorries would get through,” wrote later investigators of the episode.Footnote ⁷¹ Sao Hpom Lu and his accomplices’ testimonies corroborate this point repeatedly: only without the threat of confiscation at the Mae Sai bridge could they plan to transport 9.3 tons of opium at once.

Moreover, there were multiple moments at which the border officials could have simply seized the opium. For one, as one of Sao Hpom Lu's men explained, “There are about six to seven police stations between Taichilek and Lampang, but we were not stopped at a single one of these stations.” It was clear that “all the Siamese [Thai] police were obviously warned that this opium should pass through freely.”Footnote ⁷² Indeed, the Thai officers went to additional lengths to ensure that all 9.3 tons of opium were safely transported to Bangkok. “When the caravan got within some [8 km] of Lampang,” according to another smuggling accomplice, “Nai Hpra Pin [one of the Thai border officials] stopped it and told Hpaya Singha [another smuggler] and me to go on ... as our presence would raise suspicion if we accompanied the caravan to the railway station.”Footnote ⁷³ The circumspect border official proceeded to escort the trucks to Lampang himself, and helped store the opium, which was “loaded in rail prison vans” at the train station.Footnote ⁷⁴

Also, the Thai officers could have charged more than the 25 percent share first agreed on. There had been a minor mishap in the process of transporting the opium: a man named Chek Miao Sing saw the nine trucks driving across the Mae Sai bridge and reported the suspicious activity to local police authorities not privy to the deal.Footnote ⁷⁵ Worried that the private collusion would become a public scandal, the border officials invented a paper trail that relabeled the cross-border transportation of opium a legal seizure. A few weeks later, in February 1935, Sao Hpom Lu received a letter from the Thai director-general asking him to discard the old document, which called their deal a purchasing agreement, and accept a new document that affirmed it as a reward to informants—the Shan smugglers—who had helped with a successful seizure.

But in fact, according to Sao Hpom Lu, “There was no seizure of the consignment whatever before it got to Bangkok. The whole story was invented when the opium got back to Bangkok.”Footnote ⁷⁶ The two parties waited a few months before disposing of the opium on the black market, during which time this small fortune sat in the warehouse of the Thai Excise and Customs Department. Given that the opium was no longer in the smuggler's hands, the Thai officials could have easily reneged on the agreement or insisted on a larger share of the profits. But they did not. By November of the same year, Sao Hpom Lu and his accomplices had received their money, as did the Thai officials at the Mae Sai bridge, just in time for the new poppy harvest season.Footnote ⁷⁷ Thus, despite opportunities to renege, a collusive equilibrium was achieved between smuggler and border agents, which was incentivized by sharing a stream of the larger arbitrage rents made possible by the lower transportation costs of the official crossing.

Increased Border Enforcement and Smuggling Volumes

Smuggling continued in and out of Shan State. For decades to come, contraband opium flowed across the Mae Sai bridge, and the Burma–Thailand border more generally, with a rhythm that offers suggestive evidence for the predictions of our model. Consistent with Propositions 2 and 3, improved border enforcement that did not disrupt collusive relationships between border officials and smugglers resulted in greater rather than smaller smuggling volumes.

After 1935, the smuggler's world for people like Sao Hpom Lu began to change as the presence of state agents increased in the Shan State of Kengtung. In the wake of the Mae Sai bridge episode, neighboring countries vowed to improve surveillance over illicit activities. In 1936, efforts were made to improve telegraphic communication and information sharing among Thai officers in Chieng Mai, British officers in Kengtung, and French authorities stationed across the Mekong River to the east, in northern Laos.Footnote ⁷⁸ However, that trans-border smuggling increased rather than decreased when official presence was heightened was hardly surprising to those familiar with the collusive ties between smugglers and officials on the ground. As one British colonial officer had anticipated:

In other words, with improved technologies for border enforcement, opportunities for collusion also increased. Indeed, in 1936, one Thai district officer estimated that the volume of opium smuggled into his jurisdiction from Kengtung had increased and only 15 percent was being seized.Footnote ⁸⁰ Into the 1940s, collusion over smuggling and intensified state presence continued to go hand in hand, and with renewed vigor, as this Shan State saw an influx of officers stationed along its borders. During World War II, large numbers of new forces were stationed in this territory under both the Thai government and the Japanese imperial army. An upswing in opium smuggling and poppy cultivation occurred during these wartime years, under the Japanese army's administrative officials who controlled the borders with Thailand.Footnote ⁸¹

A familiar pattern of tighter border enforcement and continued opium smuggling also characterized Kengtung after 1949, when it was occupied by three divisions of the Chinese Nationalist army ousted by the Communists. Over two thousand soldiers settled in exile in Kengtung and were stationed along the Thai border between 1950 and 1953, a period during which the infamy of the Golden Triangle region as a global drug trafficking hub emerged, with this Shan State at its core.Footnote ⁸² The Nationalist soldiers’ colluding with smugglers and collecting fees for safe passage became a common and almost normal way of border control. Into the 1970s, US intelligence reports on Southeast Asia would continue to note the same routes that Sao Hpom Lu had once used to smuggle opium into Thailand: “Route 1,” noted one CIA report in 1971, “passes through Mae Sai, Chiang Rai, and Lampang,” that is, Thailand's major north–south highway, where “officials of the RTA [Royal Thai Army], BPP [Border Patrol Police], and Customs at the several checkpoints on the route to Bangkok are usually bribed.”Footnote ⁸³ In sum, there is an observable pattern of increasing state presence and increasing corruption and smuggling across the Burmese–Thai border that recurs over time.